This page intentionally left blank Copyright © 2006, New Age International (P) Ltd., Publishers Published by New Age International (P) Ltd., Publishers All rights reserved. No part of this ebook may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the publisher. All inquiries should be emailed to
[email protected] ISBN (13) : 978-81-224-2841-4 PUBLISHING FOR ONE WORLD NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS 4835/24, Ansari Road, Daryaganj, New Delhi - 110002 Visit us at www.newagepublishers.com Preface Rivers have been the focus of human activity since the early civilizations. Even in modern times a large number of activities of the engineers such as water supply, irrigation, water quality control, power generation, flood control, river regulation, navigation and recreation are centered around rivers. Hence considerable interest has been evinced in the society about various aspects of rivers such as their formation, hydraulics and sediment transport, erosion and sedimentation, and effect of natural and human interferences on rivers. Books have been written on rivers by geologists, geomorphologists, hydraulic engineers, hydrologists and geographers. Even though all of them have attempted to understand the behaviour of rivers that have carved their channels through the material deposited by them, the emphasis of each one of them is different from that of the other depending on his background, objectives of writing the book and the targeted readership. Yet fewer attempts seem to have been made to synthesize the contributions of these scientists into a coherent text that takes a balanced view of the subject of river morphology. To fill this gap is the objective in writing this book. Hence, the text covers history of fluvial hydraulics and geomorphology, drainage basin characteristics, erosion, fluvial morphology, hydraulics of alluvial and gravel-bed rivers, river bed and channel changes, fluvial palaeo hydrology, analytical and numerical modeling of fluvial processes, morphology of some Indian rivers, rivers and environment, and data needs for morphological studies. The text can be used for teaching a course on river morphology to graduate and undergraduate students in civil engineering and geology, and as a reference material for engineers engaged in planning and management of rivers. My interest and involvement in the study of alluvial rivers and associated problems started with late Prof. E.W. Lane, and Profs. M.L. Albertson, D.B. Simons and E.V. Richardson of the Colorado State University, Fort Collins (U.S.A.). Over four decades of teaching and research in fluvial hydraulics, and association with colleagues at the University of Roorkee (now I.I.T. Roorkee) India, have helped me in looking at rivers in a much broader perspective. My association with Central Water and Power Research Station at Pune over the last decade further enriched my association with the rivers problems. While preparing the manuscript of the book, valuable assistance has been rendered by my former colleagues Profs. K.G. Ranga Raju and U.C. Kothyari who have gone through the draft of the book and given valuable suggestions for its improvement; most of these have been incorporated. I am indebted to Profs. Rajiv Sinha of I.I.T. Kanpur, Brahma Parkash and Pradeep Kumar of I.I.T. Roorkee, and V.S. Kale of the University of Poona for making their publications available to me. I vi Preface am thankful to Dr. Z.S. Tarapore and subsequent directors of CWPRS for allowing me to work at the research station for the past thirteen years. I am particularly thankful to M.S. Shitole, Joint Director, D.N. Deshmukh, J.D. Prayag, R.A. Oak, Hradaya Prakash, Pradeep Kumar, Mukund Deshpande, Y.N. Karanjikar and others whose assistance has been valuable in finalizing the manuscript of the book. Lastly, I am thankful to my wife Vidya and daughter Rashmi for the patience shown by them while I was preparing the manuscript. December 2005 R-1 Sankul Condominium Near Deenanath Hospital Evandavane, Pune-411004 R. J. Garde List of Symbols a1,a2,a3 A Ab Af Au Au Aw b B BI C Ca CD CL CB , C d* d, d50 d16, d50, d84, d90 da di dmax D DC Dd Dmax E ER f coefficients/exponents area of cross-section, area of basin area at bankful stage, area corresponding to bed area of fan area of basin of order u mean area of basin of order u area of corresponding to wall exponent width of rectangular channel Brice braiding index Chezy’s coefficient, suspended sediment concentration at a point, climate index reference suspended sediment concentration drag coefficient lift coefficient bed material concentration in ppm by wt., total load concentration dimensionless sediment size median size of bed material, rain drop size sediment size such that 16,50,84,90 percent material is finer than this size respectively arithmetic mean size any size fraction maximum size of sediment depth of flow (WD=A) depth at the centre drainage density maximum depth kinetic energy of storm entrenchment ratio Darcy-Weisbach resistance coefficient viii f¢ f ¢¢ f1 F Fb Fbo FD Fe FL Fr Fs g G Ge G¥ DG hb hs H i I I30 j ks K Ko l L ls Lu Lu River Morphology friction factor corresponding to grain roughness friction factor corresponding to form roughness Lacey’s silt factor stream frequency Blench’s bed factor value of Fb when bed load is negligible drag force erosion factor lift force Froude number (= U/ gD ) Blench’s side factor gravitational acceleration transport rate of any section equilibrium transport rate sediment transport rate at infinity change in G head loss in bend saltation height average height at ripple or dunes, bars; relief index intensity of rain fall maximum 30 minute intensity during storm index roughness parameter erodibility index, diffusion coefficient, wave number (= 2p D/L) theoretical diffusion coefficient length, distance, length of aggradation average length of ripples or dunes, length of stream up to drainage divide saltation length total length of streams of order u mean length of streams of order u exponent percent of silt-clay in perimeter, Kramer’s uniformity coefficient, dimensionless velocity bed or water wave meander belt meander length meander width (MB-W) m M Mb ML MW List of Symbols ix index, exponent, Manning’s n Manning’s n with respect to bed Strickler’s n number of streams of order u Manning’s n with respect to wall per cent perimeter, annual rainfall average monthly maximum precipitation discharge per unit width bed load transport rate in weight/width volumetric bed load transport rate per unit width critical water discharge per unit width suspended load transport rate per unit width total sediment transport rate in volume per unit width total volumetric sediment transport rate per unit width dimensionless discharge (= q/ gd 3 ) lateral inflow per unit length on both sides water discharge = Qb/d2 gd = Qb S/d2 gd = Qb/d2 gd S flood discharge of return period 2.33 years bankful discharge bed-load discharge mean annual discharge mean annual flood discharge runoff rate per unit area suspended load discharge total sediment transport rate in weight or volume radius centre line radius of bend inner and outer radius of bend hydraulic radius, annul run off, run off parameter area ratio hydraulic radius corresponding to bed, bifurcation ratio n nb ns Nu nw pi P Pmax q qb qBv qc qs qT qTv q* q¢ Q , Qw Q1 Q2 Q3 Q2.33 Qb QB Qma Qmaf Qr QS QT r rc ri, ro R RA Rb x Rb¢, Rb¢¢ Re RL Rm Ro*2 Rs RW R* S, So S¢ S ¢¢ Sa Sf Si SW S Su SDR SE tp River Morphology Rb with respect to grain and form roughness respectively Reynolds number length ratio of Horton mean radius of meander bends = Dg s d 3 / r f n 2 bifurcation ratio for slope hydraulic radius corresponding to walls particle Reynolds number u* d/v slope, bed slope, slope at x = o slope corresponding to grain roughness slope corresponding to form roughness annual erosion rate in cm (absolute) energy slope, fan slope sinuosity water surface slope average catchment slope average slope of segments of order u sediment delivery ratio super-elevation time to peak number of years, also dimensionless excess shear {= ( t' - t 0 c ) / t 0 c } trap efficiency of reservoirs local velocity in x direction, order of stream r.m.s. value of velocity function in x direction velocity at the top of particle critical velocity at particle level shear velocity (= t 0 / r f ) shear velocity corresponding to grain roughness shear velocity corresponding to form roughness average velocity average critical velocity average velocity of particle moving as bed load average velocity of bed form or wave local velocity in y direction T TE u u¢2 ud udcr u* u*¢ u*¢¢ U Ucr Ug UW v List of Symbols xi r.m.s. value of velocity fluctuations in y direction velocity in q direction maximum velocity at any vertical velocity in r direction average velocity in the vertical local velocity in z direction, mean width of rib r.m.s. value of velocity fluctuations in z direction average width (WD = A); weight of the particle average unit weight over T years bankful width unit weight value of sediment water surface width distance in x direction, a dimensionless coefficient distance from the wall hydraulic mean depth (=A/Ws) lateral distance from the origin, actual slope of suspended sediment distribution curve, elevation of bed at given x and t; side slope of channel (Z hor.: 1 vert.) theoretical value of suspended distribution curve; bed elevation at x = 0 energy correction coefficient exponents es /em ratio of sediment transfer coefficient to the momentum transfer coefficient specific weights of sediment and fluid lag distance thickness of laminar sub-layer difference in specific weights of sediment and fluid momentum transfer coefficient sediment transfer coefficient dimensionless distance in the vertical angle Karman constant (actual) Karman constant (clear water) porosity, wave length dynamic viscosity of fluid kinematic viscosity of fluid sheltering coefficient v¢2 vq vmax vr Vcp w w¢ 2 W Wav Wb Wo Ws x y Y1 z Z Zo a a1, a2, a3 b gs, gf d d¢ Dgs Îm Îs h q k k0 l m n x xii rf rs s sg t to t0c tr, tq t* t*c j jB, jS, jT y y¢ w w0 River Morphology mass density of fluid mass density of sediment arithmetic standard deviation geometric standard deviation shear stress average shear stress on the bed critical shear stress for sediment components of shear stress on the bed along r and q direction dimensionless shear stress dimensionless critical shear stress angle of repose dimensionless bed-load, suspended load and total load transport rate respectively = Dgsd35/t0 = Dgsd35/t0¢ fall velocity fall velocity under ideal conditions Subscripts and superscripts Subscripts * dimensionless quantity c pertaining to critical condition pertaining to section 1, 2. 1, 2 Superscripts ' corresponding to grain roughness '' corresponding to form roughness Glossary of Some Terms in River Morphology Below is given meaning of some terms occurring in the text. (adapted from Easterbrook 1969) Abrasion: wearing away of particle due to friction Aggradation: rise in bed level of the stream over large length Alluvium: unconsolidated sediment deposited by river; sediment deposited in river bed, floodplains, lakes, alluvial fans etc. Alluvial fan: cone shaped accumulation of debris or sediment deposited by the stream as it descends from steep slope to a plain where the material deposits in the form of a fan Avalanche: mass of snow sliding down the mountain Avulsion: shifting of a river course Base level: the level below which a land surface cannot be reduced by running water Bed-load: material moved on or near the bed due to tractive force of the flow Bed-forms: features developed on the bed of the river due to interaction between flowing water and river bed sediments Bed-load: material moved on or near the bed due to tractive force of the flow Bed material load: material transported by the stream which has the stream bed or banks as its origin Beheaded stream: lower portion of the stream from which water has been diverted due to stream piracy Braided stream: a stream divided into a number of channels by island formation, which may join and bifurcate again and again Cirque: a deep steep walled recess in a mountain caused by erosion due to glaciers Colluvium: unconsolidated deposits, usually at the foot hills or cliff, brought down by gravity Creep: slow down-slope movement of rock fragments and soil Crevasse: a fissure formed in glacial ice due to various strains Degradation: general lowering of stream bed over large length due to deficiency of sediment load as compared to its sediment transport capacity Delta: a triangular shaped alluvial deposit formed when a stream enters lake or sea Diastrophism: the process or processes by which the crust of the earth’s surface is deformed xiv Divide: a ridge between the streams; a line of separation between drainage basins Drainage basin: the area drained by a system of rivers River Morphology Eolian: deposits which are due to transporting action of the wind Ephemeral stream: the stream which flows only in direct response to precipitation; it receives no water from ground water Escarpment: relatively steep slope or cliff separating gently sloping tracts Eustatic: pertaining to simultaneous world wide changes in sea level Floodplain: relatively flat land strip on one or both sides of a stream built by sediment deposits during flooding. It is sometimes called active flood plain Fluvial: produced by the action of rivers Geomorphic cycle: erosion cycle during which land forms are evolved which change from youth to maturity to old, each of which is characterized by distinctive features Geologic structure: it includes not only folding, faulting and uplift of the crust but also includes other factors related to the physical and chemical characteristics of rocks, relative resistance to weathering, dip, strike, jointing, stratification etc. Glacial drift: material transported by glaciers Glacial trough: U-shaped valley produced by glacial erosion Hanging valley: a tributary valley whose floor is higher than that of the main valley at the junction due to degradation of the main valley Incised meander or entrenched meander: a deep sinuous valley cut by a rejuvenated stream Levee: natural or man-made embankment above the general level of floodplain which confines the stream channel Loess: fine sized particles deposited by wind Mass-wasting: the down-slope movement of rock debris under the influence of gravity Meander scar: crescent-shaped cut in a valley side made by lateral planation of the outer part of a meander Meandering stream: a stream that follows sinuous or crooked path Misfit stream: a stream whose meanders are either too small or too large, compared to valley width Monadnock: a residual hill or mountain standing above a peneplain Oxbow: a crescent-shaped lake formed in an abandoned river bend by a meander cutoff Palaeosol: a buried soil Peneplain: a landscape of low relief formed by long continued erosion Periglacial: region beyond the margin of a glacier Piracy: diversion of one stream by the other Pleistocene: the last Ice Age Glossary of Some Terms in River Morphology xv Regimes of flow: characteristics of bed and water surface produced by water flowing on a loose alluvial bed Rejuvenation: activation of erosion of a stream by uplift, climatic changes or change in base level Relief: the difference between high and low points of the land surface Saltation load: material bouncing along the bed or moved directly or indirectly by the impact of bouncing particles Scour: local lowering of the bed of the stream usually due to presence of a hydraulic structure in the stream Suspended load: that part of the sediment load carried by the stream that is kept in suspension by turbulent fluctuations Talus: an accumulation of loose rock mass at the base of a cliff Terrace: a flat or gently sloping surface bordered by an escarpment, it is composed of alluvium or bed rock. It is flooded so rarely that it does not grow by sediment deposition Underfit stream: a stream which is too small for the valley through which it flows This page intentionally left blank Contents Preface List of Symbols Glossary 1. INTRODUCTION 1.1 Introduction 1.2 Some Problems in River Morphology 1.3 Historical Developments in Fluvial Hydraulics 1.4 Historical Developments in Geomorphology 1.5 Scope References 2. DRAINAGE BASINS AND CHANNEL NETWORKS 2.1 Introduction 2.2 Drainage Patterns and Texture 2.3 Stream Order 2.4 Horton’s Laws of Stream Numbers and Stream Lengths 2.5 Areas of Drainage Basins 2.6 Basin Shape 2.7 Lithology 2.8 Vegetation 2.9 Drainage Densities and Stream Frequency 2.10 Relief Aspects 2.11 Drainage Basin Characteristics and Hydrology 2.12 Random Walk Model 2.13 Concluding Remarks References 3. SOIL EROSION AND SEDIMENT YIELD 3.1 Introduction 3.2 Global Erosion Rates v vii xiii 1 1 2 4 7 9 10 11 11 12 14 16 19 21 21 22 24 26 29 29 31 31 34 34 35 xviii 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 Types of Erosion Factors Affecting Erosion Mechanics of Sheet Erosion Equations for Predicting Soil Loss from Agricultural Lands Measurement of Sediment Yield Sediment Delivery Ratio Process Based Modelling of Erosion Erosion Rates from Indian Catchments References River Morphology 39 41 44 48 50 56 60 64 67 71 71 72 74 74 76 77 80 82 94 104 105 107 110 110 110 120 124 137 145 150 158 164 169 169 170 176 180 4. FLUVIAL MORPHOLOGY 4.1 Geomorphology and Fluvial Morphology 4.2 Geomorphic Cycle (or Cycle of Erosion) 4.3 Rejuvenation of Erosion Cycle 4.4 Criticism of Geomorphic Cycle 4.5 Noncyclic Concept of Landscape Evolution 4.6 Geological Time Scale 4.7 Glaciation 4.8 Fluvial Morphology 4.9 Topography Produced by Streams 4.10 Variables in River Morphology 4.11 Neotectonics and Earthquakes References 5. HYDRAULICS OF ALLUVIAL STREAMS 5.1 Introduction 5.2 Incipient Motion 5.3 Modes of Sediment Transport 5.4 Bed-Forms in Unidirectional Flow 5.5 Resistance to Flow in Alluvial Streams 5.6 Bed-Load Transport 5.7 Suspended Load Transport 5.8 Total Load Transport References 6. HYDRAULIC GEOMETRY AND PLAN FORMS OF ALLUVIAL RIVERS 6.1 Introduction 6.2 Stable Channels Carrying Sediment 6.3 Hydraulic Geometry of Alluvial Streams 6.4 Empirical Relationships for Hydraulic Geometry Contents xix Non-Dimensional Relations for Hydraulic Geometry Flow Around Bends with Rigid and Alluvial Beds Shear Direction Near Curved Stream Bed and Bed Topography Braided Rivers Meandering Stability Analysis and Criteria for Plan-Forms References 186 189 194 198 202 212 223 229 229 230 230 233 233 237 241 246 253 256 256 257 258 260 262 267 271 273 275 275 277 277 282 285 285 286 286 286 288 6.5 6.6 6.7 6.8 6.9 6.10 7. GRAVEL-BED RIVERS 7.1 Introduction 7.2 Data for Gravel-Bed Rivers 7.3 Bed Material 7.4 Pavement 7.5 Hydraulic Geometry 7.6 Bed Features in Gravel-Bed Rivers 7.7 Resistance to Flow in Gravel-Bed Rivers 7.8 Sediment Transport in Gravel-Bed Rivers References 8. FLUVIAL PALAEO HYDROLOGY 8.1 Introduction 8.2 Objectives of Palaeo Hydrologic Studies 8.3 Basis of Analysis 8.4 Climatic Changes: Past and Future 8.5 Palaeo Hydrologic Estimates of Discharge and Velocity 8.6 Palaeo Hydrologic Studies in India 8.7 Fluvial Palaeo Hydrologic Studies in India References 9. BED LEVEL VARIATION IN STREAMS 9.1 Introduction Degradation 9.2 Types of Degradation 9.3 Downstream Progression Degradation 9.4 Upstream Progression Degradation 9.5 Effects of Degradation 9.6 Prediction of Depth of Degradation 9.7 Control of Degradation Local Scour Around Bridge Piers 9.8 Factors Affecting Scour xx 9.9 9.10 9.11 9.12 9.13 9.14 9.15 9.16 9.17 9.18 Equations for Predicting Scour Depth Verification of Equations for Scour Depth Scour in Gravelly Material Scour in Cohesive Soils Protection of Scour Around Bridge Piers Aggradation Occurrence of Aggradation Reservoir Sedimentation Sediment Inflow and Trap Efficiency Movement and Sediment Deposition in Reservoirs Modeling of Sediment Deposition Methods for Preserving and Restoring Reservoir Capacity References River Morphology 291 293 295 296 296 296 297 301 302 304 306 310 311 315 315 315 321 323 326 329 331 334 337 337 338 342 343 346 357 359 359 360 362 363 366 367 10. RIVER CHANNEL CHANGES 10.1 Introduction 10.2 Avulsion 10.3 Stream Capture 10.4 Erosion at Bends 10.5 Natural and Artificial Cut-Offs 10.6 Channel Pattern Changes 10.7 Longitudinal Grain Sorting References 11. ANALYTICAL MODELS OF RIVER MORPHOLOGY 11.1 Introduction 11.2 Basic One-Dimensional Equations 11.3 Analysis of Water Surfaces and Bed Waves 11.4 Analytical Models 11.5 Some Applications of Linear Models References 12. NUMERICAL MODELS FOR MORPHOLOGICAL STUDIES 12.1 Introduction 12.2 One-Dimensional Equations 12.3 Numerical Schemes of Solution 12.4 Classification of One-Dimensional Models 12.5 Convergence and Stability 12.6 Boundary Conditions Contents xxi Channel Cross-Sections and Method of Erosion or Deposition Modeling of Armouring HEC – 6 CRARIMA Applications of HEC – 6 References 368 369 372 376 378 383 386 386 388 388 391 392 393 395 396 398 402 402 402 407 410 411 414 416 419 420 422 423 424 424 427 427 429 429 430 433 436 12.7 12.8 12.9 12.10 12.11 13. MORPHOLOGY OF SOME INDIAN RIVERS 13.1 River Systems in North India Kosi 13.2 Introduction 13.3 Catchment Characteristics and Geology 13.4 Geotectonics 13.5 Hydrology 13.6 Sediment Size and Slope 13.7 Morphology of the Kosi 13.8 Management of the Kosi 13.9 Present Day Problems of the Kosi Brahmaputra 13.10 Introduction 13.11 River Characteristics 13.12 Seismicity and Landslides 13.13 Climate and Hydrology 13.14 Resistance to Flow and Sediment Transport 13.15 Plan-Forms 13.16 Flooding and Flood Protection 13.17 Drainage of Hinter Lands 13.18 River Bed Changes in Brahmaputra 13.19 Development Plans 13.20 Role of Dredging References 14. RIVERS AND ENVIRONMENT 14.1 Introduction 14.2 Actions Causing Disturbance in Stream System and Their Impacts 14.3 Environmental Effects of Hydraulic Structures 14.4 Dams and Reservoirs 14.5 Water Quality in Reservoirs 14.6 Thermal and Hydro-Power Plants xxii Recreation Stream Pollution River Action Plans Stream Restoration References 15. DATA REQUIREMENTS FOR MORPHOLOGICAL STUDIES 15.1 Introduction 15.2 Maps, Air-Photos, Satellite Imageries 15.3 Lithology and Tectonics 15.4 Vegetal Cover 15.5 Geomorphic Map 15.6 Basin Characteristics and Morphometry 15.7 Sea-Level Fluctuations, Climatic and Other Changes 15.8 Cross-Sections, Longitudinal Section and Plan-Form 15.9 Bed and Bank Material 15.10 Hydrologic Data 15.11 Sediment Load Data 15.12 Stratigraphic Studies 15.13 Water Quality Related Data 15.14 Catalogue of Information on Morphological Studies References Appendix A Author Index Subject Index 14.7 14.8 14.9 14.10 River Morphology 437 437 438 439 440 442 442 442 445 446 446 449 450 451 453 454 455 456 458 459 459 462 463 473 C H A P T E R 1 Introduction 1.1 INTRODUCTION A river carries water, sediment and solute from the drainage area to the sea and is thus of interest to hydraulic engineers, geomorphologists and sedimentologists. This is important to engineers because water is used for a variety of purposes by humanity; water courses are used as navigation channels, and also erosion, transportation and deposition of sediment cause a number of problems in the river and in the catchment that must be solved pragmatically. The direct effect of transportation of sediment and water from the geologist’s and geomorphologist’s point of view is that the structure and form of the river and adjoining areas are continually changed due to erosion and sedimentation. The rates of this change are variable. While geologists and geomorphologists are concerned about changes taking place in 103 to 106 years or more, engineers are concerned with changes in a river during a relatively short period, say 10–20 years to probably 50–100 years. These channel changes can be in the form of size, shape, composition of bed material, slope and plan-form. The engineer’s primary objective is to understand the basic mechanisms of erosion, transportation and deposition of sediment by flow in the river and develop qualitative and quantitative methods for prediction of river behaviour. The approach followed by engineers is called fluvial hydraulics or river dynamics and this approach has been developed during the past 200–300 years. The other approach taken by geologists and geomorphologists is primarily qualitative even though, in recent years some quantitative methods have been used. Morphology is defined as the science of structure or form. Hence according to Worcester (1948) geomorphology is the science of landforms; it is the interpretive description of the relief features of the earth. It thus describes the surface of the lithosphere, explains its origin and interprets its history. To understand geomorphology one should know in detail the composition and structure of the rocks of the earth and the processes which act on it. Geomorphology recognises that the earth’s surface has changed in the past and is changing at present due to internal and external processes. The internal processes are those, which originate within the earth itself and include diastrophism and volcanism. External processes shaping the earth’s surface include running water, weathering, waves and shore currents, glaciers, avalanches, and plant, animal and human 2 River Morphology activities. It may be mentioned that most of the changes taking place in the earth’s surface are slow, even though a few may be catastrophic. Conventional texts in geomorphology would deal in detail about the internal and external processes which cause changes in the landform and then deal with the topography produced by streams in humid regions, by winds in arid and semiarid regions, glaciers, shore processes, ground water, volcanoes etc. Geomorphology is sometimes called physiography. This latter term, as used particularly in Europe, includes climatology, meteorology, oceanography and mathematical geography. Inasmuch as these are not addressed in this book, the term geomorphology is preferred to physiography. The word “fluvial” means produced by river action. Hence fluvial morphology means the science of landforms as produced by river action. It can also be called river morphology; it is a branch of geomorphology and it would deal with form of the streams and adjoining areas as brought about by erosion, transportation and deposition of sediment by the running water. Both river morphology and geomorphology are descriptive sciences based mainly on careful observation and interpretation of natural phenomena. In the last century hydraulic engineers, hydrologists and geographers have also made contributions to river morphology. 1.2 SOME PROBLEMS IN RIVER MORPHOLOGY Since the dawn of civilization, mankind has used rivers for supporting and sustaining life. This has been done by harnessing and controlling rivers for the benefit of people. In doing so the regime or stability of the river is invariably disturbed. In discussing these problems caused by disturbance in the stability of rivers, it is desirable to define what geomorphologists call a graded stream (Mackin 1948). A graded stream, poised stream, balanced stream or a stream in equilibrium is defined by Mackin as the one in which channel dimensions and slope are so adjusted over a period of time that it carries incoming sediment load and water without appreciable erosion or deposition. In geologic time frame no river can be graded because of the natural tendency of land mass and rivers to erode gradually towards sea level. In a true dynamic sense also no river can be in true equilibrium since the discharge changes continuously. However, it may be mentioned that the changes related to geomorphic erosion are very slow and hence if one considers a time period of a few years to some decades, most of the streams can be considered to be in equilibrium, except a few rivers such as the Kosi, the Brahmaputra and the Yellow river which are truly unstable. This equilibrium of the stream is disturbed by natural or man-made interferences in one or more of the conditions that maintain the equilibrium. A few of these instances are discussed below. i. When a large dam is constructed across the river to store water for irrigation, water supply, flood control, generation of water power, navigation or recreation, the sediment transport capacity upstream of the dam is reduced thereby causing aggradation in the main reservoir and also in the tributaries on the upstream. This has many undesirable effects including depletion of reservoir capacity and flooding of the upstream areas. In some cases such as the Imperial dam on the Colorado river and Bhakra dam on the Sutlej in India sediment deposition has been found to occur 70-80 km upstream of the dam. The water released from the reservoir is almost sediment free and hence it picks up sediment from the bed and banks of the stream causing degradation over long reaches of the stream. It Introduction 3 ii. iii. iv. v. vi. vii. viii. may also lead to channel widening or change in the planform of the river. Needless to emphasise, degradation has many undesirable effects. It has long been recognized that water transport is comparatively much cheaper than road or rail transport and hence many streams such as the Danube, the Volga, the Rhine, the Mississippi, the Yangtze, the Ganga, the Brahmaputra and the Nile have been used for navigation since ancient times. Making the river navigable year around involves construction of dams, locks, channel widening, channel straightening and channel contraction using spurs or jetties and bank stabilization. It may also involve dredging and releasing additional water during low flows. These changes affect the stability of the river and hence executions of such changes need consideration from hydraulic and morphologic points of view. Barrages, canal head works, sediment excluders and extractors in irrigation canals are constructed for withdrawing relatively sediment free water for irrigation and water supply purposes. This disturbs the equilibrium of the stream causing aggradation in the downstream reaches. Similarly, aggradation takes place when rivers are used for dumping mining wastes hoping that the stream will safely carry the dumped material downstream. However, the stream can carry this excess load only with increased slope, which is achieved by aggradation. This happened, for example, on the Yuba river in California (U.S.A.) during gold-rush period in the latter half of the 19th century. Similarly, when sand and gravel are mined from the river bed to meet the ever increasing demand of the construction industry, the river downstream is found to degrade creating many problems in that reach. Such degradation in the river causes similar effects in the tributaries and sub-tributaries on the downstream side. In order to have equitable distribution of water throughout the country large scale transfer of water from one basin to the other is either contemplated or is being executed. This is likely to disturb the equilibrium of the streams because the balance between water distribution and sediment load distribution is likely to be disturbed. Construction of flood control works such as embankments, reservoirs, channel straightening, meander cut-offs and channel improvement also tend to disturb the equilibrium of the stream and needs careful study. Large scale dredging carried out along the river for navigation purposes also disturbs the sediment balance and hence the stream equilibrium. There are other less obvious factors that affect the stability of the stream, i.e., they affect channel slope, plan-form, cross-section, and alignment. Some of these are the following: Change in drainage basin characteristics due to change in land use such as deforestation, reforestation, agricultural land development, road construction, urbanization, and building of dams and check-dams disturb the river equilibrium by changing runoff and sediment load and trigger changes in the channel characteristics. Ruhe (1971) has described the case where straightening of a channel had repercussions throughout the basin. In the Willow river (Crawford County, Iowa, USA) straightening led to channel deepening and widening. In addition, new deeply entrenched gullies extended for many kilometres up the tributary system and developed hill slides, disrupting agricultural lands and public roads. 4 River Morphology When urbanization takes place large-scale changes are induced in the catchment, its hydrological characteristics and the sediment yield. Because of breaking of new grounds, removing of vegetation, and use of construction equipment, the runoff and storm flow increases and hence land erosion is accelerated. As a result the sediment load of the streams is often increased dramatically. Wolman and Schick (1967) recorded up to 50,000 tons/km2/yr sediment load at one site, as compared to 80-200 tons/km2/yr under normal conditions. After the urban area is developed, infiltration is reduced and ground water levels may be lowered. Untreated waste including sewage may be discharged into the streams causing pollution, which in turn, may be lethal for the aquatic life and detrimental to the use of the water in downstream reaches for drinking and recreational purposes. Due to urbanization there is an encroachment on the flood plain and hence channels are confined resulting in higher flood levels. ix. Long term changes in the climate or hydrologic regime lead to significant changes in discharge, type of sediment load and its quality which lead to change in channel dimensions, change in river course and/or change in plan-form or meander characteristics. In extreme case the river can cease to exist. x. Earthquakes and active tectonic movement such as subsidence or upheaval are found to influence the river stability. Earthquake of magnitude greater than 4 on Richter scale can trigger a number of landslides through out the region and earthquake of magnitude 8 or larger is capable of triggering tens of thousands of land slides throughout the region that extends to more than 400 km from the fault (Wilson and Keefer 1985). Heavy rainfall following such landslides can bring enormous amount of material in the stream and can change its regime. Gee (1951) has reported the damage caused by 15 August 1950 earthquake in Brahmaputra valley that was of 8.6 intensity on Richter scale. He found that 75 percent of hills in 4 3000 km2 area were mutilated by landslides. Small and large rivers became blocked by material that fell in them and some even ceased to flow. Flood following the earthquake burst these dams and large quantity of sediment and rock material was carried downstream. The rivers Dibang and Subansiri twice changed their courses. The Brahmaputra got considerably silted up near Dibrugarh, and the bed level rose by a few metres; it took several years for the excess sediment to move downstream. In engineering literature little attention has been paid to active neo-tectonic movement as a factor influencing river morphology. The rates of surficial deformation in certain region may vary from less than 10 mm/yr to more than 10 mm/yr for seismic deformation. When considered over a few decades such deformation can affect valley slope enough to affect the river morphology. If at a particular section along the river there is uplift there is aggradation on upstream and downstream side while in between there is degradation. 1.3 HISTORICAL DEVELOPMENTS IN FLUVIAL HYDRAULICS (GARDE 1995) Even though mankind has been living with sediment problems for the past several centuries, relatively little progress was made in our knowledge about sediment movement up to 16th century A.D. Earlier civilizations in the valleys of the Indus, the Tigris, the Euphrates, the Nile and the Yellow rivers were Introduction 5 using canals for supplying water for irrigation through unlined channels. These canals either took off from a weir or they were inundation canals. The common problem with these canals was silting and hence frequent sediment removal was necessary. Locating the canals on the outer side of the bend of a stream to reduce sediment entry into canal seems to have been practised. The Chinese had made considerable progress in controlling large rivers, flood diversion, and similar other problems. The Romans had made progress in water supply and sewerage. The Greeks knew about the fall velocity of different sediment particles. During 1600–1800 A.D. relatively more progress was made in understanding the physics of flow in open channels. The basic equations governing the flow, viz. the continuity equation and the equations of motion were developed during this period. d ¢ Alembert (1717–1783) gave the differential equation for continuity of flow which was generalized by Leonard Euler (1707–1783). It was also during this period that the equations of motion, commonly known as Euler’s equations were established. The French engineer Chezy (1718–1798) gave the resistance equation U = C RS where U is the average velocity, R the hydraulic radius, S the channel slope and C is Chezy coefficient. Some basic ideas about river hydraulics were initiated by Dominico Guglielmini (1655–1710) and Paul Frizi; both wrote books on rivers. Du Buat (1734–1809) gave scouring velocities for materials of different sizes. Much more progress was made during 19th century. Bouniceau, Grass, Lechalas, Suchier and Deacon conducted studies and critical velocities for different sized materials were recommended. Brahm showed that the critical velocity is proportional to (submerged particle weight)1/6. D.F. duBoys (1847-1924) gave a simple model for bed-load transport and reached the conclusion that qB ~ to (to – toc) were qB is the rate of bed-load transport, and to and toc are the average bed shear stress and critical shear stress for given size of bed material respectively. During this period two new resistance equations, which are now commonly used, were proposed. These are Darcy-Weisbach equation: and Manning’s equation U= hf = fL U2 D 2g 1 2 / 3 1/ 2 R S n ...(1.1) Here hf is the head loss in length L of pipe diameter D, R is the hydraulic radius, S is the slope and f and n are friction factor and Manning’s roughness coefficient respectively. In the latter half of 19th century O. Fargue (1827–1910) who was closely associated with the developmental work of the river Garonne, gave what are popularly known as “Fargue’s rules” of river behaviour. Finally equations of motion for laminar flow and turbulent flow, commonly known as Navier-Stokes equations and Reynolds equations were developed. Similarly Sternberg gave his law for the reduction of sediment size along the river by the combined action of grinding and sorting. It was also at the fag end of 19th century that Kennedy proposed the method for design of stable channels based on canal data from India that was later modified by Lacey and others. The first half of the twentieth century witnessed all round progress in fluvial hydraulics. G.K. Gilbert (1843–1918) performed extensive laboratory experiments and studied modes of sediment 6 River Morphology transport, and observed various bed-forms. Different investigators later used the hydraulic data collected by Gilbert to study resistance and sediment transport in channels. As regards channel resistance, Strickler analysed Swiss river data and for plane beds with coarse material proposed the equation /6 n = d1 50 /21 ...(1.2) where d50 is expressed in metres. Exner tried to explain formation of bed undulations using the equations of motion. During this period a number of investigators conducted experiments in the laboratory and developed empirical equations for critical shear stress (i.e., shear stress at which sediment of a given size just starts moving) as a function of sediment size d and the difference in specific weight between sediment and water Dgs. However, the credit for developing the rational criterion for incipient motion that is based on sound principles of fluid mechanics goes to A.F. Shields (1908–1974). Using sediments of different relative densities and sizes, he obtained a unique curve between toc/Dgs d and t oc / r f .d / n . Here toc is critical shear stress for sediment of size d and n is the kinematic viscosity of fluid. The term t oc / r f = u*c is known as critical shear velocity. In a similar manner a number of empirical equations were developed by different investigators relating rate of bed-load transport to (to – toc), (q – qc) or (U – Uc) where q is the discharge per unit width, U is the average velocity of flow, and quantities with subscript c refer to their values at incipient motion conditions. However, these equations were of limited use. In 1948 E. Meyer-Peter and R. Müller proposed an empirical equation for bed-load transport which is based on a wide range of sediment sizes and flow conditions and which is used often even today. A. Kalinske and H.A. Einstein developed bedload equations using statistical nature of sediment movement. Simultaneously progress was made in developing the theory of suspended sediment transport. The German meteorologist Schmidt gave the equation w o C + Îs dC =0 dy ...(1.3) for distribution of suspended sediment in the vertical. Here C is the concentration of sediment of fall velocity wo at a distance y from the bed and Îs is sediment transfer coefficient. This equation was integrated independently by Rouse and by Ippen using equation for velocity distribution obtained by Karman and Prandtl, and the integrated form was verified by Vanoni and Ismail. Simultaneously, bedload and suspended load samplers were developed and tested in Europe and U.S.A., which greatly helped in collecting valuable data on sediment transport by rivers. As regards the resistance to flow, Karman and Prandtl’s equations for velocity distribution for turbulent flow in pipes were adapted to open channel flow and velocity distribution laws for hydrodynamically smooth and rough surfaces were established. Einstein (1904–1963) suggested a method for separating grain resistance and form resistance of bed undulations while Einstein and Barbarossa proposed a method for predicting resistance to flow in alluvial streams. Lastly on the basis of a large volume of data from stable mobile bed alluvial channels and building on the advances made by Kennedy, Lindley, King and others, G. Lacey (1887–1980) proposed a method of channel design according to which for given Q and bed material size, the channel depth, width and Introduction 7 slope are uniquely fixed. Also data were collected about the geometry of alluvial rivers and equations have been developed to predict width and depth as a function of bankful discharge and sediment size. The last half of the twentieth century has seen considerable progress in fluvial hydraulics. The characteristics of different bed-forms have been studied and criteria for their prediction established. A number of equations have been developed to predict the resistance and sediment transport rates of uniform and non-uniform sediments. Kennedy, Engelund, Hansen and Fredsoe, have studied stability of mobile bed subjected to small disturbances to explain the formation of dunes, antidunes and plane bed. Similarly, Hansen, Callander, Parker, Hayaski and Ozaki, Engelund and Skovgaard and others have carried out stability analysis to determine the conditions under which streams meander. And finally, with the availability of high speed computers the equations of motion in alluvial streams have been solved to develop methods of prediction of bed levels in unsteady non-uniform flows such as silting of reservoirs, aggradation caused by increase in sediment load or decrease in discharge and degradation caused by increase in flow. Simultaneously field data are being collected to test various softwares developed for solving such problems. Also experimental data are being collected to study some basic problems such as armouring and pickup function. There has also seen considerable activity in understanding the hydraulics of gravel-bed rivers, their hydraulic geometry and sediment transport and scour. 1.4 HISTORICAL DEVELOPMENTS IN GEOMORPHOLOGY (Tinkler, 1985) From the Greek writings one can extract three basic principles regarding the rational investigations of landforms; these are (i) the concept of infinite time, (ii) reality of denudation i.e., loss of mass or material from the landscape and (iii) acceptance of the principle of conservation of mass. Herodotus (485– 425 B.C.) recognized the importance of yearly increments of silt and clay deposition by the Nile. He also anticipated the idea of changing sea levels that is of great significance in geomorphology. Aristotle (384 – 322 B.C.) thought that rainfall might produce a temporary torrent, but doubted that it could maintain flow in a river. Strabo (54 B.C.–25 A.D.) noted examples of local sinking and rise of the land. He also mentioned about the effect of ebbs and tides on the growth of delta. Both Strabo and Seneca (B.C.– 65 A.D.) recognized the role played by volcanic activity and earthquakes on the landforms. During the many centuries that followed the decline of the Roman Empire, there was little or no progress of scientific thought in Europe; however, some learning process continued in Arabia. During 941–982 A.D. there is reference to erosion and transportation of sediment by the streams and wind and weathering in the four-volume tretise on discourses of the Brothers of Purity. Little progress was made in Europe between the first century and beginning of the 16th century. During the fifteenth, sixteenth and seventeenth centuries landforms were explained by the philosophy of catastrophism, according to which the features of the earth were created as a result of violent catastrophic actions. Leonardo da Vinci (1452–1519 A.D.) had very advanced ideas about geologic thinking for his time. He recognized that streams cut the valleys and that the streams carried sediment from one part of the earth and deposited at other places. The Frenchman Baffon (1707–1788) thought 8 River Morphology that erosion by streams would eventually reduce the land to the sea level. He was also the first to suggest that the age of the earth was not to be measured in terms of a few thousand years. Another Frenchman Guetthard (1715–1786) also discussed about the degradation of mountains by streams and emphasized that not all the material removed by the stream would immediately be carried to the sea but a part would also deposit on the flood plains. The Swiss De Saussure (1740–1799) recognized the ability of glaciers to carry out erosional work. James Hutton (1726–1797) who entered the university at the age of 14 to study humanities was more interested in chemistry and geology. Finally, he was educated as a physician. However, instead of practising medicine he gradually switched over to agriculture and travelled through Southern England during which time he developed his interest in geology. Hutton is known for propounding the concept that “the present is the key to the past”, thus establishing the doctrine of uniformitarianism. His writings clearly express the concept of a river system and its geomorphic significance. Some other important concepts introduced by Hutton are: i. A vast portion of the present rocks is composed of bodies, animals, vegetables and minerals of more ancient formation. ii. All present rocks are going to decay and their material going to deposit in the sea. iii. The morphological process requires indefinitely long geological time. iv. There is a conceptual possibility of relative change between land and sea levels leading to upheaval. Hutton’s friend John Playfair (1748–1819) who was Professor of Mathematics and Philosophy at Edinburgh was in contact with Hutton, Joseph Black, and Adam Smith. After the death of Hutton in 1797 Playfair published “Illustrations of Huttonian Theory of Earth” in 1802 for he had realized how confused and repetitive were the writings of Hutton; Playfair’s work was smaller, cheaper, and precise with great clarity and beauty of expression. Playfair presented Hutton’s ideas and conclusions clearly. Playfair also proclaimed the ability of glaciers to erode their valleys deeply. Sir Charles Lyell (1797–1875) wrote a number of textbooks to spread the geologic knowledge. He was somewhat doubtful about the immense ability of running water to carve the valleys. It was during 19th century that there was recognition of an ice age during which much of North Europe was covered with ice sheets. Playfair had sensed the possibility of large boulders being transported by glaciers. Louis Agassiz (1807-1873), Venetz of Switzerland in 1821, Bernardi of Germany in 1832 and Jean de Charpentier in 1836 supported this concept of glaciation in Europe. In the later part of 19th century books were written to describe the principles of landform development. These were by Peschel, Richthofen and A. Penck. The basic foundation of geomorphology was laid in America in the later half of 19th century by Major J.W. Powell (1834-1902), G.K. Gilbert (1843-1918) and C.E. Dutton (1841-1912). Powell’s studies of Unita Mountains emphasized the importance of geologic structure in the classification of landforms. He also introduced the concept of the limiting level to which the land-level would reduce and called it the base level. Col. George Greenwood earlier used this concept in Europe in 1857. Powell recognized that the process of erosion, if carried undisturbed on land, would reduce it eventually to a level little above sea level. He was able to correctly interpret that various unconformities in rocks in the Grand Canyon, Colorado (U.S.A.) correspond to ancient periods of land erosion. Introduction 9 G.K. Gilbert’s contribution in experimental work carried out in California has already been described. He was a pioneer in studying hydraulic mining and its effect on stream morphology. His other contributions include recognizing the importance of lateral planation by streams in the development of valleys and his explanation of Henry Mountains of Utah (U.S.A.) as the result of erosion of intrusive bodies. Dutton gave a penetrating analysis of individual landforms. Gilbert and Dutton are given credit for initiating the concept of erosional unloading of the earth’s crest technically known as isostasy. W.M. Davis (1850–1934) had greater impact on the development of geomorphology than any one else. Of all the contributions to geomorphology, Davis is remembered for introducing the concept of geomorphic cycle. According to this concept in the evolution of landscapes there is a systematic sequence that enables one to recognize the stages of development of landforms. This sequence is called by him as youth, maturity and old age. These landsforms are explainable in terms of differences in geologic structure, geomorphic processes and the stage of development. In the development of the idea of geomorphic cycle Davis had assumed that there is a relatively rapid uplift due to diastrophism which is followed by a relatively long period of standstill which permits the erosion cycle to run its course. W. Penck and his followers questioned Davis’ idea of geomorphic cycle during 1920’s and 30’s. In spite of these objections the Davisian geomorphic cycle is still considered a reasonable model primarily because of the absence of a plausible reasonable alternative. Recent Contributions Since the end of the Second World War a large number of aspects about river morphology have been or are being studied. These include channel geometry, mathematical modelling, effect of neo-tectonics and mass movements on channels, fluvial systems, experimental fluvial morphology, palaeo climatic and palaeo hydrologic effects and gravel-bed rivers. Scientists working at U.S. Geological Survey have studied short-term morphology of river channels; they include W.B. Langbein, L.B. Leopold and M.G. Wolman. S.A. Schumm, M.P. Mosley and W.E. Weaver studied fluvial systems and performed experiments in the laboratory to study river morphology. J.R.L. Allen from U.K. has done extensive work on the character and classification of bed forms and sedimentary structures with respect to deltas, meanders and floodplains. Many investigators including K.J. Gregory, J. Lewin, V.R. Baker and L. Starkel have studied Palaeo climatic and palaeo hydrologic effects on river channels. Geographers in U.K. have given impetus to the research in gravel-bed rivers and this work is now continued in Canada, U.S.A. and New Zealand. 1.5 SCOPE The text takes a balanced view of the contributions made by engineers, geologists, geomorphologists and geographers to fluvial morphology. Introduction, morphologic problems, and history of fluvial hydraulics and geomorphology are discussed in the first chapter. The second chapter is devoted to the discussion about drainage basin and channel networks. The third chapter deals with erosion from the catchment in humid regions where erosion due to water action predominates. The fourth chapter presents basic concepts from geomorphology such as geomorphic cycle, stages of landform and rivers and discusses the erosional and depositional features developed by rivers. Chapter five deals with the hydraulics of alluvial rivers while chapter six deals with the hydraulic geometry and plan-forms in alluvial streams. The seventh chapter 10 River Morphology deals with gravel-bed rivers. Chapter eight deals with fluvial paleo hydrology while chapters nine and ten are devoted to changes in bed level and plan-form. Chapters eleven and twelve deal with analytical and numerical models used in studying the transient flows in rivers. Chapter thirteen is devoted to the discussion of morphology of the Kosi and the Brahmaputra rivers in India. Chapter fourteen deals with rivers and environment, and the fifteenth chapter dicusses the data requirements for morphological studies. References Garde, R.J. (1995) History of Fluvial Hydraulics. New Age International (P) Ltd., Publishers, New Delhi. Gee, G.P. (1951) The Assam Earthquake of 1950. Jour. Bombay Natural History Society, Vol. 50, pp. 629–638. Mackin, J.H. (1948) Concept of the Graded River. Bul. Geological Society of America, Vol. 59, pp. 463–512. Ouchi, S. (1985) Response of Alluvial Rivers to Slow Active Tectonic Movement. Bul. Geological Society of America, Vol. 96, Apr, pp. 504–513. Ruhe, R.V. (1971) Stream Region and Man’s Manipulation - in Environmental Geomorphology (Ed. D.R. Coates). Publication in Geomorphology, State University of New York, Binghamton, U.S.A. Thornbury, W.D. (1969) Principles of Geomorphology. John Wiley and Sons Inc., New York, 2nd Ed. Chapter 1. Tinkler, K.J. (1985) A Short History of Geomorphology. Croom Helm (P) Ltd., U.K., 1st Edition. Wilson, R.C. and Keefer, D.K. (1985) Predicting Areal Limits of Earthquake–Induced Land Sliding. In Evaluating Earthquake Hazards in the Los Angeles Region (Ed. Ziony, J.I.). USGS Professional Paper 1360, pp 317–345 Wolman, M.G. and Schick A.P. (1967) Effects of Construction on Fluvial Sediment Urban and Sub-urban Areas of Maryland. Water Resources Research, Vol. 3, pp. 451–464. Worcester, P.G. (1948) A Text Book of Geomorphology. D. Van Nostrand Co. Inc., New York, U.S.A., 2nd Edition. C H A P T E R 2 Drainage Basins and Channel Networks 2.1 INTRODUCTION Drainage basin is an area drained by the stream and its tributaries. It is bounded by a divide. Drainage basin is also sometimes called watershed or catchment area. It can be thought of as an open system that receives energy or input from the atmosphere and sun over the basin and loses energy or output through the water and sediment mainly through the basin mouth or outlet (Strahler 1964). The present form of any drainage basin is the result of the processes that have operated in the past on the material available locally. These processes at the basin level are the precipitation and runoff, sediment yield and rate of erosion. However, these processes in the past may not be the same in their relative importance as the ones that operate in the drainage basin at present. The importance of studying the drainage basin characteristics derives from the need of studying forms of channels and channel networks as they are related to physical characteristics of the drainage basin, and also from the need of relating physical characteristics of the basin to flow characteristics and sediment yield. The drainage pattern is the arrangement and length of small, medium and large streams in the basin. Two aspects of the development of drainage basins have been studied. In earlier years, the drainage pattern development in relation to the structure and lithology of the underlying rocks was studied. This was essentially qualitative in nature. In the recent times drainage patterns have been treated more as geometric patterns and attempts have been made to derive relationships for them (Horton 1945). The drainage pattern acquired at any time is the result of the combined effect of lithology, precipitation pattern and climate, and their variation with respect to space and time. Since the sediment eroded from the drainage basin along with water causing erosion, flows through the tributaries and the main stream, the drainage net is intimately associated with the hydraulic geometry of the stream channels and their longitudinal profile. As suggested by Schumm (1977) the drainage basin is primarily a sediment production area where climate, diastrophism and land use act as the upstream controls. 12 River Morphology Glock (1932) assumed that the drainage pattern is initiated on an essentially smooth plane due to the uplift. According to him the drainage pattern goes through the following developmental stages: initiation, elongation (headward growth of the main stream), elaboration (filling in of the previously undissected areas by small tributaries), maximum extension (the maximum development of the drainage pattern) and abstraction (loss of tributaries as the elevation is reduced through time). This sequence takes a long time in geologic sense. During this sequence the sediment yield first increases to a maximum and then decreases. However, such erosional development cannot be observed. Hence several drainage basins in different stages of development are studied at a given time. Thus what is to be observed in time domain is studied in space domain assuming the process to be ergodic. The topographic characteristics of the drainage basin can be visualised either for the basin or for the drainage network. The most important topographic characteristics for the basin are its area, length, shape and relief. The corresponding characteristics for the drainage network are area tributary to stream channels, drainage density, stream length, network shape or drainage pattern, and network relief. 2.2 DRAINAGE PATTERNS AND TEXTURE Drainage pattern is the general arrangement of channels in a drainage basin. Drainage patterns reflect the influence of such factors as initial slope, inequalities in rock hardness, structural controls, recent diastrophism, and recent geomorphic and geologic history of the drainage basin. Because drainage patterns are influenced by many factors, they are quite useful in the interpretation of geomorphic features and their study represents one of the more practical approaches to the understanding of the structural and lithologic controls on landform evolution. Looking at them in the most general manner, one can classify drainage patterns into the following categories: Figure 2.1 (a) shows dendritic or branch-like pattern that is probably the most common drainage pattern. This is characterised by irregular branching of tributary streams in many directions and at almost any angle usually less than 90o. Dendritic patterns develop on rocks of uniform resistance and indicate a complete lack of structural control. This pattern is more likely to be found on nearly horizontal sedimentary rocks or on areas of massive igneous rocks. They may also be seen on complex metamorphosed rocks. Trellised or lattice-like pattern shown in Fig. 2.1 (b) displays a system of sub-parallel streams, usually along the strike of the rock formations or between parallel or nearly parallel topographic features recently deposited by wind or ice. Radial pattern shown in Fig. 2.1 (c) is usually found on the flanks of domes or volcanoes and various other types of isolated conical and sub conical hills. Parallel drainage pattern shown in Fig. 2.1 (d) is usually found in regions of pronounced slope or structural controls that lead to regular spacing of parallel or near parallel streams. Rectangular drainage pattern shown in Fig. 2.1 (e) has the main stream and its tributaries displaying right-angled bends. This is common in areas where joints and faults intersect at right angle. The streams are thus adjusted to the underlying structure. Deranged drainage pattern, see Fig. 2.1 (f) indicates a complete lack of structural or bed rock control. Here the preglacial drainage has been affected by glaciation and new drainage has not had enough time to develop any significant degree of integration. It is marked by irregular stream courses that flow into and out of lakes and swamps and have only a few short tributaries. Drainage Basins and Channel Networks 13 a) Dendritic pattern b) Trellis Trellied or lattice like pattern or lattice like pattern c) Radial or concentric pattern d) Parallel pattern e) Rectangular pattern f) Deranged pattern g) Centripetal pattern h) Highly violent pattern Fig. 2.1 Various drainage pattern Centripetal pattern shown in Fig. 2.1 (g) is encountered locally. Here the drainage lines converge into a central depression. These are found on sinkholes, craters and other basin like depressions. Highly violent pattern shown in Fig. 2.1 (h) is characteristic of areas of complex geology. The complex drainage patterns observed in nature are a result of differing lithology, regional slopes, presence of joints and faults, and geologic activities such as glaciation, volcanism and limestone solution. Zernitz (1932), Howard (1967) and Thornbury (1969) have given full description of commonly occurring drainage patterns and their interpretation. Drainage Texture An important geomorphic concept about the drainage pattern is the drainage texture by which one means relative spacing of drainage lines. Drainage texture is commonly expressed as fine, medium or coarse. Climate affects the drainage texture both directly and indirectly. The amount and type of precipitation influence directly the quantity and character of runoff. In areas where the precipitation 14 River Morphology occurs primarily in the form of thunder showers, a larger percentage of rainfall will result in runoff immediately and hence, other factors remaining the same, there will be more surface drainage lines. The climate affects the drainage texture indirectly by its control on the amount and types of vegetation present which, in turn, influences the amount and rate of surface runoff. With similar conditions of lithology and geologic structure, semiarid regions have finer drainage structure than humid regions, even though major streams may be more widely spaced in semiarid than in humid regions. It is also noticed that drainage lines are more numerous over impermeable materials than over permeable areas. The initial relief also affects drainage structure; drainage lines develop in larger number upon an irregular surface than on the one that lacks conspicuous relief. Bad-land topography promotes fine drainage structure. Impermeable clays and shales, sparse vegetation and existence of thundershowers are responsible for very fine drainage structure. Coarse drainage structure is in particular found on sand and gravel outwash plains. Gravel plains have fewer drainage lines on them than adjacent till plains underlain by relatively impermeable clay till. The drainage structure can be qualitatively related to a parameter known as drainage density (see section 2.9) first defined by Horton (1932) as total length of streams per unit of drainage area. Drainage density varies from about 0.93 km/km2 on steep impervious areas to nearly zero for highly permeable basins. It varies from about 2.0 to 0.60 km/km2 in humid regions. As indicated by Smith (1950) and Strahler (1957), coarse drainage structure corresponds to drainage density less than 5.0 km/km2, medium drainage structure to drainage density value between 5 and 15 km/km 2 and fine drainage structure to drainage density between 15 and 150 km/km2. 2.3 STREAM ORDER A stream net or river net is the interrelated drainage pattern formed by a set of streams in a certain area. A junction is the point where two channels meet. A link is any unbroken stretch of the river between two junctions; this is then known as the interior link. If it is between the source and first junction, it is called the exterior link. Quantitative analysis of the stream network really started with Horton (1945). This analysis has been developed to facilitate comparison between different drainage basins, to help obtain relations between various aspects of drainage patterns, and to define certain useful properties of drainage basins in significant terms. According to Horton (1945) the main stream in the river net should be denoted by the same order number all the way from its mouth to its headwaters. Thus, at every junction where the order changes, one of the lower order streams is renumbered to the higher order and the process repeated. Thus in Fig. 2.2 (a) the main stream is shown as the fourth order stream right back to its source. The third order streams which are tributary to the fourth order stream are also extended back to their farthest source as the third order streams and so on. The streams joining the third order stream are second order stream and they can be extended backward. It can be immediately realized that a certain amount of subjectivity is involved in the ordering of streams according to Horton’s method. In Strahler’s (1952) system, see Fig. 2.2 (b), the headwater streams that receive no tributary are called first order streams. Two first order streams unite to give a second order stream. Two second order streams unite to give a third order stream and so on. When two streams of different order unite, the combined stream retains the order of the higher order stream. A combination of two streams of lower Drainage Basins and Channel Networks 15 a) Horton (1945) b) Strahler (1952) c) Scheideggar (1965) Fig. 2.2 d) Shreve (1967) Systems of stream ordering order, say (u – 1), with a stream of given order u increases the order of the latter by one integer, that is (u + 1). The result of this system of ordering is that it does not reflect any increments except approximately doubling the discharge if one assumes that streams of the same order in the same drainage basin carry approximately equal discharges. Scheideggar (1965) defines the order x after two streams of order u1 and u2 by x = log2 2 u1 ´ 2 u2 d i ...(2.1) His system of ordering is shown in Fig. 2.2 (c). Shreve (1967) has suggested a system of ordering streams in which, the order numbers of two streams contributing to the junction are added to arrive at the order number below the junction, see Fig. 2.2 (d). Thus each exterior link or head tributary has a magnitude 1. If links of magnitude u1 and u2 join, then the resultant downstream link has the order (u1 + u2). If we assume that the first order streams are approximately of the same magnitude and that the discharge is neither lost nor gained from any source other than the tributaries (which is not completely true) then Shreve number is roughly proportional to the discharge in the segment of the stream. It may be mentioned that Strahler’s system of ordering has been more commonly used than the other methods and the same is utilised herein. The analysis of drainage basin considering stream orders is often known as morphometry. The morphometric analysis of drainage basins carried out by Horton (1945), Strahler (1952), Rzhanitsyn (1960) and others is based on the premise that for the given conditions of lithology, climate, rainfall, and other relevant parameters in the basin, the river net, the slope and the surface relief tend to reach a steady state in which the morphology is adjusted to transmit the sediment and excess flow produced. If there are any major climatic or hydrologic changes in the region, the steady state 16 River Morphology morphologic characteristics will naturally be modified. In other words, the river net is the definite response of the drainage basin to the complex physical processes taking place over the drainage basin. 2.4 HORTONS LAWS OF STREAM NUMBERS AND STREAM LENGTHS Consider a river net in a drainage basin in which the highest order of the stream is K. Let u represent the order of any segment and Nu represent the number of streams of the order u. It has been found by Horton and other investigators that if log (Nu) is plotted against u for any river net the data fall on a single straight line with Nu decreasing for increasing u, see Fig. 2.3. Hence the relation between Nu and u can be expressed as 4 - Daddy's creek - Alleghney river - Sher river (India) 3 Rb = 4.34 log Nu 2 Rb = 4.12 1 Rb = 4.07 0 0 1 2 3 u 4 5 6 7 Fig. 2.3 Variation of log Nu with u (Horton’s ordering system) Also or log Nu = a – bu log N(u + 1) = a – b (u + 1) log Nu = b from which one gets N( u + 1) Nu = 10b = Rb N( u + 1) ...(2.2) ...(2.3) Here a and b are constants. The constant Rb is known as the bifurcation ratio. It is defined as the number of streams of order u divided by number of streams of order (u – 1). Since Nk = 1 N(k – 1)/Nk = Rb or N(k – 1) = Rb N(k – 2) = N(k – 1) ´ Rb = Rb2 Nu = Rb(k – u) ...(2.4) Drainage Basins and Channel Networks 17 It may be mentioned that for small drainage basins the relation between log Nu and u has been found to be slightly concave upwards thus deviating from the linear relationship expressed by Eq. (2.2); however the deviation becomes smaller as u increases, see Smart (1967). Horton (1945) found that the value of Rb varied from 2 to 4 for the river nets investigated by him, whereas Strahler (1964) found this range to be from 3 to 5 for the drainage basins in which geologic structures do not distort the drainage pattern. Mittal et al. (1974) found Rb to lie between 4.4 and 5.0 for sixty-two third order drainage basins in Garhwal, Himalaya (India), where lithologic conditions were represented by limestones, quartzites, phyllites, sand-shales and alluvium. This value ranged between 3.5 and 4.5 for sixth and seventh order sub basins of the Narmada, see NIH (1995). It has been found by some investigators that the bifurcation ratio Rb is not independent of the order of stream, and hence in a particular drainage basin Rb should be calculated between streams of 1 order lag with those of 2 order lag in order to reduce the difficulties introduced by order and the size of area analysed. Schumm (1956) recommends the use of weighted Rb designated as WRb WRb = S Rb ( u , u + 1) Nu + N u + 1 SN d i where Nu is the number of streams of u th order. The principle embodied in Eqs. (2.2) and (2.3) is commonly known as Horton’s Law of Stream Numbers which states that “The number of streams of different order in a given drainage basin tends closely to approximate an inverse geometric series in which the first term is unity and the ratio is the bifurcation ratio”. (Horton 1945). The fact that the bifurcation ratio remains fairly constant is interpreted to mean that the drainage basins in homogenous materials tend to show geometric similarity. Strahler (1964) has emphasized that there is a close relationship between the shape of the drainage basin, bifurcation ratio and the shape of the unit hydrograph. A very elongated basin will have a very high value of Rb (of the order of 15 or so) and will give a sustained unit graph with low peak. On the other hand a near circular drainage basin will have a low Rb value (around 2.4 or so) and would yield a unit graph with high peak and small base length. It can be seen from Eq. (2.4) that åN i =1 n u = N1 + N2 + N3 + ..... N k K -1 K -2 K -3 = Rb + Rb + Rb K -1 ( Rb - 1 ) ..... = Rb d i U | | | ..... 1 + + V | | | W ...(2.5) If one measures the total length of streams of a given order u in a drainage basin and designates it Lu, the mean length of the streams of order u, Lu will be 18 10 10 10 2 River Morphology 5 10 10 10 10 10 øu 10 10 10 10 6 4 5 }u 3 4 Nu 2 Nu and }u km 10 10 10 10 1 2 0 1 –1 0 Sessquehanna river basin (U.S.A.) –2 –1 6 2 4 6 u Order 8 Fig. 2.4 Variation of Nu, Au , Lu with u Lu = Lu/Nu Lukm 10 3 ...(2.6) If in any given basin log Lu is plotted against u one gets log Lu increasing linearly with u, thus yielding a straight line, see Fig. 2.4. This means that Lu / Lu – 1 = constant RL ...(2.7) where RL is known as the Horton’s length ratio. It follows from Eq. (2.7) that 2 L2 = L1 RL, L3 = L2 RL = L1 RL ...(2.8) and u -1 Lu = L1 RL The principle embodied in Eqs. (2.7) and (2.8) is known as Horton’s Second Law of Stream Lengths, which states that “The average lengths of the streams of each of the different orders in a drainage basin tend closely to approximate a direct geometric series in which the first term is the average length of streams of first order”. (Horton 1945). Morisawa (1962) has found that RL values ranged from 2 to 3 in Applachian Plateau Province (U.S.A.), while its value ranged between 1.50 and 2.40 for four sub basins of Narmada. These two laws of drainage composition have been substantiated by several investigators irrespective of whether Horton’s or Strahler’s method of stream ordering is used. They include Chorely (1957), Morisawa (1962) and Gregory (1966). The total length of streams of order u will be Lu Nu. Substituting the value of Nu from Eq. (2.4) and using Eq. (2.8) one gets Drainage Basins and Channel Networks 19 Lu = Total length of streams of order u = Nu Lu (u – 1) (k – u) = L1 RL Rb Hence total length of the streams of Kth order basin will be åL 1 K u = k -1 K K -2 K -1 2 K -3 L1 Rb Rb + ... L1 RL Rb + L1 RL + L1 RL Rb - 2 + L1 RL = K -1 L1 Rb R FR I FR I R | +G J +G J 1+ S | R HR K HR K T 2 L b L b L b 3 FR I + ... + G J HR K L b K -2 FR I +G J HR K L b K -1 U | V | W ...(2.9) Substituting RL/Rb = RLB one can simplify the above equation to the form å 1 K K -1 Lu = L1 Rb dR dR K LBI K LB i - 1i -1 ...(2.9) Another length parameter introduced by Horton (1945) is the length of overland flow Lo which is the length of flow path, projected to the horizontal, of non channel flow from the point of drainage divide to the point on the adjacent stream channel. Length of overland flow is one of the most important variables affecting the hydrologic and physiographic development of the drainage basin. During evolution of the drainage basin Lo is approximately equal to half the reciprocal of the drainage density. 2.5 AREAS OF DRAINAGE BASINS Basin area is hydrologically important because it directly affects the size of the storm hydrograph, and the magnitude of mean and peak flows. Amount of sediment eroded from the drainage basin is also related to the basin area. In fact, since almost every watershed characteristic is correlated with area, the area is the most important parameter in the description of form and processes of the drainage basin. The area Au of a basin of given order u is defined as the total area projected upon a horizontal plane, which contributes overland flow to the channel segment of a given order and all the tributaries of the lower order. Thus area of the basin of the third order, A3 will be the sum of areas of first and second order basins, plus all additional areas, known as inter-basin areas, contributing directly to channels of order higher than the first. Thus N A2 = S N 1 A1 + S 1 A o 2 where Ao2 is the inter-basin area contributing to second order segments. In general one can write N N N Au = { S N 1 A1 + S 1 A2 + S 1 A3 + ... S 1 Au – 1} N + {SN1 Ao1 + S N 1 Ao 2 + ... S 1 Aou } ...(2.10) Law of areas has been inferred by Horton (1945) and stated by Schumm (1956), according to which the mean basin areas of stream of each order tend closely to approximate a direct geometric sequence in which the first term is the mean area of the first order basin. Hence if log Au is plotted against u, a straight line is obtained as shown in Fig. 2.4. From this one can deduce that 20 u -1 Au = A1 RA River Morphology ...(2.11) where Au is the mean area of basin of order u, A1 is mean area of first order basins, and RA is known as the area ratio. Some attempts have been made to relate stream lengths to basin areas. It is argued that according to the laws of stream lengths and basin areas, both these parameters are related to the stream order. Hence a relation of the type L ~ An should relate basin length to the basin area. On the basis of over 300 measurements made by Langbein (1947), Hack (1957) found that this relation is of the type L = 1.16 A0.60 ...(2.12) where L is the stream length in km measured up to the drainage divide and A is basin area in km2. For geometrically similar basins one would expect L ~ A0.50. Since according to Hack L ~ A0.60, it means that drainage basin changes its shape in the downstream direction; it tends to become longer and narrower as it changes. Figure 2.5 shows variation of L with A for different regions as well as the enveloping curves. 10 3 10 2 L km 10 1 1. 2. 3. 4. 5. 6. 7. 8. W. Malaysia Deron W. USA Uganda Wales Australia Nebraska (USA) E. USA 10 0 Envelope curves 10 –1 10 3 10 2 10 1 10 A km 0 10 1 10 2 10 3 2 Fig. 2.5 Variation of total stream length with basin area Müller (see Gregory and Walling (1976)) defines three lengths to describe the stream length. These are the length of the stream channel Le, the length of valley Lv and shortest distance between the mouth and the source of stream Lm. Hack has also shown that u -1 Au = A1 RA u ( RLB - 1) ( RLB - 1) ...(2.13) Drainage Basins and Channel Networks 21 2.6 BASIN SHAPE Basin shape affects the hydrologic characteristics of the basin, namely hydrograph shape. As mentioned earlier a long narrow basin having high bifurcation ratio gives a low but sustained peak whereas round basins with low bifurcation ratio would give a sharply peaked hydrograph. Several shape factors have been suggested to describe the shape of the basins, some of which are listed below: Table 2.1 S.No. 1. 2. Form factors for basins Reference Horton (1932) Miller (1953) Schumm (1956) Chorely et al. (1957) Notation Definition Comments Reciprocal of this is used by Corps of Engineers (U.S.A.) in Hydrograph analysis C = 0.6 to 0.7 for homogeneous basins of 1st and 2nd order. For non-homogenous basin C = 0.4 to 0.50 E = 0.6 to 1.0; lower value for areas with strong relief and steep slope — Form factor Rf Basin area Au/(Basin length)2 Circularity Basin area Au/Area of circle ratio C with the same perimeter Elongation ratio E Lamniscate ratio K (Diameter of a circle with area of basin)/(Maximum basin length) (Basin length)2/4 (basin area) 3. 4. The circularity and elongation ratios can be of practical utility in predicting certain hydrological characteristics of the drainage basin. Elongation ratio has been used in the studies of sediment eroded from the basins. In general drainage basins tend to become more elongated with strong relief and steep slopes. Available data indicate that the drainage basin gets relatively elongated as its size increases. 2.7 LITHOLOGY The lithology and rock structure in the basin play an important role in influencing the hydrologic, erosional and other characteristics of the basin. The rock type and soil mantle affect the infiltration capacity. Permeable soil or rock allows water to percolate into the ground which later may be discharged into the stream. Hence the surface runoff is reduced. Basins with bed rock or soil which is relatively impermeable produce high volume of surface runoff and very little ground water flow. Rock type governs the character and rate weathering, the weathering products obtained and hence the nature of sediment and solutes supplied to the stream. The nature and effect of vegetation is also partly governed by rock type, which in turn governs the sediment supply. Hence sediment load vs water discharge relationship would depend on rock type. Similarly alluvial fan area vs drainage area relationship also depends on rock type. The rock type also influences the shape of the valley and stream because it controls resistance to erosion and also the runoff as discussed above. Morisawa (1968) found that valleys cut in unconsolidated beach sands and gravels were V-shaped, while those cut in silts and muds were flat bottomed. In the same manner Brush and Hack have found that the correlation between channel gradient S and its length L depends on the lithology and rock type. If S = a Lb the slope decreased with increase in L for all the rock types i.e., b was negative, but the rate of decrease varied with rock type. Lastly, 22 River Morphology lithology and rock structure also affect the morphometry and geometry of the drainage basins. A flatlying resistant bed will cause increase in stream length and decrease in stream slope. Where the sediments are folded, stream cutting across resistant strata will be short and steep with small drainage areas. Similarly drainage pattern is also influenced by lithology. For flat and homogenous rock surface drainage net tends to form at random and streams flowing in all directions i.e. dendritic pattern. In the case of jointed or folded rocks streams tend to erode the channel along a weakness. If joints are the weakness, their orientation determines the stream pattern. In tilted or folded strata streams tend to develop along linear bands of outcropping weak rock. Therefore, a full understanding of lithology is essential for the study of river morphology. 2.8 VEGETATION Vegetation including grass, shrubs, and forests plays an important role in the hydrologic cycle and catchment erosion. Hence, its effect is of prime importance to those working on river morphology and river dynamics. Studies by various investigators have shown that water and sediment yield, flood peaks and the time of their occurrence, and the velocity of travel of the flow peak are strongly influenced by the nature and extent of vegetation. When the pressure on the land, because of increase in the population and human activity, was not heavy, there were marginal changes in the forests, and minor disturbances in their coverage were soon made up naturally. However, because of increase in the population and industrial growth and consequent increase in food, space and energy requirements of nations, there has been indiscriminate deforestation in some parts of the world. In the early eighties, most of the tropical forests were estimated as being altered by man at around 12 million hectares per year, see Bruijnzeel (1990). Many investigators consider this as an underestimate. Deforestation includes cutting of trees for fuel, timber and other industrial uses, deforestation caused by great and small forest fires, shifting of zoom cultivation, construction activity related to logging such as creation of access roads, skid tracks and landings, clearing areas for habitation and developing industry, surface mining and similar activities. Generally speaking, a forest subjected to some of the above mentioned disturbances may recover to its previous state if left alone for a sufficiently long period. However, this is not the case when the forest is converted to permanent agriculture such as grazing, cropping or extractive tree crops. The effects of partial or complete removal of forest on climate, water yield and its seasonal distribution and on sediment production have been studied by many investigators. Below are given the salient features of these effects, (see Bruijnzeel (1990)). Rainfall and Water Yield 1. Tropical forests reflect about 12 percent of the incident short wave radiation while agricultural crops reflect 15 to 20 percent. Hence a different partitioning of energy between warming up of the boundary layer and evaporation is to be expected when tropical forests are converted to grass lands or agricultural crops. 2. As a result of extensive studies during the past four decades, it is found that the extent of forests has definite effect on rainfall. 3. It has been found that in humid tropics removal of natural forests cover may result in considerable initial increase in water yield, the increase depending on the amount of rain received. Drainage Basins and Channel Networks 23 4. The initial increase in water yield, after removal of the forest cover, gradually decreases with the passage of years and may return to pre cut flows in about eight years in case of natural regrowth. Stream Flow Regime 1. Geological, topographical and vegetative cover play an important role on floods and hence isolation of effect of vegetation becomes rather difficult. 2. If geology is favourable, cutting vegetation shifts infiltration flow to surface flow and therefore peaks will enhance. 3. Also in the absence of retarding effect, the peak is likely to occur earlier. 4. Change in evapo-transpiration and infiltration opportunities associated with change in forest cover will govern the dry season flows. If infiltration opportunities after forest removal have decreased to the extent that the increase in amount of water leaving the area as stream flow exceeds the gain in base flow associated with reduced evapo-transpiration, then the dry season flow is reduced. If on the other hand, the surface infiltration characteristics are maintained over most of the area by deliberate soil conservation practices or by some other method, then the effect of reduced evapo-transpiration after clearing will show up as increased base flow or dry seasonal flow. Sediment Production and Yield When dealing with the effect of change in forest cover on erosion and sedimentation it is helpful to distinguish between surface erosion (i.e., splash, sheet and rill erosion), gully erosion, and mass movements because the ability of vegetation cover to control the various forms of erosion is rather different. It is well known that only part of the material eroded from hill side will enter drainage network, the rest may move into temporary storage such as depressions, foot slopes, small alluvial fans or in small tributaries, behind debris basins or flood plains. The stored material may be released during large storms or caught by vegetation, or form stable topographic elements. Since these storage opportunities tend to increase with increase in area, sediment delivery ratio, which is defined as the amount of sediment passing a given section during a given time divided by amount of sediment eroded from upstream in the same time, is found to decrease with increase in catchment area. It may be years before sediment stored in temporary storages is released and its effect felt several kilometers downstream from the region of erosion. Sediment yield, which is rate of sediment passing a given section, is discussed in detail, in Chapter–III. This was found to be the case on the Brahmaputra river in Assam (India) after 1950 strong earthquake, see Goswami (1985). During August 1950 earthquake, apparently one of the most severe ever recorded, massive landslides occurred which temporarily blocked many major tributaries. Bursting of these dams after several days not only produced devastating floods downstream, but also brought down enormous volume of sediment thereby raising the beds of these rivers considerably. The mean annual suspended load and water discharge between 1955–1963 were 750 000 m3 and 16 530 m3/s as against 130 000 m3 and 14 850 m3/s during 1969–1976. Also during the former period the river reach upstream of Pandu was aggrading, whilst it was degrading during 1969–1976. 24 River Morphology Surface and Gully Erosion Studies by Wiersum (1984) have indicated that erosion is minimum (0.10 to 0.60 tonnes/km 2/year) in those areas where soil surface is adequately protected by a well developed litter and herb layer. When this layer is destroyed or removed, erosion rates rise dramatically to 500 to 5000 tonnes/km2/year. Hence protection from tree stands lays not so much in the ability of tree canopy to break the power of rain drops but rather in developing and maintaining a litter layer. When rills are formed and they grow into gullies, their lateral and head ward extension through scouring, undercutting and subsequent collapse of walls cause a large increase in sediment production. Mass Wasting Some of the highest reported natural erosion rates from rain-forested areas have been related to intense mass wasting under conditions of steep topography, tectonic activity, and intense rainfall. In mass wasting, steep slopes in combination with geological and climatic factors are more important than land use. Prasad (1975) after ten years of observations of seismic activity, rainfall and occurrence of land slides in eastern Nepal concluded that intense precipitation and associated saturation of soil were apparently more important than seismic shocks. Starkel (1972) has opined that the role of vegetation in preventing shallow slope failures (less than 3 m) is very important; Manandhar and Khanal (1988) have confirmed this in south of Khatmandu. As regards the influence of tall vegetation on slope stability, the net effect is considered positive, the major factor being the mechanical reinforcement of the soil by tree roots. 2.9 DRAINAGE DENSITIES AND STREAM FREQUENCY Drainage density is defined as the total length of streams in a basin divided by its area. Hence the drainage density Dd is given by Dd = å å K 1 N 1 Lu/A ...(2.14) and will have dimension of km–1. Here N is the number of streams of order u and K is the order of the river basin. Greater drainage density means more channels per unit area or more closeness of channel spacing. Drainage density varies over a wide range from 2 km–1 to 800 km–1 or even more depending on the character of subsoil material, vegetation and relief. Climate is equally important in determining the drainage density since it controls discharge and indirectly the vegetation. Table 2.2 illustrates the effect of these factors, namely lithology, climate and vegetation on the drainage density. Drainage density does not seem to change regularly with stream order within basins. Investigations by Morisawa (1968) indicate that drainage density of the whole basin tends to approximate the mean drainage density of the 1st order basins in the watershed. Langbein appreciated the significance of drainage density as a factor determining the time of travel of water. Since water and sediment flow through the stream channels, annual sediment yield from the catchment is found to increase with increase in drainage as sediment yield ~ Dd0.1 (Garde and Kothyari 1987). Osborn has found that mean annual flood Q2.33 is proportional to Dd2.0 . Gregory and Walling (1976) have plotted total stream length against drainage area for a large number of catchments and found that L ~ A0.378 up to 100 km2 area and beyond that the exponent of A somewhat increases, see Fig. 2.5. Hence one can conclude that L/A i.e. Dd would decrease as A increases. Drainage Basins and Channel Networks 25 Table 2.2 Effect of lithology, climate and vegetation on drainage density [Adapted from Selby 1967, NIH 1993] Location Pennsilvania (U.S.A.) Colorado (U.S.A.) Maryland (U.S.A.) Volcanic Plateau (New Zealand) South Auckland (New Zealand) South Dakota (U.S.A.) Arizona (U.S.A.) New Jersey (U.S.A.) Bihar (India) Lithology Horizontal resistant sand stone Granite, gneiss and schist Shale Pumice and ignimbrite Graywacke overlain by volcanic ash Clay and shale Horizontally bedded shale Clay and sand fill Alluvium to Granite, Gneiss Climate Humid, Continental Humid, montane Humid, Continental Temperate, maritime Temperate, maritime Semiarid Hot desert Humid continental Humid Vegetation Deciduous forest Montane forest Coniferous and deciduous forest Scrub and grass Formerly green forest, now pasture grass Sparse bunch grasses or none None None 59 per cent agriculture and 41 percent forest etc. D d km–1 2–2.5 2.5–5.6 4.4 5.4 15.7 50–160 106–220 344-825 0.377 Obtaining drainage density can be a tricky problem because a lot would depend on the scale of the map used. Hence uniform scale needs to be used in the comparison of drainage densities of different basins. Carlson and Langbein (1960) have recommended a more rapid method of estimation of the drainage density. Draw a line of known length L on the contour map and count the number of streams n which intersect this line. A minimum of 50 contour crossings is advocated to provide an adequate sample. Then drainage density equals 1.41 n/L. Strahler (1964) considered the drainage density Dd to be a variable dependent on runoff rate per unit area Qr, erosion proportionately factor K (which is mass rate of erosion per unit area per unit eroding force), relief H, mass density of fluid rf, dynamic viscosity m, and g. \ Dd = f (Qr, K H, rf , m, g) The above equation can be written in dimensionless form as Dd H = f KQr , FG H Qr r f H Qr2 , gH m IJ K The first term (Dd H) is known as the ruggedness number, (Qr K) is known as Horton number, which expresses the relative intensity of erosion processes in the drainage basin, (Qr rf H/m) is Reynolds number and (Qr2/g H) is Froude number. Schumm (1956) has introduced a parameter called constant of channel maintenance C that represents the area in km2 necessary to develop and maintain one kilometer of drainage channel. If Au is plotted against Su 1 Lu it is found that the two are related linearly as 26 Au = a + C Su 1 Lu River Morphology ...(2.15) C being the constant of channel maintenance. A basin with relatively impermeable strata requires a smaller drainage area to maintain a permanent channel as compared to the basin with permeable strata. The constant of channel maintenance is taken as a measure of erodibility of the basin. Horton (1932) defines the stream frequency F as the number of stream segments of all orders within a given basin of order K, divided by the basin area; or F = Su 1 Nu / Ak ...(2.16) From the analysis of worldwide data Peltier (1962) found that for areas of comparable average slope, stream frequency is greater in semi-arid regions; it is least in the arid regions and intermediate in humid regions. High drainage densities or stream frequencies are a reflection of increased channel development and hence should give high sediment yield, which is really the case. Melton (1958) has analysed in detail the relationship between stream frequency and drainage density both of which measure the texture of the drainage net, yet each treats the different aspect of it. According to him it is possible to construct two hypothetical drainage basins having the same drainage density but different stream frequency, and vice versa. However, in nature there is a good correlation between the two. From the analysis of 156 drainage basins covering a wide range of climatic and lithological conditions, Melton found the following relation F = 0.434 Dd2 where F is in km and Dd is in km –2 –1 ...(2.17) 2.10 RELIEF ASPECTS The relief is the difference in elevation between given points. Maximum basin relief is the difference in elevation between the basin mouth and the highest point on the basin perimeter. Alternative definition of maximum relief is the basin relief along the longest dimension of the basin parallel to the principal drainage line. Relief ratio Rk is the ratio of maximum basin relief to the horizontal distance along the longest dimension of basin parallel to the principal drainage line (Schumm 1956). Melton (1958) defines the relative relief as the maximum relief H divided by the basin perimeter P while Maxwell defines the relative relief as H divided to basin diameter. Use of the perimeter as the horizontal length dimension solves the difficulty of locating a suitable axial line in the basin. Two other parameters involving maximum relief have been defined by Strahler (1957). The ruggedness number is the product of maximum relief H and the drainage density Dd i.e. (H Dd). The geometry number is defined as (H Dd / S) where S is the ground slope. Both these parameters are dimensionless. Observed values of ruggedness number vary from 0.05 to about 1. Strahler (1964) found that the geometry number varies over a relatively narrow range viz. 0.40 to 1.0. Schumm (1954) found that for six small drainage basins in Colorado Plateau Province (U.S.A.) the relief ratio Rh correlated well with annual sediment loss giving a relationship of the form log (annual sediment loss) ~ Rh Drainage Basins and Channel Networks 27 Admittedly, relief ratio strongly influences the sediment loss since the force exerted on the surface is directly related to Rh. However, climatic factors such as rainfall and vegetal cover also affect sediment loss. Schumm’s data shown in Fig. 2.6 are taken from catchments in the same region; hence climatic conditions were similar even though the lithology changed somewhat. 10 2 0 Schumm's data 3 Shale 8 Annual sediment loss Ha.m/km 6 4 Friable sandstone 2 10 8 0 0.1 4 5 0.3 Rh 0.4 0.5 0.6 0.2 Fig. 2.6 Relation between annual sediment loss and Rh (Schumm 1954) Hypsometric Curves Let “a” be the horizontal projected area of a drainage basin at an elevation h (see Fig. 2.7) and A be the total projected area. Then one can prepare a curve between relative height h/H and relative area a/A as shown in the Figure 2.7. Such a curve is known as hypsometric curve. The analysis of large drainage basins using such curves was first done by Langbein (1947) and later used by Strahler and others. The hypsometric curve, in general, will change with time because of the gradual erosion of areas at higher levels and hence the relative position of the hypsometric curve on a/H vs h/H graph gives an idea about the stage of development of the basin landscape. Figure 2.7 shows young and mature stages of topography. This figure also shows monadnock phase in which the resistant rock in the basin may form prominent hills at isolated places giving a distorted hypsometric curve. Sometimes the integral z 1 o f (x) dx where f (x) = h/H and x = a/A is used as an index of evolution of the topography of the basin. This integral represents the rock mass that is still to be eroded. Young phase would correspond to a high value of the integral while mature phase would correspond to a relatively small value. Strahler (1964) has indicated that most of the hypsometric curves can be represented by an equation of the form Re –1 Conglomerate sandstone 8 1 sis tan t to we 2 ak roc k 28 y Divide Entire basin area A 1.0 River Morphology Original land surface Young 0.8 Mature (Equilibrium) 0.6 Area a h H 0.4 H h Summit plane 0.2 a 0 Base plane Fig. 2.7 Monadnock (Prominent hills) (x, y) y 0 0.2 0.4 a/A 0.6 0.8 1.0 Hypsometric curve F d - x a IJ y=G H x d - aK z ...(2.18) Here y and x are as shown in Fig 2.7. The exponent z increases as the topography becomes more mature. Hypsometric curves are also related to hydrologic characteristics of the drainage basin. Thus distribution of elevation in a drainage basin is closely related to the amount of flood storage available, the effect of which is to make the rising limb of hydrograph less steep, increase the time lag and make the peak lower and less pronounced. Knowledge of hypsometric curve is also useful in better estimates of rainfall, snowfall and evaporation in the basin. Channel Slopes A composite stream profile in a drainage basin can be prepared in the following way. For each first order streams vertical drop and horizontal length of the segment is determined. From these data mean drop and mean horizontal length are determined. This procedure is followed for streams of all orders. The triangles for each order are connected in sequence to produce a composite profile. Since each segment slope is governed by the average discharge and average sediment load, a segmented profile looks logical even though we tend to draw a continuous curve through these points. If S u is the average slope of the segments of order u, Horton (1945) expressed variation of S u by the law of stream slopes according to which Su = S1 RsK - u where Rs is ratio similar to bifurcation ratio and can be called slope ratio. ...(2.19) Drainage Basins and Channel Networks 29 2.11 DRAINAGE BASIN CHARACTERISTICS AND HYDROLOGY Many times a need is felt to have hydrologic data at sites where gauging station data are not available. Since there is a lack of data about precipitation (input) and stream flow (output), there is great difficulty in testing input-output models unless severe simplifying assumptions are made. Hence, scientists have worked on the premise that fluvial activity and form of the land must be related. This was reflected in Strahler’s dimensional analysis presented earlier where runoff per unit area was related to erosion, relief and drainage density. Bodhaine and Thomas (see Osborn 1980) obtained the following expression for mean annual flood Q Q = 0.638 A0.889 L– 0.037 R1.135 G ...(2.20) where L is ratio of lake area to catchment area expressed in percent, G is the geologic factor and R is the average annual runoff. A number of studies conducted in the U.S.A. and other countries have shown that basic drainage parameters such as stream length, basin length, basin relief area, drainage density, and slope are adequate to obtain correlations with different flows from the basin. The ungauged flows for which the methods have been developed are 7 day low flows of 2-yr and 20-yr return periods Q2 and Q20 respectively, average annual flow Qaa, two year and 50 year peak flows Q2p and Q50p and sediment flow Qs. One flow is considered to be functionally related to another flow of same type of different return period. Thus Q2p = f (Q50p) For low flows this general relationship is Q1L = f (Q2L)–n ...(2.22) where n is positive. Some of the successful geomorphic parameters used are (L1 . H) (LT . H), (LT H0.5) and (Dd . L1) L1, where L1 is the length of first order perennial streams, H is the relief, LT is the total length of streams and Dd is the drainage density (Osborn, 1971). It may be noted that all these parameters are dimensional. Work done on the geomorphological instantaneous unit hydrograph has been summarised by Rodriguez-Iturbe (1993). GIUH is defined as the probability density function for the time of arrival of a randomly chosen drop to the gauging site and is related to Horton’s Rb, RL, RA, average velocity of the stream flow v and length of the channel of highest order LW. The peak flow qp and time to peak tp are given as qp = 1.31 RL0.43 ULW– 1 tp ...(2.23) –1 ...(2.21) FR I = 0.44 G J HR K B A 0.55 RL–0.38 LWU ...(2.24) Here qp is in hr–1, U in m/s, tp in hr and LW in km. 2.12 RANDOM WALK MODEL The precipitation falling on a uniformly sloping plain develops an incipient set of rills near the watershed divide; these are generally oriented downhill. As the rills deepen with time, cross grading 30 Uniform spacing at origin River Morphology Fig. 2.8 Random walk model for stream network begins owing to overflow of shallow rills. The direction that the cross grading takes place and the micro piracy of the incipient rills are postulated to be a matter of chance until the rills deepen sufficiently. This randomness in the first stages of development of stream has led to formulation of random walk model for drainage network. To illustrate the basic ideas behind random walk model assume a row of equally spaced points on the boundary of the drainage basin say at 1.5 cm apart; eight such points are shown in Fig. 2.8. They can be considered as source of first order streams. Assume each point can move to the right, left or in the forward direction through a fixed distance so that the motion is downhill. As a result, a series of staggering paths will be generated and junctions may occur after which the joint path will be extended as a single unit, see Leopold and Langbein (1962), Shreve (1966 and 1967). Such artificial networks have properties and relationships closely approximating Horton’s laws. As a consequence, it has been suggested that some of these relationships are attributes common to all systems of randomly developed networks and are not really laws of orderly stream development. Of course it does not follow that stream networks are generated at random, even though random walk models approximate to them in many aspects. Some may even argue that streams do not develop from head downwards but do so from mouth upwards. Leopold and Langbein found that for such a random walk model constructed, Lu + 1/Lu came out to be 2.8, a figure which lies between 2.5 and 3.7 the range obtained by Horton (1945). Similarly, from random walk model it is found that Lu ~ A0.64 which agrees well with Hack’s relation L = 1.16 A0.60 as given in Eq. (2.13). One may argue that the development of drainage network is not so much a matter of chance but it is influenced by lithology, climate, vegetation and antecedent conditions. The present streams may reflect the effects of sequences of beds that have been eradicated by erosion during geologic past. Since random walk model ignores all these factors one must view such a model with caution. Drainage Basins and Channel Networks 31 2.13 CONCLUDING REMARKS At the end it is pertinent to mention that most of the generalities developed in this chapter have been obtained from the data on small basins in weak rocks in U.S.A. Such basins adjust rapidly to the changing conditions. Therefore one may assume that some present property or properties are controlling the stream geometry and slope which can be measured and statistical relations obtained. If variation in lithology is great and erosional history complex, the drainage net analysis may become more involved (Sparks 1972). References Bruijnzeel, L.A.(1990) Hydrology of Moist Tropical Forests and Effects of Conservation. A State of Knowledge Review. Division of Water Sciences, IHP, UNESCO, Paris (France). 224 p. Carlson, C.W. and Langbein, W.B. (1960). Rapid Approximation of Drainage Density: Line Intersection Method. USGS Water Resources Division, Bull. 11, February 10. Chorely, R.J. (1957). Illustrating the Laws of Morphometry. Geo. Mag. Vol. 94. Chorely, R.J., Malm, D.E.G. and Pogorzelski, H.A. (1957) A New Standard for Estimating Basin Shape, Am. Jour. Sci., Vol. 255, pp. 138– 141. Garde, R.J. and Kothyari, U.C. (1987) Sediment Yield Estimation. JIP, CBIP, India, Vol. 44, No. 3. Garde, R.J. and Kothyari, U.C. (1990) Flood Estimation in Indian Catchments. Jour. of Hydrology, Elsevier Science Publications, Amsterdam, Netherlands, Vol. 113, pp. 135–146. Goswami, D.C. (1985) Brahmaputra River, Assam, India: Physiography, Basin Denudation and Channel Aggradation. WR Research, Vol. 21. Gregory, K.J. (1966) Dry Valleys and Composition of the Drainage Net. Jour. Hydro. Vol. 4, pp. 327–340. Gregory, K.J. and Walling, D.E. (1976) Drainage Basin Form and Processes:A Geomorphological Approach. Edward Arnold (Publishers) Ltd., London, Paper-Back Edition, 458 p. Glock, W.S. (1932) Available Relief as a Factor of Control in the Profile of Land Form. Jour. Geol., Vol. 40, pp. 74–83. Hack, J.T. (1957) Studies of Longitudinal Stream Profiles in Virginia and Maryland. USGS Professional Paper 294 – B,. 53 p. Horton, R.E. (1932) Drainage Basin Characteristics. Trans. AGU, Vol. 13, pp. 350–361. Horton, R.E. (1945) Erosional Development of Stream Their Drainage Basins:Hydrological Approach to Quantitative Morphology. Bull. Geol. Soc. Am. Vol. 50, pp. 275–370. Howard, A.D. (1967) Drainage Analysis in Geologic Interpretation:A Summation. Am. Soc. Petroleum Geologists Bull. Vol. 51, pp. 2246–2259. Langbein, W.B. et al. (1947) Topographic Characteristics of Drainage Basins. USGS Water Supply Paper 968C. Leopold, L.B. and Langbein, W.B. (1962) the Concept of Entropy in Landscape Evolution. Theoretical Papers in Hydrologic and Geomorphic Sciences. USGS Professional Paper 500A. 20 p. Manandhar, I.N. and Khanal, N.R. (1988) Study of Landscape Processes with Special Reference to Landslides in Lele Watershed, Central Nepal. Unpublished Report, Dept. of Geology, Tribhuvan University, Khatmandu (Nepal). Melton, M.A. (1958) Geometrical Properties of Mature Drainage Systems and Their Representation in an E4 Phase. Jour. Geol. Vol. 66, pp. 35–54. 32 River Morphology Miller, V.C. (1953) A Quantitative Geomorphic Study of Drainage Basin Characteristics in the Clinch Mountain Area, Verginia and Tennessee, Project NR 389-042, Tech. Rept. No. 3, Columbia University, New York (U.S.A.). Mittal, R.S., Parkash, B. and Bajpai, I.P. (1974) Drainage Basin Morphometric Study of the Part of Garhwal Himalaya. Himalayan Geology, Wadia Institute of Himalayan Geology. Morisawa, M.E. (1962) Quantitative Geomorphology of Some Watersheds in Appalachian Plateau. Geol. Soc. Am. Bull. Vol. 73, No. 9, pp. 1025–1046. Morisawa, M.E. (1968) Streams –Their Dynamics and Morphology. Earth and Planetary Science Series, McGraw Hill Book Company, N.Y. 175 pp National Institute of Hydrology (1993) Geomorphological Characteristics of Punpun Basin of Ganga River System, Roorkee (India), CS (AR) - 125. National Institute of Hydrology (1995) Fluvial Geomorphological Characteristics of Four Sub-basins of Upper Narmada, Roorkee (India), CS(AR) - 159. Osborn, J.F. (1980) Drainage Basin Characteristics Applied to Hydraulic Design and Water Resources Management, Chapter 8, In Geomorphology and Engineering (Ed. Coates, D.R.), George Allen and Unwin, London, 1980, pp. 141– 172. Peltier, L.C. (1962) Area Sampling for Terrain Analysis. Prof. Geogr. Vol. 14, pp. 24–28. Prasad, R.C. (1975) The Landslide and Erosion Problems with Special Reference to the Kosi Catchment. Proc. of the Seminar on Landslides and Toe Erosion Problems with Special Reference to Himalayan Region. Gangtok, Sikkim. Rodriguez - Iturbe, I. (1993) The Geomorphological Unit Hydrograph, Chapter 3 in Channel Network Hydrology (Ed. Beven, K. and Kirkby, M.J.), John Willey and sons, New York, pp. 43–68. Rzhanitsyn, N.A. (1960) Morphological and Hydrological Regularities of the Structure of the River Net. Published by Gidrameterizdat, Leningrad (Translated into English by P.B. Kimgold, USDA, ARS, U.S.A.) Scheideggar, A.E. (1965) The Algebra of Stream Order Numbers, USGS Prof. Paper 5258, pp. 187–189. Schumm, S.A. (1954) The Relation of Drainage Basin Relief to Sediment Loss. International Union of Geodesy and Geophysics; 10th General Assembly, Rome, IASH Publ. 36, Vol. 1, pp. 216–219. Schumm, S.A. (1956) Evolution of Drainage Systems and Slopes in Badlands at Perth Amboy, New Jersey, Geol. Soc. Am. Bulletin. 67, pp. 597–646. Schumm, S.A. (1977) The Fluvial System. Wiley Interscience Publication. John Wiley and Sons., New York. 338 p. Selby, M.J. (1967) Morphometry of Drainage Basins in Areas of Pumice Lithology. Proc. 5th New Zealand Geography Conference, New Zealand Geogr. Soc., Auckland (N.Z.), pp. 169–174. Shreve, R.L. (1966) Statistical Laws of Stream Numbers. Jour. Geo. Vol. 74, pp. 17–37. Shreve, R.L. (1967) Infinite Topological Random Channel Networks. Jour. Geol. Vol. 75, No. 2, pp. 178–186. Smart, J.S. (1967) A Comment on Horton’s Law of Stream Numbers. WR Research, Vol. 3, pp. 773–776. Smith, K.G. (1950) Standards for Grading Texture of Erosional Topography. Am. Jour. Sci. Vol. 248, pp. 655–658. Sparks, B.W. (1972) Geomorphology, Longman Group Ltd., London, Chapter 6, 2nd Ed. Strahler, A.N. (1952) Dynamic Basins of Geomorphology, Bull. Geol. Soc. Am., Vol. 63, pp. 923–938. Strahler, A.N. (1957) Quantitative Analysis of Watershed Geomorphology. Trans. AGU, Vol. 38, pp. 913–920. Strahler, A.N. (1964) Quantitative Geomorphology of Drainage Basins and Channel Networks. Section 4-II in Handbook of Applied Hydrology (Ed. V.T. Chow ) McGraw Hill Book Company Ltd., New York, pp. 4–39 to 4–76. Drainage Basins and Channel Networks 33 Thornbury, W.D. (1969) Principles of Geomorphology. Wiley International Edition, John Wiley and Sons, Inc., 2nd Edition. Wiersum, K.F. (1984) Surface Erosion under Various Tropical Agroforestry Systems, in Proceedings Symposium on Effects of Forest. Land use on Erosion and Slope Stability (Eds C.L. D’Loughlin and A.J. Pearce.). IUFRO, Vienna and East-West Centre, Honolulu, (Hawaii). Zernitz, E.R. (1932) Drainage Patterns and Their Significance. Jour. of Geol., Vol. 40, pp. 498–521. C H A P T E R 3 Soil Erosion and Sediment Yield 3.1 INTRODUCTION Soil can be eroded from its present state by the action of water, wind and glaciers; however in the context of the theme of this book, attention is concentrated on soil erosion by water, which is by far the most important in humid and semi-humid areas. Soil erosion by water is the process of detachment of soil particles by the impact of rainfall and runoff, and its transport down the slope. Erosion from mountainous areas and agricultural lands is the major source of sediment transported by the streams and that deposited in reservoirs, flood plains, and deltas. Sediment load is also generated by erosion of bed and banks of the streams, by the mass movements of sediment such as land slides, rockslides and mud flows, and because of construction activity related to roads, buildings and dams. Part of the sediment from the above-mentioned sources, which is carried by the stream, is stored in the valley bottom and on flood plains and released later. Hence, erosion of sediment is discontinuous with time and it displays a high degree of spatial variability. Since part of the sediment eroded from an area can deposit in the lower reaches, the rate of erosion is usually greater than the rate at which sediment is carried downstream at any section; the latter is knows as the sediment yield. It may be mentioned that since landscape formation and changes in it are due to differential erosion and deposition of sediment, erosion, sediment yield and landscape formation are closely interrelated; therefore study of soil erosion and sediment yield assumes great importance in river morphology. Excessive erosion rates in the catchments of the rivers Kosi and Brahmaputra in India are responsible for the severe migration of the Kosi and change of river regime of the Brahmaputra. Similar problems are also encountered in China on the Yellow river. Reservoirs constructed on streams carrying sediment lose their capacity due to deposition of sediment in the reservoir. On an average Indian reservoirs are losing their storage capacity between 0.05 to 5.0 percent per year. In Pakistan, Mangla reservoir, which was planned to last 100 years, is now expected to last only 57 years due to excessive sediment deposition (El-Swaify et al. 1982). Dendy (1968) opined that if the present rates of sedimentation continue a large per cent of small reservoirs would lose about fifty percent capacity in the next three decades. Soil Erosion and Sediment Yield 35 Soil erosion is found to reduce crop productivity and large tracts of land are made unproductive every year. Brown (1984) estimated that about 23 billion tons of soil from croplands in the world is being lost every year. Accordingly to UNEP (1980), about 20 million-hectare areas in the world become uneconomical for cropping each year due to soil erosion and erosion induced degradation. 3.2 GLOBAL EROSION RATES Sediment going out of the catchment every year i.e., sediment yield gives a valuable idea about rates of erosion and soil loss from the drainage basin. This information is also very useful in studying the sediment problems and river behaviour. The sediment yield is made of suspended load and bed-load. Except when the depth is small and material is coarse, it is rather difficult to measure the bed-load. Hence most of available data on erosion rates only include suspended load, which is normally expressed in tons/km2/year or tons/year. The mean annual suspended sediment yield expressed as tons/km2/year varies over a very wide range. Low sediment yield is generally associated with lowland areas or areas underlain by rocks that are highly resistant to weathering and erosion, e.g., 1.0 ton/km2/year for many rivers in Poland, and 1.7 tons/km2/year for a river draining the Southern Table Lands and Highlands of New South Wales, see Walling (1988). Some of the high values of sediment yield obtained are from highly erodible loess region. Table 3.1 adapted from Walling (1988) lists some of the high sediment yield values. Table 3.1 Maximum values of specific suspended sediment yield (Walling 1988) Country China Dali Taiwan Kenya North Island New Zealand River Huangfuchuan 187 Tsengwen Perkerra Waiapu Waingaromia Drainage area km2 3199 21 700 1000 1310 1378 175 Suspended sediment yield tons/km2/year 55 500 — 28 000 19 520 19 970 17 340 High values of suspended sediment yield can be attributed to various factors such as underlying geology, topography, climatic conditions, high erodibility of soils and land use. Steep slopes and high intensity of rainfall can also cause high values of sediment yield. Holeman (1968) has given valuable information on the sediment yield of major rivers of the world. Table 3.2 gives such data for some rivers in the world, which discharge more than 104 tons of sediment each year into the sea. Some idea about erosion rates observed in various continents would also be helpful in knowing which regions contribute the highest and the lowest sediment load to the oceans. Table 3.3 is based on the synthesis of data given by Strakov, and Milliman and Meade (1983). Table 3.3 indicates that the highest sediment load is fed to the oceans every year by Asia and the next in line would be South America and North and Central America. On the basis of whatever data that were then available some investigators have produced maps of global suspended sediment yield. One such map prepared by Walling (1988) is shown in Fig. 3.1. From the analysis of such data estimates are 36 Table 3.2 S.No River River Morphology Some rivers of the world discharging more than 104 tons/year sediment to the sea (Holeman, Ref. p. 68 (1982) Location Total drainage area 103 km2 Average annual sediment load 103 tons tons/km2 2945 1563 1445 547 508 8008 67 109 914 176 7890 3117 484 422 1207 39 1.50 11.80 12.20 21.80 5.60 0.057 181.40 17.90 15.60 2.00 — 1.80 11.10 0.16 3.90 2.80 Average water discharge 103 m3/s 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Yellow Ganga Brahmaputra Yangtze Indus Ching (tributary of Yellow) Amazon Mississippi Irrawaddy Missouri Lo (tributary of Yellow) Kosi Mekong Colorado Red Nile China India Bangladesh China Pakistan China Brazil U.S.A. Mynamar U.S.A. (Missouri) China India Thailand U.S.A. Vietnam Egypt 666 945 658 1920 957 56 5709 3185 425 1354 26 61 786 630 118 2944 2080 000 1600 000 800 000 550 000 480 000 450 000 400 000 344 000 330 000 240 000 210 000 190 000 187 000 149 000 143 000 122 000 Table 3.3 Continent Africa Asia Australia North and Central America South America Europe Mean erosion rates in different continents Area 10 6 km2 29.81 44.89 7.86 20.44 17.9 9.7 Erosion rate tons/km2/year 35 - 72 208 - 229 43 84 - 113 100 - 148 50 - 75 made of the total suspended sediment load transported to the ocean every year. Some of the estimates of mean annual sediment load are given in Table 3.4. The earlier data base was meagre whereas in the estimates made in 80 have been based on data from over 2000 rivers spread over all the continents. Hence, these recent estimates are likely to be more accurate than the older ones. Soil Erosion and Sediment Yield Sediment Yield 2 1 t.km yr 1000 750 500 250 100 50 Deserts and permanent ice Fig. 3.1 Suspended sediment yield on global basis (Walling 1988) 37 38 River Morphology Table 3.4 Some estimates of the yearly-suspended sediment transport to oceans Author Keunen Pechinov Fournier Mackenzie & Garrels Holeman USSR National Committee for IHD Walling and Webb Year 1950 1959 1960 1966 1968 1974 1983 Estimated mean annual load in 10 6 tons 32 500 24 200 51 100 8300 15 700 15 000 15 000 According to the concept of geomorphic cycle, material is continually eroded from higher elevation areas and brought down to the low-lying areas and sea thereby reducing the slope of the terrain. Natural agents such as rainfall and runoff, wind and glaciers cause this erosion. Geologists have made estimates of such erosion. The time required to reduce the uplifted land surface to a gently undulating plain was estimated by Davis to be 20–200 million years. Geomorphologists use four types of evidences to estimate the rate of loss of material from the land. These are: (i) Method based on estimates of suspended and dissolved material transported by rivers; this is obtained by sampling the sediment load and discharge measurements. (ii) Measurement of sediment accumulated in reservoirs. (iii) Measurement of surface processes on slopes including rates of soil creep, surface wash and landslides. (iv) Comparison of known geological or radiocarbon dates with landform changes identified as subsequent to them. Because of the different techniques used and also because of the fact that erosion 2000 Normal Relief Steep relief 1000 Steep relief 500 Ground loss (mm/1000 yr) 200 100 Normal relief 50 10 R S 1.5 P 2.5 20 G R S P G Fig. 3.2 Ranges of rates of lowering of land surfaces (Young 1969) Soil Erosion and Sediment Yield 39 rates are governed by rock type, climate, vegetation, basin area, relative relief and steepness of slope the reported erosion rates in different environments are not rigorously comparable. Young (1969) has examined the then-available data on erosion rates and found it necessary to divide the results into two classes of relief: normal relief including plains moderately dissected areas and gentle to moderate slopes, and steep relief including mountainous areas and individual steep slopes. His results are shown in Fig. 3.2. All data have been converted into mm/1000 years and are plotted on logarithmic scale. For large variations the extreme limits are shown on the ordinate and on abscissa the method used for measurement is indicated viz. R river load, S reservoir sedimentation, P surface process measurements and G geological evidence. His analysis gives an average erosion rate of 500 mm/1000 years for steep relief and 46 mm/1000 years for normal relief. He has also mentioned that with respect to rock type there are no marked differences in rates of erosion between igneous and metamorphic rocks, siliceous sedimentaries and lime stones; unconsolidated rocks are eroded 10–1000 times faster than consolidated rocks. Schumm (1963) suggests that denudation rate of about 900 mm/1000 years be considered as an average maximum rate for drainage basins of the order of 4000 km2. On the basis of suspended sediment yield of the Kosi as reported by Khosla (1953), Schumm obtains nearly the same rate as quoted above. On the other hand, he reports data by Zeuner, Gilluly, Stone and Gutenberg, which indicate that the present maximum rates of uplift or orogeny are far in excess of rates of denudation in many areas. These are 76 m/10 000 years in California, 30 m/10 000 years in Russia, 45 m/10 000 years in Japan and 100 m/10 000 years in the Gulf area. Even though average uplift rates may be 1/3 or 1/4 of the maximum rates and further it is not known that uplift will continue at this rate, it does indicate that timeindependent landforms may not be obtained in some cases because the rates of denudation and uplift are so different. 3.3 TYPES OF EROSION Major types of soil erosion due to the action of water include sheet erosion, rill and inter-rill erosion, concentrated flow erosion on gully erosion, and stream channel erosion. Sheet erosion is the erosion of land surface caused by the impact of raindrops and transport of soil by overland flow. Sheet erosion is more or less uniform removal of soil without development of water channels. Rill and inter-rill erosion caused by surface runoff results in numerous small-eroded channels across the landscape. Rills are Fig. 3.3 Formation of gullies 40 River Morphology defined as eroded channels so small that tillage operations obliterate them every year. Both sheet erosion and rill erosion are widespread over a field and according to Foster (1988) can exceed 20 000 tons/km2 in severe cases. The topography of most fields causes surface runoff in a few major natural waterways before leaving the fields. Erosion that occurs in these areas is called concentrated flow erosion; the impact of this erosion is localized in and around the waterways. When eroded channels in concentrated flow areas become so large that they cannot be easily crossed they are called gullies. Gullies are steep sided water channels, which carry ephemeral flow during storms. Formation of gullies is shown in Fig. 3.3. Gullies are associated with accelerated erosion and hence with landscape instability. Gullies may not normally develop from rills; their development is a complex process, which is not fully understood. Some observations indicate that small depressions caused by weakening of vegetal cover get enlarged; several such depressions coalesce and form a channel, which develops into a gully. Some gully action is found to occur due to subsidence of pipes or tunnels formed underground due to subsurface flow. This normally happens in high sodium soils. In a few cases gully action has been initiated where linear landslides leave deep steep sided scars, which may be occupied by running water in subsequent storms (Morgan 1979). Discontinuous gullies represent youthful stage while fused gullies are an early mature stage of development. The sediment removed from the landscape due to formation, widening or deepening of gullies is known as gully erosion (Heede 1975, and Piest et al. 1975). Very little is known about rates of gully erosion. It may be added that ephemeral streams are those streams, which do not flow continuously. They respond only to the occurrence of precipitation. Other times they are almost dry. Perennial streams are those streams which flow continuously, their water supply coming from rainfall, snow melt and ground water. Stream channel erosion includes stream bank erosion, valley trenching, streambed lowering and flood plain scour. It can also include the material carried by streams such as that from mine wastes and construction activities (such as dams, tunnels and roads) along the banks of the channel. In general, sheet erosion is the prime offender in humid regions, whereas in more arid parts where the rainfall is experienced in short high intensity storms, channel erosion is more predominant. Material derived from sheet erosion source is fine-grained material swept from fields and carried in suspension to and through the conveyance system. Channel type erosion is a source of coarser material and this material is obtained from the areas, which are already a part of the transportation system. In general sheet erosion forms a major part of total erosion from a given area. Thus Roehl (1963) found that in 4300 km2 of well scattered area in South Eastern U.S.A. sheet erosion accounted for 66 to 100 percent of the total erosion. Mass movement includes large-scale erosion due to tectonic activity, landslides, creep rock flow or mud flows; the eroded material is ultimately fed to the stream thereby increasing the sediment concentration substantially. Gross Ventre landslide South of Yellow Stone Park U.S.A., which occurred in 1925, produced 50 Mm3 rock materials forming a 68 m high dam in the valley. The lake formed by this dam was 8.0 km long. Rockslide at Frank (B.C. Canada) in 1903 brought down 35 Mm 3 rock debris. Such landslides are a common occurrence in the valleys of Himalaya in India. Relative importance of sheet erosion, gully erosion, channel erosion, mass movement, and accelerated erosion due to construction of roads etc. varies from one catchment to the other since it depends on various factors. Robinson (1977) has given data on sediment sources and their total contribution to the sediment in streams in U.S.A., (see Table 3.5). Soil Erosion and Sediment Yield 41 Table 3.5 Sediment sources and their total contribution to sediment in streams in U.S.A. (Robinson 1977) Sediment source Agricultural lands Stream bank erosion Pasture and range land Forest lands Other federal lands Urban Roads Mining Other Total sediment in 106 tons/years 680 450 210 130 115 73 51 18 14 Percent of total 40 26 12 7 6 4 3 1 1 3.4 FACTORS AFFECTING EROSION Factors affecting erosion are briefly discussed below. Rainfall and Temperature Rainfall is the most important factor affecting erosion because of its power to detach the soil particles and its ability to produce runoff, which causes erosion and transportation of the eroded material. Erosion can be produced by a short duration high intensity storm during which the infiltration capacity is exceeded. Prolonged low intensity storms can also cause erosion. In the case of erosion due to water, the antecedent conditions of the soil with regard to soil moisture play an important role. If the soil is already well soaked by previous storm a low intensity short duration storm can also cause significant erosion. For each area one would expect a critical or threshold value of rainfall intensity above which significant erosion would take place. Depending on geologic conditions this value varies from 10 mm/hr to 30 mm/ hr. The erosive ability of rainfall depends upon its intensity and duration and velocity and diameter of the rain drops. For the same mean annual precipitation the annual erosion would depend on how this precipitation is distributed over the year. Fournier (1949) found that the ratio (maximum monthly rainfall/annual rainfall) is a better rainfall parameter for the study of erosion. Garde and Kothyari (1987) have utilised this parameter in their analysis of erosion from the Indian catchments. Temperature plays an important role in the process of weathering, especially mechanical weathering, which leads to the disintegration of rocks. Alternate freezing and thawing, and alternate heating and cooling are the processes involved in this disintegration. Rainfall is responsible for chemical weathering as well as for transportation and deposition of the eroded material. Considering the importance of rainfall and temperature in the process of erosion it is natural that mean annual temperature and mean annual rainfall be used as the criteria for classifying modes of weathering and transportation as done by Leopold, Wolman and Miller (1964), (see Fig. 3.4). For any given temperature the erosion rate first increases with increase in precipitation, reaches a maximum and then significantly reduces. This reduction is due to the growth of vegetation which protects the soil surface from direct impact of rain drops, increases infiltration and gives direct protection from erosion due to foliage lying on the ground. This is shown in Fig. 3.5. 42 30 Mechanical Chemical weathering weathering mass movement wind running water 20 running water Mechanical and chemical weathering running water 10 mass movement 0 Mechanical weathering mass movement running water River Morphology Mean annual temp. °C 10 Wind 0 20 40 60 80 100 120 140 160 180 200 Mean annual rainfall, cm. 20 Fig. 3.4 Hypothetical morphogenic regions 160 140 Effective precipitation cm Mean annual temp. 10°C 120 100 80 60 40 20 0 0 100 200 Desert shrub 300 2 Forest Grassland 400 Sediment yield tons/Km . yr Fig. 3.5 Sediment yield as related to precipitation and vegetation (Leopold et al. 1964) Soil Characteristics The erodibility of soil depends on its texture, aggregate stability, shear strength, infiltration capacity, and organic and chemical contents. Coarser the particles smaller will be their erodibility. Similarly greater the relative density less will be the erodibility. The clay content combines with organic matter and forms clods of soil. The stability of the clods determines the resistance to erosion. The shear strength parameter is more useful in the study of mass movements such as landslides. The erodibility index of the soil designated as K is used in the Universal Soil Loss Equation USLE for agricultural lands discussed in section 3.6. It can be determined for the known values of per cent of silt and clay, per cent of sand (0.10 mm to 0.20 mm), percent of organic matter, soil structure and permeability. Figure 3.6 shows the monograph for determining the value of K for the known characteristics as given by Wischmeir et al. (1971). If all the details of soil are not available one can use the following average values given in Table 3.6. Soil Erosion and Sediment Yield 43 Table 3.6 Average value of erodibility Factor K Range of K 0.40 to 0.70 0.30 to 0.40 0.10 to 0.30 0.03 to 0.10 Soil Soil loams Clay loams Sandy loams Gravely loams 0 10 20 Silt + very fine sand 0.7 %OM = 0 80 60 1 2 3 4 0.6 0.5 0.4 0.3 40 0.2 Soil erodibility factor K 30 40 50 60 70 80 90 100 1 Very fine granular 2 Fine granular 3 Coarse granular 4 Blocky massive 1234 Soil strucuture 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 6 5 4 3 2 1 Permeability 0.1 20 Percent sand (0.1 0.2 mm) 0 0 Example given 65% Silt + V.F. sand 20% Sand (0.1 = 0.2 mm) 3% Organic matter Soil structure Fine granular Permeability slow to moderate K = 0.38 6 Very slow 5 Slow 4 Slow to mod 3 Moderate 2 Mode-rapid 1 Rapid Fig. 3.6 Monograph for computing soil erodibility factor K in Universal Soil Loss Equation (Weischmeir et al. 1971) Slope Geometry Erosion is found to increase with increase in slope and length of the slope; this is due to corresponding increase in the velocity and volume of surface runoff. Erosion rate per unit area can be expressed as Erosion ~ S m Ln Area ...(3.1) where the values of m and n are found to be different by different investigators. Values of m and n obtained by various investigators as given by Morgan (1979) are listed in Table 3.7. It can be seen that m and n are functions of process of erosion, magnitude of slope, steepness, length and vegetal cover. Vegetation Vegetation or plant cover reduces erosion of soil, its effectiveness depending on the height and continuity of canopy, density of ground cover and the root density. For a given temperature, as the precipitation increases the sediment yield in tons/km2 increases and reaches a maximum value. If the 44 Table 3.7 Values of m and n in Eq. 3.1(Robinson 1977) Investigator Zingg Hudson and Jackson Hovarth and Erodi Quinn, Morgan and Smith Kirkby River Morphology m 1.40 2.0 1.60 to 0.70 0.70 to 1.0 1.0 to 2.0 1.3 to 2.0 — n 0.60 — — — — 0.3 – 0.7 1.0 – 2.0 Conditions/Comments From five experimental stations in U.S.A. From experimental stations in Zimbabwe m decreased with increase in slope in laboratory studies m increased as grass cover decreased For soil creep and splash erosion For erosion by overland flow For erosion with rilling canopy is near the ground it dissipates the kinetic energy of rain. Canopy on the ground also increases roughness and reduces the velocity of surface flow. Roots play an important role in reducing erosion rate. Roots create easy passages for water to infiltrate thereby increasing the infiltration rate and reducing the surface runoff. Small roots also bind the soil mass thereby increasing its resistance to erosion. Generally forests are the most effective in reducing erosion because of their canopy; dense grass is equally effective. Experimental evidence indicates that the erosion-cover relationship is non-linear. As vegetal cover increases from zero there is a rapid decreases in soil loss; however beyond 60 percent cover, further increase in vegetal cover reduces the soil loss marginally. Table 3.8 shows the erosion-cover relationship generalised after Elwell (1980) and Elwell and Stocking (1974). It can be seen from Table 3.8 that for adequate erosion protection at least 60–70 percent of the ground should be covered by vegetation. Table 3.8 Relationship between percent vegetal cover and percent reduction in soil loss Mean seasonal vegetal cover % Soil loss as a % of bare plot soil loss 100 0.5 80 1.5 60 5 40 10 20 32 10 60 5 70 It may be mentioned that there is an interaction between rainfall and vegetation in controlling erosion rates. Langbein and Schumm (1958) have found that vegetation bulk in kg/m2 varies as the annual precipitation raised to a power greater than unity. With increasing precipitation the vegetation changes from desert shrubs to grassland to forest. As a result, when vegetation intensity becomes adequate it inhibits erosion. Hence, on a regional scale initially erosion rate increases with increase in annual precipitation, reaches a maximum and then decreases with further increase in precipitation. Schumm (1977) expressed the effect of mean annual temperature and annual precipitation on sediment yield as shown in Fig. 3.7. It can be seen that as the annual temperature increases the peak of the sediment yield occurs at higher value of annual precipitation. This is so because at higher Mean annual sed. yield tons/km 5°C 10°C 15°C 300 200 100 0 0 40 20°C 400 2 80 120 160 Mean annual precipitation cm Fig. 3.7 Variation of sediment yield with mean annual precipitation and temperature (Schumm 1977) Soil Erosion and Sediment Yield 45 temperature there is greater evapo-transpiration; hence less amount of precipitation is available for causing runoff. As a result, peak rate of sediment yield shifts to the right. However, studies by Walling and Kleo for 1296 measuring stations all over the world, by Sharma and Chatterji for small reservoirs in Rajasthan (India), by Dunne in Kenya, by Griffiths in New Zealand, and by Duglas in Australia do not support the universality of Fig. 3.7. (Tiwari 1993). 3.5 MECHANICS OF SHEET EROSION As the rainfall occurs the overland flow normally occurs at shallow depth for a short distance without forming any small depressions or furrows called rills. The pre-rill flow is many times called inter-rill flow and associated erosion is known as inter-rill erosion. In this area the depth of flow and the corresponding shear on the surface are very small. Here the dominating factor influencing the surface erosion is rainfall impact. On the other hand, once the flow enters the rills and is concentrated, the depth of flow is large. Therefore erosion in rill-flow is related to the runoff characteristics; this erosion is sometimes called rill-erosion. It may be mentioned that rills are not a permanent feature. Rills formed from one storm are often obliterated before the next storm of sufficient intensity, which can cause rilling. Most rill systems are discontinuous i.e., they have no connection with the main stream. Rills are usually initiated at a critical distance down the slope where overland flow becomes canalised. It may also be emphasized that rill erosion accounts for majority of erosion from the hillside. Mutchler and Young (1975) found that on a 4.5 m slope plots in U.S.A., over eight percent of material was transported in rills. Relative importance of rill erosion depends on the rill spacing. Smaller the spacing between rills greater will be the rill erosion. Four processes associated with inter-rill and rill erosion can be identified as: Soil detachment by rainfall; Soil transport by rainfall; Soil detachment by runoff; Soil transport by runoff. Mutchler and Young (1975) have summarised the mechanism of soil detachment by raindrops. Raindrop sizes usually range from 7.0 mm to fine mist size and in any rainfall there are raindrops of various sizes. A normal or Gaussian distribution based on the raindrop volumes is usually assumed. Hence median raindrop diameter d is that diameter for which equal amounts of volume are contained in larger and smaller drops than d. Laws and Parsons (1943) have found a relationship between intensity of rainfall I in mm/hour and d in mm as d = 1.24 I 0.182 ...(3.2) The raindrops attain a terminal fall velocity, which depends on their size, air density and temperature. Terminal fall velocity can be obtained from CD versus Reynolds number diagram for a sphere, given in all textbooks on Fluid Mechanics. The terminal fall velocity for 5 mm drop will be about 9.0 m/s and it will be 1.0 m/s for 0.25 mm drop. Presence of strong wind has two effects on terminal fall velocity. Firstly it can increase the velocity of drops striking the land surface and secondly it causes raindrops to strike the surface at an angle to the vertical. The ability of rain to cause soil erosion is attributed to its rate and the distribution of drop size, both of which affect the energy load of a rainstorm. The erosivity of a rainstorm is attributed to its kinetic energy or momentum; both these 46 River Morphology parameters can be related to rainfall intensity or total amount of rainfall. Rose (1960), Williams (1969) and Kinnell (1973) have related the erosivity rate to momentum of rainfall. Williams and Kinnell have given the following equations for momentum M: log M = 0.711 log I – 1.461 M = 0.0213 I – 1.62 Here M is in dynes cm –2 s –1 and I is in mm/hour. The kinetic energy of the rainfall is a major factor initiating soil detachment. Kinetic energy of rainfall can be either measured or can be computed if one knows the rain drop size distribution and corresponding terminal fall velocities. Investigators have used the following three forms of equations to relate kinetic energy E of rainfall expended per unit quantity of rainfall to the rainfall intensity I. E = a + b log ( I ) E = c + (b - a I E=bI-a -1 U V W ...(3.3) U | )V | W ...(3.4) Where a, b, c are empirical constants. Wischmeir and Smith (1958) gave the following equation E = 13.32 + 9.78 log I 2 ...(3.5) where E is in J/m .mm and I is the rainfall intensity in mm/hour. Hudson (1965) has given the following equation E = 29.8 – 127.5 I ...(3.6) There are a large number of equations developed for E which are based on data from different regions such as Nigeria, Zimbabwe and U.S.A. It may be mentioned that for a given choice of equation for E, the kinetic energy for a storm having non-uniform rainfall intensity is computed by (i) dividing the storm into small time increments in which the rainfall intensity can be assumed to the uniform; (ii) determining the rainfall intensity in mm/hour for each time increment; (iii) computing Ei for each intensity Ii using the chosen relationship between E and I; (iv) determining E = SEi. When the raindrop hits the soil surface there is a splash of water and its shape is as shown in Fig. 3.8. The splash shape parameters, which define its geometry, are crater width W, splash height H, splash angle b, sheet angle a and sheet radius r. These quantities change with respect to time and their variation with time as recorded by a high-speed camera is also shown in Fig. 3.8. The erosive action of raindrop is effective very early after the impact and in the vicinity of the centre of impact. Evidence indicates that the raindrop impact is most erosive where a thin layer of water about one fifth the drop diameter is present. If the surface water depth is about three drop diameters, it protects the soil from raindrop impact. As the splash height reduces and the crater width increases a horizontal flow velocity away from the splash is caused. This velocity among other parameters also depends on the ratio of water depth to drop diameter and is maximum when this ratio is 0.33, this horizontal component of velocity greatly increases the potential of this surface flow to transport detached soil particles. Soil Erosion and Sediment Yield 47 H r Sheet radius W b a 90 a and b in° 80 70 60 50 0 4 H and W in cm 3 2 1 0 0 0.01 0.02 0.03 0.01 Sheet angle a Splash angle b 0.02 0.03 Crater width W Splash height H Time after Impact s Fig. 3.8 Changes in splash parameters with time It must also be mentioned that as the raindrop hits a thin water layer surface, a large number of smaller water droplets are produced. Mutchler (1971) found that one drop of 5.67 mm diameter on 0.10 mm water depth on a smooth glass produced as many as 4000 droplets which would eventually hit the soil surface, generate turbulence and throw additional material in suspension. Raindrop impact effects are present in rills also; but because of relatively larger water depth compared to the size of drops, the impact effect is not so pronounced. Erosivity Indices In developing equations for predicting sheet erosion some investigators have developed erosivity indices, which depend on rainfall intensity, kinetic energy and other characteristics of rainfall. Some of these indices are described below: Wischmeier and Smith (1958) use the rainfall parameter R = EI 30 where E is the total kinetic energy of the storm and I30 is the maximum 30 minute intensity of rainfall during the storm. They found that soil loss correlates well with EI30. The term I30 is computed as twice the greatest amount of rain falling in any 30 consecutive minutes; E is calculated using Eq. (3.5). The parameter R is used in Universal Soil Loss Equation (see below). Fournier (1960) developed an erosivity index for river basins on the basis of relationship between suspended load in rivers and climatic data and relief characteristics. The index called climate index C is defined as C = p2/P where p is the rainfall amount in wettest month and P is the annual rainfall. This index was subsequently modified by FAO (1977) as follows: 2 C1 = S12 1 p i /P 48 River Morphology where pi is rainfall in ith month. It is also found that the index C1 is linearly related to the index R i.e. EI30 as R = a + b C1 where a and b vary widely from region to region having different climatic conditions. ...(3.7) 3.6 EQUATIONS FOR PREDICTING SOIL LOSS FROM AGRICULTURAL LANDS Since about 1940 considerable research on soil erosion from agricultural lands has been carried out in U.S.A. and other countries. Often laboratory and field plots have been used to obtain experimental data for predicting and evaluating soil erosion. Laboratory plots are of area about 1.0 m2 or less and many times rainfall simulators are used on them. These are used to study basic erosion phases that are difficult to study on larger plots, for example, surface sealing, aggregate stability, raindrop detachment, and splash transport. In such experiments one must be careful in minimising the edge effects in such plots. The plots used in the development of Universal Soil Loss Equation are large enough to represent the complete process of rill and inter-rill erosion. These are of such size that their sediment delivery ratio is very high. There are various empirical equations, which give the rate of sheet erosion. However, because of their empirical nature the equations would be strictly valid in the region where they are developed. Hence only the functional relationships are mentioned to emphasize the variables to which soil erosion has been related. According to Ellison (1945) the soil dislodged E1 in weight per unit area per unit time can be expressed as E1 = K wo4.33 d1.07 I0.65 ...(3.8) where wo is the terminal fall velocity, d is the raindrop diameter, I is the intensity of rainfall, and K is a constant. Musgrave and his associates in the Soil Conservation Service in U.S.A. made observations and analysed rates of sheet erosion. As a result an empirical equation of the form Ei ~ F Ri So1.35 L10.35 P1.75 ...(3.9) was proposed in which Ei is the soil loss in weight per unit area per year, F is the soil factor based the erodibility of soil and other physical factors, Ri is the factor which is related to the land use, So is the steepness of slope in percent, L1 is the length of the slope and P is the maximum 30 minute rainfall expected in the locality with a 2 years return period. The constant of proportionality in this equation depends on the units used to describe these variables. Universal Soil Loss Equation (USLE) Soil erosion rates from cultivated lands in U.S.A. are predicted by using the Universal Soil Loss Equation (USLE) developed by Wischmeier and Smith (1962, 1965) on the basis of statistical analysis of a large number of plot-years of data from 47 locations in 24 states. The equation takes into account the effect of rainfall, soil characteristics, slope and length factor for the land, and crop and management practices on soil erosion. This equation is an improvement over the earlier methods in that the abovementioned factors have been quantified and used in the equation. The Universal Soil Loss Equation is E =RKLSCP ...(3.10) Soil Erosion and Sediment Yield 49 where E is the computed soil loss either in tons/acre year or tons/ha year. R is the rainfall factor in hundred of foot-ton-inches per acre-hour-year or in MJ. mm/ha h yr. It is the combined erosivity due to rainfall and runoff. It is the average number of erosion index units in a year of rain. K is the soil erodibility factor in tons-acre-hours per hundreds of foot-ton-inches-acres or tons-hahour-ha-MJ-mm. (see Fig. 3.6) L is the slope length factor S is the slope steepness factor C is the cropping management factor P is the erosion control practice factor Erosion index is a measure of erosive force of the rainfall and is computed as the product of the total kinetic energy of the rainstorm and its maximum 30 minutes intensity. This is summed for a period of record and divided by the number of years to get its average value. This product correlates well with the soil erosion. Wischmeier and Smith (1965) have prepared a map of U.S.A. indicating Iso-R value lines; R-value varies from 0 to 600 in U.S.A. Soil erodibility factor K has been discussed earlier. It is defined as the erosion rate per unit of erosion index on 72.6 feet long and nine percent slope of cultivated soil. K values give an integrated effect of the characteristics of the soil which influence its permeability and ability to resist detachment and transport by rainfall and runoff. In central and eastern U.S.A. K values range from 0.03 to 0.70. The slope length factor L accounts for the fact that as the length of slope increases, there is increased runoff. It is defined as the ratio of soil loss for a given slope length to the soil loss from 72.6 feet length, other factors remaining the same. If l is the slope length it is found that the soil loss ~ l1.3 to 1.6 and hence soil loss per unit length will be approximately proportional to l0.50. Slope steepness factor S takes into account the increase in the velocity of runoff as slope increases. Taking nine percent slope as standard, S is defined as the ratio of soil loss for a given slope to that from a nine percent slope. If So is the slope steepness in percent, S is related to So as S = 0.0076 + 0.0053 So + 0.000 776 So2 Hence the combined effect of slope length and slope steepness in USLE is given as LS = l0.50 (0.0076 + 0.0053 So + 0.000 776 So2 ) ...(3.12) Cropping management factor C accounts for the crop rotation, used tillage method, crop residue treatment, productivity level and other cultural practices. Its value is the ratio of soil loss from a field with given cropping and management practices to the soil loss from the fallow conditions used to evaluate the K factor. The C factor for individual crops varies with the stage of crop growth and has been evaluated. Erosion control practice factor P accounts for the effect of conservation practices such as contouring strip cropping, and terracing on the resulting erosion (see Blakely et al. (1955) and Meyer and Mannering (1967)). Its value is the ratio of soil loss with one of these practices to the soil loss with straight row farming. Earlier USLE is revised and updated by the Agricultural Research Service and some universities in U.S.A., (see Foster (1988)). This is done i. to incorporate recently collected data for conservation tillage and range lands into the equation; ii. to improve the applicability of USLE to other climatic regions; ...(3.11) 50 River Morphology iii. to improve the performance of USLE for conditions where no data exist; and iv. to estimate values of the factor C. Attempts are also made to use USLE to estimate soil loss from isolated storm events. Other improvement being attempted is to evaluate sediment yield by using USLE equation. However this would require use of the concept of sediment delivery ratio. At present effect of topographic features on sediment delivery ratio is not known; hence this method of estimating sediment yield is not accurate. The Universal Soil Loss Equation is used for a number of purposes. Commonly it is used to find out the soil loss under a given condition. If an acceptable value of soil loss E is chosen the slope length L required to bring down the soil loss to the chosen value can be calculated. In this way appropriate terrace spacing can be determined. Alternatively the value of C can be predicted and appropriate cropping practice is specified. It may however be mentioned that the data on which USLE is based are from east of Rocky Mountains in U.S.A. Hence values of C pertain to this region only. As mentioned by Morgan (1979), Hudson and Roose have applied this equation in Zimbabwe and Ivory Coast respectively. Morgan (1979) has pointed out that there is considerable interdependence between the variables used in USLE and some are counted twice. For example, rainfall affects both R and C factors, and terracing the L and P factors. It is also pointed out that one important factor to which soil loss is closely related namely runoff has not been included in USLE. This has been overcome by Foster, Meyer, and Onstad who have suggested replacement of rainfall factor R by R1, which depends on R, the storm runoff Q in inches and qp the storm peak runoff in in/hr. R1 is given by R1 = 0.50 R + 15 Q qp1/3 ...(3.13) However this needs further verification. McCool and Rendard (1990) have reported the efforts made in U.S.A. to revise USLE to estimate more accurately the soil loss from both crop and range land areas. The modified equation is known as Revised Universal Soil Loss Equation (RUSLE). All the factors R, K, LS, C and P have received attention. McCool and Rendard have discussed major changes incorporated in RUSLE. Thus R-values are related to (El15). Further R equivalent approach is used to reflect the combined effect of drain and snowmelt. 3.7 MEASUREMENT OF SEDIMENT YIELD Sediment yield is the amount of sediment passing through a given section in unit time. It can be expressed in tons/km2/yr. Two most common methods of determining sediment yield from river basins are by measurement of suspended load, and from reservoir sedimentation surveys. These methods and associated problems are briefly discussed below: Suspended Sediment Measurements Determining the average suspended sediment concentration and multiplying it by the discharge can measure suspended sediment. Average suspended sediment concentration in a vertical can be obtained by first taking a number of samples at different locations in the vertical and then taking the average. However, since this is time-consuming and expensive, the following procedures are adopted. A single sample at water surface or 0.6 times the depth below water surface is taken. Sampling at water surface is easier and can give reasonably good results if suspended sediment is very fine. For slightly coarser materials, an empirical coefficient can be used to get average concentration from the Soil Erosion and Sediment Yield 51 known surface concentration. However, it may be mentioned that the coefficient would really depend on suspended sediment size and flow conditions. Sampling at 0.60 depths has been used in India and some parts of U.S.A. in the hope that it gives the average concentration, presumably because the mean velocity occurs approximately at this level. Analysis of wide range of data indicates that, for reasonable accuracy, one-point measurements should be made between 0.6 and 0.8 depths, the larger value being suitable for coarser sediment. A better method would be to take concentrations at 0.2D and 0.8D and obtain the average concentration as C= F3C H8 0 .2 D 5 + C0 .8 D 8 I K ...(3.14) as suggested by Straub. The three point method involves measurement of concentration at surface, mid depth and bottom; the mean concentration can then be obtained either by giving equal weightage to all the three samples or by giving a weightage of two to the mid-depth sample and one to the other two samples. If the stream cross-section is non-rectangular the average concentration in the vertical will be different for different verticals; hence sampling verticals have to be chosen. The following methods are available: i. single vertical at the midstream; ii. single vertical at the point of greatest depth; iii. verticals at 1/4, 1/2, 3/4 width; iv. verticals at 1/6, 1/2, 5/6 width; v. four or more verticals spaced equally across the stream; vi. verticals at middles of sections of equal discharge. The final choice of the number of verticals depends on the availability of man power, funds, crosssectional shape and accuracy desired. The suspended load carried by the stream can then be determined from Qs = å N 1 qi Ci ...(3.15) where N is the number of verticals, qi is discharge at the centre of each vertical and Ci is the average concentration. A brief comment about the frequency of sampling is in order. In reality, samples must be collected at such a frequency which is satisfactory both from the point of view of accuracy needed and the expenses involved. Variations of sediment load occur due to variations in storm characteristics; size, shape, geological and topographical features of the drainage area, and characteristics of the stream. Out of these, the size of the drainage area appears to be the single most important factor. For smaller drainage areas water and sediment discharges are greatly dependent on local storm characteristics. For larger drainage areas, where the runoff accrues from different storms and sub-watersheds, the variation in water and sediment discharge with time is smaller. Therefore, as a rule, larger the drainage area smaller can be the frequency; however during a flood when discharge and sediment concentration vary rapidly, frequent sampling is required. For example, in the case of the Coon Creek, Wisconsin (U.S.A.), having a drainage area of 200 km2, it was found that 90 percent of the total sediment load for 15 months was 52 River Morphology discharged within ten days or 2.2 percent of the time, (see TCPSM (1969)). Sampling frequencies vary widely depending on agency conducting the sampling, purpose of collection of data, nature of stream and funds available. Sampling interval during low flows can vary from a day to a week. During the rising stage of a flood, intervals varying from 30 minutes to 12 hours have been utilised. After collecting such data the suspended load Qs is related to the corresponding water discharge Q; or alternately suspended load per unit width qs is related to discharge per unit width q. Several field engineers have reported a relationship between qs and q in the form qs = a qb ...(3.16) where b is found to vary between 1.9 and 2.2 and can be taken as 2.0 as an approximation. However, Leopold and Maddock (1953) found that b varies between 2.0 and 3.0 for many American rivers. The value of ‘a’ would depend on the units used. The usual practice is to develop such a relationship from data for a few years and then use it to compute suspended load for other years where only water discharge variation is known. Certain limitations of qs vs q relation need to be discussed. The qs vs q relations do not take into account such factors as sediment size, river slope, watershed characteristics, and pattern of discharge variation. Experience has shown that such relationships can be different for the rising and falling stages of the streams. In fact, these can be different for different seasons for the same stream. Significant variations can also be obtained because the peak of sediment discharge and that of water discharge may not coincide. For these reasons qs vs q or Qs vs Q relation can only be an approximate guide to the amount of suspended load and should be used with caution. To the suspended load must be added the bed-load carried by stream to get the total load. As mentioned earlier except in the case of shallow streams flowing through relatively coarse material, it is rather difficult to measure the bed-load. Lane and Borland (1951) cite the following classification of Maddock, in which percentage of unmeasured load (i.e. bed-load plus unmeasured suspended load) is related to the concentration of measured suspended load, type of bed material and the texture of suspended material, see Table 3.9. Table 3.9 Maddock’s classification to determine unmeasured load Concentration of measured suspended sediment in ppm Less than 1000 Less than 1000 1000 to 7500 1000 to 7500 Over 7500 Over 7500 Type of material forming the channel Sand Gravel, rock or consolidated clay Sand Gravel, rock or consolidated clay Sand Gravel, rock or consolidated clay Texture of the suspended sediment Similar to bed material Small amount of sand Similar to bed material 25 percent sand or clay Similar to bed material 25 percent sand or less Unmeasured load as a percentage 25 to 150 5 to 12 10 to 35 5 to 12 10 to 15 2 to 8 The average values of qS /qT as obtained from actual measurements or otherwise are available for some natural streams. Here qT is the total load. These are listed in Table 3.10. Dekov and Mozzherin (1984) found the ratio of bed-load to suspended load for large streams to be 0.08 for rivers in plain and 0.23 for mountain rivers. Soil Erosion and Sediment Yield 53 Typical values of qS / qT for natural streams in U.S.A. Sediment size in mm 0.14 0.10 0.30 0.27 0.29 0.24 0.33 0.10 0.25 Table 3.10 River Mississippi river at mouth Colorado river at Yuma Niobrara river near Cody Niobrara river near Valentine Snake river near Burge Five mile creek near Riverton Middle Loup river near Dunning Biose river near Twin Springs Moore Creek above Granite Creek Average qS / qT 0.90 0.80 0.49 0.47 0.67 0.81 0.53 0.65 0.75 Tricart (1962) has highlighted the dangers in determining the average erosion rates caused by the temporal and spatial variation in erosion. His main argument is that there are different types of discontinuities in the time domain. We have already seen that Qs vs Q relation is not truly unique. Time lags between flow and sediment are much greater for less mobile material such as coarse sand, gravel and boulders than for colloids, silts and clays, because while the former move slowly and intermittently as bed-load the latter move as suspended load and with nearly the same velocity as the flow. Then there are seasonal discontinuities, which cease more or less for long periods but recur nearly every year. Sporadic phenomena are caused by floods of large return periods. Catastrophic phenomena caused by landslides and earthquakes bring in a very large amount of sediment over a short period and only once in a while. Since the material in transport moves at different speeds, is stopped and is stored in location dictated by geomorphic evolution, the temporal discontinuities and spatial discontinuities are closely interlinked. On micro scale, the erosion-taking place from hill slopes caused by rainfall may not be uniform over the whole slope because of spatial changes in vegetation, roughness and erodibility of the material. Then as the material moves to the foot of the slope, coarse material may get deposited due to reduction in slope. This is also assisted due to reduction in flow caused by the high permeability of the fan. Further, material brought down by avalanches, land slides and source chutes is also discontinuous and sporadic in variation. Lastly, in the main river sediment is trapped by vegetation, on flood plain, in the riverbed, and at places where currents are weak. It may take years before the material is mobilised again and deposited elsewhere. This seems to be too complex a phenomenon to utilise deterministic model and hence Tricart thought that a statistical approach needs to be used. Reservoir Surveys When a large capacity dam is constructed across a stream, a backwater is caused on the upstream side of the dam, which reduces the energy gradient, and velocity of flow. This effect is felt for several kilometers in the upstream direction. As a result, the ability of the stream to transport sediment load is progressively reduced from beginning of backwater curve towards the dam and the excess sediment gets deposited. If the reservoir capacity to the annual inflow ratio is about or greater than unity, most of the sediment gets deposited upstream of the dam and only a small percent of finer material may pass over the dam and through the sluices. Since such deposition over a period of years reduces the valuable capacity of the reservoir to store water, reservoirs are periodically surveyed to determine the amount of 54 River Morphology sediment deposited in the reservoir. Hence such surveys provide valuable data on sediment load carried by the stream. There are two general methods of conducting reservoir surveys. These are the range-line survey, and contour survey. The general procedure of carrying out reservoir surveys has changed little in the past four or five decades; however significant advances have taken place in the equipment available for carrying out the surveys. Choice of the method depends on availability and character of previous mapping or survey records, the size of reservoir, degree of accuracy needed, and scope of study objectives. The range-line method is more widely used for medium and large reservoirs. In this method a number of cross sections of the reservoir are surveyed before the reservoir is first filled and then periodically resurveyed. These cross sections are called ranges. From known data for the consecutive surveys at each range line, one can determine area of sediment deposition, from which total volume of sediment deposited on the upstream side of the dam can be determined. Contour method is used for small reservoirs, which are occasionally empty, or at low stage. The contour method uses essentially the topographic mapping procedures. To apply this method first a good contour map of the reservoir is prepared before its filling. Similar contour map can be obtained periodically many times by aerial survey. The contour interval is 1.5 m to 0.5 m. From such consecutive contour maps the sediment volume deposited during certain period can be ascertained. New techniques of reservoir surveys are being used at present and these are discussed by Bruk (1985). Now a days reservoir surveys are carried out using Global Positioning System (GPS). GPS (GARMIN 2000 and Chatterjee et al. 2001) is a satellite-based navigation system made up of a network of 24 satellites placed into orbit by U.S. Department of Defence; this system is now available for civilian use. It works in any weather condition, 24 hours a day. These satellites circle the earth twice a day in a precise orbit and transmit signal information to the earth. Using signal information from three or more satellites at the same time, the receivers on the earth use triangulation techniques to calculate the exact location of the reservoir. The GPS receivers have a number of potential errors, but if Differential Global Positioning System (DGPS), is used by having two identical receivers, they provide an accurate means of surveying. The basic principle of DGPS is that errors calculated by two receivers in a local area will have common errors. Here one GPS receiver at the base station is located on the surveyed point, and the second one called the rover station is located on the motorised boat, which collects bathymetric data for reservoirs. The reference station GPS receiver knows the position of its antenna and can determine the errors in satellite signals. The error between measured and calculated is the total error. The range errors for each satellite are formatted into messages and the modular encodes these data. In an amplified form these data are radiated through antenna to roving GPS Station for real time position correction. Hence, when the two receivers are operated concurrently, by comparing and processing of signals of both the stations, the position of roving station can be obtained with adequate accuracy. The depth measuring unit consists of sonic sounding equipment, which comprises recorder, transmitting and recovering transducers and a power supply. This equipment needs frequent calibration. With such equipment depths can be measured with an error less than one percent. Once the volume of sediment deposited in a given period is known, it can be converted into corresponding weight if the average unit weight of sediment Wav over a period of T years is known. Miller (1953) has given the following equation for Wav. Soil Erosion and Sediment Yield 55 Wav = Wo + 0.434K LM T ln (T - 1)OP NT - 1 Q ...(3.17) where Wav and Wo are the average unit weight and initial unit weight in kN/m3 of the deposited sediment in T years and the coefficient K depends on the sediment size and method of reservoir operation. Values of K as recommended by Lane and Koelzer are given in Table 3.11. Table 3.11 Recommended values of K in Eq. 3.17 (U.S. Govt. and IIHR 1943) S. No. Reservoir operation Deposited sediment Boulders, gravel sand Silt Clays 0 0 0 0 0.90 0.42 0.16 0 2.51 1.68 0.94 0 1. 2. 3. 4. Sediment always submerged or nearly submerged Normally a moderate reservoir draw down Normally considerable reservoir Reservoir normally empty Knowing the percentages of the individual fractions in the deposited sediment Wo can be determined as Wo = S iN = 1 Woi pi/100. In the same way weighted K value can be determined and used in Eq. (3.17). To determine initial unit weight Table 3.12 can be used: Table 3.12 Material Clays Silts Sands Gravel Boulders Initial unit weights of sediment kN/m3 7.5 9.5 16 20 22 As has been already mentioned, some material flows over and through the dam; therefore sediment deposited in the reservoir during a given time will be less than sediment flowing into the reservoir during the same time. This ratio expressed in percent is commonly known as the trap efficiency Te of the reservoir, which will vary between 0 and 100 percent. If the trap efficiency of the reservoir is known, yearly quantity of sediment deposited in the reservoir can be converted into sediment yield using the relation: FG Annual quantity of sedimentIJ H deposited in the reservoir K Sediment yield = (Trap efficiency/100) ...(3.18) 56 River Morphology In general, the trap efficiency of a reservoir depends on the ratio of storage capacity to annual inflow, age of the reservoir, shape of the reservoir, method of reservoir operation, sediment size and its distribution and type and location of outlets. There is no general method available for the determination of trap efficiency, which takes into account all these factors. What is being used at present is the trap efficiency versus (capacity/inflow) ratio curve proposed by Brune (1953) on the basis of record of 44 normally ponded reservoirs in U.S.A., (see Fig. 3.9). On the same figure are also plotted some data from reservoirs in China, India and South Africa. At present this curve is used in most of the countries for normally ponded reservoirs. 100 Trap efficiency, To (%) 80 60 40 20 0 0.001 Envelopes Reservoirs in China Reservoirs in USA Reservoirs in S. Africa Reservoirs in India 0.01 0.1 Capacity/Inflow 1.0 10.0 Fig. 3.9 Trap efficiency of normally ponded reservoirs Sediment Yield Computations Theoretically one can use the equations for bed-load and suspended load computations given in Chapter V and determine the bed material load carried by the stream at a given discharge, which will be the sum of bed-load and suspended load. To this should be added an estimated quantity of wash load i.e., material that is washed into the stream from the drainage basin and which is usually finer than the material found in the bed and banks of the stream. If such calculations are made for various discharges, one can prepare the sediment discharge vs water discharge curve from which average annual sediment discharge can be computed. However, it may be pointed out that what is obtained from such calculations is really the sediment transport capacity; and it may be quite different from measured sediment yield especially in the upper reaches of the river. Hence this method is inferior to the other two methods discussed above. 3.8 SEDIMENT DELIVERY RATIO As mentioned earlier, sediment delivery ratio is defined as the ratio between amount of sediment load passing a given section during a certain period and the total amount of erosion from the upstream catchment during the same period. It can be either expressed as a mere ratio or as a percentage. For plots of area less than 1.0 km2, the sediment delivery ratio SDR is almost 100 percent, and it decreases as the Soil Erosion and Sediment Yield 57 catchment area increases. SDR for a particular basin is influenced by a wide range of geomorphological and environmental factors including the nature, extent and location of sediment sources, relief and slope characteristics, drainage pattern and channel conditions, vegetation cover, land use, and soil structure. Basin area is probably the most important variable with which SDR is related. As the catchment area increases, the catchment slope as well as the channel gradient decreases and hence there is an increasing opportunity for sediment deposition on flood plain and in channels. Therefore, SDR decreases as A increases. Other variables used to study variation of SDR are basin relief, annual runoff and gully density. Figure 3.10 shows the band of scatter of variation of SDR with A for some regions in U.S.A. and former U.S.S.R. This figure also shows the curve proposed by Soil Conservation Service of U.S.A. It may be mentioned that for some catchments in China, SDR is found to be 100 percent even up to catchment area of 1000 km2. This may probably be due to very fine material such as loess that is eroded and transported without any deposition. 100 Curve proposed by SCS, U.S.A. SDR 10 1.0 Central and eastern U.S.A. Corn waste lands W. Iawa, U.S.A. Blackland Prairle, Texsas, U.S.A. Mule creek, Iowa, U.S.A. South-Eastern Piedmant, U.S.A. Missouri basin loess hills, U.S.A. Pasture waste lands, Iowa, U.S.A. USSR 0.01 0.10 1.0 A km 2 Enveloping lines 10 100 1000 Fig. 3.10 Relation between SDR and A It needs to be mentioned that there are some serious difficulties in the estimation of SDR, (see Walling (1988)). Firstly, correct estimation of gross erosion must be made. This is done by estimating sheet erosion based on soil loss equation and correcting it to take into account the channel and gully erosion. This procedure has a certain amount of uncertainty. Another problem in the determination of SDR is the temporal discontinuity that may be involved in the sediment delivery as pointed out by Tricart. Sediment eroded at one location may be temporarily stored and subsequently remobilised many times before reaching the outlet of the basin. The third difficulty in relating sediment yield downstream to the soil erosion upstream is from the fact that the sediment transported by a river represents the material derived from a number of sources other than upland erosion, e.g., channel and gully erosion and mass movement etc. Their estimation is very difficult. A study by FAO (1979) has compared the sediment yield with estimate of contemporary soil erosion rates from a number of African river basins having catchment areas between 150 km2 and 157 400 km2. This comparison indicates that the soil erosion rates are about one order of magnitude greater than the reported sediment yields. One of the equations, which take into account three variables in estimating SDR, is that by Roehl (1962) which is based on the data from south eastern U.S.A. It is 58 231.7 Steepness A 0 . 23 B 2 . 79 River Morphology SDR = a f 0 . 51 ...(3.19) where steepness is defined as the ratio of the maximum difference in elevation in m and basin length along the main waterway in m, A is the catchment area in km2, and B is the bifurcation ratio. Bifurcation ratio is the weighted mean ratio of a number of streams of given order to the number of streams in the next higher order (see Chapter II). For the average value of B = 4.37 for Roehl’s data one gets SDR = 3.792 Steepness A 0 . 23 a f 0 .51 ...(3.20) Walling (1988) lists a few more equations developed for different states in U.S.A. and China. A more rational and probably a more rigorous approach to defining and investigating the sediment delivery characteristics of the drainage basin is provided by the sediment budget concept, originally advocated by Dietrich and Dunne (1978) and developed by Lehre (1982) and others. Here various sediment sources within the basin are defined and the sediment mobilised from these sources is routed to and through the channel system by considering various sinks. A typical representation of such a budget for the Coon Creek in U.S.A. for the period 1938–1975 is shown in Fig. 3.11. Walling (1988) has represented similar data for the Lone Tree Creek (California), and the Oka river in U.S.S.R. It was found that in all the cases the proportion of the eroded sediment delivered to the basin outlet is very small. However, it may be mentioned that presently the availability of techniques for quantifying the various sources and sinks involved in budgeting the sediment is very limited, and as such mean SDR vs A curve is often used to obtain erosion rate from observed sediment yield. Sources 76.7% Upland sheet and till erosion 11.9% Upland gully erosion 11.4% Channel erosion 55.7% Colluvial deposits 77.0% Upland valleys 4.9% Upper main valley 25.6% Lower main valley 6.7% Sinks Area = 360 km 2 Fig. 3.11 Sediment budget for the Coon Creek, Wisconsin (USA) (Area 360 km 2) Since there is always a gain or loss of sediment storage in the system, the input from slopes and catchment rarely equals the sediment yield. The sediment storages in the catchment include slope storage (i.e., colluvium) and stream valley storage (i.e., alluvium). Colluvium when transported by gravity or by water may partly remain colluvium, or become alluvium, or become sediment yield i.e. Soil Erosion and Sediment Yield 59 efflux. Similarly alluvium can be eroded from the channel or flood plain and redeposited as alluvium or become sediment yield. Limiting the discussion about valley storage, the most important process in valley storage gain is vertical accretion from overbank stream flow; other important storage zones are alluvial fans of small tributaries and colluvial deposits from adjacent slopes. In sediment budget a steady state would imply input equals output, and upland erosion equals sediment yield. Since steady state is a very rare, one would like to study gain or loss of sediment from the valley as a function of time, and relate the nature of variation to the external factors, which influence the gain, or loss of storage; Trimble (1995) has done this and identified five conceptual models of valley storage fluxes, which are shown in Fig. 3.12 and briefly described below. Sediment Sediment loss gain Model-1 (Quasi-steady) + Vertical accretion Steady-state Lateral erosion Model-1 (Vertical accretion with lateral erosion) 100 yrs Sediment Sediment Sediment Sediment loss gain loss gain + Vertical accretion Vertical erosion 100 yrs Lateral erosion + 100 yrs Model-3 (Valley trenching) Sediment gain + Paving of channels 20 yrs Model-4 (Urban stream) Sediment Sediment Sediment loss gain loss Moderate control Uncontrolled + Mass movements Colluvium accretion Model-5 (High energy instability, mountains and arid streams) Flushing 20-100 yrs Fig. 3.12 Conceptual models of valley storage fluxes (Trimble 1995) Model-1 (Quasi steady state) is applicable to humid regions where adequate vegetation can develop and stabilise the landscape. There will be very little upland erosion and hence very little sediment load. Lateral erosion of one bank would cause lateral deposition on the opposite bank. The perturbations in the vertical accretion of floodplain would be a few centimetres per millennium at most. This situation existed in eastern U.S.A. before European settlement. 60 River Morphology Model-2 (Perturbation of humid area quasi steady state) is applicable in humid area where sediment load in excess of transport capacity is generated by strong climatic or natural forces (e.g., mining or large construction activity). This causes vertical accretion of floodplain and the channel. When the activity in the upland area stops, this deposited sediment is gradually eroded and transported downstream. This removal of deposited sediment shows exponential decrease. If the sediment supply from the upland is low, lateral erosion of channel may take place later. Model–3 (Valley trenching and arroyo cutting) is applicable when the climate or human induced perturbations cause an incremental increase in discharge greater than incremental increase in sediment discharge. This can result in trenching or gullying. The example of this model is found in semi arid south western U.S.A. In such areas the fragile grasslands were overgrazed, the vegetation was thinned drastically and the soil compacted resulting in greater stream flows and arroyo cutting. In Model–4 (Urban streams), a brief rapid increase in erosion occurs while urbanisation in underway, but when it is stabilised due to increasing imperviousness of the area the runoff increases and erosion decreases. This initiates arroyo cutting. In order to save valuable land, if arroyos are stabilised by paving the Model-4 results, otherwise Model-3 results. Model-5 (High energy instability, mounting and arid streams) is applicable to streams with a very narrow floodplain and very steep valley sides. The sediment budget in this case is much more episodic than cyclic in nature. Net storage gain can come from vertical accretion coming from fans of small tributaries and mass movement from valley sides. Sediment loss comes from large events, which flush sediment downstream. This model shows a period of accretion followed by flushing events, and the process is repeated at uneven time intervals. Identifying the sediment budget model enhances our understanding of the fluvial processes working in the system and throws light on the magnitude and time scales of sediment storage fluxes under the given environmental conditions and natural and man made perturbations. 3.9 PROCESS BASED MODELLING OF EROSION Even though USLE summarises a vast body of regionally derived data and expresses it in the equation form, the researchers are aware of its empirical nature and its limitation that it is not universally applicable. Further, it is also recognised that USLE does not explicitly represent the processes involved in soil erosion. As a result USLE gives only an average annual soil loss. Therefore, several attempts have been made to develop methodology for prediction of erosion by modelling the basic processes involved. These are discussed by Rose (1988). Overland Flow Consider flow on a planar land surface on a slope. Let L be the length of slope. Then the sediment flux flowing out of a unit width is qs = q C 3 ...(3.21) where qs is in mass of sediment/time, width, q is volume rate of water in m /s m, and C is the sediment concentration in oven dry mass of sediment per volume of suspension. One must now obtain expression for overland flow q. One can write Soil Erosion and Sediment Yield 61 R =P–I ...(3.22) where R is the excess rainfall, P is the precipitation and I is the rate of infiltration all being function of time. If Q represents runoff per unit area Q = q/(L) ...(3.23) One can then see that R =Q ...(3.24) However, if L is large and R varies with time, it will be seen that changes in Q will lag behind those in R. Thus in general R ¹ Q. It can be shown that R » Q + Kp ¶Q ¶t ...(3.25) where Kp depends on length, slope and roughness of the plane, Q, and on whether the overland flow is laminar or turbulent. The flux q(x) at any distance is given by q(x) = Qx ...(3.26) Erosion and Deposition Processes The following three processes affect the sediment concentration: 1. Rainfall detachment in which raindrops splash sediment from the soil surface into the water of overland flow. 2. Sediment deposition, which is the result of sediment settling out under the action of gravity; and 3. Entrainment of sediment from the soil surface in which sediment is picked up from rills, interrills and in sheet flow. Rate of raindrop detachment e is expressed as e = a Ce P 2 ...(3.27) where e is in kg/m s, a is the measure of detachability of soil by rainfall rate P and Ce is the fraction of soil surface exposed to the rain drops. The rate of sediment deposition di for a given size class i of fall velocity wi is expressed as di = wi Ci ...(3.28) where Ci is the sediment concentration of size class i. The rate of sediment entrainment can be related to excess stream power over its critical value. Let the rate of sediment entrainment for a given size class be gi. Then conservation of mass principle applied to a given size class i yields ¶ ¶ (qCi) + (DCi) = ei + gi – di ¶x ¶t ...(3.29) where D is the depth of overland flow at any time. Making certain approximations, Eq. (3.29) can be reduced to ordinary first order differential equation, which can be solved to yield C(L, t) = FG ac p IJ S H QI K e I i = 1 (g i) + r f gSKC g (1 – x*/L) ...(3.30) 62 for L > xi . Here I is the number of sediment class ranges, gi = 1 + River Morphology the land slope, K = (1 + 0.2677h), where h is the efficiency of net sediment entrainment and transport, Cr is the fraction of soil surface unprotected from entrainment by overland flow, and x* is the distance down slope from the top of the plane beyond which sediment entrainment commences. The accumulated mass of sediment Ms from a plane of width W is thus given by Ms = WL FG H wi rf is mass density of water, S is Q IJ K where tR is the duration of runoff. Equation (3.30) can be written as C (L, t) = A + B ...(3.32) where A is the net contribution to sediment concentration of rainfall detachment over deposition, and B is the net contribution of entrainment over deposition. Assuming A to be negligible and taking time average values of x*, Q and h, as x* , Q and h, C (L) can be expressed as C(L) = 2700 S h Cr 1 - z t 0 R C(L, t)QDt ...(3.31) F H x* L I K ...(3.33) Dynamic Simulation Models A more elaborate model is given by Negev (1969), which is commonly known as Stanford Sediment Model. In this model, the rainfall impinging on the land surface is divided into two parts, that falling on the impervious surfaces and that falling on the pervious surfaces. The sediment supply from impervious surface is determined by a power function relationship taking hourly rainfall as the independent variable. Rain falling on the soil is assumed to loosen the material by raindrop splash. This loosened material, called soil splash is then considered as potential sediment for the stream. If overland flow occurs, as computed by Stanford Watershed Model, then all the soil splash material in previous storages is transported together with the current soil splash material. Overland flow is also used to compute the rate of rill and gully erosion using power function relationship. Rill and gully erosion is then divided into inter load and bed material storage. The input to this model consists of hourly and daily recorded rainfall, daily recorded flow and sediment load, hourly overland flow, a translation histogram for routing the sediment through the stream system, information on the sediment rating curve for use in adjusting the material assigned to inter load and bed material load from rill and gully process, and set of parameters and exponents for use in the various power functions by which the sediment erosion processes are estimated. These are adjusted during the runs to calibrate the model. Use of this model to the Napa river, St. Helena, California (U.S.A.) and the river Clyde in Scotland has given good results. Other dynamic models developed include the one developed by Simons et al., (1975). The various processes modelled in this program include, interception, infiltration, overland flow from rainfall excess, sediment detachment due to raindrop impact, sheet erosion by overland flow, channel erosion and the routing of water and sediment through the channel system. The sediment detachment is calculated during a specific time increment as a function of rainfall intensity and provision is made for Soil Erosion and Sediment Yield Storm characteristics Basin characteristics Antecedent characteristics 63 Water routing Overland flow data Overland flow routing Overland flow bed material routing Channel flow data Sizewise soil detachment by raindrop impact with provision for amounting Loose soil storage Soil detachment by overland flow considering sizewise transport capacity and supply of loose soil Loose soil storage Overland flow wash load routing Soil detachment by channel erosion Overland flow bed material routing Loose soil erosion Channel flow wash load routing Bed material load hydrograph Total sediment yield Wash load hydrograph Fig. 3.13 Flow chart for water and sediment routing model developed at Colorado State University (Simons et al. 1975) calculating the detachment of different size fractions and for the development of surface armouring. Sediment supply for the transport depends on the initial depth of loose soil remaining from the previous storms, the amount of soil detachment by rain drop impact and the amount of soil detached by surface runoff. Sediment transported by overland flow is calculated using Meyer-Peter and Müller’s formula for bed-load transport. Similar procedure is used to route the wash load and the bed material load through the channel system using continuity equation to determine occurrence of aggradation or degradation. Figure 3.13 shows flow chart for this model. It may be mentioned that in recent times several such models have been developed. Morgan et al. (1990) describe the European Soil Erosion Model (EUROSEM) developed as a collaborative project by seven European countries. Two more models can be briefly discussed. Kothyari et al. (1997) have developed a method for estimation of temporal variation of sediment yield for a single storm in small catchments. The method is based on numerical solution of kinematic wave equation for simulation of overland flow, continuity equation for sediment and expressions for sediment detachment and transport. The model is calibrated and verified using twelve experimental catchments ranging in size from 0.002 km2 to 92.5 km2. For single storm events sediment yield varied from 0.003 tons to 800 tons. Julien and Rojas (2002) have discussed a physically based model simulating hydrologic response of a watershed to distributed rainfall field, considering time-dependent processes such as precipitation, interception, infiltration, surface runoff and channel routing, and upland erosion, transport and sedimentation, the model predicts, flood and sediment load variations with time. The model was applied to 21 km2 Goodwin Creek catchment in U.S.A. 64 River Morphology Stochastic Models Lack of detailed long duration record of erosion rates has hampered the application of various stochastic and time series modelling procedures to the erosion process. Yet some attempts have been made in the application of Autoregressive Moving Average (ARMA) Models to the records of Suspended Sediment concentration. Sharma et al. (1979) describe the use of a simple system model of this type to model the monthly and daily sediment yield of several catchments in Ontario, Canada. The model used to describe daily erosion rates explained 95 percent of the variation in the erosion process of the Thames river at Ingersol, while the monthly model accounted for more than 81 percent of short-term values of sediment concentration recorded during individual storm events. 3.10 EROSION RATES FROM INDIAN CATCHMENTS In India the approaches used for prediction of erosion rates have been essentially empirical involving regression method. This is primarily so because of the lack of availability of extensive data needed for use of physically based and simulation models. Earlier Khosla (1953) analysed the then available data from Indian reservoirs and reservoirs from abroad and found that the annual sediment yield in Mm3 is proportional to A0.72 where A is the catchment area in km2. However, Garde and Kothyari (1987) found large variations from this relationship when it was tested with recently collected Indian data. Dhruva Narayan et al. (1983) used the data from seventeen catchments in India and obtained the following relations for annual sediment yield T1 in metric tons. T1 = 5.5 + 1.1 Q where Q is the annual runoff in M ham. This equation was further modified to T1 = 5.3 + 12.7 QW1 ...(3.35) where W1 = T1/A, A being in M ha. Average value of W1 was found to be 1.25 M tons/M ha. Another relationship proposed by them involved use of EI30. T1 = (0.342 ´ 10 –6)A0.84 (EI30)1.65 ...(3.36) where EI30 is the product of average annual value of the sum of maximum 30 minute rainfall intensity in cm/hr and kinetic energy value E given by E = 210 + 89 log I30 ...(3.37) E being in tons/ha m. However, these equations need to be verified with additional data before these can be used with confidence. By far the most detailed analysis of Indian data has been carried out by Garde and Kothyari (1987, 1990). They analysed the average annual sediment yield data from 50 catchments in India having areas varying from 43 km2 to 83 880 km2. These data were obtained from the surveys of small, medium and large reservoirs with sedimentation period of at least ten years. Analysis of data indicated that the average annual erosion rate Sa in cm is a function of average annual rainfall P in cm, the average catchment slope defined as S = 1 n S AiSi, the drainage density D in km –1, the ratio (Pmax /P) where Pmax A1 is the average monthly maximum rainfall in cm, and the erosion factor Fe which gives an integrated effect of vegetation on erosion. The erosion factor Fe was defined as ...(3.34) Soil Erosion and Sediment Yield 65 Fe = 1 [0.8 AA + 0.6 AG + 0.3 AF + 0.1 AW] A ...(3.38) where AA is the arable area, AG scrub and grass covered area, AF is protected forest area, and AW is the waste land area all in km2. A map showing lines of constant Fe values was prepared from available data and this is shown as Fig. 3.14. The range of variables used by Garde and Kothyari are given below: – 108.3 cm P 63.77 cm – 381.11 cm Pmax 9.0 cm – 1.00 S 0.001 – 0.200 Fe 0.28 2 2 –1 D 0.002 km – 0.31 km–1 A 43 km – 82 880 km The regression analysis of the data gave the following equation for Sa Sa = 0.02 P0.60 Fe1.70 S 0.25 Dd0.10 (Pmax/P)0.19 ...(3.39) This relationship was then used on ungauged catchments for which all other data except Sa values were available. Sa was then computed from which sediment yield was expressed in tons/km2/year. Thus using data from 154 catchments an iso-erosion rate map was prepared which is shown in Fig. 3.15. It can be seen that the erosion rates in India vary from about 350 tons/km2/year to 2500 tons/km2/year. High erosion rates in North eastern region, parts of U.P., Bihar and Punjab, and in certain areas in Andhra Pradesh are partly due to high rainfall in these regions and partly due to geologic conditions and land usages. Considering that out of the variables affecting the erosion rate, only the annual rainfall changes from year to year, the following equation was proposed by Garde and Kothyari (1987) for the estimation of annual erosion rates. Pa = 0.02 Pam Fe1.70 S – 0.25 Dd0.10(Pmax/P)0.19 ...(3.40) where Pa is the annual precipitation in cm. Here m is the exponent, which was found to be related to coefficient of variation of annual precipitation. It may be seen from comparing Eqs. (3.39) and (3.40) that P0.6 = 1 n å n i m Pai where n is the number of years. Analysis of rainfall data from 100 rainfall stations indicated that as coefficient of variation changed from 0.1 to 0.70, m, value of the exponent increased from 0.600 to 0.607. This variation is shown in the following table: Cv 0.10 0.20 0.30 0.40 0.50 0.70 m in Eq. (3.40) 0.600 0.601 0.602 0.603 0.605 0.607 Thus for annual sediment yield computation Eq. 3.40 with table for m can be utilised. For future year wise prediction of sediment yield, one must generate annual rainfall series for known P and Cv and then compute the sediment yield. The annual series in India are found to follow normal distribution. It may be mentioned that with the passage of time land use pattern as well as extent of forest and other vegetation is bound to change and hence Fig. 3.11 need to be modified at regular time intervals and so also Fig. 3.12. However Eqs. (3.39) and (3.40) will not change. 66 River Morphology 0.55 0.55 0.6 0.6 0.6 0.55 0.55 0.5 0.55 0.6 Nep al n Bhuta 0.6 0.4 0.5 0.4 0.6 0.6 0.4 0.55 0.54 0.45 0.5 0.5 0.55 Bangladesh 0.5 0.55 Notations Igneous intrusive rocks Sedimentary unconsolidated (Recent alluviums) Metamorphic (Schists) Sedimentary consolidated Unclassified crystallines Khondalite 0.54 0.45 0.55 0.45 0.5 Other igneous and metamorphic rocks Iso-erosion factor lines Geologic boundaries Sri Lanka Fig. 3.14 Lines of constant Fe superimposed on the geological map of India (Garde and Kothyari 1987) Soil Erosion and Sediment Yield 67 Fig. 3.15 Iso-erosion rate lines in tons/km2 yr (Garde and Kothyari 1987) 68 River Morphology References Blakely, B.D., Coyle, J.J. and Steele, J.G. (1955) Erosion on Cultivated Land. Soil- The 1957 USDA Year Book of Agriculture. Brown, L.R. (1984) Conserving Soils. In State of the World 1984, (Ed. Brown L.R.) Norton, New York. Bruk, S. 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(1945) Some Effects of Rainfall and Surface on Erosion and Infiltration. Trans. AGU, Vol. 26, No. 3. El-Swaify, S.A., Dangler, E.W. and Armstrong, C.L., (1982) Soil Erosion by Water in the Tropics. University of Hawaii Research Extension Series No. 024. Elwell, H.A. (1980) Design of Safe Rotational Systems. Department of Conservation and Extension, Harare (Zimbabwe). Elwell, H.A. and Stocking M.A. (1974) Rainfall Parameter and a Cover Model to Predict Runoff and Soil Loss from Grazing Trails in the Rhodesian Sandveld. Proc. of the Grassland Society of South Africa, Vol. 9. FAO, U.N. (1977) Assessing Soil Degradation. Soils Bulletin 34, Rome, Italy. FAO, U.N. (1979) A Provisional Methodology of Soil Degradation Assessment, Rome, Italy. Foster, G.R. (1988) Modelling Soil Erosion and Sediment Yield. In Soil Erosion Research Methods (Ed. Lal R.) Soil Water Conservation Society, Ankeny, Iowa (U.S.A.), pp. 97-118. Fournier, F. (1949) Les Facteurs Climatiques de l ‘Erosion du Sol. Assoc. 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W.R. Research, Vol. 4, pp. 737-747. Hudson, N.W. (1965) The Influence of Rainfall on Mechanics of Soil Erosion with Particular Reference to Northern Rhodesia. M.S. Thesis, University of Cape Town, South Africa. Janda, T. Dunne and Swanson, D.N. General Tech. Report PNW 141, Forest Service USDA Portland, Oregon, U.S.A. Soil Erosion and Sediment Yield 69 Julien, P. and Rojas, R. (2002) Computer Modeling of Upland Erosion. Proc. Of 12 APD Intl. Congress, Singapore, Vol. 1, pp. 475-483. Kinnell, P.I.A. (1973) The Problem of Assessing the Erosive Power of Rainfall from Meteorological Observations. Proc. Soil Science Society of America, Vol. 37, pp. 617-621. Khosla, A.N. (1953) Silting of Reservoirs. CBIP Publication No. 51, New Delhi (India). Kothyari, U.C., Tiwari, A.K. and Singh, R. (1997) Estimation of Temporal Variation of Sediment Yield from Small Catchments through the Kinematic Method. Jour. Of Hydrology, Vol. 203, pp. 39-57. Kuenen, P.H. (1950) Marine Geology. John Wiley and Sons, Inc., New York. Lane, E.W. and Borland, W.M. (1951) Estimating Bed Load. Trans. AGU, Vol. 32, No. 1, February. Langbein, W.B. and Schumm, S.A. (1958) Yield of Sediment in Relation to Mean Annual Precipitation. Trans. AGU, Vol. 39. Laws, J.O. and Parsons, D.A. (1943) The Relation of Raindrop Size to Intensity. Trans. AGU., Vol. 24. Lehre, A.K. (1982) Sediment Budget in a Small Coast Range Drainage Basin in North Central California. In Sediment Budget and Routing in Forest Drainage Basins (Ed Swanson, R.J.) Leopold, L.B. and Wolman, M.G. and Miller, J.P. (1964) Fluvial Processes in Geomorphology. W.H. Freeman and Co., San Francisco, U.S.A. Leopold, L.B. and Maddock, T. (1953) The Hydraulic Geometry of Steam Channel and Some Physiographic Implications. USGS Professional Paper 252. Mackenzie, F.T. and Garrel, R.M. (1966) Chemical Mass Balance Between Rivers and Oceans. Am. Jour. Sci., Vol. 264, pp. 507-525. McCool, D.K. and Rendard, K.G. (1990) The Revised Universal Soil Loss Equation. Proc. of Int. Symposium on Water Erosion Sedimentation and Resource conservation, Dehradun (India), Oct., pp. 60-70. Meyer, L.D. and Mannering, J.V. (1967) Tillage and Land Modification for Water Erosion Control. ASAE-ASASCSA Tillage Conference Proc. pp. 58-62. Miller, C.R. (1953) Determination of Unit Weight of Sediment for Use in Sediment Volume Computations. USBR, Denver, U.S.A.. Milliman, J.D. and Meade, R.H. (1983) Worldwide Delivery of River Sediments to Oceans. Jour. Geology Vol. 91, pp. 1-21. Morgan, R.P.C. (1979) Soil Erosion. Longman Group Ltd., London. Morgan, R.P.C., Quinton, J.N. and Rikson, R.J. (1990) Structure of Soil Erosion Prediction Model for the European Community. International Symposium on Water Erosion, Sedimentation and Resource Conservation - CSWCRTI, Dehradun, Oct., pp. 49-59. Mutchler, C.K. (1971) Splash Production by Water Drop Impact. Water Resources Research, Vol. 7. Mutchler, C.K. and Young, R.A. (1975) Soil Detachment by Raindrops. Proc. of the Sediment Yield Workshop, USDA, Oxford (Mississippi), U.S.A., ARS-S-40, pp. 113-117. Negev, M. (1969) A Sediment Model on Digital Computer. Stanford University, U.S.A., Civil Engg. Deptt., Tech. Rep. No. 76. Pechinov, D. (1959) Vodna Eroziya I To’rd Ottok. Priroda, Vol. 8, pp. 49-52. Piest R.F., Bradford, J.M. and Spomer, R.G. (1975) Mechanism of Erosion and Sediment Movement from Gullies. Proc. of the Sediment Yield Workshop. USDA, Oxford, Mississippi, ARS-S-40, pp. 162-176. Robinson, A.R. (1977) Relationship Between Soil Erosion and Sediment Delivery. Symposium on Erosion and Solid Matter Transport in Inland Waters, IASH, No. 122, July, pp. 159-167. Roehl, J.E. (1963) Sediment Source Areas, Delivery Areas and Influencing Morphological Factors. IASH Publication No. 59. 70 River Morphology Rose, C.W. (1960) Soil Detachment Caused by Rainfall. Soil Science, Vol. 89, pp. 28-35. Rose, C.W. (1988) Research Progress on Soil Erosion Processes and a Basis for Soil Conservation Practices. In Soil Erosion Research Methods (Ed. R. Lal. ) Soil and Water Conservation Society, Ankeny, Iowa, U.S.A., pp. 119-140. Schumm, S.A. (1963) Disparity Between Present Rates of Denudation and Orogeny. U.S. Geological Survey, Professional Pape 454-H, pp. 13 Schumm, S.A. (1977) The Fluvial System A Wiley Interscience Publication, John Wiley and Sons Inc. Sharma, T.C., Hines, W.G.S. and Dickinson, W.T. (1979) Input-Output Model for Runoff Sediment Yield Processes. J. of Hydrology, Vol. 40. Simons, D.B., Li, R.M. and Stevens, M.A. (1975) Development of Models for Predicting Water and Sediment Routing and Sediment Yield from Storms on Small Watersheds. CSU Report No. CER-74-75, DBS-RMLMAS-24. TCPSM (1969) Sediment Measurement Techniques: A Fluvial Sediment Task Force Committee on the Preparation of Sediment Manual Report, JHD, Proc. ASCE. Vol. 95, No. HY-5, September. Tiwari, A.K. 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(1969) Present Rate of Land Erosion. Nature, Vol. 224, pp. 851-852. C H A P T E R 4 Fluvial Morphology 4.1 GEOMORPHOLOGY AND FLUVIAL MORPHOLOGY The name geomorphology originates from the Greek terms geo meaning earth, morphe meaning form and logos meaning discourse. Hence, geomorphology is the science of the origin and evolution of topographic features caused by physical and chemical processes operating at or near the earth’s surface. The landforms may result or may be modified by denudational processes, depositional processes or a combination of the two. Denudational or degradational processes are sometimes called exogenous processes while the depositional processes are known as endogenous processes. Together they are known as geomorphic processes. Among the agents and processes which shape the configuration of earth’s surface, the important ones are: (i) Running water, (ii) Glaciers, (iii) Ground water, (iv) Waves and currents, (v) Wind, (vi) Weathering, (vii) Volcanism and (viii) Diastrophism. Running water is that part of rainfall or snows melt which flows on earth’s surface after infiltration requirement is satisfied; this is known as surface runoff. It collects in streams, which continually erode the land and deposit the material elsewhere. Landforms produced by glaciers are markedly different because glaciers move slowly and are capable of carrying large quantities of coarse material with them. Groundwater, while in contact with rocks, promotes solution and other types of chemical weathering. This leads to unique landforms, especially in the areas of rapidly soluble rocks, such as limestone. Waves beating against the shorelines of seas and large lakes modify shorelines by their erosive action and subsequent deposition of the eroded material elsewhere. In arid and semi-arid regions and in regions having abundant supply of loose sand, wind is an effective agent of erosion and deposition. Weathering action loosens the rocks and breaks them into smaller pieces, which can be transported by different agencies. Mechanical weathering produces angular hill-slopes whereas chemical weathering promotes smooth rounded slopes. Volcanic eruptions produce distinctive landforms such as volcanic cones and lava flows. A sudden change in land surface or part of it due to tensile or compressive forces is known as diastrophism. It can be seen that volcanism and diastrophism are endogenous processes. Since the word fluvial means produced by rivers, the term fluvial morphology can be defined as a science dealing with forms as those produced by river action. Fluvial morphology is of great interest to 72 River Morphology hydraulic engineers, geologists, geo-morphologists, geographers and environmental engineers, since many of the complex problems they have to deal with are due to the form of the streams created by the erosion, transportation and deposition of sediment carried by them. Even though several scientists have contributed to the development of the science of geomorphology, W.M. Davis in the early 20th century was primarily responsible for synthesising many of the earlier developments and presenting them in the form of a unified system for the study of landforms. Certain basic concepts developed by geo-morphologists are of significance to hydraulic engineers and these are discussed here in brief. 4.2 GEOMORPHIC CYCLE (OR CYCLE OF EROSION) The basic idea underlying the concept of geomorphic cycle or the cycle of erosion is that the topography of a stable region evolves through a continuous sequence of landforms having distinctive characteristics at successive stages of development. The process starts with the initial uplift of landmass through diastrophism. This initial uplift is tacitly assumed to take place without appreciable erosion. Since in most regions the current uplift rates are much greater than the denudation rates, the above assumption is a reasonable one. Later the cycle of erosion proceeds under prolonged tectonic stability producing various types of topography, which are characteristic of the various lengths of time for which the water has acted on it; the material is continually eroded from the land surface and deposited in the sea. The elevation of the land surface is thus gradually lowered and land surface flattened until after a very long time the whole surface is reduced to a gently sloping plain called peneplain. This is the end of the cycle and an upheaval will start a new cycle (Davis 1909, Lane 1955). Davis introduced the word peneplain to describe landscapes that have undergone long continued weathering and erosion in humid climate. In the geographical context the word plain connotes a surface of very low relief. Realising that the ultimate base level is the limit of sub-aerial erosion, which like a mathematical limit, may be approached asymptotically but never reached, Davis prefixed the word “plain” by the Latin word “pene” meaning almost. This peneplain is a surface of regional extent, resulting from long continued fluvial erosion. Another concept introduced by the geo-morphologists and which is useful in discussion of fluvial morphology in general and the cycle of erosion in particular is that of base level first formulated by Powell in 1875. In fact he wrote (Esterbrook 1969), “We may consider the level of sea to be a grand base level, below which the dry lands cannot be eroded; but we may also have, for local and temporary purposes, other base levels of erosion, which are the levels of the beds of the principal streams which carry away the products of erosion. The base level would in fact, be an imaginary surface inclining slightly in all parts towards the lower end of principal stream”. Powell’s definition of base level, thus includes three basic ideas; namely (i) The ultimate limit of sub-aerial erosion of the continent is the base level of the sea. (ii) Locally resistant rocks in the path of the stream, lakes in the stream path, or other obstacles can produce temporary base level. (iii) Tributaries may not erode below that of the main stream, and since mainstream will always have some slope, the base level need not always be a flat surface. Fluvial Morphology 73 Thus, sea level may be considered as a general, permanent base level which fluctuates from time to time but which remains normally within a range of a few metres. Local base levels such as rock outcrops and lakes are temporary; changes in base level cause changes in the mainstream, tributaries and subtributaries. The geomorphic cycle is subdivided into parts of unequal duration, each part being characterised by the degree and the variety of relief and by the rate of change, as well as by the amount of change that has been accomplished since the initiation of the cycle. The various stages in the geomorphic cycle are described in terms of age beginning with youth, which passes into maturity and then into old age. The topographic features of the first stage are spoken of as young or youthful, later ones as mature and those of the last stage as old, with further subdivisions when desirable such as, for example, early and late maturity. It may also be mentioned that each of these stages need not be of the same duration. Davis considered youth a relatively brief phase and thought old age involved a tremendously longer period of time than either of the two stages. It should also be noted that the blending of types of topographies is the rule rather than an exception. Thus in a region of general youthful characteristics, some streams and valleys may be mature. Similarly in mature plateaus there will be some youthful streams actively engaged in deepening their valleys. The span of time involved in a complete transformation of landscape may run into millions of years. Consequently during a period of scientific observation the changes in topography may be unnoticeable. Youthful Topography Youthful topography is characterised by comparatively few streams but usually they have high gradients. Drainage may be poor with lakes and swamps on the divides between the streams. Streams flow in deep walled canyons or V-shaped valleys; these will be shallow or deep depending on the height of the region above sea level. Usually streams are actively engaged in cutting their valleys deeper. Youthful topography also possesses rapids and falls. There will be general lack of development of flood plain except along trunk streams. Mature Topography When the region advances from youth to maturity in the cycle of erosion, the drainage is better developed with the number of streams increasing. The streams cut their valleys to lowermost levels, their tributaries are well established and lakes, swamps and rapids disappear. Meanders may exist. Since streams start eroding laterally, valleys are flat but the widths of the valley floors do not greatly exceed the width of the meander belt. If streams flow through homogenous rocks, tree-like drainage pattern known as dendritic pattern is developed during maturity of topography. In the regions of folded beds the drainage pattern is rectangular i.e. tributaries meet their main streams at right angles. Old Topography In old topography, all main streams have very flat slope and are meandering back and forth over their flood plains. Valleys are extremely broad and slope gently both laterally and longitudinally; valley widths are considerably greater than the widths of meander belts. Their velocities are low and transporting power for sediment very limited. The whole landscape is gently rolling. Occasionally erosional remnants stand above the general land surface. Lakes, swamps and marshes may be present but they are on flood plains and not in inter-stream tracts as in youth. The topography tends towards the 74 River Morphology ultimate form namely peneplain which is a large land area of low relief that has been reduced to nearly base level by the combined action of weathering and streams. As a rule, surfaces of peneplains are not flat but gently rolling with low hills standing island-like erosion remnants in the general surface of lands (Worcester 1948). Geomorphic cycle discussed above is for humid region. An arid region is deficient in rainfall and also in vegetation. The groundwater table is also low. As a result deep subsurface chemical weathering is light, but surface chemical weathering does take place. Strong winds that blow carry dust from wherever it is found. As a result of these differences, the landforms obtained in the youth, mature and old ages in arid region are different from those in humid region. Worcester (1948) has discussed these in detail. 4.3 REJUVENATION OF EROSION CYCLE Once initiated the erosion cycle does not always proceed to completion without interruption. Worldwide changes in sea level, tectonic uplifts of the earth’s crust and climatic changes are the three principal causes of rejuvenation. Changes in sea level are brought about by subsidence of portions of ocean basins. The lowering of base level will cause streams to cut into the valley and form incised channels whereas rise of sea levels will force streams to deposit their sediment load in channels and aggrade. Tectonic down warping or uplifting of land produces the same effects as lowering or rising of sea level. Changes in morphology due to change in climate are discussed in detail by Schumm (1969). Climatic changes affect the precipitation, which in turn affects the vegetation and surface runoff. The latter two, in turn, change the discharge in the stream, erosion pattern and sediment load. Thus climatic changes induce significant changes in drainage pattern and stream behaviour. In general, typical topography formed due to rejuvenation includes uplifted peneplains, incised meanders, stream terraces and hanging valleys. If rejuvenation takes place in this manner, the first erosion cycle remains incomplete and a new one starts. It may happen that before the new cycle completes, rejuvenation may be effected. It is, therefore, believed that partial erosion cycles may be more common than the complete ones. 4.4 CRITICISM OF GEOMORPHIC CYCLE For the purpose of exposition, Davis made several simplifying assumptions, which have become the target of critical comment (Rice 1977); one of the most important was the separation of uplift and erosion into two distinct episodes. He thereby envisaged initial uplift taking place without appreciable erosion and then erosion under prolonged tectonic stability. However, current rates of uplift so exceed those for denudation that it is clear erosion does not normally constitute a limit of continued surface elevation. It is also argued, as partly discussed under rejuvenation, that stability is unlikely to stay long enough to permit reduction of an upland area to peneplain because of persistent tectonic activity. It is thus argued that the only stage in the Davisian cycle not represented on the earth’s surface at the present day is the peneplain. It is also worth recalling that periodicity of major climatic oscillations during the Pleistocene epoch (see Sect. 4.6) seem to have been of the order of 105 years. On the basis of known denudation rates the length of time required for an erosion cycle to run its full course cannot be less than 106 years. This Fluvial Morphology 75 means that any area will almost certainly have experienced many climatic fluctuations in the course of a single cycle with consequent changes in erosional processes. Penck (Penck 1924, Bloom 1978) differed fundamentally from Davis. Even though he accepted the idea that landscapes could be reduced to the end forms of low relief, he maintained that these end forms never became the initial forms of new episode of dissection. According to him the uplift was not rapid and then zero as Davis supposed, but always began slowly, reached a maximum and then waned gradually to a stop. During the long stage of initial slow uplift, all prior forms were destroyed, and a new surface of low relief, adjusted to a balance between uplift and degradation developed. This initial surface of low relief was called Primärrumpf by Penck. He argued that the rate of crustal movement varies greatly from time to time. Hence according to him, depending on whether rate of uplift is equal to, less than or greater than down cutting, the slope profile will be straight, convex upwards or concave upwards. No erosional sequence of forms was allowed by Penck’s scheme, because each morphologic assemblage was related to certain tectonic condition. Penck also denied any climatic control of geomorphic processes other than glaciations, believing that tectonics alone determined landform assemblages. For many years, the ideas of Penck received little support from English speaking geomorphologists. However, these have attracted attention since then and found them thought provoking even though at times contradictory. King (1962) a geo-morphologist from South Africa, formulated his ideas in a predominantly semiarid region where very little geological deformation had taken place in recent times. King believes in the supremacy of cyclic erosion in the development of continental landscapes and argues that the chief defect of Davisian concept is the absence of parallel slope retreat. King’s concept of changes in valley slope is that the chief means of landscape change is the migration of valley side slopes away from the rivers without significant change of angle as shown in Fig. 4.1 (a). On the other hand, Davis concluded that during youthful stream incision, valley sides would be steep. Once rapid valley deepening has ceased, the slope processes almost solely influence the form leading to a gradual decline in the angle, (see Fig. 4.1 (b)). Stream incision Almost parallel slope receding a King Stream incision Slope reducing b Davis Fig. 4.1 Valley slope evolution according to King and Davis Both King and Davis argue that their models of landscape evolution could be adapted to a wide variety of climatic environment with only minor modifications. However, in 1909 Davis was convinced 76 River Morphology of the need to formulate a separate cycle for arid region because of (i) absence of the normal base level control in areas without perennial streams draining to the coast; (ii) increasing importance of wind action; and (iii) belief that a unique combination of the processes might lead to slope retreat without angular decline. Since then many writers such as Peltier have proposed variety of the original Davisian cycle, believed to be more appropriate to specific climatic zones. It is shown that climatic zone in which the cycle of erosion has been deemed to be significantly different from those outlined by Davis and King is the humid tropics, where chemical weathering significantly affects the development of landforms. Another climatic zone for which a distinctive cycle of erosion has been proposed is peri-glacial. 4.5 NON-CYCLIC CONCEPT OF LANDSCAPE EVOLUTION Reactions against the limitations of the Davisian cycle of erosion have led to reassessments more radical than those discussed so far. Hack (1960) views landscape as the product of competition between the resistance of crustal materials to erosion and the forces of denudation. He argues that the orderliness of stream organization first discerned by Horton (1945) will naturally lead to regularity in the overall pattern of relief. Within a single climatic region where stream and slope profiles are both controlled by the nature of bedrock, similar geologic conditions should produce similar topography. Thus Hack put forward the concept of non-cyclic approach in the form of dynamic equilibrium. He does not probably question the existence of a very long period of land form evolution, but argues that its details are now lost beyond reconstruction; hence he is more concerned about the relationship between form and processes and adopts an attitude of ignorance towards land form history. Thus, Hacks’s argument implies that landforms adapt easily to changing environmental controls; however if this logic were stretched too far it would preclude, for instance, the identification of formerly glaciated areas. It may be mentioned (Craig 1982) that during the past the geo-morphologists have developed mathematical models for slope erosion. Three models can be mentioned in this respect. The first is ¶Z ¶Z =–b ¶t ¶x ...(4.1) where Z is the elevation, t is the time, x is the distance from the divide and b is a positive constant called recession coefficient. Thus the rate of denudation is proportional to the slope. Where the denudation is proportional to convex curvature, the equation used is ¶Z ¶2 Z =a ¶t ¶x 2 ...(4.2) where a is called debris diffusion coefficient. These two equations have been brought together by Hirano (see Craig 1982) in a form, which describes the combined effects of weathering (Eq. 4.1) and creep (Eq. 4.2). The equation is ¶2 Z ¶Z ¶Z =a +b 2 ¶t ¶x ¶x ...(4.3) There is considerable difficulty in determining which equation should be used for a particular situation and hence only a few areas are subjected to this type of analysis. Fluvial Morphology 77 Hence, in spite of all the limitations of Davisian erosion cycle, it is still considered as the best because no other viable alternative meeting all the objections to Davisian cycle is available. 4.6 GEOLOGICAL TIME SCALE Historical or stratigraphical geology is mainly concerned with the description and classification of rocks with a view to arranging them in chronological order in which they were laid down on the surface of the earth. Of the three groups of rocks – sedimentary, igneous and metamorphic – only the sedimentary rocks are amenable to such an arrangement since they have been deposited layer by layer and contain the remains of organisms which flourished while they were formed. The time scales used by the hydraulic engineer and the geologist are quite different. The hydraulic engineer uses seconds or days as the unit of time when dealing with transport rates of water or sediment. When he is dealing with the morphological changes such as aggradation or degradation of the riverbed he is concerned with bed level changes occurring in a few years or a few decades at the most. As against this in stratigraphy the unit time used is million years. Thus Lord Kelvin (Rice 1977) assumed that earth started as a molten body, and applying the theory of cooling to this mass he estimated that to attain the present day temperature the earth must have taken 20 to 40 million years. For arranging the various geologic formations in the order of increasing antiquity, the geologist uses various means at his disposal. The first is the fundamental principle of superposition in which the upper beds in an un-inverted succession are dated as younger than the lower ones. The second means is the palaentological dating depending on the fossil content of the formation. Each formation encloses a fossil assemblage, which is characteristic and different from that of the underlying or over lying formations. The animal and vegetable organisms of each geological age bear special characters not found in those of other ages. It needs to be emphasised that the fossils present in a series of formations are not only a function of the period when the formation was laid down but are also a function of (i) the geological period when rocks were formed; (ii) the zoological or botanical provinces in which the locality was situated; and (iii) the physical conditions prevalent at the time, e.g. depth, salinity, muddiness of water, temperature, character of sea bottom and currents. The geological formations are named in such a manner that they indicate the stage of development of the organisms. Thus the Azoic era is completely devoid of organisms, while Proterozoic era shows traces of the most primitive life. The Palaeozoic era contains the remains of ancient plants and animals, and so on to the recent time. The third means used for determining the age of formation is the lithology. Each lithology unit may comprise a number of individual beds having more or less the same characters, when it is spoken of as a formation, and given a local or specific name to distinguish it from a similar formation of different age or belonging to a different area. Lithology is many times useful in the determination of chronology. With the discovery of radioactive elements uranium and thorium at the end of 19th and beginning of 20th century a more powerful means was available for determining the chronology of rocks and other formations. It was found that uranium and thorium emit alpha and beta radiations; alpha radiation consists of positively charged helium nuclei with two positive charges while beta radiation consists of negatively charged electrons. Depending on the nature of radioactive elements half the atoms of the element will disintegrate in this manner in a period known as half-life of the element concerned. As a result of such emission of alpha and beta radiation a new element or daughter element is formed. If the quantity of the parent element to the daughter element is known at any time, the period during which the 78 River Morphology radioactive decay has taken place can be calculated. Uranium and thorium, as a result of radioactive decay are finally converted to lead Pb206, Pb207, or Pb208 isotopes. The isotopic analysis of the minerals is carried out using the technique of mass spectroscopy. Using radioactive dating techniques, it is estimated that the age of crustal material of the earth is about 4,500 million years while the age of lunar rock ranges from 3,000 to 4,500 million years. Table 4.1 gives the era, group, system or formation or rocks, and the chief fossils found in these formations. Even though geologists are interested in all the eras from Quaternary to Azoic or Archaen, geo-morphologists consider Quaternary and Tertiary periods as of primary significance to them; this is so because it is believed that the majority of landforms are about a million years old, and the remaining not more than 20 to 30 million years old. Hence, from the geo-morphologist’s point of view it becomes crucial that the dating between Quaternary and Tertiary periods is done carefully. This aspect has been discussed in detail by Rice (1977) and the following discussion is based on his comments. The dating of Cenozoic era has become complicated because of various reasons. Earlier stratigraphic column was constructed on the basis of marine sediments and faunas raised above the modern sea level. Such continuous marine successions are rare in the late Cenozoic age, and the contemporary terrestrial beds tend to be fragmentary, of short duration and local. The second difficulty arises because of the relatively brief duration of Cenozoic era because of which the biological evolution during this period was not adequate to delimit the era. Then there were at least eight or probably even more environmental changes during this period, which have complicated building up of the chronological sequence. Lastly, as regards methods of estimating the age of the formation, K/Ar dating is most suitable for Cenozoic era; however because of the very small amount of Ar present in the formations the accuracy of the method is doubtful. Sufficient light has been thrown on the chronology of Cenozoic era by obtaining cores of materials deposited on the beds of deep seas. These deposits contain fossils of marine organisms such as foraminiferal, globorotalia menardii and diatoms in large numbers. Since these organisms have different environmental requirements, their fossils give information on the changing temperature of seawater. The change in the ratio O18/O16 of the isotopes of oxygen in the shells also indicates the temperature changes. Shells formed in the cold climate are relatively richer in O18. Such evidences have helped in fixing the chronology of later Cenozoic era. Some investigators argue that the most distinctive characteristic of Pleistocene epoch is the development of large continental ice sheets in Europe and North America. Hence the beginning of Pleistocene should be equated with dramatic fall in temperature. However, glaciation in different parts of the world leads to a very large variation in the onset of Pleistocene. Therefore many argue that it is unwise to relate glaciation to Pleistocene. Similar uncertainty prevails in fixing the Pleistocene–Holocene boundary. The term Holocene was originally intended to designate the post glaciation period. However, the melting of ice sheets being transgressive of time, the post glaciation period in one region could be glaciation period in another region. Therefore, this criterion was difficult to use. Hence the boundary between Pleistocene and Holocene is fixed arbitrarily. The most accepted boundary is that first proposed by Scandinavian workers using pollen analysis. Using this technique the period of rapid warming indicating the onset of Holocene has been fixed at about 10,000 years ago. It is necessary to emphasize that during the Pleistocene era some areas were covered by ice sheets while some were not. In glaciated areas the attention was focussed on till sheets laid down one over the Fluvial Morphology 79 Table 4.1 Geological time scale [Adapted from Wadia (1961), and Krishnan (1982)] Era Period Epoch Duration M years Cenozoic Quaternary Holocene (present) Pleistocene (Glacial) Pliocene Miocene Oligocene Eocene Cretaceons 0.01 1 7 17 13 27 75 Years before present M years (Ma) 0.01 1 8 25 38 65 140 Chief fossils Living animals Man appears; many animals dies off during glaciation Mamals, mollusca, and flowering plants dominate. Divisian largely based on proportion of living to extinct species of mollusca and the presence of mammal species Giant reptiles and ammonites disappear at the end. Flowering plants become numerous Ammonites abundant. First birds, flowering plants and sea urchins Ammonites, reptiles, amphibia abundant. Arid climate Trilobites disappear at the end Many non-flowering plants, first reptiles appear Abundance of corals, branchiopoda, first amphibious and lung-fishes Graptolites disappear at the end; first fishes; probably first land plants Abundance of trilobites and graptolites Abundance of trilobites Soft bodied animals and plants Lifeless Tertiary Mesozoic Secondary Jurassic 60 200 Triassic Permian Carboni-ferous Devonian Silurian Palaezoic Primary Ordovician Cambrion 40 50 60 60 240 290 350 410 35 60 100 445 505 605 2500 3600 Proterozoic Azoic Precambrian Archaen Precambrian Archaen other as a result of multiple glacial advances. Equal attention was given to the pollen analysis of biogenic materials entrapped within the tills. Similarly a thorough study was made of non-marine molluscs and beetles. However, it has been found that the record of terrestrial sediments in glaciated regions is small and is confined to the later part of Pleistocene era. In the unglaciated regions, at a limited number of places pollen analysis has been used. Some deep core samples have also been obtained from the desert areas where earlier lakes existed. Another technique used to determine the chronology of continental land surfaces in Pleistocene era is the carbon C14 dating which is very useful for dating of Pleistocene and Holocene eras because of short half-life of 5730 years of C14. This method depends on the fact that the atmosphere and the hydrosphere represent reservoirs of radioactive carbon C14, which are tapped by animals and plants to build up their structures and tissues. The source of radioactive carbon lies in the cosmic ray bombardment of nitrogen in the atmosphere, which converts it into C14. Carbon has three isotopes C12, C13 and C14 and it is present in the atmosphere 80 River Morphology in the form of CO2. Out of the three isotopes C14 is the only unstable isotope with half-life of 5730 years. In historical times a balance was reached between new C14 received from cosmic radiation and that disintegrated due to radioactive decay. Since living organisms absorb CO2, each organism absorbs a fixed proportion of C14 of the total carbon absorbed during the lifetime. After the death of the living organism, the replenishment of C14 ceases and C14 content declines due to radioactive decay. The ratio of radioactive to the total carbon present at any time is, therefore, a measure of the age of the organic materials such as bones, tusks, grains, wood, hide, peat etc. The method is suitable for dating up to 50,000 years. 4.7 GLACIATION Glacier is a slow moving mass of ice formed by accumulation of snow in mountain valleys and other places. Area of the continents that is covered by ice at present is close to 15 M km2, the largest part of which is concentrated in Antarctica (12.5 M km2) and in Greenland (1.7 M km2). Glaciers today, except at high altitudes and in high latitudes, are of minor importance in shaping landforms; but those that existed during the Pleistocene epoch have left their imprints on many millions of square kilometres of the earth’s surface. About 10 M km2 of the North America, 5 M km2 of Europe, 4 M km2 of Siberia and large parts of the Himalayas were glaciated. Pleistocene epoch consisted of four major glacial ages separated by interglacial ages of probably far greater duration than the glacial ones. The latest glaciation has left the most obvious imprints on the topography. Glaciers are classified into ice caps, valley glaciers, ice-streams and glacier ice. Glaciers that are continuous sheets of snow from which ice may move in all directions are known as ice caps. Glaciers that are confined to courses, which direct their movement, are called valley-glaciers and ice-streams. Glacier, which spreads in cake-like sheets over level ground at the base of glaciated areas, is known as glacier ice. Glaciation in India (Wadia 1961, Krishnan 1982) Majority of the present Himalayan glaciers are three to five km in lengths, however there are some giant glaciers of forty km or more in length such as the Milam and Gangotri glaciers of Kumon and Zemu glacier draining Kanchanjunga group of peaks in Sikkim. The latest glaciers of the Indian subcontinent are those of Karakoram discharging into the Indus river; these are Hispar and Batura of the Hunza valley, and Biafo and Baltora of the Shigar, a tributary of the Indus. These are about 50 km in length and 130 to 330 m in thickness. These are the latest survivors of the last Ice Age of the Himalayas. Presence of terminal moraines covered, many times by grass, seen in Pir Panjal moraines at the snouts of existing glaciers at low level hills of Punjab lead to the conclusion that at least this part of India experienced glacial age in Pleistocene epoch. Parts of India lying to the south of Himalayas experienced cold pluvial epochs during this period. The evidence leading to this conclusion is derived from the fauna and flora of the hills and mountains in India and Sri Lanka. According to Wadia (1961) indications of extensive glaciation in the immediate past and in the present glaciers are: (i) presence of enormous heaps of terminal moraine covered by grass and trees; (ii) presence of ice transported blocks; and (iii) smoothed or striated hummocky rock surfaces. According to geologists the Kashmir area of the Himalayas underwent four distinct glaciations separated by the interglacial warm periods; the last of the glaciations occurred about ten to twenty thousand years back. Fluvial Morphology 81 Glacial Movement and Erosion Glaciers move slowly showing erratic and sudden advances of their fronts. Glaciers reduce in size by the combined action of melting and evaporation/sublimation, a process known as ablation. Glaciers may also get nourishment and thus increase in size. Depending on whether a glacier gets nourishment or not the glacier is called an active or inactive glacier. Active glacier will have an advancing front whereas an inactive glacier will have a receding front. Abundant striations, polished and grooved rock surfaces give evidence of effective glacial erosion. The bottom topography of bedrock floor may show irregularity and over deepening which cannot possibly be explained by any other way than to assume that they are due to local glacial scouring. One of the simplest ways of assessing the rate of erosion due to glaciers is by the measurement of sediment being carried by melt water issuing from glacier snout. On the basis of observations by Reid, Thorarinson and Corbel from Muir, Hoffellsjokul and St. Sorlin glaciers respectively, Rice (1977) suggests that the mean erosion rate by active glacier lies in the range of 1 to 5 mm/year which is seen to be much higher than most of the figures for stream erosion. Glacial erosion includes two processes, namely plucking and abrasion. Plucking occurs when moving ice freezes on to the bed rock and pulls out blocks which are then carried away. Abrasion is due to grinding effect. Grooves formed on the bottom can be 2 m deep and 100 m long, even though grooves up to 30 m deep and ten km long have also been observed. Large blocks of un-weathered rock found in both glacial and fluvio-glacial deposits are mainly due to plucking. Erosional and Depositional Landforms Ice streams flowing in high mountainous areas have modified their valleys to such a great extent that their forms are distinctly different from the valleys caused by fluvial erosion. Some of the most important erosional landforms produced by glacial erosion are cirques, glacial troughs and hanging valleys. CIRQUES: Cirque is a French word-meaning amphitheatre like basin, not completely enclosed. It is the most distinctive, common landform caused by glacial erosion in mountain high lands. It is a steep sided semi-circular basin found at valley heads; but it may not Head connect in its downstream part with a valley. The name is applied wall Threshold to shallow basins which mark the steps of snow banks which Basin never grow into glaciers. A typical cirque consists of a steep head wall on the upstream side, followed by a deep basin and then a Fig. 4.2 Cirque gradually sloping up surface known as threshold, see Fig. 4.2. The longitudinal profile of cirques approximately follows the equation of the form y = (1 – x) e – x and is almost independent of rock type. Conditions which favour maximum cirque development are: (i) rather wide spacing of prelacies valleys so as to permit expansion without intersection of adjacent cirques at an early stage; (ii) adequate snowfall which can form large snow fields and glaciers, but not heavy enough to form ice-caps; and (iii) fairly homogenous rocks which permit cirque extension equally well in any direction. GLACIAL TROUGHS: Next in importance to cirques is the most distinctive topographic feature in glaciated mountains, namely glacial trough. It is the valley, which is modified, in its cross-sectional shape and the longitudinal profile due to glaciers. Most glacial troughs were originally stream cut 82 River Morphology valleys. Glacial trough heads at the lower edge of the cirque threshold; however, there is a drop from cirque threshold to the floor of glacial trough. The longitudinal profile of the glacial trough is irregular and ungraded; the profiles are seldom smooth and concave upward type. Instead, they have a series of glacial steps, which are more pronounced in the upper reaches than in the lower. Glacial steps have been attributed to differential glacial abrasion in contracting and expanding sections of the valley, effect of varying rock hardness and to preglacial irregularities. Presence of jointed rocks can also lead to glacial steps. The cross-sectional profile of a glacial trough is significantly different from that of an unglaciated valley in mountainous area. While many glacial troughs are U-shaped, stream formed valleys in mountains are usually V-shaped. Davis has suggested that the cross profile of a glacial trough follows a catenary curve. The difference in the cross profiles of glacial troughs are often related to the difference in the thickness of glacier, valley lithology, structure of rocks in which the trough is cut, and the number of times the valley is glaciated. Some portion of the glacial troughs may exhibit flat floors, which are attributed to the deposition subsequent to the trough development. The material deposited may be due to aggradation caused by deposition of outwash material by glacial recession or post-glacial alluvial deposit. HANGING VALLEYS: The tributaries usually join the river valley accordantly i.e., there is no difference in bed elevation of the main river valley and that of the tributary. However, glacial troughs often have tributary troughs or valleys joining the main trough discordantly, producing elevation drops at the junction. This is known as the hanging valley. Some valleys in Kashmir and in Sikkim exhibit hanging valleys of this type (see Wadia 1961, Krishnan 1982). However, it may be emphasised that hanging valleys cannot be interpreted as evidence of past glaciation because they can be formed due to reasons other than glaciation; for example a hanging valley can be formed if the main stream is degrading rapidly and the tributary is intermittent. Glacial deposits are usually heterogeneous and lack stratification. These deposits are of three types, namely end moraine, lateral moraine, and ground moraine, depending on whether the deposition took place at the end of, at the side of, or beneath an ice stream. Only some glaciers build end moraine; this depends on whether the ice front maintains itself in one position for a sufficiently long time. Then if the ice-fed stream emerging from the glacier is capable of transporting the end moraine, it wouldn’t deposit. Lateral moraines form along the sides of an ice stream mainly from the materials, which are contributed from the valley sides above the glacier by weathering and mass movement. Lateral moraines are usually patchy and may or may not be found on both sides. Ground moraine is more closely associated with ice caps than with ice streams. The streams flowing on, within or beneath the glacier deposit the material eroded and transported by the glaciers and ice streams. This material is known as glacio-fluviatile. The most common landforms in this material are valley trains, eskars, kame terraces, and outwash fans or deltas. These are described by Thornbury (1969). 4.8 FLUVIAL MORPHOLOGY Fluvial morphology deals with streams and stream systems as produced by the action of flowing water. The features produced on the land surface by flowing water can be aptly called fluvial landscapes. As the erosion cycle proceeds the morphology of streams also changes and the streams pass through the three stages of development as the earth’s surface namely youth, maturity and old age. Although the Fluvial Morphology 83 stage reached by the stream usually corresponds to that of the surrounding topography, this is not necessarily the case. Usually the stream is less youthful in character near its mouth than in the vicinity of its head waters (Hack 1960). If one considers a newly uplifted land mass as the starting point and traces the successive changes, which occur with time, the first stage of the stream will be youth. Here streams have relatively steep slopes and they are engaged in cutting their channels downwards. Lateral erosion and valley widening is extremely small. The cross section of the stream will be V-shaped with no or little flood plain. A youthful valley is shown in Fig. 4.3. Streams in youth may not have cut down enough resistant rock mass to attain a gradual profile; hence rapids and falls may exist along its course because sufficient time has not passed, since they were uplifted, for the stream to cut down and eliminate them. There are frequent changes in the slope of the stream caused by the differences in hardness of the strata over which they flow. Johnson (1932) suggests that early youth ends when lakes are eliminated and middle youth ends when falls and rapids are eliminated. Fig. 4.3 Youthful valley Late youth ends and early maturity starts when the rate of down cutting decreases and the rate of lateral erosion increases; establishment of grade also marks the passage from youth to maturity. Early maturity ends and late maturity begins when the valley width equals the width of the belt covered by the meanders of the stream. V-shaped valleys and rapids and waterfalls disappear which are characteristic of youthful age of stream. Figure 4.4 shows a mature valley. In the old stage there is pronounced meandering activity as a result of which width of flood plain exceeds several times the width of the meander belt. Oxbow lakes and swamps are usually present as a result of cut-offs developed naturally. Natural levees, which form banks confining stream channels, may be built up until the channel is some metres above the general level of the flood plain. Typical old stage is shown in Fig. 4.5. 84 Meander belt = Valley – floor width River Morphology Youth Mature Old Fig. 4.4 Cross-valley profiles for various stages of stream Fig. 4.5 Old-age stream It sometimes happens that during the cycle of erosion certain changes occur which cause streams to incise their channels with greater vigour. This renewed down cutting is known as rejuvenation. Three principles causes for rejuvenation are: (i) World wide changes in seal level, (ii)Tectonic changes and (iii) Climatic changes. Equilibrium in Natural Streams Geo-morphologists as well as engineers have used the concept of equilibrium in streams. A stream in equilibrium is called a graded stream or a poised stream. Mackin (1948) has given the following definition of a graded stream: “A graded stream is one in which, over a period of years, slope is delicately adjusted to provide, with available discharge and with prevailing channel characteristics, just the velocity required for the transportation of load supplied from the drainage basin. The graded stream is a system in equilibrium; its diagnostic characteristic is that any change in any of the controlling factors will cause a displacement of the equilibrium in a direction that will tend to absorb the effect of the change”. Fluvial Morphology 85 Thus, the four variables related to the concept of a graded stream are slope, discharge, channel characteristics and sediment load. In a natural stream, the discharge is continuously changing due to precipitation, infiltration, evaporation and withdrawals. Although stream tends to pick up sediment or deposit it until load equals capacity, because of rapid variations in flow it cannot do so. Hence, in very short times the stream cannot be in equilibrium. Similarly, since the tendency of the streams is to lower the land surface to the sea level, over very long periods the stream cannot be in equilibrium. Thus, neither in very short not very long periods can a natural stream be considered to be in true equilibrium (Lane 1955). Yet, for all practical engineering purposes, most of the alluvial streams are in equilibrium over periods of the order of a few decades. In such streams, the bed may go down during high flows and fill back during low flows; yet the net amount of change is not sufficiently large to be detected by quantitative measurements. Most of the alluvial streams which are not affected by human interferences can be said to be graded or in equilibrium. Construction of dams, withdrawal or addition of clear water, addition of sediment load, contraction of stream and cutting off the bends are some the ways in which the equilibrium of the stream is disturbed by human activities. Characteristics of Graded Streams To get better appreciation of the stream morphology the characteristics of graded streams are briefly enumerated here. Firstly the slope of a graded stream, in general, decreases in the downstream direction yielding a concave profile. Secondly, partly as a consequence of decreasing slope in the downstream direction, the stream drops the coarser material that it cannot transport, a phenomenon known as sorting; and partly due to abrasion, the bed material of an alluvial stream becomes finer in the downstream direction. Thirdly in humid regions as more and more tributaries join the main stream; the discharge increases in the downstream direction. However, if the stream passes through arid region, the discharge can actually decrease in downstream direction as in the case of the Euphrates in Iraq. This is primarily due to seepage and evaporation. In addition, the upper part of the drainage basin is the main source of sediment even though the runoff from this part of the catchments may be small. The runoff from the rest of the basin is large but it carries relatively less sediment. This leads to decrease in the average concentration of sediment in the downstream direction necessitating a smaller slope. Lastly, because of finer material, streams usually have relatively narrow channels i.e. larger width to depth ratio, in the downstream direction. As a result the stream has greater hydraulic efficiency and flows with a smaller slope. A graded stream may show aggradational tendency, albeit temporary, under the following conditions (Cotton 1941): 1. If dissection of upland region is in progress and a vast number of smaller new valleys and ravines come into existence in the stage of youth. To carry relatively higher load stream may increase slope by aggradation. 2. If the river after it is graded flows in a wider channel than it has hitherto had in youth, loss of depth in the stream may rebuilt in a reduction of velocity and transporting power that it needs steeper slope to carry the load. 3. As a river develops increasingly large curves by lateral corrasion, its length increases and slope decreases and hence carrying power decreases resulting in aggradation. 4. Decrease in water volume due to infiltration, evaporation or withdrawal can cause increase in slope due to aggradation. 86 River Morphology Variation of Sediment Size It is important for a river morphologist to know how the sediment characteristics change along the stream. The most important characteristic of sediment is its median size. It is found that in most of the streams there is reduction in size of sediment due to wearing or abrasion, fragmentation, weathering, dissolution and hydraulic sorting. Hydraulic sorting takes place in a stream because the sediment transport ability of the stream reduces in the downstream direction. It is difficult to know the relative importance of these processes in the reduction of sediment size. Hence, it is easier to model the reduction in size by assuming that, as done by Sternberg in 1875 (Rohan 1967), the reduction in weight of the particle dW is proportional to its weight W and the distance travelled dL. Hence dW = – CW dL ...(4.4) where C is the constant of proportionality. Integration of this equation with the initial condition W = Wo when L = 0 yields W = Wo e – CL Further since for spherical particle W ~ d and Wo ~ do , one gets d3 = do3 e – CL or a1 = d = do e– a1L ...(4.6) 3 3 ...(4.5) c is known as the abrasion coefficient. Here d is the sediment size. This equation known as 3 Sternberg’s law is found to be valid on the Rhine in Germany. In Japan it is found to be valid for sediments coarser than 4.0 mm in size. Shulits (1941) has stated that a1 ~ (particle velocity)1/4. Values of a1 are found to vary between 0.006 km –1 and 0.11 km –1; however, it is not possible to predict its value at present. If dW is assumed to be proportional to surface area of the particle and dL, and one uses the initial condition W = Wo when L = 0, the following equation is obtained from Eq. (4.4). F W = GW H 1 3 o c - 1L 3 I JK 3 ...(4.7) Lastly another formula known as Schaffernak’s formula (see Rohan 1967) is also some times used in describing the reduction in sediment size. This formula is d L = 1 – C2 do do ...(4.8) where as C and C1 are having dimensions, C2 is dimensionless. Typical values of C2 for some reaches of the Rhine, Danube and Mur vary from 4 ´ 10 –8 to 45 ´ 10 –8. It may be mentioned that the sediment size varies very slowly with L and hence with proper choice of C, C1, or C2 any of the three equations can be fitted to a given set of data. As regards the size distribution, it may be mentioned that while sandy materials are unimodal, gravely material is usually bimodal. Analysis of data of sandy and gravel-bed rivers by Garde (1972) has Fluvial Morphology 87 shown that over the entire range the sample does not follow log-normal distribution; however between d15.9 and d84.1 sizes it can be assumed to do so. The geometric standard deviation sg = is related to the median size d50 by the relation 0 .34 sg = 2.4 d50 d 1 d84.1 + 50 d15. 9 2 d50 F GH I JK ...(4.9) for 0.20 mm < d50 < 20 mm. Here d50 is in mm. Classification of Streams For systematic discussion about streams, it is advantageous to classify them; classification of streams enables one to make generalization about a group of streams having similar attributes. As can be seen below this classification is done using objective, qualitative or quantitative criteria. According to Rosgen (1996) such classification often helps in (i) prediction of river behaviour from its appearance; (ii) development of specific hydraulic and sediment transport relations for a given stream type, (iv) extrapolating site specific data to stream reaches having similar characteristics; and (v) providing a frame of reference for communicating about stream morphology among different disciplines. As discussed earlier Davis (1899) divided the streams into youthful, mature and old, depending on their stage of development in the cycle of erosion. This classification gives only qualitative attributes of each type. Davis (1890) also distinguished between consequent streams following the natural slope of land surface; subsequent streams flowing into consequent streams from the sides at right angles to the dip and parallel to the strike; resequent streams as tributaries to subsequent ones more or less parallel to consequent main streams; obsequent streams flowing against the dip of the beds; and insequent streams, which show no apparent relation to the dip of the beds. These are shown in Fig. 4.6 and discussed in detail by Worcester (1948). However, the classifications of Davis do not take into account the main hydraulic variables on which stream size, shape and plan form depend. Depending on the variation flow in the stream with time, L streams can be classified into three categories. Perennial or C B O permanent streams are those, which flow throughout the year. These get their water from lakes, snow banks or glaciers, or land C - consequent, S - subsequent, from direct precipitation, and which maintain regular flow. Those R - resequent, O - obsequent, I - insequent stream perennial streams, which have cut deep into sediment or other L - original land surface strata, may receive ground water flow also. Intermittent streams Fig. 4.6 Relation of drainage to are those whose sources of water fail intermittently. They occur topography and geological structure mainly in regions of seasonal rainfall or snowfall, and particularly (Davis 1890) common to semi-arid regions. Ephemeral streams flow only in response to precipitation; they are not fed by springs or by slowly melting snow. As discussed in Chapter II, Horton, Strahler and others have developed a system of ordering channels in a drainage network; channels of the same order show similar characteristics, as shown by Rznystin (1960). Plan-form or channel patterns can be defined as the traces of the channel in plan as obtained from air-photos or as presented on the map. Plan-forms of alluvial streams are of importance to hydraulic S 88 River Morphology engineers as well as to geo-morphologists and sedimentologists. For the hydraulic engineer not only the plan-forms but also their spatial and temporal variation is important to decide the location of bridges, barrages, levees and other structures. For the geo-morphologist they are an indication of modern river behaviour; plan-forms also throw light on the past morphology of the stream. A sedimentologist studies plan-forms and the associated sedimentary deposits in order to develop knowledge about old streams. Lane (1957) analysed data from sand-bed rivers and rivers flowing through coarser material from USA and other countries and broadly classified the streams according to plan-forms into straight, meandering and braiding patterns. He further indicated that plan-forms are essentially a function of slope and bankful discharge. Leopold and Wolman (1957) followed the same classification as that of Lane. Planforms can be classified depending on whether the stream flows in a single channel or in multi-channels. Streams flowing in a single channel can be straight or meandering. However, in nature, streams do not flow straight for more than 10 to 20 channel widths and even in straight channels the talweg shows a meandering pattern. Plan-form classification is shown in Fig. 4.7. Plan form of streams Single channel streams Multi channel streams Straight Meandering Anabranching Reticulate Deltaic Braided Incised meanders Meanders in flood plains Migrating downstream Classification according to movement Free (Lateral migration) Inactive Irregular Regular Simple Compound Underfit Overfit Classification according to valley width Classification according to shape Irregular Regular Simple (sine, parabolic, circular, etc.) Compound Fig. 4.7 Classification of plan-forms Fluvial Morphology 89 The meanders can be either incised or in plain and can take various shapes in plan. Meandering streams can be further classified depending on whether the meanders move downstream, laterally or are stationary. Chitale (1970) classified meanders into regular and flat, irregular and flat, regular and acute, irregular and acute, simple, and compound meanders (see Fig. 4.8 (a) and Fig. 4.8 (c)). He also stated that a particular stream might have a single channel in one reach and multiple channels in other reach, a fact noticed on many streams. The multi-channel streams are classified into braided, deltaic, reticulate and ana branching. These are schematically shown in Fig. 4.8(b). 0 Talweg 100 m 150 m 150 790 m Straight reach of valley creek, Pa (U.S.A.) Meander length ML Meander belt MB b Point bar MW Width Definition sketch for meandering stream Compound meanders Buyuk meanders river (Turkey) Incised meanders (irregular) Fig. 4.8(a) Plan-forms of rivers It is appropriate to describe two other forms of streams based on the relative width of meander and the valley. A mis-fit stream (Dury 1969) is defined as one, which occupies a valley formed by a stream of considerably larger or smaller discharge. An under-fit stream occupies the valley the valley formed by a stream of greater discharge. Most of the streams, which are under-fit, now have had their channel forming discharge reduced due to climatic changes. An over-fit stream occupies a valley formed by 90 River Morphology Free meanders oxbow lakes and meander scars Pembina river near Monola (Canada) High land Darling river High land Braided stream Anabranching pattern of Darling river (Australia) Reticulate pattern Diamantina river (Australia) S S L L R Deltaic pattern S L L S Valley meander scar L Valley meander lobe R Stream Under-fit meandering stream Osage-type Fig. 4.8(b) Plan-forms of rivers much smaller discharge; however an over-fit stream will usually remove all signs of small stream channel and widen its valley to conform to its present flow. Therefore, over-fit stream is a transient stage and is rarely found. Dury (1969) has discussed about another type of under-fit stream, called Osage type, which is named after the Osage river in Missouri (USA). This type of stream lacks meanders; however, it has pool and riffle sequence spaced at an interval of five channel widths. It behaves as if it were straight; however it does not reflect the curves of the valley. The apparent width to depth ratio of streams of Osage type is about forty, larger than ten as observed on meandering rivers; but actually in an underfit stream of Osage type it is the wave length of the former stream and width of the shrunken present day stream. These types of plan-forms are shown in Fig. 4.8 (c). Fluvial Morphology 91 Regular and flat meanders Irregular and flat meanders Regular and acute meanders Irregular and acute meanders Simple meanders Compound meanders Regular and flat meanders in Mahi river (Gujrat) India Irregular and flat meanders in Ken river (U.P.) India Regular and sharp meanders in Mississippi river Irregular and sharp meanders in Sai River (U.P.) India Compound meanders in Rind river (U.P.) India Fig. 4.8(c) Meander classification according to Chitale (1970) Schumm (1968, 1977) has classified stream channels flowing through sandy materials, based on the mode of sediment transport (i.e., predominantly suspended load, mixed suspended load, and predominantly bed-load), percent of silt-clay in the perimeter of the channel, and channel stability (graded, depositing i.e. excess sediment load, and eroding i.e., with sediment load deficiency). This is given in Table 4.2. It may be mentioned that Blench (1955), and Simons and Albertson (1963) have also recognized the importance of bed and bank material in shaping the geometry of stable channels. Allen (1965) has diagrammatically represented Schumm’s ideas in terms of size and sinuosity, which is shown in Fig. 4.9. Kellerhals et al. (1972, 1976) have given a further refinement in the classification of river channels, which is primarily based on the interpretation of air photos and detailed survey of Canadian rivers. The detailed data needed for classification include: (i) whether the stream is aggrading, degrading, partly entrenched, or entrenched with no flood plains, (ii) channel plan-form description, namely straight, sinuous (MB < 2 W), irregular or regular meanders, or tortuous meanders (q between channel axis and valley trend greater than 90 o), (iii) presence of islands and basis; and (iv) lateral activity namely meanders moving downstream, downstream progression and cut-offs, entrenched loop development, avulsion etc. Figure 4.10 gives Kellerhal’s classification of lateral activity. This classification is very exhaustive but rarely used in engineering design. Further, some of the attributes cannot be quantified. 92 Table 4.2 Classification of channels according to Schumm (1968, 1977) Mode of sediment transport Suspended load 85-100 percent Mixed, suspended load 65-85% bed-load 35-15% Bed-load 35-75 percent River Morphology Percent of silt-clay 100 Stable (graded) W/D less than 10 Si greater than 2 slope relatively flat Depositing (excess load) Major deposition on banks, causing narrowing of channel Eroding (Deficiency of load Bed erosion; channel widen-ing minor 30 W/D : 10 – 40 Initially major Initial stream bed deposition on banks erosion; followed by Si : 1.3 to 2 followed by stream bed channel widening Slope relative moderate deposition W/D greater than 40 Si less than 1-3 Slope relatively steep Stream bed deposition Bed erosion minimal, and island formation Channel widening predominant - W/D: width to depth ratio, Si: sinuosity Good Stabilisation of meander belt by channel fills Poor High Suspended load Low Fig. 4.9 Diagram relating stream channel stability to sinuosity and character of stream load (Allen 1965) Finally, streams can also be classified depending on the type of material on their bed, character of the sediment transported, and the slope. Boulder rivers have large size cobbles and boulders on their bed; they are found in mountainous regions with very steep slopes and they carry much finer material eroded from the catchments. Only in catastrophic floods do the boulders on the bed move. These rivers are usually entrenched. Gravel- bed rivers have gravel and sand on their bed, have steep slopes and are paved during normal flows. During the floods the pavement is destroyed. These are found in the foothills and have large width/depth ratio. Rivers in flood-plains flow through the material deposited by them, carry material forming the bed and banks of the river, and have relatively much flatter slope as compared to that of gravel-bed and boulder streams. Their bank material may be slightly cohesive and they carry varying amount of wash load. On the basis of a study of a number of streams in USA, Rosgen (1996) has proposed a hierarchical classification of streams. His classification provides the physical, hydrologic and geomorphic way of linking the driving forces and response variables at different levels of inquiry. Thus as one moves from Level I to Level IV, one progressively takes into account geomorphic characterization, morphological classification, stream condition and validation level. To facilitate the classification Rosgen used Low Channel sinuosity High Fine Calibre of stream load Coarse Fluvial Morphology 93 Entrenchment ratio ER (= width of flood prone area at an elevation twice the bankfull depth/ bankfull width) Width to depth ratio W/D = (Bankful width/mean bankfull depth) Sinuosity Si = (Stream length/valley length) and Slope S Thus at Level I, based on ER, W/D ratio, sinuosity, slope and channel pattern, the streams are classified into nine types designated as Aat, A, B, C, D, DA, E, F and G as indicated in Table 4.3. Table 4.3 Rosgen’s stream classification at level – I (Rosgen 1996) Stream Type ER W/D Si Slope S Aat < 1.4 < 12 1.0 – 1.1 > 0.10 A < 1.4 < 12 1.0 – 1.2 0.04 – 0.01 B 1.4 – 2.2 > 12 > 1.2 0.02 – 0.03 C > 2.2 > 12 > 1.4 < 0.02 D N.A. > 40 N.A. < 0.04 DA > 2.2 E > 2.2 F < 1.4 > 12 > 1.4 < 0.02 G < 1.4 < 12 > 1.2 0.02 – 0.039 Highly < 12 variable Highly > 1.5 variable < 0.005 < 0.02 N.A.-Not applicable The brief description of these nine types of streams is given below: Aat: Very deep, entrenched torrent streams, mildly curved in plan, high relief, zone of deposition, step-pool morphology A: Steep, entrenched step-pool streams, high transport of debris; erosional or depositional character, mildly curved in plan. B: Moderately entrenched, moderate slope, very stable plan, longitudinal profile and stable banks, mildly curved in plan C: Low gradient, meandering, point bar, riffle/pool topography, alluvial channel with moderate entrenchment and W/D ratio, broad valley. D: Braided channel with longitudinal and transverse bars-eroding banks with very wide channel, abundance of sediment supply, aggradational tendency. DA: Anatomising channels, well vegetated flood plain, stable stream banks, broad valley, low bedload and high wash load. E: Low gradient, highly meandering, low W/D ratio, broad valley flood plain with alluvial material, high meander width ratio. F: Entrenched meanders on low gradient, and high width/depth ratio, meanders very unstable laterally with high bank-erosion, pool-rifle morphology G: Entrenched gullies, step-pool morphology, narrow valleys, unstable high erosion rates. The Level II in the classification subdivides the streams in each class into a maximum of six categories, namely 1, 2, 3, 4, 5, 6 depending on the channel material i.e. (1) bed rock (2) boulders (3) cobbles (4) gravel (5) sand, and (6) silt and clay. These are written as A1, A2, A3, A4 …A6 etc. Thus A5 94 River Morphology stream will be of A type with sandy material. It also takes into account bankfull discharge and corresponding hydraulic parameters in determining quantities such as entrenchment ratio, W/D and Manning’s n. Aim of Level III classification is to provide description of stream condition as related to stability of stream, its potential, and function. This is based on additional inputs about hydrology, biology, ecology, and human activity. It evaluates and quantifies the channel stability, bed-stability (aggrading, degrading or stable), and bank erosion. Level IV classification is based on reach specific observations for verification of process based assessments of stream condition, potential and stability predicted from preceding analysis. The book by Rosgen contains valuable information for practicing river morphologists. Since a large number of sketches are included in the book, the text connects easily with the field conditions. 4.9 TOPOGRAPHY PRODUCED BY STREAMS During the cycle of erosion as the streams develop they bring down a large quantity of sediment which eventually goes into the sea. While streams perform the erosional work in the upper reaches and deposition of sediment in the lower reaches various types of topography are produced. According to Schumm (1971) the fluvial system can be divided into three zones, named Zone 1, Zone 2 and Zone 3 in the downstream Zone 1 Zone 2 Zone 3 direction. The upper most part of the drainage basin is (Drainage basin) (Transfer) (Deposition) primarily the sediment source area (Zone 1); the water and sediment are derived here. Zone 2 is the transfer zone Fig. 4.11 Idealized fluvial system where for stable channel, the input is equal to output. Zone 3 is the sediment sink or the area of deposition. Since the sediment is stored, transported and eroded in each zone, within each zone one process is predominant as mentioned above. The three zones are schematically shown in Fig. 4.11 are discussed below. Topography Resulting from Stream Erosion VALLEYS: Usually gullies grow into ravines and ravines into valleys. Development of valley involves three concomitant processes namely valley deepening, valley widening and valley lengthening. Valley deepening takes place due to hydraulic action, abrasion and weathering. Valley widening takes place by lateral erosion near the valley base which can lead to under cutting of slope, rain wash on the valley sides, gulleying on valley sides and mass wasting. The depth of any stream-cut valley is limited to the level of the body of water into which it flows. Valley lengthening can take place in three ways: (i) extension by the process of head ward erosion, (ii) increase in the size of their meanders, and (iii) uplift of land or lowering of sea level. The valley profile near the head will be V-shaped and will gradually change to U-shaped towards the mouth. The longitudinal profile will generally be concave upwards with longitudinal slope decreasing in the downstream direction. The stream slope changes as S = So e– a x, where So is the slope at x = 0 and S is the slope at a distance L from the upstream end, and a is a constant. This decrease in slope is due to the following reasons as mentioned earlier: (i) size of the material transported by the stream decreases in the downstream direction due to abrasion and sorting; (ii) In humid regions the Fluvial Morphology 95 discharge in the stream increases in the downstream direction. Thus there is decrease in sediment concentration in downstream direction thus requiring a smaller slope; (iii) Because of the finer material streams usually have relatively narrow channels (i.e., larger depth to width ratio) in the downstream direction, such channel is more efficient in transporting sediment at a flatter slope. If S = – d Z/dL is substituted in the equation S = So eaL where L is measured in downstream direction and the condition Z = Zo at L = 0 is used, one gets – \ dZ = So e–aL dL –Z =– ...(4.10) So –aL e + const a So = const, a The value of constant can be obtained from the condition Z = Zo at L = 0. Hence –Zo + and hence or –Z = (Z o – Z ) = S - So –aL e 1 + o – Zo a a So (1 – e–aL1 ) a ...(4.11) The low water profiles of the Mississippi river between Fort Jackson and Cairo, of the Ohio river from Cairo to Pittsburgh, both in U.S.A., and San Juan river in Argentina are found to follow Eq. 4.11. The value of a was found to be between 0.0010 and 0.00183. Brush (1961) and Hack (1957) have emphasised the importance of lithology in determining the longitudinal profile and have proposed an equation of the form S = a Lb ...(4.12) For streams in the forded Appalachions in Pensilvania (U.S.A.) they found “a” to vary between 0.013 and 0.15 and “b” between – 0.47 and –1.0, for different lithological formations. STREAM TERRACES: Stream terraces are topographic surfaces, which mark former valley floor level. They are vestiges of former flood plains although some may have little or no alluvium on them. Thus one can have either bedrock terraces or alluvial terraces, which may consist of gravel, sand and silt. Terrace formation can be explained in the following way. When the stream is graded, it forms a flat valley. Later when the stream is rejuvenated it first cuts down through valley flat to a new grade. In doing so it develops a second valley flat inside and below the first one. Repeated rejuvenation can develop successive terraces at lower levels. Individual terraces may be narrow or a few kilometres wide. Height between successive terraces may be a few metres to a few hundred meters, see Fig. 4.12. Topography Resulting from Stream Deposition FLOOD PLAINS: As the stream becomes graded the rate of down cutting decreases as compared to the lateral erosion; hence there is increased meandering activity. Impingement of flow during meandering widens the valley floor thereby producing flood plain. Thus flood plain is a strip of 96 Flood plain River Alluvium River Morphology Bed Rock T River T Scarp T2 T3 T2 T1 T1 Fig. 4.12 Development of river terraces relatively smooth land bordering a stream and over flowed at the time of high waters. When the flood discharge exceeds the bankful discharge it flows across the flood plain. Two processes which are responsible for formation of most of the flood plains of the great rivers of the world are the deposition on the inside of river curves and erosion on the outer side of meander curves. When stream is in the mature stage the width of valley floor is approximately equal to the width of the meander belt. In the lower reaches of mature stream the valley width is much larger because the stream meanders and wanders, see Fig. 4.13. Fig. 4.13 Natural levees and flood plan MEANDERING: Earlier in this chapter reference is made to meandering as one of the plan- forms of single channel streams. The word meandering comes from the name of the stream in south eastern Turkey, which was at one time known as Buyuk Meanderes (Lane 1957). This stream being very Fluvial Morphology 97 crooked in plan, a stream having a winding course and having either regular sinuous pattern or irregular pattern is known as a meandering stream. There are some streams which follow sinuous or irregular path, but which have cut into solid rock or hard strata in deep gorges. These are called incised or entrenched meanders, see Fig. 4.14. Entrenched meanders can also form in the flood plain when winding pattern is formed in a mature or old stream and rejuvenation takes place where it starts cutting down again. The terms used to describe meandering pattern are shown in Fig. 4.8 (a). Meander length ML is the tangential distance between corresponding points at the extreme limits of fully developed meanders. Meander belt MB is the width between tangents drawn outside of the meanders of the stream. Investigator such as Inglis and Central Board of Irrigation and Power, India has accepted this definition. However, Davis (1909) and others consider meander belt as the space enclosed between the tangents. In the present text the former definition has been used. Meander width Mw = MB – B where B is the width of the channel. The ratio of stream length to valley length is known as the sinuosity. Fig. 4.14 Incised meanders of the Dolores river Because of changing conditions of flow, stream slope, sediment size, sediment load and lithology the meandering pattern along the length can be regular or can change along its length; the latter are then called irregular meanders. The irregularity results from variation in discharge along the length due to tributaries, withdrawal of water, presence of lakes, rock outcrops, weirs and barrages, and nonhomogeneity of strata through which the stream flows. In most of the cases, from the point of view of analysis, it is justified to use average values of ML, MB, Mw and sinuosity to characterise the meander pattern in a given reach. Leopold and Wolman (1957) have set an upper limit of sinuosity of 1.5 for differentiating straight streams from and meandering streams. For some Indian rivers sinuosity values up to 2.5 have been reported whereas a value of about 5.5 is considered to be the upper limit. The shape of meanders is rarely truly sinuous; it is many times arc of a circle, parabola or some other curve. One may some times come across a case where the stream has a primary meandering pattern on which is superposed a meander pattern of smaller meander length and belt. This happens if the stream has more than one dominant discharge. The meander pattern in the flood plain of a stream is normally not static but it moves in the downstream at a small velocity; however it is likely to be influenced by the variables such as discharge 98 River Morphology and slope which give an idea about the erosive power of stream, and the nature of strata. The Klarafvens river in Sweden has migrated a distance of about one meander length in 2000 years (Lane 1957). There are also certain streams in which the migration process consists of gradual lateral enlargement of meander loop, with periodic cut-offs. Such meanders are called free meanders. The Tigris river in Iraq has shown this characteristic (Garde 1976). There are also some streams in which the meander pattern is stationary; these are classified as inactive meanders. NATURAL LEVEES: Natural levees are long embankments formed by the deposition of alluvial material by the rivers when they overflow their banks. When streams overflow their banks the velocity is appreciably reduced and hence the carrying capacity of the flow is decreased. This causes deposition of some of the coarser sediment load resulting in the formation low ridge along the banks of the stream; these are called natural levees; (see Fig. 4.13). Natural levees are highest near the riverbank and slope gradually away from it. Natural levees may be one or two kilometre in width. They cause the present meander belt of the river to stand up above the flood plain as a low alluvial ridge. These levees may be built up until the river channel is several meters above the general level of the flood plain. This has occurred in the case of the Yellow river in China and the Mississippi river in U.S.A. In many cases tributary streams have difficulty in breaching the natural levees and many flow in the same flood plain for many kilometres before breaking through the levee to join the main stream. DELTAS: As the stream flows into lakes, ponds, sea or in rare case in rivers, the velocity of flow is decreased and the sediment being carried by the stream is deposited forming what is known as delta, if the waves or currents in the body of water into which it empties are not strong enough to carry away the sediment brought in by the stream on which delta is formed. The amount of sediment deposited and its pattern depend on the size of sediment, changes in the water level of the body, and waves and currents. The name delta comes from the Greek word D to which the deposition pattern resembles. However, the shape of delta can vary depending on the local condition; the Nile river delta has a triangular shape in plan, whereas the Mississippi river delta and some others have long extensions of tributary channels, which are some times called bird foot deltas. Almost all the deltas are formed by splitting of the main channel into a number of branching distributaries channels. Reduction of flow in each branch due to branching causes reduction in flow in each branch causing further deposition. This deposition blocks the distributaries and more distributaries are formed. As along as the rate of supply of sediment from the stream is greater than the rate of removal by waves and currents, the shore line of the delta continues to move downstream especially in shallow seas. Advance rates of some of the deltas in the world are given (Pitty 1971) in Table 4.4. Table 4.4 River Volga Mississippi Orinoco Don Po Kilia Delta of Danube Tigris–Euphrates Yellow river (1870–1936) Rates of advance of some deltas in the world Rate in m/yr. 170 400 200 10 20 27 25–50 300–350 Fluvial Morphology 99 While the delta growth is continuous in some case, in other cases it is spasmodic. Half of the total annual growth may take place during a single week as in the case of Lactature delta in Northern Sweden. Silvister and de La Cruz (1970) have analysed the data of 53 deltas from all over the world and obtained the following relationships for the characteristics of deltas: 45 Apex to sea length L in km = FQI H 100 K bC C g s 1 0.30 0.25 46.3 Area of fan A in km2 = F Q I Ft I H 100 K H 10 K 0.80 e 2.30 Cs0 .40 Number of distributaries N = 268 FS I H 1000 K 1 where Q is the average annual discharge in m3/s, Cs is the (slope of continental shelf ´ 104), S1 is the river slope in percent, and Te is the average annual temperature in oF. They have also a relationship for maximum width of delta. Conditions favouring the deltaic accumulation are (Sparks 1972): i) large sediment load of the stream; ii) usually large river; otherwise action of sea might disperse the sediment; iii) reasonably shallow water offshore; very deep water may inhibit delta building. Thus Congo river which virtually debouches into submarine canyon has no delta; iv) coasts on which wave energy is low; and v) small tidal range. The Mediterranean, Black Sea, Caspian Sea bear witness to this in the deltas of the Nile, Rhone, Po, Danube and Volga. However, deltas can be built in areas of larger tidal range provided that the conditions (iii) and (iv) above are met. Irrawati and Ganges deltas are in the area of 5.5 m and 4.5 m tidal range respectively. In general, large rivers of the world have large deltas with a large number of tributaries. The Orinoco River in Venezuela has thirty-six tributaries. The size of the deltas of the Yellow river and the Orinoco River is nearly same. Since deltaic regions are most fertile, these are thickly populated. A few deltas are shown in Fig. 4.15. The main structural features of coarse-grained deltas differ considerably from those of fine-grained deltas. Where bed load is carried into the delta area, this material gives rise to more rapid changes in deltaic pattern and if it reaches the delta front, it may be deposited as forest beds. In fine-grained deltas, where accumulations are essentially deposited from suspended load, distinctive sets do not develop. There are also contrasts in the average inclination of sub aerial parts of the delta, those on small coarsegrained deltas being rather steep up to several meters per km and overlapping with the order of gradients U | | | | | | V | | | | | | | W ...(4.13) 100 Euphrates Tigris River Morphology Ga cca ng a Da Bhag irath i Calcutta Persian gulf Bay of Bengal Tigris-Euphrates Ganges-Brahmaputra Maha Naraj nadi Cutt ack Mahanadi False point Para dip Puri Bay of Bengal Gulf of Guinea Fig. 4.15 Some large river deltas Subaerial deltaic plain Upper deltaic plain Lower deltaic plain Delta fringe Subaqueous deltaic plain Prodelta marine Carbanaceous matter Sea level Gravel Sand Silt and clay Longitudinal section Coastal interdeltaic sediments Barrier island Delta flank bay Deltaic sediments Delta fringe distributory channels Coastal interdeltaic sediments Delta Barrier island flank bay Carbanaceous matter Sea level Cross section Silt and clay Fig. 4.16 Longitudinal section of delta Fluvial Morphology 101 on bahadas. On fine-grained deltas, the inclination is much flatter, of the order of 5 cm per hundred metres. A typical longitudinal section through the delta is shown in Fig. 4.16. ALLUVIAL FANS: When mountain stream flows out on a gently sloping plain adjacent to the ranges or flows into another stream of greater slope, its velocity decreases and coarse gravel, sand and fine sediment are deposited in the form of a fan in outline. This accumulation of sediment is known as an alluvial fan. Alluvial fans have been studied over the past eighty years or so, and an exhaustive list of references and the present state of knowledge are given by Rachocki (1981). Figure 4.17 shows the sketch of an alluvial fan and its internal structure. Fans can be classified into dry fans and wet fans. Dry fans are formed under dry conditions and their streams are ephemeral. For dry fans, mudflow and debris flow deposits frequently comprise a large part of deposits. These fans are relatively small and have been extensively studied. Wet fans are formed by perennial stream flow. Kosi fan discussed by Gole and Chitale (1966) is a wet fan and is discussed in Chapter 13. This fan is produced by the huge quantity of sediment load brought down by Kosi on the Gangetic plain. Mountain front Canyon Mud flow layers Bed rock Gravel Sand Silt Clay Fig. 4.17 Alluvial fan and its internal structure Alluvial fans are found in the foothills of mountains irrespective of climatic conditions. They were and are being formed at the fronts of ice-caps and glaciers, as well as in moderate semi-arid and arid regions. However, the largest alluvial fans are formed in the foothills of mountains in drier regions of the world. Intensive weathering together with periodic rainfall events is conducive for the production and transportation of large amounts of sediment by the ephemeral streams. Langbein and Schumm (1958) consider an average precipitation of 250 to 350 mm as optimum for the development of fans. Such conditions simultaneously reduce plant cover and ensure adequate supply of water for the transportation of sediment. 102 River Morphology Allen, Morisawa, Thornbury and others believe the commonly accepted explanation for the initiation of fan, to be the drastic reduction in slope between eroding valley and receiving plain. However, according to Bull, change in the confinement of the channel is also an important factor, which facilitates fan construction by reducing the rate of sediment transportation. Infiltration of water in the upper portions of fan further reduces the transporting capacity; this water reappears as strings in the middle and lower portions. Braided stream pattern is characteristic of streams flowing across alluvial fans, and as a result of repeated channel shifting, streams at one time or other flow down in almost every possible radius of the fan. Most alluvial fans exhibit a semi-circular shape in plan. Alternating periods of deposition and soil profile formation are characteristic of most alluvial fans, because the depositional area shifts from one part of the fan to the other during the construction of cone shaped deposit. According to Bull (1962), if sufficient time is available for weathering to occur between periods of deposition, a series of soil profiles will result. Alluvial fan deposits are composed of two main facies, water laid deposits and mass flow deposits. These deposits are poorly sorted even though layers can be distinguished. Mass flows that occurred recently in the fan’s evolution show two separate deposits. The upper part near the apex consists of large particles and lower part of mudflow. Mudflow is a type of debris flow, which consists mainly of sand and finer sediment. The particle size in general decreases in the downstream direction. Fan dissection is a general term used which includes both entrenchment and incision of the fan. Fan entrenchment is down cutting into the fan surface of a channel that is contributing sediment to the fan surface. Entrenchment usually occurs during fan construction. Fan incision is down cutting into fan surface by channel that crosses the fan margin. Incision is usually associated with fan destruction. According to various investigators, the two possible causes for dissection are tectonic movements and climatic changes. According to Lobeck, fan dissection is a natural process-taking place due to reduction of sediment load. A few words about fan dimensions are in order. The radius of the fan may range from several hundred metres to one hundred kilometres with the slopes averaging between 3° and 6°. Anstey (1965) studied fans in Western U.S.A. and Baluchistan in Pakistan. From a sample of almost 2000 fans, he found that greatest number of fans have radii between 1.6 km and 8.0 km. The largest fan in his sample had a radius of 25 km. The upstream slope values may be as high as 10° – 15° while the lower slope can be less than 3°. With the passage of time thickness of fan deposition increases under most climatic conditions. Borehole data as well as the dating techniques have been used to estimate the rates accretion from 0.50 m to 3.0 m per thousand years. Some attempts have been made to relate empirically the fan area Af and fan slope Sf to the drainage area A. According to Bull (1962) For basins underlain by 48-86 percent shale and mud stone For basins underlain by 58-68 percent sand stone Af = 2.4 A0.88 Sf = 0.023 A –0.16 Af = 1.3 A0.88 Sf = 0.022 A – 0.32 ...(4.14) ...(4.15) Here A and Af are in miles2. These results indicate that the fan slope decreases with increasing fan and drainage area of the basin. Fluvial Morphology 103 POINT BARS: When the bed of the channel bend is deformable, scour occurs on the outer side of the bend and the sediment gets deposited on the inner side of the bend forming the bar commonly known as point bar. In order to explain the process involved in the formation of point bar, consider flow in a rigid boundary bend. As the flow enters such a bend, the average velocity in the vertical U varies as 1/r where r is the radius of curvature. This free vortex flow velocity distribution gradually changes to forced vortex flow distribution along the bend length; in forced vortex flow U ~ r. To maintain this distribution a transverse slope towards the inside is caused to the water surface. The friction at the boundary causes velocity variation in the vertical. This variation in velocity in the vertical along with the transverse slope induces secondary flow in the bend which is directed towards the inside of the bend near the bottom and towards the outside of the bend near the water surface, see Fig. 4.18. According to Rozovskii (1961), the location from the beginning of bend at which development of secondary flow is complete is affected by roughness coefficient and the ratio of depth to centre-line radius, see Chapter 6. WS WS Outer Inner a ua B ub Upper layer Lower layer Fig. 4.18 Flow in a rectangular bend and development of secondary flow The secondary circulation is dissipated at a distance of 1.77 F GH C . D from the end of the bend. g I JK Interaction between the main flow and secondary flow causes redistribution of shear stress on the bed. There is higher shear stress on the outer side of the bend land smaller shear stress on the inner side. This distribution for a typical bend in trapezoidal channel is shown in Fig. 4.19. The shear stress at the bed has a small component towards the inside of the bend, which causes sediment to move towards the inside of the bend. In the case of flow around the bend in a channel with deformable bed scour occurs on the outer side of the bend and the sediment gets deposited on the inner side of the bend, forming a bar known as point bar. For a high constant discharge the bed topography is such that the sediment transport rate is the same at all the sections in the bend. The bed topography and the talweg observed in the South Esk bend are 104 FLOW River Morphology Inside edge W S 1.2 1.4 1.0 1.5 0.8 0.6 1.6 1.8 Separation 1.8 2.0 2.0 1.5 1.4 1.2 60° 1.0 0.8 0.6 1.0 1.2 Outside edge W S 1.0 Separation Fig. 4.19 Shear distribution in a trapezoidal bend shown in Fig. 4.20, as given by Bridge (1983). It is found that large-scale bed topography such as point bar changes very little with discharge. The point bar at the bend apex extends about 0.60 to 0.8 times the distance across the bend. 4.10 VARIABLES IN RIVER MORPHOLOGY As discussed earlier, Schumm (1971, 1977) divides the fluvial system in three zones as shown in Fig. 4.11. Zone 1 in which the uppermost is the drainage basin, watershed or sediment source area. Water and sediment are predominantly produced in this zone. Zone 2 consists of the main river system and can be called the transfer zone where for a stable river sediment input and output are equal. Zone 3 is the sediment sink or area of deposition, the sediment is deposited on alluvial fans, flood plains and deltas. Whereas Zone 1 is the primary concern of geo-morphologists, Zone 2 is of major concern to hydraulic and river engineers, and geo-morphologists associated with river channel morphology. Zone 3 is of main concern to geologists, coastal engineers as well as river engineers. In connection with river morphology, three “times” are considered. In Zone 1, one considers geologic time as an important independent variable. This refers to the time from the beginning of erosion cycle to the present and can be millions of years. During this period, erosion occurs in Zone 1 and characteristics of fluvial system progressively change. During graded time span which is a small part of geologic time, there may be small progressive change in landforms, but by and large the system can be considered to be equilibrium. This is the time span considered by Mackin in defining a graded stream, which is considered to be in equilibrium; this time span can be a few hundred years. During steady state time a true equilibrium may exist in which landforms are time-independent. This is the time span considered by hydraulic engineers where variables such as drainage pattern, drainage density can Fluvial Morphology 5 6 3 2 1 105 4 3 7 10 M Fig. 4.20 Observed bed topography of south Esk bend be considered constant. Steady state time can be of the order of a month or less. For geo-morphologists, the geologic time and graded time are of significance. In geologic time, the time, initial relief, geology (i.e., the lithology and structure) and palaeoclimate are the independent variables where as palaeohydrology, relief (i.e., volume of the system above base level), valley dimensions (width, depth and slope) are dependent variables. In graded time span, time is no longer an independent variable even though the drainage system as a whole may be undergoing progressive change of small magnitude. Initial relief has also no significance. However geology, palaeoclimate and palaeohydrology, relief, valley dimensions, climate, vegetation and hydrology (mean water and sediment discharge) are independent variables. The only dependent variable is channel morphology i.e. channel dimensions and slope. During steady state time (which is a short duration of a week to a month) true steady state equilibrium may exist. During this time span, channel morphology assumes an independent status because it is inherited from graded time. Hence in this state geology, palaeoclimate, palaeohydrology, relief, valley dimensions, climate (i.e., mean precipitation, temperature etc.) vegetation, hydrology (mean discharge of water and sediment) are independent variables. On the other hand, observed water and sediment discharge and hydraulics of flow are dependent variables. The dependent and independent variables in different times are listed in Table 4.5. 4.11 NEOTECTONICS AND EARTHQUAKES During the cycle of erosion the land surface is affected not only by the erosional forces but also by the internal forces, which cause displacement of earth’s surface due to movement of earth’s plates and resulting stress building. This displacement is usually slow and can be gradual uplift, subsidence or lateral displacement. Neotectonics refers to these gradual and presently active aseismic crustal deformations. If this happens in the vicinity of an alluvial stream, uplift or subsidence can cause degradation or aggradation respectively thereby altering the gradient upstream, at the axis of movement and in the downstream reach. The minimum rate of uplift estimated by Zeuner (see Schumm 1977) for the Alps and the Himalayas are a millimetre per year. In California the average mountain building rate in modern times is 0.80 mm/year. The present rate of isostatic uplift in North America is 0.50 mm/year. The subsidence in the surrounding area caused by the storage of water and sediment in Lake Mead, U.S.A. was 1.3 mm/ year. According to Schumm et al. (1987) many streams such as the Mississippi and Rio Grande in U.S.A. and Amazon, Niger, Tigris, Euphrates, Rhine and Indus are affected by such structural 106 Table 4.5 Stream variables during different times (Schumm 1977) Variable Time Initial relief Geology (Lithology and Structure) Palaeo climate Palaeo hydrology Relief or volume of system above base level Valley dimensions (width depth, slope) Climate (mean temperature, precipitation, seasonality) Hydrology (mean discharge of water and sediment) Channel morphology Observed Qw, Qs Hydraulics of flow I = Independent NR = Not relevant River Morphology Geologic I I I I D D D X X X X X D = Dependent X = Indeterminate Time graded N.R. N.R. I I I I I I I D X X Steady N.R. N.R. I I I I I I I I D D instability. In Northern Iraq (i.e., Ancient Mesopotamia) Diyala River that is the tributary of the Tigris has incised into its alluvial deposit due to uplift during the past 1000-1200 years. As a result the inundation canal system developed in the earlier times has had to be abandoned. Upwarping of the Brahmaputra basin is found to be partly responsible for flood problems in Bangladesh. Similarly, tectonic uplift is likely to be at least partly responsible for the shifting of the river Kosi through 110 km to the west in the past 200 years. Such uplift and downwarping may look innocuous during a short period but can cause aggradation, degradation or change in plan form in different stretches of the stream. This aspect has been studied by Ouchi (1985) in the laboratory and his results are summarised in the Table 4.6. Reach A: from 2.0 to 3.5 m where no significant uplift or subsidence occurred. Reach B: from 3.5 to 4.65 m, the upstream half of the uplifted or subsided zone. Reach C: from 4.65 to 5.75 m downstream of uplifted or subsided zone. Reach D: from 5.75 to 7.0 m where no significant uplift or subsidence occurred. The lateral movement along the fault may cause a lateral shift in the stream crossing the fault. Such a shift has been observed in the case of Narmada River in India. It has also been reported that prior to Uttarkashi earthquake of 20th October 1991 of magnitude 7.1, horizontal and vertical movements were noticed in Garhwal, Himalayas during 1972-1978. Horizontal movements were about 30 to 150 mm while vertical movements ranged from 10 to 90 mm. Earthquakes in Zone 1 can cause large-scale land slides and mass movement and produce enormous amount of sediment which eventually reaches the stream and can cause aggradation, change in plan form, shifting of tributaries and flooding in Zones 1 and 2. This is what happened in the Brahmaputra after 15th August 1950 earthquake of 8.6 magnitude, see Gee (1951). The effects that were observed immediately after that earthquake and in subsequent years were Fluvial Morphology 107 Effect of uplift and subsidence on channel morphology (Ouchi 1985) B 3.50 Aggradation Talweg shift Submerged bars Degradation Single Talweg Table 4.6 Zone m Briaded channel Uplift A 2.00 Axis 4.50 Degradation Terrace formation Single bars Aggradation Braided C 5.65 D 7.00 Aggradation Braided Subsidence Flooding Degradation Single talweg Meandering channel Uplift Aggradation Flooding Multiple channels Degradation Sinuosity increase Bank erosion Aggradation Flooding, cut-off Multiple channels Local scour Aggradation Subsidence Degradation Sinuosity increase Bank erosion zone of uplift or subsidence Flow Direction i) Some tributaries got blocked by temporary dams created by the debris falling in them from land slides; ii) Subsequent bursting of these dams caused large floods; iii) A large quantity of sediment was brought down in the Brahmaputra causing aggradation of the order of two to three metres over several kilometers; and iv) Some tributaries shifted their course. According to Walters (1975) channel widening and meander cut-offs in the Mississippi river in the early 19th century were due to New Madrid earthquakes of 1811 and 1812. References Anstey, R.K. (1965) Physical Characteristics of Alluvial Fans. U.S. Army Natick Laboratory, Tech. Rep. ES-20 Bloom, A.L. (1978) Geomorphology: A Systematic Analysis of Late Cenozoic Landforms. Prentice Hall Inc., Englewood Cliffs (U.S.A.), Chapter 12. Bridge, J.S. (1983) Flow and Sedimentary Processes in River Bends: Comparison of Field Observations and Theory. In River Meandering: Proc. of Conference Rivers 1983, ASCE, pp. 857-872. Brush, L.M. Jr. (1961) Drainage Basins, Channels, and Flow Characteristics of Selected Streams in Central Pennsylvania. USGS Prof. Paper 282-F Bull, W.B. (1962) Relations of Alluvial Fan Size and Slope to Drainage Basin Size and Lithology in Western Frenso County, California, USGS Prof. Paper 450-B. 108 River Morphology Bull, W.B. (1964) Alluvial Fans and Near Surface Subsidence in Western Fresno County, California, USGS Prof. Paper 237-A. Chitale, S.V. (1970) River Channel Patterns. JHD, Proc. ASCE., Vol. 96, HY 1, Jan. pp.201-222 Cotton, C.A. (1941) Landscape: As Developed by the Processes of Normal Erosion. Cambridge University Press, U.K. Craig, R.C. (1982) The Ergodic Principle in Erosion Models. In Space and Time in Geomorphology (Ed. Thorne C.E.). George Allen and Unwin Ltd., London. pp. 81-115. Davis, W.M. (1909). Geomorphological Essays. Ginn and Co., U.S.A. Dury, G.H. (1969) Relation of Morphology to Runoff Frequency : In Introduction to Fluvial Processes (Ed. Chorley R.J.) Mathuen and Co. Ltd., Chapter 9.11 Esterbrook, D.J. (1969). Principles of Geomorphology. McGraw Hill Book Co., New York, U.S.A. Garde, R.J. (1972) Bed Material Characteristics of Alluvial Streams. Sedimentary Geology. Vol.7. pp 127-135 Garde, R.J. (1978) Irrigation in Ancient Mesopotamia. ICID Bulletin, New Delhi, Vol..27, No. 2, July, pp. 11-22. Garde, R.J. and Kothyari, U.C. (1990). Erosion Prediction Models for Large Catchments. International Symposium on Water Erosion, Sedimentation and Resources Conservation. CSWCRTI, Dehradun, Oct, pp. 89 - 102. Gee, E.P. (1951).The Assam Earthquake of 1950. Jour. Bombay Natural History Society, Vol. 50, pp. 629-638. Gole, C.V. and Chitale, S.V. (1966) Inland Delta Building Activity of Kosi River. JHD, Proc. ASCE, Vol. 92, No. HY-2, March, pp. 111-126. Hack, J.T. (1957). Study of Longitudinal Stream Profiles in Virgina and Maryland. USGS Prof. Paper 294-B. Hack, J.T. (1960). Interpretation of Erosional Topography in Humid Temperature Regions. Am. Jour. Sci. Vol. 285A, pp. 80-97. Horton, R.E. (1945) Erosional Development of Streams and Their Drainage Basins: Hydrophysical Approach to Quantitative Morphology. Geo. Soc. of Am., Bull. Vol.56. Johnson, D. (1932). Streams and Their Significance. Jour. of Geol. Vol. 40, Aug. – Sept. Kellerhals, R., Church M. and Bray D.I. (1976) Classification and Analysis of River Processes JHD, Proc. ASCE, Vol. 102 No. HY 7 July pp. 813-830 King, L.C. (1962). Morphology of Earth. Oliver and Boyd., U.K. Krishnan, M.S. (1982). Geology of India and Burma. CBS Publishers and Distributors, India. 6th Edition, Chapter III. Lane, E.W. (1955). The Importance of Fluvial Morphology in Hydraulic Engineering. Proc. ASCE, Paper 745, July, pp. 1-17. Lane, E.W. (1957). A Study of Shape of Channels Formed by Natural Streams Flowing in Erodible Material. US Army Engineers Division, Missouri River, Corps of Engineers, Omaha, U.S.A. No. 9. Langbein, W.B. and Schumm, S.A. (1958). Yield of Sediment in Relation to Mean Annual Precipitation. Trans. AGU, Vol. 39. pp. 1076-1084. Leopold, L.B. and Wolman, M.G. (1957). River Channel Patterns: Braided, Meandering and Straight. USGS Prof. Paper 282-B, 85 p. Leopold, L.B. and Wolman, M.G. (1960). River Meanders. Bull. Geol. Soc. of Am. Vol. 71, pp. 769-794 Mackin, J.H. (1948). Concept of Graded River - Bull. Geol. Soc. of Am. Vol. 59, pp. 463-512. Neill, C.R. (1970). Discussion of Paper “Formation of Flood Plain Lands” JHD., Proc. ASCE, Vol. 96, HY – 1, Jan., pp. 297- 298. Ouchi, S. (1985). Response of Alluvial Rivers to Slow Active Tectonic Movement. Geol. Soc. of Am. Vol. 96, April, pp. 504-515. Fluvial Morphology 109 Penck, W. (1924) Die Morphologische Analyse. Jour. Engelhorns Nachfolger, Stuttgart. Pitty, A.F. (1971). Introduction to Geomorphology. Mathuen and Co., London. pp. 233-236. Rachocki, A. (1981). Alluvial Fans: An Attempt at an Empirical Approach. A Wiley – Interscience Publication, John Wiley and Sons, New York, U.S.A., 157 p. Rice, R.J. (1977). Fundamentals of Geomorphology. Longman Inc., New York, U.S.A. 1st Edition. Richards, K. (1982) Rivers. Mathuen and Co., London. Chapter 8. Rohan, K. (1967).On the Problems of Longitudinal Profile Stabilization in Streams Transporting Sediment. Proc. 12th Congress of IAHR, Fort Collins, U.S.A., Vol. 3 – C28, pp. 237-248. Rosgen, D. (1996) Applied River Morphology. Pagoda Spring, Colorado (U.S.A.) Rozovskii, I.L. (1961) The Flow of Water in Bends of Open Channels. Israel Program for Scientific Translations, Jerusalem. Schumm, S.A. (1969). Geomorphic Implications of Climatic Changes. In Introduction to Fluvial Processes (Ed. Chorley R.J.) Mathuen and Co., London, Chapter 11.11 Schumm, S.A. (1971). Fluvial Geomorphology: The Historical Perspective. In River Mechanics (Ed. Shen H.W.) Published by H.W. Shen, Fort Collins, U.S.A., Chapter 4. Schumm, S.A. (1977). The Fluvial System. A Wiley – Interscience Publication. John Wiley and Sons, New York, U.S.A. Schumm, S.A, Mosley, N.P. and Weaver, W.E. (1987). Experimental Fluvial Geomorphology. A Wiley InterScience Publication. John Wiley and Sons, New York, U.S.A., 2nd Edition. Simons, D.B. and Albertson, M.L. (1963) Uniform Conveyance Channels in Alluvial Material, Trans. ASCE, Vol. 128, pp. 1. Silvester, R. and de La Cruz, C.d. R. (1970) Pattern Forming Forces in Deltas. JWHD, Proc. ASCE, Vol. 96, No. WW-2, May, pp. 201-217. Shulits, S. (1941) Rational Equation for river Bed Profile. Trans. AGU, Vol. 22., pp. 522-531 Sparks, B.W. (1972). Geomorphology. Longman Group Ltd., London, 2nd Edition, pp. 275-279. Thornbury, W.D. (1969). Principles of Geomorphology. Wiley International Edition, John Wiley and Sons Inc., New York, U.S.A., 2nd Edition. Wadia, D.N. (1961). Geology of India. MacMillan and co. Ltd., London. 3rd Edition (Revised) Walters, W.H. Jr. (1975). Regime Changes of the Lower Mississippi River. M.S. Thesis, Civil Engineering Department, Colorado State University, Fort Collins, U.S.A. Worcester, P.G. (1948). A Text Book of Geomorphology. D. Van Nostrand Company Inc., New York, 2nd Edition. C H A P T E R 5 Hydraulics of Alluvial Streams 5.1 INTRODUCTION Alluvial streams are those, which flow through sandy material, carve their channels through it and carry water and sediment. In dealing with alluvial streams the material in the bed and banks of the channel is generally assumed to be non-cohesive, though some of the fine sediment in transport may settle on the banks and make the bank material cohesive. In the discussion below unless otherwise stated the flow is assumed to be steady and uniform and the channel is taken as prismatic. Gravel-bed rivers are those flowing through very coarse material with rather steep slopes, and their characteristics are discussed in Chapter VII. The following aspects of the alluvial streams are relevant to the theme of the book and are discussed below. • Beginning of motion of uniform and non-uniform material: critical shear, and critical velocity approaches • Modes of sediment transport • Bed-forms • Resistance to flow • Sediment transport s Bed-load s Suspended load s Total load 5.2 INCIPIENT MOTION Consider a channel with given slope and bed material. As the discharge (and hence the depth flow) is gradually increased and bed condition observed, it will be seen that up to a certain depth there is no movement of sediment on the bed. However, with further increase in depth a stage is reached when random occasional motion starts on the bed. This is known as the incipient motion condition or the Hydraulics of Alluvial Streams 111 condition of critical motion. In determining this condition in laboratory experiments, the criterion could be a single particle moving, a few particles moving, general movement on the bed, or the limiting condition when the rate of sediment transport tends to zero. Out of these the last one is considered more rational even though, in the past investigators have used one or the other criteria, which has made comparison of formulae for critical tractive stress difficult. Knowledge of the condition of incipient motion is important in sediment transport studies, in the design of channels carrying clear water, and degradation phenomenon. In the case of steady uniform flow the average shear stress on the bed is given by to = gf RSo where R is the hydraulic radius and So is the bed slope, which is equal to the water surface slope Sw and slope of energy line Sf. In the case of non-uniform flow this shear stress is given as to = gf RSf . The condition of incipient motion for given sediment can be related to the average shear stress on the bed to to, average velocity of flow U or velocity at the level of particle ud. Empirical Equations: Critical Shear Stress Approach During the latter part of the 19th century and first four decades of the 20th century, a number of investigators carried out experiments in the laboratory to determine the critical shear stress at which sediment of given characteristics would move. Equations proposed by Kramer, USWES, Chang, Krey, Schoklitsch, Indri, Sakai and Aki and Sato (see Garde and Ranga Raju, 2000) fall under this category. Most of these formulae can be expressed as and can take the form toc F r - r I d and M; here M is Kramer’s uniformity coefficient. However, their actual forms are GH r JK s f f Fr -r d I GH r M JK F r - r d I . All these formulae recognise that the t = const G H r M JK toc = F s f f s f f ...(5.1) oc depends on, different, because (i) each equation is based on a limited amount of laboratory data, and (ii) these are based on different criteria for defining critical condition viz. isolated, appreciable or general movement on the bed. Some theoretical and semi-theoretical analyses have also been carried out by investigators such as Shields, White, Kurihara, Iwagaki, and Egiazaroff (see Garde and Ranga Raju, 2000) to determine the incipient motion condition for cohesionless sediment particles of size d. However, we will discuss only Shields’ (1936) analysis since it is based on sound principles and even after seven decades the results are often quoted and widely used. Shields (1936) Analysis According to Shields, at condition of incipient motion of the sediment particle of size d on the bed, the drag force on the particle caused by fluid flow is equal to the force required to move the particle. Using Karman-Prandtl’s equation for velocity distribution in turbulent flow, namely 112 ud u d = f1 * u* v River Morphology F H I K ...(5.2) to ,d rf p d2 4 one can determine ud. Here ud is the velocity at the top of the particle level, u* = shear velocity is the particle size, and v the kinematic viscosity. The fluid force on the particle is given by F1 = CD rf 2 ud u2 = CD rf d ´ a2 d2 where a2 is a constant that depends on the shape of the particle. But the drag 2 2 coefficient CD = f2 Hence where F u dI = f F u dI . H vK HvK d * 3 F1 = f3 (R*) rf R* = 2 u* f12 (R*) a2 d2 2 ...(5.3) u* d v The resisting force F is related to the submerged weight of the particle and the coefficient of friction. Hence F can be expressed as F = a1 (gs – gf) d3 ...(5.4) where a1 depends on the shape of the particle and the coefficient of friction. Equating F and F1 under incipient motion condition and introducing the subscript c to indicate incipient motion condition, one gets a1 (gs – gf) d3 = f3 (R*c) rf or 2 u* c f12 (R*c) a2 d2 2 dg t oc s -gf d i = 2a 1 f (R*c) a2 where R*c = u*c d . The coefficient a1 and a2 can be assumed to be constant for particles of given shape. v Hence under the condition of incipient motion t oc =f Dgs d F u d I or t H v K *c *c = f (R*c) ...(5.5) Shields used closely graded sediment viz. sand, barite, granite, amber, and brown coal with relative density varying between 1.06 and 4.25. He used the critical condition corresponding to the case where bed-load transport is zero and produced a graph between u d t oc and * c . Later the mean curve Dgs d v F H I K Hydraulics of Alluvial Streams 113 through the points was drawn by Rouse (1939) who gave wide publicity to Shields’ work in Englishspeaking countries. Recently Shields’ work has been critically examined by Buffington (1999) who pointed out certain ambiguities in Shields’ presentation; however the writer feels that this criticism does not reduce the importance of Shields’ work. Yalin and Karahan (1979) used large volume of data on critical shear stress of nearly uniform material and prepared a modified curve between t*c and R*c. The two curves of Shields’ and Yalin and Karahan are shown in Fig. 5.1. It is relevant to mention the u d t oc vs *c bears similarity to the v Dgs d transition function for friction factor for pipes. The straight line portion on the right has d¢ < < d and is applicable for hydrodynamically rough surface. In the region 2.5 < R*c < 40, the laminar sub-layer and d significance of parameters used by Shields. The graph F H I K are of same order of magnitude and it represents the transition region. For hydrodynamically smooth and d¢ >> d. 10 0 F u d I < 2.5 the boundary is H v K *c gf)d Data from different sources for developed turbulent flow 10 1 toc/(gs Shields Yalin-Karahan 10 2 10 1 10 0 10 u*cd/v 1 10 2 10 3 Fig. 5.1 Critical tractive stress relation for developed turbulent flow according to Shields, and Yalin and Karahan Two additional comments are warranted about Shields’ diagram. Some investigators have argued that according to dimensional analysis the ratio of depth of flow to size of sediment would be another relevant parameter governing critical condition. Even though such argument looks logical, it must be realised that flow conditions including turbulence close to the wall, which are responsible for sediment movement, depend on shear velocity and relative distance from the wall measured in terms of multiples of particle diameter. The thickness of boundary layer that equals the depth of flow in open channels is not important. Secondly, Gessler (1965) has emphasised that the shear stress on the bed fluctuates and follows Gaussian law with standard deviation of 0.57. Hence in a sediment mixture there is no cut-off particle size such that one could say all particles larger than cut-off size will stay in bed and those finer will be moved. In other words the sediment movement is probabilistic in nature. The statistical variation of shear stress as well as orientation of individual particles is responsible for this. By sampling the bed surface layer, Gessler determined that size for which the probability of remaining in bed is 0.50; the average shear stress was critical for that size. In this way he obtained critical stress values for various sizes and obtained curve similar to Shields’ curve. In this analysis Gessler made no allowance for the effect of sediment non-uniformity on toc. He obtained toc values somewhat smaller than those obtained by Shields for the same F u d I . According to Gessler (1965) this has happened primarily because H v K *c 114 River Morphology Shields has considered difference between time-averaged bottom shear stress and critical shear stress in obtaining the condition for zero bed-load transport, whereas he should have used the time average of difference between instantaneous bottom shear stress and critical shear stress. According to Shields, and Yalin and Karahan, limiting value of t*c for coarse material is 0.060 and 0.045 respectively. It may be noticed that u*c occurs in both the parameters of Shields relationship; hence if one wants to determine t*c or u*c for given Dgs, rf, d and v, a trial and error procedure has to be used. This can be avoided by using another parameters R02* defined as 2 2 R0 * = (R*c) FG D g d IJ H t K s oc = D g s d3 r f v2 ...(5.6) 2 and R0 * can be plotted against t oc . Choosing different points on the curve in Fig. 5.1 the following Dgs d t oc and hence toc for known values of, Dgs, rf v Dgs d table is prepared which can give directly values of and d. t oc Dgs d Table 5.1 2 Ro * Variation of 6.40 2 with Ro according to Fig. 5.1 * 0.01 0.05 0.926 60.0 2065 3225 11764 40000 108900 and above 0.045 t oc D gs d 0.25 0.20 0.14 0.10 0.066 0.031 0.031 0.034 0.04 Mantz (1979, 1983) has carried out experiments on transport of sediment in the size range of 0.01 mm to 0.10 mm. According to him if soft water is used these sediments exhibit the same packing properties as cohesionless material. His critical shear results support Yalin and Karahan’s curve for fully developed flows. It needs to be mentioned that in turbulent flow all flow parameters fluctuate and so does the boundary shear stress. Therefore beginning of motion of sediment particles as well as its transport on the bed is a stochastic phenomenon. As mentioned earlier Gessler (1965), Grass (1970), Yalin (1977) and Mantz (1979) have used a stochastic approach in the analysis of sediment movement. Another comment that needs to be made is the role of lift force in Shields’ analysis. When the fluid flows past a spherical particle resting on the bed, a lift force is generated due to modification of flow pattern around the particle (Jeffrey 1929). The magnitude of this force would depend on the same parameters as the drag or drag coefficient, namely u*d/v. Hence lift force is implicitly taken into account in Shields’ analysis. Critical Velocity Approach The idea of using average velocity of flow for describing the incipient motion condition is logical since the average shear stress on the boundary will depend on U and D or R; further U and D or R can be more Hydraulics of Alluvial Streams 115 directly obtained than to. Earlier attempts were made by Brahms, Airy and Rubey to relate critical velocity to size and relative density of the particle (see Garde and Ranga Raju 2000). Thus equating the dynamic force on the sediment particle to its resistance to motion, Brahms obtained x u2 p d2 p d3 rf d = (gs – gf) tanq 4 2 3 ...(5.7) Here x is the fraction indicating the part of frontal area of the particle exposed to the flow, tan q is the friction coefficient, and ud is the velocity at the level of particle at which particle will move. This gives or 2 ud =kd 6 ud 1 U | V = K W| W ...(5.8) when the particle is under the incipient motion condition. Here K and K1 are constants and W is the weight of the particle. Some empirical or semi-theoretical equations have been proposed for ud or U mainly for hydrodynamically rough boundary. These are based on analysis of experimental data for nearly uniform material and are listed below. Garde (1970) udcr Dgs d = 1.51 rf ...(5.9) Neill (1968) Ucr D Dgs d = 1.414 rf d F I H K 1/ 6 ...(5.10) Garde (1970) Ucr D Dgs d = 0.5 log + 1.63 rf d F I H K ...(5.11) Levy (see Bogardi 1974) U cr D = 1.4 1 + ln 7d gd F GH I ¼ if 1.0 £ D £ 60 JK d ...(5.12) U cr D D = 1.4 ln ¼ if > 60 7d d gd F I H K ...(5.13) 116 River Morphology With certain manipulation of equation for the mean velocity in open channels and the Shields’ curve, it is possible to obtain expressions for Ucr Dg s d 3 D Dg s d as related to and Ro2* = for rf d r f v2 hydrodynamically smooth, transition and rough boundaries. For this, consider the equation u d R U x which is valid for plane surface; Here x is related to * 65 as follows: = 5.75log10 12.27 u* d65 v u* d65 11.6v F GH I JK 0.2 0.3 0.50 0.70 1.0 1.61 2.0 1.38 4.0 1.10 6.0 1.03 10 and more 1.0 x 0.7 1.0 1.38 1.56 The above equation can be written as Ucr D 1/2 + 6.26 + 5.75 log x = t* c 5.75 log d Dg s d rf LM N OP Q for uniform sediment. This needs to be used along with Shields’ relationship (in Tabular form) between 2 and t*c, Ro u*c d u d D 2 . For each value of t*c and Ro different values of are chosen and knowing *c , x d v v Ucr . Thus a set of values of Dg s d rf is determined and then D Ucr 2 , and Ro * were obtained along with Dg s d d rf u*c d . On the basis of these generated values the following equations are obtained v Smooth boundary F u d < 2.5I H v K *c D Ucr = 1.77 d Dg s d rf Transition 2.5 < F I H K 0.166 dR i 2 0.05 o F H u* c d < 7.0 v I K D Ucr = 1.38 d Dg s d rf F I H K 0.18 Rough F u d > 7.0I H v K *c D Ucr = 1.656 d Dg s d rf F I H K 0 .18 U | | | | | | | V | | | | | | | W ...(5.14) Hydraulics of Alluvial Streams 10 9 8 7 Ucr (Dgsd/rf) 117 Eq. 5.12 Le vy Eq. 5.14c 6 5 4 3 Garde 2 1 0 10 100 D/d Fig. 5.2 Comparison of equations for Ucr / ( ∆g s d / rf ) for rough boundary 1000 10000 Ne ill Eq. 5.10 Eq. 5.11 Figure 5.2 shows comparison of equations for Ucr for rough boundaries. Dg s d rf Critical Shear Stress for Non-uniform Sediments When the channel bed consists of a mixture of different sizes of non-cohesive sediment, the critical shear stress toci of any size di in the mixture can be determined by carrying out a series of experiments under steady uniform flow condition with decreasing shear stress and preparing a graph of qB vs to for each size. By setting the condition that to = toci when the dimensionless bed-load transport of size di is negligibly small (or less than a predetermined value), toci can be determined for different sizes in the mixture. Value of toci for any size di is affected due to sheltering effect caused by the presence of sediments of size greater than di and relatively greater exposure to flow for larger sizes. Hence if one t t takes arithmetic mean size da as the reference size, and further defines t*ci = oci and t*ca = *ca D g s di D g s da 118 River Morphology where toci and toca are critical shear stress for sizes of di and da respectively, it is logical to expect that t*ci d would be a function of i . t*ca da FG IJ H K Analysis of Egiazaroff (1965), Ashida and Michiue (1971), Hayashi et al. (1980) and others indicates that indeed t*ci is primarily a function of t*ca FG di IJ when the material is coarse and hence H da K viscous effects can be neglected. The equations proposed by these investigators are listed below and plotted in Fig. 5.3. Egiazaroff (1965) t*ci = FG log 19 di IJ 2 H da K FG log 19 di IJ 2 H da K 0.10 0.10 ...(5.15) Ashida and Michiue (1971) t*ci = ...(5.16) FG di IJ is between 0.40 and 1.0, they found that this equation gives a larger value than H da K Fd I observed when G i J is less than 0.40. Tentatively they assumed H da K F d I -1 t*ci = 0.85 G i J ...(5.17) t*ca H da K When for di less than 0.40. da Hayashi et al. (1980) t*ci t*ci t*ca -1 F d di I = G J for i £ 1.0 d d H aK a L log 8 OP 2 for di > 1.0 =M MN log b8 di / da g PQ da Earlier it was found that the value of t*ca varied between 0.05 and 0.02 and an average value of 0.03 was recommended. U | | | V | | | W ...(5.18) Hydraulics of Alluvial Streams 20.0 10.0 Egiazaroff (1965) Ashida-Michlue (1971) Hayashi et al. (1980) 119 t*c t*ca 1.0 0.2 0.05 0.1 di da 1.0 10.0 Fig. 5.3 Variation of t*ci /t*ca with di /da for mixtures Recently Patel and Ranga Raju (1999) have collected addition data and found that t*ca depends on the geometric standard deviation sg = t*ca = F GH d84 d16 I the relationship between the two being JK 0.045 .60 s0 g ...(5.19) t d Patel and Ranga Raju (1999) have also proposed the following relationship between *ci and i t*cs ds t*ci d = i ds t*cs FG IJ -0.96 H K ...(5.20) in which t*cs = t oc and ds = dg sg there is a relationship between t*cs and sg as listed below. D g s ds Hence for known size distribution of bed material one can determine sg, geometric mean size dg and ds = (dg sg). Then knowing t*c s from the table below for known, sg Eq. 5.20 will give t*ci for the size di. Their studies also indicated that if arithmetic mean size is used, Hayashi’s equation yields more accurate results than the other equations. Table 5.2 Relationship between s g and t *cs sg t*cs 1.0 0.045 1.5 0.03 2.0 0.21 3.0 0.15 6.0 0.13 120 River Morphology 5.3 MODES OF SEDIMENT TRANSPORT Once the shear stress acting on the bed exceeds the critical shear stress for the bed material, the sediment particles start moving in the general direction of flow and the manner in which these are transported depends on the flow conditions, ratio of densities of sediment and fluid and the size of the particle. These modes of transport can be classified into the following categories. Contact load The sediment particles that roll or slide along the bed for some time, then come to rest and again start rolling or sliding constitute the contact load. Hence contact load is the material rolled or slid along the bed in substantially continuous contact with the bed. Saltation load The sediment particles hopping or bouncing along the bed thereby losing contact with the bed for some time constitute saltation load. Hence saltation load is the sediment bouncing along the bed, or moved directly or indirectly by the impact of bouncing particles. Bed-load Since saltation load, especially in streams, is difficult to measure, it is clubbed with contact load and sediment moved on or near the bed is called bed-load. Suspended load Suspended load is the material moving in suspension in the fluid, being kept in suspension by the turbulent fluctuations. w According to the theory of suspended sediment distribution; if o > 5.0 there is no suspended u* k sediment (see section 5.7). Hence taking Karman constant k = 0.40, the material will be transported as w to bed-load if o > 2.0; however material of size d will move if is greater than that gives by D gs d u* Shields’ diagram. Hence for purely bed-load transport the conditions to be satisfied are than to is greater Dgs d t oc w and o is greater than 2.0. Dgs d u* One can also assume that when vertical turbulent fluctuation near the bed is greater than the fall u¢ 2 = 2.5 to 3.0 and u* velocity wo, sediment will go into suspension. At the edge of laminar sub-layer v¢2 u¢ 2 0.4 to 0.50. Hence it can be assumed that near the bed v ¢ 2 » u* at incipient suspension. Several D g s d3 wo to and it is found that this r f v2 u* s investigators e.g. Van Rijn, Sumer, Celik and others have related variation is fairly well represented by the empirical equation Hydraulics of Alluvial Streams 121 wo D g s d3 = 0.5 u* s r f v2 F GH I JK 0. 40 up to D g s d3 values of 20. Here u*s is the shear velocity at incipient suspension of sediment of size d r f v2 and fall velocity wo. Daniel, Durand and Condolios (1953) have presented an interesting description, albeit qualitative, of the mechanism of saltation. They have considered four idealised positions in which a particle will be found on the surface of the bed and the possibility of their movement by saltation is discussed. These positions are shown in Fig. 5.4. 1 2 3 4 Fig. 5.4 Particle position and its susceptibility to saltate Out of the four possible positions, the particle in position 2 is more likely to travel by saltation under favourable hydraulic condition. The two forces acting on the particle are the submerged weight of the particle acting vertically downwards and resultant hydrodynamic force, which consists of drag and lift. Where the lift is equal to the submerged weight of the particle, the particle will be lifted up thereby increasing the lift. The particle acquires a vertical velocity and eventually in the final stages of taking off, the movement is accompanied by a quick rotation as shown in the second part of the figure. The particle in position 1 will either slide or roll over the layer of other particles. Particle in position 3 can have the saltation movement only if the particles upstream of it move in such a way that the particle in position 3 is brought in position 2, or the particle in position 3 occupies some other position because of the impact of the particle in saltation movement. The particle in position 4 will be set in motion mostly under the condition of direct or indirect effect of particle in saltation. According to Kalinske (1942) the height of saltation, for the same particle size, is proportional to the ratio of mass densities of sediment and fluid. Hence it is apparent that the height of saltation in air is about 800 times that in water for the same particle. For this reason saltation is not very important for 122 River Morphology sand transport in water. The phenomenon of saltation is further analysed by Hayashi and Ozaki (1980). While Einstein assumed that the saltation height hs is twice the diameter of the particle, Hayashi and wo d v where t¢*, is the dimensionless grain shear stress and the value of hs/d can vary between 0.1 and 6.0 Ozaki’s analysis indicates that hs/d i.e. the dimensionless height of saltation depends on t¢* and (see Fig. 5.5); similarly the step length ls w d also depends on t¢* and o (see Fig. 5.6); however when d v wo d greater than about 100, as assumed by Einstein (1950) v ls » 100 d 10 8 6 4 2 ls d 1 8 6 4 2 10 1 1 ...(5.21) Ref = wod/v rs/rf = 2.65 CL = 0.50 R ef =1 4 0 Reg = 40 100 400 Ref ³ 2000 10 2 4 6 8 10 1 2 4 6 8 1 2 t¢* Fig. 5.5 Saltation heights (Hayashi and Ozaki 1980) At this stage it is interesting to know about the motion of individual particles moving as bed-load. With the advent of radio isotopes, some information has been gathered about the average rate at which sediment particles move on the channel bed. Such measurements by Hubbell and Sayre (1964) in the case of the Middle Loup river, and laboratory flume indicate the following. Table 5.3 Rate of movement of individual particles U m/s Middle Loup river in USA Lab. flume 2.44 m wide Lab. flume 2.44 m wide 0.527 0.610 0.326 Dm 0.76 0.317 0.317 d mm 0.29 0.93 0.19 Bed condition Dunes Long low dunes Ripples Ug m/hr 0.9 2.0 0.02 Thus, it can be seen that the average velocity of particles moving as bed-load is much smaller than the flow velocity. The analysis of Engelund and Fredsoe along with Luque and Van Beek indicates that (see Garde and Ranga Raju, 2000) the average velocity of bed particle Ug is given by Hydraulics of Alluvial Streams 200 Ref = wod/v 100 80 60 40 20 10 8 6 4 2 1 10 Reg = 40 100 10 400 ³ 2000 rs/rf = 2.65 CL = 0.50 123 ls = 100 t¢ * d R ef = 4 ls d 1 2 4 6 8 10 1 2 4 6 8 1 2 t¢* Fig. 5.6 Step lengths (Hayashi and Ozaki 1980) Ug u* = 9 1 - 0.7 F GH t *c t* I JK ...(5.22) where t*c can be obtained from Shields’ diagram. It may be further mentioned that when the particle goes into suspension it is carried by the flow in the forward direction at the flow velocity at that level. It is appropriate to mention distinction between bed material load and wash load at this place. The sediment load carried by an alluvial stream can be divided into bed material load and wash load. Bed material load is that part of the sediment load carried by the stream that has originated from the bed and banks of the stream; hence it consists of sediment sizes found in appreciable quantity in the bed and banks of the stream. Bed material load correlates well with the hydraulic conditions in the stream. The other part of the sediment load is composed of those fine sizes not available in appreciable quantities in the bed and banks of the stream. This part, known as wash load, is washed into the stream from the catchment and is usually finer. Hence, the amount of wash load carried by the stream is more related to the hydrologic conditions of catchments than to the hydraulic conditions in the stream. For this reason it is difficult to estimate the amount of wash load carried by the stream. It is usually not possible to stipulate the size limit for wash load. For sandy streams with flat slopes, the wash load may be in the clay and silt range. On the other hand in the case of mountain streams with steep slopes, wash load may be in the range of coarse to fine sand. Einstein (1950) recommends that the limiting size for the wash load may be arbitrarily taken from the mechanical analysis of the bed material, as that size of which ten percent of the material is finer. Hence one can write Total load of stream = (bed material load) + (wash load) Bed material load = (bed-load + suspended load) 124 River Morphology 5.4 BED-FORMS IN UNIDIRECTIONAL FLOW Once the critical shear stress on the bed in unidirectional flow is exceeded, the sediment particles forming the bed are transported at a rate, which increases with increase in shear stress on the bed. The bed in the process remains plane under some conditions, but under other conditions develops transversely oriented bed features known as ripples, sand waves or dunes, and antidunes as observed by Blasius, Cornish, and Gilbert and recently by Simons et al. These bed-forms travel beneath the flow, take part in the sediment transport, and govern the relationship between flow velocity, flow depth and slope. In other words, they affect the friction and sediment transport. They also leave back a characteristic imprint in the enclosed deposits. The purpose of this section is to describe the characteristics of these bed-forms and study the methods available for their prediction. Definitions of Bed-forms The Task Force of ASCE (1966) has given the following descriptions/definitions of various bed-forms: Ripples are small bed-forms with wavelengths less than about 0.30 m and heights less than approximately 30 mm. They occur only rarely in sediments coarser than approximately 0.60 mm. These are sometimes called current ripples. Dunes are bed-forms larger than ripples but smaller than bars (see below) and are out of phase with water surface gravity waves that accompany them. These are some times called sand waves or sand bars. Bars are bed-forms having lengths of the some order as the channel width or greater, and heights comparable to the mean depth of generating flow. Point bars at the bend and alternating bars fall in this category. With increased shear stress, dunes tend to get washed out and especially for finer material they can be completely washed out and a flat or a plane bed can form. At this stage Froude number U/ gD can be high but less than unity. Further increase in flow leads to the formation of symmetrical sinusoidal sand waves on the bed and similar water surface waves in phase. These are known as standing waves. Further increase in flow causes these waves to move upstream, increase in amplitude and then break. These are called antidunes. After breaking of waves the bed becomes plane and undergoes the same sequence. These bed-forms are shown in Fig. 5.7. Jackson II (1975) classifies bed-forms occurring in shearing flows on the basis of bed-form size, time span of existence, superposition, flow regime and channel process. The larger bed-forms (macroforms), such as point bars, pools and riffles respond to geo-morphological regime of the environment and are relatively insensitive to changes in fluid dynamic regime during an individual dynamic event such as a flood in a river. A two-zone structural model of turbulent boundary layer provides a genetic framework for two smaller classes of bed-forms. Meso forms, such as dunes in the rivers, respond to flow conditions in the outer zone of the turbulent boundary layer as the flow varies through the dynamic event; their life scales correspond with the duration of that event. The smallest bed-forms (micro forms) viz. the ripples are governed by the flow structure in the inner zone i.e. the laminar sub-layer; their lives are much shorter than the periodicity of dynamic events. According to Jackson II, ranges of wave lengths of the different bed-forms are: Hydraulics of Alluvial Streams 125 (a) Typical ripple pattern Weak boil (e) Plane bed (b) Dunes with ripples superposed Boil Boil (f) Antidunes, standing waves (c) Dunes (g) Antidunes, breaking waves Breaking antidune wave Pool Pod Fr < 1 Accelerating flow (d) Washed out dunes or transition (h) Chutes and pools Fig. 5.7 Bed-forms in alluvial channels Ripples Dunes Sand waves and alternate bars Sand bars, point bars 50 mm to 2.0 mm 0.40 m to 300 m 10 m to 1000 m 500 m to 5000 m As mentioned earlier, alternate bars and point bars are the largest in each environment and their dimensions compare to those of the environmental flow system. They are quite insensitive to changes in flow. Jackson II identifies four different types of super positions of bed-forms. These are as follows: 1. Imposition of lower regime bed-form upon the bed-form moulded by higher flow regime e.g. small ripples migrating over upstream face of dunes. 2. Under equilibrium condition such superposition of ripples and dunes can be explained from stability considerations. According to Kennedy (1969) perturbations of bed-load transport rates are responsible for ripple formation while perturbations of the longitudinal distribution of suspended load cause dunes. Hence when appreciable suspended load is present, ripples and dunes can be superposed e.g., in fine to medium sands. 3. Superposition of fluid dynamic bed-forms on much larger bed-forms that are more permanent e.g., large scale ripples on the point bar. 4. Superposition in which neither bed configuration responds to be local fluid dynamic regime; e.g., mid-channel islands and sand bars in braided rivers such as the Brahmaputra river as observed by Coleman. Jackson II also discusses about three universal time scales of unsteadiness and discusses the effect of each upon the bed-forms. The shortest time scale is that of the turbulent boundary layer of the flow, 126 River Morphology for which a wide spectrum of time scales exists. The shortest is the time scale of Kolmogorov and is of the order of a second. The largest corresponds to large eddies and their scales are of the order of a minute or a few minutes. Several investigators attribute large-scale ripples to the eddies of this time scale. The second time scale is related to each dynamic event taking place in the stream. It is the time interval TE in which the event occurs e.g., passage of flood. The largest time scale is the geo-morphological scale, which encompasses many dynamic events and is much longer than TE. This time scale reflects the imposition of geological controls on the development of bed-forms. Bed-forms have been observed and measured on some rivers. Lane and Eden (1940) have summarised the results of field measurements by Johnson in the Mississippi river at Helena. Sand waves of height up to 6.7 m and length up to 305 m were observed in a depth ranging from 4 to 9 m. Carey and Keller (1957) have also reported measurements on the Mississippi. Whetten and Fullam (1967) have measured dune lengths, dune heights and their migration velocity in the Columbia river downstream of Bonneville dam in USA. Measurements have also been reported by Gallay (1967) on the North Saskatchewan river in Alberta (Canada), by Singh and Kumar (1974) in the Ganga, the Yamuna and the Son rivers in India, by Itakura et al. (1986) on the Ishikari river Hokkaido, Japan and by Haque and Mahmood (1983) in irrigation canals in Pakistan. Similarly a number of laboratory studies have been conducted during 1950 to 1985 or so. These data have been utilised to study the bed-form dimensions and criteria for their occurrence. Distinction Between Ripples and Dunes Studies by Garde and Albertson (1959), Yalin (1971) and Garde and Issac (1993) have indicated that ripples form in the initial stages of sediment movement and are near-bed phenomena. Hence their length scale is obtained from u* and v as L v . Even though earlier Yalin had indicated that for ripples » 1000, u* d later he indicated that for u* d < 3.5 v u* L L = 2250 or = 2250/(u* d/v) d v ...(5.23) Garde and Albertson (1959) had also proposed that Mantz (1992) related H u d to for ripples is governed by * and . Dg s d L v u* L u H u d to and * to * and . Garde and Issac (1993) have concluded that Dg s d v v v u* d is less than 10 – 12 and Froude number v ripples will form if sediment size is less than 0.60 mm, U gD less than 0.80. If Fr is greater than 0.80 ripples are changed to symmetrical sand waves. According to them ripple length and ripple height are given by Hydraulics of Alluvial Streams 127 and F I FG t IJ H K H Dg d K FG t IJ H F u dI = H K d v H Dg d K L u d = 4115 * d v * -0 .316 o s -0.660 0.828 o s -0.717 U | | V | | | W ...(5.24) Stability Analysis The approach of explaining the formation of ripples, dunes and anti-dunes from the consideration of stability of a plane alluvial bed transporting sediment has been followed by a number of investigators such as Matsunashi, Engelund and Hansen, Kennedy, Hayashi, Engelund, Fredsoe, Parker, Reynolds, Hayashi and Onishi, and Richards. Most scientists today agree that the problem of sand wave formation is a problem of instability of an original plane bed transporting sediment when it is slightly perturbed by a small sinusoidal disturbance. As a result the flow and sediment transport are perturbed. Then there will be the following two main possibilities: 1. The change in flow pattern and sediment transport will tend to attenuate the amplitude of perturbation, so that the bed goes back to the original plane bed state. This means that the plane bed is stable. 2. The second possibility is that the flow causes the perturbation on the bed to increase with time, which corresponds to the unstable situation, ultimately leading to formation of ripples, dunes and antidunes. Basically the analysis starts with the equations of motion and continuity equation on which onedimensional sinusoidal disturbance is introduced. This causes fluctuation in velocity component and sediment transport. The analysis is essentially linear so that higher order fluctuations are neglected. The instability caused is primarily dependent on the lag distance d which is the distance by which local sediment transport rate lags the local velocity or shear stress at the bed. The total lag effect is built of the following possible contributions: 1. fluid friction, 2. rate of suspended sediment transport in relation to bed-load transport rate, 3. gravity forces on moving bed-load, 4. inertia of sediment particles, and 5. percolation in river bed. Such stability analysis has indicated the importance of the following parameters in determining the flow regime, or stable wave length KD or wave number. F H D U to 2 pD : Froude number, , , ; here K is called the L ¢ Dg s d d u* I K Dune Dimensions Since the outer region of turbulent boundary layer controls formation of dunes, the length and velocity scales that are most appropriate are the depth D and average velocity of flow U. Hence it is expected that dune length L = constant ´ D. Yalin, Hino and Van Rijn (see Garde and Issac 1993) found the constant 128 River Morphology of proportionality to be 5.0, 7.0 and 7.3 respectively. Using a large volume of laboratory and field data Garde and Issac (1993) found that L = 4.737 D ...(5.25) which has the correlation coefficient of 0.674 and for which 33.25, 57.19 and 83.38 percent of the data fell within ± 30, ± 50, and ± 100 percent error lines. The stability analysis, on the other hand, indicates 2 pD i.e. KD depends essentially on Fr. Figure 5.8 shows this graph. The empirical equation, which L fits the data reasonably well, is that Fr = 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 a f 1 + KD tanh KD 2 KD + 8 KD tanh KD ...(5.26) Flume, River and canal data 1 + tan h KD (KD) + 8KD tan h KD 2 Eq. 5.26 Fr = 2 Fr 0 1 2 3 4 5 KD 6 7 8 9 10 Fig. 5.8 Variation of KD with Fr for dunes (Garde and Isaac 1993) It was also found that as u* d u d L increases also increases especially when * is between 20 and D v v D is also an important parameter. Hence assuming that d 30. Earlier Hayashi and Onishi had found that L D = f Fr, , Garde and Issac obtained the equation D d F H I K L D = 4.58 (Fr)0.397 D d F I H K 0 .0546 ...(5.27) Hydraulics of Alluvial Streams 129 Accuracy of prediction of L by this equation is slightly superior to that of the equation L = 4.737 D. A number of equations have been proposed for dune height. Some of these are listed below: Yalin (1971): H 1 t 1 - *c = D 6 t* FG H IJ K ...(5.28) Gill (1971): H t 1 = (1 – Fr2) 1 - *c D 2na t* FG H IJ K 3 ...(5.29) where a is shape factor for dunes and lies between 0.50 and 0.637, and n is the exponent of shear parameter in the bed-load equation. Fredsøe (1975): H L f 1 0.06 1= - 0.40 t * 2 50 t* FG H IJ K ...(5.30) where f is Darcy Weisbach friction factor Allen (1978): H t* = 0.079865 + 0.0336 D t *c 3 * where t*c = 0.045 Van Rijn (1984): FG IJ – 0.004077 FG t IJ U H K Ht K | | V | F F t I t I – 0.0000045 G + 0.000239 G | J J Ht K Ht K | W 2 * *c 4 * *c *c -0 .30 ...(5.31) H D = 0.11 D d * where F I H K F t ¢ IJ T= G Ht K *c (1 – e–0.5T) (25 – T) ...(5.32) Using a large volume of data Garde and Issac (1993) concluded that most of these equations predict dune height with 29 to 35 percent of data falling between ± 30 percent error lines. They also concluded that by far Allen’s equation is marginally superior to the other equations mentioned above. Figure 5.9 shows verification of Yalin’s and Allen’s equations using a wide range of flume, canal and river data. It may be mentioned that Garde and Issac used flume and field data covering a wide range as can be seen below Sediment size Flow depth Height of undulation Length of undulations Channel slope 0.100 mm to 2.4 mm 0.051 m to 51 m 0.011 m to 5.58 m 0.090 m to 252 m 0.015 ´ 10 –3 to 14 ´ 10-3 130 1 Allen Yalin and Karahan River Morphology H/D 0.1 0.01 0.01 Flume data River data Canal data 0.1 t*c/t* 1 Fig. 5.9 Variation of H/D with t *c for dunes according to Yalin and Allen (Garde and Isaac 1993) t* On the basis of their analysis they found that the maximum value of primarily a function of d and is given by D H designated as D F HI H DK is m F HI H DK = 0.22 + 0.4 m F dI H DK 2.57 0.60 ...(5.33) and then they proposed the following equations for *c * a H / Df = 341.8 FG t IJ a H / Df Ht K a H / Df = 1 a H / Df a H / Df = 0.12 – 0.06 a H / Df F t I GH t JK m m 1.15 H . D if 0.03 £ if 0.103 £ if 0.150 £ t *c £ 0.103 t* t *c £ 0.150 t* t *c £ 0.80 t* m *c * U | | | | V | | | | W ...(5.34) Ripples and dunes are found to move in the downward direction at a velocity Uw that is given by Garde and Kondap as Uw = 0.021 Fr4.0 gD ...(5.35) Hydraulics of Alluvial Streams 131 Transverse Ribs Transverse ribs are regularly spaced rows of clustered pebbles, cobbles or boulders lying at right angles to the flow on the bars and the channels of braided streams. Their average longitudinal spacing ranges from 0.06 m to as large as 2.5 m, and their height ranges from one to two times the maximum size of bed material. Their wavelength seems to be proportional to the maximum size of the bed material, and inversely related to the stream slope. Laboratory experiments indicate that the transverse ribs are associated with near critical to supercritical flows. It must be emphasised that the above relations have been obtained assuming the flow to be steady and uniform. Even though this may be true in the case of flume studies, the flows in rivers are changing which can have effect on bed undulations. To study this effect a population of dunes or any bed-form that occur in a given reach of the channel can be considered and its statistical properties studied. In other words frequency distribution of dune height or length can be studied to determine if the distribution is uni-modal or bimodal. Bimodal distribution would imply two types of undulations. Similarly time series analysis has been carried out on a train of dunes. This type of analysis was initiated after studying changing dune characteristics in rivers such as the Fraser in British Columbia (Canada) and in the Gironde Estuary in France. Further discussion on this aspect can be seen in Chapter XII of Sedimentary Structures written by Allen. Antidunes Antidunes are symmetrical sand and water waves that are in phase and which may move upstream, downstream or remain stationary. These were first observed by Cornish and then studied in detail by Gilbert, Simons, and Kennedy. These were called antidunes because they moved against the flow even when the sediment is transported downstream. As the waves move upstream their amplitude goes on increasing. However there is a limit to the maximum steepness of water surface waves, which depends on velocity, depth and sediment size. When this limit is reached the waves break, form a plane bed on which sinusoidal waves had formed and then the process is repeated. These waves break when height to wavelength ratio reaches approximately 0.14. The wavelength of the surface waves is given by Ls = 2 pU2 g ...(5.36) Antidunes have been observed on several streams in USA, e.g., the San Juan River in Utah, the Muddy creek in Wyoming, the Mendano Creek in Colorado and on the Assiniboine river in Canada. When the antidunes form Fr number is close to or greater than unity. Prediction of Regimes of Flow For several reasons engineers, geomorphologists and sedimentologists are interested in predicting the type of bed-form that would occur for given flow conditions and fluid, sediment and channel characteristics in a stream. This is illustrated by two practically important examples. Figure 5.10 shows the variations of Manning’s n obtained in laboratory flume for sediment size of 0.45 mm when the average shear stress is varied. It can be seen that Manning’s n undergoes a three-fold change as the bedforms change from plane bed without motion, to ripples, to dunes of lower flow regime to the transition and then upper flow regime of plane bed and anti-dunes. Thus, the resistance to flow changes appreciably with flow conditions and needs to be predicted correctly. 132 Plane bed Ripples Dunes Transition Antidunes 0.18 mm Barton-Lin 0.03 River Morphology 0.02 n 0.038 0.45 mm USGS 0.03 n 0.02 0.01 0.01 0.002 0.2 1.0 Fig. 5.10 to 10 Variation of n with to As can be seen from the above figure the roughness coefficient undergoes a definite reduction as the flow changes from lower flow regime into transition while dunes are washed out and the bed becomes flat. This is reflected in the discontinuous rating curve between discharge q and depth D for the Middle Loup and the Pigeon Roost Creek in Mississippi (USA) see Fig. 5.11 (Dawdy 1963). 10 6 Hydraulic radius in feet Hydraulic radius in feet 10 6 4 4 2 2 1 1 5 3 5 3 1 2 4 Velocity in feet per second 10 1 2 4 Velocity in feet per second 10 Fig. 5.11 Discontinuous stage discharge curves for the Middle–Loup and Pigeon Roost Creek (USA) Hydraulics of Alluvial Streams 133 Part of the shear stress to, designated as t¢¢ o is used in overcoming the form resistance of bed-forms and only the remaining shear stress t¢ o = (to – t¢¢ o ) is available for bed-load transport. It is found that bedload transport rate correlates well with t¢ and not with to. Therefore, for the same shear stress and o sediment characteristics, the bed-load transport rate will be smaller when dunes than when it is flat cover the bed. Thus, regime of flow also plays an important role in sediment transport phenomenon. A number of attempts have been made to develop criteria for the prediction of regimes of flow. These are based on the valuable experimental data collected by Gilbert, U.S.W.E.S., Simons et al. at Colorado State University and others, together with data from irrigation canals and natural streams. It is to be cautioned that irregularity in channel cross-section, and unsteadiness and non-uniformly of flow in natural channels can vitiate the prediction of regime in natural rivers made using criteria primarily based on steady, uniform flows in channels with rectangular shape. In such cases the recipe for successful prediction is perhaps the combination of laboratory and field evidence. While discussing the various criteria proposed by different investigators, the writer feels that as far as possible average flow velocity should not be used as an independent variable because it is not known a priori. The most commonly used dimensionless parameters in regime predictors are Froude number stress U , dimensionless shear gD u d u D to , shear velocity Reynolds number * , * , , slope S, stream power to U, sediment size Dg s d v wo d d or D g s d 3 t* ¢ - t *c , t *c r f v2 FG H IJ and U . These criteria are listed in Table 5.4 along with some comments. K u¢ * In the opinion of the writer the most important parameter in the prediction of regime is to or Dg s d t¢ o which is an index of sediment mobility. Greater its value, greater will be the rate of sediment Dg s d transport. However t¢ to o can be computed only if average velocity U is known; for this reason Dg s d Dg s d gD is to be preferred. Then the Froude number U which is ratio of inertial force to gravity force should also be important when bed undulations are large and affect the water surface. Hence Garde and Albertson (1959) proposed to vs Fr criterion shown in Fig. 5.12. Dg s d Garde and Anil Kumar (1988) further checked this with additional data. This criterion clubs ripples and dunes together. Plotting of additional data indicated Fr » 1.0 as a reasonable line of demarcation to . Dg s d Engelund and Hansen’s U/u* ¢ vs Fr number criterion (1966) is shown in Fig. 5.13. It also works well and in addition differentiates between negative sinus bed (i.e., anti-dunes) and positive sinus bed. Positive between transition and antidunes regimes. Its limitations arise from the use of U along with 134 10 Ripple and dunes ... Blank Transitions ... Half solid Antidunes ... Solid Ripple and dunes Modified line Original line River Morphology Antidunes 1.0 t* 0.1 0.06 0.06 0.1 1.0 2 4 6 U gD Fig. 5.12 t* – U gD regime criterion of Garde and Albertson (1959) 30 25 20 15 10 5 e bed Positive sinus bed (Dunes) U/U¢* Plan Negative sinus bed (Antidunes) Transitio n Plane bed Positive sinus bed Ripple and dunes ... Blank Transition ... ... Half solid Antidunes ... ... Solid U/ gD 1.5 2.0 2.5 0 0.5 Fig. 5.13 U/u*¢ - U 1.0 gD regime criterion of Engelund and Hansen (1966) Hydraulics of Alluvial Streams 135 Table 5.4 Parameters used for prediction of regime Comments Limited laboratory data of Gilbert of 0.50 mm size; dimensional parameter Flume data with d varying from 0.011 to 4.94 mm. Predicts regimes fairly well for flume data but fails for river data. Same as above, use of dimensional parameter to ∆g s d Investigator 1. Langbein (1942) Parameters used U gR u* ud vs * wo n gd u2 * U gD vs UR 2. Albertson, Simons, and Richardson (1958) 3. Bogardi (1974) 4. Garde and Albertson (1959) vs d vs Flume and field data, works fairly well, does not separate ripples from dunes, and uses velocity. 5. Garde and Ranga Raju (1963) 6. Tsubaki and Sato (1974) S R vs (∆g s g f ) d S R vs d ( ∆g s g f ) Flume and field data; does not separate ripples from dues, works fairly well. Lines of demarcation between dunes and transition, and transition and anti-dunes differ slightly from Garde and Ranga Raju (1963). Has theoretical basis, works well with flume and field data, differentiates between positive sinus and negative sinus (anti-dunes), and uses velocity. Needs trial error solution if velocity is not known. Uses both shear and velocity. Uses primarily flume data, prediction of regimes unsatisfactory. 3 13 7. Engelund and Hansen (1966) U vs u* ′ U gD 8. Simons and Richardson (1962) to U vs d 9. Van Rijn (1984) Ft GH t o − 1 vs oc I F ∆g d I JK GH r n JK s f 2 Based on flume and some field data, predictive ability mixed. 10. Brownlie (1981) US1 3 ∆g s d rf vs d , d Flow in upper regime if S is greater than 76 ´ 10 –3. Needs trial-error solution if velocity is not known. sinus bed is one where the disturbance travels in the flow direction; however such a bed is accompanied by appreciable form drag and is converted into dune pattern. This criterion is based on stability analysis and finds qualitative support in earlier work by Matsunashi. It suffers from the same drawback as vs Fr criterion in the use of velocity U as well as shear stress. to Dg s d 136 2 ´ 10 10 2 River Morphology 2 Modified line Original line Tsubaki-Satio Garde-Raju Transition Ripple and dunes Antidunes 10 3 S/(gs/gf) 10 4 No sediment motion t0 = 0.5 (Ags)d Transition Half Solid Ripple and dunes Blank Antidunes Solid 10 5 10 10 2 R/d 10 3 10 4 10 5 Fig. 5.14 R/d – S c∆g s / g f h regime criterion of Garde and Ranga Raju (1963) The criterion proposed by Garde and Ranga Raju (1963) which uses parameters is shown in Fig. 5.14. Since fact that smaller R/d and dDg S s /g f i to is split into two parameters this criterion recognises the Dg s d S larger, and larger R/d and smaller which may have the Dg s / g f dDg S s /g f i and R/d as two b g d i to can have different regimes. It seems to work well for both flume and field data, and has Dg s d the advantage that it does not use velocity. Later analysis by Tsubaki and Sato supported this criterion even though their lines of demarcation are slightly different. Lastly it may be mentioned that according to Van Rijn (1984), same b g U | If d < 10 and 3.0 < T < 15.0 dunes will occur | If d < 10 and T < 15.0 dunes will occur | If T > 15.0 transition will occur V | | F I F t¢ - 1IJ and d = d Dg Here T = G | GH r v JK Ht K W If d* < 10 and T < 3.0 * * ripples will occur ...(5.37) 1/ 3 o * s 2 oc f Hydraulics of Alluvial Streams 137 It may be mentioned that only Van Rijn’s and Browntie’s criteria for regime predictions involve kinematic viscosity and hence these take into account the effect of water temperature on flow regimes. With the change in temperature, the fall velocity of sediment particle will change and hence its effective size will be different. This is found to have significant effect on bed-forms, resistance and suspended load discharge. Such studies by Lane, Straub and Taylor have shown increase in suspended load with decrease in temperature, other conditions remaining same. Colby and Scott (1965) found that on the Middle Loup river the bed-forms were more pronounced in summer. 5.5 RESISTANCE TO FLOW IN ALLUVIAL STREAMS As the water flows through a channel, the channel bed, sides and the interface between water and air offer resistance to flow. The resistance at the interface is usually negligible except when antidunes are formed and even then that part of resistance is included in the overall resistance of bed and banks. This resistance to flow is manifested in the slope of energy gradient Sf, which is equal to bed, slope So and water surface slope Sw in steady uniform flow. The relationship between average velocity U, hydraulic radius R, slope Sf and a coefficient representing roughness of boundary is known as the resistance law and three commonly resistance equations used in open channel are Manning’s equation Chezy’s equation Darcy-Weisbach equation : : : U= 1 2/3 1/2 R Sf n RSf 8g RSf f ...(5.38) ...(5.39) ...(5.40) U=C U= Writing these equations in non-dimensional form it can be seen that C U U R1/ 6 = = = = u* n g g g RSf 8 f where u* is the shear velocity. Any one of these Eqs. (5.38) - (5.40) can be used to determine the velocity if R and Sf (= So for steady uniform flow) along with the coefficient n, C or f are known. Using sand coated roughness of uniform size ks along with Karman-Prandtl equation, U/u* can be expressed as 12.27 Rx U = 5.75 log10 u* ks FG H FG H IJ K IJ K ...(5.41) One can relate Manning’s n to ks as 12.27 Rx R1/ 6 = 5.75 log10 ks n g 138 Here x is a function of x with River Morphology ks 11.6 v where d¢ is the thickness of laminar sub-layer d¢ = . The variation of u* d¢ ks is given in Table 5.5. d¢ Table 5.5 Variation of x with ks δ′ 2.0 1.38 4.0 1.10 6.0 1.03 10.0 and more 1.0 ks δ′ 0.2 0.7 0.3 1.0 0.5 1.38 0.7 1.56 1.0 1.61 x When ks is less than 0.25 the boundary is hydrodynamically smooth; when it is greater than 6.0 it d¢ is rough and when 0.25 < ks < 6.0 it is in transition. Thus in the case of smooth and boundaries in d¢ u* k s R and , while in the case of rough boundary they depend ks v transition C, n or f are functions of both on R R1/ 6 R only. If one were to plot vs for hydrodynamically rough surfaces, one gets the ks ks n g approximation R1/ 6 R = 24.0 ks n g FG IJ H K 1/ 6 or n = 1/ 6 ks 25.6 which can be compared with the empirical equation obtained by Strickler for a number of Swiss rivers flowing through coarse material and having plane bed, n= 1/ 6 d50 24.0 Here ks and d50 are in m. For plane bed resistance in alluvial channels, Einstein recommends ks = d65 in Eq. (5.41). Bank Resistance A in the P hydraulic computations; in such situations one can use hydraulic radius with respect to bed Rb in resistance and sediment transport relationships and to can be calculated as gf Rb S. This is computed by subdividing A into area corresponding to bed Ab, and area corresponding to sides Aw, and assuming U When the roughness coefficient of bed and banks is different, it is not correct to use R = Hydraulics of Alluvial Streams 139 and S to remain same for main channel as well as Aw. For rectangular channel of width B, depth D, average velocity U and Manning’s coefficient for wall nw, one can write A = Aw + Ab BD = 2DRw + BRb U= 1 Rw2/3 S1/2 nw or and U V W ...(5.42) Hence, Rb = D - 2 F H D Rw B I = D F1 - 2 R I K H BK w ...(5.43) Knowing Rw from Eqn. (5.42), Rb can be calculated. General Comments on Resistance to Flow with Alluvial Beds In the case of alluvial streams with shear stress greater than the critical, the analysis of resistance becomes more complex due to changing bed-forms with the change in flow condition. With the undulations on the bed the resistance of the bed is made up of the resistance due sand particles on plane surface which is called grain resistance, and the form resistance due to the presence of bed undulations. Even though grain resistance may not change significantly with flow, the form resistance will change. Another factor which influences the resistance is presence of sediment in suspension. In the beginning of the 20th century Buckley and Lacey observed reduction in the resistance to flow in the Nile and Indus rivers respectively, in the presence of fine sediment. Similar observations were made by Vanoni and Nomicos (1959) in their laboratory studies in which they showed that decrease in resistance is more significant when bed is plane than when it has dunes on it. This decrease is due to the damping of turbulence near the bed. Studies at the University of Roorkee have indicated that in plane bed channels carrying suspended sediment of fall velocity wo the friction factor decreases when 1200 while it is greater than that for clear water flow when C wo is less than US C wo is greater than 1200. Here C is the US average suspended sediment concentration is ppm by volume. Resistance of Bed Undulations In order to estimate separately the grain resistance and form resistance of bed undulations, Einstein and Barbarossa (1952) divided shear stress on the bed g f Rb S into shear stress corresponding to grain roughness t¢ o and that corresponding to form roughness due to bed-forms t² o. Hence or or to = t¢ o + t² o gf Rb S = gf R¢b S + g f R² bS Rb = R¢ b + R² b U | | V | | W ...(5.44) 140 River Morphology where R¢ ² are hydraulic radii corresponding to grain roughness and form roughness respectively. b and Rb Einstein and Barbarossa compute R¢ b using Manning’s equation along with Strickler’s equation 1/ 6 d65 25.6 where ns is for plane bed and d65 is in m. This gives ns = U Rb ¢ = 7.66 u* d65 ¢ FG IJ H K 1/ 6 ...(5.45) or using Eq.(5.41) with x = 1 and ks = d65 one gets U ¢ = 5.75 log10 12.27 Rb u* ¢ d65 For river data they determined t¢ o using above equations and then determined t² o = (to – t¢ o). Further D g s d35 U to depend on bed-load transport rate and hence on Y¢ = the relationship between assuming uo t¢ ¢¢ o U and Y¢ was obtained using data from American rivers with the following ranges u* ¢¢ F GH I JK ...(5.46) d65 R U S The coordinates of the relationship between given in Table 5.5. 0.220 mm to 7.50 mm 0.045 m to 4.09 m 0.045 m/s to 2.79 m/s 1.740 ´ 10 –4 to 1.72 ´ 10 –3 U and Y¢ as obtained by Einstein and Barbarossa are uo ¢¢ Table 5.5 Y¢ U u* ′′ Relationship between 0.70 62.0 1.0 40.0 U and Y¢ as given by Einstein and Barbarossa (1952) u*′′ 1.5 25.0 3.0 15.5 7.0 10.0 9.0 9.0 15.0 7.0 25.0 6.0 40.0 5.0 0.50 100.0 It may be mentioned that later studies to verify Einstein-Barabarossa method by Vanoni and Brooks U and Y¢ plot. One can uo ¢¢ compute stage-discharge curve for an alluvial channel using this method in the following manner. (1957), and Garde and Ranga Raju (1966) have indicated large errors on Hydraulics of Alluvial Streams 141 1. Known quantities: channel width B, slope S, d35, d65, rf and rs. Neglect bank friction; hence R¢ and R² correspond to R¢b and R² b. 2. Assume R¢ and compute U using Eq. 5.44 3. Calculate Y¢ and find u² * using Table 5.5 and then R ² 4. R = R¢ + R² for this R find D and then Q = BDU 5. Repeat the procedure with higher value of R¢ Engelund (1966) has proposed the method of estimating t¢o and t² o for known value of to by dividing S into S¢ and S². He proposed the grain resistance to be computed using the equation U = 5.75 log10 R ¢ + 6.0 u* ¢ 2 d65 F GH I JK ...(5.47) It may be noticed that while Einstein and Barbarossa use d65 as roughness length for plane bed, Engelund uses 2d65 implying that plane bed with sediment transport has greater roughness than plane bed without motion. Using some laboratory data by Guy et al. he found that t¢ *= FG t¢ IJ is related to t H Dg d K o s 35 * = to D g s d35 and regime of flow. For ripples and dunes, and plane bed he suggested the equations for ripples and dunes and for plane bed as t¢* = (0.702 [t*]–1.8 + 0.298)–1/1.8 To obtain velocity for given depth, slope, d65, d35, and Dgs one must first assume the regime flow, then obtain t¢* and R’ from Eq. (5.47) or (5.48) for known to. Now use Eq. (5.46) to determine U and U vs Fr graph in Fig. 5.13. If the assumed regime is correct the solution u* ¢ is right; otherwise assume a different regime and repeat the procedure. Lovera and Kennedy (1969) used flume and river data and showed that the friction factor for plane bed with motion increases with increase in Re for given R/d whereas the lowest values of f ¢ for given R/d are those given by Karman-Prandtl’s equation for hydrodynamically smooth boundary; see Fig. 5.15. In their analysis Alam and Kennedy (1969), instead of subdividing R into R ¢ and R ², split S into S¢ and, S² the slopes corresponding to grain roughness and form roughness respectively. Since 2 t¢ * = 0.06 + 0.4 t * t¢ * = t* for t¢ * < 0.55 for 0.55 < t*¢ < 1.0 Brownlie (1983) extended the second equation in the higher regions of upper flow regime t*¢ > 1.0 U V W ...(5.48) check the regime of flow using f= 8g RS 8g R = 2 (S ¢ + S ² ) U2 U 8 g R S ¢ 8 g R S ¢¢ + or f = f ¢ + f ² U2 U2 f= 142 River Morphology River and flume data d 0.088 to 0.788 mm D 0.03 to 3.10 m U 0.45 to 2.34 m/s f¢ 0.04 0.03 0.02 0.01 2 R = 10 d = 1 2 3 4 5 6 8 10 12 15 20 25 30 40 50 100 125 Prandtl's smooth boundary relation 4 2.5 ´ 10 6 10 5 4 Re = UR v 6 10 6 4 6 Fig. 5.15 Friction factor for flat beds according to Lovera and Kennedy (1969) where f ¢ are f ² friction factors corresponding to grain roughness and form roughness respectively. Recently Patil (1997) has obtained equation for variation of f ¢ given by Lovera and Kennedy as follows: f ¢ = m log10 Re + C where m = 0.1919 ´ 10 –4 and = 0.076 C = 0.1396 ´ 10 –3 = 0.478 Rec = 0.7256 and for R + 0.016 if d Re > Rec R £ 3000 d R > 3000 d if R + 0.016 if d if R £ 3000 d R > 3000 d f = 0.0032 + 0.221/(Re)0.237 F RI H dK 1.7735 if Re < Rec U | | | | | | | | | | | V | | | | | | | | | | | W ...(5.49) He also found that for laboratory and field data having a wide range of variables t¢¢* is given by 1.27 t¢¢* = 0.6 t * ...(5.50) Hydraulics of Alluvial Streams 143 Here t¢¢* and t * are with respect to d 50. Thus for known to and regime, t²* can be calculated and then R¢b. Then using Eq. (5.47), U can be calculated. Using Lovera and Kennedy’s relationship for f ¢, Alam and Kennedy (1969) found that f ² depends on R/d and U or U ; when R/d is greater than 3000 approximately, f ² depends only on g d50 gR (this is true for river data) or U , see Fig. 5.16. As shown by Alam and Kennedy (1969) g d50 gR determination of depth or velocity when other parameters are known is a trial and error procedure whereas determination of slope for known velocity, depth and sediment size involves no trial. 3 2 10 1 U U gd = 50 7.5 10 Legend Contours of values of FD = U gd Contours of values of F = U gRb 15 20 0.15 2 50 25 2 30 25 10 0.3 0.2 10 35 0.5 0.4 15 U gRb 0.6 20 0.7 25 30 2 35 10 3 10 2 10 3 10 4 10 Rb/d 5 Fig. 5.16 Friction factor for bed-forms according to Alam and Kennedy (1969) Total Resistance Approach A number of methods have been proposed to determine the velocity of flow in alluvial streams by considering the total resistance to flow without splitting it into grain resistance and form resistance. One of the earlier attempts in this direction is Lacey’s equation (Lacey 1932) U = 10.8 R2/3 S1/3 ...(5.51) which was proposed for stable alluvial channels but is often used for bankful discharge in alluvial rivers. Sugio (JSCE, 1974) has proposed the equation U = K R0.54 S0.27 ...(5.52) where K = 6.15 for ripples, 9.64 for dunes and 11.28 for transition regime. Thus one must first determine the regime of flow by one of the methods involving R, S and d and then use Eq. (5.52). Garde and Ranga Raju (1966) carried out dimensional analysis and indicated that U =F Dgs d rf F F RI GG H d K dD g S/ g i and g H 1/ 3 s f 1/ 2 d 3/ 2 v I JJ K 144 River Morphology First neglecting the effect of viscosity and hence of g1/2 d3/2/v, they obtained the following equation R U =K d Dgs d rf with F I FG S IJ H K H D g /g K 2 /3 s f 1/ 2 …(5.53) K = 7.66 for plane bed without motion, = 3.2 for ripples and dunes, and = 6.0 for transition regime. Later they plotted R U vs d Dgs R rf F I FG S IJ and obtained a continuous relationship for all H K H D g /g K 1/ 3 s f the regimes. The mean curve obtained them is shown in Fig. 5.17. Ranga Raju (1970) found that the scatter on Fig. 5.17 can be reduced if K1 U is plotted against K2 Dgs R rf F F RI GG s H d K GG D g Hg 1/ 3 s f I JJ where K and JJ K 1 K2 are functions of d or g1/2 d3/2/v . 3.0 1.0 D gs rf R No sediment motion Antidunes R.D. = 2.65 U 0.1 0.05 10 Ripples, dunes, transition 4 10 3 FG R FG1/3 IJ s IJ H d H KDgs / g f K s f 10 2 10 1 Fig. 5.17 Relation between U D gs R rf vs FG R IJ FG S IJ for all regimes and materials with different relative Hd K H Dg /g K 1/ 3 densities (Garde and Ranga Raju 1966) Hydraulics of Alluvial Streams 145 Patil (1997) found that for a large volume of data in ripple and dune regime covering a wide range of related variables the following equation R U = 6.05 d gd F I H K 0. 5 S0.4 ...(5.54) predicts velocity within ± 30% error for 92 percent of data. For plane bed without motion, and transition regime Equation (5.53) with K = 7.66 and 6 respectively can be used. These will reduce to Plane bed without motion U R = 7.66 d gd 2/3 and transition U gd F I H K F RI S = 6.0 H dK 2/3 S0.5 ...(5.55) 0.5 ...(5.56) A number of other approaches to prediction of velocity are available e.g., Paris, Brownlie, and that by Karim-Kennedy. These are discussed by Garde and Ranga Raju (2000). However, for geomorphic analysis Eqs. (5.54), (5.55) and (5.56) may be adequate for prediction of discharge or stage-discharge relation. It is further cautioned that in the prediction of velocity in alluvial streams, at present errors of the order of ± 30% are likely. 5.6 BED-LOAD TRANSPORT It was mentioned earlier that when the average shear stress on the bed is greater than the critical shear stress for the material, the material starts moving and there is a range of u*/wo values for which the sediment is transported as bed-load i.e. the material moves on or near the bed. The layer in which the bed material moves can be called the bed layer. The first bed-load equation was proposed by Du Boys (1879). Assuming that the sediment moves in layers, each having a thickness Dh, the layers move because of the applied shear stress to = gf DS, and the velocity of layers decreases linearly downwards from (N – 1) DV for top layer to zero at the first layer (see Fig. 5.18), one can write qB = gs N D h (N – 1) DV 2 ...(5.57) where N is the number of layers and qB is rate of bed-load transport in weight/width/time. The first layer where velocity is zero will satisfy the condition that the resisting force is equal to the shear stress. Hence to = (gs – gf ) N D h tan f where f is angle of repose. When N = 1, to = toc. Therefore to/toc = N and Eq. 5.57 can be written as qB = or g s Dh DV to (to – toc) 2 t 2 oc qB = A to (to – toc) ...(5.58) 146 W.S. River Morphology Bed Dh to (N 1) DV 2 DV DV DV = 0 Fig. 5.18 Du Boys bed-load transport model Dh DV has the dimensions m3/N. Values of A and toc were later determined by 2 t2 oc Straub and are given below (See Garde and Ranga Raju, 2000). The value of A = gs Table 5.7 Values of A/gs and toc in Eq. 5.58 according to Straub (see Rouse 1950) d mm A/gs x 10 –6 m6/N2s toc N/m2 0.125 32.32 0.766 0.250 19.45 0.814 0.50 11.75 1.054 1.0 6.89 1.533 2.0 4.05 2.443 4.0 2.43 4.310 The empirical equation proposed by Meyer-Peter and Müller (1948) is based on extensive data collected in Switzerland by Favre, Einstein and Meyer-Peter and Müller. Meyer-Peter and Mûller split S into S ¢ and S ² the slopes corresponding to grain and form roughness and found that it is only the shear corresponding to grain roughness that is responsible for bed-load transport. Since U= n S¢ = s n S 1 2/3 1/2 1 2/3 1/2 Rb S and U = Rb S¢ ns n F I H K 2 . Here ns = 1/ 6 d90 where d90 is in m. Using data covering the following range of variables 26 Relative density Slope Depth Arithmetic mean size of sediment Meyer-Peter and Müller obtained the equation t*¢ = 1.25 to 4.22 4.00 ´ 10 –4 to 2.00 ´ 10 –2 0.01 m to 1.20 m 0.40 mm to 30 mm F n I FG t IJ = 0.047 + 0.25 f H n K H Dg d K 3/ 2 s o 2/3 B ...(5.59) s a Hydraulics of Alluvial Streams 147 q fB = B gs rf rs - r f where FG 1 IJ H gd K 3 a 1/ 2 where da is the arithmetic mean size. The above equation can be written in the form fB = 8 (t*¢ – 0.047)3/2 ...(5.60) Two observations can be made here. The first is that dimensionless bed-load transport is related to excess shear (t*¢ – 0.047), and that even though Meyer-Peter and Mûller started with the division of S 3/ 2 into S ¢ and S ¢¢, the term the experimental data, in reality they have subdivided Rb into R¢ b and R² b. Ning Chien (1954) has found that Eq. (5.59) predicts bed-load transport rate as well as Einstein’s equation (see below) for uniform sediments and also for non-uniform sediments if all sediment particles in the mixture are moving and a single size da is used. Hansen has used this equation to compare the observed values of bed-load transport rate on the Skive-Karup river and found the two agreed fairly well. However, generally correct size distribution of transported bed-load is not obtained. A number of theoretical or semi-theoretical approaches have been made to study bed-load transport, namely by Einstein (1942), Kaliske, Bagnold, Engelund and Fredsøe, and Yalin out of which only Einstein’s method will be discussed here briefly. Einstein (1942) started with probabilistic approach to bed-load movement. He disagreed with the premise that a definable critical condition for bed-load movement exists. Since turbulent shear stress and lift near the bed fluctuate, Einstein assumed that a sediment particles moves if the instantaneous hydrodynamic lift on the particle exceeds the submerged weight of the particle. Once the particle is in motion, the probability of the particle being re-deposited is assumed to be equal at all points on the bed. Lastly, the average distance travelled by any particle moving as bed-load is assumed to be constant. He thus obtained relationship between bed-load parameter fB = qB gs rf rs - r f F n I FG t IJ in Eq. (5.59) really represents g R¢ S . Therefore, to fit H n K H Dg d K bD g g d s o f b s a s a FG 1 IJ H gd K 3 1/ 2 and flow parameter Y¢ = F (Y¢) was determined using laboratory and field data. Later Einstein (1950) presented a more sophisticated analysis to study fraction wise transport of non-uniform bed material. In this later version Einstein modified the bed-load function to take into account fraction wise bedload transport, by defining q i f*i = B B ib g s d g - g i d . The relationship f d g R¢ Si s f f B = FG 1 IJ dr - r i H g d K rf s f 3 i 1/ 2 where qB iB is bed-load transport rate of the fraction i and ib is the fractional availability of this size di in the bed. The parameter Y*i is defined as 148 River Morphology Y*i LM log 10.6 =x Y M MM log FH 10.6 d D N i 65 OP dg - g i d P I P g R¢ S K PQ s f i The parameter Y*i is made up of three parts. Part 1 namely xi is the hiding factor that depends on where dx is the characteristic size. Variation of x i with di is given below dx di dx Table 5.8 Variation xi with di /dx in Einstein’s method di /dx xi 0.10 150 0.2 35 0.4 6.8 0.6 2.2 1.5 and above 1.0 The fraction Y is dependent on d65 and its variation is given below in Table 5.9. d¢ Table 5.9 Variation of Y with d65 / d¢ in Einstein’s method d65 / d¢ Y 5.0 0.52 3.0 0.53 5.0 0.60 1.6 0.80 1.10 0.82 0.9 0.80 0.70 0.65 3.5 0.44 0.30 0.22 LM log 10.6 The term M MM log FH 10.6 d D N 65 OP I PP arises from the fact that lift on the particle is related to the near bed velocity K PQ dx = 0.77 D if if D > 1.8 d¢ D < 1.8 d¢ which must be measured in sediment mixture at a distance 0.35 dx above the theoretical bed. The characteristic size dx is given by and where D = dx = 0.39 d¢ d65 and x is given in Table 5.5. The third part Y*i is reciprocal of dimensionless shear stress x with respect to grain. The curve between Y*i and f*i obtained by Einstein (1950) is shown in Fig 5.19 with data by Gilbert, and Meyer-Peter and Müller plotted on it. A number of questions have been raised Hydraulics of Alluvial Streams 100 149 10 y* 1.0 f* Curve compared with measured points for uniform sediment • d = 28.65 mm Meyer Peter et al. (1934) • d = 0.785 mm Gilbert (1914) 1 1 A* = B = 0.023 * 7.0 y* 0.1 0.0001 0.001 0.01 f* 0.1 1.0 10 Fig. 5.19 Einstein’s relationship between f* and Y* (Einstein 1950) on the assumptions made in the deviation of Einstein’s bed-load function. These can be seen in Raudikivi (1976) and Yalin (1971). In spite of these questions, Einstein’s method is considered to be the most logical attempt to rationalize the complex problem of bed-load transport of non-uniform sediment. The formula of Einstein (1942) was, modified by Brown (see Rouse, 1950) using the parameters f and Y defined as and F g L r - 1O d I GH MMN r PPQ JK F g - g IJ d = 1 Y=G H t K t q f= B gs F s s f 3 1/ 2 f o * and F= 2 + 3 36 v 2 g d3 s f F r - 1I GH r JK – g d3 36 v 2 s f F r - 1I GH r JK ...(5.61) He expressed the variation of f with Y as f = 40 t3 *= 40 where Y £ 5.5 Y3 0.465 f = e– 0.39 Y where Y > 5.5 U | | V | | W The parameters F in Einstein-Brown formula appears in Rubey’s formula for fall velocity of sediment particle and was introduced to account for the fall velocity of sediment particles. Gill (1968) 150 River Morphology investigated Einstein-Brown relationship using data of Gilbert, and Simons-Richardson and found it necessary to modify it to f = 40 FG t Ht o -1 oc IJ K 3 ...(5.62) to account for deviation in f values at low shear stresses. It may be mentioned that at Roorkee (India) systematic investigations have been carried out to include effect of sediment non uniformity on the rate of bed-load and total load transport. According to Patel and Ranga Raju (1996), the fraction wise bed-load transport can be calculated as follows: 1. Divide the bed material into a number of fractions and determine the geometric mean size and availability in the bed ib of each fraction. 2. Compute toc for size da using Shields’ curve and also t¢ o 3. Determine Kramer’s uniformity coefficient M for the mixture and CM using the Equation (5.63) CM = 1 for M ³ 0.38 CM = 0.7092 log M + 1.293 for 0.05 £ M £ 0.38 4. Compute Cs for known values of to ¢ from Equation (5.64) t oc 2 3 o o o U V W ...(5.63) F F t ¢ I - 0.1949 F log t ¢ I I + 0.0644 Llog t ¢ O log C = – 0.1957 – 0.9571 G log G MN t PQ GH t JK JK H H t JK s oc oc oc ...(5.64) 5. Compute xB from Eq. (5.65) CM xB = 0.0713 Cs FG H t¢ o D g s di IJ K –0.7514 ...(5.65) and then compute xB 6. Read fB from Fig. 5.20 and determine qB iB = ib gs fB (g di3)1/2 FG t¢ IJ H Dg d K o s i F Dg I GH g JK s f 1/ 2 5.7 SUSPENDED LOAD TRANSPORT As mentioned earlier at higher shear stresses the sediment particles go into suspension. Owing to the weight of the particle, there is a tendency for the particle to settle which is counterbalanced by the turbulent motion i.e. turbulent velocity components. Also there is a continuous exchange of sediment Hydraulics of Alluvial Streams 151 10 0 10 1 10 1 fB 10 1 10 2 Data from different sources 10 to ¢ Dg s di 0 xB = Curve based on uniform sediment 10 1 10 2 10 6 10 5 10 4 xB Fig. 5.20 Variation of fB with xB fB 10 3 10 2 10 1 F τo I for field data with non-uniform sediments (Patel and Ranga Raju 1996) GH ∆γ s di JK particles from suspension to the bed and bed to the suspension. Various mechanisms have been suggested by which a sediment particle moving on the bed goes in suspension. According to the lift concept initially proposed by Jeffreys and used by Einstein, when the instantaneous lift on the particle is greater than its submerged weight, the particle moves up in the flow and is transported as suspended load. According to Laursen while the particle is moving along the bed over a dune or small irregularity, it loses contact with the bed momentarily as it is launched over the crest and is carried in suspension. According to Sutherland (1967) the turbulent flow consists of round or oval shaped eddies; these eddies are distorted and flattened as they approach the channel bed and the velocity within the eddy increases. Their impingement on the laminar sub-layer disrupts it and causes spots of high shear stress at different places on the bed and causes motion of the particles. If the turbulent velocity component at the place of impingement is large enough and in vertically upward direction, the particle can be entrained in the flow. In fact, all the three mechanisms discussed above work together in the process of suspension. When sediment goes into suspension, the concentration of suspended load in the vertical decreases with increase in distance from the bed. In general, finer the sediment, more uniform is the distribution of suspended sediment in the vertical. The two most common ways of expressing the concentration of suspended sediment are: 1. Absolute volume of solids per unit volume of water– sediment mixture. This can also be expressed in parts per million by volume or in percent. 2. Dry weight of solids per unit weight of mixture. This again can be expressed in parts per million by weight or in percent. 152 River Morphology Suspended Sediment Distribution Equation The suspended sediment is subjected to two actions: the first is the upward and downward turbulent velocity fluctuation v¢ and the second is the gravitational action that causes settling of sediment which is heavier than water. Since there is a concentration gradient ¶C at any distance y from the bed, due to ¶y ¶C where Îs is the ¶y sediment transfer coefficient. The downward transfer per unit area will be woC where wo is fall velocity of sediment and C is the concentration. Hence for steady, uniform and two dimensional flow, the continuity equation demands that turbulence, there is a net transfer of sediment in the upward direction equal to Îs Îs ¶C + woC = 0 ¶y ...(5.66) The same equation can be obtained from general diffusion equation for sediment in open channels. Equation (5.66) was first used by the German meteorologist Schmidt in 1925 to determine the distribution of dust particles in the atmosphere. If Îs and wo are assumed to be independent of y, Eq. 5.66 can be integrated to obtain C ln = Ca z y a wo dy Îs wo ( y - a) and C = e Îs Ca U | | | V | | | W ...(5.67) Here Ca is the concentration at a distance “a” from the bed. Schmidt obtained this equation in 1925. Considering that momentum transfer and sediment diffusion in vertical in turbulent flow are similar, one may assume Îs = b Îm where em is momentum transfer coefficient and b is a coefficient. If one assumes b = 1, Îs = Îm and Îm can be determined from combining the following equations and U | | | yI | F t = t 1H DK | V | t =g DS | | u ¶u = | ¶y k y | W Îm = t ¶u rf ¶y o o s * o ...(5.68) Hydraulics of Alluvial Streams 153 where D is the depth of flow, ko is Karman constant the value of which for clear water flow in open channel is 0.40; and the last term of Eq. (5.68) is obtained from Karman-Prandtl equation for velocity distribution in turbulent flow. This gives Îs = Îm = u* ko y F D - yI H D K ...(5.69) Substitution of the value of Îs from Eq. (5.69) in Eq. (5.66) and subsequent integration gives D- y a C = Ca y D-a FG H IJ K Zo where wo Zo = u* k o U | | V | | W ...(5.70) This equation was first published by Rouse in 1937 but was independently derived by Ippen earlier. For further discussion of Eq. (5.70) it is essential to state the assumptions made in its derivation because any deviation from it in its verification can be attributed to one or more of the assumptions made. These assumptions are (see Garde and Ranga Raju, 2000): 1. Derivatives with respect to t, x and z are assumed to be zero; this means the flow is steady, uniform and two dimensional in nature. 2. Higher order derivatives of C with respect for x, y, and z are neglected. This assumption is justified for small values of Zo but can introduce errors when Zo is large and sediment concentration distribution near the bed is skew. 3. Intensity and scale of turbulence for upward and downward flows are the same and v’ and mixing length l have unique values for given y. 4. While evaluating Îm it is assumed that r f is constant; yet mass density of fluid will be maximum near the bed and will decrease upwards. 5. While integrating Eq. (5.66) it is assumed that wo is independent of y; however because of concentration gradient and turbulence, the fall velocity of a particle near the bed will be smaller, and increase as y increases. 6. Îs is assumed to be equal to Îm. 7. Logarithmic velocity distribution law holds well with Karman constant k = 0.40. Vanoni, Garde, Barton and Liu and others have ascertained validity of logarithmic law for velocity distribution law; however some investigators who have determined k from the whole velocity distribution have found it to vary. However, if it is determined from the velocity variation near the bed, k is found to be essentially constant by Coleman. Two other attempts to integrate Eq. (5.66) may be mentioned. Lane and Kalinske (1941) found that as a simplification an average value of Îm = Îs = u* D/15 can be used for wide rivers. Hence integration of Eq. (5.66) gives C = e u* Ca w o 15 ( y - a) D F I H K ...(5.71) 154 Laursen (1980) expressed Îs as Îs = River Morphology F H b Îm y 1D I K where b is introduced believing sediment may not follow the turbulent fluctuations exactly and (1 – y/D) representing correlation coefficient, and integrated Eq. (5.66) to get a C = Ca y FG IJ H K wo b k o u* ...(5.72) Here value of b between 1 and 1.5 is recommended. In addition to three sediment distributions laws (Equation 5.70, 71 and 72) a few other equations have also been obtained by investigators such as Einstein, Hunt, Tanaka and Sugimoto, Navntoff, Willis and others. However, the most often used equation, because of its simplicity, is Eq. (5.70). Hence, it is desirable to consider this equation further. Equation (5.70) indicates that when y = D, C = 0 and when y = 0, C = ¥; both these boundary conditions are unrealistic. At the boundary the concentration cannot exceed sediment concentration of stationary bed, and at y = D there will be finite though small concentration of suspended load, especially for finer material. However, Eq. (5.70) gives realistic distribution in the remaining range of y. Some studies have been carried out about variation of Îs. The sediment transfer coefficient can be wo . Vanoni (1946) and Ismail (1952) found that for the fine ¶ C/¶ y sediment Îs is greater than Îm i.e. b is greater than unity while for coarse material Îs/Îm is less than unity. Raudkivi (1967) expresses Îs/Îm as obtained directly from Eq. (5.66) as Îs/Îm = Rs ls/Rl where Rs is correlation coefficient between C¢ and v¢, R is correlation coefficient between u¢ and v¢ and ls and l are mixing lengths for sediment and fluid respectively. Hence variation of Rs, R, ls and l with y will determine variation of b with y. Coleman (1970) analysed the Enoree river data on distribution of suspended sediment and studied variation of Îs / u* D with y/D and found that Îs/u*D increases with increase in y/D from 0 to about 0.25 and after which it remains essentially constant up to y /D = 1. Further for given y / D, Îs / D increases slightly with increase in wo/u*. Thus for Enoree river data Îs / D value for y / D = 0.90 increased from 0.06 to about 0.30 as wo/u* increased from 0.347 to 0.908. One can also study the effect of Zo or wo /u* on the distribution of C. When Zo is small i.e. when wo is small and/or u* is large, the concentration does not very much in the vertical. When Zo is large i.e. when wo is large and/or u* is small, concentration distribution will show considerable variation with y. In fact it can be seen that when Zo is less than 0.03, the concentration will be almost constant in the vertical (this happens for silts and clays). When Zo is greater than 5.0, suspension is insignificant. Figure 5.21 shows variation of C/Ca with (y – a)/(D – a) for a/D = 0.05 various value of Zo. Hydraulics of Alluvial Streams 1.0 0.9 0.0313 155 0.8 25 0.1 0.4 0.2 4.0 0 1. 0.3 0.5 y D a a 0.5 0 0.1 a = 0.05 D Zo= wo u * ko 0 01 Bottom 02 03 04 0.2 0.6 5 05 06 07 08 0.06 0.7 25 Fig. 5.21 Distribution of suspended load in a flow according to Eq. 5.70 The general validity of Eq. 5.70 has been shown by the experimental data collected by Vanoni, Vanoni and Namicos, Barton and Lin and others in laboratory flumes and data on rivers such as the Missouri and the Enoree. Such verification has also indicated that even though observed and computed distribution are similar, Z observed by the slope of C/Ca vs (D-y)/y curve is not equal to Zo computed as wo . This has been attributed to various reasons such as change in fall velocity due to turbulence and u* k o concentration, change in turbulence characteristics due to presence of bed-forms and concentration gradient, secondary circulation and variation in Karman constant. Integration of Sediment Distribution Equation (Eq. 5.70) It can be seen that the distribution of suspended sediment concentration in the vertical can be obtained if wo , still the u* k o reference concentration must be known. In this connection Karman anticipated that Ca would depend on size of sediment in suspension and shear stress to on the bed. Lane and Kalinske (1939) showed that for some American rivers and canals Ns/Nb depends on wo/u* where Ns is the concentration of material of fall velocity wo in suspension near the bed and Nb is the fraction of the same material found in the bed in percent by weight. Kalinske and Hsia (1945) found that Ns/Nb depends also on u* d/n. Einstein (1950) assumed that the bed-load transport rate qB iB of a given size range occurs in a bed layer of thickness 2d where d is the representative size of the range. The velocity at the edge of the layer one knows Zo and reference concentration Ca at “a”. Assuming Zo can be calculated as is 11.6 u¢ *. Hence the concentration of bed-load can be taken as C2d = 2.0 09 10 Relative concentration C/Ca q B iB ¢ 2d 11.6 u* a f = q B i B . This is 23.2 u* ¢ 156 Table 5.10 Variation of C2d with u2 * d ωo v River Morphology u*2 d according to Garde (1959) ωo v 10.0 0.06 14.7 0.40 20.0 2.0 40.0 2.0 5.0 0.01 8.0 0.02 C2d in % by weight considered as suspended load concentration at a = 2d. Garde (1959) using laboratory data of nearly uniform materials found that C2d in percent by weight depends on FG u Hw * o u* d v IJ or u d , see Table 5.10. K wv 2 * o Otherwise a single measurement of suspended load concentration at known elevation can be made. With known Ca and Zo Eq. 5.70 along with the velocity distribution law can be combined and integrated over the depth of flow to find the total amount of suspended load carried by the stream per unit width. As done by Einstein the logarithmic velocity distribution 30.2 y x u = 5.75 log u* d65 ¢ F GH I JK ...(5.73) can be used, or a simple relationship such as y u = um D F I H K n ...(5.74) can be used with free steam velocity um and n known. The suspended sediment transport rate qs can be obtained by integrating (Cudy) over the depth. The upper limit of integration is y = D. For lower limit of integration one can use y = 2d as suggested by Einstein (1950) which seems reasonable for plane bed. Brooks (1963) and, Harrison and Lidicker (1963) made the following suggestion for the lower limit of integration. They suggest that the largest of the following three be taken as lower limit. 1. a = 2 d as suggested by Einstein; 2. Value of “a” at which u = 0 according to logarithmic velocity distribution law, i.e., a = e– ko um/u* D 3. Value of a at which extrapolation of suspended sediment distribution will yield a limiting D concentration of 480 kg/m3. If Cmd is the concentration at mid depth. FG C IJ HC K md b 1/ zo = a D For details of calculation of suspended load by Einstein’s method (see Garde and Ranga Raju, 2000). Hydraulics of Alluvial Streams 157 Relations for Sediment Discharge In many morphological studies estimates of suspended load carried by the stream may be needed. Using Lane and Kalinske’s method (1941) it can be shown that qs = q Ca Pe15(wo/u*)A ...(5.75) where A = a/D where suspended load concentration is Ca, q is the water discharge per unit width and P depends on wo/u* and weakly on n/d1/6 where n is Manning’s n. The parameter P is given by P = e– 8.0 wo/ u* ...(5.76) Thus if a single measurement of Ca at ‘a’ is known along with q, D and u*, qs can be determined. Garde and Pande (1976) showed that for laboratory and field data, the following relationship holds good: qs gfq = 5.10 ´ 10 –5 FG u IJ Hw K * o 4 ...(5.77) By combining Kikkawa’s relation qs a D2S for u* >> wo and Chezy’s Equation q2 a D 3S one gets qs D a q2 which for small variation in depth of flow can be written as qs ~ q2 ...(5.78) Data on many rivers and canals indicate that the power of q varies between 1.92 and 2.20 indicating the validity of the above proportionality. Van Rijn (1984) has proposed that qs be estimated using the equation qs = gs D U Ca F ...(5.79) in which qs is in wt/width/time, Ca is the reference concentration at y = a given by Ca = 0.15 d50 T 1.5 3 a d* ...(5.80) Here “a” is taken to be equal to ks or obtained from the equation D whichever is greater. The roughness parameter ks is 100 R U = 5.75 log b + 6.25 u* ks Lastly the correction factor F in Eq. 5.79 depends on a/D and Z¢. where Z¢ is obtained from w os +f Z¢ = 0.4 b u* ...(5.81) for w 0.01 < os u* FG w IJ Hu K F w IJ FG C IJ £ 1.0, j = 2.5 G H u K HC K 2 b=1+ o * 0.8 0 .40 os * a b U | | | | V | | | | | W ...(5.81) 158 Here wos in Eq. 5.81 is for fall effective size ds and is given by ds = 1 + 0.011 (s9 – 1) (T – 25) d50 River Morphology and T = bt ¢ - t g . Variation of F with and a/D is shown in Fig. 5.22. o oc t oc 10 0 10 1 a7D =0 5 .1 F 10 2 0.0 0.0 1 10 3 0 1.0 2.0 Z¢ 3.0 4.0 5.0 Fig. 5.22 Variation of F with Z ¢ and a/D (Van Rijn 1984) 5.8 TOTAL LOAD TRANSPORT As mentioned already, the total load carried by the stream is the sum of suspended load and bed-load transported per unit time per unit width of channel. It does not include wash load which is not related to flow conditions; hence it is the bed material load. Suspended load and bed-load can be calculated for different fractions of the bed material and added to get the total load. Methods for such calculation are already discussed earlier in this chapter. For many morphological studies such refined calculations may not be needed. Therefore in this section only equations for computation of total are discussed which use only one representative size such as d50 or da. If all size fractions are moving these methods can also be used for fraction wise sediment transport; however the results are approximate because of coarser particles are not included in these methods. (1) Laursens Method (1958) Based on flume and some field data with sediment size ranging from 0.011 mm to 4.08 mm, Laursen proposed the relationship Hydraulics of Alluvial Streams 159 F d I LM t¢ - 1OP H DK N t Q 7/6 o oc C =F FG u IJ Hw K * o ...(5.82) where C is total concentration in percent by weight, toc is critical shear for median size d computed using Shields’ method and the function F (u*/wo) is obtained experimentally as below: u* wo 10-2 10-1 0.6 2.0 4.0 102 10 103 30 104 40 200 103 F FG u IJ Hw K * o 3.95 6.0 10 27 2 ´ 104 3.8 ´ 104 5.5 ´ 104 (2) Relation between qs/u* gs d and to / Dgs d Garde and Dattatri (1963) used data with size range 0.011 mm to 0.93 mm and obtained the relation qT 4.0 = 16 t* g s u* d ...(5.83) while Graf and Acaroglu (1968) used flume data of Gilbert, Guy et al. and obtained the relationship qT = 10.39 t*2.52 g s u* d ...(5.84) Here qT is total load transport ratio in weight/width/time. It is known that exponent of t* depends on mode of sediment transport. A lower value around 2 corresponds to bed-load transport whereas a higher valve indicates a substantial amount of suspended load in the total load. Hence variation in the exponent of t* in the above equations can be explained. (3) Bagnolds (1966) Approach Bagnold equated rate of doing work by transport of bed-load and suspended load to the available stream power toU and the transport efficiencies and obtained the following equation: qT = LM e + e b1 - e g u OP w Q d1 - r / r i N tan a to U s B s s B ...(5.85) f o Here u s is the average velocity of suspended load which can be taken equal to U, eB = bed-load transport efficiency whose value lies between 0.05 and 0.11, es = suspended load transport efficiency which is 0.015, tan a = coefficient of intergranular solid friction of bed material whose value varies between 0.375 and 0.75; and qT is in weight/width/time. The above equation is simplified to the form qT = d1 - r to U f LM e + 0.01 U OP w Q / r i N tan a B ...(5.85 a) s o 160 River Morphology (4) Engelund and Hansens Equation (1967) Engelund and Hansen postulated that when there are dunes on the bed, the energy required for moving a sediment particle over a dune height H can be equated to the drag forces acting on the particle during the same period. On the basis of this hypothesis they obtained the equation for sediment transport as where the friction facto f fT = 0.40 t*5/2 f = 2 g R S /U 2 U V W ...(5.86) The equation was obtained using flume data in the size range 0.10 mm to 0.93 mm with dunes, transition, standing waves or anti-dunes on the bed. It needs to be emphasized that even though the equation is derived for duned bed, it gives reasonably good results for other regime also, and subsequent verification has given good results. (5) Ackers and White (1973, 1980) Using the accepted premise that whereas bed-load transport is related to shear stress with respect to grain, total shear is responsible for sediment transport when suspended load predominates, Acker and White have obtained the equation Fu I H UK * c1 gfC D gs d = C2 where F1 F GG = GG H FG F - 1IJ HC K IF JJ G u G Dg d J G JG r K H 1 3 c1 * s f c4 ...(5.87) I JJ U 10 D J 32 log J d K 1 - c1 is the sediment mobility parameter, and the constant c1, c2, c3 and c4 are functions of dimensionless sediment size d* as given below For 1.0 £ d* £ 60.0 c1 = 1.0 – 0.56 log d* c2 = 2.86 log d* – (log d*)2 – 3.53 c3 = c4 = For 0.23 + 0.14 1/ 2 d* 9.66 + 1.34 d* d* > 60.0 c1 = 0, c2 = 0.025, c3 = 0.17, c4 = 1.5 Here C is the total load concentration by weight. Initially this equation was developed using flume data and limited amount of field data. However, later it was tested with lot more field data and found to give satisfactory results. Hydraulics of Alluvial Streams 161 (6) Yangs Equation (1972, 1973) Yang approached the problem of total load transport from the point of view of energy expenditure and related rate of sediment transport to dimensionless stream power US/wo log CT = A + B log FG US - US IJ Hw w K c o o ...(5.88) u* d u and * . Here USc is the critical stream power required to move the wo v sediment. His final equation is where A and B were related to log CT = 5.435 – 0.286 log wo d u – 0.457 log * + w v o o * o LM1.799 - 0.409 log w d - 0.314 log u w v N Ucr = wo where Ucr is the critical velocity for incipient motion and is to be calculated using the Eq. (5.90) 2.5 + 0.66 u* d - 0.06 log v U | | OP log FG US - U S IJ V | Q Hw w K | | W cr o o ...(5.89) F I H K for 0 < u* d < 70 v and Ucr = 2.05 wo for u* d > 70 v U | | V | | | W ...(5.90) Yang found that the above equation gives satisfactory results for flume data as well data from the field. (7) Shen and Hungs Equation (1971) Using regression analysis Shen and Hung started with the equation log CT = ao + a1 X + a2 X2 + a3 X3 where L US OP X=M Nw Q 0 .57 0 .32 o 0.0075 and is calculated in fps system of units. Their final equation is log CT = – 10704.5 + 324214.747X – 326309.6 X 2 + 109503.872 X 3 ...(5.91) Here CT is concentration of bed material in ppm by weight. This equation is based on over 500 data points out of which 63 correspond to river data of Middle Loup and Niobrara in USA and the rest to flume studies. 162 River Morphology (8) Effective Shear Stress Approach of Ranga Raju et al. (1981) Vittal et al. (1973) defined effective shear stress t t for ripple and duned bed as the shear stress required to give the same total load transport rate of the same sized material on plane bed. The effective shear stress is always less than the average shear stress of dune bed channel. Ranga Raju et al. (1981) after analysis of extensive data for dune bed channels found that the dimensionless effective shear stress tt is given by Dgs d t*t = t¢* FG t ¢ IJ Ht K o o –m ...(5.92) d 1/ 6 . Here m is given as 24 where t¢ o is computed using Manning’s equation with Stickler’s ns = m = 0 if and m = 0.2 u* £ 0.50 when suspended load is absent wo u* u – 0.10 when * > 0.50 wo wo When t*t is used in the sediment transport relationship, a unique relationship is obtained between fT = qT gs U | | V | | | W FG 1 IJ dr - r i H g d K rf 3 s f 1/ 2 and t*t for all bed-forms i.e. ripples, dunes, and plane bed. In the range of 0.05 £ t*t £ 1.0, this relationship can be expressed as 3 fT = 60 t ¢ * FG t ¢ IJ Ht K o o - 3m ...(5.93) This equation is based on 900 data points out of which 235 belonged to river and canal data. (9) Brownlies Equation (1981) On the basis of analysis of laboratory and field data covering a wide range of pertinent variables, Brownlie has proposed the following equation for concentration of bed material load C T in ppm by weight. CT = 7115 CF OP LM MM U - U PP g d PP MM Dr Q N cr s f 1.978 S 0.6601 F RI H dK - 0 .3301 ...(5.94) Hydraulics of Alluvial Streams 163 The coefficient CF for field data is 1.268 and for flume data it is unity. The critical velocity Ucr is given by Ucr 0 .529 = 4.596 t * S - 0 .1405 sg– 0.1606 c D gs d rf ...(5.95) Here sg is the geometric standard deviation of the bed material. (10) Karim-Kennedys Equation (1983) Unlike many other methods, Karim and Kennedy linked the problems of prediction of resistance and sediment transport in alluvial streams. Based on the analysis of 615 data points out of which about 100 points were for the Missouri river and rest from flume data, they obtained the following equation log gs LMF r - r I g d OP MNGH r JK PQ s f 3 f qT 1/ 2 = – 2.2786 + 2.9719 V1 + 0.2989 V3 V2 + 1.06 V1 V3 where V1 V3 Here d is taken as d50. F I G U JJ , V = log F D I = log G H dK GG Drg d JJ H K F u -u I = log G H D g d / r JK s 2 f * *c s f U | | | | | | V | | | | | | | W ...(5.96) Relative Accuracies of Different Total Load Equations Many attempts have been made to find the relative accuracy of the above methods of computing total load transport rates in alluvial streams. However, the difficulty in the interpretation of these results is that these investigators have used different sets of data and total number of data points are from flume studies as well as field data. The criteria used for assessing the accuracy of these equations using the same sets of data are usually the percent of data falling within ± 30 percent error lines, or percent of the data for which prediction of total load is within 0.750 to 1.5, 0.5 to 2.0, or 0.33 to 3.0 times the observed value. On the basis of such assessment the following general observations can be made. First, the equations proposed by Ackers and White, Yang, Ranga Raju et al. and Karim and Kennedy have used a large data base of laboratory and field data; hence these equations are likely to give more representative results than the other equations based on limited data. Further, even though Engelund and Hansen’s equation is based primarily on flume data, subsequent verification by other investigators have shown that it gives very satisfactory results. Coming to specific observations, ASCE Task Force (1971) applied 164 River Morphology various methods of total load estimation then available to sediment discharge measurements on the river Colorado at Taylor’s Ferry, and the Niobrara river near Cody (Nebraska) and found that Engelund and Hansens’s method gives much better accuracy than the other methods. Ackers and White (1980) used 1000 data points from flume studies and 260 points from field data and found that Ackers and White’s, and Engelund and Hansen’s equations give more accurate prediction than the other equations. Van Rijn (1983) used 500 data points from field data and found that consistently Engelund and Hansen’s equation gave best results; then came Ackers and White’s equation and then Yang’s. On the other hand Yang and Molinas (1982) reported good prediction by Yang’s equation for flume data. Hence it is felt that Yang’s equation is not very reliable for field conditions involving large depths, fine sediment, or both. Bechteler and Vetter (1989) used the data of six rivers on sediment transport rates; these were the Rhine, the Mississippi, the Rio Grande, and the Rio Puerto in New Mexico, the Five Mile Creek and the Niobrara. On these rivers the suspended load was measured and bed-load was estimated using Meyer Peter and Mûller equation. They found that among the 15 total load equations tested, Karim-Kennedy’s equation gave best results; then came Bagnold, Laursen and Yang’s equations. Nakato (1990) used data on the Sacramento river at gauging stations near Butte City and Colusa in California, U.S.A. where discharge, suspended sediment load and bed material data were available. He tested the accuracy of equations proposed by Ackers-White, Einstein-Brown, Engelund-Fredsoe, Engelund-Hansen, Inglis-Lacey, Karim, Meyer-Peter and Mûller, Van Rijn, Schoklitsch, Toffaleti and Yang. According to Nakato, the predictions are not at all satisfactory by most of these formulae and predictions would have been worst if computed depth and not measured depth were used. Considering all these observations it is prudent for the river morphologists to use three or four equations for determining the sediment transport rate in a given case and then make his own assessment on the basis of these results and his judgment. With the present state of knowledge, predictions within ± 50 percent error can be acceptable. References Ackers, P. and White, W.R. (1973) Sediment Transport: New Approach and Analysis. JHD, Proc. ASCE, Vol. 99, No. HY-11, pp. 2041-2060. Ackers, P and White, W.R. (1980) Bed Material Transport: A Theory for Total Load and its Verification. Proc. 1st Intl. Symposium on River Sedimentation, Beijing (China), March, B10–1-20. Alam, A.M.Z. and Kennedy, J.F. (1969) Friction Factors for Flow in Sand Bed Channels, JHD, Proc. ASCE, Vol. 95, No. 6, Nov. pp. 1973-1992. Allen, J.R.L. (1978) Computational Methods for Dune Time Lag: Calculations Using Stein’s Rule for Dune Height. Sedimentary Geology, Vol. 20, No. 1, ASCE Task Force on Bed-forms in Alluvial Channels: Nomenclature for Bed-forms in Alluvial Channels (1966). JHD, Proc. ASCE, Vol. 92, No. HY-3, May, pp. 51-64, Ashida, K. and Michiue, M. (1971) An Investigation of River Bed Degradation Downstream of a Dam. Proc. 14th Japanese Congress of IAHR, Paris, Vol. 3, pp. C30-1 to 9. Bagnold, R.A. (1966) An Approach to the Sediment Transport Problem from General Physics–USGS Professional Paper 422-1. Bechteler, W. and Vetter, M. (1989) Comparison of Existing Sediment Transport Models. 4th Intl. Symposium on River Sedimentation, Beijing (China) Vol. 1, 466-473. Bogardi, J.L. (1959) Sediment Transport in Alluvial Streams. Academiai Kiado, Budapest. 95p. Hydraulics of Alluvial Streams 165 Brooks, N.H. (1963) Calculation of Suspended Load Discharge from Velocity and Concentration Parameters. Proc. FIASC, USDA (Washington), Paper 23, pp. 229-237. Brownlie, W.R. (1981) Prediction of Flow Depth and Sediment Discharge in Open Channels. W.M. Keck Laboratory, Caltec (USA), Rep. No. KH-R-43A. Brownlie, W.R. (1983) Flow Depth in Sand-Bed Channels. JHE, Proc. ASCE, Vol. 109, No. HY-7, pp.959-990. Buffington, J.M. (1999) The Legend of A.F. Shields. JHE, Proc. ASCE, vol. 125, No.4, April, pp. 376-387. Carey, W.C. and Keller, M.D. (1957) Systematic Changes in the Beds of Alluvial Rivers. JHD, Proc. ASCE, Vol. 83, No. HY-4, Aug. pp. 1331-1 to 24 Chien, N. (1954) Meyer-Peter Formula for Bed-load Transport and Einstein’s Bed-load Function, IER, MRD Series No. 7. Colby, B.R. and Scott, C.H. (1965) Effect of Water Temperature on the Discharge of Bed Material. USGS Prof. Paper 462-G. Coleman, N.L. (1970) Flume Studies of the Sediment Transfer Coefficient. WRS, Vol. 6, No. 3, pp. 801-809. Daniel, P., Durand, R. and Condolios, E. (1953) Introduction a l’etude de la Saltation. La Houille Blanche, No. 2, Special B. David, J.K and Gangadhariah, T. (1983) The Effect of Nonuniformity in Grain Size on the Initiation of Grain Motion. Proc. 2nd Intl. Conference on River Sedimentation, Nanjing (China), B-16, pp. 434-439. Dawdy, D.R. (1963) Discontinuous Depth – Discharge Relationship for Sand – Channel Streams and Their Effect on Sediment Transport. Proc. FIASC, USDA (Washington), Paper No. 35, pp. 309-324. Du Boys, P. (1879) Le Rhone et les Rivers a Lit Affouillable Annales Des Ponts et Chaussees, Vol. 18, Series 5, pp. 141-195. Egiazaroff, I.V. (1965) Calculation of Non-uniform Sediment Concentrations. JHD, Proc. ASCE, Vol. 9, No.4, pp. 225-247. Einstein, H.A. and Barbarossa, N.L. (1952) River Channel Roughness. Trans. ASCE, Vol. 117, pp. 1121-1132. Einstein, H.A. (1942) Formulas for the Transportation of Bed-load. Trans. ASCE, Vol. 107, pp. 561-573. Einstein, H.A. (1950) Bed-load Function for Sediment Transportation in Open Channel Flows, USDA, Tech. Bull. No.1026. Engelund, F. (1966) Hydraulic Resistance of Alluvial Streams. JHD, Proc. ASCE, Vol. 92, No. HY-2, March pp. 315-326, and Closure of Paper in JHD, Proc. ASCE, Vol. 93, No. HY-4, July 1966. Engelund, F. and Hansen E. (1967) A Monograph on Sediment Transport in Alluvial Streams. Tensisk Forlag, Denmark. Fredsøe, J. (1975) The Friction Factor and Height - Length Relations in Flow Over a Dune Covered Bed. Institute of Hydrodynamics and Hyd. Engineering, Tech. University of Denmakr, Progress Report No. 37. Gallay, V.J. (1967) Observed Forms of Bed Roughness in an Unstable Gravel River. Proc. Of 12th Congress of IAHR, Fort Collins, U.S.A., Vol. 1, pp. 85-94. Garde, R.J. (1959) Total Sediment Transport in Alluvial Channels. Ph.D. Thesis submitted to Colorado State University, Fort Collins, USA. Garde, R.J. (1970) Initiation of Motion on a Hydrodynamically Rough Surface; Critical Velocity Approach. Jour. of Irrig. and Power of CBIP (India) Vol. 27, No. 3, July, pp. 271 to 282. 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ASCE, Vol. 109, No. 4. pp. 590-610 Harrison, A.S. and Lidicker, A.C. (1963) Computing Suspended Sand Loads from Field Measurements. Proc. FIASC, USDA (Washington), Paper 56, pp. 484-492. Hayashi, T. (1970) Formation of Dunes and Anti-dunes in Open Channels. JHD, Proc. ASCE, Vol. 96, No HY-2, Feb. pp. 357-366. Hayashi, T. and Ozaki, S. (1980) On the saltation Height and Step Lengths of Sediment particles in the Bed-Load Layer. 1st International Symposium on River Sedimentation. Nanjing (China) B13-1-10. Hayashi, T. Ozaki, S. and Ichibashi, I. (1980) Study of Bed-load Transport of Sediment Mixture. Proc. 24th Japanese Conference on Hydraulics. pp. 35-43. Hubbell, D.W. and Sayre, W.W. (1964) Sand Transport with Radioactive Tracers. JHD, Proc. ASCE, Vol. 90, HY3, May, pp. 39-68. Ismail, H.M. (1952) Turbulent Transfer Mechanism and Suspended Sediment in Closed Channels. Trans. ASCE, Vol. 117, pp. 409-434. Itakura, T., Yamaguchi, H. Shimuzu, Y., Kishi, T. and Kuroki, M. (1984) Observations on Bed Topography During the 1981 Flood in the Ishikari River. Jour. Of Hydro-Science and Hydraulic Engg., Japan Jackson II, R.G. (1975) Hierarchical Attributes and a Unifying Model of Bed-forms Composed of Cohesionless Material and Produced by Shearing Flow. Bull. Geo. Soc. of America, Vol. 86, Nov. pp 1523-1533, Jeffrey, H. (1929) On the Transport of Sediment in Stream . Proc. Cambridge Philosophical Society. Vol. 25, pt 3, pp. 272-276. JSCE (1974) Task Committee Report on Bed Configuration and Hydraulic Resistance of Alluvial Streams, Nov Kalinske, A.A. (1942) Criteria for Determining Sand Transport by Surface Creep and Saltation. Trans. AGU, Vol. 23, pt. 2, pp. 639-643. Kalinske, A.A. and Hsia, C.S. (1945) Study of Transportation of Fine Sediment by Flowing Water. Studies in Engg. Bull. No. 29, Univ. of Iowa, (USA), 30 p. Hydraulics of Alluvial Streams 167 Karim, M.F. and Kennedy, J.F. (1983) Computer – Based Predictors for Sediment Discharge and Friction Factor for Alluvial Streams. Proc. 2nd Intl. Symposium on River Sedimentation, Nanjing (China) A-18, Oct. pp. 219-233. Kennedy, J.F. (1969) The Formation of Sediment Ripples, Dunes and Antidunes. Annual Review of Fluid Mechanics, Vol. 1, pp. 147-168. Lane, E.W. and Kalinske, A.A. (1939) The Relation of Suspended to Bed material in Rivers. Trans. AGU, Vol. 20, pp. 637-641. Lane, E.W. and Kalinske, A.A. (1941) Engineering Calculations of Suspended Sediment. Trans. AGU, Vol. 22, pp. 603-607. Lane, E.W. and Eden, E.W. (1940) Sand Waves in Lower Mississippi River. Jour. Of Western Society of Engineers (USA), Vol. 45, No. 6, pp. 281-291. Langbein, W.B. (1942 Hydraulic Criteria for Sand Waves. Trans AGU, pp. 615-618. Laursen, E.M. (1958) The Total Sediment Load of Streams. JHD, Proc. ASCE, Vol. 84, No. HY-1, Feb., pp. 15301 to 36. Laursen, E.M. (1980) A Sediment Concentration Distribution Based on Revised Prandtl Mixing Theory. 1st Intl. Symposium on River Sedimentation, Beijing (China) – B-1 to 9. Li Zenru, Chen Yuaner and Zao Yun (1983) A Remark on Shields’ Diagram. Proc. 2nd Intl. Symposium on River Sedimentation, Nanjing (China) B-7, pp. 329-341. Lovera, F and Kennedy, J.F. (1969) Friction Factors for Flat Bed Flows in Sand Channels. JHD, Proc. ASCE, Vol. 95, No. HY-4, July, pp. 1227-1234. Mantz, P.A. (1992) Cohensionless, Fine Sediment Bed-forms in Shallow Flows. JHE, Proc. ASCE, Vol. 118, No. 5, May, pp. 743-764. Mantz, P.A. (1979) Incipient Transport of Fine Grains and Flakes by fluids–An Extended Shields’ Diagram. Closure of Discussion, JHD, Proc. ASCE, Vol. 106, HY-7, pp. 1173-1190. Mantz, P.A. (1983) Review of Laboratory Sediment Transport Research Using Fine Sediments. Proc. 2nd International Symposium on River Sedimentation, Nanjing (China), p. 532-557. Meyer-Peter, E. and Müller, R. (1948) Formulas for Bed–Load Transport. Proc. of 2nd Congress of IAHR, Stockholm, Paper No. 2, pp-39-64. Nakato, T. (1990) Tests of Selected Sediment–Transport Formulas–JHE, Proc. ASCE, Vol. 116, No. 3, March, pp. 362-379. Neill, C.R. (1968) Note on Initial Movement of Coarse Uniform Material. JHR, IAHR, Vol. 6, No. 2, pp-173-176. Patel, P.L. and Ranga Raju, K.G. (1996) Fraction wise Calculation of Bed-load Transport. JHR, Vol. 34, No. 3, pp. 363-379. Patel, P.L. and Ranga Raju, K.G. (1999) Critical Tractive Stress of Non-uniform Sediments, JHR, IAHR, Vol. 37, No. 1, pp. 39-58. Patil, B.M. (1997) Some Studies on Resistance to Flow in Alluvial Streams. ISH Jour. of Hyd. Engg., Vol. 3, No. 1, pp. 50-60. Ranga Raju, K.G. (1970) Resistance Relation for Alluvial Streams. La Houille Blanche, No. 1. Ranga Raju, K.G., Garde, R.J. and Bharadwaj, R.C. (1981) Total Load Transport in Alluvial channels, JHD, Proc. ASCE, Vol. 107, No. HY-2, p. 179-191. Raudkivi, A.J. 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ASCE, Vol. 108, No. HY-6, June, pp. 776-796. C H A P T E R 6 Hydraulic Geometry and Plan Forms of Alluvial Rivers 6.1 INTRODUCTION Chapter 5 was devoted to the discussion of the hydraulics of alluvial streams in which problems of incipient motion of uniform and non-uniform sediments, bed-forms, their characteristics and their effect on resistance and sediment transport, prediction of bed-forms, prediction of velocity, modes of transport of sediment and computation of bed-load, suspended load, and total load transport were discussed. In all these discussions the channels were assumed to be straight, the banks non-erodible, the channel shape nearly rectangular and the discharge constant. These conditions are seldom met in natural alluvial streams. Hence this chapter is devoted to the discussion of alluvial streams in which discharge, channel width and plan-form are varying in time and/or space. The following aspects are discussed in this chapter. Stable Channels Carrying Sediment Channels flowing through sandy material with non-cohesive bed and banks or banks with some cohesion are used to carry water for irrigation. These channels carry nearly constant discharge and carry known but small sediment load. Further their plan-form is imposed and does not change. British engineers proposed the design method for such channels in the Indian subcontinent in the early twentieth century. Further work on this was done in U.S.A. and other countries and design methods have been proposed using resistance and transport relationships. Such analysis has made possible design of channels carrying known discharge and sediment load. Hydraulic Geometry of Alluvial Streams Taking clue from stable channel relationships, attempts were made to determine relationships for width, depth, area and slope of alluvial streams assuming a constant hypothetical flow, called bankful 170 River Morphology discharge or dominant discharge or mean annual discharge, as being responsible for shaping the channel. Some optimisation techniques have also been used to determine the hydraulic geometry of channels and streams; these are discussed in brief. Lastly, relationships for hydraulic geometry obtained by using the method of dimensional analysis are discussed. Flow in Rigid-bed and Alluvial Channel Bends To understand the flow in meandering stream it is desirable to know the characteristics of flow in bends with rigid bed and sides as well as with alluvial boundaries. The aspects discussed here include velocity distribution in the longitudinal and radial directions, growth and decay of secondary circulation, superelevation, head loss in bends, shear distribution near curved stream bed and bed topography. Braiding and Meandering The two most important plan-forms, namely braiding and meandering are discussed in detail. The aspects regarding braiding that are dealt with include mechanism of braid formation, causes of braiding, types of bars in braided streams, and braiding parameters, which quantify the extent of braiding. As regards meandering attention is focussed on change from pool and riffle sequence in straight channel to that of a meandering stream, meander characteristics, processes governing meander-bend migration, and meander theories. The discussion is concluded with a discussion on the criteria for plan-forms. 6.2 STABLE CHANNELS CARRYING SEDIMENT The efforts of British engineers working in India during late 19th and early 20th centuries were aimed at obtaining dimensions of the channel and the velocity of flow which will yield non-silting and nondepositing sections of alluvial channels carrying a given discharge and sediment load, and flowing through non-cohesive sandy material. Traditionally these irrigation canals taking off from the head works are provided with elaborate arrangements for sediment removal at the head works and/or in the canals so that they carried a limited amount of bed material load (of the order of 100 to 500 ppm by weight). On the basis of work done by Kennedy, Lindley, Woods and Lacey himself, Lacey (1930) found that the area, perimeter, hydraulic radius, velocity and slope of such regime channels are uniquely determined by the design discharge Q in m3/s and size of the bed material d in mm. Specifically Lacey obtained the following equations, U | | | F QI | R = 0.47 G J | HfK V | U = 0.439 f Q | 0.0003 f | S= | Q | and f = 1.76 d W P = 4.75 Q Q5 6 A = 2.28 1 3 f1 1 13 1 13 16 13 1 16 1 ...(6.1) Hydraulic Geometry and Plan Forms of Alluvial Rivers 171 where cross sectional area A, perimeter P, hydraulic radius R and velocity U are in metric units. Here f1 is known as Lacey’s silt factor and d is the median size of bed material in mm. Out of the first four equations only three are independent and the fourth can be obtained there from. Since 1930 several investigators have attempted to modify or improve these relations; however Eq. (6.1) are more widely used. Some attempts have been made to estimate the sediment load carried by Lacey channels. Ahmad and Rahman (1962) using flume data have proposed the relation, 1000 q2 3S =1+5 C23 2 w1 o ...(6.2) where q is discharge per unit width in ft2/s, wo is the fall velocity of sediment in ft/s and C is bed material concentration in ppm by weight. Similarly, Dixon and Westfall (see Garde and Ranga Raju, 2000) have used flume, canal and river data to obtain the bed material transport rate as qT = 0.0011 U4 wo ...(6.3) Blench (1957) argued that the effect of bed and bank materials must be taken into account separately in determining the dimensions of stable channel and its slope. Hence, Blench introduced bed factor Fb and side factor Fs and defined these as Fb = U2 D U3 W ...(6.4) Fs = in which A = WD and W is mean width of the channel. The slope equation proposed by him is U2 = 3.63 (UW/n)0.25 g DS ...(6.5) The inclusion of Reynolds number UW/n was justified saying walls acted as smooth boundary; however this reasoning does not seem to be tenable. Equation (6.4) can be expressed in terms of Q, Fs and Fb as W= Fb 12 Fs Q D= FG H Fs I F J K b 13 Q1 3 S= Fb5 6 Fs1 2 n1 4 1.91 g Q1 6 U | | | | V | | | | W (a) (b) ...(6.6) (c) 172 in SI units. The bed and side factors are given by Fbo = 1.9 d mm Fb = Fbo (1 + 0.012 C B) and Fs = 0.10 for loam of very slight cohesion = 0.20 for loam of medium cohesion = 0.30 for loam of high cohesion River Morphology ...(6.7) Here, Fbo is the bed factor with vanishing bed-load and C B is the bed-load transport rate in ppm by weight. For sides made of rounded gravel embedded in fines, Blench proposed that Fs be found by the equation Fs = d 4 ...(6.8) where d is in mm. Finally, he has proposed an equation alternative to Eq. 6.6 (c) which includes bed-load concentration; however, this equation is not used much. Simons (1957), Simons and Albertson (1963) analysed data from Punjab and Sind canals along with canals in USA and found that if the perimeter P, area A and hydraulic radius R are expressed as P, A, R = mQn, the values of m and n depend on the nature of bed and bank material, thus supporting the contention of Blench that nature of bed and bank material plays an important role in determining the hydraulic geometry of stable channels. The values of m and n obtained by Simons and Albertson (1963) are given in Table - 6.1. Table 6.1 Category P m n m n m n Regime equations of Simons and Albertson, P, A, R = mQ n Sand bed and cohesive banks 4.74 0.512 2.25 0.873 0.475 0.361 Sand bed and banks 6.33 0.512 2.57 0.873 0.403 0.361 Cohesive bed and banks 4.63 0.512 2.25 0.873 0.557 0.361 Coarse non-cohesive material 3.44 0.512 0.939 0.873 0.273 0.361 A R Thus, canals flowing through sandy bed and cohesive banks, and cohesive bed and banks will have smaller perimeter, smaller area and greater depth (or hydraulic radius) than canals flowing through sandy bed and banks for the same discharge. For the first three categories, they also suggested Blench type slope equations, namely Hydraulic Geometry and Plan Forms of Alluvial Rivers 173 Sand bed and banks U2 = 0.324 (UW/n)0.370 gDS U2 = 0.525 (UW/n)0.370 gDS U2 = 0.885 (UW/n)0.370 gDS Sand bed and cohesive banks Cohesive bed and banks U | | | | V | | | | W 32 ...(6.9) Gupta (1967) and Kondap (1977) used dimensional analysis and wrote Ws A , d d2 F G and S = f G GG d H 2 Q g d , C, and n Dg s d rf 12 I JJ JJ K where Ws is water surface width and C is total load concentration. It was further found out from analysis of field data that Ws A and 2 are insensitive to variation of C. Hence, using Sind and Punjab canal data d d as also the data of US canals collected by Simons, Kondap (1977) proposed the following equations: 12 Ws = 0.212 g d FG H A d2 F GG = 2.21 GG d H 2 F GG d I J G n K GH d I JJ Q Dg d J r J K 32 0 .231 0 .855 s f 1.5 2 I JJ Q Dg d J r J K s f 0 . 458 ...(6.10) ...(6.11) As regards the slope he suggests the following equation S Dg s g f F = 0.0423 G H U Dg s d r f I FdI JK GH y JK 1 1. 095 ...(6.12) where y1 = Ws . Chang (1980) realized that for designing a stable channel to carry a given discharge Q, A and given sediment transport rate QT and flowing through non-cohesive sediment of size d, one has the 174 River Morphology resistance law and the sediment transport law to determine the width, depth and slope, even if one assumes a trapezoidal channel with given side slope Z:1. Since there are three unknowns and only two equations, Chang imposed the condition that the channel adjusts the width, depth and slope in such a manner that the stream power per unit length of channel ( Qgf S) is minimum. On this basis he has proposed the algorithm shown in Fig. 6.1 for the computation of W, D, S, for known Q, QT, d and trapezoidal channel of known side slope Z: 1. Data : Q, QT, d Z:1 Assume B Assume D Use sediment transport law and compute S Use resistance law and compute U and then Qc No IsQ Q= ?? Is =Q Q cc Yes minimum ? ? Is Is SSminimum Yes Print B, D, S No Fig. 6.1 Chang’s algorithm for design of stable channel (Chang 1980) Hydraulic Geometry and Plan Forms of Alluvial Rivers 175 White et al. (1981) have shown that optimizing (maximizing) the sediment transport rate QT for given Q, S, d and Z yields the same results as those obtained by minimizing S for given Q, QT, d and Z. Thus, it seems possible to use optimization technique for channel design. However, White et al. found that for given QT, the ratio of computed slope to observed slope ratio for existing stable channels varied between 1 and 3 whereas predicted depths and widths showed better agreement. Hence, according to them, in general the predicted results are not accurate enough for using this method in those cases where empirical equations of better accuracy can be used. However, this algorithm is of great value in the design of channels which carry large quantity of sediment load and for which Lacey type equations cannot be used. In fact Chang (1980, 1988) used the algorithm given in Fig. 6.1 with side slopes 2:1, resistance law proposed by Lacey, viz. U= 1.346 1/4 1/2 1/2 D R S Na ...(6.13) where f1 = 1.76 d , Na = 0.0225 f11/4, D is the mean depth of flow, and DuBoys bed-load equation to prepare Q vs. S/d1/2 curves for different values of Ws and D; this is shown in Fig. 6.2. Here d expressed is in mm and other quantities are in fps units. He also prepared a graph between S/d1/2 and Q with QT/Q as the third variable as shown in Fig. 6.3. Here QT has been calculated using Engelund-Hansen formula. It can be seen from Fig. 6.3 that in Sind, Punjab and Simon’s canal data QT varies from 50 to about 200 Q ppm. Chang also found that Engelund-Hansen formula produced better conformity with measured sediment loads than DuBoys or Einstein-Brown formula. He also compared the computed and the observed values of Ws and Ws/D for these canal data and found good agreement. Chang has mentioned the fact, commonly used by design engineers that in sandy material for canal to be stable, Froude number should be kept between 0.2 and 0.3 and quoted the flowing relationship between Fr and R/d Fig. 6.2 Variation of B and D with Q and S/d1/2 for stable channels (Chang 1980) 176 River Morphology Fig. 6.3 Variation QT /Q with Q and S/d1/2 for stable channels (Chang 1980) proposed by Athauallah and Simons R Fr = 4.388 F I H dK - 0 .31 ...(6.14) 6.3 HYDRAULIC GEOMETRY OF ALLUVIAL STREAMS Dominant Discharge Use of a constant hypothetical discharge in the study of hydraulic geometry of streams was more or less simultaneously done in India, Europe and USA so that simple relationships could be developed for P, A, R or D and U, which are similar to those for stable canals. In following this approach one must bear in mind some important differences between flow in stable canals and alluvial or gravel-bed rivers, because of which this extension has to be done cautiously. These are: 1. Wide variation in the discharge and sediment load carried by the streams and very large difference between their maximum and minimum values. On the other hand canals carry a fairly constant discharge with limited variation in sediment load. 2. Large variation in the size of bed and bank material is found in streams; as a result armouring can take place in streams having large standard deviation of bed material. 3. Whereas stable canals have more or less regular shape, river cross sections are invariably irregular. 4. The plan-form of stable canals is fixed whereas in streams it changes along the length. 5. The slope of the river as well as the characteristic size of bed material change along the length, whereas canal sections are designed for a constant Q, S and d. In spite of these limitations river channel dimensions seem to be adjusted by erosion and deposition so that the channel can contain all but the highest flows it experiences. Hence, it seems reasonable to explore if one or more geometrical characteristics of river cross-sections can be related to a hypothetical constant discharge. Hydraulic Geometry and Plan Forms of Alluvial Rivers 177 Bankful and other Characteristic Discharges This concept of a constant discharge has been used widely to describe the river regime. In order to make stable canal formulae applicable to rivers, Inglis (1947) introduced the concept of dominant discharge; according to him, “there is the dominant discharge and its associated charge and gradient to which the river channel returns annually. At this discharge the equilibrium is most closely approached and tendency to change is least. This condition may be regarded as an integrated effect of all varying conditions over a long period of time”. Expressed differently, dominant discharge is a hypothetical constant discharge which would produce the same result (average width or meander dimensions) as caused by the actual varying discharge. Intuitively he assumed this discharge to be bankful discharge for Indian rivers in plains and that it could be used in relations for width, depth, meander width etc. He further found that for Indian rivers in the plains of North India, bankful discharge is ½ to ¾th of the flood discharge. While studying the hydraulic geometry of rivers in the Great Plains of USA, Leopold and Maddock (1953) used the mean annual discharge Qma and found that this discharge had a frequency of twenty five percent, i.e., for 91 days in a year the discharge was equal to or greater than Qma. Nixon (1959) studied the bankful discharges of 22 non-tidal rivers in England and Wales to explore the possibility of obtaining Lacey-type equations for rivers in U.K. Comparison of bankful discharge of 22 rivers at 29 sites led Nixon to conclude that bankful discharge is such a discharge, which is equaled or exceeded 0.60 percent of the time. Further this percentage is not dependent on the magnitude of the discharge. This conclusion was based on the data for two to five year period except for the river Thames for which 72-year data were available. It may also be mentioned that percentage of time varied from 2.91 to 0.10 in individual cases. Williams (1978) has discussed the merits and demerits of various methods of determining the bankful stage and corresponding discharge obtained there from. Williams distinguishes between the active flood plain where water spreads every year during the flood and sediment deposition occurs, and the inactive flood plain or terrace which is part of the valley flat which is submerged only during the rare floods and where sediment deposition does not occur. Among eleven methods available in literature which are proposed by geologists and geomorphologists, he prefers the following three methods for the determination of bankful stage. 1. Average elevation of active flood plain; 2. If elevation vs. W/D ratio is studied, the elevation at which this ratio is minimum; 3. If log-log plots of area of cross-section versus width are prepared, the elevation at which the slope of the curve suddenly changes. Once the bankful stage is determined, the corresponding discharge can be determined from the rating curve at the nearby gauging station. Alternatively, knowing Q vs A, W or D graphs at a station, one can find the bankful discharge for the known depth. The method would be to use Manning’s equation for a reach after averaging out the hydraulic parameters at the bankful stage at two or more cross-sections and choosing an appropriate value of n. He also studied the flow frequency duration curves at the gauging stations and determined the frequency of bankful discharge. On the basis of analysis of data at 28 gauging sites in Western USA with 233 data points he found that determining the bankful discharge Qb at a given site gives inaccurate results and hence this method should not be used; instead bankful discharge in a given reach is more meaningful. Further, rating curve approach is recommended. He has proposed the equation 178 1.23 0 .31 S Qb = 4.0 Ab River Morphology ...(6.15) 2 3 where Ab is cross-sectional area at bankful stage in m and Qb is the bankful discharge in m /s. This equation is based on the following ranges of Ab, S and Qb Ab = 0.70 m2 to 8510 m2, S = 0.000 041 to 0.081, Qb = 0.50 m3/s to 28 320 m3/s This equation gives an average standard error of 41 percent in Qb. Similar equation was also proposed by Riggs (1976). 1. 295 0 .316 S Qb = 3.39 Ab ...(6.16) which was found to give larger error than Eq. (6.15). As regards frequency or return period for bankful discharge for active flood plain stations, Williams found the average return period mode of about 1.5 years on the annual maximum series; however because of the wide range (1 to 32) years, the spread and skewness of the distribution, the average value loses its significance. Hence, he did not recommend this method for the determination of bankful discharge. For record it may be mentioned that the recommended values of return periods for bankful discharge by some investigators are Nixon (1959) Leopold et al. (1964) and Carlson (1965) Dury (1973) 2.2 yrs 1.5 yrs 1.58 yrs Hence, the only two characteristic discharges that seem to be preferred for studying bankful geometry are the mean annual discharge Qma and the bankful discharge Qb; the relationship between the two was graphically represented by Chang (1979) using the data of Schumm and Carlson. Garde et al. (2002) plotted the data of Kellerhals et al. and obtained the relationship (see Fig. 6.4) 0.843 Qb = 17.253 Qma ...(6.17) 10 10 10 10 Qb 10 10 7 6 5 Qb = 17.253 Qma 0. 8 43 4 3 2 Carlson Schumm Kellerhals Best fit line 10 10 10 2 10 3 10 Qma 4 10 5 10 6 Fig. 6.4 Relation between Qb and Qma Hydraulic Geometry and Plan Forms of Alluvial Rivers 179 Here Qb and Qma are in m3/s. In studying river bed variation in transient flows in alluvial streams one would prefer to use a characteristic discharge related to sediment transport or bed level variation rather than using bankful discharge. This concept has been used by Schaffernak (1950) who introduced the term bed-generative discharge which he defined as the discharge that transports the largest volume of coarse material. Figure 6.5 illustrates how this discharge is computed; Fig. 6.5 (a) shows the frequency-discharge curve while Fig. 6.5 (b) is the sediment discharge vs. water discharge relationship for the stream. In Fig. 6.5 (c) the abscissa is obtained by multiplying the frequency DF of a particular discharge by the corresponding sediment discharge rate Qs while the ordinate is the discharge. The discharge that gives the maximum Qs DF is the bed generative discharge. (a) (b) (c) Q Q Q DF Qs Qs DF Fig. 6.5 Determination of bed generative discharge Komura (1969) defines the dominant discharge as that constant discharge which will transport the same quantity of sediment load as is transported by the varying discharge during the same period or year. Hence, Qd = N S1 QTi Qi N S1 QTi ...(6.18) where N is the total number of mean daily discharges, Qi and QTi are the corresponding total sediment discharges. According to Komura in the above equation mean monthly discharges be used if flood has a long duration, and mean daily discharge or maximum monthly discharge if flood duration is small. Further, if one utilizes the empirical relation between discharge and sediment load in the form QT = a Qb, the above equation reduces to Qd = N S1 Qi(1 + b ) N S1 Qib ...(6.19) NEDCO (1959), defines the dominant depth Dd as Dd = z z O T DQT dt T ...(6.20) QT dt O where D is the depth at sediment transport rate QT. 180 River Morphology Enough information is not available about the relationship between Qb and Qd or bed generative discharge. Gandolfo (1955) found that the bed generative discharge is greater than Qd corresponding to average sediment transport rate and that the latter is greater than Qma. The relationship between Qb and Qma is already given in Fig. 6.4. 6.4 EMPIRICAL RELATIONSHIPS FOR HYDRAULIC GEOMETRY W = a Qb D = c Qf U = k Qm Qs = p Qj Leopold and Maddock (1953) explored the applicability of equations of the type U | | V | | | W ...(6.21) at a station for variable discharge, and along the stream length for mean annual discharge Qma, by using data from American rivers in Great Plains and South-West. Since Q = WDU it follows that for both these types of relationships ack = 1 and b + f + m = 1. For twenty cross-sections representing a variety of rivers Leopold and Maddock found that “at a station” the average values of b, f and m were b = 0.26, f = 0.40 and m = 0.34. Since the depth increases faster than the width, the (width/depth) ratio decreases with increase in discharge. The relationship between suspended load discharge Qs and Q at a station showed greater scatter, with j values ranging between two and three. Since j is greater than unity, it is obvious that at a station Qs/Q i.e., suspended sediment concentration increases as Q increases. While relating width, depth and velocity to discharge along the stream, they preferred to use mean annual discharge Qma which had an average frequency of 25 percent, i.e., it is equaled or exceeded one day in every four days over a long period. With this discharge Qma in Eq. (6.21), average values of b, f and m were b = 0.50, f = 0.40 and m = 0.30. It may be noted that values of b and f and m agree fairly well with those obtained by Lacey. In as much as the percentage of land not contributing sediment increases in the downstream direction and percentage of land contributing water discharge increases in downstream direction, one would expect Qs/Q to decrease in the downstream direction, as concluded by Rubey (1933). However, individual rivers may differ in this respect. Experience has shown that “at a station” relationships are significantly affected by the climatic changes, namely depending on whether the stream is perennial, ephemeral or in arid or semi-arid region. Nixon (1959) while studying the hydraulic geometry of rivers in England and Wales found that the bankful discharge Qb is equaled or exceeded 0.6 percent of the time i.e., on the average about two days in a year. He further found that in the equation P = W = aQb the coefficient “a” depends on the frequency of discharge used, see Table 6.2. Table 6.2 Dependence of constant of proportionality in W = aQb on the frequency of discharge (Nixon 1959) Percentage frequency “a” in W = aQb in SI units 30 8.87 20 7.61 10 6.16 5 5.23 3.7 4.84 0.6 3.00 Hydraulic Geometry and Plan Forms of Alluvial Rivers 181 Nixon also mentioned that if the mean annual discharge were used, the constant in the above equation would be 7.66 which is not much different from that for 20 percent frequency. For rivers in England and Wales, Nixon found that 1/ 2 W = 1.65 Qb 1/ 3 D = 0.545 Qb 1/ 6 U = 1.112 Qb 3/ 4 Qs = 0.9 Qb U | | V | | | W ...(6.22) in SI units for Qb ranging from 10 m3/s to 500 m3/s. After Leopold and Maddock as well as Nixon’s works were published, a number of investigators in U.S.A., U.K., Norway, Malaysia, Brazil and Puerto Rico applied the same technique using either bankful discharge or discharge of certain frequency and obtained the exponents b, f, m. Similar studies were also conducted in U.S.A., U.K. and other countries on gravel-bed rivers (see Chapter VII). Langbein (1964) considered streams in humid regions in which the discharge increases in the downstream direction. He stipulated that along with the three equations of Leopold and Maddock for W, D and U two additional equations can be considered as S a Qz and Manning’s n so that and n a Qy U | V | W ...(6.23) b+f+m=1 m= 2 z f+ –y 3 2 since in the downstream direction stream would satisfy continuity and Manning equation. In addition, he stipulated that (i) streams have a tendency for uniform distribution of work per unit width along the channel, and (ii) the rate of work in the whole system is also as small as possible. On these premises he showed that S= or z= W Q2 b –1 2 U | V | W ...(6.24) Further, to fulfill the conditions mentioned above he argued that | b2 + f 2 + m2 + z2 + (1 + z 2 )| should be minimum. This condition is satisfied by the following values. b = 0.53, f = 0.37, m = 0.10, z = – 0.73 These values of b. f and m agree fairly well with those obtained by Leopold and Maddock. Some support to this approach of studying the hydraulic geometry of rivers was provided by Smith (1974) who represented a straight stream channel as a surface U | | V | | W 182 y = y (x, z, t) River Morphology ...(6.25) subjected to the following three conditions: (i) sediment mass is conserved during the transport; (ii) channel has the form just sufficient to carry the total discharge of water given the law of water movement; and (iii) the channel has the form just sufficient to carry its total sediment discharge given the sediment transport law. Smith also assumed that the channel is carried in non-cohesive material and that one has the freedom to choose a time scale for which the channel has a steady state form. He further assumed that Q and Qs increase linearly with x, and lateral sediment transport rate is equal to longitudinal transport rate multiplied by ¶ D . He used Manning’s equation for flow velocity and ¶z sediment transport equation of the form qs = const q2 S2 ...(6.26) Rather than solving the system of equations, Smith tried to find out the values of the exponents which will satisfy all the imposed conditions. He thus obtained 7 /11 3 /11 1/ 11 - 2 / 11 , D ~ Qb , U ~ Qb and S ~ Qb W ~ Qb ...(6.27) in the downstream direction. These values are comparable to those obtained by Leopold and Maddock, and by Langbein. In order to study the variation of the exponents b, f and m. Park (1977) analysed data from 139 “at a station” sites and data from 72 “in the downstream” direction. The ranges of variation in b, f and m obtained by Park are listed below in Table 6.3. In the analysis of data in downstream direction Q used is the observed or estimated Qb or Q with a return period of 2.33 years. Table 6.3 indicates that values of b, f and m vary over a wide range and hence for a given stream these values can be very different from those given by the theory. To study further the simultaneous variations of these exponents, Park plotted b, f and m on tri-axial diagram with one side for each exponent. Typical tri-axial diagrams for at a station and downstream exponents in different climatic conditions are shown in Figs. 6.6 and 6.7. The climatic factors did not seem to affect “at a station” exponents. Hence, Park suggested that local factors such as the composition of bank material, differences between braiding and meandering reaches, between pools and riffle sections, flow magnitude, suspended load and channel migration might be responsible for such variations. Table 6.3 Summary of distribution characteristics of hydraulic geometry exponents data (Park 1977) At a station; N = 139 Exponent Range Modal class Theory (1) Theory (2) * ** In downstream direction; N = 72 m 0.07 – 0.71 0.40 – 0.45 0.35 B 0.20 – 0.59 0.01 – 0.10 0.23 f 0.06 – 0.73 0.30 – 0.40 0.42 b 0.03 – 0.89 0.40 – 0.50 0.55 0.68 f 0.09 – 0.70 0.30 – 0.40 0.36 0.30 m 0.51 – 0.75 0.10 – 0.2 0.09 0.90 (1)* Leopold and Langbein (2)** Smith Hydraulic Geometry and Plan Forms of Alluvial Rivers 183 Fig. 6.6 Tri-axial graph of at-a-station hydraulic geometry exponents (Park 1977) As regards the “downstream” data, Park found that for perennial streams in semi-arid regions the exponents are similar to those found in humid temperate climate, whereas ephemeral streams in semiarid region tend to have lower b and high f exponents. In addition local factors such as lithology, variation in bank erodibility, channel instability, coarser bed material, and the downstream variation in slope are also responsible for the variation in b, f and m. On the basis of this study of tri-axial diagrams under various environments, Park casts doubt on the use of mean values of the samples of exponents to characterise the hydraulic geometry of streams in particular areas, and suggests that quoting mean values gives a misleading impression. While Park concentrated on the effect of environmental factors on b – f – m variation, Rhodes (1977, 1987) concentrated on the effect of hydraulic factors. Some recent studies do not endorse Leopold and Maddock’s conclusion that this is a rational or even a good way of describing cross-sectional channel adjustment. Some have also questioned whether log-linear model of hydraulic geometry is either appropriate or meaningful. However, the greatest 184 River Morphology Fig. 6.7 Tri-axial graph of down stream hydraulic geometry exponents drawback seems to be the non-inclusion of sediment size, difference in specific weights of sediment and water, and channel slope from the downstream relationships. However, in spite of these limitations investigators continue to use this analysis as a basis, since in regional and climatically homogenous regions they may give good approximation of hydraulic geometry. Studies of Leopold and Maddock, and Langbein indicate that for downstream geometry m = 0.05 to 0.10 indicating that velocity at bankful stage or for mean annual discharge varies very slowly in the downstream direction. Leopold, Wolman and Miller (1964) show constancy of U for 50 year and 5 year floods in Yellow Stone basin, see Fig. 6.8. Some studies indicate that constant velocity along the length of the stream is attained at a stage between mean annual discharge and modest over-bank stage of 5 year flood (Chorley 1969). This needs further study in view of the commonly accepted view that stream velocity decreases as it flows from mountains to the plains. Some other efforts to include additional variables to describe the hydraulic geometry, include the investigations of Schumm (1977) who analyzed the data on channel dimensions, mean annual discharge Hydraulic Geometry and Plan Forms of Alluvial Rivers Q50 Discharge cfs 10 185 Mean velocity in ft/s 5 Q5 Discharge cfs 10 5 1,000 10,000 100,000 Discharge in cfs 1,000,000 Fig. 6.8 Variation of average velocity at Q5 and Q50 in Yellow stone river basin and down stream (Leopold et al. 1984) Qma and bed and bank sediments at 36 cross-sections from semi-arid to humid regions in the Great Plains of U.S.A. and Plains in New South Wales in Australia in sand-bed streams. Schumm indicated that (width/depth) ratio in these channels was related to the percentage of silt-clay M in the perimeter of channel (see Fig. 6.9), and obtained the equations W/D = 255 M–1.08 0.38 W = 0.38 Qma / M0.39 0.29 D = 0.6 Qma M0.342 U | | V | | W ...(6.28) Width/Depth Ratio (F) Fig. 6.9 Variation of width to depth ratio with M (Schumm 1977) 186 River Morphology where Q is expressed in ft3/s and D and W in ft. Gregory and his associates (see Fergusson 1981) studied bankful dimensions vis-à-vis the catchment area in humid areas and found that for catchment area A between 0.1 and 4.0 km2, W ~ A0.32, D ~ A0.16 and channel capacity ~ A0.48. Hey (1982), and Hey and Thorne (1986) while analyzing gravel-bed river data from U.K. related width and depth to bankful discharge, d50 and the sediment transport rate Qs. These types of relationships developed in different countries are listed by Wharton (1995). Since in the relationships discussed above some have used bankful discharge and some mean annual discharge, it is difficult to compare their results. Further, in studying the transient flows discharge needs to be replaced by some hypothetical constant discharge related to sediment transport or riverbed variation. Lastly, the relationships developed above do not contain other variables such as slope, sediment size, Dgs and are not dimensionally homogenous. These aspects are discussed in the next two sections. 6.5 NON-DIMENSIONAL RELATIONS FOR HYDRAULIC GEOMETRY Some attempts have been made to obtain non-dimensional form of equations for W, D and U or A. Thus Rybkin in 1947 (see Goncharov 1962) used the data from the upper Volga and the Oka basins and proposed the following equations W = a1 D = a2 U = a3 FG w IJ LM Q FG g S IJ OP H g S K MN w H w K PQ FG w IJ LM Q FG g S IJ OP H g S K MN w H w K PQ FG w IJ LM Q FG g S IJ OP H g S K MN w H w K PQ 2 o b o 2 o 2 o b o 2 o 2 o b o 2 o 2 a1 2 a2 2 a3 where wo is the fall velocity of bed material and a1 , a2 and a3 as well as a1, a2 and a3 are constants. In 1950 Velikanov proposed the following form of the equations U | | | | | | V | | | | | | W ...(6.29) W Qb = a1 2 d d gdS D = a2 d b F GH F GH d 2 I JK I Q gd S J K a1 a2 U | | V | | | W ...(6.30) According to his analysis a1 = 0.50 to 0.53 and a2 = 0.25 to 0.27. Ananian (1961) obtained a1 = 2.70 and a1 = 0.42. Mukhamedov and Ismaghilov (1969) analysed the data from the middle and lower reaches of the Amu Darya and obtained the following equations for W and D Hydraulic Geometry and Plan Forms of Alluvial Rivers 187 Q gs WS = 3.8 2 b Dg s d d gd S g DS = 0.095 2 Dg s d d LM MN and LM MN F S I OP GH Dg / g JK P Q F S I Q gdS G H Dg / g JK s f b s f 0 .48 5 / 2 0.48 5 / 2 0.28 OP PQ U | | | V | | | W ...(6.31) which can be reduced to a simpler form as W Qb = 3.8 2 d d gd S I F S I JK GH Dg / g JK F Q I F S I D = 0.095 G d H d g d S JK GH Dg / g JK F GH s f 0 .08 b 2 s f 0.20 - 0 .30 U | | V | | | W ...(6.32) These equations have not been tested using data from other countries. Garde et al. (2002) have analyzed a large volume of data on the hydraulic geometry of rivers from different countries given by Leopold and Wolman (1957), Schumm (1969) Chitale (1970) and Kellerhals et al. (1972). The ranges of basic variables used by them are Qb = 4.24 m3/s – 52 800 m3/s W = 5.80 m – 943 m S = 4.1 ´ 10–5 – 6.8 ´ 10–3 U | V | W ...(6.33) They studied the possibility of relating W/d, D/d and A/d2 to Q1 = Q3 = Qb Q S , Q2 = 2 b and d gd d gd 2 Qb Q S . The second parameter Q2 = 2 b represents the dimensionless stream power while d gdS d gd the third parameter is that earlier used by Ananian and others. In general the results were more accurate with Q1 and Q3 than Q2. These equations are listed below along with percent of data giving less than ± 50 percent error. 2 Equation W/d = 7.5 Q10 .425 D/d = 0.14 Q10 .430 A/d2 = 1.80 Q10.855 U | | V | | W % of data giving error between ± 50% 78 74 82 ...(6.34) 188 0 .402 W/d = 2.9 Q3 River Morphology D/d = 0.06 0 .405 Q3 0.807 A/d2 = 0.16 Q3 U | | V | | W 79 56 74 ...(6.35) see Fig. 6.10, 6.11 and 6.12 corresponding to Eq. (6.35). Fig. 6.10 Variation of W/d with Q3 for River data (Garde et al. 2003) Fig. 6.11 Variation of D/d with Q3 River data (Garde et al. 2003) The two equations which give velocity at bankful discharge with reasonable accuracy are Lacey’s equation U = 10.8 D2/3 S1/3 and U D =2 d gd F I H K 0.60 S0.40 U | | V | | W ...(6.36) Hydraulic Geometry and Plan Forms of Alluvial Rivers 189 Fig. 6.12 Variation of A/d 2 with Q3 River data (Garde et al. 2003) 6.6 FLOW AROUND BENDS WITH RIGID AND ALLUVIAL BEDS While discussing point bars, some introductory comments were made about secondary circulation developed in channel bends and its effect on shear distribution and formation of point bar. In this section, flow around bends in rigid-bed and alluvial channel bends is discussed further. The aspects discussed below include velocity distribution in radial and transverse directions, the development and decay of secondary circulation, super-elevation and transverse bed profiles in alluvial bends. Velocity Distribution in Rigid Bed Bends The analysis of flow in rigid-bed bends is carried out using Reynolds’ equations of motion in cylindrical-polar coordinate system. To obtain tangible results, the following assumptions are made: 1. The flow is steady so that 2. 3. 4. 5. 6. ¶ = 0; ¶t The depth of flow is much smaller than the channel width or the radius of the bend; Pressure distribution in the vertical is hydrostatic; Purely viscous stresses involving m or n are neglected in relation to Reynolds stresses; Eddy viscosity is assumed to be constant and scalar; Except in the regions close to the walls the velocity component vy is very small compared to vq and vr and hence can be neglected; and ¶ ¶ ¶ = 0 and << . ¶q ¶r ¶y 7. Secondary flow is fully developed and hence Hence Reynolds’ equations of motion reduce to – 2 2 ¶ 2 vr vq ¶ =– (g D) + Î ¶r ¶ y2 r (a) ¶ 2 vq g Ie + Î =0 ¶ y2 (b) U | | V | | | W ...(6.37) 190 and continuity equation ¶ (vr r) = 0 ¶r River Morphology ...(6.38) Velocity Distribution vo ( y): Rozovskii (1957) has studied four types of velocity distributions vo as a function of h = y/D namely Eqs. (6.39), (6.40), (6.41) and (6.42). Logarithmic Law 1 v max - v y = ln v* D k F I H K which can be reduced to g v y = 1+ 1 + ln kC D Vcp Here, v* = gDS , vmax = Vcp FG F I IJ OP ...(6.39) H H KKQ F1 + F g I I , k = Karman constant, the value of which recommended GH GH k C JK JK LM N by Rozovskii is 0.50, C is Chezy’s coefficient, and Vcp is average velocity in the vertical. It may be mentioned that the subscript q is omitted here for convenience. Power law y v = hn, where h = v max D or v Vcp v Vcp and v v max U | | V | = (1 + n) h | W L m - m a1 - hf OP where m = 22 to 24 = M1 + N 3C C Q 3.3 = 1 - P a1 - hf where P = 0.37 + C n 2 2 ...(6.40) ...(6.41) ...(6.42) Out of these equations, Rozovskii found that Eq. (6.39) gives reliable results while Zimmerman (1977), and Zimmerman and Kennedy (1978) used Eq. (6.40) in their analysis. Velocity Distribution vr: The velocity distribution in radial direction for hydrodynamically smooth and rough surfaces has been obtained by Rozovskii by using Eq. (6.39). Hydro-dynamically smooth bend 2 g vr D =4 F2 h F1 h C Vcp r LM a f N a fOP Q ...(6.43) He found that change in Chezy’s C from 60 to 30 made very little difference in distribution of nr except near the bed and water surface. Hydraulic Geometry and Plan Forms of Alluvial Rivers 191 Fig. 6.13 Variation of F1 (h), F2 (h) and F4 (h) with h Hydro-dynamically rough bend 2 g vr D F4 h F1 h =4 C Vcp r where F4 (h) = F2 (h) + 0.8 (1 + ln h) LM a f N a fOP Q ...(6.44) The functions F1 (h), F2 (h) and F4 (h) are plotted in Fig. 6.13, while experimental data are compared with Eq. (6.43) in Fig. 6.14 which shows correctness of Eq. (6.43). 1.0 0.8 0.6 h 0.4 0.2 0.0 –10 h –8 –6 –4 –2 vr r Vcp D 0 2 4 6 Fig. 6.14 Comparison of Eq. (6.43) with experimental data (Rozovskii 1957) 192 River Morphology Growth and Decay of Secondary Circulation In a long bend, Rozovskii defines the angle qlim as the angle at which the growth of circulation is practically complete, and qlim is given by qlim = 2.3 C D g rc ...(6.45) Here, D can be taken as average depth and rc is center line radius of the bend. Decay of vr : If vro is surface velocity at the exit of the bend, it will decay with x the distance measured from the end of the bend according to the law Vrx =eC D Vro Hence the length required to reduce vro to vrx is g x ...(6.46) x C V = ln ro Vrx D g and if one assumes that when vrx / vro = 0.10, the circulation has died out, the length required is L C = 2.303 D g ...(6.47) Distribution of Longitudinal Velocity Over Width According to Rozovskii’s observations, the maximum velocities move nearer the convex (inner) bank and are stronger, the sharper the bend. However, then the transformation takes place gradually and the maximum velocity gradually moves over to the concave (outer) bank. If the bend is sufficiently gentle, on emerging from it, the maximum velocity is already found near the concave bank. On emerging from the bend, the velocities become sharply redistributed with their maximum coming almost in to contact with the continuation of concave bank. Super Elevation Super elevation (SE) is the difference in water levels between the outer and inner banks of the bend, and can be obtained from the equation of motion in the r direction, namely 2 Vcp ¶D = rf gf r ¶r ...(6.48) where Vcp is the average velocity in the vertical at radial distance r. If it is known how Vcp varies with r, the above equation can be integrated to obtain SE = (Do – Di) = 1 g z ro 2 Vcp rt r dr Hydraulic Geometry and Plan Forms of Alluvial Rivers 193 Here, Do and Di are the depths at outer and inner banks respectively. 1. If Vcp is constant across the bend, integration of the above equation gives SE (Do – Di) = 2 Vcp g LMln r OP N rQ o i ...(6.49) 2. If Vcp varies according to free-vortex law, as assumed by Shukry (1950) i.e. Vcp = K/r, one gets SE = K2 2g LM 1 - 1 OP Nr r Q 2 i 2 o ...(6.50) Assuming the depth of flow upstream of the bend to be the average depth in the bend, and U to be the average velocity, Ippen and Drinker (1962) reduced the above equation to SE = U2 2W 2 g rc LM MM 1 MM1 - FG W IJ N H 2r K c 2 OP PP PP Q OP PP PP Q ...(6.51) 3. If it is assumed that velocity variation follows forced vortex pattern i.e., higher velocities near the outer bank and lower near the inner bank, Vcp ~ r, this assumption together with the assumption of constant average specific energy leads to the equation SE = U2 2W 2 g rc LM MM 1 MM1 - FG W IJ N H 2r K i 2 ...(6.52) Apmann (1973) studied the relationship between super elevation and discharge, to predict the latter if the former is known. On the basis of the analysis of data from rectangular and trapezoidal channels, natural channels and ducts with included bend angle varying from 45° to 360°, Apmann expressed super elevation as K1 U 2 = SE 2g ...(6.53) rc q , the relation being W He found that the coefficient K1 is primarily a function of ro/ ri and r 5 r q tanh c ln o W 4 ri K1 = F I FG IJ H K H K ...(6.54) 194 River Morphology As regards separation of flow on the inner side of the bend, Rozovskii has found that the possibility of separation is greater, the deeper the stream and the gentler the bank slope, or in short the greater the friction on the bank. With small depths and vertical walls, flow without separation is possible even when rc / W is equal to unity. Thus, he found that in streams with small (depth/width) ratio, formation of eddy zone at very sharp turns is possible along the convex bank, but along the convex banks which have steep slope, it is less likely to occur. Head-loss in Bends Head loss in a bend is caused because of the following reasons (Rozovskii 1957): 1. Altered velocity distribution of longitudinal velocity component over the width of the stream; 2. energy required to cause secondary circulation; 3. increase in boundary friction due to circulation; 4. increase in energy loss of internal friction due to presence of secondary circulation; 5. altered velocity in the vertical; and 6. energy loss due to separation in sharp bends. The equation proposed by Rozovskii for head loss in open channel bends is hb = LM 24 g + 60 g OP N C C Q 2 2 r U D 2g ...(6.55) No independent check on this equation seems to have been made. By qualitative reasoning Bagnold (1960) has postulated that the resistance in bends in pipes and open channels can be partly attributed to force required to the creation of secondary flow and partly to overcome the boundary friction and written f= r D + const c rc D and shown that at rc / D values between 2 and 3 the resistance is minimum. Leopold and Wolman (1960) have also compiled field evidence to suggest that in meandering streams, bends commonly tend to have a value of rc / W between 2 and 3. Hence, Bagnold argued that some principle of energy minimization may be involved in meander formation. 6.7 SHEAR DIRECTION NEAR CURVED STREAM BED AND BED TOPOGRAPHY Because of the presence of secondary circulation, radial shear stress is caused on the bed which is directed from outer towards inner side of the bend in radial direction. As a result, the resultant shear stress has a small radial component, which is responsible for cross-sectional bed deformation in alluvial channel bends. This aspect of flow in bends is studied by Engelund (1974), Kikkawa et al. (1976), Zimmermann (1977), De Vriend (1977), Zimmermann and Kennedy (1978), Odgaard (1982) and Hydraulic Geometry and Plan Forms of Alluvial Rivers 195 Fig. 6.15 Motion of a particle on transverse sloping plane others. Figure 6.15 shows the directions of bed shear tq in streamwise direction, shear in radial direction tr and the resultant shear to. From geometry one can write, to = tan y = 2 t2 q + tr tr = tq to Ft I 1+ G J Ht K r o tr 2 ...(6.56) tan y » tr tq since tr << to. Here y is the angle between stream wise shear stress and resultant shear. To obtain an expression for tr, the average shear stress around the wetted perimeter in radial direction was calculated by equating its moment about the center of cross-section to the moment produced by the interaction of the vertical velocity gradient and the streamline curvature. Using Eq. (6.40) and expressing the exponent n as n = 113 . , Zimmermann obtained the following expressions for to and tr. f to = tr = r f f U2 and 8 113 . f + f 1 D 2 rf U 2 3 3 113 . + 2.26 f rc hence, where a f F DI tan y = b( f ) G J Hr K F 9.04 + f I b( f ) = G H 3.83 f + 6.78 f JK c ...(6.57) ...(6.58) 196 River Morphology Fig. 6.16 Variation of b(f) with f (Zimermann 1977) Figure 6.16 shows variation of b(f) with f according to Eq. (6.58). It can be seen that b( f ) and hence tan y decrease rapidly as f increases; this decrease is attributed to more uniform vertical distribution of streamwise velocities as the channel becomes rougher. For large values of f, b ( f ) decreases gradually. It may be mentioned that Engelund (1974) obtained value of b ( f ) as 7.0 for smooth channels, while Rozovskii (1957) recommends a value between 10 and 12 for rough as well as smooth beds. The method of estimation of variation of depth along the radial direction as given by Engelund (1974) is given below. Considering the motion of a sediment particle on a channel bed with a small transverse bed slope a and with shear stress deviating by an angle d from the local flow direction, the drag force on the particle in the longitudinal direction will be FD = LMdg N s -gf d i p6 3 - FL OP Q tan f cos a where f is the angle of repose, and FL is the lift force on the particle. In the transverse direction the forces on the particle have the component LMdg N tan d = s -gf d i p6 3 - FL sin a – FD tan y OP Q Hence, tangent of the deviation angle d will correspond to the ratio between transverse and longitudinal force components; or tan a – tan y tan f ...(6.59) This result is valid only as long as the angle a is small and sediment is transported predominantly as bed-load. In the case of steady, uniform flow in a circular alluvial bend, there will be a small sediment transport in the radial direction which will be balanced by the radial bed slope developed giving increased depth at the outer wall. Thus inward sediment transport is balanced by the outward component due to transverse bed slope. Equilibrium will be attained when y is equal to d. Engelund obtained Hydraulic Geometry and Plan Forms of Alluvial Rivers 197 tan y = 7 7 which on integration gives D , r D 1 dD = tan j d r r D = C1 r7 tan f. The constant of integration can be determined from the condition that at r = rc, D = Dc. Hence, the depth D at any radial distance will be given by D = Dc FG r IJ Hr K c 7 tan j ...(6.60) Engelund recommends the value of f = 30° The particle size distribution in a bend is not uniform when the river bed material is graded; the coarser sediment accumulates near the concave bank and finer near the convex bank. Odgaard (1981, 1982 and 1984) has suggested a method for prediction of the particle size distribution in a bend. As a first approximation, he assumed that the bed profile is a straight line and further assumed that the dimensionless critical shear stress tc is proportional to d-2/3, and obtained the particle size distribution in the radial direction as d D = dc Dc FG IJ F r I H K H rK 5/ 3 c 1/ 6 c c 3/ 2 ...(6.61) He has also found that the radial distribution of average velocity in the vertical is given by Vcp Vcpc = F d I FG D IJ F r I H dK HD K H rK 2/3 c 1/ 2 ...(6.62) Here Dc and Vcpc are the centre line depth and centre line average velocity in the vertical. River bends can be either entrenched or meandering surface bends. Entrenched bends include those bends, which follow the bends in the valley. The river on the floor of valley forms meandering surface bends, which is erodible. In these bends the nature of bank material predominantly determines the radius of curvature of bends. These bends are also classified into free bends, limited bends and forced bends. The banks in free bends are composed of alluvial material, which is easily erodible. In limited bends, the banks are composed of consolidated parent material, which limits lateral erosion, as in entrenched bends. In forced bends, the stream impinges straight on the parent bank at an angle between 60° to 100° approximately. For these bends rc varies from 4.5 to 5.0 for free bends, 7.0 to 8.0 for limited bends and W 2.5 to 3.0 for forced bends. Meandering rivers assume a natural alignment consisting of bends and shallows in the crossings between bends. The profile of the talweg consists of successive deeps and pools in the bends and shallows or shoals in the crossings. 198 River Morphology 6.8 BRAIDED RIVERS The basic mechanism of initiation and development of braiding has been studied through laboratory experiments carried out by Leopold and Wolman (1957), Edgar (1973), Zimpfer (1975), Hong and Davies (1974) and Ashmore (1982). Leopold and Wolman (1957) have suggested the following sequence of events in the development of braided reach. In an originally single or undivided reach a short submerged bar is deposited during high flows. The head of this gravel bar is composed of coarse fraction of bed-load that is moving along the center of the channel. Most of the finer particles move over it, some are trapped on or behind it leading to its growth in the downstream direction. Simultaneously it grows laterally. When it becomes sufficiently wide, it starts affecting the channel along its side by increase in velocity, which initiates widening of the channel. The bar gradually gets stabilized due to vegetation that induces some more deposition on and around it. Later similar process starts in the divided channels leading to island formation and division of channels. Observation by Hong and Davies (1979), Ashmore (1982), Zimpfer (1975) and Edgar (1973) at Colorado State University indicate that the channel division can occur either by separation around middle bar; or incision of a new channel across the diagonal bar. Ashmore (1991) has shown that braiding can be accomplished in four ways: accumulation of a control bar, chute cutoff of point bars, conversion of transverse unit bars to mid channel braid bars, and dissection of multiple bars. The Brahmaputra river in Assam (India), the Kosi in Bihar (India) and parts of the lower Mississippi are excellent examples of braided streams. A braided river reach is characterized by a number of alluvial channels with bars and islands between meeting and dividing, and present the intertwining effect of a braid when seen from the air. Braided rivers may be considered as a series of channel segments that divide and rejoin in more or less regular and repeatable manner. However, even in a braided reach a single dominant channel can be distinguishable. Plan-form of braided rivers can change radically with the change in discharge; hence some investigators e.g., Bristow and Best (1993) have opined that the fluctuations in discharge are a prerequisite for braiding especially in sand bed rivers, even though flume experiments in gravel carried out by Ashmore at constant discharge discount this observation. A few rivers act as single channels at bankful stage and have characteristic braided pattern at lower stages; however in many other rivers some of the islands are permanent and at low stage as well as at high stage the rivers show braided pattern. It seems that presence of wide range of sediment sizes in the bed material is conducive to bar formation and hence braiding. Braiding has been observed and studied in laboratory flumes as well as in rivers as large as the Brahmaputra and the Mississippi. Plans of braided rivers often reveal the gross similarity in the appearance of braided patterns. Study of braided rivers is not only important from the point of view of river morphology; braided alluvial deposits form substantial hydrocarbon reservoirs, sites for deposition and accumulation of heavy minerals, and important sand gravel reserves (Schumm 1977). Leopold and Wolman (1957) on the basis of study of the hydraulic characteristics of divided and undivided channels indicate that for a divided stream (i) the slope is steeper, (ii) width is larger, and (iii) depth is smaller, than that for an undivided stream. The ratio of slope of divided to undivided stream varies for 1.3 to 2.3, while the ratio of corresponding widths ranges from 1.05 to 2.0. Causes of Braiding It has been observed that the important variables that affect the braiding of rivers are discharge and its variability, the size distribution of the bed material and the rate and size distribution of sediment load, Hydraulic Geometry and Plan Forms of Alluvial Rivers 199 width, depth, slope, climate and geologic factors. It is observed on many rivers that a given channel can change in a short distance from a braided to meandering and vice versa; such changes are therefore attributed to the variations in locally independent variables. It is also observed that those rivers dominated by braided as against the meandering channels have on the average a higher flood peakedness, higher total discharge range and higher monthly discharge variability. Braiding is developed by sorting as the stream leaves behind those fractions of the load it is incompetent to transport. If the stream is competent to move all sizes that it is transporting but is overloaded aggradation may take place without braiding. Lane (1957) studied plan-forms of a number of streams as well as their history, and concluded that there are two primary causes of braiding; these are (i) overloading i.e., stream may be supplied with more sediment than it can carry and hence part may be deposited; and (ii) steep slopes causing a wide shallow stream in which bars and islands may readily form. All steep slope type braided channels have many characteristics in common in addition to that of multiple channels; these are i) relatively straight course of main channel; ii) steep longitudinal slopes; iii) wide channels; iv) shallow depths; v) sand or coarse bed material; and vi) usually high bed-load. Since braided form can be due to steep slope or due to aggradation resulting from the overloading of stream with sediment, or due to combination of the two, braided streams can be classified into the following five subdivisions as per Lane (1957): I Braiding due to steep slope: II Braiding due to aggradation: a) Braiding due to steep slope with degradation b) Braiding due to steep slope with approximate equilibrium c) Braiding due to steep slope with aggradation d) Braiding due to moderate slope with aggradation e) Braiding due to low slope with aggradation Types of Bars in Braided Rivers As described by Miall (1977) the bars occurring in a braided river can be classified as under (see Fig. 6.17) Fig. 6.17 Principal types of bars (Miall 1977) 200 River Morphology Longitudinal Bars These are diamond or lozenge shaped in plan and are elongated parallel to flow direction. They are bounded by active channels on both sides and may have partially eroded margins. Bars formed in gravel are most commonly of this type. Longitudinal bars are the classical braid bars of Leopold and Wolman (1957) and the sequence of events leading to their formation is discussed earlier. The initial bar relief may be no greater than the size of the largest fraction of the bed material but as growth continues it may increase to as much as metre. Bar length may reach several hundred metres. The internal structure of the bars is massive or crude horizontal bedding. Linguoid or Transverse Bars Linguoid or transverse bars are most typical of sand braided rivers. They are found to occur in channels that are deep and confined within narrow banks. The characteristic shape of linguoid bars is rhombic or lobate, with upper surfaces that dip gently upstream towards the preceding bar and downstream facing avalanche – slope terminations. These bars vary in width from a few metres to 150 m and length up to 300 m. Most typical heights of these bars range from 0.50 to 1.0 m. Dunes and ripples commonly cover Linguoid bars that are exposed to view in modern rivers. Transverse bars are geometrically similar to linguoid bars, except that they tend to have straighter crests. Point Bars, Side Bars, Lateral Bars Geometrically these bars are similar. They form in the areas of relatively low energy such as inside of the meander. Point bars are usually associated with a meandering river, but they also occur in a braided environment. Side bar is the longitudinal deposition along the side. Other large-scale structures are observed in fairly large rivers. Thus sand waves observed by Coleman (1969) in Brahmaputra, and dunes and bars observed in rivers such as the Lower Red River (Alberta) fall in this category. Figure 6.17 shows longitudinal bar, Linguoid bar, point bar and side bar. Large and sudden changes in water discharge mean the bed is seldom if ever in equilibrium with the flow. Such reduction in flow has two effects on the bed – higher relief structures may be eroded or dissected, and smaller scale structures may be superimposed. Bar relief tends to be smoothened over as a result of reduction in flow and consequent sheet flow or wave action. In the last stage of decreasing flow the deposition of this sheet of silt or mud takes place and the channel fills in inactive areas. After an extensive study of literature and braided stream deposits, Miall (1977) has classified these deposits into three gravel facies Gm, Gt and Gp, five sand facies St, Sp, Sr, Sh and Ss, and two finegrained facies Fi and Fm. Their description, associated sedimentary structures, and interpretation are given in Table 6.4. Braiding Parameters In recent times some thought has been given to characterise the braiding pattern, see Friend and Sinha (1993). As a result, three parameters have been proposed (see Fig. 6.18). Brice Index BI = 2 S Li/ Lr where S Li is the length of the islands or bars in a reach and Lr is the reach measured midway between the banks of the channel. The factor two accounts for the total length of the bars. Hydraulic Geometry and Plan Forms of Alluvial Rivers 201 Table 6.4 Lithofacies and sedimentary structures of modern and ancient braided-stream deposits (Miall 1977) Facies identifier Gm Lithofacies gravel, massive or crudely bedded, minor sand silt or clay lenses gravel, stratified gravel, stratified Sedimentary structures ripple marks, cross beds in sand units, gravel imbrications broad, shallow trough cross-beds imbrications planar cross-beds Interpretation longitudinal bars, channellag deposits minor channel fills linguoid bars or deltaic growths from older bar remnants dunes (lower flow regime) linguoid bars, sand waves (upper and lower flow regime) ripples (lower flow regime) planar bed flow (lower and upper flow regime) minor channels or scour hollows deposits of waning floods, overbank deposits drape deposits formed in pools of standing water Gt Gp St Sp sand, medium to very coarse, may be pebbly sand, medium to very coarse, may be pebbly sand very fine to coarse sand, very fine to very coarse, may be pebbly sand, fine to coarse, may be pebbly sand (very fine), silt, mud, inter-bedded mud, silt solitary (theta) or grouped (pi) cross beds solitary (alpha) or grouped (omikron) planar cross beds ripple marks of all types, including climbing ripples horizontal lamination, parting or streaming lineation broad, shallow scours (including eta-cross-stratification) ripple marks, undulatory bedding, bioturbation, plant rootlets, caliche rootlets, desiccation cracks St Sh Ss Fl Fm Fig. 6.18 Calculation of braiding indices of Brice (1964), Rust (1978) and Sinha (1993) 202 Braiding parameter of Rust (1968) RI = S Lb Lm River Morphology where S Lb is the sum, in a reach, of the braid lengths between the channel talweg divergences and confluences, and Lm is the average of meander wave lengths in the reach. Friend and Sinha (1993) have proposed braid–channel ratio BR which is defined as BR = Lctot / Lcmax where Lctot is the sum of mid-channel lengths of all the segments of primary channels in a reach, and Lcmax is the mid-channel length of the widest channel through the reach. The ratio BR is a measure of tendency of the channel belt to develop multiple channels in a reach. If the reach has a single channel, BR will be unity. For the Gandak river in India BR was found to vary from 1 to 5.5. Modeling of Braiding In order to explain why and under what conditions alluvial streams braid, Engelund and Skovgaard (1973), Parker (1976), Fredsøe (1978) and Kishi and Kuroki (1985) have treated braiding as a stability problem. A double periodic disturbance with different wave lengths in the flow direction x and lateral direction z is introduced on the bed of an alluvial channel and the resulting flow is analysed using shallow water flow model. It is found that the deviation of sediment from the mean flow direction has an important effect on the amplification of the disturbance leading to braiding. This analysis is usually linear in that higher order of the disturbances and their derivatives are neglected. Such analysis has t o , width to depth ratio W/D, Froude number Fr = U and gD Dg s d slope are the important parameters that decide whether the stream will braid or meander. The criteria for formation of braiding are discussed later in this chapter. Another approach to explain braiding phenomenon is that of random walk model proposed by Rachocki (1981). In this approach it is assumed that at the mouth of the valley a stream channel may move downstream in one of three ways: to the right, to the left or it can bifurcate. The minimum distance traveled in uni-directional flow in the model is termed as the step. Each step is graphically represented by the diagonal of grid square. After the first step, the channel is again able to follow one of these three options. Choosing three dice from a set of thirty, which avoids systematic error, generates the model. The dice are changed after every three model generations. The following procedure was used by Rachocki (1981). After the dice have been thrown, their values are added. If the total is even, the stream deviates to the right, if it is odd it deviates to the left, and if the number is divisible by three it bifurcates. After several steps are followed the pattern obtained is that of a braided stream, (see Fig. 6.19). It may be seen that the approach is purely statistical and does not involve any consideration of fluvial dynamics, bank erodibility etc. as such the approach is unlikely to satisfy river morphologists. shown that dimensionless shear stress 6.9 MEANDERING In Chapter IV a brief mention has been made about the classification of plan-forms of alluvial streams. In this section additional hydrodynamic information will be presented regarding process of meandering, theories of meandering, meander parameters and criteria for the prediction of major plan-forms. Callander (1978) has given an excellent review about the state of knowledge on meandering. Hydraulic Geometry and Plan Forms of Alluvial Rivers 203 Fig. 6.19 Random walk model of braiding (Rachocki 1981) Meandering appears to begin with the establishment of pools and riffles sequence. Straight laboratory channels with bed comprising of homogenous material deform into pools and riffles sequence when water flows over the bed and sediment transport takes place. Kinoshita (1957, 1961) observed that the free meanders of a stream start first with the formation alternate bars, or pools and riffles sequence; these change the streamline curvature and velocity variation to induce bank erosion and deposition; this starts meandering process when banks are erodible. The average pool spacing is about five times the bed width. As the meanders form, the alternate pools migrate to alternate sides giving approximate wave lengths of two inter-pool spacing of ten bed widths as observed in nature (see Fig. 6.20). It is interesting to briefly mention about the studies conducted by Agarwal (1983) who imposed a two-dimensional harmonic disturbance near the bed of sediment transporting channel. With 0.27 mm sand and disturbances having frequency of 1.8 to 3.4 Hz, he found that when bed is covered with dunes (low Fr) the disturbance did not have any effect on the bed. On the other hand when the bed was plane and transporting sediment (Fr = 0.8) the disturbance produced alternate bars and pools over 27 m long flume. He also carried out some runs in which alternate bars and pools were formed in the initial length of flume due to disturbance and then the disturbance was removed. In such runs, after sufficient time the entire flume was covered with bars and pools. His studies thus showed that two dimensional harmonic disturbance can induce formation of alternate bars and pools, and that if such disturbance is introduced on the upstream side it can change the bed downstream to alternate pools and bars. Once the talweg takes a sinusoidal course due to formation of alternate bars and pools it causes redistribution of velocity; it also initiates development of secondary flow. If the banks are erodible they are eroded on the convex side of the talweg and more sediment is brought into the channel, which is transported to the other side by secondary flow thus developing the point bar. In this way, in an erodible channel formation of alternate bars and pools leads to meandering of the channel. Field studies have shown that riffles tend to be eroded somewhat at lower stages of flow and the eroded material deposits in the pools. As the discharge is increased to approximately the bankful discharge, the pools are scoured 204 W Initial straight channel Meandering talweg River Morphology 5W Pool 10 W Riffle Meandering channel Fig. 6.20 Formation of pools, riffles and meandering channel and scoured sediment forms riffles. Hence, hydraulic geometry of meandering streams is related to the channel-forming discharge. Since the channel width is related to Qb as W ~ Qb1/2, it seems logical to relate meander parameters to W. Once a meandering pattern is developed it is likely to persist unless some really powerful factor comes into play. Experience on the Mississippi, the Ganga and other rivers has shown that the obstacles including the variation in the cohesiveness of alluvium distort or even suppress the meanders. Hence meander geometry is significantly affected by the nature of strata through which it flows. In natural streams, alternate bars will form if the stable width for channel- forming discharge (e.g., Lacey width) is less than the confining width, which is fixed by rigid banks or “khadir”, and the discharge is low. Thus they occur in channelised flows at lower stages. Alternate bar formation has been experimentally and analytically studied by Kinoshita, Hayashi (1980), Sukegawa (1972, 1974) and Parker (1976). A typical meandering stream is shown in Fig. 6.21. As mentioned in Chapter-4 meandering loops are irregular most of the time; further they change their shape and size in the downstream direction. Hence any average values of meander characteristics for a given reach only give us an approximate idea about their dimensions. It must also be mentioned that along the reach of the river, it may be braiding in one reach and meandering in another, since local conditions governing the plan form may change. Rivers cutting into bedrock have also been found to meander. In such rivers the erodibility of the bed rock along its length would govern the meandering pattern. Further such meanders would be more or less stationary unlike meanders in alluvial strata (see Leopold and Wolman 1960). It is interesting to note that the relationship between width and ML for such meanders of the Gulf stream of North Atlantic follow the same trend as that for meanders in rivers in plains. Laboratory experiments of Friedkin (1945), Inglis (1949), Agarwal (1983) and field studies on many rivers have indicated that the meander pattern as a whole moves downstream in many rivers; this is by far the most common situation. Hickin and Nanson (1975) used dendro-chronological method to measure the rate of migration of bends of the Beatton river. The average rate of migration of ten bends was 0.475 m/yr. The maximum rate occurred when Rm/W ratio was approximately 3 implying a rapid approach to limiting value of this ratio to 2.5. Here Rm is mean radius of the bends. However, on some streams such as the Tigris in Iraq and the Hydraulic Geometry and Plan Forms of Alluvial Rivers 205 Fig. 6.21 Typical meandering river-the White river in Arkansas (U.S.A.) Pembina river near Manola, Alberta (Canada) the migration consists of gradual lateral enlargement without or with small downward movement. Such meanders are called free meanders in Russian literature. The enlargement of loops can occasionally result in natural cutoffs. According to Neill (1970) downstream migration seems to be usually associated with alluvial fills in narrow valleys whereas free meandering tends to occur in broad flats. In engineering applications to river training it is essential to study historical changes of the river under consideration while planning river improvement works. Processes Governing Meander Bend Migration (Chang 1988) Meander bends may migrate downstream or laterally as mentioned earlier. This process is governed by channel curvature, flow curvature and variation of secondary circulation along the bend. As long as there is an angle between the flow path and the channel path, the primary flow and secondary flow have components in streamwise and cross-stream directions. As mentioned in the section on flow in bends, secondary circulation is responsible for transporting sediment from the concave bank downstream and towards the convex bank. Essentially the migration of a bend depends on the relative depth of flow and sharpness of the bend, and delayed response of flow curvature to channel curvature. The longitudinal component of shear caused by the main flow causes bank erosion wherever the flow hugs the bank; this area is shown hatched in Fig. 6.22; deposition occurs along the banks away from the flow path. The bank resistance, vegetation on the banks and mode of bank failure also govern the method of migration of bends. Figure 6.22 shows four cases of different combinations of channel curvature and flow condition. In Case–A with low flow and mild bend curvature, secondary flow develops and the flow line is more in line with channel configuration; the maximum flow curvature is close to apex and hence lateral migration of bend takes place. Case–B refers to mild channel curvature and high flows. In this case flow changes its direction slowly due to inertia and hence maximum flow curvature takes place 206 River Morphology Fig. 6.22 Common modes of meander bend deformation in relation to flow pattern (Chang 1988) further downstream from the apex thereby causing downstream migration. In Case–C with low flow and sharp bend, the flow is unable to follow bend curvature and attacks the outer bank downstream of apex, thus leading to downstream migration. In Case–D corresponding to high flow and sharp bend, there is sufficient difference in bed and flow curvature. This leads to downstream migration together with reduction in bend curvature. Meander Characteristics The main characteristics of a meandering river are the shape, size and mobility of meander loops. These characteristics play an important role in the location, design and maintenance of hydraulic structures such as bridges, barrages, flood embankments and guide bunds. An arc of a circle, a sine curve or a parabolic curve can describe meander shape, even though the common practice is to fit an arc of a circle and characterise it by the average radius Rm. The other two length dimensions that characterise meanders are meander length ML and meander belt MB. These characteristics depends on whether meanders are incised or are in flood plain, process and stage of development of meanders, discharge, slope and sediment size, and terrain through which the river flows. Therefore, these parameters cannot be precisely estimated by any theory and the most commonly used technique for their estimation is statistical correlations using laboratory and field data collected by Friedkin, Ackers and Charlton, Ferguson, Jefferson, Inglis, Bates, Shaw, Leopold et al, Carlson, Schumm, Chitale and others. Most of these relationships are of the form ML, MB = const. Q1/2, where Q is mean annual discharge or bankful discharge. However since channel width W ~ Q1/2 one can expect ML, MB and Rm to be related channel width. Those relationships, which are based on use of dimensional analysis or some form of stability or theoretical analysis, take the form ML M Q2 or B = f 2 d d d gd F GH I or JK ML S = f (Fr) where Fr = D used by the investigators. U . Some of these relation-ships are listed in Table 6.5 along with the data gD Hydraulic Geometry and Plan Forms of Alluvial Rivers 207 Table 6.5 Relations for meander geometry Investigator Furguson (1863) Jefferson (1902) Inglis (1938) Relations proposed ML = 6.0 W MB = 17.6 W ML = 6.06 W = 29.6 Q MB = 17.6 W = 84.7 Q1/2 Rm = 20.64 Q1/2 ML= 11.45W = 25.4 Q1/2 MB = 27.3 W = 56.4 Q1/2 Rm = 14.0 Q1/2 ML= 27.4 Q1/2 ML = 10.9 W1. 01 MB = 2.7 W1.1 ML = 4.7 Rm 0.98 ML = 32.9 Q 0.55 ML = (10 to 14) W ML = 15 W ML = 38 Q0.467 MB = 18.5 Q0.505 ML = 1890 Q0.34/M0.74 ML = 20 W1. 04 ML ~ Ai 0.3 to 0.4 Si = 1.429 (d/D)–0.077 S*0.052 (W/D)–0.065 ML = 123 Q / d 2 d 1/2 Data used Ganga data American and European rivers Jefferson’s data Remarks For rivers in flood plains Incised streams Jefferson’s data Inglis (1939) Leopold et al. (1964) Shaw’s data for 16 rivers in Orissa Fifty rivers ranging from models to large rivers Rivers in flood plains Dury (1958) Prus-Chinsky Ackers and Charlton (1970) Schumm Lewin (1961) Chitale (1970) American river data. Relation used in Europe as design criterion Laboratory data with d = 0.15 mm Thirty eight sites on Australian and Western USA rivers English and Scottish river data 42 river data M = % of silt and clay in banks A1is catchment area in km2 Si = S ´ 104 Si is sinuosity Ackers and Charlton (1970) F GG H Dgs d rf I JJ K 0. 378 River and flume data Anderson (1967) ML Ac = 72 Fr1/2 Ac = cross sectional area Hansen (1967) 56 D ML = f f Darcy–Weiscbach coefficient Altunin (see Kondratev 1950) Kudryashov (195458) (see Kondratev 1950) ML = (12 to 15) W ML = 449 Q0.5 S0.50 MB = 142 Q0.74 Rivers of Central Asia Laboratory data Contd. 208 Contd. River Morphology Hayashi and Ozaki (see Hayashi 1980) Hansen (1967) Agarwal (1983) ML = K W Data from Japanese rivers, Leopold and Wolman, Schumm & Chitale K is a function of Fr ML S/D = const Fr 2 ML = Nonlinear function of Q1/2 ML = 2.1 MB Si = 0.97 Q / d 2 Based on field and flume data with Q up to 104 m3/s F GG H D gs d rf I JJ K 0. 033 S0.04 It may be seen from the above table that many of the equations proposed for ML and MB are not dimensionally homogenous. Dimensional homogeneity requires that ML = K1 MB = K2W and Rm = K3W. According to Hayashi and Ozaki (see Hayashi 1980), in the relation ML = KW, K depends on Froude number U and decreases with increase in Fr as indicated below gD Fr 0.10 0.20 0.40 1.0 K 40 20 10 7 Agarwal’s relation (1983) between ML and Q is shown in Fig. 6.23. Any one of the relations given in Table 6.5 or Fig. 6.23 can be used to estimate ML. On the other hand, for rivers in flood plains MB = 3 ML, ML/W = 10 to 14 and minimum value of Rm/W = 2 to 3 seem to be good thumb rules. Fig. 6.23 Variation of ML with Q (Agarwal 1983) Hydraulic Geometry and Plan Forms of Alluvial Rivers 209 Relations such as those mentioned above overlook the random character of meandering. Wallis (1973) repeated the same experiment 60 times in a small flume using crushed polythene of median diameter 2.6 mm and relative density 1.46 and measured meander characteristics at 30 s interval using photographic technique. His measurements indicated the stochastic nature of meander properties. The wave-lengths followed uni-modal distribution with a coefficient of variation of 0.22. Both mean and standard deviation increased with time but the ratio of the two remained nearly the same. Spectral analysis approach has been used by Toebes and Chang (1967), Speight (1965) and Fergusson (1975). Theories of Meandering Engineers and geomorphologists have given a number of reasons as to why streams meander. These are briefly discussed below. Excess energy concept Schoklitsch (1937) and Inglis (1947, 1949) have argued that meandering is the natural way of reducing excess energy (and hence excess slope) of the stream by increasing its length. On the basis of Bagnold’s findings that for a large number of natural bends the ratio of radius of bend to channel width lies between 2 and 3 at which the bend loss is minimum, Leopold and Wolman (1960) believe that some principle related to minimization of energy is associated with meander formation. A somewhat similar principle is used by Ramette (1980). On the other hand, Joglekar argues that the primary cause of meandering is excess sediment load. According to Indian engineers, the excess sediment load during floods tends to deposit on the bed and increase the slope. This deposition creates shoals on the bed causing deviation in the flow. If the banks are erodible this deviation in flow direction can initiate meandering. However, this hypothesis cannot explain the formation meanders in glacial streams, observed by Leopold and Wolman (1960). Yang (1971) also has questioned the validity of the hypothesis that streams meanders in order to dissipate excess energy. Hence, he has introduced a law of least time rate of energy expenditure according to which, during the evolution towards its equilibrium condition, a natural stream chooses its course of flow in such a manner that the time rate of potential energy expenditure per unit mass of water along its course is minimum. Or DH = f (discharge, valley slope, sediment concentration, geological constraints) Dt However, this concept is not further developed linking flow parameters to meander characteristics. Earths rotation theory Gilbert (1884), Eaking (1910) and Neu (1967) have given earth’s rotation as a cause of meandering. Due to rotation of earth, a body on the earth’s surface experiences a Coriolis force which represents inertia of the body to partake in the rotational motion. Due to this force a body moving in the north-south direction in the northern hemisphere will experience a force towards the east which can deflect the body in that direction. The tendency of the Mississippi river and some other rivers in Alaska to deflect to the right is often quoted in support of this theory. Neu (1967) has shown that the secondary circulation developed due to earth’s rotation is proportional to D/U of the stream and the latitude of the place. The deviations caused by this circulation can be of the order of 10° to 20°. However it is argued that if earth’s rotation alone were responsible for meandering, all the streams at or near the equator should be straight, 210 River Morphology whereas meandering streams are found on the equator as well as elsewhere on the earth’s surface. Further, it has been shown by Quaraishy (1944) that the tendency of the stream to deflect either to the right or to the left is just a chance, and force due to earth’s rotation is relatively small. Lastly the erodibility of banks plays a major role in meandering, which is not taken into consideration in such a theory. Hence it is felt that even though earth’s rotation may play a small part in the meandering process, it cannot be the sole reason. Disturbance theory Proponents of disturbance theory argue that any disturbance caused on the bed or in the flow at the upstream end causes changes in the flow pattern in the downstream direction leading to meandering. This disturbance can be differential deposition across the channel width in an overloaded stream, or transverse oscillations in the flow, or an inclined entry into the channel. Earlier Griggs (1906), Werner (1951) and Hjulstrom (1957) have suggested this mechanism. Friedkin (1945) was able to initiate meandering in a laboratory channel with mobile boundary by allowing flow at an angle. Agarwal (1983) was able to obtain alternate bars in a laboratory flume by imposing a two-dimensional harmonic disturbance near the bed. Lewin’s (1976) observation on the Ystwyth river where a straight channel changed to a meandering one without apparent changes in geological or hydro-geological conditions supports this theory. The change in Ystwyth river began with the formation of lobate transverse bar. Since the disturbance imposed on the flow can be decomposed into harmonics and for a given flow condition, one of the harmonics can cause instability to form meanders, disturbance theory can be linked to instability theory discussed later where the investigators have assumed that meanders occur as a result of unstable response of the bed to a small perturbation. Helicoidal motion theory Some investigators argue that helical motion or secondary circulation is somehow responsible for occurrence of meandering. Since secondary flow is present in all the channels, it is believed that secondary circulation has to become unsymmetrical so as to cause meandering. This is probably caused by unsymmetrical cross-section of the channel and/or by the changing resistance characteristics of bank and bed along the channel length, see Leliavsky (1955), Prus-Chacinsky (1954), Onishi et al. (1976), Jain and Kennedy (1976), and Shen (1983). Prus-Chacinsky has shown that by introducing an artificial secondary flow at the entry of the first bend, it is possible to produce various patterns of secondary flow at the entry of the first bend, and various kinds of secondary flows in the next successive bends. This in turn, affects the circulation in the next bend, and so on. Prus-Chacinski ascribes meandering to any disturbance which produces the initial circulation. Onishi et al. (1976) have concluded that the most important cause of meandering is secondary flow, which produces point bars, modifies the distribution of velocity across the channels, modifies the shape of ripples and dunes on the bed and affects the entrainment and transport of sand on the bed. This concept is loosely linked to disturbance theory. Conceptual model of Leopold and Langbein Leopold and Langbein (1978) have proposed a model according to which the meander form is the same as the most favourable itinerary of a rod of fixed length and defined by a random walk process between two points. They obtained a curve analogues to the rod buckling in with some real meanders. The concept is true provided that the constraints (discharge variation, erodibility, and human interference etc.) can be included in the random walk process. However, it is felt that inclusion of such constraints would result in a different shape. Hydraulic Geometry and Plan Forms of Alluvial Rivers 211 Ramettes approach According to Ramette (1980) the five characteristics of river geometry, namely width W, depth D, free surface slope S, meander wave length ML and meander amplitude MB are functions of discharge Q, d50, d90 and valley slope Sv which vary along x direction. His model computes the first five when the last four are specified. According to Ramette the river characteristics adjust in such a manner that its efficiency of bed erosion is maximum under two constraints: the discharge Q is the bankful discharge and flow is saturated with sediment i.e., it is carrying the maximum possible sediment load. Hence he uses the following relationships 1. Sediment discharge formula of Meyer-Peter and Müller QB = K W (to – toc)3/2 2. Manning-Stricker equation Q = K1 (WD)5/3 (W + 2D)–2/3 (S)1/2 3. Reduction in sediment size according to Sternberg’s law 4. Maximum value of channel slope equal to valley slope: Sv £ S 5. Saturation of flow ¶ QB =0 ¶x 2 Q U 2 - Uo The potential energy of erosion from sand surface to the depth D of liquid mass is QgD/2, while kinetic energy recovered after erosion is d 2 Uo is initial velocity. The energic efficiency of erosion of bed is maximum when 2 Q U 2 - Uo i where U is velocity at depth D and width W, and d i 2 2 U 2 - Uo 2 i.e., is maximum, or QgD gD d i d dx R dU - U i U | | S V =0 | T gD | W 2 2 o From the above equations, Ramette has shown that the efficiency is maximum and the flow is saturated when b = W/D lies between 15 and 21. According to Ramette, in the upstream reach of the river where Sv = S, W, D, Q and da are such that the saturation condition is satisfied but not the maximum efficiency condition, W/D is less than 15 and river is straight and tending to equilibrium ( b and da decreasing). Here da is arithmetic mean size of bed sediment. When 15 < b < 21 the river is near equilibrium. If da is less than da1 then S is less than Sv and river meanders. The limiting diameter da1 is a function of discharge, valley slope and initial value of da / d90. When b is greater than 21, the river is of braided type. Thus if variation of da along the river axis is known, it is possible to find the distance x1 upstream of which S is equal to Sv, and downstream of which meanders will appear. As a result of his analysis, Ramette has given a criterion for plan form determination in terms of da, Q0.465 with W/D as the third variable on which regions of straight, meandering and braided reaches are indicated, see Fig. 6.24. Further assuming that Rm / W = 2.5 for meanders as indicated by Leopold and Wolman, he has shown that ML/ MB = 2.5 and ML/ W = 7 to 11. Ramette’s criterion has been checked by Agarwal (1983), but the results are not encouraging. 212 River Morphology Fig. 6.24 Ramette’s criterion for plan-forms 6.10 STABILITY ANALYSIS AND CRITERIA FOR PLAN-FORMS As mentioned earlier bank erosion constitutes the necessary requirement for the occurrence of meandering in alluvial rivers. According to the experiments of Kinoshita (1957) meandering is caused first by the erosion of bed leading to the formation of alternate bars in channels with non-erodible vertical walls, which then leads to meandering if the walls are erodible. Hence the theory of alternate bar formation in non-erodible walled channel can provide an insight into the formation of meanders and braids. This theory is based on a stability analysis in which small perturbations that are double harmonic functions of x and z coordinates are introduced on the sediment transporting bed in rigid walls channel and the conditions under which these are attenuated or amplified are studied. For such an analysis the equations of continuity for flow and sediment, and sediment transport and resistance laws are used. Depending on whether the analysis is two or three dimensional, the investigators have used two or three equations of motion. Most of the investigators use linearisation so that higher order terms involving perturbations are omitted. Reynolds (1965) and Hayashi (1967), Callander (1969), Sukegawa (1971, 1972), Hayashi and Ozaki (1978) and Parker (1978) have used shallow water flow models, while Engleund and Skovgaard (1973) have used turbulent shear flow model. In these theories the factor causing the instability of the erodible bed is the phase difference existing between shear stress gradient and bed form gradient in the flow direction. However, these theories lead to the unjustifiable conclusion that larger the mode of the braids m is in Eq. (6.63), larger is the growth of braid unless some additional characteristic of sediment transport is taken into account. Here m is the braiding mode in the equation for double sinusoidal migrating disturbance on the bed h = ho cos 2p x pmz sin L W ...(6.63) In Eq. (6.63) h is the disturbance imposed on the otherwise flat bed, m is the mode of sinusoidal disturbance in z direction, W is the channel width, L is the wave length of disturbance in the flow Hydraulic Geometry and Plan Forms of Alluvial Rivers 213 Fig. 6.25 Meandering and braiding direction x, and z is the lateral direction. When m = 1 the pattern is meandering while m = 2 or 3 will represent braiding modes as shown in Fig. 6.25. According to Hayashi and Ozaki (1978) it is the spatial lag distance d between the local bed-load transport rate and local shear stress that plays an important role in the formation of braids of mode m = 1 i.e. meandering. This lag-distance that was originally estimated by Einstein as 100 d has been modified to or LM OP R U D S | | d = l d 1+ 4a S V MM r / r - 1i d | P d | T W PQ N L OP R | fD U | F d = l d M1 + 5 a S V P MM r / r - 1i d | d | T W PQ N 3 o f 1 * s 3 o 1 * 6 r s f U | | | | V | | | | W ...(6.64) where S is average channel slope, f is average friction factor of the bed, Fr = U , U and Do are g Do average velocity and depth of flow in the undisturbed flow, l1 = 100 and a* = 4.35 as proposed by Einstein. Since d is greater than l1 d, spatial lag distance is greater than the step length l1 d. For nonequilibrium flow Einstein and Brown formula for bed-load transport is modified as 214 fx (x, z) = River Morphology fz (x, z) = a f F r - 1I g d GH r JK q a x, z f F r - 1I g d GH r JK q Bx x , z s f Bz s f × F = 40 á t* (x – d), z ñ 3 3 × F = fx (x, z) × 3 w x, z u x, z a f a f i U | | | | V | | | | W ...(6.65) where F= 2 36 v 2 + 3 g d 3 rs / r f - 1 d i g d 3 rs / r f - 1 d 36 v 2 t* = t* (r s - r f )g d Here qBx and qBz are the x and z components of volumetric bed-load transport rate, d is the characteristic size of sediment, u and w are the components of average velocity in x and z directions respectively, fx and fz are dimensionless transport rates, and F is dimensionless fall velocity of sediment particle. The two dimensional equations of motion, continuity equations for flow and sediment, and resistance law are R F ¶ D + ¶ hIJ + t - g S = 0 ¶u ¶u +w +gG u | | ¶ x ¶z H ¶ x ¶ xK r D Dynamic Equations S F ¶ D + ¶ hIJ + t = 0 ¶w ¶w | u +w +gG | T ¶x ¶z H ¶z ¶zK r D x f z f Continuity Eq. for flow Continuity Eq. for Sediment ¶ ¶ (u D) + (w D) = 0 ¶x ¶z ¶ h ¶ q Bx ¶ q Bz + + =0 ¶t ¶x ¶z Resistance law r f u2 u w × tz = tx and f = 2 * tx = f 2 u U F I H K F I H K 2 =2 S Fr2 U | | | | | | | | V | | | | | | | | W ...(6.66) When the disturbance of the form of Eq. (6.63) is imposed on the bed, small perturbations in various quantities with respect to steady flow condition will be (see Fig. 6.26) Hydraulic Geometry and Plan Forms of Alluvial Rivers 215 Fig. 6.26 Definition sketch h=h x=x u = u + u¢, w = w¢ D = Do + x – h tx = to + t¢x tz = t¢z qBx = qBo + q¢Bx qBz = q¢Bz Here uo, Do and qBo are steady state average velocity, depth of flow and sediment transport rate respectively, h and x are displacements imposed on the bed and displacement of free surface respectively, to is average bed shear stress in steady flow and primed quantities represent the perturbations. These are then substituted in the equations of motion Eq. (6.66), and linearisation is done with respect to perturbed quantities. The resulting equations are then non-dimensionalised after eliminating t¢x, t¢z, q¢Bx and q¢ Bz and solution postulated in the form hr = ho cos lzr exp [i k (xr – Ctr)] ur = uo cos lzr exp [i k (xr – Ctr)] + i y1 wr = wo cos lzr exp [i k (xr – Ctr)] + i y2 xr = xo cos lzr exp [i k (xr – Ctr)] + i y3 U | | | V | | | W U | | | V | | | W ...(6.67) Here ho, uo, wo and xo are the normalized values of h, u, w and x at t = 0, k and l are the dimensionless wave numbers of sinusoidal disturbances in x and z directions respectively, namely k= l= 2 p Do and L m p Do W and y1, y2 and y3 are phases of ur, wr and xr with respect to hr respectively. Also complex velocity C = Cr + i Ci where Cr is dimensionless velocity of disturbance and Ci is the amplification factor. For m = 1, the dominant wavelengths are expected to be those for which the initial rate of growth of hr are 216 River Morphology positive and maximum. Solution of this system of equations constitutes the Eigen value problem and Hayashi and Ozaki have done this. They have arrived at the following conclusions 1. When FG SW IJ H pmD K o 2 << 1 the rate of growth of hr is largest for waves of mode m = 1 i.e., for sand waves associated with meandering, and the ratio L/W is given by L/W = f1 (Fr) 2 where f1 (Fr) = m LM MN - d5 + 8 Fr 2 + 5 Fr 4 + 25 + 110 Fr 2 + 141 Fr 4 + 44 Fr 6 + 4 Fr 8 i d10 + 19 Fr 2 + 7 Fr 2 i » 3.66 F 1 + FrI H Fr K OP PQ 1/ 2 ...(6.68) and the effect of lag distance on formation of meandering is crucial. 2. When FG SW IJ H mp D K o 2 >> 1, the dominant wave length is given by L = W 6 1 2 p m3/ 2 FG W S IJ HD K o 1/ 2 ...(6.69) and the rate of growth has a maximum for certain value of mode m. Hence the braid of such a mode is theoretically possible. 3. When FG W S IJ H pmD K o 2 » 1, the dominant wave length is given by L 1 = f2 (Fr) W m and f2 (Fr) = 2 2 R 18 - 10 Fr + 7 Fr U S V T 9 + Fr W 2 4 2 ...(6.70) 1/ 2 and the rate of growth is largest when m = 1. Analysis of laboratory data indicated that alternate bars are formed when WS /Do < 0.31 which agrees with the above conclusions. Hence Hayashi and Ozaki have related L with W and Fr as third variable, see Fig. 6 27. It may be noted that L corresponds to meander length ML. Criteria for Prediction of Plan-forms The earlier predictors for plan forms were based on the relation between discharge and slope. Thus Lane (1957) analyzed data from models and rivers in USA with average discharge varying from 2.8 ´ 10 –3 to 25,000 m3/s and slope S varying from 1.59 ´ 10-5 to 5.49 ´ 10 –3 and found that Hydraulic Geometry and Plan Forms of Alluvial Rivers 217 Fig. 6.27 Comparison of predicted and observed meander length (Hayashi and Ozaki 1978) when and when S ³ 4.1 ´ 10 – 3 Q –0.25 the channel is braided S £ 7.0 ´ 10 –4 Q –0.25 it is straight When the slope lies between these two limits the channels are meandering. It may be mentioned that Lane did not propose a quantitative criterion to distinguish between straight and meandering channels. Leopold and Wolman (1957) analysed the data from American and some Indian rivers with mean annual discharge varying from 8.4 to 28 000 m3/s and slope varying from 8.9 ´ 10 –5 to 3.6 ´ 10 – 2 and found that if and if S ³ 0.0125 Q –0.44 streams are braided S £ 0.0125 Q –0.44 streams are meandering while relatively straight channels with sinuosity less than 1.5 were scattered on both sides at this line. Leopold and Wolman have also observed that the channel patterns braided, meandering or straight, each occurs in nature throughout the whole range of possible discharge and slope. Some of the largest rivers in the world are braided e.g. the Lower Ganges, the Amazon, the Brahmaputra and parts of the Mississippi. Leopold and Wolman’s principal point of discussion is that there is continuum of stream channels having different characteristics that are reflected in the combination of hydraulic factors— each pattern is associated with certain of these combinations. Henderson (1963) has included the effect of sediment size in Q – S criterion and modified the equation demarcating braided streams from meandering ones to S = 0.517 d 1.14 Q –0.44 where d is in m and Q in m3/s. 218 River Morphology Fig. 6.28 Regime channel geometry for sand bed rivers (Chang 1980) Chang (1980) used the condition of minimization of stream power and proposed a criterion between S and Q for identifying the plan-forms, see Fig. 6.28. Region below line 1 represents the condition of d no transport of bed-load. Region between lines 1 and 2, called region I, represents stable channels with flat slopes, low velocity and low bed-load transport rate and width to depth ratio of 4 to 20; natural channels in this region have a meandering pattern and occasionally straight channel for which valley slope is equal to channel slope. According to Chang, rivers falling in region II have smaller of the two slope minima and are less stable. The channel geometry is sensitive to slope and slight increase in slope tends to increase the channel width and decrease the depth of flow. Rivers falling in this region are often braided. For rivers in region III width and depth are sensitive to slope and those rivers are braided, the extent of braiding being directly related to slope. Rivers in region IV are highly braided and have width to depth ratio greater than 100. On Fig. 6.28 Chang also gives contours of equal depth and width. The equations of three lines in fps units are Line 1 S - 0.51 = 0.00238 Qb d S - 0.55 = 0.05 Qb d S - 0.51 = 0.047 Qb d Line 2 Line 3 U | | V | | | W ...(6.71) Precise location of line L is not known. Here Q is expressed in cfs and d in mm. When Q is expressed in m3/s and d in mm, the constants in the above equations are 0.000 386, 0.007 04 and 0.007 63 respectively. Hydraulic Geometry and Plan Forms of Alluvial Rivers 219 Hayashi and Ozaki (1978) have proposed the criterion for prediction of plan-forms, using the method of stability analysis. According to them the plan-form depends on WS and Fr = Do U . g Do Fr ³ 3.16 F W S IJ 3.16 G HD K F W S IJ 2G HD K FG W S IJ HD K o o o 1/ 2 1/ 2 FG W S IJ HD K F W S IJ ³ Fr ³ 2 G HD K F W S IJ ³ Fr ³ G HD K o o o 1/ 2 Straight 1/ 2 Transition from straight to meandering 1/ 2 Coexistence of meandering and braiding 1/ 2 ³ Fr Braiding see Fig. 6.29. Using regime type relationships, Hayashi and Ozaki expressed Do, W and U as a function of Q namely Do ~ Q0.36, W ~ Q0.55 and U ~ Q0.05 and converted Fr – namely WS criteria into S – Q criteria, Do Fig. 6.29 WS/Do – Fr criterion for channel patterns (Hayashi 1980) 220 S ³ 7.0 ´ 10 –3 Q – 0.37 braiding S £ 7.0 ´ 10 – 3 Q – 0.37 meandering River Morphology Agarwal (1983) has verified S vs. Q criterion using available flume and field data, and concluded that this criterion does not predict the plan-form correctly. This may partly be due to the fact that some data especially laboratory data have constant discharge while field data have either bankful discharge or mean annual discharge. On the basis of the stability theory, Parker (1976) has concluded that in rivers transporting sediment, when Do / W < 1.0 at the formative discharge (both these conditions are almost universally satisfied), the tendency towards either meandering or braiding exists. Further meandering occurs when S / Fr << Do / W, braiding occurs when S / Fr >> Do / W and transition between meandering and braiding occurs when S / Fr lies between these two limits see Fig. 6.30. This criterion is based on the laboratory data of SAF, Wolman and Brush, Schuum and Khan, Ashida and Narai, Ackers and Charlton and Qurashy, and field observations of Simons and some rivers. Fig. 6.30 S/Fr – Do/W criterion of Parker (1976) Ramette (1980) has proposed d vs Q0.45 S criterion as shown in Fig. 6.24 for prediction of plan forms, and verified it with a few experimental data of Henderson. Agarwal has used data from a number of laboratory studies and field data and found that most of the points for straight channels fall in the correct region while the data for meandering and braiding channels are scattered widely and hence he found the criterion to be unsatisfactory. Many Japanese investigators have proposed criteria for alternate bars and braids. Sukegawa (1971, u WS 1973) has developed a criterion using * vs u* c Do FG W S IJ HD K o F I GH JK 1/ 4 graph, whereas Ikeda (1973) uses u* vs u* c 1/ 3 plot. Kishi and Kuroki (1975) have used u* WS vs u* c Do FG IJ H K 1/ 2 plot and Tamai et al. (1978) have Hydraulic Geometry and Plan Forms of Alluvial Rivers 221 used WS u* vs plot. It may be mentioned that Muramoto and Fujita (1977) have developed planu* c Do Do W vs graph. Do d FG IJ H K form criterion using F I H K It may be pointed out that stability analysis and other approaches have revealed that the parameters D W u t , Fr, S, f, * , o , o and lag distance d. These are related by six Do u* c t c d equations (see Hayashi 1980, and Hayashi and Ozaki (1978)) and hence one can choose only three as governing plan forms are independent parameters. Three possibilities are (i) W W u W t , S, Fr, (ii) , S, o or * and (iii) , S, Do Do u* c Do tc u* W WS . The analysis indicates that and S occur as . u* c Do Do Agarwal (1983) has analysed a large volume of laboratory and field data from various countries to verify the plan form criteria proposed by Lane, Leopold and Wolman, Parker, Ramette and those proposed Hayashi and Ozaki, and other Japanese investigators and found that these criteria do not predict the plan-forms correctly. Therefore he has proposed two criteria, first between t* and Fr, and other between t* and WS which seem to demarcate plan forms reasonably well, see Fig. 6.31 and 6.32. Do Fig. 6.31 Criterion for river channel patterns (Agarwal 1983) 222 River Morphology Fig. 6.32 WS /Do – t* criterion for plan-forms (Agarwal 1983) Lastly Kuroki and Kishi (1985) have used stability analysis and developed a criterion for prediction W S 0 .2 and S. On this diagram Do (see Fig. 6.33) three regions where no bars occur, bars and braiding occur are indicated. Figure 6.33 also of plan-forms. Their analysis indicated that plan-forms depend on t*, Fig. 6.33 Criterion for meso scale bed-forms (Kuroki and Kishi 1985) Hydraulic Geometry and Plan Forms of Alluvial Rivers 223 W S 0 .2 W S 0 .2 is less than 4 to 5, bars occur if 5 < < 20 Do Do shows that for large values of t*, no bars occur if to 30 and braiding occurs for W S 0 .2 values greater than 50.They also found that the dimensionless Do length of bars L/ W primarily depends on t*, decreasing with increase in t* for small values of t* and gradually increasing with increasing in t* for larger t* values. For t* between 0.1 and 6, L/W varies between 2 and 6 with an average value of 4. References Agarwal, V.C. (1983) Studies on the Characteristics of Meandering Streams. Ph.D Thesis, I.I.T. (formerly University of Roorkee), Roorkee. Ahmad, M. and Rahman, A. (1962) Appraisal and Analysis of New Data from Alluvial Canals of West Pakistan in Relation to Regime Concepts and Formulae. Proc. of West Pakistan Engg. Congress, Lahore, Vol. 46, Paper 351. Allen, J.R.L. (1965) A Review of the Origin and Characteristics of Recent Alluvial Sediments, Sedimentology, Vol. 5, pp. 89-191. Ananian, A.K. (1961) Determination de la Formation du Lit des Riveres, Cree Par Suite de L’Abaissement de la Cote des Leurs Bases d’Erosion. Proc. of 9th Congress of IAHR, Dubrovnik, pp. 1102-1113. Apmann, R.P. (1973) Estimating Discharge from Super-elevation in Bends. JHD, Proc. ASCE, Vol. 99, No. HY1, Jan, pp. 69-79. Ashmore, P.E. (1982) Laboratory Modeling of Gravel Bedded Stream Morphology. Earth Science Processes, Vol. 7, pp. 201-225. Ashmore, P.E. (1991) How Do Gravel – Bed Rivers Braid? Canadian Jour. of Earth Sciences, Vol. 28, pp. 326-341. Bagnold, R.A. (1960) Some Aspects of the Shape of River meanders. USGS Prof. Paper No. 282-E. Blench, T. (1957) Regime Behaviour of Canals and Rivers. Butterworth Scientific Publications, London. Bristow, C.S. and Best, J.L.(1993) Braided Rivers : Perspectives and Problems. In Braided Rivers (Eds. Best J.L. and Bristow C.S.), Geo. Soc. Special Publication No.75, pp.1-11. Callander, R.A. (1969) Instability and River Channels. JFM, Vol. 36, Pt. 3, pp. 465-480. Callander, R.A. (1978) River Meandering – Annual Review of Fluid Mechanics, Vol. 8, pp. 129-158. Carlson, C.W. (1965) The Relation of Free Meander Geometry to Stream Discharge and its Geomorphic Implications. Am. J. Sci. Vol. 263, pp. 864-885. CBIP (1989) River Behaviour, Management and Training. Central Board of Irrigation and Power, New Delhi, Vol. 1, pp. 36-37. Chang, H.H. (1979) Minimum Stream Power and River Channel Patterns. Journal of Hydrology, Elsevier Scientific Publishing Co., Amsterdam, Vol. 45, pp. 303-327. Chang, H.H. (1980) Stable Alluvial Canal Design. JHD, Proc. ASCE, Vol. 106, No. HY5, May, pp. 873-891. Chang, H.H. (1988) Fluvial Processes in River Engineering. John Wiley and Sons, New York. A Wiley Interscience Publication, pp. 271-284. Chitale, S.V. (1970) River Channel Patterns. 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(1957) A Study of the Shape of Channels Formed by Natural Streams Flowing in Erodible Material. US Army Engineer Div., Missouri River, Corps of Engineers, Omaha (Nebraska) USA, MRD Series No. 4, 106 p. Langbein, W.B. (1964) Geometry of River Channels. JHD, Proc. ASCE, Vol. 90, No. HY2, March, pp. 301-347. Leliavsky, S. (1955) An Introduction to Fluvial Hydraulics. Constable and Co. Ltd., London, pp. 115-120. Leopold, L.B. and Langbein, W.B. (1978) Les Meanders des Rivieres. La Bibliotheque “Pour La Science” Les Phenomenes Naturrels. Leopold, L.B. and Maddock, T. (1953) The Hydraulic Geometry of Stream Channels and Some Physiographic Implications. US G.S. Professional Paper 252, 58 p. 226 River Morphology Leopold, L.B. and Wolman, M.G. (1959) River Channel Patterns : Processes in Geomorphology. W.H. Freeman and Co., San Francisco (USA). Leopold, L.B. and Wolman, M.G. (1960) River Meanders, Bull. of Geo. Soc. of America, Vol. 71, pp. 769-794. Leopold, L.B., Wolman, M.G. and Miller, J.P. 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ASCE, Vol. 104, No. HY1, Jan.. pp. 33-48. Zimpfer, G.L. (1975) Development of Laboratory River Channels. M.S. Thesis, Colorado State University, Fort Collins, USA, 111 p. C H A P T E R 7 Gravel-Bed Rivers 7.1 INTRODUCTION Gravel and boulder-bed rivers are those rivers that flow through predominantly gravelly and bouldery materials respectively. Bathurst characterizes boulder rivers as those rivers in which the width is an order of the magnitude greater than the median size of the bed material, the depth is of the order of magnitude of the bed material size, and the slope is unlikely to exceed 0.05. Not much is known about boulder rivers, even though some studies have been conducted about their resistance characteristics. However, the last three decades have seen significant research activity on gravel-bed rivers. Gravel-bed rivers differ from the commonly encountered sand bed rivers in many respects. Gravelbed rivers flow through much coarser material having a much wider spectrum of sediment sizes–from cobbles to fine sand–than sand bed rivers. Their slopes are much steeper (0.001 to 0.05 or even larger) than those of sand bed rivers. In sand bed rivers all the fractions of bed material move for most of the discharges except the very small ones; however in gravel-bed rivers all the fractions of bed material move only at a few flows in a year. During the rest of the time sediment transport takes place over the pavement (see below). The other difference pertains to the bed forms. Unlike in sand-bed rivers, ripples and dunes do not form in gravel-bed rivers; instead large bed features known as bars, transverse and diagonal bars, riffles and pools, and transverse ribs of coarse material are common features in gravelbed rivers. These bed features not only offer resistance to flow but also act as sediment storage spaces. Further, since the slope of gravel-bed rivers varies over a wide range, the Froude number U/ gD for the gravel-bed rivers can be less than unity to greater than unity. As regards the plan form, sand-bed rivers are either meandering, transitional or braiding and they may change from one plan-form to another dramatically as the discharge changes. Gravel-bed rivers have a much greater tendency to be transitional or braided. For cobble and boulder rivers it is rare to find reaches that meander significantly. In other words, it is rather easy to define talweg for sand bed streams; yet for cobble and boulder rivers it is impossible to define its location. 230 River Morphology Since upland areas supply sediment to the river systems, gravel-bed rivers are closer to the sediment source. Because the sediment supply events, such as landslides are discontinuous, the sediment transport in gravel-bed rivers shows greater variability than the sediment transport in sand-bed rivers. In fact, sediment transport in gravel-bed rivers can be unsteady and non-uniform even for steady water discharge. Depending on the supply of sediment to the channel, there may be two orders of magnitude of variation in sediment transport rate for a given discharge. This does not happen in sand-bed rivers. Lastly, it is found that gravel-bed rivers are more stable than sand-bed rivers. Hence rapid and large bed level variations that often occur in sand-bed rivers do not occur in gravel-bed rivers. The study of gravel-bed rivers poses some complexities that should be mentioned. The first relates to the size distribution of the bed material. Since the bed material size varies from cobbles to fine sand, different methods should be used to analyse different size fractions. Also, with such wide variation in the bed material size, difficulty is experienced in choosing the characteristic size of the bed material for studies related to resistance, sediment transport and hydraulic geometry. Further complexities are caused by the formation of the pavement and its destruction that affect the size distribution of the transported material which also causes a sudden increase in the transport rate once the pavement is destroyed. 7.2 DATA FOR GRAVEL-BED RIVERS Several studies have been conducted on gravel-bed rivers in U.S.A., U.K., New Zealand, Canada, Italy and other European countries and these data are available in literature. These data pertain to the hydraulic geometry and resistance to flow either at bankful discharge or other discharges. In many cases the size distribution of bed material and information on whether the bed was mobile or paved has been given. Data collected by Leopold and Wolman (1957) for many American rivers, Kellerhals (1967) for some rivers in British Columbia, and Bray (1979) for rivers in Alberta (Canada), are useful for the study of hydraulic geometry of rivers at bankful discharge. Data useful for resistance analysis of mobile and paved bed at variable discharge are given by Samide (1971) for the north Saskatchewan and Elbow rivers in Canada, Milhaus (1973) for the Oak Creek in U.S.A., Griffiths (1981) for the rivers in New Zealand, Thorne and Zevenbergen (1985) on the Boulder Creek in Colorado, U.S.A., Michalik (1989) on the Wisloka and the Dunajee rivers in Poland, Colosimo, Copertino and Veltri (1988) for gravel rivers in Italy, and by Gladky (1979), Church and Rook (1983) and Hey and Thorne (1986, 1988). These data have been tabulated by Garde et al. (1998). Field data on bed-load transport in gravel-bed rivers have been mentioned by Bathurst (1987). These are for the rivers Pitzbach in Austria, Elbow in Alberta (Canada), Clearwater in Idaho, Snake in Idaho, Oak Creek in Oregon, Slate in Idaho and Tanana in Alaska, all in the U.S.A. and Aare in Switzerland. The median size of the surface material for these rivers varied from 12 mm to 260 mm while the water discharge varied from 3.0 m3/s to 1680.0 m3/s. 7.3 BED MATERIAL The sampling of the surface of gravel-bed rivers is usually carried out by one of the following methods: 1. Grid or Transect Sampling: Wolman (1954) has proposed grid sampling. In this method a grid is established over the surface and particles immediately below the grid points are sampled. In transect sampling all the particles lying along the predetermined line are collected and analysed. Gravel-Bed Rivers 231 2. Areal Sampling: All the particles exposed within a predetermined area are sampled. This method was used by Lane and Carlson (1953). 3. Volumetric Sampling of the Surface Area: In this method the sample is acquired either by the photographic method proposed by Adams (1979), or by removing particles from this area by using adhesive or grease. In order to see if d50 of the gravel-bed rivers can be predicted, it was plotted against slope S. In spite of the scatter it was found that (see Garde et al. 1998) an equation of the form d50 = 882.5 S 0.492 ...(7.1) can be fitted through the data; here d50 is in mm. The large scatter is attributed to the fact that the data used are from diverse lithological environments and also there is a large variation in the dominant discharge. It has been reported that gravel-bed materials exhibit bimodality. There usually is a lack of particles in the range 1 mm to 8 mm. The reasons advanced to explain these characteristics include catchment geology, mixing of sediments transported in two different modes viz. traction and suspension, restriction in sediment sizes supplied by the source area and abrasion and sorting during the transport. Odgaard (1984a) found that the size distribution of surface layer particles follows normal distribution. Analysis of size distribution data for bed materials of gravel-bed rivers has indicated that the size distribution neither follows normal nor long normal distribution over the entire range of sizes in the sample. Fig. 7.1 Variation of d /d50 with percent finer for gravel-bed river materials Figure 7.1 shows the size distribution plotted as d/ d50 versus percent finer on normal probability paper. It can be seen that the average curve passes through d50/ d16 = 2.88 and d84/ d50 = 2.121. Further, even though there is considerable scatter in the magnitude of d99.9/ d50, (from 6 to over 10), its average magnitude can be taken as 8.2. The mean curve passing through these points on the normal probability paper can be represented by the straight line using the transformation: 232 dt / d 50 = {(d / d50) l – 1}/l River Morphology ...(7.2) where l is the parameter to be determined by trial and error, such that the transformed distribution is gaussian. The value of l was found to be 0.40. This value along with the known median size will give the size distribution when the above equation is used. It is also interesting to know how the geometric standard deviation for bed material of gravel-bed rivers varies with d50. Earlier studies of bed materials of sand-bed rivers by Garde (1972) and Kothyari (1994) indicate that the geometric standard deviation sg increases as d50 increases and follows the equation 0.34 sg = 1.4 d 50 ...(7.3) where d50 is in mm and sg = 1/2 ( d84/d50 + d50/d16 ). This is based on data for d50 varying from 0.14 mm to 17 mm. Kothyari also analysed the data with d50 varying from 0.15 mm to 37 mm. Figure 7.2 shows the variation of sg with d50 for sandy and gravelly bed materials. It can be seen that for gravelly-bed materials, sg decreases with increase in d50. Since in general d50/ d16 and d84/ d50 have different values, variation of d50 /d16 and d84 /d50 with d50 was studied by Garde et al. (1998). It was found that for gravelbed materials d84/d50 is nearly constant; however d50/ d16 decreases with increase in d50. As a result sg = 1 2 FG d Hd 50 + 16 d84 d50 IJ decreases as d K 50 increases. Fig. 7.2 Variation of sg with d50 for sandy and gravelly bed materials As regard the size distribution of river bed sediments it may be mentioned that Moss (1962, 1963) has shown that the river bed sediments are deposited as composites and are made up of three populations, each of which is related to a specific sediment process. Vischer (1969) found each of these three sub-populations to follow log-normal distribution. Since these three populations would be mixed in different proportions, it is very unlikely that the river bed material samples as a whole would follow log-normal distribution. Gravel-Bed Rivers 233 7.4 PAVEMENT River beds composed of heterogeneous mixtures of gravel and smaller particles form a surface layer with thickness of the size of coarse particles. Bray and Church (1980), and Andrews and Parker (1987) have explained the distinction between armouring and paving. If there is no sediment supply from the upstream as in the case of downstream of large capacity dams, the bed surface will get progressively coarser and eventually become immobile for all discharges less than the maximum sustained flow. If higher flow occurs, the bed particles will be entrained, the bed will degrade further and the bed surface will become somewhat coarser. Such conditions occur downstream of dam and the immobile bed is considered to be armored. The coarse surface layer in gravel-bed rivers, known as the pavement, is maintained by successive periods of bed-load transport during which essentially all sizes move. This sediment is supplied from the upstream side and hence the channel remains in equilibrium. The particles on the bed are transported frequently within a span of several years. In this process, even if occasionally a few coarse particles on the bed move, it does not affect the stability of the pavement and hence there are no general motions. Thus pavement is present in gravel-bed rivers even while most available sizes are transported. Studies by Harrison (1950) and Andrews and Parker (1987) have indicated equal mobility of all particle sizes present in the sub-pavement material; that is the ratio of transport rate of a given size fraction to its percentage abundance in the sub-pavement material is approximately constant for all sizes. This has been confirmed by the data on the East Fork, the Snake and the Clear Water rivers all in USA. If equal mobility is to be achieved with respect to the subsurface material, the surface layer must be considerably coarser than either the subsurface material or the bed-load. The bed-load and the subsurface size distributions are approximately equal because the lesser mobility of coarser size fractions is counterbalanced by their abundance in surface. Field experience has indicated that for gravel-bed rivers, the ratio of median size of the pavement to that of the sub-pavement material ranges from 2.0 to 6.0 with an average value of 2.71. Neill (1968) has suggested the value of toc/D gs d50 = 0.03 constitutes the criterion for braking of the pavement; here d50 is the median size of the pavement. If d50 of the subpavement is used, the corresponding criterion will be toc/ D gs d50 = 0.081 since d50 of the pavement is equal to 2.71 times d50 of the pavement. 7.5 HYDRAULIC GEOMETRY The average width or perimeter, depth of flow or the hydraulic radius, flow area at the bankful discharge, and the slope, describe the hydraulic geometry of the rivers. The knowledge of hydraulic geometry is needed for the study of problems related to river training, location of bridges and barrages and for navigation. The hydraulic geometry of alluvial rivers and channels has been studied by Lacey (1930), Inglis (1947), Leopold and Maddock (1953) and others. They have related the perimeter P or width W, depth D or hydraulic radius R and the area A to the dominant discharge Q and in some case d50 or silt factor f1. It is found that P or W ~ Q0.50 D or R ~ Q0.33 A ~ Q0.8 U | V | W ...(7.4) 234 River Morphology approximately. Langbein (1964) has applied the principle of minimum expenditure of power per unit of the bed area, and minimum work rate in the whole river system to obtain the parameters of hydraulic geometry and found that W ~ Q0.53, D ~ Q0.37, U ~ Q0.10 and S ~ Q – 0.73. Considering the channel to be in an unstable state, Knighton (1977) studied whether development of the channel to a new state represented an attempt by the system to approach some form of dynamic equilibrium. His analysis led to the condition that b2 + f 2 + m2 ® minimum where W ~ Q b, D ~ Q f and U ~ Q m The hydraulic geometry of gravel-bed rivers has been studied by Kellerhals (1967), Bhowmik (1968), Charlton (1977), Parker (1979), Bray (1982) and Hey (1982). While Kellerhals, Bhowmik, Charlton and Bray have related W, D and U to the bankful discharge Q and median sediment size, Parker has used the functional relationship: W/d, D/d, S, U Dgs d = F Q/ d 2 rf F GH Dgs d rf I JK ...(7.5) Dgs d , he obtained the following rf thus taking the slope as independent variable. If Q1 = Q/ d2 equations: W/d = 4.400 Q10.50 D/d = 0.253 Q10.415 S = 0.223 Q1–0.41 U 0.616 = 0.898 Q1 Dgs d rf U | | | V | | | W ...( 7.6) In general, these studies have shown that the geometric parameters strongly depend on Q whereas d occurs to a very small power. Recently Garde et al. (1998) have analyzed the available gravel-bed river data with paved as well as mobile bed conditions and studied the hydraulic geometry at bankful discharge. The first question that they wanted to answer was whether the slope can be taken as dependent or independent variable. On any given river the slope decreases in the downstream direction as Q increases and d decreases in the downstream direction. When all the available data were plotted as S vs Q, even though S decreased as Q increased, there was considerable scatter which is believed to be due to the difference in terrain, length of river, lithology and bankful discharge, see Fig. 7.3. Interpreting the scatter on Fig. 7.3 as implying that S should be taken as an independent variable along with Q and d, Garde et al. (1998) used the functional relationship: Gravel-Bed Rivers 235 Fig. 7.3 Variation of slope with bankful discharge for gravel-bed rivers W, D, A = F (Q, d, D gs, rf and S) ...(7.7) The viscosity was not considered since we are dealing with very coarse material. As a first approximation the geometric standard deviation sg of bed material was also not considered. Using dimensional analysis the following alternative functional relations were obtained for the study of geometry of gravel-bed rivers. W, D, A, = f (Q) W/d, D/d, A/d 2 = F1 Q / d 2 (a) W/d, D/d, A/d = F2 2 W/d, D/d, A/d 2 = F3 Hence F GH F QS / d GH F Q/ d GH 2 2 I JK Dg d I , J = F (Q ) r K I Dg d S J = F (Q ) r K s Dgs d , S = F1 (Q1, S) rf (b) 2 2 (c) f s 3 3 (d) f U | | | | | V | | | | | W ...(7.8) Q1 = Q / d 2 Dgs d, Q2 = QS rf F D g I d and Q = Q/d F D g I dS GH r JK GH r JK s 2 s 3 f f 236 River Morphology Using 140 data points for both paved and mobile bed at the bankful discharge, the following equations were obtained. It may be mentioned that the data for paved and mobile bed intermingled and hence the relationships valid for both the cases were developed using Eq. (7.8). It was found that relationships involving Eq. (7.8 (a)) and (7.8 (b)) gave the same accuracy and were more accurate than Eq. (7.8 (c)). Further relationships involving Eq. (7.8 (d)) were most accurate. Below are given equations corresponding to Eq. (7.8 (b)) and (7.8 (d)) and are recommended for use since they are dimensionally homogeneous. W/d = 7.675Q10.448 D/d = 0.504Q10.373 A/d2 = 3.872Q10.821 W/d = 3.872Q30.396 D/d = 0.308Q30.330 A/d2 = 1.108Q30.726 U | | V | | W U | | V | | W ...(7.8 b) ...(7.8 d) It may be mentioned that Q2 = QS / D g s d / r f can be interpreted as the dimensionless stream power. The parameter Q3 where slope occurs in the denominator has been used in Russia to study the hydraulic geometry. Further, equations involving Q3 viz. Eq. (7.8 (d)) give smaller errors than the equations involving Q alone or Q1, and in addition the former are dimensionless while the latter involving Q are in dimensional form. Hence, it is recommended that Eq. (7.8 (d)) be used for predicting W, D and A for gravel-bed rivers. For the data used, these equations predicted W, D and A within ±, 30 percent error for 58%, 85% and 71% of the data respectively. Variation of W/d, D/d and A/d2 with Q3 are shown in Figs. 7.4, 7.5 and 7.6 respectively. Fig. 7.4 Variation of W/d with Q3 Gravel-Bed Rivers 237 Fig. 7.5 Variation of D/d with Q3 Fig. 7.6 Variation of A/d 2 with Q3 7.6 BED FEATURES IN GRAVEL-BED RIVERS As mentioned in the introduction to this chapter ripples and dunes commonly observed in sand bed rivers, do not form in gravel-bed rivers. Instead large scale sedimentary accumulations called bars are present in gravel-bed streams. They represent major storage spaces for bed-load sediment that is moved once in a while and also offer resistance to flow. Taking clue from Jackson II (1975) bed features can be classified in the following manner. 238 River Morphology The micro and meso forms in the form of ripples and dunes are rather rare in gravel-bed rivers. Antidunes have been found to occur at steep slopes. Hence as regards the gravel-bed rivers, one is interested in sedimentary accumulations whose scale is channel width or greater. These are loosely called bars. Their height is comparable with the depth of flow. Bars persist for a long time and are radically modified only during high floods. Bars fall in the category of macro and mega forms. Table 7.1 Classification of bed features (Jackson 1975, Church and Jones 1987) Class Microforms Mesoforms System scale d D Typical wave length 10 –2 Time scale << tc ~ tc Features Ripples, lineation Dunes Remarks Absent in gravelbed rivers Rare in gravel-bed rivers. Probably absent if d > 0.1 D Uncommon, of gravel-ribs A large variety of sedimentation zones. to 10 m 0 100 to 102 m Macroforms Megaforms W ³=l 101 to 103 m > 103 m > = tc Regime time Antidunes, unit bars, channel bars Bar assemblages tc = time for the flood wave to pass through the reach l = wavelength of bed-forms When in a portion of the channel carrying sediment the shear stress is reduced, the bed-load being transported deposits and forms a bar. Hence bars occur at the apex of the channel bends along the convex bank, places where the channel widens, at the junctions and at flow divergence. According to Church and Jones (1987), if D is less than 3d bars will not occur. Further if t* is to be greater than 0.05 g f DS D g f d90 = 0.05 and if D gs / gf = 1.65, S @ 0.08 d90 D Substituting d90 / D = 0.30 one gets S = 0.025. Hence the upper limit of the slope for the bar formation is about S = 0.05 after which the sediment would be washed off. Smith (1978) has identified five unit bar features, these are: 1. Longitudinal or spool bars: These are formed in the centre of the channel at a relatively wider section. These are convex and elongated and they grow by upstream deposition of coarse material and downward deposition of finer material. Crescent bar is its early form. 2. Transverse bars: These tend to form at an abrupt channel expansion. They have lobate front and an upstream ramp. 3. Point bar: Point bars occur near the convex bank of a curved channel. In gravel-bed rivers point bars often possess a steep outer face and a chute or secondary channel between it and the shore. 4. Diagonal bars: These are oriented obliquely across the channel and are attached to both the banks. The upstream side is usually anchored at the concave bank. There is an upstream ramp and there may be an avalanche face on the downstream front. Bars that are attached to the banks tend to be more stable than those that are detached. Gravel-Bed Rivers 239 5. Alternate bars: These bars form on alternate sides of the channel and talweg meanders between them. Pools form opposite the bars while riffles form at the cross over point between bars. Alternate bars are a feature of straight channels. Since alternate bars are a three dimensional phenomenon, their formation is related in part to the channel width. Twice the pool to pool spacing l = aW where the constant a is found to vary between 4 and 17 with an average of 10. According to Chang et al. lS = 3 Fr2 D ...( 7.9) According to Ikeda (1984) l 0.55 W = 22.6 f (W / D) H = 0.189 f (W/ D)1.455 ...(7.10) D where H = bar height and f is Darcy-Weisbach friction factor. Different bars are shown in Fig. 7.7. and Point bar Longitudinal bar Transverse bar Point bar Meandering talweg Diagonal bar Alternate bar Fig. 7.7 Different bars Another bed feature occurring in gravel-bed rivers and which is important from the point of view of resistance is riffle-pool sequence. Riffle primarily represents a hydraulic resistance element and may store little or no transient material. Riffles seem to develop by selective scour and deposition along the 240 River Morphology Fig. 7.8 Riffle-pool sequence channel and are formed in gravel-bed rivers when their slope is less than 0.05. These are diagonal riffles. Material eroded from the convergence of flow towards one bank is deposited in the “cross-over zone”, where the flow diverges and the main current moves from one bank to another. Such erosion and deposition cause riffle and pool sequence shown in Fig. 7.8. The sediment texture strongly affects the character and relative stability of pool-riffle sequences. When the river bed material is widely graded, the largest sizes are moved more rarely than the remaining material; this is deposited on the riffle. This material on the riffle which induces deposition of more material, which increases the stability of riffle for long periods between the floods. When the bed sediments are narrowly graded, all the material is moved relatively frequently and riffles as such do not form. Riffles are then merely leading edge of sediment storage bar. Analysis of data has indicated that: pool to pool distance = (5 to 7) times channel width. Keller and Melhorn (1973) found that Pool to pool distance l = 5.42 W1.01 in SI units. The channel width is also found to vary between pools and riffles. Generally riffles are wider than the neighbouring pools as a result of flow divergence causing bank erosion. Pool and riffle sequences are generally very stable and in some cases found to be stationary and moving downstream at a speed of only 150–500 m/yr. Parker has given a stability analysis leading to the development of pool-riffle sequences. Theories of pool–riffle sequences are summarized by Richards (1982) and Langbein and Leopold (1968). The latter have proposed a kinematic wave model in which sediment particles move in groups along the channel. Richards suggests that the generation of turbulent eddies cause alternate acceleration and deceleration of the flow which is responsible for their formation. Transverse ribs: Transverse ribs are a set of regularly spaced cobble or gravel ridges oriented transverse to the flow and are found on riffles and steep slopes. Ribs comprise the coarsest sediment particles in the channel while finer material is exposed between the ribs. Maximum flow depth in the ribbed reaches is about twice the size of largest median axis of the sediment. The bed material size and channel slope are the two primary factors which determine the rib spacing. Most studies indicated that ribs are upper flow regime bed forms. According to Koster (1978): Gravel-Bed Rivers 241 W = 0.47 l dmax = m l Mean rib width where l is the mean rib wave length and m = 0.075 to 0.165. U V W ...(7.11) 7.7 RESISTANCE TO FLOW IN GRAVEL-BED RIVERS The resistance relationship is the relationship between average velocity U in the channel, depth D or hydraulic radius R, channel slope S and the coefficient dependent on the resistance offered by the channel boundary. If the flow is steady and uniform S is the channel slope; however for unsteady, nonuniform flow S should be the slope of the energy line. Three most often used equations for U are those of Manning, Chezy, and Darcy-Weisbach. Equating the relationships for U, the following relationships obtained between n, C and f. U C 1 R1 / 6 = = = gRS g n g 8 f ...(7.12) where gRS = u* the shear velocity. The objective of this discussion is to obtain predictors for n, f and C. For gravel-bed rivers n is found to vary from 0.02 to 0.2, and f from 0.01 to 0.5. For boulder rivers these values will be still higher. When considered in the above form n, f and C will include the frictional resistance of the bed and sides, form roughness due to bed deformation, changes in cross sectional shapes, wave resistance due to surface waves and form resistance due to changes in channel profile in plan. Since the flow in gravelbed rivers takes place over very coarse surface material, the boundary would act as hydrodynamically rough; as a result Reynolds number in the form of UR/v or u* d/ v will not affect resistance. Further, most of the data available for gravel-bed rivers have width/depth ratio between 10 and 100. Hence, bank resistance can be safely neglected and depth D used in place of R in the resistance relationships. It has already been pointed out that conventional ripples and dunes whose character changes with the flow do not form in gravel-bed rivers; various bars or bed features that occur in gravel-bed rivers have been discussed earlier. Bars have a close relation with channel shape in plan and these are fairly stable being radically modified only during high floods. Therefore, it seems more logical not to consider their effect on resistance separately and include it in the overall resistance coefficient. However, it may be mentioned that some investigators e.g., Hey (1988) have studied the bar resistance separately. As regards the characteristic size of bed material Ks to be used, there is considerable discussion in the literature; various sizes such as d35, d50, d65 and d90 have been used and then the effect of nonuniformity is neglected. The recommendations of some of the investigators are listed below (see Van Rijn 1982) Ackers and White Einstein Engeland and Hansen Hey Mahmood Kamphus Ks = 1.35 d35 Ks = 1.00 d65 Ks = 2.00 d65 Ks = 3.50 d84 Ks = 5.10 d84 Ks = 2.50 d90 242 River Morphology Van Rijn (1982) after analyzing 120 data points from flume and field studies for the plane bed condition and with width/depth ratio greater than five, found that Ks/d90 varied from a very small value to almost 12 as (to – tc)/ Dgs d50 varied over a wide range, but there was no correlation between the two. The average value of Ks/d90 was three. Since in many data sets the size distribution is not given and only median size is known it is preferable to use d50 in the expression for Ks which is done here. Lastly some investigators such as Colosimo et al. (1988) have recognized that when Froude number U/ g D is greater than 1.65 the flow in the open channel becomes unstable and hence resistance coefficient f should be related Fr, in addition to the relative roughness. Further if t*/t*c is greater than unity, f should also depend on this parameter. Thus according to them 1 bD = a log + f1 (Fr) + f2 (t*/ t*c) ks f Here t* = to /Dgs d50 and t*c = toc / Dgs d50 Alternatively the expression for velocity can be written in most general dimensional form as FG IJ H K U U = const d50 gD FG IJ H K x Sy or U/ gd50 S = const (D/d50)x } ...(7.13) and the constants x and y are determined from the analysis of field data. Results of The Analysis As mentioned earlier Garde et al. (1998) have analyzed a large volume of data in gravel-bed rivers for the prediction of resistance to flow. Their results are briefly discussed below. Resistance at bankful discharge Since the shear stress acting on the bed depends on the stream slope, some investigators e.g. Golubstov (1969) and Bray (1979) have related Manning’s n to S. In general n increases with increase in S. For paved as well as mobile bed data at bankful discharge the equation obtained is: n = 0.168 S0.245 ...(7.14) However, the mobile bed data scattered more than the paved bed data. The exponent of S obtained by Bray was 0.177 while Golubstov obtained the value of 0.33. Because of large scatter around the mean line, the above equation is not recommended for use. Since according to Strickler (n/d)1/6 = constant, one can plot (n/d) 1/6 vs D/d. When this was done the following relation was obtained. n/d1/6 = 0.092 F DI H dK - 0.135 ...(7.15) Here d is d50. However the variation of (n /d)1/6 with D /d being weak one can approximate the above equation by Gravel-Bed Rivers 243 Fig. 7.9 Variation of D1/6/n with D/d50 (n/d)1/6 = 0.073 for D/d values between 2 and 200. Equation (7.15) shows that (n d 1 6 ) FG d IJ = 0.092F DI H dK HD K 16 16 - 0 .135 F DI HdK - 0 .166 or D1 6 D =F n d F I H K ...(7.16) This type of relationship in the form of log-law was suggested by Limerinos (1970). The data gave the equation (see Fig. 7.9) D D1 / 6 = 14.05 log d50 n FG IJ + 12 H K whereas using d84 in place of d50 the values of coefficient of log F D I and constant obtained by H dK Limerinos were 10.27 and 17.7 while Bray (1979) obtained the values 9.66 and 19.50 respectively. This equation gives reasonably good predictions of n at the bankful discharge. Among the equations using Darcy-Weisbach friction factor f, the following equation: 1 D = 1.229 d50 f F I GH JK 0 .302 ...(7.17) gd50 S and was found to be satisfactory. Lastly at bankful discharge the relationship between U D d50 can be obtained. Alam’s analysis has suggested this type of relationship. This relationship obtained for the data is (see Fig. 7.10) U D = 3.475 d50 gd50 S FG IJ H K 0 .802 ...(7.18) 244 River Morphology Fig. 7.10 Variation of U gd 50S with D for bankful discharge d 50 Resistance at varying discharge Here also preliminary analysis indicated that for any resistance analysis, mobile bed and paved bed data intermingle and hence all data are treated together including those at bankful discharge. The variation of FG n IJ Hd K 50 1/ 6 with D gave the equation: d50 FG n IJ Hd K 50 1/ 6 = 0.0702 FG D IJ Hd K 50 - 0.011 ...(7.19) However considering the very small value of the exponent of it is recommended that all the data is: FnI GH d JK 50 F D I and the relatively large scatter, GH d JK 50 1/ 6 = 0.08 is a good approximation. Limerinos type equations obtained for D D1 / 6 = 9.132 log d50 n F I + 15.41 GH JK ...(7.20) Gravel-Bed Rivers 245 Other best fit results for f are: 1 D = 1.557 d50 f and 1 f FG IJ H K F D I + 1.74 = 1.031 log G H d JK 0 .183 50 ...(7.21) ...(7.22) The other two equations for U which are obtained by optimizing the values of exponents of and S so that the error in the prediction of U is minimum are U D = 4.403 d gd50 S 50 F DI GH d JK 50 and U g d50 FG IJ H K F D IJ = 2.586 G Hd K 50 0.639 ...(7.23) 0.631 S0.372 ...(7.24) see Fig. 7.11. It is recommended that if the conditions at the bankful stage are to be predicted, one should use the equations specifically obtained from bankful discharge data. Fig. 7.11 Variation of U g d 50 S with F DI GH d JK 50 for variable discharge 246 River Morphology Universal stage discharge relation While discussing about resistance to flow, on which the stage discharge relation depends, it is worthwhile to mention about Grishanin’s (1967) work. Through dimensional reasoning he has shown that, as an approximation D gW a f Q 0 .25 0 .25 remains constant. For 25 sites on 21 rivers in plains, he selected three discharges on each site namely smallest, largest and close to the mean discharge. It was found that for these data: D gW a f Q = 0.904 D gW ...(7.25) with the standard deviation of 0.158. For gravel-bed river data it is found that a f Q 0.25 is a function of FG D IJ and the relationship between the two is: Hd K F D IJ D ag W f = 0.459 G Q Hd K 50 0 .25 50 0.117 ...(7.26) so that one gets the relationship of depth D as D = 0.459 (g W)0.25 Q or FG D IJ Hd K 50 0 .117 ...(7.27) ...(7.28) 0.234 Q = 14.863 W0.50 D1.766 d50 It should be noted that the above equation does not involve slope. Hence at best it will be an approximate relationship. 7.8 SEDIMENT TRANSPORT IN GRAVEL-BED RIVERS In sand bed rivers relatively large amount of sediment is transported as suspended load. However, in gravel-bed rivers the reverse is usually the case; they carry 10 to 50 percent of total load as bed-load. The other characteristic of sediment transport in gravel-bed rivers is that the transport of coarser material does not take place on continuous basis as in sand bed rivers but is episodic. In such rivers a large fraction of bed material is immobile even at bankful discharge and moves only during floods. When the transport takes place it is unsteady and nonuniform because external sediment supply to the stream is from overland and gully flows and by landslides and bank collapses. The overland flow supplies finer material that is transported as suspended load. However, the material produced by landslides, and cliff collapse is usually coarser. This material once it enters the channel may be temporarily stored in the Gravel-Bed Rivers 247 channel in the form of bars and will be released during floods. Short term variations in bed-load can also occur due to disruption of pavement layer and scour or fill. All these effects cause unsteadiness and nonuniformity in bed-load transport. The non-uniformity of the bed sediment plays an important role in sediment transport. A pavement is formed on the bed and at low flows finer material may move over the pavement layer. In such case, the characteristic size of transported material may be smaller than that of the parent material as well as that of pavement. Once the pavement is broken the material is exposed and the size distribution of the transported material is significantly changed. Under such conditions all sizes of the particle have equal mobility. Another factor that affects the rate of sediment transport in gravel-bed rivers is the availability of sediment, which is important in the case of flows over a paved bed. In this case if the transport rate is calculated for a given case assuming it to be uniform, then the actual rate of transport for that size over paved bed may be much different because the bed may be unable to satisfy the capacity of flow to transport that sized material. As shown by Misri et al. (1984) and others the bed-load transport of non uniform sediments can be correctly predicted if exposure and hiding corrections are applied. Once the pavement is broken all sizes can be transported and the effect of non-uniform size distribution is minimum. Bed-load sampling in gravel-bed rivers To study the applicability of available bed load equations and develop new equations one needs to carefully collect laboratory and field data on bed-load transport and its size distribution. In the last three decades bed-load transport in gravel-bed rivers has been measured in New Zealand and U.S.A. on streams such as the Snake, Clear-Water, Willamete and in the rivers in U.K., Canada, Austria, Switzerland and Poland with the bed material varying from 1 mm to 100 mm or even more. Yet not enough data are available for sediment transport in gravel-bed rivers when the bed is paved and when the pavement is destroyed. Further not in all the above cases the size distribution of the transported material is given. In fact establishments of sediment transport equation for the gravel-bed rivers has met with limited success because of the difficulties associated with (i) sampling of bed material and bed-load in streams; (ii) extreme non-uniformity of bed material; and (iii) non-equilibrium bed-load transport associated with transient runoff events and episodic events associated with storage and release of bedload. Three methods have been used to measure the bed-load in gravel-bed rivers. In 1971 Helley and Smith developed a pressure difference type sampler specifically for use in rivers with bed material from coarse sand to medium gravel range. This is described by Garde and Ranga Raju (1985); this sampler was used by Klingeman and Emmett to measure bed-load in East Fork river and had an efficiency of 100 percent for particles ranging from 0.5 mm to 16 mm. The conveyor belt system was developed for measuring bed-load in East Fork river. Material falling into 0.4 m wide and 0.6 m deep tough on the bed of the river through 0.25 m wide and 14.6 m long slot is carried from the trough to the bank and then into the hopper standing over the weighing machine. Thus the sediment falling per minute was recorded. Vortex bed-load sampler has been used on the Oak Creek and has been discussed by Klingeman and Emmett. The sampler develops a vortex flow to move bed-load through a flume embedded in the floor of the weir structure and across the width. The bed-load and portion of the stream flow are removed to an off-channel where the bed-load sample is collected. The water returns to the creek. The trap efficiency of vortex tube was found to be 100% for coarse sand and higher fractions. The general design of vortex tube is discussed by Garde and Ranga Raju (1985). 248 River Morphology Bed-load equations White and Day (1982) and Bathrust, Graf and Cao (1987) have studied the applicability of some bedload equations using laboratory data , and laboratory and field data respectively. White and Day, using flume data found that if Ackers and White’s method is used for the analysis of data, one can use the mobility parameter LM A=M MM MN where OP L OP M u PP M u P M Dg 10 D I P F d P M 32 log H d K PQ r PQ N F D g I d > 60 and n = 0 for G H r v JK F D g I d for F D g I n = 1 – 0.56 G GH r v JK H r v JK n * n * s f 1/ 3 s 2 f 1/ 3 s 2 s 2 f f 1- n ...(7.29) 1/ 3 d < 60 If for uniform material A is the value of the mobility parameter (to which transport rate is related) and A¢ is its value for the size di in the mixture, it was found that di A¢ = 0.6 dA A and dA is given by dA d50 FG H Fd = 1.6 G Hd 84 16 IJ K IJ K - 0 .5 + 0.6 - 0 .28 ...(7.30) ...(7.31) White and Day proposed use of Ackers and White’s relationship for the computation of fraction wise bed-load transport. Assuming uniform size and using the above relations for computing the mobility parameter, the transport rate is calculated and multiplied by the fraction of this size available in the bed to get the bed-load transport rate of this size. The calculations are repeated for all size fractions and the quantities added to get the total bed-load transport rate. The critical condition for the movement of bed-material is normally expressed for gravel-bed rivers using the dimensionless critical discharge q*c = qc 3 gd50 where qc is the critical discharge at which bed material moves. Bettess (1984) has obtained the equation: q*c = 0.134 1.221 log S S F H I K ...(7.32) for constant toc and rs/rf = 2.65. The plot of q*c versus S for the flume data indicated that the best fit line has the equation Gravel-Bed Rivers 249 q*c = 0.15 S–1.2 ...(7.33) and that Bettess equation gives equally good results. The equation proposed by Schoklitsch namely qc F r - 1I = 0.26 G H r JK s f 5/3 3/ 2 d40 S7/ 6 ...(7.34) when d40 is replaced by d50 gives about 10% higher value of qc. Bathurst, Graf and Cao (1987) used laboratory data with bed material size varying from 2.9 mm to 260 mm and assessed the accuracy of bed-load equation proposed by Ackers and White (1973), Meyer-Peter and Müller (1948), Smart (1984), Bagnold (1980) and Schoklitsch (1962). These equations are: Ackers and White qTV = 0.025 where Fgr = LMgd MN 35 LM F - 1OP N 0.17 Q LM OP 1 U MM PP F I F r - 1I OP M 5.657 log G 10 D J P GH r JK PQ MN H d K PQ qd35 D 1.5 gr 0 .5 s f 35 ...(7.35) where qTV = volumetric sediment transport rate per unit width. This equation is to be used only for few flows with Fr less than 0.80. Meyer and Peter and Müller’s equation: q*BV = F r - 1I d gG H r JK s f QBV =8 3 a LMF n I NH n K s 3/ 2 t * - 0.047 OP Q ...(7.36) Here da is the arithmetic mean size of bed material, ns is Strickler’s value of Manning’s roughness g f DS coefficient, while n is the Manning’s coefficient for flow, and t* = D g s da Smart’s Equation: This equation is based on flume experiments using sediment sizes up to 29 mm and slopes up to 20 percent. The equation is LF d = 4.0 MG MNH d F r - 1I d gG H r JK QBV s f 3 a 90 30 IJ OP K PQ 0. 2 S0.6 U 0. 5 t * (t* – t*c) u* ...(7.37) 250 Mizuyama’s (1977) equation River Morphology q*BV LM12 - 24 S = MM cos q N 1/ 2 t * m 1.5 - S d 1/ 2 i FGH1 - a 3/ 2 2 t *cm t*m IJ K LM1 - a F t I OP OP MN GH t JK PQ PPQ 1/ 2 * cm *m -1/ 2 ...(7.38) Here, a = f (S) and t*m and t*cm are for d = d50. Bagnold’s equations: q BV = = q BV ¢ LM w - w OP F D I F d I MN bw - w g¢ PQ H D¢ K H d ¢ K -2 / 3 c c ...(7.39) Here, w = stream power q rf S per unit width, wc is the critical value of w and the prime refers to standard measured values from a reliable experimental plot. Schoklitsch’s equation: qBV = and qc in SI units is given by: d 2.5 rs / r f i s f S3/2 (q – qc) ...(7.40) qc Fg GH g = 0.26 I - 1J K 5/ 3 3/ 2 d 40 S7/ 6 ...(7.41) Verification of the equations using flume data indicated that Schoklitsch’s equation gave better performance than the rest of the equations. Further its performance is improved if qc value obtained q BV , S3/ 2 data for small and large rivers behave differently, see Fig. 7.12. Large rivers with S £ 1.0 percent and relatively narrow range of sediment sizes (1 to 100 mm) as well as ready supply sediment within channel, show relatively closer agreement with Schoklitsch’s Equation than data for small rivers with S ³ 1 percent and relatively wider range of sediment size (1 to 1000 mm). While in the former case the data fall within one order of magnitude of the line of Schoklitsch’s equation, in the latter case sediment transport is over predicted by two orders of magnitude. Hence Bathurst et al. (1987) concluded that while Schoklitsch’s equation can be applied with caution to large rivers, it should be applied to small rivers for extreme flows when the whole bed is moving. from qc* = 0.21 S –1.2 are used. In the case of field data it was found that when (q – qc) is plotted Parker, Klingeman and Mcleans equation After examining the data of the Oak Creek (U.S.A.) Parker et al. (1982) found that when the shear stress acting on the bed is greater than the critical shear stress for the pavement and thus the pavement is Gravel-Bed Rivers 251 Cache la Poudre, Colorado Fig. 7.12 Variation of qBv/S3/2 with (q – qc), river data compared with Schoklitsch equation broken, as a first order of approximation the size distribution of the bed-load is nearly the same as that of the sub-pavement. Under this condition the rate of bed-load transport is governed by the hydraulic conditions rather than the availability of material. This information is used to develop an empirical equation for bed-load transport rate as a function of shear stress and d50 of the sub-pavemnent in paved bed channels. Careful analysis of the Oak Creek data indicated the validity of similarity approach. However small systematic change in size distribution with the shear stress was observed especially near the critical condition. Using the similarity approach proposed by Ashida and Michiue, Parker et al. (1982) used two dimensionless parameters Wi* F r - 1I gq = G H r JK s f BVi R Ft I U | | f G J V and t S | Hr K | T W 3/ 2 0 f i * i tc = D g s di U | V | W where qBVi is the volumetric bed load transport rate of size di per unit width of the channel and fi is the fraction of size available in the sub-pavement. Plotting Wi* vs ti* for each size range, the value of ti* 252 River Morphology * * designated as t* ri at which Wi has the pre-chosen value of 0.002. Further denoting t r50 as the value of t*i when di = d50 it was found that d1 t* ri = d t* 50 r 50 FG IJ H K - 1.0 ...(7.42) Wi* is plotted Wr* * and t*r50 = 0.0876. Defining fi = t*i / t* ri and taking W r = 0.002, they found that when against fi the data tend to plot around a single curve whose coordinates are Table 7.2 fI 0.90 10 – 4.5 1.0 2.3 ´ 10 –3 Coordinates of fi Vs W*i 1.1 1.15 ´ 10 –2 1.2 3.7 ´ 10 –2 1.3 8.0 ´ 10 –2 1.4 1.9 ´ 10 –1 Wi* Wr* This is based on ten size ranges for the Oak Creek in the range of 0.60 to 102 mm. However a systematic deviation was apparent, viz. as fi increase, the value of Wi* for the finer material tends to fall below the mean curve. Parker et al. showed that the above relationship can be integrated to obtain the total bed-load transport rate in the form W* = G (f50) Wr* ...(7.43) where W* is the dimensionless bed-load transport for poorly sorted gravel-bed when the pavement is broken, W*r = 0.002 and f50 = t* 50 with t* r50 = 0.0876. The above functional relation takes the form: * t r 50 W* = 0.0025 e[14.2 (f50 – 1) – 9.28 (f50 – 1)2] W*i ...(7.44) = 0.002 G (fi ) for 0.95 < f50 < 1.165. It is interesting to note that the coordinates of the two curves and W*r = 0.0025 exp. [14.2 (f50 – 1) – 9.28 (f50 – 1)2] match. Parker et al. showed that data for the rivers Elbow, Snake and Vedder reasonably conform to the above equation for W*. For data with f50 > 1.65 the following equation gives the variation of W* and f50 W* r F 0.822 IJ = 11.2 G 1 H j K 50 4 .50 ...(7.45) Parker et al. also obtained three empirical equations for three size ranges of the bed material for f50 greater than 0.95. However these equations need further verification using data from other streams. Gravel-Bed Rivers 253 References Adams, J. (1979) Gravel Size Analysis from Photographs. JHD, Proc. ASCE, Vol. 105, No. HY-10, October, pp. 1247-1285. Ackers, P. And White, W.R. (1973) Sediment Transport: New Approach and Analysis. JHD, Proc. ASCE, Vol. 99, No. HY-11, November, pp. 2041-2060. Bagnold, R.A. (1980) An Empirical Correlation of Bed-load Transport Rates in Flumes and Natural River, Proc. RSL, A372, pp. 453-473.. Bathurst, J.C. (1978) Flow Resistance of Large Scale Roughness. JHD, Proc. ASCE, Vol. 104, No. HY-12, December, pp. 1587-1603. Bathurst, J.C. (1985) Flow Resistance Estimation in Mountain Rivers. JHE, Proc. ASCE, Vol. 111, No. 4, April, pp. 625-643. Bathurst, J.C. 1986. Some Aspects of Gravel-Bed Rivers (Lecture Notes for the British Council Visit), February. Bathurst, J.C. Graf, W.H. and Cao, H.H. (1987) Bed-load Discharge Equations for Steep Mountain Rivers, Chapter 15 in Gravel-Bed Rivers. (Eds. Thorne, C.R., Bathurst, J.C. and Hey, R.D.) John Wiley and Sons Ltd., pp. 453-492. Bettess, R. (1984) Initiation of Sediment Transport in Gravel Stream. Proc. Inst. of Civil Engineers (London), Vol. 77, Pt. 2, Technical Note 407, pp. 79-88. Bhowmik, N.G. (1968) “The Mechanics of Flow and Stability of Alluvial Channels Formed in Coarse Materials”, Ph.D. Thesis, Colorado State University, Fort Collins (U.S.A.). Bray, D.I. 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(1950) Report on Special Investigation of Bed Sediment Seggregation in a Degrading Bed. Rep. Series 33, Issue No. 1, University of California, Berkeley, U.S.A., September. Hey, R.D. (1982) Design Equations for Mobile Gravel-Bed Rivers, Chapter 20 in Gravel-Bed Rivers. (Eds. Hey, R.D., Bathurst, J.C. and Thorne, C.R.) John Wiley and Sons Ltd., pp. 553-580. Hey, R.D. and Thorne, C.R. (1986) Stable Channels with Mobile Gravel-beds. JHE, Proc. ASCE, Vol. 112, No. 8, August, pp. 671-689. Ikeda, S. (1984) Prediction of Alternate Bars Wave Length and Height. JHE, Proc. ASCE, Vol. 110, No. 4, April, pp. 371-386. Inglis, C.C. (1947) Meanders and Their Bearing on River Training. Proc. Inst. Of Civil Engineers (London), Maritime Paper No. 7, January, pp. 3-54. Jackson, R.G. II. (1975) Hierachical Attributes and a Unifying Model of Bed Forms Composed of Cohesionless Material and Produced by Shearing Flow. Geol. Society Am. Bull., Vol. 86, pp. 1523-1533. Keller, E.A. and Melhorn, W.N. (1973) Bed Forms and Alluvial Processes in Alluvial Stream Channels : Selected Observations, In Fluvial Geomorphology (Ed. Morisawa, M.) Intl. Series No. 4, (Bingham Symposium in Geomorphology), Alley and Unwin Ltd., London, pp. 253-284. Kellerhals, R. (1967) Stable Channels with Gravel Paved Beds. JWHD, Proc. ASCE, Vol. 93, No. WW-1, February, pp. 63-84. Knighton, A.D. (1977) Short Term Changes in Hydraulic Geometry, Chapter 7 in River Channel Changes. Ed. Gregory, K.G., Wiley Interscience Publications, U.S.A., pp. 101-119. Koster, E.H. (1978) Transverse Ribs, their Characteristics, Origin and Palaeohydraulic Significance in Fluvial Geomorphology. E.D. Miall, Memoir 5 of Canadian Society of Petroleum Geologists. Kothyari, U.C. (1994) Frequency Distribution of River Bed Materials. Jour. Of Sedimentary, Vol. 42, No. 1, pp. 283-291.. Lacey, G. (1930) Stable Channels in Alluvium. Minutes of Proc. Inst. Of Civil Engineers (London), Vol. 229, Paper No. 4736, pp. 258-292. Lane, E.W. and Carlson, E.J. (1953) Some Aspects Affecting the Stability of Canals Constructed in Coarse Granular Materials. Proc. 5th Congress of IAHR, Minneapolis, U.S.A., September, pp. 37-48. Langbein, W.B. (1964) Geometry of River Channels. JHD, Proc. ASCE, Vol. 90, No. HY-2, March, pp. 301-347. Langbein, W.B. and Leopold, L.B. (1968) River Channel Bars and Dunes - Theory of Kinematic Waves. USGS Professional Paper 422-L, p. 20. Leopold, L.B. and Maddock, T. (1953) Hydraulic Geometry of Stream Channels and Some Physiographic Implications. USGS Professional Paper 252, Washington D.C., 57 p. Leopold, L.B. and Wolman, M.G. (1957) River Channel Patterns: Braided, Meandering and Straight. USGS Professional Paper 252, Washington D.C., pp. 39-85. Limerinos, J.T. (1970) Determination of the Manning’s Coefficient from Measured Bed Roughness in Natural Channels. W.S. Paper USGS, 1898-B, Washington D.C., p. 47. Meyer-Peter, E. And Müller, R. (1948) Formulas for Bed-Load Transport. Proc. 2nd Congress of IAHR, Stockholm., pp. 39-64. Michalik, A.S. (1989) Some Aspects of the Bed-Load Transport in Mountain Rivers. Proc. 4th International Symposium on River Sedimentation, Beijing, China, pp. 579-586. Milhaus, R.T. (1973) Sediment Transport in a Gravel-Bottomed Stream. Ph.D. Thesis, Oregon State University, U.S.A., p. 232. Gravel-Bed Rivers 255 Misri, R.L., Garde, R.J. and Ranga Raju, K.G. (1984) Bed-Load Transport of Coarse Non-uniform Sediment. JHE, Proc. ASCE, Vol. 110, No. 3, March., pp. 312-328. Mizuyama, T. (1977) Bed - Load Transport in Steep Channels. Ph.D. Thesis, Kyoto University, Japan, p. 118. Moss, A.J. (1962) The Physical Nature of Common Sandy and Pebby Deposits I. Jour. Am. Science, Vol. 260. Moss, A.J. (1963) The Physical Nature of Common Sandy and Pebbly Deposits II. Jour. Am. Science, Vol. 261. Neill, C.R. (1968) Note on Initial Movement of Coarse Uniform Bed Material. JHR, IAHR, Vol. 6, No. 2, pp. 173176. Odgaard, A.J. 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Miall, A.D., Memoir 5 of Canadian Society of Petroleum Geologists, Ottawa, pp. 85-88. Thompson, S.M. and Campbell, P.L. (1979) Hydraulics of Large Channel Paved with Boulders. JHR, IAHR, Vol. 17, No. 4, pp. 341-354. Thornbury W.D. (1964) Principles of Geomorphology. Wiley International Edition, John Wiley and Sons Inc., New York, U.S.A., 2nd Edition. Thorne, C.R. and Zevenbergen, L.W. (1985) Estimating Mean Velocity in Mountain Rivers. JHE, Proc. ASCE, Vol. III, No. 4, April, pp. 612-624. Van Rijn, U.C. (1982) Equivalent Roughness of Alluvial Bed. JHD, Proc. ASCE, Vol. 108, No. HY-10, October, pp. 1215-1217. Vischer, G.S. (1969) Grain Size Distribution of Depositional Processes. Jour. Sedimentary Petrology, Vol. 39. Wadia D.N. (1961).Geology of India. MacMillan and Co. Ltd., London. 3rd Edition (Revised) Walters W.H. Jr. (1975) Regime Changes of the Lower Mississippi River. M.S. Thesis. Civil Engineering Department, Colorado State University, Fort Collins (U.S.A.) White, W.R. and Day, T.J. (1982) Transport of Graded Gravel-bed Material, Chapter 8 in Gravel-Bed Rivers. Eds. Hey, R.D., Bathurst, J.C. and Thorne, C.R., John Wiley and sons Ltd., pp. 181-223. Wolman, M.G. (1954) A Method of Sampling Coarse River Bed Material. Trans. A.G.U., Vol. 35, No. 6, Pt. 1, December, pp. 951-956. Worcester P.G. (1948). A Text Book of Geomorphology. D.Van Nostrand Company Inc., New York, 2nd Edition. C H A P T E R 8 Fluvial Palaeo Hydrology 8.1 INTRODUCTION The word palaeo hydrology was probably first used by Leopold and Miller (1954) in the study of postglacial chronology of alluvial valleys in Wyoming (USA). In this case they were concerned about the interaction of climate, vegetation, stream regime and runoff, which were obtained under several climatic conditions, each different from the present one; this led to the use of the word palaeo hydrology. Since then several investigators such as Schumm (1965, 1977) and Cheetham (1976), have given different definitions of palaeo hydrology. In connection with Quaternary palaeo hydrology Schumm (1965, 1977) stated that palaeo hydrology treats the phenomenon of occurrence of water in the atmosphere, its distribution and composition on the surface of the ground and underground, but has reference to the past. The term is restricted to that portion of hydrologic cycle that involves the movement of water over the surface of the earth, because runoff and the accompanying sediment load are of major importance in determining the non-glacial erosional and depositional features of the Quaternary. Since the composition of water on surface would naturally involve sediment, and its movement, palaeo hydrology also involves consideration of quality and quantity of the sediment moved through the palaeo channels. According to Cheetham (1976) palaeo hydrology is the study of fluvial processes operated in the past and their hydraulic implications. Fluvial palaeo hydrology is that branch of palaeo hydrology which deals with erosion, deposition and the characteristics of former channels. Since the study of palaeo hydrology involves the use of new techniques, conceptual advances and more interdisciplinary research, International Geological Correlation Programme (IGCP) was formulated and initiated in 1973 as IUGS/UNESCO activity. In palaeo hydrology progress has been made through developments in climatology, hydraulics, geomorphology and sedimentology. The fields related to palaeo hydrology are: Palaeo climatology: Study of paleao climates which are climates in periods of geologic past. Palaeo geomorphology: The geomorphology of ancient landscapes, especially as represented today by features that are buried or newly exhumed. Fluvial Palaeo Hydrology 257 Study of quantitative relationships between hydraulic parameters of rivers (e.g., depth, width, slope, discharge, sediment type) Palaeo pedology: Study of palaeo soils i.e., soils that formed by the landscape of the past. In palaeo hydrology the interest in hydrologic and fluvial processes goes back to the times when systematic hydrologic data were not collected, say 10 000 to 15 000 years before present (B.P.), i.e., during Quaternary period and Holocene and Pleistocene epochs. Evidence available for palaeo hydrology of the temperate zone in the past 15 000 years is primarily sedimentological, morphological and historical. Sedimentological evidence includes information deduced from the physical properties of sediments and from organic deposits; this information is useful in the reconstruction of environment during the past and assessing the discharges and the changing rates of erosion. Morphological information can be obtained from the analysis of palaeo channels. Additional historical information is obtained from old maps, records, other historical sources and the dating techniques. As indicated by Gregory et al. (1987), in palaeo hydrology as well as historical geomorphology, a retrorespective approach is preferred because it is desirable to reconstruct palaeo hydrology against the basic definition of hydrology of contemporary environment. An understanding of the present day processes is therefore a must for the interpretation of past hydrological processes. It is also necessary to attempt to extract a considerable amount of information of recent human impact before analysing the prehistoric palaeo hydrology. In this endeavour a better understanding of the relation of sedimentary deposits and river morphology to hydrology is necessary so as to construct palaeo environmental models of terraces, palaeochannels, and other deposits e.g., deltaic deposits. Hence information and discussion in chapters five, six and seven and in earlier chapters is useful in palaeo hydrologic studies. Since climatic changes have occurred during the post-glacial period, it is necessary to know or infer what these climatic changes were and how these changes affected the flood and channel forming discharge which, in turn, would affect the palaeo channels: their dimensions, plan-form and its variation, and such other characteristics. It is presumed that the hydraulic data such as flood discharge were not measured and hence have to be inferred indirectly from whatever measures of palaeo channels that are available. The dating of changes has to be done separately using study of ancient soils, tree rings, pollens and spores, ancient cultural evidence e.g., archaeology, written or oral records, sediments (sedimentology and stratigraphy), land forms (geomorphology and Quaternary geology), ancient floral and faunal distribution, and isotope chemistry of ancient waters and elements such as oxygen and carbon. Palaeo hydraulics: 8.2 OBJECTIVES OF PALAEO HYDROLOGIC STUDIES The broad objectives of palaeo hydrologic study are to reconstruct components of hydrologic cycle, of the water balance and of sediment budgets for the time before continuous hydrologic data were collected. Continuous hydrologic and hydraulic data including meteorological data, stream gauges, evaporation etc. are available for a little over 100 to 150 years, while some hydrologic records date back to more than 2000 years. Hence, palaeo hydrologic studies can be visualised prior to this period up to glacial age. The study of fluvial palaeo hydrology would deal with climatic changes in the past and their influence on vegetation, erosion and deposition, palaeo channel geometry, plan-forms, channel forming discharges, palaeo velocities and probable changes in river courses. Such studies are also useful in 258 River Morphology predicting future changes in fluvial channels and erosion or deposition caused by probable climatic changes and man-made interferences. The knowledge of palaeo hydrology and fluvial palaeo hydrology is useful in interpreting the behaviour of alluvial streams, location of hydraulic structures, choosing sites for storing hazardous wastes, and for exploring valuable deposits in ancient fluvial sediments (Schumm 1977).Hence for studying fluvial palaeo hydrology one should enquire into how and why climatic changes took place in the past and what was their effect on vegetation, runoff and erosion rates in arid, semiarid and humid regions. How can one estimate palaeo velocity and palaeo discharge from observed dimensions of palaeochannels? How would such climatic changes affect the plan-form characteristics? The information presented in this chapter is based on the excellent texts and papers written on palaeo hydrology and related topics by Schumm (1977), Gregory (1983), Berglund (1986), Gregory et al. (1987), Dury (1976) and others. 8.3 BASIS OF ANALYSIS It is reasonable to assume that climate and climatic changes would affect the erosional and depositional processes and hence the landscape and rivers. Even though climate influences the weathering and soil formation, from the point of view of palaeo studies, the effects of climate on vegetation, runoff and sediment yield from mountainous areas are more relevant. Studies by Langbein et al. (1949), Langbein and Schumm (1958) and Noble (1965) indicate how mean annual precipitation, average temperature and vegetal cover affect mean annual runoff and sediment yield. Using data from gauging stations at which the discharge was not materially affected by diversions or regulation, Langbein et al. (1949) showed the effect of mean annual temperature on the mean annual runoff, see Fig. 8.1 Fig. 8.1 Variation of mean annual runoff with mean annual precipitation and average temperature (Langbein et al. 1949) For a given mean annual precipitation, as the temperature increases the mean annual runoff decreases. Also, Langbein and Schumm (1958) obtained a relation between annual sediment yield and effective precipitation for drainage basins of approximately 3800 km2 for temperature at 10°C, see Fig. 8.2. The definition of 10°C curve is based on known values of runoff for each drainage basin from Fluvial Palaeo Hydrology 259 Fig. 8.2 Variation of sediment yield with climate (Langbein and Schumm 1958) which sediment yield data were obtained. These observed values were converted to an effective precipitation, which is the annual precipitation required to produce the known runoff at 10°C using Fig. 8.1. On Fig. 8.2 are also shown the range of vegetation as effective precipitation increases. According to Langbein and Schumm the precipitations as well as the temperature influence the sediment yield from the catchment. This is so because as the temperature increases, higher precipitation is required to produce a given amount of runoff. The variation in sediment yield with precipitation is explained by the interaction of precipitation and vegetation on runoff and erosion. As precipitation increases so does the vegetation that tends to reduce the erosion. On the other hand, as precipitation increases erosion tends to increase. Langbein and Schumm found that when precipitation exceeds 30 cm, sediment yield decreases with increasing precipitation due to more effective grass cover. According to Fournier (1949), in monsoonal climate the sediment yield may increase again after rainfall exceeds 125 cm under the influence of highly seasonal climate. The role played by vegetation in controlling the rate of erosion is indicated by the studies by Noble (1965) on an experimental watershed in Utah (USA). He found that the erosion rate decreased from 2935 kg/ha/storm to a negligible value as the percentage of ground cover changed from 20 to 90. The effect of temperature and vegetation on mean annual runoff and erosion rate has also been studied by Kothyari and Garde (1991), and Garde and Kothyari (1986). Using such type of information it is possible to predict what may have been the effect of change in mean temperature, mean annual precipitation and vegetal cover on the changes in runoff and sediment yield during inter-glaciation and post-glaciation periods. While studying palaeo hydrology it is generally assumed that in relatively recent geologic times, during the later part of the Tertiary and the entire Quaternary period, there has been no significant change in vegetation. Hence the relations between mean annual temperature and precipitation can be used to show how both sediment yield and runoff changed with climatic changes in the geologic past. The second tool available to study fluvial palaeo hydrology is Lane’s balance analogy according to which Qs d ~ QS ...(8.1) where Qs and Q are sediment and water discharge in the stream, d is the sediment size and S is the stream slope. This analogy would qualitatively predict what would happen to stream slope if Qs or Q are 260 River Morphology changed or there is change in the base level due to sea level changes. Here one can use either mean annual discharge or mean flood discharge. The above proportionality is helpful in interpreting channel changes due to climatic changes resulting in change in Q and Qs in palaeo conditions. However, this relationship does not throw light on the changes in the plan-form of the stream. Another important relationship is the qualitative relationship for sediment discharge Qs Qs ~ W ML S DSi ...(8.2) Here W is the average channel width, Si is the sinuosity, and ML meander length. Hence from relationships 8.1 and 8.2 one can express what happens to W, D, ML, S, Si if either the water discharge Q or sediment discharge Qs is increased (+) or decreased (–). Thus one can write + Q + , » W + , D+ , M L , S - , Si- Q » + QS » QS » - W , D , ML , S-, + W + , ML , S + , D- , W - , ML , S - , D+ , - - Si+ Si+ Si+ U | | V | | W …(8.3) Another important tool that can be used in palaeo hydrology is the resistance relationship relating flow velocity U to the depth D or hydraulic radius, slope S, and roughness coefficient e.g., Manning’s n or Chezy’s C, or friction factor f defined in Chapters five and seven. This can be used if palaeo stage is known along with slope S. The slope that has to be used is the terrain slope or palaeochannel slope assuming the flow to be uniform. The roughness coefficient can be estimated knowing the size of the bed material and Strickler type equation discussed in Chapters five and seven. Alternatively, one can use other equations such as Eqs. (8.21) or (8.22). Another method would be to estimate Q knowing the contemporary relation between Q and meander length ML. Analysis of transverse sections of the valley floor enables one to explain the changes caused by lateral erosion, aggradation and avulsion of channels. Examination of longitudinal profile of flood plain allows one to evaluate the influence of eustatic and tectonic factors in fluvial history. For this reason one needs to consider carefully the history of tectonic and neo-tectonic activity in the region and its effect on channel change. Sedimentological methods are used to distinguish various facies of fluvial deposits. The facial setting is different in braiding and meandering systems and hence facial study of fluvial deposit assumes importance. Stratigraphic analysis of undisturbed deposits of palaeo channels is also important. Size distribution of facial units, presence of fills of different ages and recognition of rates of deposition can assist in the reconstruction of many parameters of the past environment. 8.4 CLIMATIC CHANGES: PAST AND FUTURE (SCHNEIDER AND ROOT 2000) Earth’s climate is very different now from what it was 100 million years ago. It is different from what it was 20 000 years ago when ice sheets covered much of the Northern Hemisphere. These climatic Fluvial Palaeo Hydrology 261 changes in the past were driven by natural causes such as variations in the earth’s orbit or CO2 content of the atmosphere. However, climatic changes in future will probably have another source namely human activity because human actions can indirectly alter the natural flow of energy enough to create significant climatic changes. One example is enhancing the natural capacity of the atmosphere to trap radiant energy near earth’s surface – known as green house effect. Burning of fossil fuel that releases CO2 and using land for agriculture or urbanisation leading to large-scale deforestation will cause global warming of 1° to 5°C in the next century. Computer simulation models based on basic laws of thermodynamics and Newton’s laws of motion can be used to predict future changes in climate. The last major glacial ice age occurred about 20 000 years ago and the current 10 000 years long interglacial period (Holocene) began. This has been determined from the ratio two oxygen molecules O16 and O18 isotopes having different molecular weights entrapped in the ice. Ice cores taken from holes drilled into some 2000 m of ice in Greenland and Antarctica also provide information on the presence of CO2, important in studying greenhouse effect. Carbon dioxide concentrations during cold periods were much less than in interglacial periods. The temperature during the past 10 000 years (before 1700 A.D.) was remarkably constant. During the transition of Ice Age to Holocene, which took 5000 to 10 000 years, the average global temperature increased by 5°C and sea level rose by 100 m. Thus, average rate of natural temperature rise was 0.5° to 1.0°C per thousand years. Thus, climate change was responsible for the well known extinctions of woolly mammoths, sabertooth cats, etc. The climatic change was also responsible for change in vegetation. During the last Ice Age most of Canada was under ice; study of pollen cores indicate that as the ice receded, boreal trees moved northward chasing the ice cap. It suggests that the biological communities move intact with a changing climate. It was further noticed that even though during the transition from last Ice Age to the present inter-glaciation nearly all the species moved northward, they moved individually and not as a group. Since due to increased human activity on the globe the temperature changes on the earth will be more severe than during inter-glaciation period, such changes are bound to affect vegetation patterns. Causes for Climatic Changes The causes for climatic changes can be external or internal. Stating which components are external or internal to climatic system depends on the time period and spatial scale being examined, as well as on the phenomena being considered. External causes can be: a. Fluctuations in heat radiated by the sun – perhaps related to sun spots – are external to climatic system. b. Influences of gravitational tugs of other planets on the earth’s orbit are also external to climate system. According to some scientists such tugs gave rise to 40 000 year ice cycle in the past 2.5 million years, 100 000 year ice age and inter-glacial cycles. c. Changes in volcanic dust or CO2 in the atmosphere. On short time scale these factors are external. d. Effects of green house gases on temperature, on 20 year scale are also external. e. Effect of changes in character of land surface caused by human activity is an external cause. Some of the internal causes for climate changes are: a. Dust generation caused by change in plant cover due to changes in climate; b. CO2 and methane levels may rise or fall with ice age cycles; these are internal on a 10 000 years time scale. 262 River Morphology c. If vegetation cover changes because of climatic change, the land surface change becomes internal; change in plant cover can influence the climate by changing albedo (i.e., reflectivity to sun light), evapo transpiration, surface roughness and humidity. d. Unusual patterns of ocean surface temperature – such as the El Nino - are an internal cause. Climate Change Forecasts To predict the significant ways the climate might change, one must specify what people do that modifies how energy is exchanged among the atmosphere, land surface, and space because such energy flows are the driving forces behind climate. Estimating societal impetus involves forecasting the plausible set of human (or societal) activities affecting pollution over the next century. The next step is to estimate the response of the various components of the earth system to such societal forcings. The earth system itself consists of the following interacting sub-components, atmosphere, oceans, cryosphere (snow, seasonal ice and glaciers) and land surface systems. Since knowledge about societal impetus that will actually occur and the scientific knowledge of each sub-system are still incomplete, such models are not yet full developed. Global Warming Forecasts Global warming forecasts for 21st century will depend on the projections of population, consumption, land use and technology. The forecast of amount of CO2 emitted per unit energy will depend on the projections of population and affluence that are increasing and the amount of energy used to produce a unit of economic product. Hence, it is estimated that CO2 emissions will rise several fold over the next 100 years (of course this will depend on what kind of energy system is used). Roughly 50 percent of CO2 emitted will remain in the atmosphere every year i.e., about 3 billion tons of carbon as CO2. This is half of fossil fuel injected CO2. Then one needs to estimate CO2 concentration in the atmosphere using carbon cycle model and this should be fed in computerised climatic models to estimate its effect on climate. The simplest model will give the global average temperature while complex atmospheric models predict time evolution of temperature plus humidity, wind, soil moisture, sea ice and other variables in the three dimensions in space. Such a model is known as general circulation model. Ecologists use these inputs to produce forecasts of regional climatic changes in the future. Further, global heating or warming is not uniform but different for centres of continents, oceans and oceans closer to poles. These temperature differences can cause droughts, high rainfalls, hurricanes and similar other effects. According to Inter-governmental Panel on Climate Change there is likely to be 1.5° to 4.5° C average global rise in temperature in the 21st century. 8.5 PALAEO HYDROLOGIC ESTIMATES OF DISCHARGE AND VELOCITY In palaeo hydrology considerable attention has been given to prediction of palaeo flood velocity or palaeo flood discharge from observed channel dimensions or meander characteristics. Prediction of former river discharges is the primary purpose of palaeo hydrology. Ability to calculate former river discharge makes it possible to determine the quantitative water balance of the drainage basin, the hydrologic regime of the river, and some elements of climate, as well as to detect and specify quantitative changes of some hydrologic and climatic parameters in a given period of the Quaternary and, possibly for older geologic periods too. Fluvial Palaeo Hydrology 263 Theoretically there are two ways in which one can determine the past river discharge on the basis of its effects, firstly through the analysis of preserved morphological effects caused by a given discharge. Unfortunately, the connections between the deposit, its structure, and statistical parameters of grain size distribution and the discharge are so complicated and obscure that they cannot be expressed in any quantitative models. Grain size distribution and its parameters enable one to specify at most the local velocity at which the deposition of given sediment took place. The top level of deposition gives an indication of lowest palaeo flood level. The other method used is known as slack water deposit (SWD) method which gives an idea of the stage of palaeo flood and is described later. The second method is to use relation between characteristic discharge, such as mean annual discharge, Qma bankful discharge Qb or mean annual flood Qmaf and the morphological parameters which can be cross-sectional parameters at bankful discharge such as maximum depth Dmax, hydraulic radius R, channel slope S, width to depth ratio and cross-sectional area A, and channel pattern parameters such as meander length ML, meander belt MB and meander curvature radius Rm. It must be emphasised that these relations are valid only for some types of rivers. The relations between discharge and channel cross-section parameters apply to meandering and straight rivers, while the relations between discharge and channel pattern parameters concern only meandering rivers. No such relationships are available at present for braided rivers. Such analysis assumes that these geometric (cross-sectional and channel pattern) parameters are only a function of characteristic discharge, even though it is known that other parameters such as slope, sediment size and sediment discharge can influence the relationship. Several investigators have worked on developing such empirical relationships between geometric parameters and discharge; a few among them are Jefferson, Carlson, Inglis, Leopold and Maddock, Dury and Williams. They have shown and confirmed that simple power type relationships can be obtained between geometric parameters and discharge viz. D, R, ML, MB ~ Qm. All these relationships have been developed to predict the geometrical parameters for known discharge. On the other hand, in palaeo hydrology, these relations are used to predict characteristic discharge for observed characteristics of palaeo channel. Hence, the accuracy of these equations can be much different than that given by authors when discharge predictions are made from these equations. The palaeo channels commonly appear in the form of (1) exposed cross-sections, (2) abandoned channels on the earth’s surface and (3) rarely as exhumed (or buried) channels. Based on such exposures palaeo fluvial estimates i.e. stream flow of the former channels and channel characteristics can be made from (a) palaeo channel bed sediments (particle size, dune height, etc.), (b) palaeo channel plan-form properties (ML, sinuosity etc.) (c) palaeo channel cross-sectional features e.g., bankful width and (d) palaeo drainage features e.g. stream length, basin area etc. A large number of investigators (see Williams 1986) have dealt with use of (b) and (c) for palaeo fluvial estimates. One question that needs to be discussed is out of the mean annual discharge Qma, bankful discharge Qb and mean annual flood Qmaf , which one should be used in finding the relationship between discharge and channel characteristics ? The use of bankful discharge Qb seems to be justified because many authors believe it to be the channel-forming discharge, and further it value lies between mean annual discharge Qma and mean annual flood Qmaf i.e. Qma < Qb < Qmaf. Also, the bankful stage is the only characteristic stage that can be determined on the basis of well-preserved channel or meandering channel. It must further be emphasised that these equations being empirical and based on limited data, the accuracy of prediction would depend on the size of the sample and the climatic zone from which the sample is taken. 264 River Morphology Palaeo Velocity Determination One of the simplest method of determination of mean flow velocity U for specified depth D or hydraulic radius R is Lacey’s equation U = 11 D0.67 S0.33 ...(8.4) where S is the water surface or channel slope. This is based on 188 observations on canals and rivers with sandy beds. Bray (1979) applied it to 67 gravel and cobble bed rivers for a discharge of 2 year return period and found it to give velocity estimates with a standard deviation of 30 percent. This equation has the advantage that it does not require estimation of resistance coefficient as in the case of equations of Manning, Chezy or Darcy-Weisbach, namely Manning Chezy Darcy-Weisbach U= 1 2 / 3 1/ 2 R S n ...(8.5) ...(8.6) ...(8.7) U = C RS U = (8g RS/ f )1/ 2 The main difficulty in using the above three equations is regarding correct estimation of Manning’s n, Chezy’s C or Darcy-Weisbach friction factor f. Chow (1959) and Benson and Dalrymple (1967) have discussed about estimation of Manning’s n based on a base value of n and further increments in it to account for vegetation, channel alignment etc. However, such refinement in case of palaeo studies may not be warranted and estimation of n, C or f by simples equation would suffice. On the basis of analysis of 1352 measurements for the Odra river basin in Poland, Rotnicki (1983) proposed the equation U= F 0.791I R H n K 2/3 S1/ 2 +0.141 ...(8.8) with a standard error of 12 percent. Here slope was obtained from topographic maps. Palaeo Discharge Determination Rotnicki (1983) has proposed a modified version of the above equation to predict discharge at a particular instant of time as Q= F 0.921I AR H n K 2/3 S1/ 2 + 2.362 ...(8.9) with a standard error varying from 7 to 26 percent depending on the discharge. Williams (1988) used 233 river cross sections from a variety of environments and developed the empirical equation for bankful discharge Qb. 1. 21 0 . 28 Qb = 4.0 Ab S ...(8.10) Fluvial Palaeo Hydrology 265 where Ab is flow area at bankful stage and S is the slope. This is applicable for 0.5 £ Q £ 28 320 m3/s, 0.7 £ Ab £ 8510 m2 and 0.000 041 £ S £ 0.081. For braided channels Cheetham (1980) has analysed Leopold and Wolman’s data and proposed the equation Qb = 0.000 585 S –2.01 ...(8.11) for 0.0000 66 £ S £ 0.003 In the case of palaeo fluvial studies Williams (1988) prefers to use average daily flow for a number of years Q in m3/s. He quotes the equation of Osterkamp and Hedman for 252 sites of various environments in West Central USA, Q = 0.027 Wb1. 71 ...(8.12) where Wb is the bankful width in m. This is applicable in the range 0.8 £ Wb £ 430 m. It may be mentioned that Osterkamp and Hedman realised that the size of bed and bank material would affect the coefficient in the above equation and have given their values in a tabular form (see Williams 1988). Schumm (1972) analysed data of 33 sites in the Great Plains of USA and three sites on the Murrumbidgee River in Australia. His data yields the equation 1.10 Q = 0.029 Wb1. 28 Dmax ...(8.13) Cariston (1965) used data for 31 rivers in Central United States and related meander wavelength ML to Q as 2 .15 Q = 0.000017 M L ...(8.14) which is applicable to meandering rivers with 145 £ ML £ 15,500 m. Some investigators have used flood data at a gauging station and related flood discharge of a given return period to the bed width B, meander wave length ML, cross sectional area, A and river sinuosity Si. Thus according to Dury (1976, 1977) analysis of 135 data points of un-braided under-fit streams gave the following equation Q1.58 = Q1.58 Q1. 58 FG B IJ U H 2.99 K | | | | F M I V =G J H 32.857 K | | = 0.83 A S | | W 1.81 1.81 L 1. 09 i 1.81 ...(8.15) When the values of B. ML, A and Si are known, Q1.58 can be determined from LMF B I GH 2.99 JK M N Q= + FG M IJ H 32.857 K L 1.81 + ( 0.83 A1.09 Si ) 3 OP PQ ...(8.16) 266 River Morphology Palaeo Velocity and Palaeo Discharge in Gravel-bed Rivers Maizels (1983) has stated that in the case of gravel-bed rivers it is preferable to assume that critical conditions prevail at bankful stage. If d is the characteristic size of bed material, for coarse sediment critical shear stress will be given by Shields’ function t 0c = 0.056 ( Dg s ) d or for Dgs = (1.65 ´ 9787), toc = 0.092 d toc = 0.078 d ...(8.17) ...(8.18) while for streams with 10 percent suspended sediment concentration Knowing the palaeo channel slope S, critical depth Dc is obtained as Dc = 0.092 d S –1 or 0.078 dS –1 ...(8.19) The flow depth can also be determined from geomorphic evidence of high water levels, bankful depth from the thickness of sedimentary deposits or from field measurements of exposed palaeo channels. Maizels found that for a series of 69 palaeo channels on the abandoned West Greenland computed critical depth Dc was greater than the observed depth D and the ratio D/Dc was highly variable, its mean value and standard deviation for clear water, and sediment laden flows being (0.5 and 0.44) and (0.83 and 0.49). Once Dc and S are known, Manning’s n can be found using either Strickler’s equation 1/ 6 n = 0.039 d50 ...(8.20) or Limerinos equation n= FG116 DI . + 2 log J d K H 84 1/ 6 0.113d50 ...(8.21) or Darcy-Weisbach friction factor f using f = 0.113 FD I Hd K c 50 1/ 3 ..(8.22) and velocity Uc determined. Some other equations discussed in Chapter VII can also be used. Maizels has discussed the following four methods of palaeo discharge determination. (1) Empirical discharge equations relating mean annual flood discharge, mean annual discharge or bankful discharge to the channel dimensions or channel form parameters (2) Empirical drainage area-discharge relations such Q = aAb ...(8.23) Fluvial Palaeo Hydrology 267 (3) Relations of the type Q as a function of S as proposed by Cheetham (1976) for Leopold and Wolman’s braided river data Qb = 0.000 585 S –2.01 ...(8.24) (4) Regime type relations in which bankful discharge is related to width or depth Maizels has opined that none of these methods is very useful for coarse-bed palaeo channels; hence he recommends those methods based on palaeo velocity determination. Further, he made palaeo discharge computations from palaeo velocity determined by five methods namely (1) using Chezy’s equation with C = (8g/f )1/2 1/ 6 (2) using Manning’s equation with n = 0.039 d50 (3) Manning’s equation with n obtained from Limerinos equation (4) Darcy-Weisbach equation with f = 0.113 FD I HdK c 1/ 3 (5) Darcy-Weisbach equation with f obtained from White-Colebrook equation and then discharge obtained as Qc = Uc DW. The discharges Qc obtained by these methods for 69 palaeochannels were compared. On the basis of this comparison Maizels recommended that for palaeo channels with coarse gravel-bed, ManningLimerinos approach is better if channel widths are uncertain, whereas Darcy-Weisbach approach is better for well defined channels. 8.6 PALAEO HYDROLOGIC STUDIES IN INDIA The palaeo hydrologic studies in India are primarily related to establishing palaeo flood records of some rivers in Central and Western India. The method used for these studies is the analysis of slack water deposits. Slack water deposits (SWD) are fine-grained sand and silt deposit that falls rapidly out of suspension during large floods in protected areas, where the fall velocity is markedly reduced. Such deposits take place in stable bed rock canyons expansion and contractions, back flooded tributaries, meander bends, caves, and abrupt channel. The upper layers of SWD closely approximate the actual stage of flood peak. These depths provide a lot of information on palaeo floods. The age of the deposits are determined by radiometric dating of associated organic or archaeological material. It is shown that the thickness and grain size of SWD is directly proportional to the flood magnitude. The tops of SWD generally provide a minimum estimate of flood peak stage and hence it is possible to estimate minimum peak discharge with each deposit. In the last two decades some studies have been conducted on five rivers in Central and Western India with the following objectives in mind : (i) to identify temporal patterns of large floods during late Holocene; (ii) to identify periods of high and low floods; and (iii) to examine the relationship between flood regime and palaeo climate. The rivers studied (see Kale 1999) have been the Narmada at Punasa, the Godavari at Papikonda, the Krishna at Srisailam, the Tapi at Ghuttigarh Khapa and the Luni river at Bhuka. The maximum thickness of SWD ranged from 2.5 m to 10.5 m and 11 to 37 floods are documented in these deposits. Tributary mouths are the most common geomorphic sites for SWD. The slack water deposits at three places on the Luni river near Bhuka in the Tahr desert in North Western India as reported by Kale et al. (2000) are shown in Fig. 8.3. These deposits were dated using luminescence technology. The textural 268 River Morphology Fig. 8.3 Slack water deposits on the Luni river (Kale et al. 2000) and stratigraphical analysis of SWD indicated that near the tributary channel there is higher variability in sediment size and predominance of finer sediment units. With increasing distance and elevation the percentage of sand increases and the sorting improves. Change in sedimentological and stratigraphical characteristics distinguish the individual units. These characteristics imply sediment deposition by flood waters and also suggest that the sediments deposited at higher level were emplaced by higher magnitude floods and some of the sediments closer to tributary channel were also deposited by moderate magnitude floods. The deposits and their dating suggest that the river has experienced at least 17 extreme floods in the last millennium. Evidence at this site also suggests that no floods comparable in magnitude to July 1979 mega flood have occurred during this period. This observation is in conformity with palaeo flood record of central India. Comparison of long-term monsoon rainfall series for the Luni basin and the region reveals a clear link between the two and indicates that the clustering of large floods in the last few decades and during the medieval warming period is a regional phenomenon associated with wetter conditions. Long-term fluctuations in Indian monsoon rainfall in the past have been explained in terms of large climatic changes in the Asian monsoon region. For completeness of information it may be mentioned that the river Luni at Gandhar has a catchment area of 35 000 km2, width 120-150 m and depth 4 to 10 m. Maximum one-day rainfall of 100 years return period is 200 to 257 mm. The 1979 mega flood had a discharge of about 4300 m3/s. The flood of 1990 was of similar magnitude. Kale et al. (1993) have examined the SWD on the Choral river near Barjar in Central Narmada Basin, India. At several locations, sequences of fine-grained sandy flood deposits have been preserved Fluvial Palaeo Hydrology 269 on the channel margins. The stratigraphic studies of the deposits using radio carbon dating revealed that 510 + 135 B.P. record of floods is preserved in SWD. It was found that during this period discharges greater than 4500 m3/s must have occurred. At least 7 flood units separated by scree deposits, slope wash and charcoal were obtained; see Fig. 8.4. Geomorphic investigations revealed the presence of boulders with intermediate axis between 23 and 42 cm. Such studies have been carried out on the Narmada near Punasa, the Godavari at Papikonda, the Krishna at Srisailam, and the Tapi at Ghuttigarh Khapa and the Luni at Bhuka (see above). The maximum thickness of SWD ranged from 2.5 m to 10.5 m and 11 to 37 floods are documented in these deposits. Lithosection SWD- Choral Flood cm Units 150 1 C1 2 100 3 C3 4 50 6 C4 C6 0 Rubble Rubble 5170 ± 135 Yrs BP Sand Charcoat C2 Rubble Shells CH O R BARJAR AL C0 Rubble 74 0¢N Location map KA MA R Rubble 22 15¢ N Rubble Slope wash 0 4 8 kms Fig. 8.4 Slack water deposits on the Choral river near Barjar (Kale et al. 1993) Figure 8.5 given by Kale et al. (2000) summarises the palaeo flood chronology for Central and Western India during the late Holocene climatic changes. The top scale indicates C-14 years before present (B.P.). The second scale shows the global temperature changes (RW – Roman Warm, DAC – Dark Ages Cold, EMC – Early Medieval Cool, MW–Medieval Warm, LIA – Little Ice Age, MOW – Modern Warm). Below these are given the chronology of palaeo floods in the Narmada, the Luni and the Godavari. This study shows distinct century scale variations in flood frequency and a noteworthy clustering of large floods during the late Holocene period. The study further indicates a period of significantly reduced frequency of large floods during late Medieval and Little Ice Age periods (i.e. 1500 A.D. to 1800 A.D.), and an enhancement in the magnitude and frequency of large floods in the post 1950 period. The last one thousand years of relatively better resolutions of palaeo flood records demonstrates a good association between palaeo floods and late Holocene climatic changes recognised in wide spread area of the world. Hence the authors concluded that the century scale variations in flood frequency and magnitude are linked to long term variations in the monsoon precipitation which are in 270 River Morphology Fig. 8.5 Palaeo floods chronology for Central and Western India (Kale et al. 2000) turn connected with large scale shift in global circulation patterns and ENSO (El Nino Southern Oscillations) activity. Similar studies about obtaining monsoonal activity have been carried out by analysing the deposits in the lakes, studying ice cores in glaciers, and deposits in Arabian Sea. Kumar Sagar (1995) studied the lake deposits in Jammu and Kumaon regions. The rates of deposition of sediment were assumed to be proportional to yearly rainfall. This deposition rate varied from 0.55 mm to 1.05 mm/year in the three lakes in Kumaon region while in Naukuchital it was between 0.16 mm to 3.08 mm/year. Kashmir lakes showed the deposition rate of 5.5 mm for the top 30 cm. A multidisciplinary proxy palaeo climatic investigation in Mansar Lake, Jammu indicated periods of enhanced rainfall between 580 B.C. and 300 A.D. This period is indicative of wet humid phase. From 300 A.D. to 1400 A.D. the area experienced a relatively dry and arid phase with Medieval warming. Thompson et al. (2000) recovered three ice-cores from the Desuopu glacier, Tibet using an electromechanical drill. Their lengths varied from 149.2 m to 167.7 m at about 7000 m above mean sea level. These cores were analysed over the entire length for their oxygen isotope ratio, chemical composition, and dust concentration. In addition they were analysed for hydrogen isotope, chloride – – (Cl–), sulphate (SO 4 ) and nitrate (NO 3 ). The bulk of annual precipitation in the Himalayas arrives during the summer monsoon season and at Desuopu it is net 1000 mm water. The high annual accumulation allows preservation of distinct seasonal cycles. These studies revealed that the site is sensitive to the fluctuations in the intensity of South Asian monsoon, reduction in monsoonal intensity are recorded by dust and chloride concentration. Deeper and older sections of Desuopu cores suggests many periods of drought in the region, but none have been of greater intensity than the greatest recorded drought during 1790-1796 A.D. of last millennium. 20th Century increase in anthropogenic activity in India and Nepal, upwind from this site, is recorded by doubling of chloride concentrations and four fold increase in dust. Like other ice cores from Tibetian Plateau, Desuopu suggests large scale plateau-wide 20th century warming trend that appears to be amplified at higher elevations. Fluvial Palaeo Hydrology 271 Sarkar et al. (2000) collected sediment cores from Arabian sea in water depths ranging from 280 m to 1680 m and analysed O18 and C13 composition of foraminifera. It appears that excess of evaporation over precipitation steadily appears to have decreased during the last 10,000 to 2,000 years, most probably due to increasing trend in summer monsoon rainfall, contrary to land-based palaeo climatic data from the region, which indicates onset of aridity around 4000 years ago. This result is consistent with the hypothesis that significant spatial variability in the monsoon rainfall observed today was persistent during most of Holocene. The analysis of data also indicated significant periodicities of 700 and 1450 years. Similar periodicities have also been reported from North Atlantic and Arabian sea sediment cores. 8.7 FLUVIAL PALAEO HYDROLOGIC STUDIES IN INDIA As regards fluvial palaeo hydrologic studies in India, mention may be made of the efforts to trace the course of the river Saraswati about which reference is found in ancient Indian literature. About one hundred years back the British engineer C.F. Oldham sparked the modern quest for the river Saraswati by questioning why the seasonal river Ghaggar should have a width of about three kilometres in places unless it earlier occupied the bed of a wider river. Since then wind blown sand dune area of Gantiyalji near Longewal has been studied extensively by the specialists in remote sensing, hydro geologists, archaeologists and the historians by taking undisturbed cores of sediment plus water from a depth of 70 m below the ground surface to trace the course of lost river Saraswati, along which prehistoric culture flourished in the historic past. The river course has been studied not only from the historic point of view but also with the hope that it may ultimately lead to providing sweet water for drinking and irrigation purposes in otherwise saline area. The records indicate that the river disappeared around 1500 B.C. while the decline started about 3700 years ago. Two logical questions that need to be answered in this regard are: What courses did the river follow? and Why did it dry up ? In order to trace the river course water samples collected from underneath were tested using carbon dating technique and it was estimated to be 3000-4000 B.P. (Before present) old, i.e., of the Rig Vedic era. Rough course of some buried channels has been traced and sediment samples collected to determine their age; the river course has also been confirmed from satellite imageries. Along the river the drilling has been done to provide sweet drinking water, which is obtained at a depth of 30 m below the surface. The river course can be clearly seen from marks of palaeo channels as wide as 12 km. One hundred and seventy five archaeological sites have been found along the alluvial plain of the Ghaggar river. Since ancient times the civilisations flourished along the river providing water for drinking and irrigation, it is argued that the Ghaggar must have been the mighty Saraswati of the Vedic period. The Saraswati was originally fed by two show-fed sources namely Bunderpunch massif in the Garhwal and Kapalshikar near Manasarovar in Shivaliks. At Pipli in Haryana the Saraswati probably crossed the Grand Trunk Road of the present and the Saraswati statue is erected there. There is reference in Mahabharat that Kurukshetra was to the south of the Saraswati and to the north of the Drashadvati. The river is traced from West Garhwal in the Himalayas to the Gulf of Khambat in Gujarat. Various shifting courses of the Saraswati, as constructed by Ghosh et al. (1983) from all the available evidence, are shown in Fig. 8.6. The oldest course obtained by joining abandoned, buried channels passed through the present cities of Nohar, Surjansar, Samrau and Panchpadra (course 1). With the onset of aridity during Pleistocene and advancement of sand from south-west, the river started 272 River Morphology Fig. 8.6 Old and new courses of the Sarswati river shifting and eventually followed the course 2 towards west. At that time the present cities of Sirsa, Lunkaransar, Bikaner, Samrau and Panchpadra were on its right bank. Probably during the early Holocene period, there was another shifting of the Saraswati towards west between 10,000 and 3800 B.C. The two courses followed are shown as course 3. It turned towards west near Nohar and flowed though Rangamahal, Suratgarh, Anupgarh and Sakhi; hence it severed its confluence with Luni at Panchpadra and discharged into Rann of Kutchh through a river course called Hakra or Nara (Pakistan). Due to increased Aeolian sand that the river had to carry during this period the river aggraded and ultimately took another course through Jakhal, Sirsa, Hanumangarh, Pilibangan, Suratgarh, Anupgarh and Sakhi (course 4). Further around 3800 B.C. the Saraswati further made a westward shift at Anupgarh and joined Indus drainage system in Pakistan (see course 5). What caused the disappearance of the Saraswati? Because of tectonic effects the old Arawali hills cut off the head waters of the Saraswati. The branch of river the Chambal cut deep into the strata Fluvial Palaeo Hydrology 273 northwards and gradually diverted water of the Saraswati first by the Yamuna and then by the Sutlej. The new channel migrated eastward became the Yamuna; similarly the Sutlej migrated westward and joined Indus. This diversion caused a drastic reduction in the flow of Saraswati. When the Saraswati flowed in south-westerly direction, it was flowing against north easterly moving sand advance in Thar desert. Therefore, the Saraswati river could not overcome such sand advance and hence started drifting towards the north with rotational migration in clockwise direction until it became buried in the Anupgarh plains. References Baker V.R. (1983) Large Scale Palaeo Hydrology. In Background to Palaeo hydrology (Ed. Gregory, K.J.). A Wiley Interscience Publication, John Wiley and Sons, New York, Chapter 20, pp. 453-478. Benson M.A. and Dalrymple T. (1967) General Field and Office Procedures for Indirect Discharge Measurements. Technical W.R. Investigation (USGS) Book 3, Chapter A1, pp. 1-30. Berglund B.E. (Ed.) (1986) The Handbook of Holocene Palaeo ecology and Palaeo hydrology. John Wiley and Sons, Chicester. Bray, D.I. (1979) Estimating Average Velocity in Gravel-Bed Rivers. JHD, Proc. ASCE, Vol. 105, HY-9, Sept. pp. 1109-1122. Cheetham G.H. (1976) Palaeo Hydrological Investigations of River Terrace Gravels. In Geo-archaeology (Eds. Davidson, D.A. and Shakley, M.L.), Duckworth, London, pp. 335-344. Chow V.T. (1959) Open Channel Hydraulics. McGraw Hill Book Co., New York. Dury G.H. (1976) Discharge Prediction, Present and Former, From Channel Dimensions. Jour. of Hydrology, Vol. 30, pp. 219-245. Dury G.H. (1977) Underfit Streams: Retrospect, Perspect and Prospect. In River channel Changes (Ed. Gregory, K.J.). A Wiley Interscience Publication, John Wiley and Sons Ltd., Chicester, Chapter 18, pp. 281-289. Garde R.J. and Kothyari U.C. (1986) Erosion in Indian Catchments. Proc. 3rd International Symposium on River Sedimentation. The University of Mississippi (USA), pp. 1249-1258. Ghosh B., Kar A. and Husain Z. (1983) Comparative Role of the Aravalli and Himalayan River Systems in the Fluvial Sedimentation of the Rajasthan Desert. In Geomorphology (Ed. Dixit K.R.) Heritage Publishers, New Delhi, pp. 209-213. Gregory K.J. (Ed) (1983) Background to Palaeo hydrology. A Wiley Interscience Publication, John Wiley and Sons, Chicester. Gregory K.J., Lewin J. and Thornes J.B. (Eds) (1987) Palaeo hydrology in Practice: River Basin Analysis. A Wiley Interscience Publication, John Wiley and Sons, Chapter 1. Kale V.S. (1999) Late Holocene Temporal Patterns of Palaeo floods in Central and Western India. Man and Environment, Vol. 24, No. 1, pp. 109-115. Kale V.S., Mishra S., Baker V.R., Rajguru S.N. Enzel Y and Ely L. (1993) Prehistoric Flood Deposits on the Coral River, Central Narmada Basin, India. Current Science, Vol. 65, No. 11, pp. 877-878, Dec. 10. Kale V.S., Singhvi A.K., Mishra P.K. and Banerjee D. (2000) Sedimentary Records and Luminescene Chronology of Late Holocene Palaeo floods in the Luni River. Catena, Elsevier Publishers, Vol. 40, pp. 337-358. Kothyari U.C. and Garde R.J. (1991) Annual Runoff Estimation for Catchment in India. JWRPM, Proc. ASCE, vol. 117, No. 1, Jan/Feb., pp. 1-10. 274 River Morphology Kumar Sagar M.G. (1995) A Comparative Study of Monsoonal and Non-Monsoonal Himalayan Lakes, India. Proc. 15th International C14 Conference (Eds. Cook G.T., Harkness D.D., Miller B.F., and Scott E.M.) Vol. 37, No. 2, pp. 191-195. Lacey G. (1934). Uniform Flow in Alluvial Rivers and Canals. Min. of the Proc. Inst. C.E. (London), Vol. 237, Pt. 1, pp. 421-453. Langbein W.B. et al. (1949) Annual Runoff in the United States. USGS, Circular-54. 14 p. Langbein W.B. and Schumm S.A. (1958) Yield of Sediment in Relation to Mean Annual Precipitation. Trans. A.G.U., Vol. 39, pp. 1076-1084. Leeder M.R. (1973) Fluviatile Fining – Upward Cycles and the Magnitude of Palaeochannels. Geol. Magazine, Vol. 110, No. 3, pp. 265-276. Leopold L.B. and Miller J.P. (1954) Post Glacial Chronology for Alluvial Valleys in Wyoming. USGS Water Supply Paper 1261, pp. 61-85. Maizels J.K. (1983) Palaeo velocity and Palaeo discharge Determination of Coarse Gravel Deposits. In Background to Palaeo hydrology (Ed. Gregory K.J.) A Wiley Interscience Publication, John Wiley and Sons Inc., New York, Chapter 5, pp. 101-139. Noble E.L. (1965) Sediment Reduction Through Watershed Rehabilitation, USDA, Misc. Publ. 970, pp. 114-123. Rotnicki K. (1983) Modelling Past Discharges of Meandering Rivers. In Background to Palaeo hydrology (Ed. Gregory K.J.) John Wiley and Sons Inc., New York, Chapter 14, pp. 321-346. Sarkar A., Ramesh R., Somayajulu B.L., Agnihotri R., Jull A.J.T. and Burr G.S. (2000) High Resolution Holocene Monsoon Record from Eastern Arabian Sea.. Earth and Planetary Science, Letters, Vol.117, pp 209-218. Schneider S.H. and Root T.L. (2000) Climate Change. Available on Internet. Schumm S.A. (1965) Quaternary Palaeo hydrology. In the Quaternary of the United States (Eds. Wright H.E. and Frey D.G.) Princeton University Press, Princeton. pp. 783-794. Schumm S.A. (1977) The Fluvial System. A Wiley Interscience Publication, John Wiley and Sons , Chicester. Thompson L.G., Yao T., Mosley-Thompson E., Davis M.E., Henderson K.A. and Lin P.N. (2000) A High Resolution Millennium Record of the South Asian Monsoon from Himalayan Ice Cores. Science Magazine, Vol. 289, No. 5486, pp. 8. Williams G.P. (1978) Bankful Discharge of Rivers. W.R. Res. Vol. 14, No. 6, pp. 1141-1154. Williams G.P. (1988) Bankful Palaeo fluvial Estimates from Dimensions of Former Channels and Meanders. In Flood Geomorphology (Eds. Baker V.R. Kochel R.C. and Patton P.C.) A Wiley Interscience Publication, John Wiley and Sons, New York, Chapter 19, pp. 321-334. C H A P T E R 9 Bed Level Variation in Streams 9.1 INTRODUCTION The concept of a graded stream or stream in equilibrium has been introduced in Chapter 4. The balance between yearly water discharge Q, yearly bed material discharge Qs, channel slope S, and the bed material size d for such streams is expressed qualitatively by Lane’s balance analogy (Lane 1955) QS ~ Qs d ...(9.1) This qualitative statement is illustrated in Fig. 9.1 and is valid when channel plan-form and channel width remain the same. This equilibrium can be disturbed by natural causes or man-made changes, and then the channel adjusts to the new conditions by either increasing the slope over a reach (known as aggradation), or by decreasing the slope over a reach (known as degradation). Thus, if Qs increased keeping Q and d the same, the slope will increase by sediment deposition so that with the increased slope and unaltered Q and d, the stream can carry the increased sediment load. In a similar manner, if Q is increased keeping Qs and d the same, a smaller slope will be required to carry this sediment load; this is achieved by lowering of the bed levels resulting in reduction in slope and thus degradation results. Since a stream in equilibrium must satisfy continuity equations for flow and sediment, and resistance and sediment transport relationships, one can get the exact form of Eq. (9.1) if choice is made of resistance and sediment transport relationships. Assuming Q and d to remain unchanged along the length of the stream and using Manning’s and Du Boys equations, one can write Q = BDU 1 2 / 3 1/ 2 Q = n ( BD) D S constant BD 2 S 2 Qs = Bqs = d 3/ 4 U | | | V | | | W ...(9.2) 276 River Morphology Q S Ag gra dat ion g De rad ati on Qs d Fig. 9.1 Lane’s balance analogy Eliminating D from these equations, one gets (Garde and Ranga Raju 2000) Q 6 / 7 S 7 / 5 ~ Qs d 3 / 4 B1/ 5 n - 6 / 7 or Q 6/7 S 7/ 5 ~ Qs d 3/ 4 U V W ...(9.3) if channel width B and Manning’s n are assumed to be constant. Similar analysis has been presented by Jensen et al. (1979) and Klaassen (1995). If some other equations were used for resistance and rate of sediment transport, the exponents of Q, S and d would have been slightly different; however Lane’s balance analogy would still be valid qualitatively. If the rate at which sediment entering a given reach of the stream is less than that at which it is going out, the excess sediment will be picked up from the bed and banks, and there will be lowering of bed level unless the bed is non-erodible; this is known as degradation or retrogression. Thus for degradation ¶ Qs must be positive. On the other hand, if the rate at which sediment enters a given reach of ¶x a stream is greater than the rate at which it goes out, the channel bed experiences deposition of sediment; to occur ¶ Qs must be negative. Aggradation or ¶x degradation occurs over large lengths and both are slow processes. Degradation particularly may proceed for years before it becomes evident. Aggradation and degradation taking place upstream and downstream of large dams respectively are well studied and documented. When alluvial streams are partially obstructed by hydraulic structures such as bridge piers, guide bunds, spurs or abutments, the local flow pattern around the structure is drastically changed causing high velocities and shear stresses in the vicinity of the structure causing local lowering of the bed level. This is known as local scour. Local scour occurring around structures such as bridge piers can endanger this is known as aggradation. For aggradation to occur Bed Level Variation in Streams 277 their foundations causing bridge collapse. This chapter is devoted to the discussion of degradation, local scour around bridge piers, aggradation, and aggradation upstream of dams. DEGRADATION 9.2 TYPES OF DEGRADATION Mention of the phenomenon of degradation is found in Irrigation Manual by Mullins published in 1889, in his book on Irrigation works in India by Buckley in 1905, and in U.S.A. by Gilbert (1917) when he clearly differentiated between scouring and degradation. Degradation occurring in a stream can proceed either in the downstream or in the upstream direction depending on the basic cause of degradation (Galay 1980, 1983). If the reduction in the slope is caused by reduction in Qs, reduction of d or increase in Q at the upstream end, downstream-progressing degradation will occur. On the other hand, if an increase in slope is imposed at the downstream end, upstream Q, Qs and d remaining the same, upstreamprogressing degradation will result. Upstream-progressing degradation occurs if the level of the lake in which the river discharges drops suddenly. It is found that, in general, upstream-progressing degradation takes place at a much faster rate than the downstream-progressing degradation, because in the former case, increase in slope results in substantial increase in the bed material discharge. In the case of downstream-progressing degradation, the slope is progressively reduced and the bed material discharge is asymptotically reduced to zero; hence, it takes much longer time. Occurrences of downstream and upstream-progressing degradation are shown in Fig. 9.2. Degradation Progress No Tributaries River Situation Tributary Tributary with D/s D/s D/s D/s U/ s D/s D/ s U/ s U/s U/s U/ s D/ U/s s U/ s U/s D/s U/s D/s D/s U/s U/ s D/ U/s s U/ s U/s Note: D/s = downstream progressing degradation U/s = upstream progressing degradation Fig. 9.2 Upstream and downstream progressing degradation (Galay 1980) 278 River Morphology The composition of bed material of the degrading stream plays an important role in the process of degradation. Consider degradation taking place downstream of a large capacity reservoir which traps most of the sediment load carried by the stream. If the bed material is uniform and the stream slope is relatively large, the flow deficient of sediment load picks up more sediment from upstream reaches and relatively less from the downstream reach. As a result, stream slope reduces by rotation of stream bed about some downstream control where the water level is held constant. When the slope has reduced to the extent that shear stress on the bed is critical for that size, degradation will stop; see Fig. 9.3. This is known as rotational degradation. Fig. 9.3 Definition sketch for rotational degradation However, if the bed material of the degrading stream is non-uniform and the shear stress exerted by the flow is such that all the particles on the bed are moving, initially rotational degradation will take place thereby reducing the shear stress acting on the bed. When the reduced shear stress t o 2 is equal to the critical shear stress for the d80 or d90 of the bed material, the coarsest fractions of the bed material which could not move start accumulating on the surface. Fifty to sixty percent areal coverage by such material on the surface forms an effective protective armour coat which stops further reduction in slope and hence rotation of the bed. Now degradation takes place by the removal of finer particles at essentially a constant slope. This is known as parallel degradation. For given parent material, any shear stress smaller than t o 2 will give one size distribution of armour coat and increasing shear stress will coarsen the armour coat. The armour coat is coarsest at t o 2 for a given non uniform bed material. Harrison (1950) has studied the armour coat formation. He found that i) Progressive coarsening of surface layer in armour coat development causes an increase in the effective roughness ii) A layer of non-moving particles of one particle size thickness is effective in preventing erosion. iii) The non-moving particles in the pavement arrange themselves in a characteristic shingling formation. iv) As per Einstein’s bed-load theory movement. Dg s di = 27 gives the limiting size beyond which there is no t0 Bed Level Variation in Streams 279 Fig. 9.4 Gessler’s criterion for incipient motion The concept of parallel degradation was first introduced by Gessler (1965). Gessler conducted experiments on degradation using non-uniform sediment at a constant slope and the experiments were stopped when the bed was armoured resulting in practically no movement. The surface layer was sampled and the ratio of fraction of sediment of a given size range di in the top layer of armour coat to its fraction in the parent material was determined. This ratio pi was taken as the probability of the size remaining stationary for the applied shear stress t 0. This value was also interpreted as the probability that instantaneous shear stress on the bed was smaller than the critical shear stress for that size. The average shear stress was considered critical for that size fraction for which pi was 0.50. In this way the critical shear stress curve similar to Shields’ curve was prepared. This curve is shown in Fig. 9.4. When t0 obtained in this manner was plotted against pi on normal – probability scale, it yielded a straight t0c line as shown in Fig. 9.5 with a standard deviation of 0.57, thereby indirectly indicting that shear fluctuations on the bed follow normal distribution. Later studies by Little and Mayer (1972) and Davies (1974) have given slightly smaller values of the standard deviation viz. 0.43 and lower value of critical shear stress for coarser material. Use of Figs. 9.4 and 9.5 enables one to compute size distribution of armour coat for parallel degradation for known parent bed material. Gessler found that for grain size having Dg s di greater than 50, pi can be taken as 100 percent. t0 Figure 9.6 shows qualitatively the regions of no motion, parallel degradation and rotation degradation in relation to size distribution of bed material and initial shear stress. Here da is the average size of the bed material size. According to Egiazaroff (1965) if applied shear stress is less than the critical shear stress for di = 0.4 da, there will be no movement; if the shear stress is greater than the critical shear stress for di = 0.4 da and less than the critical shear for di = 3.0 da parallel degradation 280 River Morphology Fig. 9.5 Relation between probability of movement Pi and dimensionless bed shear stress t0 (Gessler 1995) t 0c Fig. 9.6 Regions of no motion, and parallel and rotational degradation would result. If applied shear is greater than critical shear for di = 3.0 da, rotational degradation results. The demarcating value of shear stress between parallel and rotational degradation has been obtained by Mittal (1985) by using Gessler’s method for some hypothetical mixtures. The mean curve between Bed Level Variation in Streams 281 d 0 i 100 d 50 i 50 t0 i D g s d501 å and Kramer’s uniformly coefficient M defined as M = å D pi D pi along with available data plotted on it is shown in Fig. 9.7. The coordinates of the mean curve in Fig. 9.7 are given in Table 9.1. Fig. 9.7 Variation of toi with M (Mittal 1985) D g s d 50i Table 9.1 Variation of M 0.20 0.19 toi with M (Mittal 1985) D g s d 50i 0.30 0.10 0.40 0.06 0.80 0.04 toi D g s d 50i Little and Mayer (1972) have proposed the equations d50 a = 0.908 d50 i s gi s ga s gi F u I GG JJ H dr / r - 1i g K 3 * f s 0.353 ...(9.2) = 1.317 – 0.2458 sgi 282 Here u* = River Morphology t oi and sgi and sga are geometric standard deviations of parent material and armour rf coat respectively. Using limited data Shen and Lu (1983) proposed the following equation for d50a t¢ d50 a o = 0.853. t oc d50 i FG IJ s H K 0.885 gi ...(9.3) in which t¢o is the shear stress with respect to grain roughness and sgi is geometric standard deviation of parent material of median size d50i. Using Little and Mayer’s data and the data from San Luis Valley canals, Odgaard (1984) found that the size distribution of armour coat follows normal distribution. Recently Garde et al. (2004) have plotted size distribution data for armour coat from a number of studies in the form of di vs percent d50 a di . d50 a Here d50a is median size of the armour coat. The distribution has a standard deviation of 0.57. Hence, if d50a can be determined for known size distribution of the parent material and known to, armour coat size distribution is known. Garde et al. (2004) have proposed the following equation for d50a finer and found Odgaard’s conclusion to be true except for very small and very large values of d50 a d50 i R U | | - 1.648 | | M = 0.3 + 1.361 exp. S V F D I | | t G J | d T H K | W 1.241 *i 50 i ...(9.4) t 0i and D is depth of flow. D g s d50 i This equation is based on a large volume of data and is found to be more accurate than Eqs. (9.2) or (9.3). Here M is Kramer’s uniformity coefficient of initial mixture, t*i = 9.3 DOWNSTREAM-PROGRESSING DEGRADATION As mentioned earlier, downstream-progressing degradation is related to the changes in Q, Qs or d at the upstream end. The situations under which downstream-progressing degradation takes place are discussed below. Degradation Downstream of High Dams and Barrages When a high dam is constructed on a movable bed river, it traps a very large percent of the incoming bed material load; this percentage can be as high as 95 percent. As a result, water released from the dam is Bed Level Variation in Streams 283 deficient in sediment load as compared to its sediment transport capacity. Hence the flow picks up sediment from the bed (and from the banks if bed is non-erodible) and the bed level goes down thereby decreasing the slope. The rate and extent of degradation depends on many factors such as flow releases from the dam, downstream slope, size distribution of the bed material and its variation with depth, downstream control. Extensive observations have been made in U.S.A. and other western countries on degradation occurring downstream of dams on several streams. In this connection papers by Stevens (1938), Hathaway (1948), Bondurant (1950), Vetter (1953) and Galay (1983) may be seen. Table 9.2 gives the information on the extent and length of degradation, duration and bed material description for few dams, Galay (1988) has observed that degradation across the stream may not always be uniform. He mentions the case of degradation below the Gardiner dam on the South Saskatchewan river in Canada, where at a section 1.6 km downstream of the dam about 200 m of the 1000 m width had experienced 2–3 m lowering while it was much less in the rest of the channel width. This is likely to be due to nonuniform releases of flow from the dam as well as the non-uniformities in bed material across the width. A brief discussion is necessary about the changes in bed level downstream of barrages in IndoGangetic plain of the Indian subcontinent, where thick alluvial strata exist. Barrage is a low–height gated weir used to raise the water level so that canals can take off from the upstream of the barrage. The Islam Weir on the Sutlej River failed due to excessive degradation. Two metres of degradation caused the failure of part of the weir. It has been found that downstream of such weirs the bed degrades for a few years which is followed by aggradation. This occurs probably because of the manner in which the gates are operated. The data on barrages in India, Pakistan and Egypt indicate that degradation of the order of 0.8 m to 2.0 m has occurred in the past. Table 9.2 River Saalach (Germany) Missouri (U.S.A.) Wisconsin (U.S.A.) South Canadian (U.S.A.) Rio Grande (U.S.A.) Wolf Creek (U.S.A.) Colorado (U.S.A.) Colorado (U.S.A.) Yuba (U.S.A.) Yellow (China) Mainstee (Canada) Data on degradation downstream of high dams (Adapted from Garde 1955 and Galay 1983) Dam Reichenhall Fort Peck Praire Du Sac Conchas Elephant Butte Fort Supply Hoover Imperial Sanmexia Junction Degradationm 3.0 1.5 2.3 3.1 2.1 to 2.4 2.4 7.1 3.1 4 to 5.5 4 3.7 Strata Alluvial Sandy Sand and gravel -doSand Sand and gravel -doGravel Fine sand Sand and clay Length of degradation km 9.0 km up to confluence with Saalach River About 80 km 32 km About 150 km 111 km 68 - Period of observation years 21 11.5 18 10 2 4.5 14 18 2 4 12 284 River Morphology Data on four weirs Khanki, Rupar, Rasul and Marala on the rivers the Chenab, the Sutlej, the Jhelum and the Chenab respectively during the period 1891-1927 indicated (see Garde 1955) that the rate of degradation varied from 3 cm/year to 24 cm/year while the rate of recovery ranged from 6 cm/ year to 13 cm/year. It may be mentioned that the degradation that has occurred on the Ratmau torrent in North India over a period of 100 years has been well documented and discussed briefly in Chapter 11. Increase in Water Discharge An alluvial river will experience degradation if water discharge in the stream is increased by flow diversion. Since increased flow with the same slope and sediment size has higher sediment transport capacity, the flow picks up sediment from the bed and banks of the river, and degradation occurs; see Fig. 9.13(b). Such degradation has been observed by Kellerhals et al. (1977) on the Mattagami river flood way (Adam Creek) in Ontario, Canada, and also on the Five Mile Creek in Wyoming (U.S.A.) where clear water flow was added to the creek from waste water of the irrigation project (Lane 1955). Change of land use, such as deforestation, can also increase flood discharge and cause degradation, however the extent of degradation would depend on the supply of sediment from the upper part of the catchment. In a similar manner, an exceptionally high flood can cause lowering of stream bed in the downstream direction. However, degradation occurring during high flood seems to depend on the nature of flood and sediment concentration hydrographs. Degradation will occur during the rising limb of hydrograph if river is carrying relatively less sediment load compared to its capacity. Such lowering of the order of five metres occurred during 1933 on the Yellow river reach of about 50 km around Lungmen (Todd and Eliassen 1940). Gravel Mining When sediment is removed from the channel bed for construction activity, the sediment transported by the stream will get deposited in the depression created by removal of material, and hence the flow downstream will have less sediment load compared to its capacity. As a result, degradation occurs in the downstream reach. Such degradation of a few metres was observed on the Cherry Creek near Denver (U.S.A.) (Lane 1947). Similarly, extensive degradation along with local scour has been observed at a major bridge in Canada by Cullen and Humes (see Galay 1983). Storage of Bed Material Downstream-progressing degradation has also been found to occur below alluvial fans. As the river emerges from a single steep channel from the mountainto the plain, it deposits most of its coarse bed material on the alluvial fan and the river flows in multiple channels. When such channels join into a single channel at the base of the fan, it is deficient in bed material load; hence, degradation can take place. Such degradation has been observed by Galay (1983) in Iran. Degradation at Channel Bifurcations Downstream-progressing degradation also occurs at channel bifurcations. Consider a channel taking off from the main stream and further assume fifty percent of the flow is diverted. If the stream is carrying appreciable quantity of bed load, the diversion channel will carry a very large percent of bed load due to formation of secondary circulation at the bend. As a result the main branch will carry less bed load and will experience degradation, while the branch may experience aggradation. Bed Level Variation in Streams 285 9.4 UPSTREAM-PROGRESSING DEGRADATION If the water level of the lake or the sea into which the river discharges falls, an increased water surface slope is imposed on the river. Hence, the river picks up material from the bed to fulfill its increased transport capacity and degradation occurs. Such degradation has been observed in rivers in Iran and Russia due to lowering of Caspian sea level (Ananian 1961). Such degradation progresses upstream and if upstream flow and sediment load conditions remain the same, final degradation profile would be parallel to the original bed. If a tributary is joining such a degrading stream, the tributary also experiences upstream-progressing degradation. Such degradation has occurred on the Big Sioux river in U.S.A. and on the Peace river in Canada (Galay 1983). Execution of cut-off in a meandering river causes increase in the bed slope in the cut-off leading to degradation upstream of the cut-off and aggradation downstream as shown in Fig. 9.13(d). Yearke (1971) has reported 4.5 m of lowering of bed level following the development of cut-off on the Peabody river. Similarly, removal or shift in the control section along the river channel can also cause degradation or aggradation. If the main river, to which a tributary joins, shifts towards the tributary due to channel shifting, the tributary will experience upstream-progressing degradation. The tributary will experience aggradation if the main river shifts away from the tributary; see Fig. 9.13(c). This is due to lowering or rises in temporary base level of the tributary. Under special conditions, a combination of downstream-progressing and upstream-progressing degradation can occur simultaneously in a given stream. Such occurrence on the Brenta River in Italy is reported by Galay (1980). Upstream and downstream-progressing degradation is shown in Fig. 9.2. 9.5 EFFECTS OF DEGRADATION Lowering of riverbed due to degradation has beneficial as well as harmful effects. Some of the important effects are discussed below (Garde and Ranga Raju 2000). i) Lowering of bed level downstream of a dam can affect the functioning of the hydraulic jump based energy dissipator. Lowering of tail water can move the hydraulic jump downstream and in the extreme case the jump may form outside the stilling basin. ii) Degradation downstream of dams and weirs on permeable foundation will increase the effective head and hence the uplift. iii) Lowering of bed level downstream of the dam lowers the water level at irrigation outlets and may make them ineffective. Similarly in the case of navigable rivers, considerable lowering of water level may make the navigation locks ineffective. iv) Lowering of bed levels in the main river can initiate degradation in the tributaries and subtributaries, and cause additional scour at bridges and abutments. v) Degradation in a stream causes lowering of ground water levels in adjacent areas. vi) Increase in effective head (i.e. difference between head and tail water levels) at the dam means that additional power can be generated. This can be anticipated and provision can be made in the design. Such provision for increased power generation was made at Uppenborn powerhouse on the Saalach River in Germany and Praire Du Sac dam on the Wisconsin River in U.S.A. vii) Degradation causes increase in the capacity of the channel and hence helps in lowering high flood levels. 286 River Morphology 9.6 PREDICTION OF DEPTH OF DEGRADATION Prediction of the depth of degradation needs to be discussed separately for in rotational degradation and for parallel degradation. Let us assume that Q, S, Qs and d are known as well as the location of the control section, and that the sediment supply is completely cut-off. Hence first rotational degradation will occur and shear stress to on the bed will reduce to to2. Hence one has two equations t02 = gf D2 S2 and Q= 1 5/3 1/ 2 S2 B D2 nf U | V | W ...(9.5) If nf is known, these equations can be solved to determine D2 and S2. Using Stricker type equation for known d50a, d, nf can be calculated; thus depth D2 and S2 can be known. Then depth of degradation at the dam will be L (S – S2) where L is distance of control section from the dam. Subsequently parallel degradation will take place at constant slope. Gessler (1965) has found that the lowering of bed level in parallel degradation is about 2 d90 of the original mixture. Transient degradation profiles can be obtained using any one of the mathematical models available, see Chapter 12. However, in using these models one has to use some conceptual model for coarsening of the bed material with time. These are summarized by Murthy et al. (1998). 9.7 CONTROL OF DEGRADATION In recent times, three methods have been tried to control degradation. These are artificial feeding of sediment, artificial armouring of the bed and construction of weirs (Scheuerlein 1989). Artificial Sediment Feeding When the stream is degrading due to deficiency in sediment load, the degradation can be reduced or arrested if properly estimated sediment load of known sizes is fed every year on regular basis. This method was first applied at the Upper Rhine River downstream of Iffezheim barrage. The sediment feeding began in 1978 and has been continued without interruption. Since the original river bed is in the gravel range, sand mixed with gravel and having an average size of 20 mm is being fed at 10,000 m3/ year to 21 000 m3/yr. The conditions favourable for using this method are that there is no barrage on the Rhine downstream of the Iffezheim barrage, and that the feeding material is available close at site. The feeding material is transported and dropped by means of barges over a length of 760 m. The annual cost in 1986 was seven million D.M. Artificial Armouring Artificial armouring means formation of a complete cover on the bed with a layer of coarse material which is capable of resisting the shear exerted by the flow. To stop washing away of fine material underneath, a filter of graded material or geotextile can be used. The armour thickness should be 0.8 to 1.0 m. The size distribution of the armour coat can be obtained using Gessler’s analysis combined with estimation of design flood of 100-year return period. Scheuerlein (1989) quotes one case where this method is applied, namely in one of the two Danube branches in Vienna, called Neue Donau. The area covered is 3 Mm2. The armour coat can be constructed on dry bed, or at low velocity. Bed Level Variation in Streams 287 Construction of Weirs or Dams If a weir or dam is constructed in a reach which is degrading because of an upstream dam, it creates backwater and reduces velocity, thereby reducing degradation. It can also cause aggradation which can offset the degradation due to the dam upstream. Construction of a series of dams also moderates the flood, thereby reducing the transport capacity. This has been actually observed on the Colorado River in U.S.A. where a series of dams – Hoover, Parker and Imperial – is constructed. In the case of Naga Hemadi barrage on the Nile River, degradation of the order of 0.8 m occurred after eight years of operation. A subsidiary weir had to be constructed to control the degradation. It must however be mentioned that all these methods usually protect a certain reach of the river from further degradation. Degradation would occur downstream of that reach if the flow is still capable of transporting sediment and there is no supply from the upstream. Progress of degradation is also sometimes arrested by the presence of non-erodible material such as rock reef or lenses of heavy gravel. LOCAL SCOUR AROUND BRIDGE PIERS Scour is the local lowering of the stream bed around a hydraulic structure. Scour takes place around bridge piers, abutments, spurs and breakwaters due to modification of flow pattern causing increase in local shear stress which, in turn, leads to removal of material and hence scour. Huber (1991) has reported that since 1950 over 500 bridges have failed in U.S.A. and majority of failures were due to scour of foundation material. Such failure is primarily due to three causes: i) Inadequate knowledge about scour phenomenon when the bridge was constructed ii) Inadequate data and knowledge about design flood; and iii) Increase in the loading on bridges due to increase in the size of trucks and wagons and frequency of loading. The total lowering of stream bed at any site can take place due to four reasons (see Garde and Kothyari 1995). 1. Degradation taking place at bridge site due to dam upstream. In extreme cases, the bed can go down by as much as 4 to 6 m. 2. In the case of bridges on rivers in Indo-Gangetic plain, the river width in the vicinity of the bridge is reduced by providing embankments and guide bunds. If the approach flow width and depth are B1 and D1, and B2 and D2 represent width at bridge site and depth of flow, these are related as D2 B = 1 D1 B2 FG IJ H K 0.60 to 0. 79 ...(9.6) Hence, reduction in width can lead to lowering of bed level. 3. Lowering of bed level that takes place due to modification of flow pattern; this is known as local scour. 4. Additional lowering of bed level can take place due to concentration or non-uniform flow distribution across the river width at the bridge. 288 River Morphology Fig. 9.8 Vortex system and definition for scour In this section, attention is focused on local scour that takes place due to modification of flow pattern. Earlier studies have indicated that depending on the type of pier and free stream conditions, an eddy structure comprising all or anyone or none of the vortex systems can form. These include horseshoe vortex system, the wake vortex system, and/or the trailing-vortex system. Figure 9.8 shows the formation of a horseshoe vortex at the pier. This increases the local shear and causes scour. Measurement of shear stress around bridge pier has shown that the average shear stress around the pier can be about four times the shear stress in main channel, while the instantaneous shear stress is about 10 to 12 times the average shear stress in the main channel. 9.8 FACTORS AFFECTING SCOUR A number of experimental investigations on scour around bridge piers have been carried out since 1940. Two excellent reviews published in 1975 and 1977 summarise the state of art on scour at that time. The first was prepared by U.P. Irrigation Research Institute and published by CBIP (1975), and the second is by Breusers, Nicollet and Shen (1977) published in the Journal of Hydraulic Research of IAHR. On the basis of these reviews and work published since then, factors affecting scour depth can be summarized as follows. 1. Whether the incoming flow is clear water flow or sediment transporting flow: when u* is less u* c than unity, clear water flow occurs; when it is greater than unity sediment transporting flow Bed Level Variation in Streams 289 g D S is average shear velocity in the channel and u*c is its value when the occurs. Here u* = d i bed material just starts moving. Other conditions remaining the same clear water scour is about ten percent more than scour in sediment transporting flow; further clear water scour depth dsc increases asymptotically while equilibrium scour depth dsc in sediment transporting flow is attained in finite time. 2. Depth of flow: Melville and Sutherland (1988) have shown that when depth of flow to pier width ratio D/b is greater than 2.6, the scour depth does not depend on the depth of flow; however for smaller depth, depth of flow affects the scour depth. 3. Effect of Shape of Pier Nose: The shape of the pier nose affects the strength of horse-shoe vortex as well as the separation around the bridge pier; hence it affects the scour depth. This effect is quantified by the coefficient Ks, which is defined as the ratio of the scour around the pier of given shape to that around a cylindrical pier under identical conditions. The values of Ks have been determined on the basis of works of Tison, Laursen and Toch, Chabert and Engeldinger, Larras, Garde and Paintal, and Garde (Garde and Kothyari 1995), and are tabulated below. Table 9.3 Average values of shape coefficient Ks Ks 1.0 1.1 to 1.25 0.93, 0.79, 0.70 1.0, 0.86 0.45, 0.61, 0.75, 0.88, 0.94, 1.00 Shape Cylindrical Rectangular (d/b = 2 to 6) Lenticular (2 : 1, 3 : 1, 4 : 1) Elliptical (2 : 1, 3 : 1) Triangular with apex angle 15o , 30o , 60o, 90o, 120o , 150o 4. Angle of Inclination of Pier with Flow: When the pier axis makes an angle with the general direction of flow, two major changes take place in the flow field. First is that the separation pattern is drastically changed except in the case of cylindrical pier. Secondly the open width between piers, perpendicular to the flow direction is reduced as the angle of inclination is increased. This effect is incorporated by introducing a coefficient Kq for non-circular piers, which is defined as the ratio of scour around the bridge pier at a given angle of inclination to that at 0° angle of inclination under identical conditions. On the basis of works by Laursen, and Varzeliotis, the following values are recommended (Garde and Kothyari 1995). Table 9.4 Effect of angle of inclination q on scour for rectangular pier (–/b = 60) q° Kq 0 1.0 7.5° 1.17 15° 1.37 30° 2.37 45° 3.77 5. Opening Ratio: The opening ratio a is defined as a = B spacing of piers and b is pier diameter, or width. Analysis of extensive data by Garde et al. a B - bf where B is centre to centre 290 (1987) has shown that River Morphology –0.3 . Here Dsc or Dse are scour depths measured below D water surface for clear water and sediment transporting conditions respectively. 6. Bed Material Characteristics: Scour depth is affected by relative density of sediment, its median size and geometric standard deviation. For all field problems, relative density of sediment can be taken as 2.65. According to Lacey’s approach Dse ~ d–1/6 where d is the sediment size. Kothyari (1989) has experimentally found that in clear water scour dsc ~ d–0.31 while in sediment transporting flow dse ~ d– 0.07. Here dsc and dse are scour depths below average bed level in clear water and sediment transporting flows. The effect of sediment non-uniformly is studied by Ettema (1980) and Kothyari (1989). If Ks is defined as bD sc or Dse g ~a Ks = Equilibrium scour depth for non - uniform sediment of given d50 Equilibrium scour depth for uniform sediment of size d50 then the variation of Ks with geometric standard deviation sg of the bed material is as follows. Table 9.5 Variation of Ks with s sg Ks £ 1.5 1.0 2.0 0.75 2.5 0.40 3.0 0.30 2.5 0.24 4.0 0.19 4.5 0.13 Kothyari (1989) has further suggested that to take into account the effect of sediment nonuniformity, one can alternatively use effective sediment size deu defined as follows: deu = d50 if sg £ 1.124 deu = 0.925 d50 sg0.67 if sg £ 1.124 U V W ...(9.7) 7. Effect of Stratification and Unsteadiness of Flow: Effect of the stratification on scour has been studied by Ettema and Kothyari in the case of clear water scour. It is concluded that stratification in which a relatively thin coarse top layer covers a thick fine bottom layer is the critical condition which should be considered for design. Similarly, unsteadiness of the flow also affects the scour depth. This aspect has been studied by Kothyari (1989) and a method has been developed to estimate scour under unsteadiness of the flow. 8. Flow Parameters: Most of the equations developed using experimental or field data can be classified into the following groups: Group – I Here d se b is related to in the form D D d se b =f D D F I H K F I H K ...(9.8) Bed Level Variation in Streams 291 Thus, Breusers and Ettema have proposed the equation d se b =K D D F I H K ...(9.9) Where K = 1.4 according to Breusers and 3.0 according to Ettema. According to Laursen and Toch d se b = 1.35 D D Group – II Here Dse D or se is related to Fr = D b Dse b = 2.1 D b F I H K 0. 70 ...(9.10) U b and . Thus according to U.S. Corps of Engineers D gD 0.65 F I H K Fr0.20 ...(9.11) While according to Coleman Dse b = 1.39 D D F I H K 0.90 Fr0.20 ...(9.12) Group – III Here Dse D or se is related to or Fr, Ns = b D Ub U or Re = . Two typical equations in this v Dg s d rf category are those of Shen et al. (1969) and Carsten (1975). Shen et al. (1969) dsc = 0.000223 Re0.619 Here dsc is in ft and Re = Carsten (1975) d sc N s2 - 1.64 = 0.546 N s2 - 5.02 B Ub . v ...(9.13) LM N OP Q 0.83 ...(9.14) 9.9 EQUATIONS FOR PREDICTING SCOUR DEPTH Even though a number of equations have been proposed for estimation of depth of scour around bridge piers, only four methods are discussed here and verified with field data. 292 River Morphology Lacey-Inglis Equation According to Lacey the depth of flow DLQ at the dominant discharge Q is given by DLQ F QI = 0.47 G J HfK l 1/ 3 ...(9.15) in which f1 is Lacey’s silt factor given by fl = 1.76 dmm . Inglis found that on the basis of data on 14 bridges in North India, equilibrium scour depth below W.S. Dse is given by Dse = K DLQ ...(9.16) where K varied from 1.76 to 2.59 with an average value of 2.09. When this equation is used for design purposes, discharge that is to be used is the one with return period of 50 or 100 years. In the light of discussion above regarding factors affecting scour, it stands to reason that K in Eq.(9.16) should depend on factors such as sediment size, pier shape and obliquity of flow. Further, since Lacey’s equation is valid for sandy non-cohesive material and data on scour by Inglis are also from bridges in alluvial rivers, Lacey-Inglis method should not be used for clayey or gravelly beds. Another method developed on the basis of extensive data using uniform and non-uniform sediments is the one proposed by Kothyari et al. (1989). According to this method, the scour in clear water flow is given by d sc b = 0.66 d d F I F DI H K H dK 0. 75 – 0 .11 0.16 LM U - U MN D g d / r 2 s 2 c f OP PQ 0. 40 a–0.30 ...(9.17) where the average critical velocity is given by 2 Uc b = 1.2 d D g s d /r f F I H K F DI H dK 0.16 ...(9.18) Similarly, scour under sediment transporting flow is given by d sc b = 0.88 d d F I F DI H K H dK 0.67 0. 40 a–0.30 ...(9.19) These equations are for uniform sediment. When sediment is non-uniform, effective size deu is used in place of d in the above equations. Alternatively, one can compute dsc or dse for uniform sediment and multiply it by Ks which depends on sg. It may be mentioned that Melville and Sutherland have proposed an equation for maximum possible scour depth as dsem = 2.5 b ...(9.20) This scour depth below the general bed level is reduced by multiplying factors which depend on whether the scour is clear water scour, depth is shallow and sediment is non-uniform. These coefficients are determined using experimental data. Bed Level Variation in Streams 293 9.10 VERIFICATION OF EQUATIONS FOR SCOUR DEPTH The equation proposed by Lacey-Inglis, Laursen-Toch, Melville-Sutherland, and Kothyari et al. were verified (see Garde and Kothyari 1995) using scour data for 17 bridges in India, 55 bridges in U.S.A., 6 bridges in New Zealand, and 5 bridges in Canada. The result of this verification is summarized in Table 9.6. and comparison of observed versus computed depth of scour by Lacey-Inglis and Kothyari et al. methods are shown in Fig. 9.9 and 9.10 respectively. 10 2 Line of perfect agreement 10 1 (ds)c in m 10 0 10 –1 Legend : U.S. data Newzealand data U.G. canal data ganga at Mokameh Other data of RDSO Ravi river data Inglis data Canadian data –1 10 10 0 10 (ds)o in m 1 10 2 Fig. 9.9 Comparison of (Ds)c vs (Ds)o using Lacey-Inglis method (Garde and Kothyari 1995) 2 10 Line of perfect agreement 10 (ds)c in m 1 10 0 Legend : U.S. data Newzealand data U.G. canal data ganga at Mokameh Other data of RDSO Ravi river data Inglis data Canadian data 10 –1 10 –1 10 0 10 (ds)c in m 1 10 2 Fig. 9.10 Comparison of (ds)c vs (ds)o using Kothyari et al. method (Garde and Kothyari 1995) 294 River Morphology Table 9.6 Relative accuracy of prediction of scour depth by different equations Percent of data falling within given error band Method Lacey-Inglis Laursen-Toch Melville-Sutherland Kothyari et al. ± 30% 59 38 79 86 ± 50% 85 65 95 96 ± 90% 100 98 100 100 From this study it was concluded that among the four methods studied, methods given by Kothyari et al. and Melville-Sutherland yield nearly the same accuracy and are better than Lacey-Inglis or Laursen-Toch method. Their added superiority lies in the fact that they take into account all factors which affect the scour depth. The time variation of scour has been studied by Islam et al. (1986) who found that scour depth ds at any time t is given by ds pt = sin 2 t max d se LM N OP Q 1/ m ...(9.21) where m and tmax are given by F DI HdK m = 0.135 F DI H bK 0 .087 0.25 ...(9.22) Equations (9.21) and (9.22) are based on the following ranges of related variables: Sediment size d 0.20 mm–7.8 mm Fall velocity w 0.026 m/s–0.41 m/s Flow depth D 0.02 m–0.70 m Pier diameter b 28.5 mm–240 mm Velocity U 0.10 m/s–1.30 m/s It must be mentioned that to use Eq. (9.21), one must estimate dse by one of the method discussed earlier. The time variation of scour as well as scour depth for clear water scour can be determined using the algorithm proposed by Kothyari (1989); this algorithm is shown in Fig. 9.11. First the diameter of the horse-shoe vortex is computed. Then it is assumed that the average shear stress at the pier nose is four times the average shear stress in the channel, and when the former reaches the critical value, scour stops. As the scour develops, the horse-shoe vortex sinks into the bed and its area increases by ds2 where 2 tan j Bed Level Variation in Streams Start Red b,d,D,S,B,U,gs, ds and rf Calculate horse-shoe vortex diameter Dv Dv /d = 0.28 (b/D)0.85 Ao = PD v / 4 R = BD/(B + 2D) to = gf RS ds 2 tan f 0.57 2 2 295 ds is the scour depth and f is the angle of repose of bed material. Due to increase in the area, the shear stress in the vortex decreases, and its is assumed that shear at any time t, tpt it is given by tpt = 4 t0 FG A IJ HAK 0 t cl ...(9.23) where Ao and At are the original and new areas of vortex and c1 is a constant. The time required to move a single particle is assumed to be t* = probability pot is given by p0t d c2 and the p0 t u * t At = A0 + tpt = 4(A/At) to 3 .45 . Pot = 0.45 t *pt F t IJ = 0.45 G H Dg dK pt s 3.45 3. 45 = 0.45 t * pt ...(9.24) to = 0.05d/potU * t No Is t £ t*c *pt t1 = tl–1t* ds = Id Print tI and dsI End where t*pt = t opt Dgs d . I=I+1 Yes Fig. 9.11 Algorithm for computing time varying scour (Kothyari 1989) When a single particle is removed, the time elapsed is t*. By repeating the process one can calculate S t* i.e. the time required to cause scour depth of a, 2d, 3d … etc. When the shear stress in the scour hole reaches critical value for size d, no further scour will take place. By calibrating the model with known data of scour depth variation with time, the constants c1 and c2 in the above equations were found to be 0.57 and 0.05. This model can also be used to study scour depth variation with time when discharge is varying with time. 9.11 SCOUR IN GRAVELLY MATERIAL As discussed in detail in Chapter – 7 gravel-bed rivers are basically different from alluvial rivers. The bed material in gravel-bed rivers is very coarse and has a large standard deviation. Further, these rivers transport sediments on the surface and ultimately form the pavement or armour layer. As mentioned earlier the standard deviation of the pavement is around two. Not enough is known about scour in gravel-bed rivers and the data are very few. In the absence of adequate data, the IRC-78-2000 code recommends that scour depth in gravel-bed rivers be estimated using Lacey-Inglis approach and estimating depth of flow by the formula 296 River Morphology DLq Fq I = 1.13 G J HfK 2 l 1/ 3 ...(9.25) where q is discharge in m3/s, and sill factor of fl = 24 is recommended. However, this method has not been supported by field data. Further, since relationship between depth and discharge for gravel-bed rivers is different than Lacey’s (see Chapter 7) it is not logical to base estimation of scour depth in gravel-bed rivers on Lacey’s equations. On the other hand, since the methods of Kothyari et al. and Melville and Sutherland take into account the size of bed material its gradation and stratification, these are likely to give more reliable results as shown by Garde and Kothyari (1995). 9.12 SCOUR IN COHESIVE SOILS The process of scour in non cohesive materials is discussed above. However when the river bed consists of gravel, sand, silt and clay the scour phenomenon becomes more complex, and very little is known about variation of scour depth with time, maximum depth of scour and extent of scour. A few measurements of scour in clayey soils are available (Kand 1993, Namjoshi 1992). Laboratory experiments have been carried out by Ansari (1999) and Ansari et al. (2002). These references along with that of Briaud et al. (1999) may be seen in this regard. 9.13 PROTECTION OF SCOUR AROUND BRIDGE PIERS A number of devices have been tried to reduce scour depth around bridge piers. These devices either modify the flow pattern created by horseshoe vortex or provide a hard surface which prevents horseshoe vortex from sinking or protects the surface from erosion. These include piles, collar plates, deltawing-like passive device and slot in the pier or vanes. Their relative effectiveness has been studied among others by Gangadharaiah et al. (2003). Except piles and vanes, the other devices have not been tested on prototype bridges. In the laboratory these devices are found to reduce scour by 40 to 70 percent. Another method which has greater potential of using in the field, is the use of rip-rap of proper size around the pier which will resist scour. This has been studied by Wõrman (1989), and Bhalerao and Garde (2003) and used in the field by Wörman. As mentioned earlier the instantaneous shear stress around the pier can be 10 to 12 times the average shear stress in the channel. If the median size of the armour layer is so chosen that it is stable at this shear stress, and if riprap has a standard deviation of about two, one or two layers of rip-rap adequately protect the bed from scouring. AGGRADATION In general, aggradation in a stream takes place when the stream is carrying more sediment than its transport capacity. If the sediment load coming into a reach in a given time is greater than the sediment load going out in the same time, i.e. when bed and the bed level rises i.e. are discussed below. ¶ Qs is negative, the excess sediment gets deposited on the ¶S ¶Z is positive. Aggradation occurs under a variety of conditions; these ¶t Bed Level Variation in Streams 297 9.14 OCCURRENCE OF AGGRADATION Increase in Sediment Load The increase in sediment load can take place for different reasons. Thus, during the gold rush period (1850-1905), large quantities of mining waste were dumped in the Yuba river in California as a result of which the general bed levels increased gradually. This was reflected in the rise in low water level at Marysville, see Table 9.7. When the mining was stopped because it became uneconomical, the bed levels were lowered gradually. Similarly, large quantities of gravel have come down in gravel-bed rivers in the Doon Valley (Uttaranchal, India) partly due to mining activity and partly due to erosion due to deforestation; as a result in some rivers bed levels have risen by as much as 3 to 4 m; see Fig. 9.12 and Fig. 9.13(a). Table 9.7 Rise in low water level at Marysville on the Yuba (Bolt et al. 1975) Year 1850 1860 1870 1880 1890 Water level elevation (m) 12.10 13.40 14.70 16.90 16.80 Year 1905 1910 1920 1930 1940 Water level elevation (m) 17.90 17.00 16.10 14.60 14.40 Fig. 9.12 Aggradation in the Doon valley stream Excess sediment can be brought into the stream as a result of landslides and heavy rainfall. Thus, in the Mu-Kwa river in Taiwan (see Lane 1955) the bed level rose by as much as 12 metres in three years and the powerhouse was completely buried in sediment. Sometimes the landslides and destruction of hills result from high intensity earthquake followed by floods, as occurred in the Brahmaputra after 1950 earthquake. As a result, the bed levels rose by 2-3 m in long stretches of the river (see Chapter 14). 298 River Morphology The increase in the sediment load in the tributaries and the main stream can also occur due to reduction in vegetal cover as a result of overgrazing, deforestation, climatic changes or man’s activities such as road building etc. As a result, the tributaries and main stream can experience aggradation. Lastly, irrigation channels may aggrade if excess sediment enters into it when sediment excluders and ejectors are either not provided or are not functioning properly. This has happened in the case of Eastern Kosi main canal in which bed levels have risen by 2 to 3 m in a reach of 4 km during nine years. The canal was designed according to Lacey’s method and had a bed material size of 0.20 mm (Sahay et al. 1980). Aggradation of 11.5 km reach of the Ganga Canal from its head works at Mayapur up to Pathari powerhouse in Uttaranchal (India) needs special mention (Mohan and Agarwal, 1980). This canal takes off from the river Ganga at Mayapur near Haridwar (India). The canal is about 150 years old and carries a maximum discharge of 311.5 m3/s. It has a slope of 0.000725 in the first 1.6 km and 0.000230 up to Pathari powerhouse 11.6 km downstream. Because of landslides and heavy rainfall in the Alakananda, a major tributary of the Ganga, sediment concentration in the Ganga ranged from 36 000 to 13 500 ppm during 21st July to 27th July 1970. In the feeder channel at Bhadrabad near Pathri the suspended sediment concentration ranged from 16 286 to 15 584 ppm. During this period the canal discharge gradually reduced to 71 m3/s while the water level at Pathri was held constant. It was found that the canal had silted to the extent of 2 to 3 m in this reach. This resulted in the closure of the canal for a few months leading to disruption of supply of water to irrigation and considerable expenditure on removal of sediment. Later for proper functioning, of the canal a limit on maximum permissible concentration to be allowed in the canal was fixed. Withdrawal of Clear Water If relatively sediment free water is diverted from a stream, otherwise in equilibrium, downstream of the point of withdrawal the river cannot carry the sediment load with reduced discharge; hence it will experience aggradation. This withdrawal can be for irrigation or water supply purposes. Such aggradation has occurred on the Rio Grande, and the Arkansas rivers in U.S.A. (see Lane 1955). When aggradation occurs either due to increase in sediment load or reduction in water discharge, the transient and equilibrium bed profiles obtained are shown in Fig. 9.13(a). Such a reduction in peak flows and discharge can also be caused by stream piracy in which part of the water is diverted to the pirated stream. Profiles obtained due to withdrawal of sediment load or increases in discharge are shown in Fig. 9.13 (b). Aggradation Due to Reduction in Water Slope (or Increase in Water Level) The aggradation occurring upstream of the section of increase in sediment load or decrease in discharge is due to rise in water level at section 0-0. Aggradation occurring upstream of dam falls in this category. When a dam is constructed on a stream to store water for irrigation, water supply, power generation or for flood control, a backwater is caused as a result of which velocity of flow reduces as one approaches the dam. Hence, reduction in sediment transport capacity leads to deposition of coarser sediment upstream where backwater starts while finer sediment gets deposited closer to the dam; see Fig. 9.13 (b). Sedimentation of reservoirs reduces their capacity to store water, raise water levels in the upstream reaches of the river, and increase evaporation due to increase in water surface area. In literature one Bed Level Variation in Streams O DQs DQ Final bed Transient bed levels O Original bed 299 finds several cases of reservoirs getting filled in a few years. The 14 m high dam on the NanShik-Chi river in Taiwan was filled completely in 8 years. Whereas the river slope was 1 in 120, the final slope of bed was 1 in 250. Similarly, 53 m high Ichari diversion dam on the Yamuna River has silted up to the crest in five years from 1972 to 1979. Reservoir sedimentation is discussed in detail later in this Chapter. (a) Aggradation due to increase in Qs or decrease in Q O DQ DQs Original bed Aggradation at Channel Bifurcation If a channel takes off from the main stream, the off taking channel will carry relatively more bed load compared to the main stream because of the development of secondary flow. Hence, if the main stream is carrying appreciable bed load, the off taking channel is likely to aggrade. Transient bed levels O Final bed (b) Degradation due to increase in Q or decrease in Qs Aggraded profile Tributary Old position New position Other Cases of Aggradation A stream which discharges into a lake or the sea builds its delta. With the passage of time, the (c) Aggradation of tributary due to shifting of main stream delta grows into the lake or sea thereby causing increase in the length of the river and reduction in slope inducing aggradation. This aggradation fills the river channel and the river spills over the banks forming new channels. Similar A increase in length leads to aggradation of the B cut-off C tributary if the main stream to which it joins a D b shifts away from it due to migration. This is New bed shown in Fig. 9.13 (c). c Similar situation also occurs on alluvial d Original bed fans. In many cases fan can start as delta (d) Aggradation and degradation at cut-off formation in a lake and after enough time has Fig. 9.13 Bed profiles in aggrading and degrading stream elapsed, the lake will be completely filled. Then the river just keeps building the fan higher and higher (Gessler 1971). Change of hydrograph can also lead to aggradation. In many rivers, most of the bed changing actions take place during peak flows. If by building one or more dams in series, the flood peak is moderated, the total annual sediment transport capacity of the stream is significantly reduced. And yet the sediment supply from the tributaries on the downstream side of dam will be unaltered and so the stream will not be able to carry this load; hence bed level can rise or part of the degradation can be offset. 300 River Morphology Degradation, Aggradation and Planned Removal of Dams It is reported that 85 percent of dams in U.S.A. will be at the end of their operational design lives by 2020 (Evans et al. 2000). Hence, planned removal of dams as a viable river management alternative is being considered seriously in U.S.A., and some case studies in this regard have been conducted in order to gain information on physical, chemical and biological impacts of removing dams. In the context of the theme of this chapter, important issues that need to be addressed include rates and mechanics of sediment removal from reservoirs; how watershed geomorphology and hydrology affect these rates and mechanisms; how far and quickly the sediment will be transported downstream, and how downstream sedimentation will affect channel morphology and biotic communities. Doyle et al. (2003) have reported the channel adjustments that have taken place following two dam removals in Wisconsin (U.S.A.). When the dam is removed upstream reach will experience degradation while downstream reach will experiences aggradation. The details of two small dams removed are as follows: River Dam Catchment River slope u/s of dam River slope d/s of dam Sediment Dam height Koshkonong Rockdale 360 km2 0.0007 0.004 Silt to coarse gravel 3.3 m Baraboo Lavalle 575 km2 0.0005 0.0002 Mixture of fine sand and silt 2.0 m The changes that took place after removal of dam can be the summarized as follows: Immediately following the dam removal water surface elevation decreased dramatically but the reservoir sediment surface remained undisturbed. Channel flow during this period was wide and shallow with low velocity. Next, the channel bed incised and the flow concentrated into a narrow, deep channel with steep bank and high flow velocity. Head cut formed at the upstream boundary. Large amount of fine and then coarse sediment was mobilized and transported downstream. As the incision continued beyond critical bank height, the channel started widening and large quantities of the material were transported downstream. With this, the downstream channel started aggrading initially coarser sediment was deposited and then the finer one as water surface slope decreased adequately. Effects of Floods According to Bull (1985), the following factors tend to promote net aggradation during floods: i) Abundance of stored sediment on hill slopes as a result of either abundant soft rock types and/ or rates of rock weathering that exceed denudation rates. ii) Climatic changes that greatly decrease vegetative cover on hill slopes, or increase rainfall intensity. iii) Fires that remove the vegetative cover or expose the hill slopes to accelerated erosion. iv) Unstable slopes subject to landslides that introduce large volumes of sediment directly into stream channels. v) Lack of relative vertical uplift. Bed Level Variation in Streams 301 Streams that aggrade during floods include watersheds with abundant landslides. Climatically induced decreases in vegetal cover and concurrent increases of hill slope sediment yield have favoured aggradation of valley floors in extremely arid to extremely humid climatic settings. Aggradation can be estimated by determining the new equilibrium slope for changed conditions. The transient bed profiles can be computed using methods described in Chapters 11 and 12. RESERVOIR SEDIMENTATION Dams are constructed on rivers so that they form reservoirs which impound water that is later used for irrigation, water supply and industrial purposes, power generation, recreational purposes and flood control. They also help in controlling the variations in flow in the downstream channel. Most reservoirs serve multiple purposes. When water is impounded in the reservoir, the flow velocity is smallest near the dam and it gradually reaches the velocity in the stream at the end of the backwater. As a result, the sediment transport capacity of flow progressively reduces towards the dam and coarse material gets deposited in the upstream reach while medium and finer material gets deposited near the dam. Very fine material which remains in suspension at the dam will travel downstream over the spillway and through outlets. This deposition progressively reduces the storage capacity of the reservoir. Even though a predetermined dead storage is provided assuming that sediment would deposit there, yet significant amount of sediment may start depositing in the upstream reaches right from the beginning and cause depletion of the reservoir capacity. Depletion of reservoir capacity with the passage of time is a serious problem because ultimately the usable capacity of reservoir will be completely lost and a new reservoir may have to be built. Dams are very expensive and alternate reservoir sites are not easily available. Some idea can be given about rates of reservoir sedimentation. Yasuoka reservoir on the river Tenrya in Japan which had a capacity of 51 Mm3 lost 80 percent of the capacity in 13 years. The Ichari reservoir on the river Yamuna in India lost almost 100 percent capacities in five years of operation. Zuni reservoir on the river Zuni in New Mexico, U.S.A. lost 58 percent capacity in the first two years. On the basis of survey of 132 reservoirs all over U.S.A., spanning over a period of 20-30 years, the average annual loss of capacity is found to be 0.70 percent. Sedimentation rates in China are much higher. Twenty large reservoirs in China were losing their capacity at an average rate of 2.3 percent per year during 1960-1978; the maximum rate was 7.1 percent for Quintgonxia reservoir on the Yellow river, see IRTCES (1985). For eleven large reservoirs in India, the sedimentation rate varied between 0.08 and 1.78 percent per year, while average loss was 0.65 percent. There are many direct and indirect effects of sedimentation in reservoirs. These are discussed in detail in the UNESCO (1985) publication and are briefly enumerated below. Upstream Effects 1. Raising of bed level and water level in the upstream reach; rise in the water table which results in the appearance of marshes. 2. Increase in water surface area causes increased evaporation loss and weed growth. 3. Accumulated sediment upstream of dam may choke the bottom outlets. 4. Since a very large percent of sediment is trapped in the reservoir, the flow in the downstream channel is deficient in sediment load; this causes degradation in the channel and/or channel widening. Effects of the degradation have been discussed earlier in this chapter. 302 River Morphology 5. Construction of dam and impoundment of water reduces low and medium floods in the downstream channel. This may stop the erosion of cones of sediment deposits at the confluence of steep gradient tributaries joining the main stream. 6. The water released from the dam is free of sediment and contains mainly dissolved solids. This leads to impoverishment of biomass in downstream channel, which leads to decrease of productivity of fish and breeding. 7. There are a number of economic consequences of reduction in the storage capacity of reservoir, which include reduction in energy production, agricultural production, and non-availability of water for domestic and industrial use. Discussion of Reservoir Sedimentation needs consideration of the following aspects: • Sediment inflow and trap efficiency • Movement of sediment in reservoirs and sediment deposition • Modelling of sediment deposition • Methods of preserving or restoring reservoir capacity 9.15 SEDIMENT INFLOW AND TRAP EFFICIENCY Annual sediment inflow can be assessed in different ways. If any reservoirs are in operation in the region and their surveys are available, the same rate in tons/km 2/yr can be used for the reservoir under consideration. For a better accuracy erosion rate can be calculated using the equations proposed in Chapter 3 where it is related to annual rainfall, catchment slope, drainage density, catchment area and vegetal cover factor. If suspended sediment measurements are available for few years and discharge inflows for longer duration, a certain percent of suspended load can be taken as bed load and, flow and sediment duration curves can be prepared to determine average annual sediment inflow rate (see Chapter 3). If no sediment load (suspended or bed load) measurements are available, one has to use one of the total sediment transport equations described in Chapter 5 to prepare Q vs QT curve and then assess average sediment transport rate. For future predictions flows can be generated using available techniques in hydrology and then determine QT determined from QT vs Q curve. Ideally, sediment transport data are required for a period, at least equal to half the life of the project (Mahmood 1987). Since this is seldom available, engineers and planners have to work with inadequate data, and effort is made to extend it using statistical techniques. It may also be emphasized that hydrologic series show greater variability in arid or semi arid climates than in humid climates. In assessing the sediment inflow, the impact of natural events such as high magnitude earthquakes, eruption of volcanoes, landslides, and catastrophic flood play an important role, even though quantification of their contribution may be difficult or impossible. A few examples can be cited here in support of this statement. New Madrid earthquakes between December 1811 and February 1812, the greatest earthquakes in U.S.A. in Southern Missouri, were felt over 100 000 km2 area. These brought in large quantities of sediment in the Mississippi river and changed its channel morphology (Mahmood 1987). The 1950 earthquake in the Brahmaputra Valley brought into the stream very large quantity of sediment, which affected the morphology of the Brahmaputra. Had there been a reservoir on the river in the downstream, it would have shown very rapid sedimentation. Similarly, the 1971 heavy monsoon and landslides in the Alakananda valley brought down huge quantities of sediment in the Ganga River and Bed Level Variation in Streams 303 caused sedimentation problem in the Ganga canal. Lastly, volcano eruption of Mt. St. Helens (U.S.A.) in May 1980 brought in 50 million tons of debris and mud flows in the Cowlitz river channel. It is estimated that in the four months after eruption, about 140 million tons of suspended sediment were deposited by the Cowlitz river into Columbia River in U.S.A. As a result, of Mt. St. Helen’s eruption, sediment yield of the Columbia River had increased to 40 million tons/yr from the pre-eruption value of 10 million tons/yr (Mahmood 1987). Trap efficiency has been defined in Chapter 3 as the percentage of incoming sediment load that is retained in the reservoir. It depends on a number of factors such as the size of sediment, variation in the flow coming into the reservoir, characteristics of the reservoir, method of reservoir operation and time. A method, which takes into account all these factors on the determination of trap efficiency, is not available at present. However, Brune’s (1953) curve which is based on data obtained from 44 normally ponded reservoirs covering drainage areas of 4-480 000 km2, and which relates trap efficiency Te to the ratio of reservoir capacity to annual inflow is often used to determine Te. This has been later verified using data from reservoirs in India, China and South Africa; this is given in Fig. 3.9. The mean curve can be represented by the equation LM OP 1 Te = 100 M1 F MM H1 + 50 C IK PPP I Q N ...(9.26) where C is the reservoir capacity upto mean operating level and I is the average annual inflow both expressed in the same units. The period of computation for Brune’s method should not be less than ten years. Heinemann’s (1981) data show that Brune’s curve overestimates trap efficiency for small reservoirs. Swamee and Garde (1977) have analysed laboratory and field data on sedimentation of reservoirs and found that the reservoir capacity Ct after sediment deposition, at any time t is given by Ct C FG t IJ Ht K = LM1 + F t I MN GH t JK e e m 4 m 0.25 OP PQ ...(9.27) Here C is the original capacity of reservoir and te is the period required to fill the reservoir up to height of dam. This can be estimated by dividing C by average annual rate of sediment inflow. The exponent m varies between 0.75 and 1.0, and m and te can be determined by plotting Ct vs t on log-log C scale for few years and fitting a straight line in the initial period of silting. The exponent m is the slope of the straight line and t = te when Ct = C. 304 River Morphology 9.16 MOVEMENT AND SEDIMENT DEPOSITION IN RESERVOIRS Three agencies which control the movement and deposition of sediment in reservoirs are river flows, wind effects and solar inputs. When wind blows over the water surface in the lake formed by a dam, it exerts a shear stress on the water surface and causes water surface to move in the direction of wind. This leads to formation of waves, water surface currents and the associated counter currents underneath. These counter currents carry the near-bed settling suspension. The solar heating is also responsible for developing currents and transporting sediment in the reservoir. The difference in temperature between deep layers and surface layers causes thermal currents. Lastly, when river flows into the reservoir, it carries with it bed material which moves as bed load or in suspension, wash load and dissolved solids. As a result of interaction between river flows, and wind and solar effects there can be three types of flows of sediment-laden water, which are shown in Fig. 9.14. Inflows which are of high density because of heavy suspended load or which are colder than water in the reservoir will cause underflow. If the inflowing water is warmer than the surface water in the reservoir, it may flow over the surface as overflow. When the inflowing water is slightly colder than the surface water, it flows as interflow. The coarsest sediment may get deposited as deltaic deposits. Fig. 9.14 Overflow, interflow and underflow in reservoir Lane (1953) has classified the deposits in the reservoir into bottom-set beds, fore-set beds, top-set beds and density currents, see Fig. 9.15. Bottom-set beds are formed of fine sediments brought into the reservoir and which move farther near the dam before they settle. The fore-set bed is formed of the coarser sediment carried by the stream on or near the bed, and is deposited where the current is retarded as it flows into the lake. This happens when horizontal water surface in the reservoir intersects the current. These beds are more inclined downwards in the direction of flow. Top-set beds are mainly composed of coarser sediment (sand and gravel) and are usually sloped upstream at a low gradient from the edge of fore-set beds. They extend as far back as the backwater curve extends upstream of reservoir. The top-set bed deposits do not reduce the reservoir capacity, but they cause flooding problems in upstream reach due to rise in bed and water levels. Zhou Zhide (1991) has analyzed the slopes of top-set beds of a number of reservoirs in China and found that, on the average their slope is about 0.5 So where So is river slope. Bed Level Variation in Streams 305 Fig. 9.15 Longitudinal section through a reservoir showing various types of the deposits When the water entering the reservoir carries large concentration of fine material, because of low velocities in the reservoir the sediment settles near the bed and forms a thick layer of high density which moves slowly towards the dam. These are known as the density currents. By provision of very low level outlets the density currents can be vented out of the reservoir. Conditions favourable for the formation of density current are (i) high sediment concentrations (ii) fine sediment (iii) steep stream slope, and (iv) large depth of flow. Density currents have been found to occur in both Lake Mead and Elephant Butte reservoirs on the Colorado River in U.S.A., and Naodehai reservoir on the Liuhe River in China. Experience has shown that under most favourable conditions only 5 to 20 percent of sediment in the reservoir can be vented out in the form of density currents. Basic mathematical description of the appearance, propagation, modification and outflow of density currents is briefly described in UNESCO (1985) Report. Shape and Deposition Profiles The shape of deposition profile in the reservoir depends on a number of factors such as river slope, normal pond level and its variation, size distribution of sediment, shape of the reservoir, and ratio of incoming sediment load to the reservoir capacity. These profiles are classified into three categories namely deltaic deposits, wedge-type deposits and narrow band type deposits, and are shown in Fig. 9.16. Deltaic deposits are by far the most common where the material is not very fine and water level is kept relatively high for a considerable length at time. Such deposition has occurred in the Gobindsagar reservoir on the Sutlej River in India, and in Guanting reservoir on the Yongting River in China. Wedge type deposition occurs in gorge-type reservoirs in which the storage capacity is small compared to the incoming load. Hence the sediment soon reaches upto the dam resulting in a wedge shaped profile. Such deposition has occurred in Bajiazui reservoir on the Pu river in China, the Matatila reservoir in India and in Heisonglin reservoir on the Yeyu River in China. In some gorge-type reservoirs where the incoming load is small and fine in size, the sediment deposits more or less uniformly in the form of a thin band if water level in the reservoir fluctuates to a great extent. Such narrow-thin band type of deposition has occurred in Mayurakshi reservoir in India and in Fengman on the Mudan River in China. Based on the experience on the Chinese reservoirs, IRTCES (1985) has given the following criteria for formation of deltaic and wedge-type deposits. 306 Average reservoir capacity in m 3 > Average annual sediment inflow in tons Elevation in m River Morphology F.R.L. 515.11 500 Deltaic deposit 1975 1970 1966 470 2.0 and DH < 0.15 : Deltaic deposits H 440 1962 410 Original bed - 1958 Years Average reservoir capacity in m 3 < Average annual sediment inflow in tons 380 350 26.51 32.41 15.54 21.64 44.80 50.90 55.82 10.41 63.09 10.67 37.49 75.28 80.16 DH < 0.15 : Wedge type H Here DH and H are average yearly fluctuation and head at dam respectively. 2.0 and Elevation in m Distance in km u/s of dam Gobindsagar reservoir 311 305 Spillway crest 301.45 m 299 293 Min. drawdown level 295.66 m 1971 1964 Top of dam 310.9 m Full reservoir level 308.46 m Wedge-type 9.17 MODELING OF SEDIMENT DEPOSITION Modeling of sediment deposition can be done either by using empirical methods or by using mathematical modeling. Here two empirical methods are described while the mathematical modeling is discussed in Chapter 12. 287 Original bed (1957) 281 Wedge-type deposit 275 0 5 10 Distance in km u/s of dam 15 20 Matatila reservoir 122 Narrow-band Elevation in m Empirical Area Reduction Method 116 Live storage 110 (1963-63) The empirical area reduction method proposed by Borland and Miller (1958) is developed on the basis of the analysis of data from 30 reservoirs in U.S.A. having capacities ranging from 4.9 ´ 106 to 7.6 ´ 108 m3 and is based on the premise that the sediment load in narrow Mayurakshi reservoir reservoir will travel farther, because the average velocity of flow will be higher in Fig. 9.16 Deltaic, wedge-type and narrow band deposits in narrower reservoirs than in wide reservoirs. reservoirs Further, a steep narrow reservoir has a better chance of developing density currents than the one that is wide and flat. On the basic of this, reasoning Borland and Miller have classified the reservoirs in four categories depending on the exponent q in the equation 98 Dead storage = Sx 0.0 15 01 104 Original bed (1955) 92 Narrow band deposit 86 0 4 8 12 14 16 18 20 Distance in km u/s of dam C (h) = a hq ...(9.28) where h is the height depth measured above the river bed at dam axis C (h) is the storage capacity at depth h; see Table 9.8. Bed Level Variation in Streams 307 Table 9.8 Reservoir classification and distribution parameters (Borland and Miller 1958) Type I II III IV Description Lake Flood Plain–Foot hill Hill Gorge Q in Eq. 9.28 3.5 – 4.5 2.5 – 3.5 1.5 – 2.5 1.0 – 1.5 Position of deposition Top Upper middle Lower middle Bottom C1 3.42 2.32 15.88 4.23 m 1.50 0.50 1.10 0.10 n 0.20 0.40 2.30 2.50 Analysis of sediment volume deposited versus fraction of reservoir depth curves obtained for these reservoirs were converted into relative depth p versus dimensionless relative areas Ap see Eq. (9.29). Ap = C1 pm (1 – p)n Here and As = 1 As where K1 = As dp and As is area of sediment deposit at relative elevation p. the 0 K1 values of m and n were computed by trial and error procedure using least square technique, and then with m and n known, C1 is fixed by the consideration that the total areas under the curve must be unity. The computations can be carried out in Tabular form given below. z ...(9.29) Table 9.9 Computations using empirical area reduction method Elevation m Original area m 2 Original capacity m 3 Relative depth p Ap Sediment area m2 1st Trial Sediment volume m3 Procedure 1. 2. 3. 4. 5. 6. 7. Determine q from reservoir capacity vs. depth curve Determine the type of reservoir Fill in columns 1, 2, 3 from known data at regular intervals of h Find in m3 the apparent volume of sediment to be deposited at the end of T years Determine the value of p for elevations in Col. 1 and enter Col. 4 Determine Ap values for p values in Col. 4 using Eq. (9.29) and enter in col. 5 Assume zero elevation at the dam up to which sedimentation has reached and carry trial No. 1. Areas at and below approximated zero elevation at each increment will be those in col. 2. New areas for each contour elevation above assumed zero elevation are obtained by dividing the original areas at zero elevation in Col. 2 by corresponding Ap values in Col. 5 and multiplying this by the ratio K1 values at each succeeding increment. Thus, if assumed elevation is 4190 where surface area is 3000 and Ap at elevation 4190 is 1.125, K1 = 3000/1.125 = 2667. 308 River Morphology The new area at each succeeding elevation is the Ap at that elevation times 2667. This is entered in Col. 6. 8. Increment sediment volume between two elevations h1 and h2 is DV = A1 + A2 ´ (h2 – h1) 2 and is entered in Col. 7. 9. If the assumed elevation is correct, summation of terms in Col. 7 will be equal to sediment volume to be distributed. 10. If they are not equal, assume a different elevation and repeat the procedure. A solved example is given by Borland and Miller (1958) which can be seen. Some comments on this method are necessary. This method does not account for temporary or prolonged reservoir draw down brought about as an operational necessity or as deliberate sediment sluicing operation. It also does not consider the sediment size distribution as a factor in the problem. In practice these conditions can be accounted for by shifting the computed reservoir type in Table. 9.8 upwards or downwards. Thus, if fine material forms a large part of the sediment load, or if the reservoir experiences considerable draw down, its type can be shifted downward (Mahmood 1987). Further, it needs to be emphasized that the empirical area reduction method is to be applied for sediment accumulated over long periods, such as few decades and not for year-to-year accumulation. Also, many times a reservoir may not have a unique value of q for its entire depth. In such cases, the reservoir type is selected on the basis of q value in the segment where most of sedimentation will occur. Figure 9.17 shows percent of depth plotted against percent of deposition for the four types of reservoirs along with data for Panchet Hill, Nizamsagar, Gobindsagar, Maithon, Mayurakshi, Matatila, Fig. 9.17 Depth-wise sediment distribution in Indian reservoirs (Murthy 1971) Bed Level Variation in Streams 309 and Margomahally reservoirs as given by Murthy (1971). It may be noted that except for very deep Gobindsagar reservoir formed by Bhakra dam and Margomahally, deposition occurs mostly in the upper part of reservoir i.e. almost half of the sediment is deposited where the depth ranges from 20 to 30 percent of the maximum depth. Mirakis Method On the basis of analysis of deposition profiles in nine reservoirs in India where delta type triangular deposition profiles were obtained, Miraki (1983) has suggested the following method for computing deposition profile at any time t. The annual sediment volume entering the reservoir can be computed using Garde and Kothyari’s Eq. (3.39) and using Brune’s trap efficiency curve, the volume of sediment depositing in the reservoir can be calculated and converted into apparent volume depositing in the reservoir at the end of T years. The triangular profile is characterized by upstream slope Su, downstream slope Sd and maximum depth of deposition Zp (see Fig. 9.18). These are given by Fig. 9.18 Definition sketch for deposition in reservoir Zp H Su So Sd So FTI = 0.717 G J Ht K FTI = 0.34 0 G J Ht K FTI = 3.850 G J Ht K e e e 0 .285 - 0 .08 0.20 U | | | V | | | W ...(9.30) Here H is average depth at the reservoir and So is average channel slope. The term te is the number of years required to fill the reservoir completely. Hence te = R S TAnnual vol. of sediment ´ trap efficiency in flow ´ Volume of reservoir at FRL 2650 average unit wt. of sediment U V W 310 River Morphology The volume of sediment deposited under a given profile requires average width of deposition over the reach of deposition. Once this is determined from the reservoir characteristics, the two volumes can be compared and made equal by changing Su or Sd slightly. The first peak occurs a distance of 0.42 Lr from the reservoir where Lr is length of the reservoir defined as shown in Fig. 9.18; at this place, flow depth is 0.51 H. The peak was found to move in the downstream direction at a speed of 300 m/yr approximately. This method was used for the Almatti reservoir on the river Krishna in India and the results were compared with those obtained by HEC-6 model. The two results were comparable. 9.18 METHODS FOR PRESERVING AND RESTORING RESERVOIR CAPACITY (UNESCO 1985, IRTCES 1985) Various methods are adopted by engineers and planners to decrease the quantity of sediment entering into reservoir, to reduce the quantity of sediment depositing in the reservoir, and to recover part or whole of the capacity lost for storage. These are briefly discussed below. Methods to Reduce Sediment Deposition in Reservoirs 1. Soil Conservation: Sediment entering the reservoir can be reduced by following soil conservation methods such as watershed land-treatment measures which reduce sheet erosion; these methods are soil improvement, proper tillage methods, strip-cropping, terracing and crop rotation. Reforestation of barren areas also reduces erosion. These methods are very effective in small areas, but in large areas, it is a slow process and the effects cannot be seen in short time. The success of this method has been demonstrated in the Tungabhadra reservoir project in India, the Gunating reservoir on the Yongding River in North China and Eel river basin in California (U.S.A.) (UNESCO 1985). Construction of various structures such as check dams on tributaries and gullies, stream bank revetments to reduce bank erosion and sills for bed stabilization also help in reducing sediment entry into the reservoir. 2. Vegetative Screens: Vegetative screens, either natural or artificial at the head of the reservoir reduce the velocity of flow and cause sediment deposition, thereby reducing sediment entering in the reservoir. However, such screens have adverse effects in that they cause flooding of the area and rise in water table. Such screens were used on the Pecos River above Lake McMillan, and the Elephant Butte dam on the Rio Grande in U.S.A. and the Hongshan reservoir on the Loaha River in North East China. The effects of vegetative screens have been discussed by Lara (1960) and Maddock (1948). 3. Flow Regulation: Flow regulation is effected during floods by lowering the reservoir level by opening bottom outlets under controlled or uncontrolled condition, so that flood waters containing high sediment concentration are allowed to flow out and only water with less sediment concentration is stored. This has been practised on the Heisonglin and Sanmenxia reservoirs in China. 4. Venting of Density Currents: When conditions in the reservoir are favourable and density current is formed, allowing it to pass through outlets is a good method of reducing sediment deposition. This has been done in the case of the Elephant Butte and Lake Mead reservoirs on the Colorado river, U.S.A., Iril Emda reservoir in Algeria, and Nebeur reservoir in Tunisia among others. It is estimated that in most favourable conditions 5 to 20 percent of total sediment entering the reservoir can be vented out in this manner. Bed Level Variation in Streams 311 5. Drawdown Flushing: In this method the water level in the reservoir is lowered so that velocity is increased and sediment deposition is reduced. Lowering of water level can also induce erosion of deposited sediment. This has been done on many reservoirs such as the Ouchi– Kurgan reservoir in USSR. Recovery of Storage This can be achieved by flushing, dredging or siphoning of deposited material 1. Flushing: Periodic emptying and flushing operations can be used in large reservoirs to recover large percent of storage. This has been done on Hengshan reservoir in China and Sefidrud reservoir in Iran. 2. Dredging: Generally dredging is undertaken when other methods are not effective, the reservoir is relatively small and it is economical in terms of use of water e.g. when reservoir is used for drinking water purposes or irrigation. This has been used in the case of few reservoirs such as Akiba and Miusa reservoirs in Japan, Rand Mines reservoir in South Africa and Lake Roslyn in Oregon in U.S.A. 3. Siphoning: Siphon dredging uses the hydraulic head difference between upstream and downstream water levels of the dam to induce suction which removes sediment. This has been done at Rioumajou dam in France. References Ananian, A.K. (1961) Determination de la Formation de Lit de Riviers Cree’ par Suite de l’abaissement de la Cote de Leurs Bases d’Erosion. Proc. 9th Congress of IAHR, Dubrovnik (Yugoslavia), pp. 1102-1113. Ansari, S.A. (1999) Influence of Cohesion on Local Scour. Ph.D. thesis, University of Roorkee, Roorkee (India). Ansari, S.A., Kothyari U.C. and Ranga Raju, K.G. (2002) Influence of Cohesion on Scour Around Bridge Piers. JHR, IAHR, Vol. 40, No. 6, pp 717- 729. Bhalerao, A.R. and Garde, R.J. (2003) Design of Rip-rap for Protection Against Scour Around Bridge Piers. Workshop on Bridge Scour, River Training and Protection Works, New Delhi (India), Oct. pp. 1-9. Bolt, B.A., Horn, W.L., Macdonald, G.A. and Scott, R.F. (1975) Natural Hazards, Springer Verlag, Germany. Bondurant, D.C. (1950) Sediment Studies at the Conchas Reservoir in New Mexico, ASCE, Proc. Separate, No. 29, Borland, W.M. and Miller, C.R. (1958) Distribution of Sediment in Large Reservoirs. JHD, Proc. ASCE, Vol. 84, No. HY2, Pt. 1, pp. 1587- 1 to 9. Breusers, H.N.C., Nicollet, G. and Shen, H.W. (1977) Local Scour Around Cylindrical Piers. JHR, IAHR, Vol. 15, No. 3, pp. 211-252. Briaud, J.L., Ting, F.C.K., Gudavali, R., Perugu, S. and Wei, G. (1999) SRICOS: Prediction of Scour Rate in Cohesive Soils at Bridge Piers. JGGE, ASCE, Vol. 125, No.4, pp 237- 246. Brune, G.M. (1953) Trap Efficiency of Reservoirs. Trans. A.G.U., Vol. 34, No. 3, pp. 409-418. Bull, W.B. (1985) Floods, Degradation and Aggradation. Chapter 10 in Flood Geomorphology (Eds. Baker, V.R. Kochel, R.C. and Patton, P.C.), A Wiley Interscience Publication, John Wiley and Sons, N.Y. pp. 157-165. CBIP (1975) Local Scour: A Review. Literature Review 34 Compiled by UPIRI, Roorkee (India). Davies, B.E. (1974) Armouring of Alluvial Channel Beds. M.E. Thesis, University of Canterbury, Christchurch, New Zealand. 312 River Morphology Doyle, W.M., Stanley E.H. and Harbor, J.M. (2003) Channel Adjustments Following Two Dam Removals in Wisconsin. W.R. Research. Vol.39, No.1, ESG 2, 1-15. Egiazaroff, I.V. (1965) Calculation of Non-uniform Sediment Concentration. JHD, Proc. ASCE, Vol. 91, No. HY4, July, pp. 225-247. Ettema, R. (1980) Scour at Bridge Sites. University of Auckland, Auckland, New Zealand, Rep. No. 117. Evans, J.E., Mackey, S.D., Gottgen, J.F. and Gill, W.M. (2000) Lessons from a Dam Failure. Ohio Jour. of Science, Vol. 5, pp. 121-131. Galay, V.J. (1980) Engineering Aspects of River Bed Degradation. Annual Conference of Canadian Soc. of Civil Engg, Winnipeg, H/7:1 -16. Galay, V.J. (1983) Causes of River Bed Degradation. W.R. Research, Vol.19, No. 5, Oct., pp. 1057-1090. Gangadharaiah, T., Sethia, B. and Sheshagiri Rao, R. (2003) Scour Protection Around Bridge Piers and Abutments. Workshop on Bridge Scour, River Training and Protection Works, New Delhi (India), Oct. pp. 2741. Garde, R.J. (1955) A Report on Degradation Below Dams. Report submitted to Civil Engg. Dept., Colorado A. and M College, Fort Collins (USA). Garde, R.J. and Kothyari, U.C. (1995) State of Art Report on Scour Around Bridge Piers. Report Submitted to IIBE, Pune. 109 p. Garde, R.J. and Ranga Raju K.G. (2000) Mechanics of Sediment Transportation and Alluvial Stream Problems. New Age International Publishers, New Delhi. Garde, R.J. and Ranga Raju K.G. and Kothyari, U.C. (1987) Effect of Unsteadiness and Stratification on Local Scour. Research Report, Civil Engg. Dept., University of Roorkee (India). Garde, R.J. Sahay, A. and Bhatnagar, S. (2004) Grain Size Distribution of Armour Coat. Proc. of Intl. Conference on Hyd. Engg. Research and Practice, I.I.T. Roorkee (India), Oct. Gessler, J. (1965) The Beginning of Bed Load Movement of Mixtures Investigated as Natural Armouring in Channels. Laboratory of Hyd. Research and Soil Mechanics, Swiss Federal Institute of Technology, Zurich, Rep. No. 69. Gessler, J. (1970) Self Stabilizing Tendencies of Alluvial Channels. JWWHD, Proc. ASCE, Vol. 96, No. WW2, pp. 235-249. Gessler, J. (1971) Aggradation and Degradation. In River Mechanics (Ed. Shen, H.W.), Published by H.W. Shen, Fort Collins, U.S.A. Vol. 1, pp. 8-1-24. Gilbert, G.K. (1917) Hydraulic Debris in the Sierra Nevada. USGS Professional Paper No. 105, 154 p. Harrison, A.S. (1950) Report on Special Investigation of Bed Material in a Degrading Bed. IER, Univ. of California, Berkley, U.S.A., Series No. 33, Issue No. 1. Hathaway, G.A. (1948) Observations on Channel Changes, Degradation and Scour Below Dams. Paper Presented at 2nd Conference of IAHR, Stockholm, pp. 287-307. Heinemann, H.G. (1981) A New Trap Efficiency Curve of Small Reservoirs. W.R. Bulletin, Vol. 17, No. 5, Oct. Huber, E. (1991) Update : Bridge Scour. Civil Engineering ASCE (U.S.A.), Sept. IRTCES (1985) Lecture Notes of the Training Course on Reservoir Sedimentation. Beijing (China). Islam, M.N., Garde, R.J. and Ranga Raju, K.G. (1986) Temporal Variation of Local Scour. Proc. of IAHR Symposium on Scale Effects in Modelling Sediment Transport Phenomenon, Toronto, Canada. Jensen, P.Ph., Bendegom, L. Van, Berg, J. Van den, deVries, M. and Zanen, N. (1979) Principles of River Engineering: The Non-Tidal Alluvial river. Pitman and Co., London, Chapter 4. Kand, C.V. (1993) Scour-Sand, Clay and Boulders. Bridge Engineering (India), Vol. 9 and 10 Bed Level Variation in Streams 313 Kellerhals, R. Church, M. and Devies, L.B. (1977) Morphological Effects of Interbasin River Diversions. Paper Presented at Hydro-technical Conference, Canadian Soc. Civil Engg. Quebec City. Klaassen, G.J. (1995) Lane’s Balance Analogy. Proc. of 6th International Symposium on River Sedimentation, New Delhi (India), pp. 671-686. Kochel, R.C. (1985) Geomorphic Impact of Large Floods : Review and New Perspectives on Magnitude and Frequency, Chapter II in Flood Geomorphology (Eds. Baker V.R.., Kochel, R.C. and Patton, P.C.) A Wiley Interscience Publication, John wiley & Sons, N.Y., pp. 169-187. Kothyari, U.C. (1989) Effect of Unsteadiness and Stratification on Local Scour. Ph.D. Thesis, Civil Engineering Department, University of Roorkee (India). Lane, E.W. (1953) Some Aspects of Reservoir Sedimentation. JIP, CBIP (India), Vol. 10, No. 2 and 5, April and July, pp. 3-14. Lane, E.W. (1955) The Importance of Fluvial Morphology in Hydraulic Engineering. Proc. ASCE, Paper 745, pp. 1-17. Lara, J.M. (1960) 1957 Sedimentation Survey of Elephant Butte Reservoir. Bureau of Reclamation, USDI, U.S.A. Little, W.C. and Mayer, P.G. (1972) The Role of Sediment Gradation on Channel Armouring, School of Civil Engineering, Georgia Institute of Technology, Atlanta, Georgia (U.S.A.), ERC-0672. Maddock, T. (1948) Reservoir Problems with Respect to Sedimentation. Proc. Federal Interagency Sedimentation Conference, USDI, pp. 9-14. Mahamood, K.C. (1987) Reservoir Sedimentation : Impact, Extent and Mitigation. World Bank Technical Paper No. 71, 118 p. Melville, B.W. and Sutherland, A.J. (1988) Design Method for Local Scour at Bridge Piers. JHE, Proc. ASCE, Vol. 14, No. 10, Oct., pp. 1210-1226. Miraki, G.D. (1983) Sediment Yield and Deposition Profiles in Reservoirs. Ph.D. Thesis, University of Roorkee (India). Mittal, M.K. (1985) Parallel and Rotational Degradation. Proc. of 2nd International Workshop on Alluvial River Problems. University of Roorkee, pp. 17-22. Mohan, J. and Agarwal, A.K. (1980) Aggradation of Upper Ganga Canal. Proc. of 1st International Workshop on Alluvial River Problems. Roorkee (India), pp.2-61-72. Murthy, B.S., Surya Rao, S., Rajagopal, H., Tiwari, S.K. and Rajesh Kumar (1998) Flood and Sediment Routing in River Systems Mathematical Models. Report Submitted to INCH by Civil Engineering Department, I.I.T., Kanpur, 159 p. Namjoshi, A.G. (1992) Anticipated Scour Depth in Non-Alluvial/ Clayey Beds. Proc. Intl. Seminar on Bridge Structure and Foundations. Conference Documentation 3, Vol. 2 NIH (1986) Sedimentation in Reservoirs. Report R.N. 26, National Institute of Hydrology, Roorkee, 98 p. Odgaard, A.J. (1984) Grain Size Distribution of River-bed Armour Layer. Proc. ASCE, JHE, Vol. 110, No. 10, pp. 1479-1485. Sahay, R.N., Pande, P.K. and Garde, R.J. (1980) Aggradation in Eastern Kosi Main Canal. Proc. 1st International Workshop on Alluvial River Problems. Roorkee (India), pp. 2-73-78. Scheuernlein, H. (1989) Critical Review of Various Methods to Prevent or Control Degradation in Rivers. Proc. of 4th International Symposium on River Sedimentation. Beijing (China), Vol. 2, pp. 1095-1102. Shen, H.W. and Lu, J.Y. (1983) Development and Prediction of Bed Armouring. JHE Proc. ASCE, Vol. 109, No. 4, pp. 611-629. Stevans, J.C. (1938) Effect of Silt Removal and Flow Regulation on the Regime of Rio Grande and Colorado Rivers, AGU, Pt. 2, pp. 653-661. 314 River Morphology Swamee, P.K. and Garde, R.J. (1977) Progressive Reduction of Reservoirs Capacity Due to Sedimentation. Civil Engg. Department, University of Roorkee, Research Report. Todd, O.J. and Eliassen, S. (1940) The Yellow River Problem. Trans. ASCE, Vol. 105, pp. 346-416. UNESCO (1985) Methods of Computing Sedimentation in Lakes and Reservoir : A Contribution to IHP-II Project, A-2.6.1 Panel, Feb., 224 p. Vetter, C.P. (1953) Sediment Problems in Lake Mead and Downstream on the Colorado River. Trans. AGU, Vol. 30, No. 2, April, pp. 291-295. Wörman, A. (1989) Rip-rap Protection without Filters. JHE, Proc. ASCE, Vol. 115, No. 12, Dec. pp. 1615-1630. Yearke, L.W.C. (1971) River Erosion Due to Channel Relocation. Civil Engineering (Canada), Vol. 4, No. 8, pp. 39-40. Zhide, Z. (1991) Empirical Methods of Estimation of Loss of Reservoir Capacity. Lecture Notes of Regional Training Course on Reservoir Sedimentation, New Delhi, pp. 3.6.1-3.6.34. C H A P T E R 10 River Channel Changes 10.1 INTRODUCTION It is seen in Chapter 9 that human interference in terms of change in Q, Qs or water surface slope in an equilibrium stream can induce aggradation or degradation. Such changes in bed level also take place because of change in land use, catastrophic floods, and tectonic or neo-tectonic activity. In this discussion it was assumed that the channel width or plan-form remains unchanged. The changes in bed level resulting from human interference were widely studied by engineers in the first six decades of 20th century. Since then considerable interest has been evinced in changes in drainage pattern and channel changes as can be seen from the works of Allen (1965), Leopold et al. (1964), Schumm (1969, 1971, 1977), Gregory (1977), and Gurnell and Petts (1995). These changes are briefly discussed herein. Lewin (1977) classifies channel changes into two categories namely autogenic changes and allogenic changes. Autogenic changes are the ones which are inherent in the river regime and involve avulsion, channel migration, cut-offs and crevassing. Allogenic changes are the ones which occur in response to system changes involving climatic fluctuations and altered sediment load or discharges, as a result of human activity. If a channel is migrating in the valley created by it, some geomorphologists consider such a stream, in regimen. Newson (1995) has given a sketch indicating the type of changes that take place in the stream as it debouches from mountains and joins the sea. This is shown in Fig. 10.1; this figure indicates that avulsion is more likely to occur when stream is about to enter from steep slope region into the plain with flatter slope. Bank erosion, bar formation and meander shifting occur in the middle reaches, slumping of banks, building of flood plain and channel migration take place in the lower reaches. 10.2 AVULSION Horizontal instability of a single channel alluvial stream can take two forms, either avulsion or pattern change. Avulsion is a sudden abandonment of part or whole of the stream for a new course at a lower level of floodplain. This has occurred in the recent history of such streams as the Mississippi and the Rio 316 Upland River Morphology Knock-on effect of the sediment system Slope failure Channel blockage Channel aggrades and bank erodes Transfer Erosion of banks as bars acrete Build up on bank followed by collapse Lowland Erosion of banks due to slumping Conveyance loss of Conveyance loss of fines to floodplain fines to floodplain Fines washed out to sea Fig. 10.1 Alluvial stream problem problems involving erosion, deposition etc. (Newson 1995) Grande in U.S.A., the Meandros in Turkey, the Rufiji in Tanganyika, the Kosi in India (Allen 1965), and the Yellow river in China. In an aggrading stream or a stream shifting its position in meander belt, the river bed rises and forms an alluvial ridge. Greater the height of the ridge above the floodplain, the more likely it is that local crevassing will result in some permanent change in the stream course and it will flow through one of the palaeo channels or carve a new course. As mentioned by Frisk (1944) the Mississippi recently built in its floodplain at least five alluvial ridges along meander belts up to 80 km apart. Richards et al. (1993) consider the avulsive channel system, in which the key depositional process involves the relationship between channels within the system, rather than the behaviour and properties within a channel. In such a system there is areal sedimentation so that the basin fills relatively uniformly over time scales of a few thousand years. Such a system exists in the Gangetic plain at the foothills of the River Channel Changes 317 Himalayas. The mechanism of evolution of the present day avulsive systems includes (i) aggradation of channel and floodplain by the accumulation of bed-load and suspended load, (ii) increasing but never the less subtle topographic differences and flood overspills; and (iii) avulsion due to over spilling and stream capture. The Gangetic plain consists of 400-600 m thick alluvial deposit in the tectonically controlled Himalayan foredeep basin. This area has experienced two earthquakes in 1934 and 1988 of magnitudes 8.4 and 6.5 respectively on the Richter scale. Avulsion has taken place at varying rates across the basin. The higher rate of sediment supply in the northern margin of the Gangetic plain has caused rapid aggradation and more frequent channel shifts on the Kosi mega-fan. Mega-fans are large size fans of 100-200 km in width and 100-150 km length in the humid environments. They are triangular in shape with their apex at the gorge mouth, convex in form and are characterized by steep gradients (20 cm/km). The Ganga plain consists of several fan and inter-fan areas viz. Yamuna-Ganga mega-fan, Sarda fan, Gandak mega-fan and Kosi mega-fan. Inter-fan areas (intercones) are reverse in plan, tapering from Himalayas, slightly concave at edges and with gradients 10 cm/km or less (Jain and Sinha 2003). East-west trending Gangetic plain is characterized by geomorphological diversity in terms of morphology, hydrology and sediment transport rates of the rivers. Most of the rivers such as the Ganga, the Kosi and the Yamuna display braided as well as meandering plan-forms, and some such as the Kosi, the Bagmati and the Rapti show change from braided to meandering pattern. Further, most of the streams draining the area are known for their rapid and frequent avulsions albeit with varying frequencies. As discussed in Chapter 13, the Kosi has migrated 110 km in 200 years before it was embanked in 1963. (see Fig. 13.7). The primary reasons for this migration are high sediment load, tectonic activity, frequent floods and general westward slope. The Sarda river has undergone shifting and river capturing during the last 80 years (Tangri 2000) and the Gandak has migrated eastward by 80 km during the past 5000 years. Data on lateral migration of alluvial steams were collected by Wolman and Leopold (1957). It was found by them that while since streams showed continuing tendency for lateral migration over a period of years, in some instances the stream channel maintained a reasonably stable position and had little lateral movement over a long period of time. However, the same site experienced very rapid movement during a succeeding period. In other words, the lateral movement can be continuous or discontinuous. Further, it was found that in general larger streams seem have larger rates of migration. The migration rate of the Kosi during 1936-1950 periods varied 0.18 km/yr to a maximum of 2.63 km/yr during 19221933. The Ramganga river in north India moved westward at 80.5 m/yr during 1795-1806 while it moved eastward at 4.3 m/yr during 1806-1883 and westward at the rate of 4.0 m/yr during 1883-1945. Table 10.1 gives data on lateral migration rates of some rivers across valleys. In the case of the Yellow river in China, Chien (1961) has shown that the channel shifting (lateral migration) varies with the fluctuations in discharge quantified as ratio of maximum flood discharge to the bankful discharge. In the case of the Yellow river the migration rate varied from 20 m/day to 200 m/ day. Such large variation is due to heavy sediment carried by the river. He also found that the amount of shifting is controlled by the spacing of constrictions or control points along the river. Jain and Sinha (2003) have studied in detail the avulsive tendency of the river Bagmati using survey of India topographic maps and satellite imageries. The Bagmati river draining north Bihar plains is an anabranching stream with repetitive avulsive history. Figure 10.2 shows the avulsions in the Bagmati for 318 Table 10.1 River Watts Branch near Rockville Md. North River, Va Ramganga river, India Kosi river, India Colorado river near needles, California Yukon river, at Holy Cross, Alaska Missouri river, near Peru, Nebraska Mississippi river near Rosedale, Mississippi River Morphology Data on lateral migration rates of some rivers across valleys (Adapted from Wolman and Leopold 1957) Drainage area km2 10 128 256 000 … 437 000 Period of measurement 1953-1956 1834-1884 1795-1806 1806-1883 1883-1945 150 years 18581883 1903-1942 1896-1916 1883-1903 1930-1945 Rate of movement m/yr 0.60 2.44 80.50 (W) 4.30 (E) 4.00 (W) 750.00 243.00 30.00 36.60 76.20 45.20 Comments From topographic map Local observation For one bend Local Observer Rate varied from 15 m/ yr to 150 m/yr 819 200 896 000 2816 000 the past 230 years in which it may be noted that the river has shifted first towards east, then northeast, south and southwest. The primary causes for the instability of the Bagmati are believed to be variability in the peak discharge, frequent over-spilling and relatively high sediment load. Effect of channel avulsion resulting in the abandonment of bridge on the Bagmati is shown in Fig. 10.3. Avulsion of the Tigris It is also interesting to discuss the avulsions of the Tigris and the Euphrates rivers in ancient Mesopotamia (now known as Iraq). Mesopotamia is in fact one huge delta formed by joining of the Tigris and the Euphrates to the Persian Gulf. The ancient city of Ur which was founded about 4000 years B.C. on the still marshy limits of the gulf and which served as a seaport during historical times, now lies about 150 km inside (Garde 1978). The Tigris has undergone three shifts, see Fig. 10.4; the first shift was between slightly south of Samara and slightly north of Baghdad. The old course shifted to the new one in the 13th century. The second shift south of Ctesiphon is also shown. Both these shifts are inferred by McAdams from the archaeological sites of the Parthian period (311 B.C.–226 A.D.). The third shift is shown in the bottom figure. Presently the Tigris follows a winding course in the south-east direction downstream of Baghdad for about 400 km. The combined river is then called Shat-al-Arab (the Arab stream). However, in the Muslim period up to the 16th century, the Tigris came about 160 km below Baghdad, then came straight south by a channel known as Shat-at-Hai to Wasit. Then 700 km below Wasit the river lost most of its water by irrigation channels and finally became lost in the swamp. River Channel Changes 319 Fig. 10.2 Avulsion of the Baghmati (Jain and Sinha 2003) Fig. 10.3 Effect of avulsion in the Baghmati river 320 River Morphology Fig. 10.4 Changes in the courses of the Tigris Avulsion of the Yellow River (Xu Fuling 1982, Lin and Li 1986) Another example of avulsion is the Yellow river in Peoples Republic of China. This river is known all over the world for the heavy sediment load it carries with relatively small volume of runoff, and is often known as “river of sorrow”. The Huanghe (or the Yellow river) which originates at Togo has an upper reach of 3461 km with a drop of 3480 m; the major tributaries in this reach are the Datonghi, the Taohe, the Huangshui, the Julihe and the Shanshuihe. This reach of the river carries relatively less sediment, the total annual sediment load being only 11 percent of the whole river, while the annual runoff from this reach is 56 percent of the entire river. The middle reach from Togto to Taohuayu is 1235 km long in which the major tributaries the Wudinghe, the Yianshui, the Fenhe and others, flowing through Loess region, discharge into the Yellow river. Hence this reach carries a heavy sediment load. From Taouayu to the estuary is the lower reach after which the river joins the Bohai sea. This lower reach is 768 km long and flows through a region in which more than 100 million people live. This reach has a flat slope of River Channel Changes 321 0.000 125 and the flood discharge in this reach is 4000 m3/s to 5000 m3/s but can reach 10 000 m3/s. Long-term average sediment concentration in the lower reach is 34 kg/m3 while the maximum observed is 594 kg/m3. The sediment concentration in the tributaries can reach as high as 1000 to 1500 kg/m3. The sediment transported has a size range of 0.002 mm to 0.05 mm. Because of the high concentration and flat slope, almost 50 percent of the sediment carried by the lower Yellow river at Zhenzhou (see Fig. 10.5) is deposited in the river. As a result of this aggradation, the river bed between the flood embankments is higher than the ground level outside by 3 to 5 m and is rising at an average rate of 0.1 m/ yr. At some places this difference is as large as 10 m. Huhehaote Yin chu an Wu din gR Tuo ket uo Beijing Bohai sea eR Ta iyu an Qi ob Xining Lanzhou Fe Yan'an Jin he H n ua gh e R Jinan Fig. 10.5 The Yellow river Levees or flood embankments in the lower reach of the Yellow river are about 1370 km long which are attacked during the flood and breaches occur causing flooding of low lying areas and change in the river course. This avulsive tendency in the lower reach of the Yellow river is present since historic times. Changes in the course of the river since 2000 BC to the present time are shown in Fig. 10.6. As can be seen, the river has swept over a big fan-shaped area between the Huaihe river in the south and the Haihe river in the north. In the past 1000 years 1593 breaches of the levees have been recorded out of which 26 breaches resulted in extensive flooding and the river changing its course to a new channel. To control floods, the levees have been raised by 2 to 6 m to a height of 10 m; they have also been widened so that the top width is now 7 to 15 m and berms have been provided on the landside. Also to provide additional protection, more than 300 km length of the levees has been provided with stone pitching and more than 5000 short spurs have been constructed. ns hu iR Lu oh eR Welhe R Yellow sea Zengzhou R Xi'an 10.3 STREAM CAPTURE (WORCESTER 1948, LOBECK 1939) Stream Capture results when one stream flowing in the lower region works head-ward and intercepts head waters of the stream draining in higher area. The stream flowing at the lower level always has the advantage. An example of stream capture is shown in Fig. 10.7. Figure 10.7 (a) shows the conditions just before the capture. The river heading in the escarpment can, because of its steep gradient cut back rapidly into the drainage area of the stream flowing on the plateau above, even if the rocks of the region are all homogeneous and of equal resistance to erosion. Figure 10.7 (b) shows the condition shortly after 322 Beijing Tianjin River Morphology Hu Fu Julu 0 Zhanghe R tu o R Ca J no xia ingh ai n Bohai sea Wu yi Lij in ya ng R 3 3 2 1 Ga 6 Heze 4 ot an g Jinan Xia oq ing R ing Pu ya Dongping Lake Yanjin Zhengzhou 7 Lankao Weishan Lake 5 Shangqui Dangshan Yin h Wo h eR Xuzhou eR Huaiyan Ho ng he R Huaihe R Yangzhon Changian Nanjing 0 1149 AD 0 1494 AD 0 1855 AD 0 1938 AD 0 About 2000 BC 0 602 BC 0 11 AD 0 1048 AD Fig. 10.6 Historical migration of the Yellow river (Lin and Li 1986) the capture. The captured stream has been diverted by the captor stream and now turns sharply at the point of capture, known as the elbow of capture. The difference in level of the two streams results in a waterfall. The captor stream has its discharge increased by the addition of captured stream and begins to show signs of rejuvenation. Its gorge in deepened, and its tributaries on either side below the point of capture cut back rapidly to form other gorges. The beheaded stream, having lost much of its discharge, acquires mature characteristics. It develops small meanders, not suited to the size of its valley. It becomes a misfit or underfit stream. Its tributaries build alluvial fans on the valley floor because the beheaded stream in its shrunken condition can no longer transport its sediment load. Figure 10.7 (c) shows the conditions long after the capture. The headwaters of the captor stream have all developed gorges. The falls at the point of capture have retreated upstream to head of the diverted stream. With further development all the falls and rapids disappear and the only evidence of capture remaining will be the angular bend. Stream capture also takes place in the case of stream migrating on the cone or the fan developed by it due to sediment deposition. During its avulsion in a new course, the stream can capture smaller stream. Similarly when the streams meander widely over flood plains, stream capture is common due to lateral cutting and intersection of meanders. River Channel Changes 323 Fig. 10.7 River capture (Lobeck 1939) 10.4 EROSION AT BENDS Some studies have been carried out in the past to find out the variables which govern the rate of erosion or migration of bends in alluvial rivers. Wolman (1959) has reported rates of erosion in cohesive river banks and recognized the important of seasonality in the rates of erosion. Daniel (1971) has monitored the effect of erosion in the form of changes in outer bank of meander bends along streams in Indiana. According to Dury (1961) annual flood magnitude is of importance in this erosion, while Harvey (1975) has commented on the effectiveness of intermediate discharge. Hughes (1977) made measurements on three meander arcs on the river Cound in U.K. during 1972-74. This river has width to depth ratio of 15. The rates of erosion were measured using 92 pegs and monitoring the distance of the bank line from these pegs. The discharge during the study duration varied from 1.0 m3/s to 10.0 m3/s. It was found that 324 River Morphology the two meander arcs having large bend radius had average erosion rates of 1.61 m/peg and 1.51 m/peg while the third arc which had a smaller radius showed erosion rate of 1.9 m/peg. It was also found that for discharge less than 2.0 m3/s the erosion rate of banks was minimum. For discharges between 2.0 and 8.0 m3/s the erosion rate was moderate, and for discharge greater than 8.0 m3/s major erosion changes occurred. The corresponding return periods for 2 m3/s and 8.0 m3/s were estimated as 10-12 times/yr and 1.5 yrs respectively. Similarly Hooke (1995) studied the migration of bends on five streams in East Devon (U.K.) having catchment areas between 110 km2 and 620 km2. He found the average rate of migration to be 0.37 m/yr while the maximum was 1.32 m/yr. Studies of Nanson and Hickin (1983) and Hickin and Nanson (1984) throw light on the parameters on which dimensionless migration rate M1/W, where M1 is migration rate in m/s and W is the channel width, depends. According to them Stream power, erosional resistance of concave bank material, height of M1 r =f concave bank, sediment supply rate, c W W F GGH I JJK Further, it stands to reason that average bed material size d should come in the picture and it can assumed that sediment supply rate should be related to stream power QS. The above relation can then be written as M1 W F G =fG GG d H 2 QS , erosional resistance of concave bank material, Dgs d rf I J h r J , D WJ JK c where rc is the centerline radius of curvature of the bend, h is the height of concave bank above water level and D is depth of flow. Further, Hickin and Nanson (1984) found that when rc/W = 2.5 the migration rate of the bend is maximum. This maximum value of to be a function of stream power, M1 denoted by K is intuitively assumed W r r h M1 and erosional resistance. Hence he has plotted vs c for c KW D W W ranging from 1.18 to 13.0 for bends and for which K = bM g 1 max W was 0.02. The graph between M1 and KW rc is shown in Fig. 10.8 and it is anticipated that data for other bends would follow the same trend. W Nanson and Hickin (1983) have further stated that channel migration is discontinuous as a result of seasonal fluctuations in flow; hence short-term migration rates are not indicative of the average migration rate of the bend. River Channel Changes 325 1.0 0.8 0.6 0.4 0.2 0.0 Beatton river data M1 KW 0 2 4 6 8 rc/W 10 12 14 Fig. 10.8 Variation of M1 r with c KW W The seriousness of bank erosion can be illustrated by discussing erosion upstream of the Farakka barrage on the river Ganga (Majumder 2004), see Fig. 10.9. Farakka barrage was constructed across the river Ganga in 1971 to divert 1135 m3/s (40 000 cfs) of water to its tributary, the Hooghly river, in order to keep Kolkata port navigable throughout the year. This diversion has been effected by constructing a 3.8 km long feeder channel from Farakka barrage. Upstream of the barrage, the river slope is 0.000 06 and the bed is made of fine to medium sand. The flood discharge over the past 32 years has varied between 36 290 m3/s and 77 778 m3/s. Further, while the distance between the permanent banks is about 16 km, the river width is about 2 km in the river reach upstream of the barrage. Prior to the construction of barrage, the river was flowing straight from Rajmahal to the barrage site. However in 1963 the course of the river started gradually shifting towards the left and attacking the village on the left bank e.g. Panchanandpur about 20 km upstream of the barrage, see Fig. 10.9. The rate of bank migration has varied from year to year, but over the past 30 years the apex of the bend has migrated through approximately 8000 m giving an average rate of migration of 36.7 m/yr. Configuration of the bend is such that the bend radius is about 14 km giving radius to width ratio of about seven. As a result of migration of the bend to the east for the past six years, the area eroded has varied from 100 to 415 ha per year. The area being fertile it is thickly populated, and hence during a flood, loss of the order of 500 to 1000 crores of rupees takes place. Further, to the northeast of Farakka barrage flow smaller streams the Kalindri, the Pagla, the Old Bhagirathi, and the Mahananda. It is possible that if the migration towards the east continues, the Ganga may capture the above mentioned streams one after another and then flow along the Mahananda thus changing its course drastically. Hence some steps have been taken to arrest this migration; these include building of retired embankments as erosion proceeds, and construction of spurs. However, these measures seem to have only a marginal effect. It seems that effective management of this problem should involve firstly the stabilization of the eroding bank by giving proper slope to the bank and then providing bank protection. The next step that needs to be taken is to reactivate the existing small channel on the right side so that it starts carrying increasing amount of 326 River Morphology Mahananda Bhagirati 2002 2001 2000 1999 1998 1997 NH34 Pagla Railway Kalindri Panchanandpur Farakka barrage 1939 1922 1967 1939 1922 Bhuti Diara Manikchak Rajmahal Fig. 10.9 Bank-line changes upstream of Farakka barrage on the Ganga flow there by decreasing the flow along the left bank. This can be assisted, if necessary, by dredging downstream of Rajmahal. Hooke (1995) has summarized information about mechanisms of bank erosion. These are broadly classified into three broad categories namely bank weakening, fluvial erosion or entrenchment, and mass failure. Bank weakening can be due to pre-wetting downwards by precipitation front, inwards from the river or upwards by the water table. Similarly bank weakening can occur by desiccation condition of high temperature and low moisture which can lead to cracking and spalling. Similarly freezing and thawing action can also make the bank more susceptible to erosion. Fluvial erosion can be direct removal of non-cohesive material when flow and shear stress near the bank exceed a certain limit during flood. Resistance to such type of erosion is affected by vegetation, composition and state of the material and its cohesivity. Mass failure can be of two types. Shear, beam and tensile cantilever failures occur mainly on composite banks. Initial fluvial failure takes place of basal coarse materials and then failure of the upper fine blocks takes place. The second type of mass failure is shear failure. This occurs in cohesive materials associated with increased bank angle and/or bank height, high moisture content and pore pressures. Failure takes places after occurrence of peak flow. 10.5 NATURAL AND ARTIFICIAL CUT-OFFS In most of the cases the meanders in alluvial streams are not stationary but move slowly in the direction of flow. During the development and movement of meanders there is a gradual lengthening of meanders which imparts a lateral movement to meanders. Hence in few cases movement of meanders is in lateral direction thereby increasing the amplitude of meanders. Increased frictional and bank resistance tends to halt the lateral movement. When the bend and bank resistance become too large for continued River Channel Changes 327 stretching of the loop, it is easier for the flow to cut across the neck of the loop than to flow along the bend, resulting in a natural cut off. The two ends of the loop that is cut get gradually silted up and give rise to an oxbow lake. Usually small and narrow side channels are available within a neck of the meander loop. These channels are either part of the main channel when the stream was flowing along that course or are formed by spilling of floods over the banks. Cut-off may develop along these small channels. The development of a small channel in the neck into a major natural cut-off primarily depends on the assistance this channel receives from the major floods in increasing its cross-section. If a large flood lasts for a relatively long period, the channel gets sufficient time to develop into a full waterway. Development of such a natural cut-off requires two to three years, or probably even more time. Natural cut-offs have occurred on the Mississippi river in U.S.A. and other rivers in the world. On the Mississippi, natural cut-offs have taken place when the cut-off ratio i.e. arc distance along the bend to the neck distance ratio, was between 8 and 10. Analysis of historical data on 145 natural cut-offs on relatively smaller streams in England and Wales has shown (Lewis and Lewin 1983) that cut-offs have occurred for rc/ W ratio ranging from 1.0 to 12.0. However, a large number of these cut-offs have occurred at rc/W values between 1 and 4. Assuming that the meander pattern is made up of arcs of a circle, Chatley (1940) has shown that, from purely geometric point of view, cut-off occurs when MB = (2 + 3 ) rc because at this value the neck distance will be zero. According to Frisk (1944) natural cut-offs are of two types: Neck Cut-off This cut-off forms in response to river flow across the narrow neck of the over extended meander loop. For neck cut-off to occur, the neck has to be narrow enough so that the flood water breaks through and forms a cut-off. This type of cut-off rapidly abandons the old bend, forms an oxbow lake and is rapidly silted up at its end since the sediment can then enter the oxbow lake only from local inflow or from over bank flood flows; further deposited sediment consists of finer sediment, normally decreasing in size with distance from the new channel. Chute Cut-off This type of cut-off forms in response to the development of a chute across a low lying swale within the enclosed point bar area of an over extended meander bend. The old channel is abandoned slowly and with the gradual reduction in flow, is filled with silt and sand material and finally with clay. These two types of cut-offs are shown in Fig. 10.10. Friedkin (1945) noted in his flume tests that there was a limiting size for each meander pattern and that, when for any reasons this size was exceeded, chute cutoffs invariably occurred. In natural streams they have been observed to occur during flood flows that tended to follow a straight path and during lesser flows when either the loop in question or the adjacent loop became excessively enlarged. Artificial cut-offs are executed on the streams to reduce the stream length and thereby reduce the flood heights and flood periods, and to shorten the travel distance and increase the manoeuvering ability of water vessels during navigation along the bends. Pickles (1941) has estimated that if all the bends in a typical alluvial river are cut-off, the average velocity in the stream will increase by about forty percent. In the past artificial cut-offs have been executed on many rivers in the world such as the Mississippi, the Arkansas and the Missouri rivers in U.S.A., the Tisza river in Hungary, the Hai river in China and some 328 River Morphology Neck cut-off Point bar Chute cut-off Fig. 10.10 Chute and neck cut-offs streams in New Zealand. By execution of such cut-offs the length of the Mississippi has been reduced from 720 km to 480 km and that of the Tisza from 1299 km to 745 km. The execution of artificial cut-offs is done slightly differently in Europe and in U.S.A. In Europe, the cut-off is made in the dry and to its full dimensions, and the river is allowed into it. American and New Zealand practices are similar, in which a pilot channel of small cross-section is made which can initially carry about 8 to 10 percent of flood discharge and it is allowed to develop by itself. This channel develops fully in about 3 to 4 years. Pickles (1941) has given the following suggestions in the design and execution of cut-offs. i. The pilot channel should be tangential to the incoming flow as well as while leaving the cut. ii. The pilot channel should be made on a slight curve, the curvature being less than the dominant curvature of the river. iii. Entrance to the pilot channel should be made bell-mouthed. iv. Cut-off should be excavated to the mean river cross-section. v. When a series of cut-offs is to be made, the work should progress from downstream to the upstream. When a cut-off is executed, there are some short term and some long-term changes in the rivers; these need to be properly understood. As soon as the cut-off is executed the water surface slope within the cut-off reach is increased. This causes M2 profile upstream of cut-offs and M1 profile downstream. Further this change in water surface slope in the upstream reach will reduce the storage and the peak discharge downstream of cut-off is likely to be increased. The long period change will be in the bed profile. Reach upstream of the cut-off will experience degradation while that downstream will experience aggradation. The effectiveness of cut-offs as means of flood control is discussed by Pickles (1941). As mentioned earlier, if all the bends are removed, the flow velocity is likely to be increased by about forty percent. Whether the expenditure involved in straightening is justified as a flood control measure depends on the width of the flood plain. If the flood plain is approximately 0.8 km wide of less, the channel improvement using cut-off is justifiable because cost of levee construction will be prohibitive. River Channel Changes 329 If the flood plain is 1.5 to 6.5 km wide, cut-offs together with levee construction are the accepted method of flood protection. For every wide flood plain, flood protection is seldom attempted using cut-offs. However, cut-offs can still be executed if the stream is used for navigation. Lastly, it needs to be emphasized that when cut-off is executed the banks in that reach need protection, otherwise stream will have a tendency to develop a meander loop again. 10.6 CHANNEL PATTERN CHANGES Sinuosity is earlier defined as length of stream divided the length of the valley. The sinuosity values range from 1 to slightly greater than 3.5. Analysis of American rivers by Leopold and Wolman (1960) indicated that the sinuosity varied from 1.0 to 3.0. The average sinuosity of the Mississippi is 2.3 while its maximum value at the Greenville Bends at Greenville was 3.3. In single channel stream it is interesting to study variation in the sinuosity of the stream. Studies by Schumm (1977) have indicated that the sinuosity is significantly affected by the differences in the flow variation. To support this argument he has given example of two streams the Tanoro and the Guanipa. The characteristics of these two streams are given below. River Tonoro Guanipa d mm 0.35 0.35 Mean annual discharge Qma m3/s 11.34 17.00 Qmax m3/s 535.6 104.9 Qmax/Qma 47.23 6.17 Si 1.1 2.3 From this it seems that Qmax/Qma ratio is morphologically important in determining the sinuosity; higher sinuosity is associated with lower value of Qmax/Qa. Experiments in a laboratory flume by Khan (1971) have indicated that the sinuosity was function of slope. For small slopes the channel was straight; when the slope exceeded a certain limit the channel meandered and sinuosity increased with increase in slope and reached a maximum value. Further increase in slope decreased the channel sinuosity and then the channel became straight and braided. Similar variation between valley slope and sinuosity has been reported for the Mississippi between Cairo (Illinois) and Head of Passes (Louisiana) by Schumm (1977). Schumm argues that the valley slope reflects the past discharges and sediment loads while the channel slope corresponds to the present discharge and sediment load variations. By plotting valley slope versus channel slope for some streams and palaeo channels, he found that channels with low percentage of silt and clay in channels, had sinuosity of unity and the two slopes were almost the same, while for channels with higher values of percentage of silt and clay, channel gradient was smaller than valley gradient and streams were sinuous with different sinuosity. In a river system, it is many times found that for essentially constant discharge and sediment load, change in river pattern or plan form occurs along the length. The fact that in many cases the channel slope varies slightly but the slope of the valley changes explains this significantly. Within the valley; there are reaches of valley floor that are steeper or gentler than the average stream gradient. This happens wither due to tectonic movements or by the large difference between sediment load of the tributary and the mainstream. Hence to maintain relatively constant gradient, the stream lengthens its course on steeper reaches. 330 River Morphology Agarwal (1983) analysed the field data and some laboratory data and found that sinuosity depends on slope and discharge. Khan found that sinuosity is related to slope. Schumm (1977) has plotted sinuosity against stream power toU and found that for low values of toU the channels are straight, then for a certain range of toU channels meanders, the sinuosity increases and reaches a maximum value and then decreases. Beyond another threshold value of toU, the stream braids. It is quite possible that sinuosity would correlate well with dimensionless stream power QS/d2Ö(Dgs d/rf). It many times happens that with time a river may undergo a complete change of morphology if changes take place in discharge and sediment load. Schumm (1969) calls such change the river metamorphosis. The changes taking place in bed elevations leading to aggradation or degradation have been discussed in Chapter 9. Here change in plan form such as in meander length, sinuosity, and width to depth ratio of the stream are briefly discussed. The geomorphic approach to such changes is based on the work done by Schumm (1969, 1971 and 1977) and is briefly discussed below. Schumm’s work has indicated that at characteristic discharge such as mean annual discharge, W~ Q 0.38 M 0.39 M - 0 .38 Q - 0.32 Q 0.34 M 0.74 Q 0.38 M 0.39 S~ ML ~ D~ Si ~ M0.24 and assuming total bed material load ~ Qs » U | | | | | V | | | | | W ...(10.1) 1 for constant discharge, one can write M ...(10.2) W, ML , S D, Si Here M is the percent of silt and clays in the bank material. By using plus or minus exponent to indicate how various aspects of channel morphology will change if Q or Qs is increased or decreased, the following relationships can be written Q+ » W+, D+, ML+, S– Q– » W–, D–, ML–, S+ Q+S » W+, D–, ML+, S+, S–i Q–S » W–, D+, M–L, S– S+i U | | V | | | W ...(10.3) River Channel Changes 331 Above equations indicate how W, D, ML and S change with change in mean annual discharge, and how increase or decrease in Qs at constant discharge affect these variables along with sinuosity Si and width to depth ratio F. Width to depth ratio of the channel is found to be mainly influenced by the type of sediment load; as the load increases, F decreases and vice versa. Since in nature change in discharge or sediment load will rarely occur alone, Schumm considers four possibilities and represents changes in morphology that will result by the relationships + Q+ Q+S » W+, D±, ML+, S±, S– i, F – Q+ Q–S » W±, D+, ML±, S–, S+ i, F Q Q – Q+S Q–S »W ,D , ± – – ML±, M –L, S , S ± + S–i , F + – »W ,D , ± S+ i, F– Schumm (1971) has further indicated that when channel width, depth, sinuosity and meander length are required to be modified because of a hydrologic change, then a long period of instability could be envisaged with considerable bank erosion and lateral migration occurring before stability is restored. A couple of examples given by Schumm (1971) are briefly discussed here to emphasize the changes that take place and time required to effect the change. The length of the Mississippi river from the mouth of the Big Sioux river to the mouth of the Platte river was approximately 400 km in 1804 while this length reduced to 240 km in 1935. This reduction is attributed by Towl (see Schumm 1971) to the cutting of timber on the flood plain, and the great flood of 1881 and subsequent floods. These floods by reducing the length of river, steepened the slope and widened the river cross-section. It may be found that in a given reach of a stream the sinuosity has changed over a period of time. This can happen when the river length changes over a period of time due to natural or artificial cut-offs, or due to growth of the delta. Such changes in length will affect the slope and hence the sinuosity or plan-form of the stream. Such fluctuations in the length of the Mississippi river have been found by Winkley (1970) who showed the river length has changed from about 1680 km to 2056 km and then reduced to about 1472 km over the past 2000 years. Schumm (1969, 1971) has given a few more examples of changes in river morphology due to changes in hydrologic regime over a long period. The other approaches is make judicious use of relationships and criterion discussed in the earlier chapters to predict change in S, W, W/D ratio and plan-form when changes are effected in Q or QT or S. Thus for a given discharge when S is changed, plan-form changes can be assessed using Lane’s Q vs S criterion (see Eq. 9.1). Alternately Chang’s diagram (Fig.6.28) between Q and S/d1/2 can be used to predict width, depth and plan-form. When aggradation or degradation takes place equilibrium depth, width and width/depth ratio can be assessed using Eqs.(6.34) or (6.35) proposed by Garde et al. However, it is difficult to predict the time required to effect such changes because the width adjustment is rather slow and depends on the cohesivity of banks. U | | V | | | W ...(10.4) 10.7 LONGITUDINAL GRAIN SORTING As mentioned in Chapter 4, the size of bed material of alluvial streams reduces in the downstream direction. This has been verified on a number of streams such as the upper Rhine, the Danube, the Niger, 332 River Morphology the Mississippi, the Rio Grande and the Ganga. Sternberg attributed this to abrasion and developed Sternberg’s law as given by Eq. (4.6) Similar reduction in size of bed material is also found on beaches where littoral drift occurs. The phenomenon of abrasion has been discussed by Pettijohn (1957) in relation to rates obtained on size reduction in laboratory experiments and reduction of bed material size in the downstream direction in the streams. He has concluded that 1. Abrasion depends very much on the resistance of minerals to wear and on the diameter of particles; the abrasion rate of gravel is much greater than that of sand. 2. Abrasion is also a function of the composition of the material tested. 3. Abrasion rates obtained in experiments by Lane, Daubree, Thiel and others show that abrasion cannot generally be accepted as the sole cause of decrease of particle size in rivers. Hence, it is believed that some sort of hydraulic sorting process can explain this reduction in size of bed material of the streams in the downstream direction. Hydraulic sorting can be local over distances of the order length of the bed-form or general over much larger lengths. Thus local sorting takes place over dunes and in the bends. The general or longitudinal grain sorting primarily takes place because of spatial variation of transport of different sediment sizes forming the bed material, and has been studied by Rana et al. (1973), Diegaard and Fredsøe (1978) and Diegaard (1980). Rana et al. (1973) considered a stream in which the longitudinal bed profile is in equilibrium i.e. mean bed level of the stream does not change with time, and developed the model for longitudinal grain sorting after making the following assumptions: 1. The flow is steady and constant along channel length. 2. The channel is wide and prismatic. 3. The channel profile is an independent variable and the channel slope decreases according to the relationship S = So e– a1 ...(10.5) in which S is the slope at distance L, So is slope at L = 0, and a1 is a constant. 4. The channel is in equilibrium but the channel bed has been initially formed by aggradation of material transported from the upstream. 5. The bed material at any section in the reach has the same size and gradation as the bed material discharge in the upstream section. 6. The bed material size at the most upstream section is known and is log-normally distributed. The analysis is carried out in the following manner. 1. The bed material is divided into ten fractions and using Einstein’s bed-load fuction the total bed material discharge and the ratio of total bed load to suspended load fractions is determined. 2. The median diameter and gradation of the computed bed material discharge at the upstream section 1 is determined. 3. Knowing the bed material discharge, water discharge and bed material load gradation at section 1, the energy slope required at section 2 to maintain the some q and bed material discharge between sections 1 and 2 is obtained. River Channel Changes 333 4. For the slope obtained in step 3, L is determined using the slope, Eq. (10.5) And at this distance section 2 is located. 5. The process is repeated taking section 2 as section1 and following steps 1 through 3 and the bed material size at each section is obtained. This size was found to decrease in the downstream direction and followed the law d = do e–a1 and the value of a1 was found to vary with q and total bed material discharge. Further, for a given combination of these values there was a reduction in the value of a within the bed material size range of 0.45 mm to 0.65 mm. It was also inferred by Rana et al. that if the major reduction in size of bed material is assumed to be due to hydraulic sorting, then under the assumptions made in the analysis, the size of bed material at any section would change with time. A slightly different approach has been used by Diegaard and Fredsoe (1978) and Diegaard (1980). The assumptions made by them are: 1. The channel is assumed to be prismatic and of constant width. Further, the discharge per unit width is constant at all sections. 2. The longitudinal profile of the river bed is described by the exponential function Z = Zo e–aL where Z is bed elevation at L, Zo is bed elevation at L = 0 and a is constant. 3. The rate of sediment discharge at L = 0 is constant. 4. The median size d and its standard deviation s at the upstream section is known and follows normal distribution law. 5. At the end of the river, the water surface level is assumed to be constant and there is no backwater effect in the stream. Using Engelund and Fredsoe’s equation for bed-load and using it for different size fractions, fraction wise bed-load transport is calculated. Similarly fraction wise suspended load transport rate is calculated using their method for determining reference concentration and Einstein’s method. The model works as follows. The river divided into a number of reaches of length DL, and sediment transport into a section qT (x) and sediment transport out of the section qT (x + DL) is calculated. The resulting change in bed elevation is computed using the continuity equation for sediment. By using sediment continuity equation for each size fraction, mixing it with the active layer of the bed (assumed to be 0.15 times the depth of flow) and resistance law of Engelund-Hansen, the size distribution of the bed material as well as changes in bed elevation due to aggradation are computed at time Dt. However, the time scales for grain sorting and changes in bed profile are much different and the bed profile changes very slowly. Hence, grain sorting can be treated as a quasi-steady process. Diegaard has used this model to predict the reduction in bed material size of the river Niger, the Mississippi and the Rio Grande. His results for the Niger and the Mississippi rivers along with the measured data points are shown in Fig. 10.11. It is found that the data scatter around mean predicted curves, but in some cases the scatter is large. The scatter can be attributed partly to various simplifying assumptions made in the analysis, sampling errors, and to the fact that joining of tributaries can vitiate the results. 334 (a) Niger river q = 10.6 m /s, S = 1.07 ´ 10 1.0 0.8 0.6 Measured Computed 2 –4 River Morphology d mm 0.4 0 100 200 L km (b) Mississippi river (Vicksburg) 0.6 0.5 300 d mm 0.4 Computed 0.3 Measured 0.2 0 100 200 300 L km 400 500 600 Fig. 10.11 Variation of observed and computed diameter of bed material with length (Diegaard 1988) References Agarwal, V.C. (1983) Studies on the Characteristics of Meandering Streams. Ph.D Thesis, University of Roorkee, Roorkee (India). Allen J.R.L. (1965) A Review of the Origin and Characteristics of Recent Alluvial Sediments. Sedimentary, Vol. 5, pp. 89-191. Chatley, H. (1940) Theory of Meandering. Engineering (London), Vol. 149. Chien, N. (1961) The Braided Stream of the Yellow River – Scientia Sinica – Vol. 10, No. 6, pp. 734-754. Daniel, J.F. (1971) Channel Movement of Meandering Indiana Streams, USGS Professional, Paper 732-A. Diegaard, R. (1980) Longitudinal and Transverse Sorting of Grain Sizes in Alluvial Rivers. Institute of Hydrodynamics and Hyd. Engg., Technical University of Denmark, Series Paper 26, 106 p. Diegaard, R. and Fredsoe J. (1978) Longitudinal Grain Sorting by Currents in Alluvial Streams. Nordic Hydrology, Vol. 9, pp. 7-16. Dury, G.H. (1961) Bankfull Discharge: An Example of its Statistical Relationships. Bull Intl. Association of Hydrology, Vol. 5, pp. 48-55. Ferguson, R.I. (1977) Meander Migration: Equilibrium and Change, In River Channel Changes (Ed. Gregory, K.J.) John Wiley and Sons, Chichester, A Wiley Interscience Publication, Chapter 15, pp. 235-248. River Channel Changes 335 Ferguson, R.I. (1981) Channel Form and Channel Changes. In British Rivers (Ed. Lewin J.). George Allen and Unwin Ltd., London, Chapter 4, pp. 90-125. Friedkin, J.F. (1945) Laboratory Study of the Meandering of Alluvial Rivers – USWES, Vicksburg, Mississippi (U.S.A.), p. 40. Frisk, H.N. (1944) Geological Investigations of the Alluvial Valley of the Lower Mississippi River. Mississippi River Commission, Vicksburg, (Mississippi), U.S.A. Garde, R.J. (1978) Irrigation in Ancient Mesopotamia. ICID Bulletin, Vol. 27, No. 2, pp. 11-22. Gregory, K.J. (Ed.) (1977) River Channel Changes. A Wiley Interscience Pulication, John Wiley and Sons, Chichester, (U.K.), 448 p. Gurnell, A. and Petts, G. (Eds.) (1995) Changing River Channels. John Wiley and Sons, Chichester (U.K.), 440 p. Harvey, A.M. (1975) Some Aspects of the Relations Between Channel Characteristics and Riffle spacing in Meandering Streams. American Journal of Science Vol. 275, pp. 470-478. Hickin, E.J. and Nanson, G.C. (1984) Lateral Migration Rates of River Bend. JHE, Proc. ASCE, Vol. 110, No. 11, Nov., pp. 1957-1967. Hooke, J.M. (1995) Processes of Channel Plan-Form Change on Meandering Channels in the U.K. In Changing River Channels (Eds. Grunell, A. and Petts, G.). John Wiley and Sons, Chichester, pp. 87-115. Hughes, H.J. (1977) Rates of Erosion on Meander Arcs. In River Channel Changes (Ed. Gregory K.J.) John Wiley and Sons, Inc., A Wiley Interscience Publication, Chapter 12, pp. 193-206. Jain, V. and Sinha R. (2003) River Systems in the Gangetic Plains and their Comparison with Siwaliks : A Review. Current Science, Vol. 84, No. 8, 25 April, pp. 1025-1033. Jain, V. and Sinha R. (2003) Hyperavulsive – Anabranching Bagmati River System, North Bihar Plains, Eastern India, Z. Geomorphologie, N.F. Berlin, Vol. 47, No. 1., pp. 101-116. Khan, H.R. (1971) Laboratory Study of River Morphology. Ph.D. Thesis, Colorado State University, Fort Collins, (U.S.A.), 189 p. Leopold, L.B. and Wolman M.G. (1964) River Meanders – Geol. Soc. of Am., Bull., No. 71, pp. 769-794. Leopold, L.B., Wolman M.G. and Miller, J.P. (1964) Fluvial Processes in Geomorphology. W.H. Freeman and Company, San Fransisco. Lewin, J. (1977) Channel Pattern Changes. In River Channel Changes (Ed. Gregory, K.J.) John Wiley and Sons. Chapter 8, pp. 167-184. Lewis, G.W. and Lewin, J. (1983) Alluvial Cut-offs in Water and Borderlands, Special Pub., Intl. Assoc. of Sedimentologists, Vol. 6. Lin, P.N. and Li Guifen (1986) The Chanjiang and Huanghe. Circular No. 1, IAICES, Beijing. 17 p. Lobeck, A.K. (1939) Geomorphology: An Introduction to the Study of Landscapes. McGraw Hill Book Co. Inc., New York, pp. 198-201. Lu Jianyi (1982) Mouth of the Yellow River, Its Evolution and Improvement. The Yellow River Vol. 3, In Selected Papers of Researchers on the Yellow River and the Present Practice (Ed. YACC) Oct. 1987, pp. 95-105. Mazumder, S.K. (2004) Aggradation/Degradation of Ganga Near Farakka Barrage. National Symposium on Silting of Rivers Held in New Delhi, C.W.C., 10 p. Nanson, G.C. and Hickin, E.J. (1983) Channel Migration and Incision on the Beatton River. JHD, Proc. ASCE, Vol. 103, No. 3, March, pp. 327-337. Newson, M.D. (1995) Fluvial Geomorphology and Environmental Design. In Changing River Channels (Eds. Gurnell, A. Petts, G.) John Wiley and Sons. Chapter 19, pp. 413-432. Pettijohn, F.J. (1957) Sedimentary Rocks. Harper and Brothers, New York, 2nd Edition. 336 River Morphology Pickles, G.W. (1941) Drainage and Flood Control Engineering. McGraw Hill Book Co., New York, Chapter 11. Rana, S.A., Simons, D.B. and Mahmood, K. (1973) Analysis of Sediment Sorting in Alluvial Channels. JHD, Proc. ASCE, Vol. 99, No. 11, No. pp. 1967-1980. Richard, K., Chandra, S. and Friend, P. (1993) Avulsive Channel Systems: Characteristics and Examples. In Braided Rivers (Eds. Best, J.L. and Bristo C.S.) Geological Society Publication No. 75, pp. 195-203. Schumm, S.A. (1969) River Metamorphosis. JHD, Proc. ASCE, Vol. 95, No. HY1, Jan. pp. 255-273. Schumm, S.A. (1971) Fluvial Geomorphology. In River Mechanics (Ed. Shen H.W.) Published by Editor, Fort Collins (U.S.A.), Chapter 5, pp. 5.1 to 5.22. Schumm, S.A. and Khan H.R. (1972) Experimental Study of Channel Patterns. Geol. Soc. of Am. Bull. Vol. 83, pp. 1755-1770. Schumm, S.A. (1977) The Fluvial System. John Wiley and Sons, A Wiley Interscience Publication, New York, Chapter 5. Sinha, R. (1996) Channel Avulsion and Flood Plain Structure in Gandak-Kosi Interfan, North Bihar Plains, India. Zeitscrift fûr Geomorphologie N.F. Supp. Bd. 103, pp. 249-268. Tangri, A.K. (2000) Proceedings of the Workshop on Fluvial Geomorphology with Special Reference to Flood Plains. IIT Kanpur, pp. 3.1 to 3.12. Winkely, B.R. (1970) Influence of Geology on the Regimen of A River. ASCE, Natl. Water Resources Meeting (Memphis) Preprint 1078, 35 p. Wolman, M.G. and Leopold, L.B. (1957) River Flood Plains: Some Observations on Their Formation. Geo. Survey Professional Paper 282-C, pp. 87-107. Wolman, M.G. (1959) Factors Influencing Erosion of a Cohesive River Bank. Am. Jour. of Sciences, Vol. 257, No. 1, pp. 204-216. Worcester, P.G. (1948) A Text Book of Geomoprhology. D Van Nostrand Co., New York, 2nd Edition, p. 150. Xu Fuling (1982) A Brief Account of Changes of Course of the Lower Yellow River in Past History. The Yellow River No. 3, In Selected Papers of Researchers on the Yellow River and the Present Practice (Ed. YRCC) Oct. 1987, pp. 47-52.Hug C H A P T E R 11 Analytical Morphological Models 11.1 INTRODUCTION Various changes that take place in the longitudinal profile of an alluvial river as a result of man-made or natural disturbances introduced in the river are discussed in chapters nine and ten. Those can be studied either by using a physical model or an analytical or a numerical model. If the changes taking place are local, very often a physical model is used; however when the changes take place over large lengths and are slow, thus requiring a very long time for attaining equilibrium or near equilibrium condition, it is advantageous to use analytical or numerical models. Problems solved by using physical models with movable bed include location of bridges, design of guide bunds, location and dimensions of spurs, optimum design of sediment excluders and ejectors, execution of cut-offs, control of sediment entry into canals and rejuvenation of dying channels. Design of physical movable bed model is based on the determination of the dimensionless parameters that govern the process under consideration. These parameters include ratios of lengths, velocities, mass densities, and forces. These need to be kept the same in the model and the prototype so that the model satisfies the conditions of geometric, kinematic and dynamic similarities. If all the corresponding length ratios have the same value in the model and the prototype, the model is geometrically similar; otherwise it is geometrically distorted. Similarly, the model can have material distortion or force distortion. Alluvial river models are usually distorted and hence the designer of the model has to see what will be the effects of distortion on the behaviour of the model and the interpretation of results from model to the prototype. Hence, designing a movable bed model and interpretation of results from model to the prototype is still an art and each laboratory has its own method of model design and interpretation of results. Further, each physical model may serve the purpose of that specific problem only and cannot be used for other rivers. Analytical and numerical models used to study the morphological changes are based on using governing equations of motion namely, momentum equation, and continuity equations for flow and sediment, and resistance and sediment transport relations. These equations are then combined and solved for known initial and boundary conditions. To get analytical solutions, one has to make some drastic simplifications. Such simplifications include one-dimensional flow, linearisation in respect of 338 River Morphology friction, convective acceleration term, and sediment transport rate derivative, and assumption of uniform sediment. In spite of these restrictions, under certain conditions analytical models provide rough and useful results. When one does not wish to make such simplifications, numerical models can be used where the system of equations are solved using numerical techniques with known initial and boundary conditions. Numerical models need calibration and proving with the past data; once the model is proved, it can be used to make predictions. A number of such models are available and these differ from one another in the degrees of sophistications used in its formulation (see Chapter 12). This chapter includes a brief description of the governing equations for one-dimensional flows in alluvial streams, their simplifications to get different analytical models and some of their applications. De Vries (1993) initiated this approach and since then some investigators have used these models to get results for a few practical problems. 11.2 BASIC ONE-DIMENSIONAL EQUATIONS For solving problems concerning transient bed profiles in alluvial rivers, the basic equations that are used are continuity equations for flow and sediment, dynamic (or momentum) equation, and resistance and sediment transport relationships. These are derived or discussed below for one-dimensional flows in which average velocity U, average depth D and sediment transport rate QT or qT are functions of x and t; here QT = B qT where B is channel width and qT is volumetric sediment transport ratio per unit width. (a) Continuity Equation for Flow The continuity equation for flow, which is also called the equation for conservation of mass, when written for open channels, states that the net rate of mass inflow into the control volume would result in the rate of increase of mass within the control volume (see Fig. 11.1); or ¶ ¶ (rf A d x) + (rf AU) d x + rf q¢ d x = 0 ¶t ¶x ...(11.1) Here rf is mass density of fluid which is taken as constant assuming sediment concentration to be very small, A is the cross sectional area, U is the average velocity at a section and q¢ is the lateral in flow rate per unit length from both sides. Taking rf as constant, Eq. (11.1) gives ¶ A ¶Q + + q¢ = 0 ¶t ¶x ...(11.2) where Q = AU is the discharge in the channel. If lateral inflow is zero, the above equation takes the form ¶A ¶A ¶U +U +A =0 ¶t ¶x ¶x ...(11.3) and for rectangular channel of constant width B, Eq. (11.3) reduces to Analytical Morphological Models 339 1 2 W.S QT + ¶QT dx ¶x U D h QT Dz Z Dx Channel bed Datum Fig. 11.1 Definition sketch for sediment continuity ¶D ¶D ¶U +U +D =0 ¶t ¶x ¶x ...(11.4) since A = BD and D is the average depth of flow. This equation can be used for sediment-laden flows if the sediment concentration discharge per unit width. qT is much smaller than unity; here qT and q are sediment and water q (b) Continuity Equation for Sediment The continuity equation for sediment can be derived in the same manner as the continuity equation for flow. Here, the difference between the rates of sediment inflow and outflow from a control volume will cause deposition on the bed or erosion from the bed, thereby changing the bed level, see Fig. 11.1. Therefore, ¶ ¶ (B Z d x) + (QT) d x = 0 ¶t ¶x QT = BqT ¶q T 1 ¶Z + =0 ¶t 1- l ¶x and since a f Here B is assumed to be constant; qT is volumetric sediment transport rate and l is the porosity. This equation is exact if qT represents bed-load only. When some material goes into suspension, an additional term needs to be included in Eq. (11.5) to take into account change with respect to time of the suspended ¶ (DCs) where Cs is average concentration of suspended ¶t load. If this term is not included when appreciable amount of suspended load is present, Eq. (11.5) is U | | V | | W ...(11.5) sediment load in the control volume, viz., 340 approximate. Equation (11.5) indicates that River Morphology ¶Z ¶ qT is positive i.e., aggradation will occur if is ¶t ¶x negative i.e., qT decreases as x increases; in other words qT at section 1 is greater than qT at section 2. (c) One-dimensional Dynamic Equation The dynamic equation for non-uniform and unsteady flow in an open channel is obtained from the principle of conservation of momentum. With reference to Fig. 11.2, for the control volume ABCD, Fig. 11.2 Definition sketch for momentum equation (Rate of momentum outflow) – (Rate of momentum inflow) + (Change of momentum within the control volume) = (Summation of components in the direction of flow of all the external forces acting on the control volume) These force components are (see Fig. 11.2) Frictional force = – to P d x Component of gravity force = r g A d x sin q Component of pressure force in the direction of flow = – r g cos q Therefore the momentum equation takes the form ¶ ¶ ¶D (rf A U) d t = – to P d x + rf g A d x sin q – rf g cos q d x ...(11.6) r f U 2 A dx + ¶x ¶t ¶x ¶D dx ¶x d i Here U is the average velocity of flow over cross sectional area A, P is the perimeter, to is the average shear stress on the perimeter, and q is the angle of inclination of channel bed. Assuming rf to be constant and dividing all terms by (rf A dx), one gets t ¶U U ¶U ¶U U 2 ¶ A ¶D + +2U + = – o + g sin q – g cos q ¶t ¶x ¶x A ¶x A ¶x rf R ...(11.7) Analytical Morphological Models 341 However, according to Eq. (11.3) 1 ¶ A A ¶U ¶A =– – U ¶t U ¶ x ¶x Further, for small values of q, sin q » tan q = So » – ...(11.8) ¶Z and cos q » 1.0. Also B = constant for ¶x rectangular channel for constant width. With these substitutions Eq. (11.7) becomes t ¶U ¶U ¶D ¶Z +U +g +g =– o ¶t ¶x ¶x ¶x rf R ...(11.9) This is momentum equation and the assumptions made in its derivation are i) constant width of rectangular channel; ii) no lateral inflow; iii) rf is constant which is true if qT is very small; q iv) flow being one dimensional, at a section we have average values of U and D, and hence momentum correction factor b = 1.0, further pressure distribution is hydrostatic; and v) q is very small. (d) Resistance Relations One can use either Chezy’s equation or Manning’s equation with constant value of C or n. Using Chezy’s equation the term gU 2 to can be written as 2 and hence Eq. (11.9) takes the form C R rf R gU 2 ¶U ¶U ¶Z +U +g =– 2 ¶t ¶x ¶x C R ...(11.10) It may be mentioned that in alluvial streams a different resistance equation is applicable since bed conditions change with the flow conditions. In unsteady, non-uniform flow C or n will be functions of stage, x and t. However, for obtaining analytical solutions n or C is assumed to be constant. (e) Sediment Transport Relation ¶ qT in the continuity equation one must use a sediment transport formula. de Vries ¶x recommends use of a relation of the type To evaluate the term qT = a U b ...(11.11a) Here, a and b are assumed to be constant for the range of depth under consideration. Alternately, some have used equation of the type 342 qT = a u*b River Morphology ...(11.11b) where a can be function of other parameters such as sediment size etc. but constant; here u* is the shear velocity. It is further assumed that sediment size is uniform. 11.3 ANALYSIS OF WATER SURFACE AND BED WAVES ¶Z ¶ f ¶U + =0 ¶t ¶U ¶ x Combining Eqs. (11.11) and (11.5) one can write ...(11.12) where qT = f (U). Further from Eqs. (11.4), (11.10) and (11.12) the following equation is obtained 2 2 –U3 w + 2 U Uw + g D -U + LM N a g ¶qT 1 - l ¶U f OP U – Ug ¶ q = 0 Q a1 - lf ¶U t w ...(11.13) dx is the celerity of the wave. Writing Eq. (11.13) in dimensionless form by introducing dt the dimensionless parameters Here Uw = M= one obtains Uw , Fr = U U , and y1 = gD LM b OP ¶ q N a1 - lf D Q ¶ U T M3 – 2 M2 + (1 – Fr–2 – y1 Fr–2) M + y1 Fr–2 = 0 ...(11.14) It may be mentioned that y1 is proportional to the sediment concentration. Equation (11.14) is a cubic equation and hence has three roots namely M1, M2 and M3 and these are functions of Fr and y1. These are given by M1 = (1 + Fr–1) and it is dimensionless velocity of a small surface disturbance in the direction of flow; –1 M2 = (1 + Fr ) and it is dimensionless velocity of a small surface disturbance traveling in direction opposite to the flow; M3 = d1 - Fr i 2 y1 when Fr is less than unity and it is the dimensionless velocity of bed form. It is significantly affected by the sediment transport rate. It is worth noting that when Fr is less than unity, M3 will be positive and the bed disturbance travels in the direction of flow; however when Fr is greater than unity, M3 will be negative and the disturbance moves in upstream direction. Figure 11.3 shows variation of |M| with Fr and y1. It can be seen from this figure that M1 and M2 are much greater than M3 when Fr number is less than approximately 0.8. Therefore, if the main interest is in the computation of flood or water levels, it is safe to assume M3 » 0 i.e., the bed is stationary. On the other hand, if one is interested in predicting the bed level variations, it Analytical Morphological Models 343 10 10 1 M1 0 M2 M3 10 10 10 –1 –2 –2 y2 = 10 10 –2 |M| –3 10 –3 10 –3 10 10 –4 10 –4 10 10 0.8 Fr 1.2 –4 –5 10 0 –5 –5 0.4 1.6 Fig. 11.3 Relative velocities in alluvial channel can be assumed that |M1, M2| ® ¥ i.e., water depth and velocity variations occur very rapidly. In other ¶U ¶D and can be neglected with respect to other ¶t ¶t terms in Eqs. (11.4) and (11.9). This is known as quasi-steady formulation. Another implication of differences in relative values of M1, M2 and M3 is that the numerical analysis can be carried out in decoupled mode; it means that bed can be first assumed stationary and water levels computed using momentum equation and then assuming water levels to be stationary, bed levels are computed using continuity equation for sediment and sediment transport law. words, flow can be considered quasi-steady and, 11.3 ANALYTICAL MODELS The analytical models can be obtained from the quasi-steady formulation of the equations discussed earlier i.e., U gU 2 ¶U ¶D ¶Z +g +g =– 2 C D ¶x ¶x ¶x U ¶D ¶U +D =0 ¶x ¶x 1 ¶Z ¶ qT ¶ U = =0 1 - l ¶U ¶ x ¶t a f qT = f (U) U | | V | | | W ...(11.16) ...(11.15) ...(11.12) ...(11.11) 344 These equations can be combined into one differential equation ¶ Z ¶ qT – ¶t ¶U River Morphology F I GG g JJ qg GH U - U JK 2 1 ¶Z = ¶x 1- l a f F H g Sf qg U- 2 U I K ¶ qT ¶U a f 1 1- l ...(11.17) The analytical models are obtained after linearisation of the above equations and therefore their solutions give only the rough estimates of the correct solutions. The non-linearity arises from the terms U2 U3 ¶U ¶q the friction term g 2 i.e., g 2 and the term T . Even though linearisation of these terms C D C q ¶x ¶U introduces some error, it gives an advantage that resulting equations are amenable to analytical solutions. Taking original bed as the x axis and assuming small changes in the bed level i.e., Z << Do the initial uniform flow depth, and various degrees of linearisation the following models have been obtained and studied. U Parabolic Model ¶U ¶D and are neglected during the transient condition i.e., there is no draw down or ¶x ¶x backwater profile and flow is uniform. Thus, Here the terms ¶U ¶D ¶D = 0, = 0 and =0 ¶x ¶x ¶t Hence, Eq. (11.16) reduces to U3 ¶Z =– 2 C q ¶x ...(11.18) Differentiating Eq. (11.18) with reference to x one gets 3U 2 ¶ U ¶2 Z = – C2 q ¶ x ¶ x2 ...(11.19) Further, according to continuity equation for sediment 1 1 ¶Z ¶ qT ¶Z ¶ qT ¶ U + = 0 or + =0 1- l ¶x 1 - l ¶U ¶ x ¶t ¶t a f a f Hence, substituting the value of ¶U from Eq. (11.19), one gets ¶x Analytical Morphological Models 345 C 2 q ¶ qT / ¶ U ¶Z – 3 1- l ¶t U2 a f FG ¶ Z IJ = 0 H ¶x K 2 2 or C 2 q ¶ qT / ¶ U ¶Z ¶2 Z = Ko where Ko = 2 3U 2 1 - l ¶t ¶x a f ...(11.20) Equation (11.20) is the diffusion equation – of the type used in heat conduction – and Ko is known as the diffusion coefficient, which can be expressed as 1 U ¶ qT / ¶ U Ko = 3 So 1 - l a FU I f HUK o 3 where Uo is the average velocity under uniform flow condition. If one uses the approximation U » Uo, the above expression simplifies to Ko = b qTe 3 So 1 - l a f ...(11.21) where qTe is the equilibrium transport rate. Equation (11.19) being parabolic in nature represents the parabolic model for solving transient problems in alluvial streams. Vreugenhill and de Vries (1973) stated that parabolic model is applicable when x is greater than 3 D/So when Froude number is small. It may be mentioned that earlier Culling (1960) had used parabolic model probably for the first time by assuming that bed load transport rate was directly proportional to local bed slope i.e., qTe ~ ¶Z . He ¶x developed solutions for simple hypothetical problems of channel erosion and development of longitudinal river profiles using time invariant boundary conditions. In spite of the crude assumptions made in the derivation of the parabolic model it gives useful results when applied with care, as shown later. It can be seen that Eq. (11.17) is of the form ¶Z ¶Z + (M 3 U ) = a (U) ¶t ¶x in which (M3 U) represents celerity of bed wave and a (U) is a measure of damping of disturbance. If a (U) is taken as zero, one gets an equation for the propagation of a simple wave the solution of which is known. Thus, the so called wave model is represented by ¶Z ¶Z + (M 3 U ) =0 ¶t ¶x ...(11.22) Analytical solution of the wave equation given above is possible if the equation is linearised i.e., (M3 U) and a (U) are taken as constants. If the assumption of uniform flow during the transient stage is not made but still the linearisation is done, one gets the hyperbolic model for river bed variation, namely 346 Ko ¶ 2 Z ¶Z ¶2 Z – – Ko =0 M 3 U ¶ x ¶t ¶t ¶ x2 River Morphology ...(11.23) Here Ko is the same as given by Eq. (11.21). It needs to be mentioned that in the derivation of Eq. (11.23), a constant discharge is assumed whereas for parabolic model such assumption has not been made. Vreugdenhill and de Vries recommend that hyperbolic model can be used for x less than 3 D/So. Equation (11.23) can be written as U M3 ¶ Z ¶ – ¶x Ko ¶ t FG ¶ Z + UM H ¶t FG ¶ Z + UM H ¶t 3 ¶Z ¶x IJ = 0 K IJ = 0 K ...(11.24) UM3 is very small, the above equation can Ko here Ko, M3 and U are constants, U being taken as Uo. If be approximated to ¶ ¶x ¶Z ¶Z 3 by neglecting the first term in Eq. (11.24). The above equation can be integrated to yield the wave model ¶Z ¶Z + UM3 = constant ¶t ¶x On the other hand, if UM3 ¶ is large, the second term in Eq. (11.24), ¶x Ko FG ¶ Z IJ can be neglected; H ¶t K then Eq. (11.24) reduces to parabolic model ¶2 Z ¶Z = Ko ¶t ¶ x2 Thus the ratio UM3 seems to play an important role. Ko 11.4 SOME APPLICATIONS OF LINEAR MODELS Parabolic Model Let us first consider the parabolic model. Probably this method was first proposed by Culling (1960) who assumed that sediment transport is proportional to terrain slope and combining it with the continuity equation obtained the diffusion equation which is in fact heat conduction equation. He has also proposed solution of diffusion equation for different boundary conditions. It may be mentioned that a number of solutions of diffusion equation for different boundary and initial conditions are given by Carslaw and Jaeger (1947). Analytical Morphological Models 347 t=O W.S W.S t = O, Z =0 Original lake level ¥ Original bed level t Changed lake level t ¥ Final bed Transient bed profile Fig. 11.4 Degradation due to lowering of lake level De Vries (1975, 1993) has applied parabolic model to determine transient bed profiles in a stream when the lake level to which it joins at the downstream end is suddenly dropped over a vertical height Zo, see Fig. 11.4. By neglecting the effects of drawdown one can assume that at t > 0 the flow is uniform. Measuring x in up stream direction the boundary conditions are Initial condition Boundary condition and Z (x, 0) = 0 Z (x, t) = 0 as x ® ¥ Z (0, t) = – Zo Equation (11.20) which is a partial differential equation can be reduced to ordinary differential equation by substituting h = x 2 Ko t f ¢¢ + 2 h f ¢ = 0 where Z = f (h). The solution of this equation for the above boundary condition is Zo x Z =–erfc Zo 2 Ko t F GH I JK ...(11.25) Transient bed profiles are shown by dotted lines in Fig. (11.4). Vittal and Mittal (1980) have used parabolic model for the prediction of degraded profile of the Ratmau torrent caused by trapping of sediment in the upstream. Soni (1975), Soni et al. (1980), Mehta (1980), Garde et al. (1981), Jain (1981), Gill (1983) and others have used parabolic model to study aggradation of river bed due to overloading. Experiments conducted by Soni and Mehta at Roorkee University in a 30 m long and 200 mm wide flume using nearly uniform sediments of size of 0.32 mm, 0.50 mm and 0.71 mm and overloading ratio D qT from qTe 348 Section of sediment injection DQT Qte W.S. Zo Do Us River Morphology Transient bed profile at t > 0 Original bed Fig. 11.5 Aggradation due to overloading 0.50 to 16.0 form the basis of most verifications of parabolic and hyperbolic models. In these tests equilibrium conditions were established for a given discharge and slope and equilibrium transport rate qTe was determined. Then, for given increase in sediment load at upstream end, transient bed and water surface profiles were obtained. In fact studies by Soni and Mehta have revived the interest in analytical models since then and parabolic and hyperbolic models have been studied in greater detail. With reference to Fig. 11.5 wide rectangular channel has uniform depth Do and velocity Uo and equilibrium transport rate QTe for channel slope of So; the sediment supply rate at the upstream section is increased by a constant rate DQT. Using the parabolic model, the initial and boundary conditions are (see Jain 1981): Z (x, 0) = 0 for t ³ 0 The second boundary condition can be obtained from the fact that sediment volume under transient bed profile at time t is given by DqT t = ¥ o z (1 – l) Z d x which on differentiation with t yields DqT = (1 – l) z ¥ o ¶Z dx ¶t Substituting the value of ¶2 Z ¶Z ¶Z from = Ko , one gets ¶t ¶t ¶ x2 DqT = (1 – l) Ko But, since = FG ¶ z IJ at (¥, t) = 0, the second boundary conditions reduces to – K FG ¶ z IJ at (0, t) H ¶ xK H ¶ xK o FG ¶ z IJ H ¶ xK o a f D qT 1- l Analytical Morphological Models 349 The solution of diffusion equation with these boundary conditions is Z= 2 D qT Ko 1 - l h= LMF K t I a f MNH p K o 1/ 2 exp in which erfc 2 p z FG - x IJ - x erfc F H 4 K t K 2 GH 2 2 o x Ko t I OP JK PQ ...(11.26) ¥ h e - h dh 2 From Eq. (11.26), Zo is given as that value of Z at x = 0, or 2 D qT Zo = Ko 1 - l F K tI a fH p K o 1/ 2 or Zo = Ko t 2 D qT p Ko 1 - l a f ...(11.27) Equation (11.26) can be written in dimensionless form as 2 Z = e - h - h p erfc h Zo af ...(11.28) Z = 0.01, one gets from Eq. (11.28) Zo Further, if length of aggradation is that length l where l = 3.2 Ko t ...(11.29) Gill (1983) has solved the diffusion equation for aggradation due to overloading by the method discussed above as well as obtaining the solution of diffusion equation by Fourier series. If So is the initial slope, S¥ is the final slope of bed commensurate with increased sediment load, and L is the length of the channel, the boundary conditions are Z (x, 0) = S0 (L – x) Z (x, ¥) = S¥ (L – x) Z (L, t) = 0 which stipulates that bed at down stream end remains unaffected and – FG ¶ Z IJ H ¶xK = x=o qT¥ where qT¥ is the equilibrium Ko 1 - l transport rate a f U | | | | | V | | | | | W ...(11.30) Assuming solution to be of the type Z (x, t) = F (x) + f (x, t) he found that F (x) = S¥ (L – x) ...(11.31) ...(11.32) Using the boundary conditions listed above, it is shown that f (x, t) is given as 350 f (x, t) = River Morphology 8 L So - S¥ p 2 b gå ¥ n = 1, 3, 5... 1 - n2 p 2 Ko t npx exp cos 2 2 2L 2L n FG H IJ K ...(11.33) so that Eq. (11.31) becomes Z (x, t) = S¥ (L – x) + 8 L So - S¥ p 2 b gå ¥ n = 1, 3, 5,... - n2 p 2 Ko t 1 npp exp cos 2 2 2L 2L n FG H IJ K ...(11.34) It is also shown that sediment transport rate satisfies diffusion equation, viz. ¶ 2 qT ¶ qT = Ko ¶t ¶ x2 ...(11.35) and for the boundary conditions qT (o, t) = qT¥ and qT (x, o) = qTe qT (x, ¥) = qT¥ and The solution of Eq. (11.35) is x qT - qTe = 1 – erf qT¥ - qTe 2 Ko t ¶ qT L, t = 0, ¶x a f F GH I JK ...(11.36) Adachi and Nakatoh (1969) have applied the diffusion equation for studying silting of reservoirs and have obtained Fourier series solution. They have also determined the value of Ko at dominant discharge for the river Tenryu in Japan. Tsuchiya and Ishizaki (1969) have used a sediment transport formula of Sato, Kikkawa and Ashida, namely qB ~ u3* and Manning-Strickler type resistance law and obtained the diffusion equation. Further, they have applied this equation to predict river bed profiles upstream of Hongu dam on the Joganji river in Japan. This dam on the torrential river was constructed in 1935 and was completely filled in 1939. As mentioned earlier, Mehta and Soni have studied the application of parabolic model for aggradation due to overloading. As shown by Jain (1981), for 0.32 mm data of Soni, transient bed profiles obtained by theory using Ko values agreed reasonably well with observed data, even though for large x values there was relatively more scatter. However, Mehta (1980) found that 0.50 mm and 2 Ko t x Z vs h = plot when theoretical values of Ko were Zo 2 Ko t 0.71 mm data gave considerable scatter on used. Hence, he modified the values of Ko for each run so that the transient bed profile matched with Eq. Analytical Morphological Models 1.2 1.0 0.8 Different runs (d = 0.32 mm) 351 Z/Zo 0.6 0.4 0.2 0 0 1.0 0.2 0.3 0.4 0.5 0.6 h 0.7 0.8 0.9 1.0 1.1 1.2 Fig. 11.6 Variation of Z with h for aggradation due to overloading using modified values of K Zo (11.28). His modified values of Ko called K were found to be function of f FG Dq IJ . Figures 11.6 and 11.7 show variation of Z Z Hq K T Te K So 1 - l D qT and = qTe qTe a f vs o K So 1 - l x and =f qTe 2 Kt a f FG D q IJ as Hq K T Te obtained by Mehta. The need for modification of Ko to K has been attributed to the assumptions made in the derivation of parabolic model. Jaramillo and Jain (1983) applied linear parabolic model to channels of finite length. Park and Jain (1984) have used computer based numerical experiments to determine the rate and extent of aggradation of the bed resulting from overloading. For this they have used Karim and Kennedy’s sediment discharge and friction factor relations. It was found that, if of Z = exp (– h2) – h p erfc (h) is fitted for variation Zo Z with h, the diffusion coefficient K and Zo were found to be functions of Co, So, DC and t as Zo K = 100.364 Co0.968 So–0.982 DC0.102 Zo = 100.11 DC0.960 Co0.517 So0.489 t0.50 Here, Co is the initial sediment concentration by volume, DC is increase in concentration, So is the initial slope and t is time. Application of parabolic model has been studied by Vittal and Mittal (1980) and Gill (1983a), for degradation. Vittal and Mittal have applied parabolic model to predict transient bed profiles of the Ratmau torrent in U.P., India. This torrent crosses the Upper Ganga Canal at Dhanauri where a level crossing has been constructed in 1850 in which 192 m wide escape for the torrent and 72 m wide regulator is provided for the canal (see Fig. 11.8). Initial bed slope of the torrent was 0.001558 and has a maximum discharge of 2250.98 m3/s, while minimum flood discharge has been about 200 m 3/s. Over 352 4.0 River Morphology 3.2 K So (1 – l) qTe 2.4 1.6 Symbol 0.8 d mm 0.32 0.50 0.71 Investigator Soni Mehta Mehta 0 0 2 4 6 8 DqT/qTe 10 12 14 16 Fig. 11.7 Variation of K So (1 – l) qTe with DqT/qTe Fig. 11.8 Level crossing of Ganga canal and Ratmau torrent the past 150 years the bed slope of the torrent downstream of the escape is decreasing as shown in Fig. 11.9 while the bed slope upstream of the escape has increased due to aggradation. Hence, it is concluded that the cause of degradation in the lower reach of the torrent is due to reduction in sediment supply. In the absence of detailed data they estimated the average transport rate using Engelund-Hansen’s relation Analytical Morphological Models 353 Legend Year Notation 1845 1877 1924 1939 1947 1954 1966 1976 1977 Fig. 11.9 Reduction of bed elevation of the Ratmau torrent with time (Vittal and Mittal 1980) and for various trap efficiencies 30, 40 and 50 percent, the bed profiles were computed for years 1924, 1947, 1954 and 1976, using parabolic model. The computed profiles for trap efficiency of 40 percent agreed reasonably well with the observed ones, as can be seen in Fig. 11.10. It may be mentioned that Vittal and Mittal used modified values of K as given by Soni and Mehta. Gill (1983 a) has considered the case of degradation downstream of a dam where due to trapping of sediment on the upstream of the dam, the sediment supply to the stream is suddenly reduced from qTe to qT¥. Hence, the boundary conditions are Z (x, o) = So (L – x) Z (x, ¥) = S¥ (L – x) = – S¥ for t > 0 x=0 and FG ¶ Z IJ H ¶xK Here, S¥ is the equilibrium slope for reduced sediment supply rate qT¥. These boundary conditions being exactly the same as those used for aggrading channels, earlier solutions also hold well in case of degradation. These are Z (x, t) = S¥ (L – x) + 8 L So - S¥ p 2 b gå ¥ n = 1, 3, 5.. n 2 p 2 Ko t 1 exp 4 L2 n2 FG H IJ cos n p x K 2L ...(11.37) Error function solution for infinitely long channels or relatively small times 354 264 262 260 258 Bed elevation in m River Morphology Original bed line 256 254 252 250 248 246 244 242 0 2 4 6 Predicted profile for DqT/qT = 0.40 Observed profile after flood of 1976 8 Distance in km 10 12 14 Fig. 11.10 Verification of bed level variation of the Ratmau torrent (Vittal and Mittal 1980) Z (x, t) = So (L – x) – (S¥ – So) x e r f c Studies by Hou and Kawahita (1987) have demonstrated that solutions to linear parabolic model display unrealistically high values of sediment diffusion. They have numerically indicated that nonlinear parabolic model predicts even larger diffusion than the linear one. Consequently, the non-linear model is applicable only when the exponent of empirical constant in the sediment transport formula determined under equilibrium conditions is modified to include the non-equilibrium processes. LM MN F GH 2 Ko t x x2 exp -2 p 4 Ko t Ko t I JK FG H IJ OP K PQ ...(11.38) Hyperbolic Model For sudden drop in the downstream bed level, Vreugdenhill and de Vries (1973) have obtained the solution of linearised hyperbolic model (Ko and M3U constant) as well as parabolic model using the technique of Laplace transforms and expanded the resulting solutions for large values of time. If q= M U x x2 and to = 3 o , the expansions are: 2 Ko t Ko Hyperbolic model Z »1– Zo 2q 1 1 1 1- q + + ... p 8 t2 2 6 t o o 2q q 1 - + ... p 6 and parabolic model Z »1– Zo LM MN LM N F GH I OP JK PQ ...(11.39) OP Q ...(11.40) Analytical Morphological Models 355 It may be noted that the two expressions will be almost identical if q is smaller than 0.25 and/or, if to is large (say greater than 10). The latter condition can be transformed into a workable criterion by 3 Do . So Thus, parabolic model is a good approximation for large distances; the approximation may also be good substituting the values of Ko and M3. Hence to greater than ten correspondents to l greater than at small distances for small q i.e., large times. The variations of Z with to and q for parabolic and Zo hyperbolic models and for asymptotic expansions are shown for degradation case in Fig. 11.11. 0.7 0.6 0.5 Z/Zo to = 1 0.4 0.3 2 4 6 to = 1 2 4 6 0.2 0.1 0 0 1 Parabolic model id; asymptotic expansion Hyperbolic model id; asymptotic expansion q 2 3 Fig. 11.11 Variation of Z with to and q according to parabolic and hyperbolic models (Vreugdenhil and de Vries 1973) Zo Linear hyperbolic model has been studied by Zang and Kawahita (1990) which is applicable to alluvial channels of finite length and include a general case of an arbitrary function, of either sediment transport or channel bed specified as an upstream boundary condition. They have shown that nonuniformity in both sediment transport rate and river bed is important for short time intervals. For large times, the diffusion process becomes dominant and similarity solutions are acceptable. The linear 356 River Morphology solutions provide fair predictions of river bed if the upstream loading DqT/ qTe is less than 4.0. Linear theory also indicates that the sediment celerity is constant, directly proportional to the sediment transport rate and inversely proportional to the sediment transport rate and inversely proportional to water depth. Non-linear hyperbolic model has been studied by Zang and Kawahita (1988). Wave Model The wave model was first used by Exner (1925) to explain the mechanism of formation of ripples in alluvial channels. Assuming that acceleration in the flow causes erosion while deceleration would cause deposition, Exner wrote the following equation ¶Z ¶U +E =0 ¶t ¶x ...(11.41) Here Z is the bed elevation, U is the average velocity at a section and E is the erosion coefficient. If h represents the elevation of water surface above the datum, (h – z) represents the flow depth and for constant Q and channel width B, the continuity equation for flow takes the form (h – Z) BU = Q ...(11.42) Assuming water surface to be horizontal and taking B as constant, the above two equations can be combined to yield EQ ¶Z + ¶t B h- Z a f 2 ¶Z =0 ¶x ...(11.43) which is the wave equation. Exner assumed that at t = 0 the bed elevation is given by Z = ao + a1 cos 2p l F x - EQ tI GH B a h - Z f JK 2 ...(11.44) The resulting bed undulations at various times are characterized by constant a1 and velocity of bed forms equal to B h- Z a EQ f 2 . Since the crest of the wave moves faster than the trough, initial symmetrical bed form becomes unsymmetrical with time, taking the approximate shape of ripple. The resulting bed form has a flat upstream face and steep downstream face. Exner has further improved this analysis taking into account water surface slope, friction and changes in channel width. However, the major criticism against Exner’s analysis is that it does not explain as to how a plane bed would develop symmetrical waves in the beginning. Silva and Kennedy (1989) have used kinematic wave model to analyse river bed degradation downstream of a section of an alluvial river where sediment discharge is cutoff. They have also included the effects of bed coarsening and armoring by using validated mathematical expressions for these phenomena. They assumed that sediment transport rate in a degrading stream is primarily a function of depth of flow, say qT » f (D). This relation is modified to take into account bed coarsening and velocity changes. Finally, Silva and Kennedy have obtained an implicit expression for D (x, t). This solution was Analytical Morphological Models 357 compared with the solution obtained by IALLUVIAL software for specific problem and the agreement was reasonably good. It may be mentioned that de Vries has used kinematic wave model for filling of trench (see de Vries 1993). References Adachi, S and Nakatoh, T. (1969) Changes of Top-Set Bed in a Silted Reservoir. Proc. of 13th congress of IAHR, Tokyo (Japan), Vol. 5.1, 3.16 – pp. 269-272. Carslaw, H.S. and Jaeger, J.C. (1947) Conduction of Heat in Solids. Oxford University Press, New York, U.S.A. Culling, W.E.H. (1960) Analytical Theory of Erosion. Jour. of Geology, Vol. 68, No. 3, pp. 336-344. de Vries, M. (1965) Consideration About Non-steady Bed Load Transport in Open Channels. Proc. of 11th Congress of IAHR, Leningrad, Vol. 3, 3.8 – pp. 1-11. de Vries, M. (1975) A Morphological Time Scale for Rivers. Proc. of 16th Congress of IAHR, Sao Paulo, Brazil, Vol. 2, B3 – pp. 17-23. de Vries, M. (1993) Lecture Notes on River Engineering. Delft, 139 p. Exner, F.M. (1925) Ûber die Wechuwirkung Zwischen Wasser und Geschiebe in Flûssen-Sitzber-Akad-Wiss. Wien pt 1a, Bd 134 Garde, R.J., Ranga Raju, K.G. and Mehta, P.J. (1981) Bed Level Variations in Aggrading Alluvial Streams. Proc. of 19th Congress of IAHR, New Delhi, Vol. 2, pp. 247-253. Gill, M.A.(1983) Diffusion Model for Aggrading Channels. JHR, IAHR, Vol. 21, No. 5, pp. 355-268. Gill, M.A. (1983a) Diffusion Model for Degrading Channels. JHR, IAHR, Vol. 21, No. 5, pp. 369-378. Hou, Z. and Kawahita, R. (1987) A Nonlinear Mathematical Model for Aggradation in Alluvial Channel Beds. JHD, Proc. ASCE, Vol. 113, No. HY3, pp. 353-369. Jain, S.C. (1981) River Bed Aggradation Due to Overloading. JHD, Proc. ASCE, Vol. 107, No. HY-1, Jan. pp.120124. Jaramillo, W.F. and Jain, S.C. (1983) Characteristic Parameters of Non-equilibrium Processes in Alluvial Channels of Finite Length. Water Resources Research, Vol. 19, p. 952-958. Mehta, P.J. (1980) Study of Aggradation in Alluvial Streams. Ph.D Thesis, University of Roorkee (Now I.I.T. Roorkee). Park, L. and Jain, S.C. (1984) River-Bed Profiles With Imposed Sediment Load, JHE, Proc. ASCE, Vol. 112, No. 4, April, pp. 267-279. Silva, J.M. and Kennedy, J.F. (1989) Proc. of 4th International Symposium on River Sedimentation, Beijing (China), Vol. 2, pp. 1072-1079. Soni, J.P. (1975) Aggradation in Stream Due to Increase in Sediment Load. Ph.D. Thesis, University of Roorkee (Now IIT Roorkee). Soni, J.P., Garde, R.J. and Ranga Raju, K.G. (1980) Aggradation in Stream Due to Overloading. JHD, Proc. ASCE, Vol. 106, No. HY1, Jan. pp. 117-132. Tsuchiya, B. and Ishizaki, T. (1969) Estimation of River Bed Aggradation Due to Dam. Proc. of 13th Congress of IAHR, Tokyo (Japan). Vol. 1, A-33, 297-304. Vittal, N. and Mittal, M.K. (1980) Degradation of Ratmau Torrent Downstream of Dhanauri. Proc. of 1st International Workshop on Alluvial River Problems, Roorkee (India), pp. 5-43-54. Vreugenhill, C.B. and de Vries, M. (1973) Analytical Approaches to Non-steady bed Load Transport, Delft Hydraulic Laboratory, Research Report S-78-III, 17 p. 358 River Morphology Zang, H. and Kawahita, R. (1988) Non-linear Hyperbolic System and Its Solutions for Aggradaing Channels. JHR, IAHR, Vol. 26, No. 3, pp. 323-342. Zang, H. and Kawahita, R. (1990) Linear Hyperbolic Model for Alluvial channels. JHE, Proc. ASCE, Vol. 116, No. 4, Apr., pp. 478-493. C H A P T E R 12 Numerical Models for Morphological Studies 12.1 INTRODUCTION In the previous chapter analytical models for studying transient morphological processes have been discussed. It may be recalled that a number of assumptions had to be made to obtain analytical solutions. ¶U ¶D and be omitted. Assumption of ¶t ¶t steady state water flow is not valid while computing bed level changes during unsteady flow conditions. It is also not strictly valid even if the discharge is constant, since water surface profile computations depend on bed slope which varies with time. Further, the channel was assumed to be sufficiently wide and of constant width. In addition, a constant value of Manning’s n or Chezy’s was assumed implying that change in C or n due to changes in bed-forms during transient stage is neglected. Still further, the bed material was assumed to be uniform or of small standard deviation so that it could be characterized by d50 alone. As a consequence, effects of armouring and grain sorting were not included in those models. Also, the sediment transport law used was in the simplest form namely qT ~ U n or qT ~ t on. However, it must be accepted that in spite of these assumptions one gets solutions which are simple and can be used as the first approximate solution to transients in alluvial streams. Hence, analytical solutions have been obtained for degradation and aggradation at a dam, aggradation due to increase in sediment load, withdrawal of water, and filling of trench. However, when the above restrictions are violated the analytical solutions do not give acceptable and accurate results. As such since about 1970 a number of numerical models have been developed to solve problems of morphological changes in alluvial streams. This chapter is devoted to further discussion of the governing equations, boundary conditions and the basic techniques of numerical computation along with related aspects; a discussion of some available software packages and the For example, flow was assumed to be quasi-steady so that 360 River Morphology results obtained from them are also presented. In writing this chapter the author has heavily depended on the excellent works of Cunge et al. (1980), de Vries (1993), and Murthy et al. (1998). 12.2 ONE-DIMENSIONAL EQUATIONS One-dimensional form of the dynamic equation (St. Vennant equation) for unsteady flow in open channels was derived in Chapter 11. As indicated by Cunge et al. (1980) this equation can be written in different forms, depending on the choice of dependant variables. (i) Q (x, t), D (x, t) ¶Q ¶ Q2 ¶D + + gA + gA (Sf – So) = 0 ¶t ¶ x A ¶x FG IJ H K ...(12.1) Here B = B (D) and A = A (D). (ii) U (x, t), D (x, t ) ¶U ¶U ¶D + g (Sf – So) = 0 +U +g ¶t ¶x ¶x ...(12.2) It may be mentioned that the channel cross section can be of arbitrary shape and may vary along the length. The continuity equation for flow is ¶ A ¶Q + =0 ¶t ¶x ...(12.3) when there is no inflow from the sides. This can be written as ¶A ¶A ¶U =0 +U +A ¶t ¶x ¶x ...(12.4) The continuity equation for sediment is (1 – l) which for wide channels reduces to (1 – l) ¶ Z ¶qS + =0 ¶t ¶x ¶ A ¶ QS + =0 ¶t ¶t ...(12.5) ...(12.6) for wide channels. Here l is the porosity. If the bed of the channel is composed of non-uniform sediment, this equation has to be applied for each size fraction; this is necessary for simulating degradation and armouring. For i th reach and k th fraction of the sediment, one can write D Zik D qsk 1 + =0 Dt (1 - l ) D t ...(12.7) Numerical Models for Morphological Studies 361 where D Zik = change in bed level in the i th reach due to imbalance in sediment transport capacity for the k th fraction. Total change in k th reach is D Zi = åD Z k =1 m ik ...(12.8) Resistance Law and Sediment Transport Law As discussed in Chapter 5 a number of predictors are available for the resistance coefficient and sediment transport rate, and some studies have been carried out to study their relative accuracy. With the present state of knowledge prediction of average velocity U within ±20 to 30 percent error and prediction of transport rate within ±40 to 50 percent error are considered acceptable. The effect of errors in prediction of U or transport rate on the prediction of bed levels over long periods needs to be studied. One can use either Chezy’s or Manning’s equation with constant C or n, or C or n changing with changes in stage or discharge. One can also use any other resistance law which may involve prediction of regime or a trial solution for U, or may be function of sediment transport rate. Sediment Transport b In analytical models the transport equation of the form qT = mU n or qT = a t* have been used. EngelundHansen formula corresponds to n = 5 while in Meyer-Peter and Müllers’ formula n=3 FG1 - 0.047IJ H t K * Some softwares such as HEC-6 has an option of choosing any one of the five or six formulae for the computation of transport capability. Most of the sediment transport formulae in vogue are based on some basic assumptions which include (i) the flow is steady and uniform, (ii) river-bed is in equilibrium, (iii) there is negligible wash load transport, (iv) the sediment is uniform or with small standard deviation, and (v) all size fractions are moving. In numerical modeling these formulae are used for unsteady, non-uniform flow by replacing So by Sf . The validity of this extension of use is yet to be verified. Further, in most of these formulae it is assumed that sediment transport rate at any section is governed by the local hydraulic conditions. When such an equation is used for computing transport rates for different size fractions it is usually assumed that the transport rate of kth fraction of sediment size is equal to transport rate for that size using a given formula multiplied by the fraction of that size range available in the bed. This assumption may be acceptable if standard deviation of the bed material is small and all the sizes are moving. However, for large standard deviations and partial transport of sediment (during armouring process), the results will be affected due to sheltering effect for smaller sizes and greater exposure for sizes larger than the average size. Realising the complexities in sediment transport formulae and their accuracies, it is prudent to use a simpler formula. Using some available data the engineer should try different formulae and choose the one that gives acceptable results. 362 River Morphology 12.3 NUMERICAL SCHEMES OF SOLUTION The differential equations governing morphological processes in alluvial streams can be solved either by finite element method (FEM) or by finite difference method (FDM). Comparing these two methods Zienkieweiz et al. (1975) have observed that for slow flow, where convective terms are insignificant, FEM was superior. They also found that with high velocities, when the convective terms become important, and in transient problems, FDMs retain some superiority. Similarly in the preliminary stages, studies by Palaniappan (1991) indicated that FEM did not have any superiority over FDM in one dimensional alluvial stream transients. Cunge et al. (1980) also expressed similar view that in modeling of river dynamics FEM has not found wide spread applications and it is found that the method has no advantage over finite difference one-dimensional models. The real strength of FEM is in solving 2-D and 3-D problems. One of the FDMs viz. the method of characteristics is discussed in detail by Abbott (1966) and Cunge et al. (1980). This method requires very small time steps, whereas in alluvial stream transients computations involve very large times such as 10 to 30 years. Hence while the method of characteristics can be used for flood propagation involving a few days, it is uneconomical and hence not suited for computation of bed level variations in alluvial stream involving large times. Two methods of computation are available in the other finite difference scheme: these are the explicit method and the implicit method. In the explicit method a variable at (n + 1) the time level is expressed fully in terms of known quantities at n th time. Two schemes of explicit finite difference method that are often used are the Lax scheme and the Leap-frog scheme. With reference to Fig. 12.1 in the Lax scheme the time derivative and space derivative are expressed as f jn + 1 - [a f jn + (1 - a )( f jn+ 1 + f jn- 1 )] ¶f = ¶t Dt n n ¶ G (G j + 1 - G j - 1 ) = 2D x ¶x ...(12.9) ...(12.10) where a is the weighting coefficient. Substituting these in the continuity type equation for sediment, one gets f j n + 1 = a f j n + (1 – a) LM f MN n j +1 n + fj -1 2 OP - D t (G PQ 2 D x n j +1 + Gj - 1) n ...(12.11) Thus f can be calculated for (n + 1) time level for known values of f and G at nth level. In the Leap-frog scheme the time and space derivatives are expressed as n n ( f jn + 1 - f jn - 1 ) ¶f ¶ G (G j + 1 - G j - 1 ) = and = 2 2D x ¶t ¶x ...(12.12) Numerical Models for Morphological Studies 363 t (n 1) n (n + 1) j 1 j j+1 Fig. 12.1 Computational grid and substitution in sediment continuity equation gives fj n + 1 = fj n – 1 – Dt n (G n j + 1 – G j – 1) 2Dx ...(12.13) When D t / D x = g Do and a = 0 both the schemes give exact solution of fully linearised flow equations. The finite difference implicit scheme can be written in general form as y f jn++11 + (1 - y ) f jn + 1 - y f jn+ 1 + (1 - y ) f jn ¶f = Dt ¶t ...(12.14) and +1 n +1 n q Gn + (1 - q) G n j +1 - Gj j + 1 - Gj ¶G = ¶x Dx ...(12.15) When the weighting coefficient y = 0.50 and the coefficient q is given a value between 0.5 and 1.0 (and preferably slightly greater than 0.50) it represents Preissmann 4-point scheme. There are a few variations in this scheme also. The implicit method involves solution of a matrix resulting in escalation of cost of computation. 12.4 CLASSICIATION OF ONE-DIMENSIONAL MODELS One-dimensional mathematical models are quite useful in prediction of bed and water surface profiles, average depth, velocity and transport rate as a function of x and t. These have been used for solving problems such as i) bed level variation during flood in lower reaches of the river; ii) sedimentation upstream of a dam; 364 River Morphology iii) degradation downstream of a dam; iv) modification of a river profile due to construction of embankments and execution of cutoffs; v) changes in river morphology due to addition or withdrawal of sediment or water; vi) long-term evolution of river bed. One-dimensional numerical models can be classified depending on whether quasi-steady or full unsteady flow equations are used, and on whether uncoupled or coupled scheme of computation is used. In quasi-steady models the terms case where ¶D ¶U and are neglected. As pointed out earlier, this excludes the ¶t ¶t ¶U ¶D is very small but has to be considered. This situation arises for a river with a ¶t ¶t ¶D . In unsteady flow ¶t reservoir where, Q being a function of t, there is storage which is a function of case these terms are retained. In uncoupled scheme of solution the continuity equation and the dynamic equation for flow are solved along the river course for time D t assuming that the bottom elevations Z (x) do not change during D t; the solution consists of water stages, water discharges and average velocity at the end of time interval D t. Then using the water depth, velocity and slopes that are computed at the nodal points, the transport capacities are computed at the nodal points, and using sediment continuity equation, changes in bed elevation D Z and new bed profile are computed over the whole reach at the end of D t. The process is then repeated for the next D t. Since in this scheme the water flow equations and sediment continuity equation are uncouples during D t, it is called uncoupled scheme. When the Froude number is less than 0.60 or so (which is usually the case in alluvial rivers), the velocities of propagation of water wave are much greater than that of bed wave propagation and hence this scheme of computation is justified in many cases. In quasi-steady coupled models, the quasi-steady equations for full momentum equation and the continuity for flow and the sediment continuity equation are solved using implicit finite difference scheme. The resulting non-linear algebraic equations are solved simultaneously to achieve coupling between water flow and sediment movement. In a similar manner unsteady uncoupled, and unsteady coupled one-dimensional models can be described. In all the four types of one dimensional models discussed above, one can use either the explicit or the implicit scheme of computations. However, it may be noted that most of unsteady coupled models use implicit scheme to solve the governing equations. Although large computational time steps can be used with these schemes, they involve solution of a system of equations using matrix inversion during each computational step. Lyn (1987) has suggested that complete coupling between full unsteady flow equations and sediment continuity equation is desirable in the cases where the conditions are changing rapidly at the boundaries. Lyn’s results along with those of Yen et al. (1995) support the view that uncoupled models with quasi-steady flow have considerable utility in solving alluvial stream transients. Their accuracy can be improved by using more reliable methods of computing sediment transporting capacity, armouring processes, and friction factor predictors. The investigations by Cui et al. (1996) and de Vries (1993) indicate cost effectiveness of explicit schemes. Cui et al. (1996) compared the numerical results obtained using coupled and quasi-steady Numerical Models for Morphological Studies 365 uncoupled models for the cases where Froude number is close to unity and also for cases in which upstream water discharge, sediment inflow rate and the downstream water level varied strongly. There was a very good agreement between numerical results obtained using the two models, although uncoupled models are inherently unstable than the coupled ones. Hence, uncoupled explicit schemes are many times preferred and due consideration is given to the convergence and stability. Some One-Dimensional Models A number of one-dimensional numerical models have been developed and used since 1970’s for solving transients in alluvial streams. Some of the models are listed below giving name of the model, developer of the model, and its description, see Table 12.1. Table 12.1 Summary of some one-dimensional models for mobile bed simulation Name 1. Delft Hydraulics Laboratory 2. SOGREAH CHAR-2, CHAR-3 3. HEC-2 with sediment routing 4. KUWASER 5. UUWSR 6. HEC-6 Developer de Vries et al. Cunge et al. Simons et al. Details Quasi-steady, one-dimensional, qT = aUb, n or C assumed constant Quasi-steady, 4-point implicit scheme to solve coupled system. Quasi-steady, uncoupled, uses M.P. and Müller’s or Einstein’s equation for sediment transport; armouring effect included Quasi-steady, qT = aUb Dc, uncoupled. Unsteady, uncoupled, uses 4-point implicit scheme for flow and explicit scheme for sediment qT = aU b Dc Quasi-steady, variable Manning’s n, choice of sediment transport formula, armouring included, uses explicit scheme. Unsteady, uncoupled, width changes allowed, Graf or Engelund-Hansen formula for sediment transport, uses explicit scheme for sediment and implicit scheme for flow. Quasi-steady, uncoupled, uses Ackers-White or Engelund-Hansen transport formula, implicit scheme, armouring included. Quasi-steady, partially decoupled, single load mechanism, saturated capacity, armouring included, multi-size predictor. Quasi-steady, fully decoupled, single load mechanism, multi-size predictor. Unsteady flow, partially coupled, single load mechanism, saturated capacity, single size predictor. Unsteady, flow, fully coupled, single load mechanism, single size predicator. Unsteady flow, fully decoupled single load mechanism non-saturated capacity, multi-size predictor. Unsteady flow, fully coupled, separate bed-load mechanism, non-saturated capacity, multi-size predictor Simons et al. Tucci et al. Thomas 7. FLUVIAL – II Chang and Hill 8. HRS Wallingford Bettess and While 9. IALLUVAL 10. RESSED 11. CHARIMA 12. MOBED 13. FLUVIAL – II 14. SEDICOUP Karim, Kennedy et al. Chen Holly et al. Krishnappan Chang Holly and Rahuel 366 River Morphology Out of all these models, HEC-6 is discussed here in detail followed by a brief account of CHARIMA. This is followed by two applications of HEC-6 to study effect of levee spacing on bed elevations in the Kosi and sedimentation studies upstream of a dam in India. 12.5 CONVERGENCE AND STABILITY (CUNGE ET AL. 1980) The basic idea of convergence is that the discrete solutions to the governing flow equations should approach the exact solutions to those equations when D x and D t approach zero. However, since the full non-linear partial differential equations do not have analytical solutions, it is impossible to directly compare analytical and numerical solutions for convergence. Hence, the numerical method is tested on the corresponding linear form of equations to obtain information about the convergence of the scheme. For linear equations the convergence is ensured if the conditions of Lax theorem are satisfied. The theorem states: “Given a properly posed initial-value problem and a finite difference approximation to it that satisfies the consistency condition, stability is the necessary and sufficient condition for convergence”. Consistency means that the finite difference operators approach differential equations when D x and D t lend to zero. Numerical stability means that the solutions obtained using the numerical scheme are bounded, that a small rounding-off error remains small during computational steps however long and never become as large as the prescribed significant number. Thus stability means the errors introduced by small perturbations remain smaller than a prescribed value. In studying the numerical stability, two partial differential equations ¶U +g ¶t ¶D + DO ¶t ¶D =0 ¶x ¶U =0 ¶x and U | V | | W ...(12.16) are used. When the numerical scheme is utilized, the numerical computations can have different harmonics resulting from the truncation errors, and if during the computations | C + U | Dt Dt is or C Dx Dx always kept less than one, the damping factor for all the harmonics will be less than one and hence the solution will be stable. This condition is known as Courant condition or Courant-Friedrichs-Levy (CFL) condition. CFL condition of stability is directly linked to the theory of method of characteristics. Courant number Cr is less than one expresses the fact that the computational point (n + 1, j) lies within the domain of determinacy of the point of intersection of two characteristics from the neighbouring point at n D t level. In general explicit methods are conditionally stable, Courant condition limiting the permissible time step D t. Implicit methods, on the other head, can generally be made unconditionally stable. Preissmann and Delft Hydraulics Laboratory methods are unconditionally stable if q ³ 0.50. Because of conditional stability of implicit schemes, they have been used often. Numerical Models for Morphological Studies 367 12.6 BOUNDARY CONDITIONS (CUNGE ET AL. 1980, DE VRIES 1993) The boundary conditions required for solving alluvial stream transients are in four forms, namely initial conditions, upstream conditions, downstream conditions and internal conditions. These are briefly discussed below. Initial Conditions At time t = 0 the bed elevation Z at all places 0 < x < L must be known i.e., Z (x, 0) is known. In the case of a meandering channel, since the bed level varies across the width, it is reasonable to take average bed elevation there. In flood problems initial water level along the river length should be known. Upstream Conditions Two conditions are imposed at the upstream; the first is variation of Q with t should be known, i.e., Q (0, t); this is inflow hydrograph and is needed for solving the momentum equation. Inflow hydrograph is usually obtained from historic data for as many years as possible. The other upstream condition needed is regarding variation of incoming sediment load with time, i.e., Qs (0, t ). This is prepared from suspended load measurements. Since it is difficult to measure the bed load, it can either be calculated using one of the bed-load equations or estimated and added to Qs (0, t) so that it represents bed material discharge. This is needed for solving the sediment continuity equation. Alternatively one can prepare relationship between measured bed material discharge and Q and use it. Downstream Conditions For sub-critical flow, downstream water level must be known in order to determine the water surface profile for known bed elevation and discharge. This usually follows from discharge rating curve h = h (Q). However if the bed level at x = L changes with time due to erosion or deposition, then the downstream condition can be placed far downstream so that the bed level does not change during the time of interest. Internal Boundaries If within 0 < x < L one or more of the parameters are discontinuous, then the internal boundary conditions are required. Such situations arise in cases such as withdrawal of discharge D Q (t), withdrawal of sediment load D Qs (t), change in river width, confluences and bifurcation. These discontinuities can create discontinuity in bed elevation. Thus, if two streams 1 and 2 join and form the stream 3 the conditions to be satisfied are Q1 + Q2 = Q3 QT 1 + QT 2 = QT 3 U V W U V W ...(12.17) For a bifurcation of river 1 into two streams 1 and 3 Q1 = Q2 + Q3 QT 1 = QT 2 + QT 3 ...(12.18) Further, the distribution of Q1 into Q 2 and Q3 should be such that the stage discharge relations for the two branches 2 and 3 lead to the same water level at the point of bifurcation. The local geometry of the branches determines the ratio QT 2/QT 3. 368 River Morphology Consider the problem of aggradation upstream of a dam. If x is measured from the dam in the upstream direction, Initial condition: Z (x, 0) should be known for 0 = x and L Downstream boundary condition: D (0, t) should be specified for all t Upstream boundary condition: Q (¥, t ) should be specified and Qs = f (¥, t) should also be given 0 £ x £ L and t = 0. In the similar manner boundary condition for degradation downstream of dam can be given. If x is measured from the dam in the downstream direction, Initial condition: Bed level and water level should be known for 0 = x and L at t = 0 Upstream boundary condition: at x = 0 QT (0, t) = QT for t < 0 QT (0, t) = QT 1 for t > 0 where QT 1 < QT QT (L, t ) = QTe for L large value of L 12.7 CHANNEL CROSS-SECTIONS AND METHOD OF EROSION OR DEPOSITION Even with the assumption of one-dimensional flow, the channel cross section can be irregular and can have floodplain on one or both the sides of the main channel as shown in Fig. 12.2. n1 n2 n3 n5 n4 Fig. 12.2 Channel with floodplain In such a case the channel is usually divided into a number of sub-sections each having a different value of n or C. Defining the conveyance K as Q= 1 AR2/3 Sf1/2 = K S f n one can write Q = Q1 + Q2 + Q3 ……. where Q1, Q2, Q 3 … are discharges in each subsection and Q is the total discharge. Hence K S f = S Ki S f or K = S Ki Further, it is recognized that the floodplain areas often act as storage zones. They store water whose velocity in the general direction of flow is nil. Hence, models such as HEC-6 define a movable bed width at each section and erosion or deposition occurs in that width only. Numerical Models for Morphological Studies 369 Fig. 12.3 Methods of deposition In a one-dimensional model even though the flow is one-dimensional sediment movement is three dimensional in nature because of secondary circulation and presence of beds. However, to simplify the analysis the sediment transport is assumed to be one-dimensional. Also when erosion or deposition occurs within a section, it can be assumed to occur in one of the following three ways as shown in Fig. 12.3. 1. the cross section rises or falls through D Z without change in shape; 2. only those parts of the cross section which are below water level move up or down; 3. attempt is made to distribute sediment laterally in relation to tractive force (Chang and Hill 1976) or based on other information. As discussed later in HEC-6, movable bed width is identified at each section and effective width between two sections is also determined. Then knowing the volume of sediment to be deposited or eroded in time D t, bed level change D Z is computed. 12.8 MODELING OF ARMOURING Starting with Harrison (1950) a number of laboratory investigations have been carried out by investigators such as Hasan (1965), Jaswant Singh (1974), Gessler (1967), Little and Mayer (1972), Garde et al. (1977) Shen and Lu (1983), Odgaard (1984) and Garde et al. (2004). Most of these studies were aimed at the prediction size distribution of the armour coat for known size distribution of the parent material and the initial flow conditions. The results of some of these investigations have been described in Chapter 10. Garde et al. (1977) conducted laboratory studies to determine time variation of surface layer of a degrading stream. It was found that the major part of coarsening takes place in a relatively short time; thereafter the process is very slow. If do and df are the median sizes of the parent material and the final surface layer, and dt is the median size of the surface layer at any time t, they found that (1 - F ) = 0.32 (t / t0 . 75 ) - 0 .17 for t / t0 . 75 < 0.40 and (1 - F ) = 5.5 (t / t 0 . 75 ) - 3. 40 for t / t0 . 75 < 4.0 U | V | W ...(12.19) Here F = (dt – do)/(df – do). The final value df varied along the length according to Sternberg’s law. Here t 0.75 is the time at which F = 0.75. To use the above equation one must know df and t 0.75. Borah (1989) has also proposed a method for predicting the depth of degradation. 370 River Morphology Some attempts have been made to study the time evolution of the armour coat, which is required in any mathematical model used for predicting time variation of erosion and deposition. In HEC-6 model (1993) developed by Thomas and Prashun (1977) the armouring process is analysed assuming the bed to consist of two layers: (1) the active layer which predicts the bed surface degradation and armouring, and (ii) the inactive layer beneath the armour layer. Using Manning’s equation for U, Strickler’s equation for Manning’s n, and the condition for insignificant sediment transport as proposed by Einstein viz. y = Dgs d/to = 30, an equilibrium depth De is defined as the minimum water depth required for a given particle size d to be immobile on the bed, and is given by De = (q/10.21 d1/3)6/7 2 ...(12.20) in which q is expressed in ft /s, De in ft, and d in mm. When the bed is composed of a mixture of different sized particles, the erosion depth Dse required to accumulate one particle size thick layer of coarse non-moving material is calculated using the equation, Dse = 2 SAE.d/3Pc ...(12.21) Here SAE is the ratio of surface area of potential erosion to the total surface area (which is also taken as equal to the ratio of erodible material remaining in the active zone to the total volume in inactive zone) and Pc is the fraction of the bed material coarser than size d, which can be determined from the known size distribution curve of the bed material, which is divided into different segments starting from the coarsest fraction as shown in Fig. 12.4. 100 2 Percent finer 1 3 4 5 6 9 8 7 d mm Fig. 12.4 Segmented size distribution curve of bed material Consider the segment 1-2 and determine the equilibrium depths Deq1 and Deq 2 for sizes 1 and 2 respectively using Eq. (12.20). If the actual depth of flow Dw is less than Deq2.1, the straight line segment from 1 to 2 in Fig. 12.4 determines the value of Pc and then the final equilibrium depth is calculated as Deq = Dw + Dse. If Dw is greater than Deq 2, computations move to segment 2-3 and so on, until either the proper segment is located or the smallest particle size in the bed material is sufficient for armouring the bed, in which case scour or erosion does not occur. The depth between bed surface and equilibrium depth is the active layer (see Fig. 12.5), and below the equilibrium depth and the erodible limit is the inactive layer. The thickness of the active layer changes with change in U, Dw and slope. Numerical Models for Morphological Studies 371 W.S Deq1 Deq2 Dw Deq Deq = Dw + Dse Active layer Inactive layer Fig. 12.5 Definition sketch Ashida and Michiue (1971), Bayazit (1975) and Palaniappan (1991) use the concept of mixing volume on the bed surface to simulate the armour coat. In these models when sediment flows out of a mixing volume, an equal quantity by weight is added to the mixing volume in each computational step. The added sediment has the same grain size distribution as that of the current surface. Armouring procedures used in CHARIMA (Holly et al. 1990) are identical to those used in IALLUVIAL. It is assumed that as the armouring develops with increasing degradation, the bed surface is segregated into two parts: armour coat and part of the bed containing movable size fractions. Hence fraction of the bed covered by non-moving particles Af (t) at any time t can be used as a measure of the degrading bed. This process depends on the size distribution of the bed material and its variation with depth, intensity of water discharge and sediment transport, formation and height of bed undulations, and the stochastic character of the sediment movement. According to the analysis of Karim et al. (1983), Af (t, k) is given by Af (t, k) = Af (t – 1, k) + CA (t, K ) ×(1 – l) D Z (t)× = 0 when k £ l (t) and Af ( t ) = Pk dk ...(12.22) å m k = l(t ) A f (t , k ) Here Af (t, k) = fraction of the bed area covered by particle size interval k at any time t ; D Z (t) = incremental depth of degradation during current time interval; l (t) = index for lowest grain size interval which is immobile according to Shields’ criterion, and forms the armour coat at time t ; CA (t, k) = a positive coefficient; Pk = fraction of bed material in the k th fraction, and m = total number of fractions. The constant CA (t, k) = 1.9 for plane bed while the following empirical equation is used for CA (t, k) CA (t, k) = 1.902 ad qk to take into account the effect of bed forms on armouring. Here ad is a function of dune height to water depth ratio and hence of t*/t*c; ad = 1.0 when t*/t*C = 1.0 and when t*/t*c = 1.5. Its variation between these two limits is given by a function. Also qk is the probability of k th sediment size fraction to remain on the bed. 372 River Morphology Armouring of the bed surface tends to reduce the sediment transport capacity of the flow and reduces the average height of dune and mixed layer. This reduction is assumed to be linear in CHARIMA. qsa = qs (1 – Af [t]) qsa = H (1 – Af [t]) 2 Here qsa and qs are the transport rates with and without armouring; Tm is the mixed layer thickness and H is the dune height. 12.9 HEC-6 HEC-6 is a one-dimensional quasi-steady uncoupled model designed to simulate and predict long term changes in river bed profile over moderate times. It was developed by W.A. Thomas of the Corps of Engineers of U.S.A. in 1976 and since then the model has been improved upon a few times; the latest version 4.1 was presented in 1993. It handles a river system consisting of the main, tributaries, and local inflow or outflow points. Hence the model can analyse network of streams, channel dredging and various levee and encroachment alternatives. It faithfully deals with sub-critical flows and approximates the super critical flow by normal depth. Input Data The input data include the geometric data, the sediment data and the hydrologic data. The geometric data include cross-sections along the length of the reach, Manning’s n values, movable bed width in each section and depth of sediment material in the bed. Each cross section is defined by a maximum of 100 points with station and elevation data. Typical cross-section is shown in Fig. 12.6 indicating main channel, left and right over banks, movable bed limit and erodible-bed. Left over bank Main channel Movable bed limit Right over bank Bed material available for scour Fig. 12.6 Channel details Numerical Models for Morphological Studies 373 The conveyance limits are also specified so that section beyond those limits does not contribute to water conveyance. The channel is divided into a number of sub-sections for each one of which Manning’s n can be specified which can vary with stage of the discharge. For given water level, the effective depth and effective width are defined. Hence for given Q, velocity can be computed. The sediment data include fluid and sediment properties, inflowing fraction wise sediment load data, the size distribution of the stream bed material, sediment transport capacity’s relationships, and unit weight of sediment. The sediments are classified into silt, clays, sands and boulders using classification of the American Geographical Union. These are divided into different size ranges and are represented by the geometric mean size. Sediment transport rates for sizes up to 2048 mm are computed and material coarser than 2048 mm only participates in armour coat formation. The sediment inflow data at the upstream section is given as QT vs. Q curve according to size class. Other properties of sediment that are needed such as relative density, shape factor, unit weight and fall velocity are also specified. The sediment transport capacity at each section is calculated by using one of the alternatives provided in HEC-6 programme; these include methods of Toffaleti, modifications of Laursen’s method by Madden, and Copeland, Yang, DuBoy’s transport function, Ackers-White, Colby, Meyer-Peter and Müller. The hydrologic data include water discharges, temperature, downstream water surface elevations and flow duration. To reduce the number of time steps used to simulate a given time period, the continuous flow hydrograph is treated as a sequence of discrete steady flows; this is sometimes known as computational hydrograph. Boundary Conditions HEC-6 needs specification of upstream as well as downstream boundary conditions and internal boundary conditions. The upstream boundary conditions that are needed are discharge vs. time discrete hydrograph, corresponding water temperature and sediment discharge data. HEC-6 provides three options for downstream boundary conditions. These are: (i) rating curve giving Q versus water surface elevation data, (ii) water surface elevation as a function of time, or (iii) a combination of the first two options. The second option is used with reservoirs where water surface elevations are a function of time. The internal boundary conditions are specified at the internal points within the reach at which water surface elevations may be specified. This is usually done either by specifying a constant head loss for all discharges, or by specifying a rating curve at the internal boundary. Method of Calculation Since HEC-6 is a quasi-steady, uncoupled model, it first uses one-dimensional energy equation for computing the water surface profile, starting from downstream section and moving upstream, using standard step method. Knowing the initial bed levels at all the sections, and water surface elevation at downstream section 1, the following equation is solved for water surface elevation at section 2. WS2 + a2 2 U2 U2 = WS1 + a1 1 + he 2g 2g ...(12.23) Here WS1 and WS2 are water surface elevations, a is the energy correction coefficient based on the distribution of average velocities in the subsections and he is the head loss due to friction and expansion 374 or contraction; the latter is computed as Ce River Morphology 2 - a1 U12 ) (a 2 U 2 where Ce is specified. Equation (12.22) is 2g solved by assuming WS2 and comparing the terms on the left and right hand side of the equation; a maximum of twenty iterations are carried out. The computations are performed at all sections and hydraulic parameters U, D and W are computed. For computing the sediment capacity, effective depth and effective width are used which are defined as follows: Effective depth (EFD) = åD 1 N 1 N av ai 2/3 Dav Effective width (EFW) = åa D i 2 /3 av ( EDF ) 5 / 3 where ai = flow area of each trapezoidal element, Dav = average depth of each trapezoidal element, and N = total number of trapezoidal elements in a sub-section. Knowing velocity, depth and movable bed width at each section these are converted into representative values in each reach for their use in calculating transport capacity. This is done as follows: Interior points: U | | W = 0.25 W ( I - 1) + 0.5 W ( I ) + 0.25 W ( I + 1)| | S = 0.5[ S ( I ) + S ( I + 1)] | | For upstream boundary: | U = U ( I ), D = D ( I ), W = W ( I ), S = S ( I ) V | Downstream boundary: | S = 0.5[U ( I ) + U ( I + 1)] | | D = 0.5 [ D ( I ) + D ( I + 1)] | W = 0.5[W ( I ) + W ( I + 1)] | | S = S (I) W U = 0.25 U ( I - 1) + 0.5 U ( I ) + 0.25 U ( I + 1) D = 0.25 D ( I - 1) + 0.5 D ( I ) + 0.25 D ( I + 1) ...(12.24) Now the sediment transport capacities at any section at a given time are calculated using one of the equations listed earlier and the computations proceed from the upstream towards the downstream direction. Sediment continuity equation is then used in finite difference form. With respect to Fig. 12.7, one can write Numerical Models for Morphological Studies 375 Section t 4 3 2 1 Time p Dt p L4 Ld x (Upstream) (Downstream) Fig. 12.7 Definition sketch ¢ - Ysp ) Bsp (Ysp Gu - Gd + =0 0.5 ( Lu + Ld ) Dt where Gu and Gd are upstream and downstream transports of sediment in time Dt, in (vol./time), and Bsp is width of movable bed at P, ¢ are depths at sediment before and after the time step at P Ysp and Ysp Gu is size wise sediment load entering the section and Gd is calculated considering the transport capacity at P, sediment in flow, availability of material in the bed and armouring. The time step can be variable, a fraction of a day for high flows to several days or month for low flows. It should be such that during the time step the bed level change is less than 0.3 m or 10% of depth of flow whichever is smaller. The gradation of the bed material is recalculated after each time interval by computing the fraction of bed material size available in the active bed. When scour or deposition occurs during a time step D t, HEC-6 adjusts the cross-section elevations within the movable bed portion of the cross-sections. For deposition, the stream bed portion is moved vertically only if it is within the movable bed specified and is below water surface. Scour occurs only if it is within movable bed, within the conveyance limits, within the effective flow limits and below water surface. Once scour or deposition ( volume of sediment eroded or deposited) gives change in bed elevation effective width ´ length of control volume ( Lu + Ld ) in time D t. When bed scours, armouring process may start which has been discussed earlier. For other details one may see HEC-6 user’s manual (1993). limits are known, Model Output HEC-6 gives a variety of outputs which include hydraulic data for each trial elevation in each backwater computations at all the sections, volume of sediment entering and going out of each reach, trap 376 River Morphology efficiency, bed level changes, water surface elevations, sediment transported at each section along with its gradation, and bed material surface composition at each time step. It also gives some additional information. Model Calibration Numerical models such as HEC-6 usually need calibration with the known conditions. During the calibration of the model, the constants in the equations, time step, sediment transport and resistance formulae used are changed so that the historical conditions are simulated. The known conditions used for calibrating the model can be water levels and or bed levels at certain times. Such a calibration also accounts for any inaccuracies in hydraulic and sediment load data as long as consistently the same techniques of measurements are used. Once the model is calibrated it is assumed that it will predict the results for the future with reasonable accuracy. However, it may some time happen that such data for calibration of the model are not available; in such a situation the modeler has to use his past experience in choosing the coefficient and the equations. Limitations of HEC-6 HEC-6 programme has the following limitations: i) The model being one-dimensional, development of meanders and lateral bank erosion cannot be accounted for. ii) Further, bifurcation of flows and closed loops (i.e., flow around islands) cannot be modelled. iii) Only one junction or local inflow is permitted between consecutive sections; and iv) The model analyses long term erosion or deposition; hence analysis of the single flood events must be done with great caution. 12.10 CHARIMA This one-dimensional model was developed at Iowa Institute of Hydraulic Research (U.S.A.) in 1988 to study braided river channel network of the Sestina river in Alaska. The model can simulate processes such as sediment sorting, bed armouring, flow dependent friction factor, and alternative flooding and drying of perched channels. In addition to the assumptions made in St. Vannant equation, channel network (i.e., total number of channels and their inter connections) is assumed to remain same and cross-sections rise and fall during deposition of degradation. The effect of bends cannot be accounted for in the model and lateral inflow be accounted for by channels joining at regular intervals. The model has been used for flow analysis by CWPRS (1999). Governing Equations In addition to continuity equations for flow and sediment, and momentum equation for unsteady flow, CHARIMA requires Sediment discharge predictor: Friction factor predictor: Channel geometry predictor: F1 (Q, A, d50, Sf , D, Qs, ASF) = 0 F2 (Q, A, d50, Sf , D, Qs, ASF) = 0 A = A ( D, x) B = B ( D, x ) Numerical Models for Morphological Studies 377 Hydraulic sorting: Armouring of bed surface: n+1 n D 50 ® d 50 ACF N = ACF N + 1 Here Sf is the energy slope and ACF is a coefficient. Solution Procedure The solution of these equations is obtained in decoupled mode. CHARIMA follows Preissmann implicit scheme to discretise the water flow and sediment continuity equations. In the first stage sediment discharge equations, friction factor equation, channel geometry equations and discretised equation for water flow are solved in hydraulic sweep. During this sweep the bed elevation Z, d50, armouring coefficient ACF are held constant assuming the bed to be temporarily stationary. During this stage at grid point C, water flow, water level, and the sediment transport capacity for each size fraction of the bed material are computed. In the stage 2, discretised sediment continuity equation is solved in downstream sweep to get new n +1 bed levels at each grid point i. The sediment discharge Qs computed in stage 1 is treated as constant assuming that it is unaffected by bed evolution process, armouring, and grain sorting. In this stage accounting procedure is executed using aggradation or degradation computed in stage 2 (i.e. sorting of bed material to compute new d50 and new armouring factor ACF n + 1). This procedure is uncoupled because it assumes that these processes occur sequentially and not concurrently in given Dt. CHARIMA essentially follows the following flow chart. Load boundary conditions Time loop Compute W.L., discharge etc. solve continuity and momentum equations Compute friction factor and sediment discharge Iteration loop Compute bed level changes n using sediment continuity eq . Execute sorting and armouring procedure Fig. 12.8 Flow chart for CHARIMA 378 River Morphology During execution of CHARIMA the sediment load capacities can be determined from anyone of the sediment transport formulae of Karim and Kennedy, Engelund and Hansen, modified Peter Ackers and White formula, or the power law predictor. Dune height can be obtained either from Yalin’s relation or Allen’s relation. It also takes into account and model i) hydraulic sorting of bed material; ii) changes in the composition of bed material; iii) armouring of the bed surface or armouring factor ACF which is defined as the fraction of bed surface area covered by non-moving particles; iv) effect of bed forms on armouring; v) effect of armouring on sediment discharge and the mixed layer thickness. Armouring process used in CHARIMA is briefly discussed earlier. Many of the procedures and relations used in CHARIMA are those used in IALLUVIAL model developed at Iowa Institute of Hydraulic Research (U.S.A.) CHARIMA has been used to study long-term evolution of the Missouri river reach between Gavins point dam and Rulo (Nebr), a reach of about 313 km, short term prediction of bed evolution of the Cho-Shui river system in Taiwan and the Sestina river in Alaska. For details of the model one can refer Holly et al. (1990). 12.11 APPLICATIONS OF HEC-6 To illustrate the applications of the above-mentioned numerical models, two applications of HEC-6 will be briefly discussed here. The first relates to the aggradation of the Kosi river in the leveed reach, while the second is concerned with aggradation upstream of a dam in India. Aggradation of the Kosi The river Kosi which is a major tributary of the Ganga originates in Nepal and flows through the state of Bihar before it joins the Ganga at Kursela. The morphology of the Kosi is discussed in detail in Chapter 13 and the index map of the Kosi can be seen there; the Kosi has been known for its lateral migration which has been attributed to excess sediment load it carries, eastward slope of the region and tectonic and neo-tectonic activity in the region. To control frequent flooding and lateral migration the barrage was constructed at Bhimnagar and embankments on both sides were built between the barrage and the place called Mansi. Downstream of Mansi, the river is embanked only on the eastern side upto Koparia. Between 1964 and 1974 it was found that approximately 50 percent of the sediment load of the Kosi was deposited upstream of the barrage and the major part of the remaining load was deposited in between levees thereby raising the bed levels. The spacing between eastern and western embankments varies significantly along 100 km reach that seems to be responsible for bed level variations. Table 12.2 lists the cross-section number, distance from the barrage in km and levee spacing in meters. At the request of Ganga Flood Control Commission the Kosi problem was investigated at the University of Roorkee (Now IIT Roorkee) by Garde et al. (1990) to study: 1. causes of frequent breaches in the embankments; 2. bed level changes that are likely to occur in the embanked reach up to 2005; Numerical Models for Morphological Studies 379 Table 12.2 Cross-section number 33 41 48 53 63 65 67 69 75 81 87 91 Levee spacing at selected reaches on the Kosi Distance from the barrage, km 1.27 11.25 23.25 31.25 48.00 53.75 55.50 60.00 68.75 78.50 84.25 94.25 Levee spacing m 7458 7323 5505 11335 12722 15600 18540 17434 11156 9279 7972 8853 3. bed level changes that are likely to occur if spacing between the embankments is reduced selectively; and 4. calculate sediment load brought into the Ganga by the river Kosi during 1985-2005 with and without forward embankments. Figure 12.9 shows the leveed portion and the locations of different sections. The slope of the river between the barrage and 40 km downstream is about 5.5 ´ 10–4 and it reduces to 2.70 ´ 10–4 upto Mansi. The median size of bed material is 0.25 and has a standard deviation of 1.45. For very low flows the river is braided but at medium and high flows it flows in a single channel within embankments; hence it was treated as unbraided in the model. Fig. 12.9 Leveed portion of the Kosi 380 River Morphology Analysis of the past records gave average monthly discharges which varied 13 170 cfs (373 m3/s) in January to 167 365 cfs (47 544 m3/s) in the month of July. From the discharges available, ten daily computational hydrograph was prepared. On the basis of measurements of average suspended sediment concentration data at the dam site, the relationship between sediment discharge G in tons/day and Q in cfs was obtained in the form G = a Qb in which a and b varied as follows: Table 12.3 Values of a and b in Eq. (12.25) Range of d in mm Range of Q in cfs ...(12.25) D less than 0.075 mm a b –13 0.075 < d < 0.15 mm D > 0.15 mm a 2.89 ´ 10 1.84 ´ 10 –9 –6 a 1.08 ´ 10 –9 –5 B 2.86 1.89 b 2.76 2.13 5000 = Q = 30 000 30 000 = Q = 40 000 4.33 ´ 10 0.012 3.86 1.53 2.043 ´ 10 After a few trial runs it was decided to use Laursen-Madden’s equation for determining sediment transport capabilities. The model was calibrated using bed level data in the leveed portion for the period 1975-1984. Values of D x and D t were determined from the following considerations. A typical flood wave would take about 7 hours to cover 200 km reach. The time step Dt chosen was much greater than this, namely 10 days during the monsoon period and 30 days during non-monsoon period, while D x equal to 10 km was used. For downstream control the water levels at Kursela were estimated from analysis of the Ganga river data and used in HEC-6. Bed level profiles during 1975-1984 were used with the above mentioned D x and D t values and the best value of Manning’s n which could satisfactorily estimate those bed levels was found to be 0.20; this value was used in further studies. For the bed level predictions between 1985-2005, monthly discharges were generated using Thomas-Fiering model and using characteristics of monthly flow data from the historic data available. Analysis of Data Detailed analysis of cross sections at various times and the occurrence of breach at any section, indicated that prior to the actual breach, the deep channel gradually shifted towards the embankment near that section. The average lateral rate of deep channel shifting was about 200 m/yr. It was therefore recommended that the cross-sectional data in the leveed reach be monitored every year after flood season and the places where the deep channel is close to the embankment be determined. The sections downstream of that would be prone to breaching. Bed Level Variations Observations of the longitudinal profiles in the leveed reach for different years indicated that aggradation or bed lowering occurring from section to section was primarily due to the variation in width between levees along the river length. It was found that if a narrow section was followed by a Numerical Models for Morphological Studies 3 1995 2 2000 2005 381 Bed elevation m 1 0 Scheme 6 1 Barrage 2 0 20 Leveed portion 40 60 80 100 120 km from barrage 140 160 180 200 Fig. 12.10 Rise and fall in bed levels in the Kosi with 1984 as the basis wider section, the material scoured from the narrow reach was deposited in the wider reach causing aggradation. Taking 1984 bed profile as the basis, bed profiles were obtained by using HEC-6 for the years 1990, 1995, 2000 and 2005. The rise and fall in bed levels along the river reach with respect to 1984 levels (both leveed and not leveed) are shown for the years 1995, 2000 and 2005 in Fig. 12.10. It can be seen that maximum rise in the bed level at about 2.6 m is likely to occur at about 48 km from the barrage (section 63) in the year 2005. The computation of water levels indicated that the water level between sections 63 and 91 will be about 1.37 m to 2.13 m below the top of the levee. A number of proposals for reducing the spacing between the levees thereby reducing aggradation were considered and tested using HEC-6. These were: i) uniform reduction in width to 90 percent of the present; ii) uniform reduction in width to 80 percent of the present; iii) uniform reduction in width to 70 percent of the present; iv) reduction in width to 70 percent of the present width in 12 km reach between sections 63 and 69; v) reduction in width between sections 53 and 75 to 75 percent to 0 percent width; vi) reduce width between sections 67 and 75 gradually from 70 percent at section 69 to 0 percent at section 75. The first three proposals were rejected because these caused increased deposition and rise in water level at most of the sections. Schemes (v) and (vi) are shown in Fig. 12.11. Effect of scheme (vi) on the bed levels within the leveed reach and the downstream of it can be seen in this Fig. 12.10. It may be noted that the proposed scheme (vi) does not significantly alter bed levels downstream of leveed reach, and significantly brings down rise in bed levels between sections 63 and 75. At critical section 63 aggradation reduces from 2.59 m to 1.71 m in 2005. 382 River Morphology N Eastern flood embankment (existing) 50 53 Ba g 59 63 rn fl ood (exi emba Forward stin g) nkmen embankment t as per scheme-V and VI We ste 75 ir ive r 67 m 71 at 69 Forward embankment as per scheme-VI Forward embankment as per scheme-V Fig. 12.11 Recommended spacing of levees in the Kosi The study also indicated that if the jacketing proposal (vi) is adopted, the sediment load entering the Ganga may increase from (9.8 ´ 107) tons/yr to (.1 ´ 108) tons/yr, which seems to be only a marginal increase in view of the high discharges in the Ganga at Kursela. Sedimentation Studies Upstream of a Dam As a second example of application of HEC-6, computation of sediment deposition profiles upstream of a dam is discussed. The dam under discussion is located on a river in Southern India and has a height of 35.3 m and length of 1560 m. Average riverbed slope in 275 km reach is 0.000091 and bed material of size 0.90 mm and sg of 5.5. At about 240-250 km upstream of dam the irrigation scheme and diversion weirs are in operation. Hence it was required to be found out if sedimentation in the upstream of the dam would affect the function of these diversion structures and would raise the flood levels beyond acceptable limits. Since further details about operation of the dam were not available, it was assumed that full reservoir level of 519.6 m will be maimed and flood discharges will be released accordingly. Ten daily discharge hydrograph flows varied from 125 m3/s in June to 3150 m3/s in July and about 100 m3/s in October. The inflow sediment discharge obtained from suspended load measurements was represented by the equation Qs = 1.5 Q1.65 in which Qs is expressed in tones/day and Q in m3/s. A tributary joining just upstream of the dam, having ten-daily discharge variation from 40 m3/s to 200 m3/s was also modeled. The Manning’s for the main channel and the flood plain were estimated to be 0.025 and 0.05 from the meager data available. The bed profiles obtained for 10, 20 and 30 years of operation, for a constant water level of the dam, obtained by using HEC-6 are shown in Fig. 12.12. It was found that the bed levels at 245 km upstream of the dam where lift irrigation scheme is in operation would rise by about 2.20 m in 30 years. When the maximum Numerical Models for Morphological Studies 383 Fig. 12.12 Transient bed profiles upstream of the dam observed flood of 13 320 m3/s was passed over 30 year bed profile with 519.6 water level at the dam, the flood levels rose by nearly 2.0 m within 60 to 260 km upstream of the dam. References Abbott, M.B. (1966) An Introduction to the Method of Characteristics. Thames and Hudson, London. Ashida, K. and Michiue, M. (1971) An Investigation of River Degradation Downstream of a Dam. Proc. of 14th Congress of IAHR, Paris, Vol. 3. Bayazit, M. (1975) Simulation of Armour Coat Formation and Destruction. Proc. of 16th Congress of IAHR, Sao Paulo (Brazil), B 10, pp. 73-78. Borah, D.K. (1989) Scour Depth Prediction Under Armouring Conditions. JHE, Proc. ASCE, Vol. 115, No. 10, pp. 1421-1425. Chang, H.H. (1982) Mathematical Model for Erodible Channels. JHD, Proc. ASCE, Col. 108, No. HY5, pp. 678688. Chang , H.H. and Hill, J.C. (1976) Computer Modelling of Erodible Flood Channels and Deltas. JHD, Proc. ASCE, Vol. 102, No. HY9, pp. 1464-1477. Chen, Y.H. and Simons, D.B. (1975) Mathematical Modelling of Alluvial Channels. Proc. of Symposium on Modelling Techniques, ASCE, San Francisco, pp. 466-483. Chen, Y.H. and Simons, D.B. (1980) Water and Sediment Routing for the Chippewa River Network System. Proc. of International Conference on Water Resources Development, Taipei (Taiwan), Vol. 2. 384 River Morphology Correia, L.R.P., Krishnappan, B.G. and Graf, W.H. (1992) Fully Coupled Unsteady Mobile Boundary Flow Model. JHE, Proc. ASCE, Vol. 118, No. 3, pp. 476-494. Cui, Y., Parker, G. and Parola, C. (1996) Numerical Simulation of Aggradation and Downstream Fining. JHR, IAHR, Vol. 34, No. 2, pp. 185-204. Cunge, J.A. Holly, F.M. and Verwey, A. (1980) Practical Aspects of Computational Hydraulics. Pitman Publishing Ltd., London, 420 p. CWPRS (1999) Mathematical Model Studies for Proposed Storm Water Drainage System of Central and North Region of Vasai-Vihar. Central Water and Power Research Station, Khadakwasla, Pune. Tech. Report 3655, 65 p. De Vries, M. (1993) Lecture Notes on River Engineering, Delft International Course, Delft, 139 p. Garde, R.J., Ali, K.A.S. and Diette, S. (1977) Armouring Process in Degrading Streams. JHD, Proc. ASCE, Vol. 103, No. HY9, pp. 1091-1095. Garde, R.J., Ranga Raju, K.G., Pande, P.K., Asawa, G.L., Kothyari, U.C. and Srivastava. R. (1990) Mathematical Modelling of the Morphological Changes in River Kosi. Hyd. Engg. Section, Civil Engg. Dept., University of Roorkee, Roorkee, 92 p. Garde, R.J. Sahay, A. and Bhatnagar, S. (2004) Armour Coat Formation in Parallel Degradation. Report Prepared for Indian National Science Academy, CWPRS, Pune., 45 p. Gessler, J. (1967) The Beginning of Bed Load Movement of Mixtures Investigated as Natural Armouring in Channel. Translation T-5, W.M. Keck Laboratory of Hydraulics and W.R., Caltec (U.S.A.). Harrison, A.S. (1950) Report on Special Investigation of Bed Sediment Segregation in a Degrading Stream. University of California, Inst. of Engineering Research, Berkeley (U.S.A.), Series 33, No. 1. Hasan, S.M. (1965) Experimental Study of Degradation. M.E. Thesis, Civil Engg. Dept., University of Roorkee, Roorkee. Holly, F.M., Yang, J.C., Schwarz, P., Hsu, S.H. and Einhellig, R. (1990) CHARIMA – Numerical Simulation of Unsteady Water and Sediment Movement in Multiply Connected Network of Mobile Bed Channels. Iowa Institute of Hydraulic Research, Iowa, Rep. No. 343. Karim, M.F., Holly, F.M. and Kennedy, J.F. (1983) Bed Armouring Procedure in IALLUVIAL and Application to the Missouri River. Iowa Institute of Hydraulic Research, Iowa, Rep. No. 269. Krishnappan, B.G. (1985) Modelling of Unsteady Flow in Alluvial Streams. JHE, Proc. ASCE, Vol. 112, No. 2, pp. 257-265. Little, W.C. and Mayer, P.G. (1972) The Role of Sediment Gradation in Channel Armouring. School of Civil Engineering, Georgia Institute of Technology, Atlanta (U.S.A.). Lyn, D.A. (1987) Unsteady Sediment Transport Modelling. JHE, Proc. ASCE, Vol. 113, No. 9, pp. 1-15. Murthy, B.S., Surya Rao, S., Rajagopal, H., Tiwari, S.K. and Kumar, R. (1998) Flood Estimation Routing in River System : Mathematical Models. Report Submitted to INCH, IIT Kanpur, Kanpur, 151 p. Odgaard, A.J. (1984) Grain Size Distribution of River Bed Armour Layers. JHE, Proc. ASCE, Vol. 110, No. 10, pp. 1479-1485. Palaniappan, A.B. (1991) Numerical Modelling of Aggradation and Degradation in Alluvial Streams. Ph.D. Thesis submitted to University of Roorkee, Roorkee. Rahuel, J.L., Holly, F.M., Chollet, J.P., Belleudy, P.J. and Yang, G. (1989) Modelling of River Bed Evolution for Bed Load Sediment Mixtures. JHE, Proc. ASCE, Vol. 115, No. 11, pp. 1521-1542. Shen, H.W. and Lu, J.Y. (1983) Development and Prediction of Bed Armouring. JHE, Proc. ASCE, Vol. 109, No. 4, pp. 611-629. Numerical Models for Morphological Studies 385 Singh, J. (1974) Variation of Bed Material Size in Degrading Channel. M.E. Thesis, University of Roorkee, Roorkee. Thomas, W.A. and Prashun, A.L. (1977) Mathematical Modelling at Scour and Deposition. JHD, Proc. ASCE, Vol. 103, No. 8, pp. 851-863. U.S. Army Corps of Engineers (1993) HEC-6 : Scour and Deposition in Rivers and Reservoirs. User’s Manual, Hydraulic Engineering Centrer, Davis, (U.S.A.) 164 p. with Appendix. Yen, K.C., Li, S.J. and Chen, W.L. (1995) Modelling Non-uniform Sediment Fluvial Process by Characteristic Method. JHE, Proc. ASCE, Vol. 121, No. 2, pp. 159-170. Zienkieveiz, J.C. Gallagher, R.H. and Hood, P. (1975) Newtonian and Non-Newtonian Viscous Incompressible Flow- Temperature Induced Flow-Finite Element Solution. MAFELAP. C H A P T E R 13 Morphology of Some Indian Rivers 13.1 RIVER SYSTEMS IN NORTH INDIA From the point of view of morphology of rivers in alluvial material, the Indian rivers originating from the Himalayas and flowing through thick alluvial stratum need special mention. These rivers broadly belong to three basins, namely the Indus basin, the Ganga basin and the Brahmaputra Basin (Rao 1979). The Indus system of rivers comprises the main river Indus and its tributaries the Kabul, the Swat, and the Kurram joining from the west, and the Jhelum, the Chenab, the Ravi, the Beas and the Sutlej joining from the east. The five tributaries from the east join the Indus which flows 960 km before joining Arabian Sea. The Indus river originates in Tibet near Manasarovar Lake, passes through the mountain ranges of Kashmir and Gilgit, enters Pakistan and emerges out of the hills near Attock. From Attock to its mouth in the Arabian Sea, south of Karachi, it traverses a distance of about 1610 km out of its total length of 2880 km. The eastern tributaries pass through northwest part of India namely through Kashmir, Punjab and Himachal Pradesh and then flow out to join the Indus in Pakistan. The Himalayas in the north, and the Vindhyas in the south bound the Ganga basin. The Ganga is not known by this name either in the beginning or at the end of its length. Downstream of the confluence of the Alaknanda and the Bhagirathi at Dev Prayag, the river is known as the Ganga. After traversing a distance of 250 km the river descends on to the plains at Rishikesh, and passing through Hardwar and Narora it meets the river the Yamuna at Allahabad. It further passes through Varanasi, Patna and Bhagalpur and then turns towards south. Upstream of Varanasi the Ganga is joined from the north by major tributaries the Ramganga, the Gomti and the Tons, and from the south by the Chambal, the Betwa, the Sinda and the Ken. Downstream of Varanasi, when the river enters Bihar, other important tributaries like the Ghagra, the Gandak, Son, the Bagmati and the Kosi join from the north. In the lower Ganga basin only the Mahananda joins the Ganga. Of all these tributaries the Kosi is known for its instability due to high sediment load and braided plan-forms; hence its morphology is discussed later. About hundred kilometers downstream of Rajmahal the river ceases to be called Ganga. It bifurcates into Bhagirathi the lower portion of which below Kalna is called the Hooghly which continues in India and the Padma, which flows in Bangladesh and forms the southern boundary between India and Bangladesh Morphology of Some Indian Rivers Delhi Kabul Lucknow Kanpur Ahmedabad Nagpur Kolkata Jhelum Chenab Mumbai Chenab Sutlej Indus Ra vi Beas Bhakra Nangal Lakshadwip Chennai Andaman and Nicobar Islands Sri Lanka Tsangpo Delhi Sarda Ganga Yamuna Chambal Gandhi Sagar Ghaghara Allahabad Son Gandak Kosi Kosi Brahmaputra Kurusela Betwa Narmada I Narmada n d i Mahanadi Hirakud a Kolkata Fig. 13.1 Basins in Indo-Gangetic plain in Indian subconinent 387 388 River Morphology for some distance. After traversing 220 km further down in Bangladesh the Padma is joined by the Brahmaputra at Goalundo and after meeting the Meghana 100 km downstream, the Ganga joins the Bay of Bengal. Figure 13.1 shows a sketch of these basins in the Indian subcontinent. The Brahmaputra river rises in the Kailash range of the Himalayas at an elevation of about 5000 m. It is about 2880 km long. After flowing about 1600 km parallel to the main Himalayan range, it enters India and after traversing 720 km joins the Padma at Goalundo. The combined stream is then known as the Padma. In Tibet and India a number of tributaries join Brahmaputra. The Brahmaputra is known for its instability, floods, and bank erosion causing innumerable miseries to the people living in north-east India. Hence, the morphology of the Brahmaputra is also discussed later. There are certain common characteristics of rivers in these basins namely the Kosi and the Brahamputra which are responsible for their morphological behaviour. These rivers are fed by rainfall as well as snowmelt; hence, their hydrographs have in general two peaks. Further, major parts of their catchment lie outside India; as a result, India can do very little in terms of soil conservation measures as well as construction of dam etc., without active cooperation from neighbouring countries. Further, these streams originate or pass through fragile Himalayas which erode fast, and hence they carry relatively heavy sediment load. Also, the entire Himalayan belt from Kashmir to Assam being tectonically active with frequent earthquakes and neotectonic movements, the morphology of rivers in these regions is affected by tectonic activity. It may be mentioned that there are a number of subsurface transverse faults in the region, which influence the morphology of the streams. Further, hilly areas are prone to landslides, which occur because of unstable hill slopes, earthquakes and intense rainfall. As a result, heavy sediment load enters these streams. The streams in these regions are classified by Jain and Sinha (2003) into three categories namely mountain-fed, foothills-fed and plain-fed streams. These differ significantly in morphological, hydrological and sediment transport characteristics. Mountain-fed rivers are generally multi-channel, and braided systems, characterized by many times higher discharges and sediment load in comparison to single channel sinuous foothill-fed and plains-fed river systems. Mountain-fed rivers such as the Ganga, the Gandak and the Kosi transfer large quantities of sediment from their source areas of high relief and consequently form large depositional areas (e.g., fans) in plains. The foothill-fed rivers (the Bagmati and the Rapti) and plain-fed rivers (the Gomati and the Burhi Gandak) derive their sediments from foothills and plains and a large proportion of this material is re-deposited in the plains after reworking. It may also be pointed out that many rivers in Ganga basin show tendency towards avulsion. KOSI 13.2 INTRODUCTION The river Kosi, which is a major tributary of the Ganga and which is the life line of the state of Bihar in North India, originates at an elevation of about 6000 m in the Himalayas and finally discharges into the Ganga at Kursela, see Fig. 13.2. Plate 1 shows the aerial view of the Kosi. The river is also sometimes called the Saptakosi with seven tributaries namely the Sun Kosi, the Arums, the Tamur, in the upper reaches and the Trijuga, the Balan, the Kamla and the Bagmati in the plains. In Sanskrit literature this river is referred to as the Kaushiki. It may be mentioned that Kaushiki was the legendary ascetic low- Morphology of Some Indian Rivers 389 Tibet N nd ak riv er Ga MT Everest ive r un r Khatmandu Sun Kosi river riv er Ta m ur Ar Sikkim at Gh ir rive Ea agh ive Nirmali r Kamrail India Pumea ara North Bihar Katihar Kursela r a Gang riv Patna Badiaghat n So riv er er Monghyr 32 miles Scale Rajmahal Fig. 13.2 Kosi river basin caste woman who, after being left by her Brahmin lover, became frivolous and went to various places in quest of pleasure. Hence, there is considerable similarity between the ever-wandering Kosi river and Kaushiki. The river Kosi traverses a total distance of 468 km passing through Tibet, Nepal and India. The Kosi is known for shifting its course laterally and thus creating problems of flooding and causing considerable loss to human lives, cattle, property, public utilities and agriculture. Hence the river is known as the “Sorrow of Bihar”. The Kosi is also one of the largest braided rivers in the world. The Kosi catchment consists of the Himalayas in the eastern part of Nepal and Tibet. The transHimalayan portion is a high plateau while the Himalayan portion comprises mountain ranges running eastward separated by cross-ribs. Portions of the catchment above the elevation of 4900 m are covered by perennial snow, the snowline being at 3000 m in winter and 4500 m in summer. It may be mentioned that ten percent of the Kosi catchment is perpetual snow zone of Himalayas and this has a major effect on the nature of annual flood hydrograph. The catchment area within India is flat and lies in the Gangetic plains. Out of the remaining, seventy percent is under cultivation and a very small percent under forest cover in India. The Kosi forms an inland delta or fan in the Gangetic plain (Gole and Chitale, 1966). The apex of the fan is a few kilometers downstream of Chatra, the base extending over a distance of 120 km and height being about 100 m. It has a slope from north to south and west to east. Kosi fan covers an area of 16 000 km2 lying partly in Nepal and partly in north Bihar. It lies between altitudes of 152 m and 34 m ri Mahananda ver Ba gm W es Balan river te rn ste em rn ba em nk ba m nk en m en t t Nepal Ka ml ar ive r Tribeni Darjeeling Barahakshetra Chatra Barrage ak nd Ga er riv Jogbani 390 River Morphology Plate 1 Aerial view of the Kosi Morphology of Some Indian Rivers 391 above the sea level. This fan is covered by old courses of the Kosi now occupied by smaller streams (known locally as dhars), old channel lakes (known locally as chaurs), oxbow lakes and dune-like mounds along the abandoned courses of the Kosi. Their existence is due to the westward shifting of Kosi through 112 km in 223 years (Gole and Chitale 1966). 13.3 CATCHMENT CHARACTERISTICS AND GEOLOGY The Kosi basin falls within longitude 85° to 89° (E) and latitude 25° 20’ to 29° (N). On its north is the Tsangpo (Brahmaputra) and on the south is the Ganga river. On eastern side is the ridge separating it from the Mahananda catchment and on the west is the ridgeline separating it from the Gandak/Burhi Gandak catchment. There is an 87 m drop in elevation in the 160 km reach between the Chatra gorge and Kursela near the confluence with the Ganga. The total catchment area of Kosi is 95 156 km2 out of which 20 376 km2 lies in India. Thus, nearly eighty percent of total catchment of the Kosi lies in Tibet and Nepal. The rivers the Trijuga, the Kamla Balan, the Bhutahi Balan and the Bagmati are the tributaries, which join the Kosi from the right in the plains in Bihar. The distribution of the catchment area in the Kosi river system is given in Table 13.1. Table 13.1 Distribution of catchment area in Kosi river system In India (km2) Out side India (km2) 63 430 2465 7080 706 1105 74 786 Total (km2) 74 500 5445 13 400 706 1105 95 156 Kosi including hilly tributaries Kamla Balan Bagmati Trijuga Bhutai Balan Total 11 070 2980 6320 20 370 The three hilly tributaries are the Arun, the Sun Kosi and the Tamur. The Arun Kosi is the longest of the hilly tributaries, which drains the Mount Everest. Its catchment area is 34 650 km2 and it contributes 37 percent of flow and 36 percent of sediment load of the Kosi at Tribeni. The Sun Kosi is the second longest tributary. Its catchment area is 19 000 km2 and it contributes 44 percent of flow and 42 percent of sediment load of Kosi at Tribeni. Tamur Kosi drains Mount Kanchanjunga; its catchment area is 5900 km2 and it contributes 19 percent of flow and 22 percent of sediment load of Kosi at Tribeni. The Bagmati originates in Sheapore range hills at an elevation of 1500 m and has a catchment area of 13 400 km2 and length of 589 km. The Kamla Balan originates in Nepal and has a catchment area of 5445 km2 almost half of which is in the plains. Its length is 320 km. The Trijuga and the Bhutai Balan have catchment areas of 706 km2 and 1105 km2 respectively. The geology of the Kosi basin can be divided into three parts, namely the geology of the Mount Everest and the Kanchanjunga, which lie in the upper northern most part and form the upper catchment, the Siwalik deposits which lie towards south of Mount Everest and up to Chatra, and the terraces below Chatra. The upper-most part is made up of folded Jurassic strata composed of black shales and argillaceous sand stones. This stratum is 100 to 150 m thick, and contains calcarius, pyrites and ferrous partings. Underlying the Jurassic shales are dark limestones and below it thick series of metamorphosed 392 River Morphology limestone, quartzites etc. The Siwalik deposits are alluvial detritus derived from wastes from mountains which are swept down by streams and deposited at their foot. These former alluvial deposits have been involved in the upheavals of the Himalayas because of which they may have been folded and elevated into their outermost foothills. Weathering of Siwalik rocks has been proceeding at an extraordinarily rapid rate since their deposition. Because of this, the topography produced is made up of very large escarpments and dip-slopes separated by broad longitudinal valleys intersected by deep meandering ravines. The terraces below Chatra are made up of conglomerates and thick beds of sand, boulders and shales. The Kosi flood plain is made up of alluvial deposits in the form of a trough, which is tectonic in nature and is formed in front of Himalayan chains. Hence, during the past and present times it is subjected to slow neo tectonic movements and earthquakes (NIH 1994). Figure 13.3 shows the geological map of the Kosi basin. 13.4 GEOTECTONICS The entire Kosi basin area has been the subject of study by Bordet, Gansser, Hagen and Akiba et al. (see Gohain and Parkash, 1990). The major north dipping thrusts – the Main Central Thrust and Main Boundary Thrust – are present in the area and are active even at present. One can see from Fig. 13.3 a major fault FF’ at the edge of the Kosi fan which causes an offset of the Siwaliks by about 20 m. This area has also experienced over 45 earthquakes of magnitudes ranging from 4.0 to 8.3 on Richter scale, the most severe earthquake being the one that occurred on 15th Jan. 1934 and was of magnitude 8.3; this Kosi alluvium F¢ Alluvium of the Ganga River Alluvium of the other south, southeast and east flowing streams Younger alluvial piedmont Older alluvial piedmont Upper Siwalik sediments Middle siwalik sediments Archaean Burhi Gandak R Kosi R Ganga 0 20 km Scale Lesser Himalayan Rocks Faults lineaments Faults after raiverman et. al., 1983 Fan boundary Fig. 13.3 Geological map of the Kosi alluvial fan and adjacent area (Gohain and Parkash 1990) Morphology of Some Indian Rivers 393 earthquake had its epicenter within 100 km of Barakshetra where a high dam was earlier proposed on the Kosi. This earthquake was felt all over north Bihar and Nepal and the cities of Munger and Bhatgaon (in Nepal) were completely destroyed while the cities of Patna, Kathmandu and Darjeeling felt the shocks of the earthquake. Kosi basin is also subjected to slow neotectonic upheaval, which may be partly responsible for the westward migration of Kosi. 13.5 HYDROLOGY The Kosi catchment is fed by monsoon rainfall as well as snowmelt. As mentioned earlier ten percent of the catchment up to Chatra is above perpetual snow zone of the Himalayas. Kosi catchment gets rainfall due to monsoon, which begins around June, and retreats in the middle of October. This accounts for eighty percent of the annual rainfall. During April and May, thunderstorms occur in the catchment. The annual rainfall decreases from 1200 mm at the foothills to 350 mm on the southern slopes of the Himalayas. In the Tibetian catchment it is about 250 mm while in the lower parts of the Kosi catchment it varies from 1380 mm to 1500 mm. July and August provide the maximum rainfall. Mookerjee and Aich (1963) have estimated that 74 percent of the discharge of Kosi can be accounted for by the precipitation in the form of rainfall. Analysis of peak flow in Kosi indicates that the peak flow can be ten times as large as the mean discharge in a single year. Flow duration curve for the Kosi at Barakshetra is given by Gohain and Parkash (1990). Its approximate coordinates are given in Table 13.2 Table 13.2 Monthly average discharge in m /s Percent of time equaled or exceeded 3 Flow duration curve for Kosi at Barakshetra 300 100 400 80 600 60 700 50 1400 40 3600 20 4300 10 4800 5 5800 1 The average annual runoff at Barakshetra is estimated to be 53 040 Mm3 out of which 80 percent is contributed from June to October. The minimum annual runoff at the same place is approximately 38.83 Mm3. Discharge and Sediment Measurements It was only after 1947 that the government agencies realised the necessity of having adequate and accurate flow and sediment data for the management of Kosi and established gauging sites. At present the Kosi has eight sediment and gauge-discharge observation sites. These are at Barakshetra, Bhim Nagar barrage, Baltara and Basua on the Kosi, on the Sun Kosi, the Arun and the Tamur at Tribeni, and at Machhuaghat on the Arun. The annual peak flows observed at Barakshetra between 1948 and 1978 are listed by NIH (1994). These are given in Table 13.3. It can be seen that the maximum observed flow at Barakshetra was 25 880 m3/s in 1968 and water surface elevation for this discharge was observed to be 132.18 m. Analysis of sediment load carried on the Kosi at Barakshetra for the period 1948-1981 has revealed that on the average it carries 95 Mm3 of sediment annually, of which coarse, medium and fine sized materials are 18.95, 25.11 and 55.94 percent respectively. Similar measurement made at Baltara between 1973-1981 have given average sediment load as 57.35 Mm3 of which coarse, medium and fine 394 Table 13.3 13587 24236 7198 10825 10718 9829 14322 11346 8379 12283 7085 8309 8842 9456 13343 9170 10223 7190 River Morphology Peak flows in m3/s at Barakshetra during 1948–1998 9647 5441 10514 25880 11428 7792 8171 9257 11226 7538 7651 8142 9209 7990 14831 6987 9646 10570 10769 13880 9489 6912 11332 7136 5424 5979 6660 12186 7783 8818 13391 6949 are 8.2, 19.8 and 72.0 percent respectively. Garde et al. (1990) analysed the sediment load data at the barrage and found that the sediment load in Tons/day is related to Q in m3/s as QT ~ Q3.86 for sediment finer than 0.075 mm QT ~ Q2.86 for 0.075 < d < 0.15 QT ~ Q2.76 for d > 0.15 mm These are shown in Fig. 13.4. It is observed that sediment concentration of the Kosi increases in the head reach up to Hanuman Nagar. This increase is primarily due to increase in fine fraction due to 10 5 Fine sediment (d < 0.075 mm) Medium sediment (0.075 < d < 0.15 mm) Coarse sediment (d ³ 0.15 mm) Sediment load in tons/day 10 4 10 3 Scatter of data 10 2 Scatter of data Scatter of data 10 1 Datum 10 3 4 5 ´ 10 10 0 10 5 5 ´ 10 10 3 4 10 5 ´ 10 10 Q cfs 5 3 4 10 5 10 6 Fig. 13.4 Relation between sediment load and Q at the barrage on the Kosi Morphology of Some Indian Rivers 395 erosion of Belka hill region. Beyond Hanuman Nagar however, the sediment concentration progressively reduces due to deposition of coarse and medium fractions. At Kursela where the Kosi joins the Ganga, the average sediment concentration is only 24 percent of that at the gorge. This progressive deposition causes great instability in the river (Godbole 1986). 13.6 SEDIMENT SIZE AND SLOPE Garde et al. (1990) have analysed the data collected from three boreholes at different cross sections of the now embanked Kosi. These bore holes were at the left, right and the center of leveed portion. This size distribution is shown in Fig. 13.5. It can be seen that d50, d84.1 and d15.9 sizes are 0.25 mm, 0.37 mm and 0.175 mm respectively giving geometric standard deviation sg = d84.1 d 1 = + 50 d50 d15. 9 2 F GH I as 1.455. On JK the same figure are plotted data given by CWPRS, Pune. The Central Water Commission has divided the entire reach of Kosi in four segments and the slope in each reach has been given as follows during 1982. 100 Left bank Centre 80 Right bank CWPRS data Percent finer 60 40 20 0 0.06 0.08 0.10 0.2 0.4 d in mm 0.6 0.8 1.0 2.0 Fig. 13.5 Size distribution of bed material of the Kosi at section 63 396 Extent of reach (in km) below Chatra 0 – 42 km 42 – 68 km 68 – 134 km 134 – 160 km River Morphology Bed slope 0.001 400 0.000 716 0.000 450 0.000 110 The longitudinal section of the Kosi river as obtained in 1975 is shown in Fig. 13.6. It can be seen that between Chatra and the barrage at Bhim Nagar the average bed slope is 9.38 ´ 10 – 4, between the barrage and up to next 32 km downstream the average slope is 5.5 ´ 10– 4, while downstream for the next 64 km the average bed slope is 2.70 ´ 10 –4. The differences in the slopes between 1975 and 1982 are evidently due to aggradation/degradation. 106 98 Chatra 90 82 9.38 ´ 10 –4 Bed Levels m 74 66 58 50 Barrage 5.50 ´ 10 –4 2.70 ´ 10 42 –4 Datum 34 0 16 32 48 64 80 96 Distance in km from Chatra 112 128 144 Fig. 13.6 Longitudinal profile of the Kosi 13.7 MORPHOLOGY OF THE KOSI Investigators have opined that quite possibly, in the earlier times the Kosi joined the river Mahananda through the present course of the river Parman near Araria in Purnea district. This view is supported by the presence of long stretch of depression varying in width from 30 m to 60 m passing from Forbesganj Morphology of Some Indian Rivers 397 side towards Araria. However, since 1736 the river has shifted towards the west through 112 km in 223 years. In this process, it has deposited sand over 7680 km2 land in Bihar and 1280 km2 in Nepal making the land almost infertile. Positions of the Kosi during different years are shown in Fig. 13.7. The shifting has always been towards the west and the average shifting rate has varied from 0.19 km/year to 1.8 km/ year with an average rate of 0.478 km/year at Purnea to Belhi. It can be seen in Fig. 13.7 that the river has shifted westward by abandoning its old channels. Since the Kosi carries high sediment load, much of the sediment gets deposited during the recession of the flood thereby choking mouths of some of the channels. As a result, during the next flood the river activates a new channel which gets developed with the passage of time. Observations indicate that when the Kosi was in flood, the water spread over 16 to Fig. 13.7 Lateral migration of the Kosi river 398 River Morphology 32 km laterally. In the dry season, the river flowed in a number of channels; some of these were deep and others shallow, indicating that the river was braided in nature. The flow velocity during flood used to be so high in deep channels that a large animal such as an elephant could be washed down. The country area looked like a series of islands. In 1883 there was apprehension that Kosi may suddenly change its course and flow in the abandoned channels on the east. Shillingford in 1885 published a paper in the Asiatic Society of Bengal and opined that the eastward movement of the Kosi would probably be accomplished in one great swing and cause great loss to property and life. Some probable reasons for the westward movement of the Kosi have been proposed. The one earlier mentioned is the differential deposition of sediment during the recession of flood causing closure of some channels and opening newer ones in the next flood. The second reason that is often quoted is the general westward slope on the Kosi flood plain. Lastly, it is already mentioned that the Kosi plain and adjoining areas are subjected to earthquakes and neotectonics that can cause this shift. 13.8 MANAGEMENT OF THE KOSI To reduce the flood and sediment problems of the Kosi a number of expert committees have given their recommendations a few among them being those of Inglis, K.L. Rao, Leopold and Maddock, Kanwar Sain and Mitra. Along with these reports there were some review committees of Central Water Commission of the Govt. of India. They generally agreed that for the proper management of Kosi, the following recommendations be implemented. 1. Catchment area treatment for the Sun, the Arun and the Tamur tributaries; it is estimated (see Carlson 1985) that the average rates of denudation of Tamur, Sun Kosi and Arun catchments are 2.56, 1.43 and 0.51 mm/year, which are quite high and are the source of large sediment load of the Kosi. 2. Construction of a high dam in Nepal which would arrest a large percentage of coarse sediment and reduce aggradation downstream. It will also provide for flood control, power generation and irrigation in Nepal. 3. Construction of a barrage at Hanuman Nagar near Bhim Nagar at a distance of 48 km downstream of Chatra. This would reduce water surface slope between Chatra and the barrage and thus reduce excessive bank erosion between Chatra and the Barrage. 4. Construction of afflux bunds upstream of the barrage and flood embankments downstream of the barrage. 5. Construction of canals on both sides of the barrage for the development of Irrigation of 1.05 Mha. and power generation of about 20 000 kW. The first two recommendations have not been implemented because these areas of catchment and where a large dam was to be constructed lie in Nepal. The construction of the barrage was started in 1959 and completed in 1963. Afflux bunds have been provided on the upstream of the barrage on the east and west. Afflux bund on the east is 40 km long while that on the west is 14 km long which prevent inundation due to ponding in non-monsoon season and afflux caused by the barrage obstruction during the flood time. These are shown in Fig. 13.8. Some of the details of barrage are as follows. Total length No. of bays at barrage = 1150 m = 46 each of 18.3 m width, Morphology of Some Indian Rivers 399 Fig. 13.8 Kosi flood embankments No. of under sluice bays = 6 on the left and 4 on the right each18.3 m widths Spillway gates = 16 Numbers of 18.3 m ´ 6.4 m The maximum discharge at barrage is about 14 000m3/s and minimum of 1000 m3/s. To provide water for irrigation and generate waterpower, irrigation canals have been taken from the barrage. The one on the east is known as Eastern Kosi main canal while that on the west is known as Western Kosi main canal. Right from the beginning both these canals are facing severe problems of sedimentation. This is illustrated by discussing about Eastern Kosi Main Canal whose head works has 32 tunnels covering four bays of the barrage. The canal was designed to carry 424.5 m3/s; however subsequently a sediment ejector was provided at 646 m downstream of the head regulator; hence the discharge at head regulator was increased to 485 m3/s to provide for flushing water requirement for sediment ejector as 400 River Morphology discussed by Sahai et al. (1980). The canal discharge decreases from 424.5 m3/s to 40.5 m3/s over a length of 41.3 km. In the same distance the bed width changes from 189.7 m to 19.8 m, the full supply depth changes from 3.5 m to 2.13 m and slope from 0.99 ´ 10 – 4 to 1.333 ´ 10 – 4. Also at 3600 m downstream of the head regulator there is 4 m drop, which is used for generation of power. This canal runs in heavy cutting from the head regulator to about 9.15 km downstream. While the power house was under construction, the canal discharge was gradually increased from 44 m3/s in 1964 to 251 m3/s in 1969. Extensive sediment deposition took place in the 41.15 km reach; the yearly sediment volume deposited being 0.14 to 0.25 Mm3. It has been found that both the sediment excluder and ejector have failed to function properly. The Western Kosi Main Canal is also plagued with similar problems (Sinha 1986). Flood-Embankments Construction of flood embankments was taken up in 1955 and was completed in 1959. These are 144 km long on the left bank and 123 km long on the right bank, and are designed for flood discharge of 24 000 m3/s which is a flood of about 150 year return period. The right bank embankment will be extended up to Kursela except where the Bagmati and the Kamla join Kosi. The left bank embankment has been extended up to Koparia, see Fig. 13.8. These embankments provide flood protection to 0.214 Mha in India and 51,400 ha in Nepal. Sedimentation studies have shown that upstream of barrage the bed slope changed from 0.00 061 to 0.00 042 between 1963 and 1968. It was also estimated (Chitale 2000) that between 1963 and 1970, 35.05 Mm3 of sediment was deposited in 10 km reach upstream of the barrage giving an average depth of deposition of 0.40 m in eight years. It has also been found that during 1963-1970 there was a general lowering of bed level downstream of barrage for a length of 23 km. Further downstream there was tendency towards aggradation. Earlier studies by Sanyal (1980) and others indicated significant aggradation in the lower reaches of the Kosi. Concerned about the continuous aggradation in lower reaches of the embanked reach of the Kosi, Ganga Flood Control Commission, Govt. of India referred the problem to University of Roorkee which used HEC-6 1-D model to study aggradation by using Laursen-Madden relation for sediment transport and D x = 10 km, D t = 10 days for non-monsoon and 30 days for monsoon periods. Table 12.2 gives the levee spacing at various sections downstream. The model was calibrated using 7 year’s data of discharges and river cross sections for the period 1975-82 and then the model was run for the period 1984 to 2005, using discharge data generated using Thomas-Fiering model. The model indicated a rise in the bed level by about 2.44 m with reference to 1984 bed levels bringing the water level within 1.37 m to 2.13 m of the top of the embankment near Nirmali. Hence, it was concluded that the primary reason for aggradation was large spacing between the levees. Aggradation can be offset by either reducing the spacing between levees, or by providing spurs. Some have suggested giving proper slope to the stream in different reaches so that aggradation can be avoided; however the latter solution does not seem to be practicable. The morphology of the river-bed in the leveed reach from Gopalpur to Koparia has been studied by Gohain and Parkash (1990) by field investigation and also by interpretation of black-white air photos with a scale of 1:25 000. They have identified the following topographic levels and larger bed features. Morphology of Some Indian Rivers 401 Level 1 : Active channel course with low bars; Level 2 : 0.5 to 0.9 m higher than water surface on level 1 during low flows; no vegetation, submerges with a small increases in flow. Level 3 : About 1 m higher than level 2, sparsely vegetated, submerged during high flows of flood. Level 4 : Between 0.5 and 0.8 m higher than level 3, it comprises the surface the islands and banks. These levels are best developed in the braided reach of the river. The Kosi with the artificial embankments is a confined braided stream. Figure 13.9 shows braided reach downstream of the barrage. Levels 2 and 3 are relatively unstable and are dissected intensively every year during the flood. Grass and shrubs along the reach cover level 4. Extensive agricultural activities and settlements are seen on this level and these are flooded when discharge at Barakshetra exceeds 8400 m3/s. Considering a distinct change in the slope of flow duration curve at about 1000 m3/s. (see Table 13.2), it is interpreted that levels 1 and 2 correspond to low flows in November–February period while levels 3 and 4 correspond to monsoon discharges. Gohain and Parkash found that there are a number of channels at any section that can be divided into primary channels which are deep and carry water even at low stages. Usually there are one or two primary channels. The sub-channels are defined as part of the river-bed which has only bars with level 2, hence at high flow these get submerged. Barrage axis 33 Eas tern 41 53 gm r 63 ati Fig. 13.9 Braided reach in leveed portion of the Kosi river downstream of barrage Channel Patterns In the Zone 1 between Chatra and Karaya, a distance of about 20 km, the slope is 0.000 45 and one primary braided channel is present. Zone 2 is from Karaya to Dumra, a distance of about 96 km. Here the slope is 0.000 48. This is the main braided zone of the river, having two primary channels and a few meandering channels on level 4. Zone 3 is a 40 km reach from Dumra to a few km upstream of Koparia in which average slope is 0.0001. One straight channel of sinuosity 1.01 to 1.16 is present. Zone 4 extends for a distance of 160 km downstream of Zone 3 up to Kursela. Here the mean slope is 0.000 05 Ba Western flood embankment rive 69 75 81 87 91 flood em bankment 402 River Morphology and the stream meanders all along its course. Point bars and sidebars are a common occurrence. Abandoned channels with chute cutoffs and neck cutoffs are common in flood plain. 13.9 PRESENT DAY PROBLEMS OF THE KOSI One of the major problems faced on the Kosi is breaching of sections of embankment almost every year leading to huge maintenance cost. It is found that the deep channel takes a different course every year and affects new reach of levees. Since it is very difficult to predict the behaviour using a mathematical model, every year after the flood has receded, bed levels are taken at different sections and the bed in the movable bed physical model is laid for the new condition. The model is then run for flood discharge to identify the sections of the embankment that are likely to be attacked during the next flood season. Protection works are undertaken on the basis of the above study as well as on the basis of advice of highlevel committee, which visits the site before the monsoon. The protection methods include direct strengthening of embankment or construction of spurs. The physical model studies are carried out at Central Water and Power Research Station, Pune (India). The second aspect of concern is the continuing aggradation taking place in the major length of leveed reach. Even though reduction of spacing between levees can reduce or stop aggradation, no action has been taken. Aggradation can reduce if sediment is stored upstream behind a large dam; however no serious effort is made in this direction also. The third concern is about the malfunctioning of both the canals taking off from barrage, as a result of which there is under utilization of the irrigation potential that has been created. Also, water-logging problems have occurred in the Eastern Kosi command area and there are also problems related to proper drainage behind leveed reach. BRAHMAPUTRA 13.10 INTRODUCTION The Brahmaputra is one of the largest rivers in the world and is known for its high floods and sediment load, flood damages and instability. The river originates near Manasarovar at an elevation of about 5000 m. Within 160 km of this lake are also the sources of two other largest rivers in the Indian subcontinent, namely the Indus and the Ganges. The Sutlej, a large tributary of the Indus also originates in this area. Figure 13.10 shows the course of the river Brahmaputra, while Plate 2 shows the aerial view of the Brahmaputra. The Tibetan portion of the Brahmaputra is known as the Tsangpo, it is called Siang and then Dihang when it enters Arunachal Pradesh in India. The words Siang and Dihang mean the “big or great river”. Brahmaputra means son of the God Brahma. It is interesting to know that Brahmaputra is probably the only river having masculine name. Near the upstream border of Assam, just upstream of Sadiya it is joined by two tributaries the Dihang and the Lohit. Here the river turns in the westerly direction and flows through India passing along the cities of Kobo, Dibrugarh, Jorhat, Tezpur, Guwahati, Dubri and Goalpara, and then turns towards south. After flowing for about 337 km the Brahmaputra joins the Padma at Goalundo in Bangladesh. The total length of the Brahmaputra up to the confluence with the Padma is 2 880 km out of which 1625 km is in Tibet, 918 km in India and 337 km in Bangladesh. Similarly the river has a catchment area Morphology of Some Indian Rivers Bhutan From manasarowar Tsangpo N Himalaya N5 N1 Dhuri Goalpara Barpeta Mangaldoi Guwahati Embankments Silighat N2 N3 N4 Teepar Gamirighat North lakhimpur N6 Dibrugarh Sibsagar Jorhat S3 S4 N7 N8 India S1 Fig. 13.10 Brahmaputra river system along with the embankments N ag a pa Meghalaya plateau tk S2 hi lls Embankment Scale 1 cm = 20 km Nomenclature of the rivers North bank Soutth bank N1 Manas S1 Kapil N2 Pagladiya S2 Dhanairi N3 Pachnoi S3 Dessng N4 Jia bhargil S4 Lohit N5 Ranganadl N6 Jladhol N7 Dihang N8 Dibang ai 403 404 River Morphology Plate 2 Aerial view of the Brahmaputra basin Morphology of Some Indian Rivers 405 of 29 300 km2 in Tibet, 19 500 km2 in India, 4500 km2 in Bhutan and 4700 km2 in Bangladesh, thus making a total of 58 000 km2 drainage area up to the confluence with the Padma. As the Brahmaputra flows through India, large and small tributaries join the river both from the north and from the south. In the entire course of its journey, the Brahmaputra receives as many as 22 major tributaries in Tibet, 33 in India and 3 in Bangladesh. The northern tributaries come from higher rainfall region, pass through fragile Himalayas and have steeper slopes. In general, they carry high sediment concentration comprising cobbles, coarse gravel and sand. These tributaries are braided and have migrating channels over major portion of their lengths. Some of the important tributaries of the north are the Subansiri, the Ranganadi the Jia Bhareli, the Sankosh, the Pagladiya and the Manas. The tributaries on the south bank emerge from comparatively lower levels from Naga-Patki, Khasi and Garo hill ranges and flow towards north or north-west at flatter slopes. These tributaries have deep meandering channels and they carry relatively finer sediment at smaller concentrations. Some of the south bank tributaries are the Lohit, the Buri Dihing, the Desang, the Kopili and the Dikhu. These are shown in Fig. 13.10. It may be mentioned that the Brahmaputra is closer to the hills on the south probably because the river has been pushed southwards during the past because of sediment deposition on the northern side. Another characteristic that is worth noting is that in general, the north bank, at many places is at a higher elevation than the south bank by three to ten meters as noted by Baruah (1969). The Brahmaputra valley width has a minimum value of 60 km and an average value of 86 km, while the river width varies from 15 to 19 km. Within India the Brahmaputra is braided for most of its length except where its width is restricted and the river is stable with well-defined nodal points. Such restrictions in width occur at a number of places; these locations and average width in km are listed in Table 13.4. These constrictions in the channel would create backwater and changing water surface profile along the river, thereby causing tendency towards aggradation especially for medium flows. At other places the river width varies from 5 000 m to about 19 000 m. Typical cross sections at Pandu and Pancharatna where the river is constricted and at Jogighopa where it is much wider are shown in Fig. 13.11. Table 13.4 Location Murkong - Selek Near Dibrugarh Near Dikhumukh Near Helem Silghat Near Tezpur North of Dihang Downstream of Laterisuti Mirkhameri Guwahati Near Pandu Hathimura Jogighopa Chandor Dinga Constrictions in the Brahmaputra (Baruah 1969) Total width (km) 1.92 2.08 1.60 2.0 2.56 2.40 1.36 2.56 2.56 1.44 0.90 1.15 1.36 2.00 3.00 Width of perennial channel (km) 0.16 0.80 0-.48 0.72 0.32 1.76 1.04 1.36 0.72 0.72 1.15 0.90 1.12 1.12 0.56 406 41 38 Elevation (m) River Morphology 35 32 29 26 23 20 0 500 1000 1500 2000 2500 Chalnage (m) Cross Section of Brahmaputra at Pancharatna 60 55 Elevation (m) 50 45 40 35 30 25 0 500 1000 HFL = 47.40 m 1500 2000 2500 3000 3500 Chalnage (m) Cross Section of Brahmaputra at Pandu 38 36 Elevation (m) HFL = 36.12 m 34 32 30 28 26 24 22 0 1000 2000 3000 4000 5000 6000 7000 8000 Chalnage (m) Cross Section of Brahmaputra at Johlghopa Fig. 13.11 Typical cross sections of the Brahmaputra Morphology of Some Indian Rivers 407 13.11 RIVER CHARACTERISTICS River Slope The longitudinal profile of the Brahmaputra as given by Goswami (1985) is shown in Fig. 13.12. The slopes of the river prior to 1950 and in recent times are given by Baruah (1969), and by WAPCOS (1993) respectively. These are listed below. Range Kobo to Dibrugarh Dibrugarh to Neamati Neamati to Silghat Silghat to Guwahati Guwahati to Goalpara Goalpara to Dubri Reach between Kobo to Dubri Reach within Bangladesh Slope 0.000 300 0.000 182 0.000 135 0.000 115 0.000 1136 0.000 105 0.000 147 Reduces from 0.000 09 to 0.000 03 5000 Manasarowar 4000 China Shigatse Elevation m 3000 Tesla dihong Pe 2000 1000 Enters India Pasighat Enters Bangladesh Pandu 4 0 0 28 24 20 16 12 Distance in 100 km 8 Fig. 13.12 Longitudinal profile of the Brahmaputra bed Recent alluvial deposits comprising clay, silt, sand and shingle cover the major part of the Brahmaputra valley. The average thickness is about 300 m. Drilling at Pasighat bridge and for oil wells in Ningru plains of Arunachal Pradesh have provided useful data about the thickness and nature of alluvial deposits. These borings show repeated sequences of clay, fine sand, coarse sand, coarse sand with cobbles, pebbles and boulders. Figure 13.13 shows the borehole data on the Dihang near Pasighat, 408 Pictorial representation R.L. in meters 155.190 153.190 150.190 60 to 70% of boulders in compacted red soil 148.190 70 to 80% Boulders (1500 mm to 3000 mm) 144.190 Filled up sand Sandy soil mixed with gravel and boulders Strata description River Morphology Boulders medium and large size (300 mm 3000 mm) 140.190 139.190 138.190 137.190 Boulders of size upto 1200 mm Boulders of size upto 800 mm Silt and sand mixed gravel Silt sand and shingles (size about 63 mm) 129.800 Silt sand and gravel (size 50 mm to 5000 mm) 128.300 Silt sand and boulders (size between 800 mm to 1000 mm) 127.900 Boulders (size between 600 to 1000 mm) Fig. 13.13 Bore log data for bed material on the Dihang near Pasighat Morphology of Some Indian Rivers 409 which illustrates the stratified nature of sediment deposits. Presence of coarse fractions would be helpful in controlling the scour around hydraulic structures such as bridge piers, as well as excessive degradation due to formation of an armor coat. Bed material in the Brahmaputra river mostly comprises silt and fine sand. Goswami (1985a) has reported the size distribution of bed and bar material in the Brahmaputra river at Dibrugarh, Salmara, Hatimura, Guma, Goalpara and Pandu. The median size of the samples varied from 0.03 mm to 0.30 mm; such a large variation is probably due to the fact that some samples were collected on the bars while others in the depressed portions. Recently several more samples were collected by WAPCOS (1993) over a long stretch. It was found that median size of the bed material varied from 0.223 to 0.085 mm with an average of 0.16 mm and the standard deviation varied from 1.294 to 2.043 with an average of 1.476. The average size at Pancharatna was 0.138 mm with the standard deviation of 1.52. Pancharatna is between the outfalls of Manas and Dubri. At Pancharatna 10% of the material is finer than 0.06 mm and only 2% of material is coarser than 0.40 mm. Normally the median size of the sediment decreases in the downstream direction due to abrasion and sorting; however, such tendency is not noticed in the case of the Brahmaputra. There is no systematic reduction of median size of bed material along the river length. This is attributed to the number of tributaries joining Brahmaputra on its way and mixing of their bed material with that of the Brahmaputra. Also abrasion is unlikely to be unimportant in the Brahamputra since most of the sediment moves as suspended load. The bed material of the Brahmaputra river is composed mainly of varying proportions of fine sand and silt, with only occasional presence of small amount of clay, less than 5% (Goswami, 1985). Particle size distribution of bank material at Dibrugarh, Hatimura and Dubri, given by Goswami shows that sizes range from 0.001 mm to 0.20 mm with d50 between 0.05 to 0.15 mm. The vertical profiles generally include two distinct parts – a relatively fine-grained top stratum and a coarser substratum. The coarse sediments probably represent channel bars and islands accreted laterally through wandering channel, and the finer sediments represent vertical accretion from over bank flow. Bank Instability The bank line of the Brahmaputra is extremely unstable for most of its length. Bank failures are rampant and seem to be function of the hydraulic character of the flow and the engineering properties of the bank material. According to Coleman (1969) several factors are responsible for short-term changes in the bank line. These are i) rate of rise and fall of water level; ii) number and position of channels active during the flood stage; iii) angle at which the talweg approaches the bank line; iv) amount of scour and deposition that occurs during flood; v) formation and movement of large bed forms; vi) cohesion and variability in the composition of bank material; vii) intensity of bank sloughing; and viii) relationship of abandoned river courses to present-day channel. Shear failures in the upper bank material seem to be by far the most widespread model of bank failures. This is caused either by undercutting of the upper bank material by the current during high flows, producing an over-hanging cantilevered block which eventually fails, or by over steepening of 410 River Morphology the bank materials due to migration of talweg closer to the bank during falling stages. High moisture content, low percentage of clay and good sorting of the bank materials in the Brahmaputra make them highly susceptible to erosion by the river. 13.12 SEISMICITY AND LANDSLIDES Brahmaputra basin is located in a geodynamically unstable region characterized by active faults and continuing crustal movements. According to plate tectonics the Indian plate moving in the north – northeasterly direction is under thrusting the Eurasian plate and is causing deformation and instability in the Brahmaputra basin. It is believed that many E-W and transverse faults that dissect the Meghalaya – Mikir blocks are active and are responsible for high seismicity. In the 60 years prior to 1980, over 450 small and large earthquakes have taken place in this area. Their distribution is as follows Richter magnitude 8 or greater 7–8 6–7 5–6 No. of earthquakes 3 15 167 270 Major earthquakes in this region appear to be separated by quiescent periods of about 30 years (Goswami, 1985). Among the earthquakes that have taken place in the region, the two most severe earthquakes were those of 1897 and 1950. The 1897 earthquake of Richter magnitude of 8.7 had its epicenter in Shillong plateau. It was felt over 450 000 km2 and its effects were noticed even after ten years. The entire lower portion of the basin up to Goalpara district was affected. The 1950 earthquake of intensity 8.7 occurred on 15th August and its epicenter was at 50 km north east of India’s border. Its effects are very well recorded by Gee (1951). The following description is taken from his paper “Many hills, a few hundred meters in height were shattered from top to bottom, their sides crushing down into the valley below. Rivers, both small and large became blocked by huge dams of rock, earth and vegetation, and in cases ceased the flow. Even the Subansiri, which had swollen with monsoon rains practically dried for few days. Then came the bursting of dams, one by one in some cases, in other cases simultaneously. Vast flood waves surged down the valley carrying everything below them. In some cases lakes thus formed in the hills by these temporary dams endured for longer period. Thus at the head waters of the Tidding river, a tributary of the Lohit, a lake nearly 6.5 km in length and 0.40 km wide was formed and lasted throughout the winter of 1950 and spring. It disappeared in 1951 monsoon. Seventy five of the hills in 27 000 km2 area were mutilated by land slides. About half of the landslides appeared to have occurred on the day of the earthquake and remaining subsequently when heavy rain occurred. The Dihang became so silted up that its tributaries, the Jigiapani, Deopani and Ghurmura could not enter it. These were diverted by the newly formed silt banks of the Dihang up to the town of Sadiya. Lohit was silted up to the extent of one to two meters while Brahmaputra was silted up to two to three meters at Murkong Selek and at Dibrugarh. This earthquake had radically Morphology of Some Indian Rivers 411 altered the slope of Brahmaputra, stopping the flow temporarily and bringing about flooding and rapid accumulation of enormous volume of sediment in the channel. The low water level rose by as much as 3 m at Dibrugarh as a result of this earthquake”. The sediment deposited in the river as the result of the earthquake moved downstream at a low velocity as sediment wave, and its effects were noticed even in 1971. In addition to the tectonic activity, neotectonic effects have also been noticed as reported by Valdiya (1999). Leveling observations made three times during 1910-1976 have indicated that blocks of Guwahati-Dergaon section have been consistently rising up at the rate of 0.30 mm to 4.5 to 31 mm per year at Dergaon (30 km west of Jorhat). Similar uplifting activity is noticed in Guwahati-Goalpara sector. Such movements gradually change the slope of the stream and can cause aggradation or degradation. Along with the earthquake, landslides also influence significantly the morphology of alluvial streams. Landslides in the Himalayan region of India occur during the monsoon season. Further, it has been observed that reactivation of old Himalayan landslides, invariably occurs during the monsoon season after heavy and/or prolonged rains. It has been observed that in all those cases of large landslides in Himalayan region, the rainfall ratio defined as ER = Average 24 hour, 2 year rain fall Average annual rainfall is greater than 0.08. In fact ER greater than 0.08 and earthquake magnitude greater than 7.0 have produced all the large landslides in this region, see Garde and Kothyari (1989). Figure 13.14 shows map-showing landslide – prone regions of India, while Fig. 13.15 shows locations of epicenters of high magnitude earthquakes. Foothill region of Arunachal Pradesh is characterized by tightly folded mega structures of alternate stratified layers in which building up of pore pressure is responsible for slope failures. As mentioned earlier, such land slides brought down heavy debris during 1950 earthquake resulting in stream blockages, stream diversion and aggradation. 13.13 CLIMATE AND HYDROLOGY The annual rainfall in the Brahmaputra catchment varies from 100 cm to 400 cm; the map showing isohyets is shown in Fig. 13.16. Most of the rainfall occurs during June to September. The eastern part of the catchment experiences pre-monsoon thunder-showers during March-May period. Of the total annual rainfall, about 60 to 70 percent falls during the monsoon period, while 40 to 30 percent occurs during pre-monsoon season. Only a small percentage of rainfall occurs during the winter. Analysis of storms has indicated that majority of storms are of 2, 3 or 4 days duration. Natural vegetation in the Brahmaputra basin varies with altitude from tropical evergreen and mixed deciduous forests within the valley and foothills to alpine meadows and steppes in the higher ranges, and in Tibet about 20 percent of the Brahmaputra valley is forested. Discharge data are collected at 33 stations on the north bank tributaries, 58 on the south bank tributaries and about 60 stations on the main river where gauge discharge or gauge-discharge-sediment measurements are made. 412 36° ER = 0.085 32° Srinagar Shimla ER = 0.105 28° Delhi Lucknow 24° River Morphology Devastating landslide Landslide – pone areas Earthquake of magnitude between 7.0 to 8.0 Main central thrust Main boundary thrust Earthquake of magnitude more than 8.0 Dehradun ER = 0.08 Gangtok ER = 0.115 ER = 0.09 Imphal 68° 72° 76° 80° 84° 88° 92° 96° Fig. 13.14 Land slides-prone areas in India (Garde and Kothyari 1989) 36° 32° Fault Ridge Earthquake of magnitude 5.0 to 6.9 on Richter scale Earthquake of magnitude 7.0 to 8.0 on Richter scale Earthquake of magnitude more than 8.0 on Richter scale 28° 24° 68° 72° 76° 80° 84° 88° 92° 96° Fig. 13.15 Locations of epicenters of high magnitude of earthquakes in India Morphology of Some Indian Rivers 413 N Bhutan West Bengal 350 300 250 50 0 0 40 35000 3 250 Arunachal 200 180 A s Brahmaputra 250 s 350 a m 400 350 300 25 300 0 N 0 500 400 300 la aga nd 250 0 2 0 150 Burma Bangladesh 16 0 18 0 14 250 200 300 35 0 20 0 20 40 60 80 100 km Fig. 13.16 Isohyetal map of Brahmaputra valley and adjoining highlands Rao (1979) has prepared a diagram showing contribution of mean annual runoff by different tributaries to the Brahmaputra and variation of mean annual runoff along the Brahmaputra. This is shown in Fig. 13.17, which shows that contribution of the Subansiri, the Jia Bhareli, the Manas and the Sankosh from the north, and the Buri Dihang, the Dikshu, the Dhangiri, and the Kopili from south are significant. Regional flood frequency approach has been used by Jakhade et al. (1984) who found that the Brahmaputra basin rivers can be grouped in two hydro meteorologically homogenous zones A and B. Broadly zone A covers Manas to Dihang in the north and Burhi Dihing in the south. Zone B covers all the southern tributaries in the valley below Burhi Dihing, Sankosh in the north and the main river below Pasighat. Goswami (1985) has analysed annual flood discharge data at Pandu for the years 1971-1974 using log-Pearson type III distribution. His analysis gives the mean annual flood at Pandu as 51 156 m3/ s with a recurrence interval of 2.1 years while bankful discharge which just overtops the banks has the magnitude of 34 940 m3/s with a recurrence interval of 1.02 years. It may be mentioned that the maximum observed flood occurred in 1962 and was 72 784 m3/s while minimum observed discharge is 1757 m3/s. Flood frequency analysis carried by WAPCOS (1993) has given floods of 25, 50 and 100 years return period at Pandu as 65 692, 68 964 and 72 028 m3/s respectively. It needs to be mentioned that difference in water levels between 25 and 100-year floods is less than 1.0 m and hence a large area gets flooded even with floods occurring once in 2 or 3 years. Analysis of flood data on the Brahmaputra has also shown that the magnitude and time of occurrence of maximum flood in the tributaries play an important role in maximum discharge and its occurrence at various places along the Brahmaputra. The depth of river, measured from the top of the 30 0 414 Sankosh (O) 16556 Manas (85) 32258 Dhubri Dhansiri (270) 2295 Jia Bhareli (338) 28890 Subansiri (430) 57296 Tezpur Kobo River Morphology Goalundo Dihang 186290 589000 510450 359241 268936 Dibang 39085 Jogighopa Bangladesh India Guwahati Pandu Bhurbandka Bessamara Dibru garh Lohit 46564 Dikshu(505) 3511 Kopilikalang(220) Dhansiri(420) 6084 8640 Buri Dihang(540) 10996 Disang(515) 5010 Notes: Figures represent average annual runoff in Mm Figurehs in bracket indicate chainage from India–Bangladesh border upstream Fig. 13.17 Average annual runoff of the Brahmaputra (Rao 1979) River Ganga at Harding Bridge (India) Godavari at Dhauleshwaram (India) Brahmaputra at Pandu (India) Padma at Chandpur (Bangladesh) Amazon at Obidos (Brazil) Mississippi at Columbia (U.S.A.) Q max/A m3/s km2 0.067 0.280 0.297 0.114 0.048 0.03 bank varies from 4.6 m in a crossing near Dibrugarh to approximately 30 m near the mouth of the Manas river. At the latter location, the river is confined to a single channel. Low water depths in bends where a single channel exists vary from 12 to 21 m. In passing it may be mentioned that the ratio of maximum observed discharge per unit catchment area is quite large in the Brahmaputra river as compared to other rivers in the world as can be seen from the above table. 13.14 RESISTANCE TO FLOW AND SEDIMENT TRANSPORT Resistance analysis has been carried out in a given reach at Pancharatna gauging station. Manning’s n value is found to vary from 0.05 to 0.03 for low flows and it reduces 0.04 – 0.02 for high discharge of the order of 30 000 m3/s. The depth at the deepest section at Pancharatna is about 15 m for a discharge of around 35 000 m3/s. WAPCOS (1993) had used different methods of predicting resistance and found that Garde–Ranga Raju and Engelund’s methods give better results than the methods of Sugio and Paris. Since Manning’s n values are much greater than 0.011 obtained by using Strickler’s equation, it Morphology of Some Indian Rivers 415 can be inferred that the bed is covered with dunes for low and medium flows. Some measurements were made in 144 km reach upstream of Dubri during the month of May 1989. The data indicated bed undulations of height about 8 m occurring at a wavelength of 8 to 10 km. Superimposed on these were smaller undulations or bed forms. Coleman (1969) has reported some echo-sounding measurements on the Brahmaputra in Bangladesh at Sirajang, Nagabari and Aricha throughout one flood season. Coleman observed ripples (height a few cm to 30 cm), mega-ripples (height ranging from 0.30 m to 1.5 m and length ranging from 3 m to over 150 m), and dunes (height ranging from 1.5 m to 7.5 m and wave length ranging from 40 m to 480 m). He also found sand waves with heights ranging from 7.5 m to 15 m and wave length ranging from 180 m to 900 m; their maximum speed was about 30 m per hour. Relatively high values of n at medium and large flows in the Indian portion of the Brahmaputra indicate the presence of fairly large bed-forms. The larger n values at very low flows are due to formation of islands in braided regime. Most of the suspended sediment measurements are carried out at 0.6 depth and concentration there is taken as the average suspended sediment concentration. This is divided into three size fractions: fine, medium and coarse. The assumption of taking concentration at 0.6 depths as the average concentration may be satisfactory for fine sediment, but it can underestimate sediment load in medium and coarse fractions. Usually suspended sediment discharge Qs is related to the corresponding water discharge and a relation of the form Qs = a Qb established for each river. Using mean monthly values of Qs and Q, Goswami (1988) found b to be 1.78 and 2.53 at Pandu for 1971-76 and 1977-79 data respectively. The analysis of suspended load indicate that the river carries relatively more fine material compared to medium and coarse size fractions. The percentage of fine sediment varies from 70 to 90. Using sediment measurements at Pandu for 1955 to 1980, Goswami (1985) found the sediment yield at Pandu to be 804 tons/km2/year while at Bahadurgarh in Bangladesh it is 1128 tons/km2/year. The major tributaries contributing high rates of sediment yield are given in Table 13.5 along with their catchment areas. Table 13.5 Tributary Dibhing Subansiri Ranganadi Jia Bhareli Dhansiri (N) Puthimari Pagladiya Beki (Manas) Lohit Buri Dihing Erosion rates at the tributaries of the Brahmaputra (Goswami, 1985) Catchment area A km 2 12 120 27 400 3077 11 300 1657 1787 38 300 36 300 22 077 4923 Sediment yield in Tons/km2/year 3765 959 1569 4721 463 2887 1883 1581 1960 1129 It can be seen that the tributaries from the north bank have almost three times the sediment yield of south bank tributaries. This is due to different geologic conditions, rainfall and the character of sediment. Similarly, for the catchment of the size of the Brahmaputra, its sediment yield is three to four times that of many rivers of the world. 416 River Morphology No bed-load measurements have been made on the Brahmaputra. However, some efforts have been to estimate it by Goswami (1988) using well-known bed-load equations of Schoklitsch, Kalinske, Meyer-Peter and Müller, Einstein, and Bagnold. It may however be mentioned that these equations have been developed using very coarse material whereas the bed material of the Brahmaputra is very fine. Hence the results are questionable. WAPCOS (1993) has used total-load equations of Samaga, Ranga Raju et al. and Laursen and computed total load; knowing measured suspended load, ratio of QB/QS was obtained for various discharges at Pandu. The average of these results indicate the following: Q m3/s QB/Q s 3600 0.053 9600 0.501 18 800 0.189 36 000 0.087 Even though the results are erratic, above analyses of Goswami and WAPCOS indicates that, the assumption that the river carries 10-15 percent of suspended load as bed-load may be a good approximation. On the basis of yearly sediment transport rate, estimates have been made of the annual depth of erosion in different catchments. These are tabulated below. River Amazon Mississippi Yangtze Ganga Brahmaputra Kosi Average erosion rate in mm/year 0.09 0.07 0.33 0.57 0.41 to 0.81 1.88 It can be seen that average rates of erosion are quite high in the Kosi and Brahmaputra catchments. Goswami (1988) studied the discharges which carry significant amount total suspended load and found that flow events which occur one day or more in a year carry on the average 65.5 percent of the total suspended load, while flow events which occur 7.0 days in year carry on the average 31.25 percent of total suspended load. Thus he showed that maximum flows do not necessarily carry the maximum percent of yearly sediment load. Information about flow duration curve and sediment transport rates can be utilized to determine the characteristic discharges for the stream. It has been mentioned that bankful discharges at Pancharatna and Pandu are approximately 30 000 m3/s and 27 000 m3/s respectively while the mean annual discharges at these stations are 16 154 and 15 756 m3/s. The bed generative discharge at Pancharatna is estimated to be 56 000 m3/s. 13.15 PLAN-FORMS As mentioned earlier, for the major part in India the Brahmaputra is braided. The configuration of the channel undergoes major changes in response to variations in the flow and sediment load. During Morphology of Some Indian Rivers 417 November to March when the river discharge is low, the channel is highly braided with a number of bars and islands. After April-May when discharge starts increasing these islands and bars get submerged and river looks straight. It is interesting to note that when low flow data are plotted on t * vs. WS/D criterion of Agarwal, these data indicate braided plan form, while t * vs. WS0.2/D criterion of Kishi indicates presence of multiple bars. In general, in the case of braided rivers, the number of channels formed by islands depends on width to depth. Figure 13.18 shows the braided pattern at Dibrugarh in 1928, 1976 and 1987. The changes in the channel patterns and their numbers as well as changes in islands in their shape and number may be noted. The braiding index defined by Brice as the ratio of twice the sum of lengths of bars and islands in a reach to the length of the reach measured mid-way between the banks has been calculated at Dibrugarh and upstream of Palasbari by Goswami (1988) and found to be between 5 and 7 indicating the highly braided nature of the river. Some of the islands formed are small and they get submerged and changed as flood level rises; new or modified islands are formed during the recession of floods. However, some islands become permanent and can grow due to vegetation grown on them. Majule is one such and is the largest island in the Brahmaputra, north of Jorhat at the confluence of the Subansiri with the Brahmaputra. The island is about 80 km in length along east-west direction 10 to15 km in north-south direction, and is habitated by 140 000 people. Originally it was 1245 km2 in area prior to 1950 earthquake and due to continuous erosion its area was reduced to 924 km2 in 1971 and to 880 km2 in 1993. This is a matter of great concern to engineers (see NIH, 1998) and efforts are being made to control erosion. Another aspect of changing islands is the change of talweg of main branch of the braided river with change in flow. This change is large during medium flows, relatively little during high flows, and very erratic during the falling stages i.e. during November to March. This is very important when the river is used for navigation. This aspect of wandering of the talweg and its relation to bank erosion has been discussed by Coleman (1969). With the Brahmaputra carrying heavy load of sediment, bed condition changes rapidly and drastically with change in flow. Deposition of sediment at one place causes erosion at other place and triggers changes in talweg from one position to another within the bank-line. Study of stage and position of talweg at Sirajgang (Bangladesh) indicated that during the rising stage the amplitude of movement of the talweg is large, as much as 3000 m and the movement is gradual; during the peak-flows it is relatively small and the talweg remains more or less stable. However, during the falling stage the talweg movement is irregular and sudden in fashion. During low water stage the main channel in a braided river, which carries large portion of the discharge, is commonly situated near one of the river-banks and is slightly curved moving from one bank to other. During the rising stage when the flow increases rapidly, while the flow tends to follow the deep channel, it is not able to develop rapidly to accommodate increasing flow and hence there is tendency for bank-cutting and sloughing. This action helps migration of the talweg in lateral direction. Bank sloughing depends on the nature of the bank material. In as much as the nature of bank material varies along the length, sloughing is not uniform; hence the erosion of the banks is different at different locations thereby changing the river path. The shifting of the talweg is also influenced by the movement of sand bars and mid-channel islands. This occurs most frequently during the falling stage and the shift is erratic and sudden. Shifting of the talweg close to the bank causes bank erosion. 418 1928 Sonarighat River Morphology N Dibrugarh Bur Mai jan Dib rive r i dih ru ang rive (a) r Scale 0 5 10 rive r 20 km 1976 Sonarighat N Dibrugarh Bur i dih ang rive Mai Di r jan bru Scale 0 5 10 20 km rive r riv er (b) 1987 Sonarighat N Dibrugarh Bur i dih ang rive r Scale 0 5 10 20 km Ma ija nr Di ive r bru riv (c) Fig. 13.18 er Plan form of the Brahmaputra near Dibrugarh in years 1928, 1976 and 1987 Morphology of Some Indian Rivers 419 13.16 FLOODING AND FLOOD PROTECTION Floods in Assam valley seem to have increased in frequency and intensity since 1950 earthquake when the hills were mutilated to a great extent. Floods are caused due to heavy rainfall in the mountains and valley, and melting of snow in the mountains. Eighty to ninety percent of rainfall occurs during May to September during which time snow also melts. Considerable construction activity and deforestation brings down large quantities of sediment along with the flow which is responsible for aggradation in some reaches. The valley being wide and flat, an increase of 1 m water level during normal annual flood inundates large areas of flood plain. Encroachment on flood plain and islands accentuates the flood problem. Based on the analysis of satellite imageries it is found that during 1988 flood, flood plain 10 to 50 km in width on northern side and 5 to 30 km wide on southern side was inundated. When the Brahmaputra level is high the tributaries are not able to drain into the main river and cause inundation in their valleys due to backwater effect. Handique and Borgohain (1991) have given the statistics of flood damage in Assam valley as indicated below. Table 13.6 Flood damages during 1953-1989 in Assam valley (Handique and Borgohain, 1991) Maximum (1988 figures) 3.823 334.10 663.84 232 Total area affected in M ha Crop area affected in M ha Damage to crops in crores Rs Total damage to crops, houses and public utilities in crores Rs Lives lost Average 0.97 26.67 54.67 38 Another effect of floods is erosion of banks which causes embayment. This sometimes continues till it joins the neighboring tributary. This results in shifting of outfall of the tributary. This is particularly true for south bank tributaries, since slope of tributaries on the south is flatter than that of tributaries on the northern side of the Brahmaputra river. To protect certain areas from flooding embankments (or levees) have been built on the northern and southern side of the river. Between 1954 and 1989 embankments over a total length of about 940 km of embankments have been constructed at critical reaches on both sides, these are shown in Fig. 13.10. These levees have top width ranging from 2.5 to 4.6 m, river side slope 3:1 and country side slope 2:1 and 8:1 with berm. Usually the free board is about 1.5 m. These levees are subjected to erosion and breaches at many places during high floods necessitating frequent costly repairs, and provision of spurs. Over 300 breaches have occurred since the levee system was established. Since earlier embankments were constructed with inadequate data, these had to be raised and strengthened as the data on higher floods were obtained. Some towns also had to be protected by dykes. The present day system of embankments provides protection to about 14 000 km2 of about 30 000 km2 of the total flood prone area. Many times the embankments have been cut by lateral erosion, not at the highest flood but at somewhat lower stages and hence the low lying areas have been flooded even though the level of water in the river is below that of the embankment. As mentioned earlier, floods in the tributaries are also caused when the Brahmaputra river flows at a higher level than the tributaries thereby causing backwater in them. 420 River Morphology To overcome the problems of flood control, bank protection, maintaining navigation channel for river commerce and to protect cities, towns and other man-made structures, various types of works have been constructed. These are (see Weller, 1970). 1. Bandals: These are made from bamboo poles driven 1 to 2 m into river bottom and spaced at 0.5 to 1.0 m center to center. Mats of woven bamboo 0.8 m ´ 0.5 m are placed on bamboo poles near the water surface. Bandals are inclined 30° – 40° with current. These slow down the current and induce deposition, direct the flow into proposed channel and provide adequate depth for navigation. 2. Bottom Panels: Bottom panels are structures arranged on the bottom at such angles to flow so as to divert bottom current out of existing channel and induce accretion in that area. Each panel is composed of corrugated metal sheets 1.0 m high and 4 to 5 m long. They are placed against bamboo poles driven 0.6 to 1.0 m apart. 3. Bamboo Palisading: this is composed of a row of bamboo poles 7.5 to 10 cm in diameter placed closely together and driven 1.2 to 1.5 m into the river bed and 1.8 to 2.4 m of bamboo extended above the bed. This structure is strengthened by split bamboo placed horizontally at 0.3 m apart and tied to the vertical bamboo poles with wire. The structure is also adequately braced. This is placed immediately offshore and approximately parallel to the bank to be protected. 4. Bamboo spurs. 5. Tree spurs. 6. Anchored trees. 7. Tree Branch Revetment: This is a method of bank protection in which a mattress of tree branches is placed against the bank to arrest erosion. Three or four branches of trees each 3.0 to 3.6 m long are tied together by wire and weighted with stones placed in sacks. This assembly is anchored to the bank with wire ropes and sunk to the river bottom. Other bundles are placed, each over lapping the last until the line of branches is extended from deep water to the bank. 8. Floating rafts and cages made from bamboo. 9. Permeable screens made from bamboo. 10. Timber and stone spurs. 11. Stone revetment in which 15 to 25 cm diameter crushed stones are placed with a thickness of 0.5 to 0.6 m on 1 V: 1.5 H slope. Figure 13.19 shows bamboo porcupine spur, permeable pipe spur and RCC porcupine screen used on the Brahmaputra. 13.17 DRAINAGE OF HINTER LANDS Because of inadequate hydrologic data in the earlier times, adequate numbers of sluices have not been provided in the embankments as a result of which there occurs drainage congestion in some areas, because the natural drainage from protected areas is cut off. It may also be mentioned that physiographic features of the region as a whole are responsible in causing, at least partly, widespread floods. The valley is surrounded on all sides by hills and mountains with only one inadequate outlet near Dubri though which the entire discharge of the Brahmaputra must pass. The rivers in the region are also marked by the absence of lakes that exercise moderating influence on floods. Morphology of Some Indian Rivers 421 Fig. 13.19 Some river training structures on the Brahmaputra 422 River Morphology 13.18 RIVER BED CHANGES IN BRAHMAPUTRA Bed level changes in the Brahmaputra have been studied by different methods. Panchang (1964) plotted the yearly-observed low water level and observed flood level at Dibrugarh for the period 1912 to 1963, see Fig. 13.19, on which he also indicated the occurrence of earthquakes of moderate and severe intensity. WAPCOS (1993) report extended the range of data up to 1966. This figure clearly shows the gradual rise of high flood level; however since these levels are for different flood discharges, one has to examine the trend of yearly lowest water levels. Since daily low water stages for the season are believed to be comparable from year to year the same can be taken as a reflection of river bed from year to year. This curve in Fig. 13.20 shows lowering of bed during 1914-1918 at the rate of 143 mm/year, 1918-1922 period shows gradual aggradation of bed at the rate of 210 mm/year. Similarly during 1947-51 there is rapid aggradation at 832 mm/year. These changes are partly due to occurrence of earthquakes in the region and passage of bed-wave in the downstream direction. The other approach is based on sediment balance using continuity equation for sediment, according to which during a given time Inflow of sediment U RInflow of sediment from U ROutflow from U R Net storage or U R S T from upstream V W+S T in between tributaries V W-S T the reach V W=S Tloss of sedimetnV W This method was used by Goswami (1985); his studies have indicated that during the period study 1971-1979, the Bessamara–Burabandha, and the Pandu–Jogighopa reaches have undergone excessive aggradation, while the Ranaghat–Bessamara and the Bhurabandha–Pandu reaches have experienced some degradation. WAPCOS (1993) had also collected the cross-sectional data at 65 stations along the length of the Brahmaputra for the period 1957-1989. On the basis of the analysis of these data WAPCOS concluded that there was no significant deposition or erosion in different reaches; however the erosion Earthquake with strong intensity felt in Assam 106 104 Water level m Earthquake with mild intensity felt in Assam Yearly observed highest W.L. 102 100 Yearly observed lowest W.L. (1931 - 66) y = – 0.44 + 0.0536x (1951 - 66) y = 112.37 + 0.058x 98 96 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 Years Fig. 13.20 Brahmaputra water levels at Dibrugarh (1913 – 66) Morphology of Some Indian Rivers 423 or deposition was not uniform in different reaches. Aggradation of 5 cm/year to erosion of 7 cm/year was observed at different locations during 1957-1971. During 1971-1977 about 11.3 cm/year erosion has taken place. During 1981-1989, aggradation of 2.7 cm/year on the average is noticed; this aggradation has taken place upstream of Dibrugarh at the rate of 16.8 cm/year during this period. During 1959-1989, on the average aggradation has occurred at most of the places at the rate of 1.8 cm/year. On the whole it was concluded that large quantities of sediment, which entered the Brahmaputra in 1950, moved downstream till 1971 and hence deposition is indicated at various places. After 1971 up to 1981, the sediment is eroded at decreasing rate and started aggradation after 1981 up to 1989. It is felt that additional data are needed to study aggradation/degradation problem in the Brahmaputra and relating it to flow conditions as well as channel contractions and expansions. 13.19 DEVELOPMENT PLANS The development plans and activities in the Brahmaputra basin are designed to find the solution to problems discussed earlier and to make the maximum use of the water resources for the betterment of people in the region. Specifically the plan focuses on 1. control of floods; 2. aggradation of river channel; 3. drainage problem of hinter land; 4. extending embankments and controlling breaches as well as bank cutting and thereby protecting towns on the banks of the stream; and 5. development leading to extension of irrigation, water power and navigation. To achieve these objectives Brahmaputra Board has been established in 1981 and has been given the responsibility of preparing the master plan for development. In the first phase of development additional hydrologic, hydro meteorological and micro-earthquake recording stations are being established. Modernization of flood forecasting network is also being done. Construction of additional length of embankments and improvement of the existing ones are being undertaken. Further, new schemes for the removal of drainage congestion are identified and will be undertaken. In the second phase, multipurpose dam projects on the tributaries Pagladiya, Dihang and Subansiri and watershed management and soil conservation programmes will be undertaken. The recent studies (see Goswami, 2004) indicate that even though Brahmaputra basin as a whole has a forest cover of 59 percent, in some parts such as Assam it is only 20 percent and is reducing due to deforestation. Shifting cultivation involving slash and burn technique of agriculture, being widely practised in the hills of North –East and Bhutan, is also a major cause of land degradation and excess sediment. Hence, watershed management programme would control sediment load and reduce aggradation problem. The Brahmaputra has been serving, for a long time, as an important means of communication in Assam (India), and this water route was linked to Kolkata, Bihar and U.P. Assam used to transport oil, tea, jute, timber, coal, paddy and rice by inland waterways. Prior to 1950 earthquake, 93 percent of tea and 90 percent of jute crop used to be transported to Kolkata by river. However, after 1950, due to extensive deterioration of the Brahmaputra channel due to earthquake, and the establishment of effective rail and road transport, these percentages gradually dropped to 65 for tea and 25 for jute in 1965. By 1990 the total inland waterways transport was only 2 to 3 percent of total traffic by road, rail and inland waterways transport. 424 River Morphology Even though the first steam boat service on the Brahmaputra started only thirty years after the first steam boat service started on the Mississippi in 1801, the inland navigation developed much faster on the Mississippi because of massive and sustained investments on the water course and development of navigation over 150 years. On the other hand, the Brahmaputra remained essentially in its natural, unregulated and undisciplined state, with the only major concern for flood control. Hence, in the recent times Inland Waterways Authority of India and the Directorate of Inland Water Transport of Assam have taken some initial steps to carry preliminary studies (see IWAI 1990) to develop water transport on the Brahmaputra and its tributaries. There are a number of inland ports on the Brahmaputra such as Dibrugarh, Neamati, Tezpur, Guwahati, Pandu, Jogighopa, and Dubri. However, modern facilities of permanent nature for cargo handling do not exist in any of these ports; hence these are being planned. Plans are being formulated for fully utilizing the potential of the Brahmaputra for inland water transport. In the first stage design vessel of 100 m length, 12 m width and 2.5 to 3.0 m draft are suggested. To make the river fully navigable, a number of actions need to be taken such as stabilization of river course, checking formation of shoals, providing minimum depths and widths at low flows, adequate bend radii and moderate velocity. 13.20 ROLE OF DREDGING There is some discussion as to the role of dredging in the management of the Brahmaputra river. In the past (see Baruah and Gogoi, 2004) experimental dredging has been used in the Chimna area near Palasbari, 30 km downstream of Guwahati in 1974-75. The objective was to control erosion of the embankment system, which was in danger. It was proposed to dredge cut a channel of 30 m width, and 7 km length to channelise the flow and reduce the flow through channel near northern bank. However, before the work of dredging was completed, flash flood came. It was later found that the proposed channel did not develop. However, dredging at Alikash area 40 km from Guwahati on the south side of Brahmaputra, to control erosion by dredging a pre-aligned channel of length 2.24 km, width 50 m and side slope 1V:2H was successful. Similarly dredging has been used on come tributaries to change the local flow, remove blockages or opening mouths of the tributaries. However, it is the considered opinion that dredging on the main river over long stretches to reduce aggradation is not feasible and economical. However, when the river is used for navigation and generates adequate resources, dredging can be used to maintain minimum depths at critical sections and for other local adjustments of the section. References Baruah, B.B. (1969) Flood and Erosion Control in the Brahmaputra Valley by Making Use of Natural Features, Central Fuels Research Institute, 59 p. Baruah, B. and Gogoi, P.K. (2004) Experiences of Dredging in Brahmaputra and Tributary, Seminar on Silting of Rivers, Problems and Solutions, CWC, New Delhi, 6 p. Bristow, C.S. (1993) Sedimentary Structures Exposed in Bar Tops in the Brahmaputra River, Bangladesh. In Braided Rivers (Eds. Best, J.L. and Bristow C.S.) Geol. Society, Special Publication No. 75m, pp. 277-289. Carlson B. (1985) Erosion and Sedimentation Processes in Nepalese Himalays. International Centre for Integrated Mountain Development (ICIMOD), Occasional Paper No. 1, Khatmandu, Nepal. Morphology of Some Indian Rivers 425 CBIP (1986) Seminar on Morphology of Ganga River. Central Board of Irrigation and Power, New Delhi, November, 146 p. Chitale, S. V. (1984) Kosi -The Problem River of North Bihar. Journal of Irrigation and Power of CBIP, Vol.41, no.2, April, pp.197-202. Chitale, S. V. (2000) Future of the Kosi River and the Kosi Project. Journal of Institution of Engineers (India), Vol. 81, December, pp.109-114. Coleman, J.M. (1969) Brahmaputra River: Channel Processes and Sedimentation. Sedimentary Geology, Vol. 3, pp. 129-239. CWPRS (2002) Mathematical Model Studies for Proposed Bridge on Kosi River at NH-57 Crossing (Bihar). Central Water and Power Research Station, Technical Report No. 3926, Sept. Dhanju, M.S. (1976) Study of Kosi River Flood Plains by Remote Sensing. Hydrology Review, vol.2, No.4, October, pp. 43-48. Garde, R.J. and Kothyari, U.C. (1989) Land Slides and Their Effects on River Regime, Proc. 4th Intl. Symposium on River Sedimentation, Beijing (China), Vol. 2, pp. 819-831. Garde, R. J., Ranga Raju, K. G., Pande, P.K., Asawa, G. L., Kothyari, U. C. and Srivastava R. (1990) Mathematical Modelling of the Morphological Changes in the River Kosi. Civil Engg. Department, University of Roorkee (Now IIT Roorkee), 58p. Gee, E.P. (1951) The Assam Earthquake of 1950. Jour. Of Bombay Natural History Society, Vol. 50, No. 3, pp. 629-635. Godbole, M.L. (1986) Morphology of the Gandak and the Kosi Rivers – A Comparison. Seminar on Morphology of Ganga. CBIP, New Delhi, November, pp. 29-51 Gohain, K. and Parkash B. (1990) Morphology of the Kosi Megafan. Chapter 8 in Alluvial Fans: A Field Approach (Ed. Rachocki, A. H. and Church, M.) John Wiley and Sons Ltd., pp.151-177. Gole, C.V. and Chitale, S.V. (1966) Inland Delta Building Activity of Kosi River. JHD, Proc. ASCE, Vol. 92, No. HY-2, March, pp. 111-126. Goswami, D.C. (1985) The Pattern of Sediment Yield from River Basins of the Brahmaputra System, N.E. India. The North Eastern Geographer, Vol. 71, Nos. 1 and 2, pp. 1-11. Goswami, D.C. (1985a) Brahmaputra River, Assam, India: Physiography, Basin Denudation and Channel Aggradation. W.R. Research, Vol. 21, No. 7, July, pp. 959-978. Goswami, D.C. (1988) Estimation of Bed-Load Transport in the Brahmaputra River, Assam. Indian Journal of Earth Sciences, Vol. 15, No. 1, pp. 14-26. Goswami, D.C. (1988) Magnitude and Frequency of Fluvial Processes in the Brahmaputra Basin, Assam: Some Observations. Geomorphology and Enviironment, The Allahabad Geographical Soc., Allahabad (India), pp. 203-211. Goswami, D.C.(1990) Morphology of Brahmaputra (Cyclostyled Unpublished Lecture Notes). Goswami, D.C. (2004) Alluvial Regime and Channel Morphology of the Brahmaputra River : Some Observations. Seminar on Silting of Rivers, Problems and Solutions, CWC, New Delhi, 8p. Handique, G.R. and Borgohain, J.K. (1991) The Brahmaputra River System, The Senteniel, April 13. Handique, G.R. and Borgohain, J.K. (1991) Long Term Projects. The Senteniel, April 20. IWAI (1990) Detailed Report for Development of Inland Water Transport on national Waterway No. 2, Inland Waterways Authority of India Report. Jain, V. and Sinha, R. (2003) River Systems in the Gangetic Plains and Their Comparison with Siwaliks: A Review. Current Science, Vol. 84, No. 8, April, pp. 1025-1033. 426 River Morphology Jakhade, G.S., Murthy, A.S. and Sethurathinam (1984) Frequency Floods in Brahmaputra Valley. Journal of Irrigation and Power, CBIP (India), Jan., pp. 41-47. Mookerjea D, and Aich, B.N. (1963) Sedimentation in Kosi -A Unique Problem. Journal of Institution of Engineers (India) vol.43. b) Godbole, M.L. Morphology of the Gandak and the Kosi Rivers -A Comparison. pp39-S2. NIH (1998) Majuli River Island: Problems and Remedies – North Regional Research Centre, National Institute of Hydrology, Guwahati, 27p. NIH (1994) Erosion, Sedimentation and Flooding in River Kosi. National Institute of Hydrology, Roorkee, SR -26, 229p. Panchang, G.M. (1964) High Floods in Brahmaputra – A Retrospect. Journal of Irrigation and Power, CBIP (India), Jan., Vol. , pp. 67-71. Rao, K.L. (1979) India’s Water Wealth: Its Assessment, Uses and Projections. Orient Longman Limited. 267p. Sahai, R.N., Pande, P.K. and Garde, R.J. (1980) Aggradation in Eastern Kosi Main Canal. Proc. of 1 st Intl. Workshop on Alluvial River Problems, University of Roorkee (Now I.I.T., Roorkee), 2-73 to 78. Sanyal, N. (1980) Effect of Embankment of River Kosi. Proceedings of 1st International Workshop on Alluvial River Problems, Roorkee. Sinha, R.K. (1986) Morphology of the River Kosi, M. E. thesis, Water Resources Development Training Centre, University of Roorkee (Now IIT Roorkee), 51 p. Sinha, R. (1995) Sedimentology of Quaternary Alluvial Deposits of Gandak-Kosi Interfan, North Bihar Plains. Journal of Geol. Society of India, vol.46, November. pp. 521-532. Sinha, R., Friend P.F. and Switsur, V. R. (1996) Radiocarbon Dating and Sedimentation Rates in the Holocene Alluvial Sediments of the North Bihar Plains, India. Geol. Magazine, Vol.133, No.1, pp.85-90. Valdiya, K.S. (1999) Why Does the River Brahmaputra Remain Untamed? Current Science, Vol. 76, No. 10, 25 May, pp. 1301-1305. WAPCOS (1993) Morphological Studies of Brahmaputra River. Unpublished Report Prepared by Water and Power Consultancy Services (India) Ltd., New Delhi. Weller, H.E. (1970) Brahmaputra River Bank Protection in India. Journal of Irrigation and Power, CBIP (India), April, Vol. No., pp. 177-189. C H A P T E R 14 Rivers and Environment 14.1 INTRODUCTION Streams in natural condition generally exist in a state of dynamic equilibrium, in which the amount of sediment delivered to the channel from the drainage basin is in long-term balance with the capacity of the stream to transport sediment; in such a case, channel dimensions and slope remain fairly invariant and over a period of time there is neither aggradation or degradation. In such streams, a balance also exists between communities of aquatic organisms inhabiting in the stream and the biochemical processes that recycle nutrients from natural pollution sources to the water. The physical processes such as aeration, dispersion, currents and sedimentation, chemical processes such as photosynthesis, metabolism, and biological processes such as biological flocculation and precipitation act together and naturally purify water. Aerobic purification processes require free oxygen, and are dominant in natural streams, although anaerobic processes occur as well where free oxygen is absent. Organic matter and nutrients in the streams are decomposed and resynthesised through chemical reactions in association with aquatic organisms. The material is transformed by cycles of nitrogen, carbon, phosphorus and sulphur in aerobic decomposition. These processes create Biological Oxygen Demand (BOD) that depletes the dissolved oxygen in water. Re-oxygenation is effected through aeration, absorption and photosynthesis. Riffles and other turbulence creating units such as dunes, bars, and bends in the stream enhance aeration and oxygen absorption. Fish and other aquatic organisms that utilize dissolved oxygen in water for respiration may suffocate if oxygen concentration is severely depleted. Excessive loading of streams with organic matter and nutrients can create significant biochemical oxygen demand and reduce dissolved oxygen to critical levels. Pollution sources can be grouped into point sources and non-point sources. Domestic sewage and industrial wastes are called point sources because they are generally collected by a network of pipes and channels and carried to a single point of discharge. Pollution by point sources can be prevented by passing the pollutant through a properly designed waste treatment plant prior to discharging it into the stream. On the other hand, urban and agricultural runoffs are characterized by multiple discharge points. 428 River Morphology Treatment of non-point source wastes is generally difficult. Nutrient enrichment causes rapid multiplication of algae, blooming, death and decomposition during the low flow periods resulting in severe depletion in oxygen and fish kills. The aquatic organisms inhabiting natural streams can be classified into: Aquatic plants: These include seed bearing plants, mosses and liverworts, ferns, horse tails and algae. Aquatic organisms: Moulds, bacteria and viruses. Aquatic animals: These include vertebrates and invertebrates Vertebrates: Fish and amphibians Invertebrates: Mollusks (Mussels, snails, slugs) and anthropoids (insects spiders, mites), worms and protozoa Streams in their natural state tend to maintain equilibrium between populations of aquatic organisms and available food. The population dynamics of aquatic organisms in a stream ecosystem involves substrate utilization, food web, nutrient spiraling and the growth curve. The waste organic substances in the stream form the substrate on which micro organisms grow and become part of the food web. Growth of micro organisms follows sequent portions of the growth curve including nutritionally unrestricted exponential growth, nutritionally restricted growth, and stationary or declining growth due to environmental conditions. The circulation, capture, release and recapture of nutrients is known as nutrient spiraling. The ability of the stream to a assimilate nutrients and store them in the living tissue of plants and animals is termed as the assimilative capacity of the stream. The streams, which have a relatively high assimilative capacity, are known as healthy streams and this is needed for maintaining good water quality. The presence of larvae of stoneflies, caddisflies and dragonflies generally indicates good quality of water, whereas large populations of rat-tail, maggot, blood worm and sewage fungus indicates polluted water. Conditions or health of a stream ecosystem is reflected by its biological activity. Biological integrity is defined as the ability of an aquatic ecosystem to support and maintain a balanced, integrated, adaptive community of organisms having a species composition, diversity and functional organization compatible to that of the natural habitats of the region. The main factors and some of their important chemical, physical and biological components that influence and determine the integrity of surface water resources are: i) Flow Regime: Precipitation, run-off, high and low flows, stream velocity, base flow, land use, etc. ii) Habitat Structure: Channel morphology, pool-riffle sequence, bed material, slope, in stream cover, canopy, substrate, width/depth ratio, sinuosity, bank stability, etc. iii) Energy Source: Sunlight, organic matter inputs, nutrients, seasonal cycles, primary and secondary production. iv) Chemical Variables: Dissolved oxygen, pH, temperature, alkalinity, solubility, adsorption, hardness, turbidity and nutrients. v) Biotic Factors: Reproduction, disease, parasitism, feeding, predation and competition. Any natural disturbance or human activity that affects one or more of the above factors will affect the biological integrity and hence water quality. Rivers and Environment 429 14.2 ACTIONS CAUSING DISTURBANCE IN STREAM SYSTEM AND THEIR IMPACTS (OSMG 2004) Stream system can be affected by human actions or natural disturbances in the catchment, in the stream corridors or in the stream. These actions include: i) Deforestation, construction activity and agricultural activity in the basin. ii) Construction of dams and reservoirs and other hydraulic structures such as energy dissipators, spillways, hydro-power plants, bridges, irrigation outlets, locks, bank protection works and embankments. iii) Development of water resources projects, water-power projects and thermal projects along stream banks. iv) Development of irrigation, flood plains and uplands. v) Stream canalization for navigation and flood control using methods such as cut-offs, stream straightening and flow diversion. vi) Dredging of channels and disposal of dredged material. vii) Use of streams for discharging urban sewage, industrial wastes and heated discharges. As a result of the above mentioned actions causing disturbance in the stream system, the following changes may take place in the stream ecosystem: i) Changes in physical and chemical aspects of water quality and in-flow regime. ii) Modification of channel and ecosystem morphology. iii) Excessive non-point source pollution including sedimentation and nutrient enrichment. iv) Deterioration of stream substrate quality and stability. v) Destabilization of stream banks and bed. vi) Modification of water temperature regime by removal of tree canopy, induction of thermal discharge, and alteration of base flow regime. vii) Introduction of exotic species that disrupt dynamic balance. viii) Problems arising out of displacement and resettlement of population such as transfer of diseases. It is not possible to discuss the impacts of all these activities on river channels and water quality in the context of the theme of the text. Hence, only effect of construction of dams and reservoirs and power plants, and some aspects of pollution of river waters will be discussed here. 14.3 ENVIORNMENTAL EFFECTS OF HYDRAULIC STRUCTURES When one wants to study the effects of hydraulic structures on the environment, one should study the probable effects on water quality, land, atmosphere and society. Parameters to be studied for water quality have already been mentioned in general earlier and details are given in sections 14.4 and 14.8. As regards the land one should consider salts, sedimentation, erosion, aggradation or degradation, vegetation, landslides and reservoir induced seismicity, terrestrial animals, ground water levels and recreation. The aspects related to atmosphere are air pollution, humidity, temperature and evaporation. Social aspects will be many which may include displacement, development and prosperity. 430 River Morphology It is necessary to ensure that the identified effects are truly significant and that some significant effects have not been overlooked. TCEEHS (1978) recommends the effects be described by one of the four numbers 1, 2, 3, 4 to indicate the dependence; thus 1. Variable may be increased by causal factor, 2. Variable may be decreased by causal factor, 3. Variable may be increased or decreased by causal factor, and 4. Variable is unaffected by causal factor. The hydraulic structures that can be considered include reservoirs, dams, outlets, energy dissipators, power plants, bridges, sediment excluders and ejectors, embankments, spurs and channel rectification works such as cut-offs, channel contractions and dredging. 14.4 DAMS AND RESERVOIRS Since ancient times dams have been constructed on streams and reservoirs have been formed. Generally dams and reservoirs serve many purposes such as flood control, power generation, supplying water for irrigation, drinking and industrial use, navigation and recreation. Since independence, India has witnessed rapid growth in the construction of large dams and elaborate canal networks. Over 4000 projects have been constructed in last five decades and 700 projects have been proposed to meet increased demand for power and achieve larger irrigation potential (Raghuvanshi et al. 2000). This activity has caused several social, ecological and economic problems. As a result of completion of such water resources projects, the society is greatly benefited in terms of dependable and clean drinking water, greater availability of food, better health, sanitation and increased per capita income; availability of increased power has also resulted in greater industrial activity and better living standards. Tourism and recreational facilities created by water resources projects have led to social and cultural improvements e.g., Brindavan gardens, Ramganga garden, Kalinadi Kunj, Jaikwadi garden and Gobindsagar reservoir. (Goel and Agarwal, 2000). Flocking of rare species of birds and increase in wild life have also been reported near Ramganga, Rihand and Matatila reservoirs. As against these beneficial effects, a number of adverse effects have also been reported. Formation of reservoirs due to construction of dams submerges large areas including those of forests and a number of people are ousted from submerged areas. Table 14.1 gives some data on submergence, ousted number of people and installed power capacity. Thus, it can be seen that as a result of construction of these dams, large areas including forests have been submerged and ousted a large number of people from their homes. Resettlement and compensation to inhabitants of the submerged areas include determination of areas that will be submerged, evaluating compensation for their properties, selection of alternative sites for settlement and distribution of land. Such considerations were not made in the case of the Volga lake in Ghana which submerged about 8200 km2 area. The submergence area was greatly underestimated. Similarly, in the case of the Roseires reservoir on the Blue Nile river in Sudan, only a few months before submergence people were asked to move and submergence was underestimated by two metres (Murthy 1976). Submergence of forest areas affects the habitat of many wild life species as can be seen from Table–14.2. Rivers and Environment 431 Table 14.1 Project Narmadasagar Ukai – Kakrapur Bargi Sardar Sarovar Omkareshwar Idukki Tehri Submergence areas and number of oustees under some existing and proposed hydroelectric projects (Raghuvanshi et al. 2000) Total area of submergence 91 348 60 000 36 729 34 996 9393 6475 5200 Forest area submerged (ha) 40 332 22 260 18 000 11 640 2471 6475 1600 Number of oustees 150 000 50 000 114 000 45 515 12 295 4500 85 600 Installed capacity (MW) 1000 300 90 690 390 230 2400 Table 14.2 Sr. No. 1. 2. 3. 4. 5. 6. 7. 8. Submergence of forests and wild life habitats under hydroelectric projects (Raghuvanshi et al. 2000) Forest area under submergence (ha) 40 332 11 600 6475 2800 1690 1600 990 280 Project name Narmadasagar multipurpose project Sardar Sarovar multi-purpose project Idukki hydroelectric project Parmbikulam Aliyar project Kariakutty Karapara multi-purpose project Tehri hydroelectric project Rajghat irrigation project Ramganga hydroelectric project Characteristic wild life species in submergence zone Tigers, sambar, chital, fishing cat and otter Four horned antelope, crocodile and otter Elephants Tiger, elephant, gaur Lion tailed macaque, nilgiri langur, tiger, elephant, sloth bear, gaur Himalayan mountain sheep Tiger, black buck, crocodile, great Indian bustard Tiger, elephant, hog bear, gharial Two other environmental effects of construction of large dams for water storage and its utilization are water logging and salinization, and water-borne diseases. About 2 to 3 million ha of land every year is going out of production due to salinity problems. Water logging results primarily from inadequate drainage and over irrigation, and to a lesser extent, from seepage from canals and ditches. Water logging concentrates salts, drawn up from lower portions of the soil in the plant’s rooting zone. The build up of sodium in the soil is particularly detrimental form of salinization which is difficult to rectify. The irrigation-induced salinity can arise as a result of use of any irrigation water, irrigation of saline soils, and rising levels of saline ground water combined with inadequate leaching. Water-borne or water related diseases are commonly associated with the introduction of irrigation. The diseases most directly linked with irrigation are malaria, bilharzias, filaria, cholera, gastroenteritis, viral encephalitis and goitre. Other irrigation related health risks include those associated with increased 432 River Morphology use of fertilizers, herbicides and pesticides. The occurrence of these diseases in the population have been noticed in Ghana, Nigeria, Egypt, Ethiopia and other countries. Large versus Small Dams Construction of large dams and reservoirs usually entails enormous costs and displacement of a large number of people as can be seen from Table 14.1. Resettlement of these oustees is many times neglected and hence leads often to protests, hunger strikes, stoppage of work and costly litigations that further delay the work. Unfortunately, people who are likely to be affected are not consulted or taken into confidence. Further, we do not have a National Rehabilitation Policy and credible implementing and monitoring procedures for rehabilitation. There is always a complaint that these people do not get fair compensation and a guaranteed share in the prosperity that the project brings. These conditions need immediate improvement. Considering these effects, many environmentalists argue that instead of building one large dam, a few small dams should be built. However, this idea is not feasible for the following reasons (Indiresan 2000). i) A number of small dams cannot control floods or generate electricity as a high dam can. ii) Per 1000 m3 of storage, the capital cost for large, medium and small dams varies in the ratio of approximately 1:3:6; hence it will be costlier to build smaller dams than a single large dam for achieving the same storage. iii) Other things being equal, doubling height of dam increases the storage by about eight times and power potential sixteen times; hence it is better to build large dams when feasible. iv) Since rainfall in India is erratic and occurs in 3 or 4 months, water needs to be stored to meet irrigation, water supply and power needs especially when drought occurs. This is unlike in Europe where precipitation occurs all through. Hence large dams are needed. v) Evaporation loss in India is about 1.2 to 1.4 m annually; hence, storage required has to be large. Further, it has to be realized that providing food, drinking water and power to millions of people is more important than preventing displacement of a few thousand people. This is not to say that the legitimate needs and aspirations of the oustees should be overlooked. Similarly, legitimate actions have to be taken to protect the environment. In the three gorges project about one third of the investment has been set aside for rehabilitation and environmental protection. Considering all these aspects it may prudent to have good mix of large and small dams for the development of water resources in the country. Reservoir Induced Seismicity It has been found all over the world that in some cases, after the reservoir is filled, the adjacent areas are subjected to reservoir-induced earthquakes (Kolhi and Bhandari 1991, Gupta 1992). Such reservoir– induced earthquakes have occurred after impoundment of the Shivajisagar lake formed by Koyna dam and at Bhatsa dam in Maharashtra, and at Sriramsagar dam on the Godavari in India. Such earthquakes have also occurred at Hsinfengkian reservoir in China, at lake Mead formed by Hoover dam on the Colorado river in U.S.A., Nurek and Tokgotul reservoirs in Russia, Aswan dam in Egypt and at many other places. A few details about reservoir-induced earthquakes at Koyna dam can be given. The Koyna dam of height 103 m and the Shivajisagar reservoir are located in peninsular India about 200 km from Pune. Rivers and Environment 433 Soon after impoundment of the reservoir in 1962, the nearby area started experiencing earth tremors and the frequency of these tremors increased from the middle of 1963 onwards. These tremors were accompanied by sounds similar to those of blasting. Between 1963 and 1967, five earthquakes occurred which were strong enough to be recorded by many seismological observatories in India. The major earthquake at Koyna occurred on December 10, 1967, which had a focal depth of 10 km ± 2 km and had a magnitude of 6.0. This earthquake claimed about 200 lives, injured over 1500 people and rendered thousands homeless. It also caused damage to hoist tower of the dam and developed horizontal cracks on both the upstream and downstream faces of a number of monoliths, and damaged a large number of houses, bridges and culverts. Realising the socio-economic importance of reservoir induced seismicity, UNESCO formed a working group on these phenomena and since then a number of symposia on reservoir-induced seismicity have been organized. A number of theories/explanations have been suggested to explain why and under what conditions the seismicity is caused. Investigation of fluid injection-induced earthquakes at the Rocky Mountain Arsenal near Denver, Colorado, (U.S.A.) during 1960’s and Evan’s work on the mechanism of triggering earthquakes by increase of fluid pressure have helped in understanding the phenomenon of reservoir-induced seismicity. Gough and Gough have explained triggering of earthquakes due to incremental stress caused by water load in the reservoir. Gupta et al. (see Gupta 1992) identified the rate of increase of water level, duration of loading, maximum levels reached and the duration of retention of high water levels among the important factors affecting the frequency and magnitude of reservoir-induced earthquakes. Other studies by Nyland, and Bell and Nur have also indicated that the three main effects of reservoir loading relevant to inducing earthquakes are (i) the elastic stress increase that follows the filling of the reservoir; (ii) the increase in pore fluid pressure in saturated rocks due to decrease in pore volume caused by compaction in response to elastic stress increase; (iii) and pore pressure changes related to fluid migration. It is also found that reservoir-induced earthquakes are associated with shear fracturing of rocks. The shear strength of rocks is related to the ratio of the shear stress along the fault to the normal effective stress across the fault, the latter being equal to normal stress minus the pore pressure. Hence, increase in pore pressure can trigger earthquake if rocks are under initial shear stress. During the past four decades, scientists have gained some knowledge about RIS but a lot more needs to be learned. It may be mentioned that the largest reservoirimpoundment triggered earthquakes have exceeded magnitude of six. On the basis of RIS observations on a number of dams, it has been well established that major RIS events are produced by enhanced foreshock activity. Such analysis has indicated that, if two earthquakes of magnitude greater than 4 occur at RIS site within a short interval of say 2-3 weeks, there is an enhanced probability for occurrence of earthquake of magnitude greater than 5. Studies have suggested that in the case of a large reservoir (volume in excess of 1000 Mm3 usually impounded behind a dam height greater than 100 m) it is desirable to carry out geological mapping for the entire reservoir area to determine faults and competence of rocks (Gupta 1992). 14.5 WATER QUALITY IN RESERVOIRS Construction of a dam forms a reservoir the capacity of which is progressively reduced due to sedimentation. Since depending on the capacity to inflow ratio for the reservoir, the water is stored in the reservoir for different time periods before it is released; the quality of water in the reservoir is different from that flowing in the stream. The following factors need to be considered in the study of water quality in reservoirs (TCEEHS 1978). 434 River Morphology Temperature Temperature plays an important role in controlling many hydraulic, chemical and biological phenomena. In this regard, the temperature range as well as rate of temperature change are important. The temperature affects the behaviour of biological organisms, and the rates of chemical and biochemical reactions. A 10°C rise in temperature approximately doubles the reaction rate. Similarly, thermal stratification takes place in deep reservoirs. Near the water surface is the layer known as epilimnion in which temperature is fairly constant and it is in aerobic condition. Near the bottom is a cold-water layer known as hypolimnion in which there is depletion of dissolved oxygen. Rise in temperature upto a certain limit may increase the growth rate of fish and beyond that limit a rapid die-off takes place. Warm water fish may survive in temperature higher than 34°C. At higher temperature, fish may starve due to increased rate of respiration and higher food requirement. Temperature is also found to affect reproduction ability, digestion and longevity of fish. Turbidity The turbidity of water due to suspended material reduces the light transmission characteristics of water. Hence, increase in turbidity decreases the algae growth. Suspended solids can also clog gills of fish and cover benthic organisms. pH pH is the logarithm of the reciprocal of hydrogen ion concentration in water and it normally varies from 6 to 9. A value of pH less than seven indicates acidic liquid while value greater than seven indicates alkaline liquid. pH plays an important role in many chemical and biological reactions. Extremes in pH as well as fluctuations in its value can have adverse effect on aquatic life. Anaerobic activities in the hypolimnion of some reservoirs can reduce pH resulting in slightly acidic waters. Salinity Dissolved solids can enter the reservoir through the inflowing water or through ground water infiltration. Salinity of the reservoir water can also increase as a combined result of high evaporation rates and long detention times. High salinity water entering a reservoir can establish density stratification patterns similar to thermal stratification. In such cases mixing of oxygen-rich surface waters into oxygen-depleted bottom water is inhibited at the interface named chemocline. Water of increased salinity may result in discharges that are less suited as a source of water for industrial and irrigation uses. In addition, higher the salinity, the lower is the oxygen saturation concentration for water. Dissolved Oxygen (DO) Dissolved oxygen concentration in water plays an important role in determining the quality of discharged water. Adequate DO is necessary for the life of aquatic organisms and fish. Equilibrium concentration of DO resulting when water is in contact with air is known as saturation concentration and this is directly proportional to pressure and inversely proportional to salinity and temperature. Ultimately DO concentration is equal to net oxygen sources and sinks affecting the aquatic system. Oxygen is obtained by water by photosynthetic activity by aquatic plant and re-aeration from the atmosphere. Dissolved oxygen is consumed by the following processes: (i) biochemical oxygen demand Rivers and Environment 435 resulting from oxidation of nitrogenous and carbonaceous matter; (ii) respiration by benthic organisms, fish, zooplankton and other species; (iii) chemical oxygen demand resulting from oxidation of methane, hydrogen sulphide and certain other compounds of iron and manganese; and (iv) inflow of water with low dissolved oxygen. When dissolved oxygen concentration becomes very low, toxic and noxious substances can be generated and in extreme case fish kills can result. Iron and Manganese The source of these metals in impounded water can be from geological out croppings in reservoir bottom, from inflow of tributary streams, ground water infiltration, and decomposition of organic material by biological action. For drinking water, their concentrations should be limited to 0.30 mg/ l and 0.05 mg/ l respectively. Phosphorus Phosphorus is an essential nutrient for the growth of aquatic plants; but only a small amount is required for this growth. Orthophosphate form of phosphorus is readily taken up and assimilated by phytoplankton and periphyton. Reservoirs tend to reduce phosphorus content of water discharged through mechanisms of biological uptake and assimilation, chemical precipitation and physical adsorption. Most soluble phosphorus released to the water results from decomposition of sediments. Under anaerobic conditions, high concentrations of phosphorus occur in the hypolimnion of reservoir. If this water is released downstream, it can result in algae blooms which reduces the dissolved oxygen. Nitrogen If dissolved nitrogen concentration in water is very large it can cause gas bubble disease in fish in which gas bubbles develop under skin, in the fins, tail and mouth, and behind eye-balls. This can lead to gas embolism and death. Nitrogen is available in water in five forms: Nitrogen gas, organic, nitrite, nitrate and ammonia nitrogen. The nitrogen cycle can operate either in aerobic or anaerobic conditions. Under aerobic conditions, nitrates are reduced to ammonia form and then assimilated in cellular form. Under anaerobic conditions, different reactions take place in nitrogen cycle and nitrates are reduced to ammonia and then under certain conditions to nitrogen gas, a process known as nitrification. In aquatic nitrogen cycle, other process that may take place is nitrogen fixation in which molecular nitrogen, in the presence of energy source, is incorporated into biological material. Vaidya et al. (2004) have analysed the water quality data from two reservoirs–Panchet and Ujjani– in the Bhima basin in Maharashtra (India). Panchet is located in the hilly regions and is less affected by human activity; Ujjani on the other hand is a much larger reservoir and is affected by quality and quantity of water received from upstream industrial areas. Over a year phosphorus as orthophosphate, phytoplankton and secchi disk depths indicating clarity of water were measured. High concentration of soluble reactive phosphate or orthophosphate helps in growth of algae and depletion of dissolved oxygen. In both reservoirs orthophosphates over the entire depth varied between 0.10 to 0.25 mg/ l , while secchi depth in monsoon and in winter ranged 0.8 to 2.0, and 2.0 to 4.0 m respectively. 436 River Morphology 14.6 THERMAL AND HYDRO-POWER PLANTS Often thermal and nuclear power plants are built near reservoirs or rivers. These plants release a large amount of heat as waste heat. Part of it is released in air through chimneys and the remaining heat is extracted by cooling water circulated in condensers. This heated water passes through an open channel and then is discharged into a cooling pond such as reservoir or a stream. The temperature of cooling water rises through 8°–10°C during the passage through condensers. Discharge of this water back into the reservoir or stream poses a major engineering and environmental problem. As discussed earlier temperature change causes physical, chemical and biological effects on aquatic organisms, as well as the thermal structure of water body. Hence, Environmental Protection Act 1986 stipulates that the temperature rise of cooling water discharge from thermal power stations to the receiving body should not be more than 5°C higher than the intake water temperature. The water body receiving heated discharge is usually divided into two zones: (i) small near field of high temperature where dissipation of heat takes place primarily due to entrainment of cold water from the surrounding, and (ii) large far field with relatively lower temperature where head loss is due to evaporation and radiation. Since temperature continuously decreases as one goes away from discharge point, Maharashtra Pollution Control Board states that the temperature in the receiving water at 15 m from the discharge point shall not be more than 5°C above the ambient temperature. Vaidhankar and Deshmukh (1992) who carried out survey of reservoir temperatures at Obra, Jatpura and Korba thermal power stations found temperature rise of 5°C or more over relatively short distance. The length of initial mixing zone for deep pond of Obra was about 100 m while for shallow reservoir of Korba it was 500 m. Further depending on the depth of reservoir, vertical stratification was found to exist with temperature difference of 3° to 10°C between bottom and the surface. As regards the hydropower plants, a few environmental problems can be briefly mentioned. Water passing through the turbines entraps nitrogen and water released downstream in some cases is found to be super saturated with nitrogen (El-Shami 1977). This causes gas-bubble disease and increase in fish mortality rate in the tail race channel. In some cases, the turbine water releases have low dissolved oxygen concentration partly due to inflow water having low dissolved oxygen and additional depletion of oxygen in the hypolimnion of the reservoir. Since a depletion of DO concentration below a certain limit is harmful to aquatic organisms, in extreme cases artificial re-aeration can be resorted to. This was studied in laboratory and pilot field tests on Fort Patrick Henry dam in U.S.A. (Ruane et al. 1977). In this case, laboratory and small-scale field studies were conducted to select the most promising diffuser on the basis of oxygen transfer efficiency, operation and maintenance problems and economics. The selected diffuser from small-scale experiments was tested in a pilot scale tests and then modifications were made in it. Change in discharge releases in the downstream channel because of construction of hydropower plant on a stream can cause some positive and some adverse effects. Drastic reduction in flow in the downstream channel will reduce plant and animal populations associated with the area. Further, regulated flow in the downstream channel could prevent the adverse effects on the aquatic habitat, given that a certain minimum flow is always maintained. Rivers and Environment 437 14.7 RECREATION With rapid growth in population, the demand for outdoor recreation is continually increasing. Since water-oriented activities play an important role in outdoor recreation, rivers and reservoirs are increasingly used for fishing, hunting, boating and other water sports. Sedimentation and erosion can seriously hamper these activities, increase the maintenance cost and reduce the life of such facilities. A few of the problems associated with recreation that are caused by erosion and sedimentation are briefly discussed below (Bondurant and Livesey (1965): 1. Deposition of inert silt and sand is sterile as far as propagation of either fish or fish food is concerned. Similarly, thin deposits of fine sediment and sludge seal the surface against circulation of water and oxygen and can wipe out hatches of various food species. Formation of normal reservoir delta also tends to inhibit reproduction of fish that travel to open river upstream of reservoir to spawn. 2. Small inlets to reservoirs, known as coves, are ideal sheltered places for boat docks and launching ramps. If these are blocked by sedimentation, recreation can be hampered. Such deposition can also occur due to littoral drift caused by wave action. Adequate provision of a dyke can control the situation. 3. Erosion of bank line by wave action is also undesirable from the point of view of recreation. Hence, if bank line is eroding, proper bank protection needs to be given. 4. Fishing and boating are also practised in the clear water releases below a dam. Many times sand bars in such area are used for docking and launching of boats. If such bars are not protected, they are likely to be washed away in a degrading stream. 14.8 STREAM POLLUTION Rivers while they flow from mountains to plains and then to the sea experience withdrawals of water along their courses for agricultural, industrial or municipal use. Similarly, on their way pollution in the form human and animal waste, agricultural drainage water and industrial effluents are discharged in them. If the existing pollution in flow is greater than the natural assimilative capacity of the stream, the quality of water deteriorates in the downstream direction, as is the case in many Indian rivers. Pollution results in loss of aquatic flora and fauna leading to loss of livelihood for river fisher folk, impact on human health from polluted water, loss of habitat for many bird species, and loss to inland navigation potential. Further, many Indian rivers are linked with history and religions beliefs of the people and are used for bathing and religious rites. Hence, people expect the rivers to be clean and unpolluted. However, since many cities and villages on the stream banks do not have sewage and wastewater treatment facilities, untreated sewage and industrial wastewater are dumped in the rivers. Floods tend to wash down this polluted water but in lean season, the problem is aggravated. Table 14.3 lists the major pollutant categories and principal sources of pollutants. The major pollutant categories are briefly discussed below. Anything that can be oxidized in receiving water uses molecular oxygen in water and consumes dissolved oxygen (DO). Human wastes, food residue, waste from food processing and paper industries, crop residues, leaves etc. fall in this category. Nitrogen and phosphorus are the major nutrients required for growth. Problem arises when they become excessive and the food web is grossly disturbed. Excessive nutrients lead to growth of 438 Table 14.3 River Morphology Major pollutant categories and principal sources of pollutants (Davis and Cornwell 1998) Point sources Non-point sources Agricultural runoff Yes Yes Yes Yes Yes No Yes No Pollutant category Oxygen demanding material Nutrients Pathogens Suspended Solids/Sediment Salts Toxic Metals Toxic Organic Chemicals Heat Domestic wastes Yes Yes Yes Yes No No No No Industrial wastes Yes Yes Yes Yes Yes Yes Yes Yes Urban runoff Yes Yes Yes Yes Yes Yes No No algae, which in turn becomes oxygen-demanding material when they die. Major sources of nutrients are detergents, fertilizers and food processing wastes. Pathogenic organisms are micro organisms found in wastewaters and include bacteria, viruses and protozoa excreted by diseased persons and animals. Excess of pathogenic organisms in water make it unfit for drinking and swimming. Organic suspended solids may exert demand on oxygen. Inorganic suspended solids create problems for fish spawning. Colloidal suspended material reduces penetration of light in water. High concentration of dissolved solids make the water unfit for drinking if its concentration increases beyond a certain level, even crops can be damaged and soils may become unfit for agriculture. Toxic metals and toxic organic compounds enter rivers through agriculture runoff, urban runoff and industrial wastes. These include pesticides, herbicides and zinc. These are concentrated in food chain and are very harmful to aquatic species and human beings. As discussed earlier heat is discharged in reservoirs and rivers by thermal power plants and also by some industrial processes. It can be beneficial to some aquatic fish while harmful to others. The general parameters determined from laboratory analysis, to evaluate water quality and degree of pollution are pH, conductivity, BOD, Nitrate-N, Nitrite-N, and fecal coliform. The general parameters estimated once a year or so include phenophelne alkalinity, total alkalinity, dissolved solids, total suspended solids, nitrogen, hardness, fluoride, phosphate, chlorides etc. Similarly, micropollutants in water and sediment that are determined when needed include heavy metals, cyanide, total iron and pesticides. 14.9 RIVER ACTION PLANS For maintaining the quality of river water, the pollution levels in the Indian rivers have been obtained by monitoring a limited number of physical, chemical and biological parameters, which could determine the changes in the characteristics of water. In view of the deterioration in water quality over the past few years, the Government of India has taken initiative to improve the water quality of the Ganga and other rivers, and given water quality criteria for designated best uses (DBU) as listed in Table 14.4. A brief mention may be made of Ganga Action Plan, which was launched in 1985 to prevent pollution of the Rivers and Environment 439 Table 14.4 Water quality criteria for designated best uses Parameters pH DOMg/l BODl mg/l 2.0 or less 5.0 or less 3.0 or less - Class Total coliform MPN/100 ml 50 500 5000 - Free ammonia mg/l 12 A B C D E Drinking water source without treatment but with disinfection Outdoor organized bathing Drinking water source after treatment and disinfection Wildlife and fisheries Irrigation, Industrial cooling and controlled waste disposed 6.5 – 8.5 6.5 – 8.5 6.5 – 8.5 6.5 – 8.5 6.5 – 8.5 6.5 or more 5.0 or more 4.0 or more 4.0 or more Electrical conductivity 22-60µ mho/cm Sodium absorption ratio 26 Boron: 2.6 mg/l Ganga river and improve its waste quality. The plan was initiated after the initial survey by Central Pollution control Board which indicated that out of the total pollution load on account of the municipal sewage, 80 percent came from class 1 towns having population over 100 000. The plan was cast to restore river water quality to the following standards. BOD not greater than 3 mg/l DO not less than 5 mg/l Total coliform not greater than 10 000 MPN per 1000 l Fecal not greater than 2500 MPN To accomplish this task, 281 schemes have been sanctioned under Ganga Action Plan, which include interception and diversion schemes, sewage treatment plants, low-cost toilets and electric crematories. With the completion of these schemes, improvement has been notices in levels of BOD and DO. Hence, second phase of GAP and NRCP (National River Conservation Plan) has been started along 18 interstate rivers. 14.10 STREAM RESTORATION Stream restoration and mitigation is a process that involves recognizing natural and human induced disturbances that degrade the form and function of the stream and riparian ecosystems or prevent its recovery to a sustainable condition. Restoration includes a number of activities designed to enable stream corridors to recovers dynamic equilibrium and function to maintain channel dimensions, pattern and profile so that over a period of time the stream channel does not degrade or aggrade. FISRWG (1998) identifies three levels of stream improvement: (a) restoration (b) rehabilitation and (c) reclamation. Restoration is defined as the establishment of the structure and function of ecosystems. Ecological restoration involves returning an ecosystem as closely as possible to the pre-disturbance conditions and function. Restoration also implies that it will provide the highest level of aquatic and biological diversity possible. The basic principles of stream restoration include: 440 River Morphology 1. analysis of channel history and evolution; 2. analysis of cause and effect of change; 3. analysis of current condition; 4. development of specific restoration goals and objectives prior to design; 5. holistic approach to account for channel process, riparian and aquatic function; 6. consideration of passive practices such as fencing against livestock; 7. natural channel design to restore function. Rehabilitation is defined as a procedure for making the land useful again after a disturbance. It involves the recovery of ecosystem functions and processes in a degrading habitat. Rehabilitation establishes geological and hydrologically stable landscapes that support biological diversity. Reclamation is defined as a series of activities intended to change the function of an ecosystem, such as changing wetland to farmland. Restoration principles, practices and methods of monitoring are being evolved on the basis of studies on small and medium sized streams in some western countries such as U.S.A. and U.K. The structures used in stream restoration include vegetation, wood, and constructed rock and wood structures. In U.K. (see Brookes 1995) river restoration project (RRP) was formed to promote restoration of rivers for conservation, recreation and amenity. The project utilizes the expertise of river ecologists, engineers, planners, fisheries biologists and geomorphologists to establish demonstration projects to show how restoration techniques can be utilized to recreate natural ecosystem in damaged river corridors (Brookes 1995). Research needs to be carried out to study their effectiveness in degrading and aggrading streams, and to extend the methods to larger streams. References Bondurant D.C. and Livesey, R.H. (1965) Sedimentation Aspects in Recreational Planning. JHD, Proc. ASCE, Vol. 91, No. HY5, Pt. 1, Sept. pp. 51-64. Brookes, A. (1995) River Channel Restoration: Theory and Practice. In Changing River Channels (Eds. Gurnell, A. and Petts, G.) John Wiley and Sons, Chichester, pp. 369-388. Davis, M.L. and Cornwell, D.A. (1998) Introduction to Environmental Engineering. WCB McGraw Hill Company, 3rd Edition. El-Shami, F.M. (1977) Environmental Impacts of Hydro Electric Power Plants. JHD, Proc. ASCE, Vol. 103, No. HY9, Sept., pp. 1007-1020. FISRWG (1998) Stream Corridor Restoration: Principles, Processes and Practices. Federal Inter Agency Stream Restoration Working Group. National Technical Information Service, Springfield, Va (U.S.A.). Gupta, H.K. (1992) Reservoir Induced Earthquakes. Development in Geotechnical Engineering, No. 64, Elsevier Book Co., Amsterdam, 364 p. Goel, R.S. and Agarwal, K.K. (2000) River Valley Projects and Environment: Concerns and Management in India context. In Environmental Impacts Assessment in Water Resources Projects (Ed. Goel, R.S.), Oxford and IBH Publishing Co., New Delhi, pp. 71-87. Indiresan, P.V. (2000) Dams or Damn: Perceptions and Facts. In Environmental Impacts Assessment in Water Resources Projects (Ed. Goel, R.S.), Oxford and IBH Publishing Co., New Delhi, pp. 89-103. Rivers and Environment 441 Kolhi, S. and Bhandari, R.K. (1991) Reservoir Induced Seismicity in Peninsular India. Proc. Institution of Engineers (I) Civil, Vol. 72, pp. 47-55. Murthy, B.N. (1976) Men-made Lakes and its Effects on Ecosystem. CBIP (India), Miscellaneous Publication No. 6, 26 p. OSMG (2004) Natural Stream Processes. Ohio Stream Management Guide No. 3, 8 p. Raghuvanshi, A., Mathur, V.B. and Mukherjee, S.K. (2000) Hydropower Projects and Challenges to Wildlife Conservation in India – An Overview. In Environmental Impacts Assessment of Water Resources Projects (Ed. Goel, R.S.) Oxford and IBH Publishing Co., New Delhi, pp. 389-401. Ruane, R.J., Vijander, S. and Nicholas, W.R. (1977) Aeration of Hydro Releases at Fort Patric Henry Dam. JHD, Proc. ASCE, Vol. 103, No. HY10, Oct. pp. 1135-1145. TCEEHS (1978) Environmental Effects of Hydraulic Structures. Task Committee on Environmental Effects of Hydraulic Structures. JHD, Proc. ASCE, Vol. 104, No. HY2, Feb. pp. 203-221. Vaidhankar, D.V., and Deshmukh, D.N. (1992) Environmental Effects of Hot Water Releases From Power Plants and Some Practical Aspects of Regulation Acts in India. Proc. of 1st National Symposium on Environmental Hydraulics, CWPRS, Pune (India), June 1992, pp. 274-293. Vaidya, S., Swain, K.K., Kamble, K.J. and Basu, A.K. (2004) Tropic State of Panchet and Ujjani Reservoirs in Relation to Phosphorus Concentration and Other Factors. International Conference on Hydraulic Engineering: Research and Practices. IIT Roorkee (India), Vol. 2, Oct. pp. 407-416. C H A P T E R 15 Data Requirements for Morphological Studies 15.1 INTRODUCTION When one plans to develop the water resources of the basin and utilise them fully, it is necessary to have the master plan for the development which will take into account the needs of the population at present and in near future, and the potential for development of the water resources. Such a plan may include conservation of water for irrigation, domestic and industrial use, power generation, flood control to protect certain areas from flooding, and channel improvement for stabilizing the river channel to make the whole or part of the stream navigable. It may also include use of water bodies for recreational purposes and environmental management of the basin. Further these developments may have to be carried out on the main river and the tributaries. In all probability these developments would be executed over a long period spanning a few decades, even though the general overall plan may be developed in the initial stages, and based on the experience gained and the performance of the project during earlier stages, the plan may be modified later. Irrespective of the details about the development, the engineer concerned with planning must carry out the morphological study of the river which would indicate the present health of the river and would also indicate how the river regime would change after the developmental works are executed. Such a morphological study is essential for every river. Even though some data required for such a study will be purpose specific, it is possible to discuss, in general, about the data required for the morphological studies and their significance. Geologists, hydrologists, hydraulic engineers, cartographers, archaeologists and other scientists collect these data. 15.2 MAPS, AIR-PHOTOS, SATELLITE IMAGERIES An index map showing the river reach under consideration and on which are shown the major tributaries, locations of various structures (weirs, dams, bridges) on the river, gauging-sites and Data Requirements for Morphological Studies 443 important cities is the starting point. Further information can be obtained from topo-sheets; topo-sheets would give information about valley or river slope, rough idea about plan-form of the river, and changes in it along the stream length. If such older topo-sheets are available it is possible to examine them to find out if the river has tendency for shifting its course or changing its plan-form; also range of shifting and control points can be identified. Such control points are of great use in locating bridges and barrages. Aerial photographs for general purpose (1:50000 scale) and for special purpose (1:10000 to 1:5000 scale) that can cover 10-15 km length of the river can be used for the same purpose. Such photographs are also utilised to study changes in the channel induced by human activities such as regulation, reservoir construction, gravel dredging, deforestation, afforestation, changes in agricultural practice, urbanisation, mining activity, bank stabilisation, and channel straightening. Also considerable information about the terrain surrounding the valley, valley features, terraces, floodplain, presence of bars and channel patterns, ox-bow lakes and abandoned channels can be obtained from such photographs. In this connection one is referred to an excellent publication by Kellerhals et al. (1972) that gives a set of aerial photographs of some rivers in Alberta (Canada) along with relevant hydraulic data. Historical changes in the river can many times be discerned from archaeological excavation as was done in the case of the Tigris river in Mesopotamia (Modern Iraq) and the river Saraswati in India. Since in the earlier times the villages or the settlements used to be located on the banks of the river, it was possible to find out the changes in the courses of the Tigris, Euphrates and Diyala from archaeological excavations, see Garde (1978). Figure 10.4 shows the present and ancient course of the Tigris. Historical data on channel changes can be studied in relation to the climatic, hydrological and environmental changes that have taken place in earlier times. Hence such information is very valuable. Remote Sensing (Lillesand and Kiefer 1994) The technique of remote sensing derives information about the objects on the earth’s surface without physically coming in contact with it. The process involves (i) making observations using sensors mounted on platforms; (ii) recording the observations on a suitable medium; (iii) transmission of data to the ground station; (iv) corrections to data to remove geometric and radiometric distortions, which is called pre-processing; and (v) generation of output in the form of photographic enlargements with appropriate rectification. These are called satellite imageries. The sensors used are either active sensors or passive sensors. Sensors, which illuminate the target with energy and measure the reflected/scattered radiation from the target are called active sensors e.g., active radiometers and radars. Sensors which sense reflection/radiation from the earth illuminated by a natural source such as the sun are called passive sensors. While discussing about the sensors the spatial resolution and spectral resolution need special mention. Spatial resolution is the length of the side of the area on the ground represented by a picture element (commonly called as pixel) on the image. Spectral resolution is the width of the spectral band and the number of spectral bands in which the image is taken. Narrow band widths in certain regions of electro-magnetic spectrum allow one to discriminate various features more easily. Hence one needs to have more number of spectral bands each having narrow band width and these bands together should cover the entire spectral range. The sensors are mounted on a platform such as a balloon, an aircraft or a satellite, which are at a considerable height from the earth’s surface. The size of the object that can be discriminated by the sensor depends on the resolving power of the sensor and the height of the platform. As one goes higher and higher, larger areas can be seen and covered by the sensor; however the size of the object appears 444 River Morphology smaller as one goes higher and in fact certain objects may not be seen at all beyond a certain height. The satellites used for remote sensing are of two types, namely geostationary and near earth, polar orbiting. Geostationary satellites are stationary with respect to the earth and are at an altitude of about 36000 km. These are used for meteorological applications. Near earth, polar orbiting satellites are at a much lower altitude, a few hundred to few thousand kilometres. In India, the National Remote Sensing Agency (NRSA) at Hyderabad has been carrying out air borne remote sensing surveys on behalf of various users. With the flight facility, air surveys from about 150 m to 10,000 m altitude can be carried out. The sensors available with NRSA are aerial survey cameras, air borne multi spectral scanner, air borne magnetometer systems, ocean colour radiometer and side looking air borne radar. NRSA also acquires data from Indian and various other satellite missions. Some of these are IRSA-1A, 1-B, 1-C, 1-D, IRS-P2. Satellite radar data are also available from ERS-1, ERS-2 and Japanese Earth Resources Satellite Fuyo-1, in addition to Landsat and SPOT archival data. Similarly very high resolution data are available from Russian DD-1, KVR-100 and KFA-3000 systems. Their ground resolution varies from 70 m to about 2 m. The data are recorded in high density digital tapes (HDT) or digital linear tapes (DLT), CD-ROMS, or 8 mm exabyte digital tapes on a variety of media and formats such as photographic products [black and white, false colour composite (FCC)] and digital products (CD-ROMS and DATS). These data products can be effectively used in morphological, water resources and other studies. To obtain satellite data one needs to specify i) area of interest i.e., latitude and longitude; ii) survey of India topo-sheet number; iii) satellite mission; iv) path and row; v) date of pass; and vi) sensor. Knowing these details one can browse through the imageries at NRSA site for different dates of pass and for different satellites and sensors and choose the desired ones Digital Image Processing Visual interpretation of an imagery or photograph requires extensive training and intensive labour, and the special characteristics are not always fully evaluated because of limited ability of the eye to distinguish tonal values of an image. Hence, in the applications where spectral patterns are highly informative, it is preferable to analyse digital, rather than pictorial image data. The digital image data are composed of a two-dimensional array of discrete picture elements or pixels. The intensity of each pixel corresponds to the average brightness or radiance measured electronically over the ground area for that pixel. In digital image data, each pixel in a grid stores a digital number (DN) which is a positive integer quantifying original electrical signal from the sensor, using analogue to digital conversion. Typically the DN values of the digital image range from 0 to 255, the range representing the set of integers that can be recorded using 8-bit binary computer coding scale. The digital image processing (DIP) involves manipulation and interpretation of digital images with the aid of computer. The digital image is fed into the computer one pixel at a time. The computer is programmed to insert these data into an equation or series of equations, and store the results of the Data Requirements for Morphological Studies 445 computation for each pixel. These results form a new digital image that may be displayed or recorded in pictorial format or it may be further manipulated by additional programme. The digital image processing further involves three operations namely, (a) pre-processing (b) image enhancement, and (c) image classification. Pre-processing operation involves the initial processing of data to correct geometric distortions, to calibrate the data radiometrically, and to eliminate noise present in the data. Image enhancement operation involves use of techniques for increasing the visual distinctions between features in the scene in order to increase the amount of information that can be visually interpreted from the data. The enhanced image can be displayed on the monitor or can be recorded in a hard copy format in black and white or in colour. Image classification is done to automatically categorise all pixels in an image into land cover classes or themes. Normally multi-spectral data are used to perform the image classification. Such classification can distinguish land mass, water bodies, vegetal cover etc. Remote sensing can be used to study the following aspects of river morphology: 1. flood inundation mapping, 2. variability and changes in channel plan-form, 3. flood plain geomorphology–identification of flood plain features such as ox-bow lakes, levees, scroll bars, 4. identification of bank erosion zones, 5. vegetal cover in the catchment and its variation, and 6. types of land use in catchments including agricultural, urban and industrial developments and their spatial and temporal variation. The special advantage of remote sensing lies in the fact that data can be obtained at regular intervals of time and hence time varying phenomena in river morphology can be monitored and studied. Further, some areas may be inaccessible and hence visiting such places and collecting data may be otherwise impossible; in such situations remote sensing methods are useful. 15.3 LITHOLOGY AND TECTONICS Information about lithology is important to the river engineer in many ways. Some information on the type of rocks underlying the surface material is provided on the geomorphic map. Additional information can be collected from bore hole data at bridge and dam sites, from bore wells and other sources. Such data can be used to prepare lithological map. The infiltration, soil erosion from the catchment and overland flow are affected significantly by lithology, in addition to climate, vegetation, the rock type and structure, the drainage structure, drainage density and drainage frequency. River channel shape and longitudinal slope also depend on rock type; the plan-form of the river is also controlled by the material through which the river passes. Further, lithology governs the initial particle size of the bed material, its resistance to abrasion and therefore the reduction of sediment size along the river length. The reduction in slope along the length is related to reduction in sediment size and hence to lithology. The occurrence of large and medium earth quakes in the basin brings about important changes in the river regime because large quantity of sediment can be brought into the tributaries and main river due to land slides triggered by the earthquakes. A map showing major faults, and locations of such earthquakes along with their magnitude should be prepared. There are instances where rivers have been 446 River Morphology completely blocked due to such land slides and subsequently causing flash flood wave due to bursting of earth embankments, and ultimately affecting the river channel dimensions and plan-form. Slow uplift and subsidence of land is commonly known as neo-tectonics. Neo-tectonic activity can also include significant rates of movement along faults. Such slow uplift or subsidence of a few centimetres per decade can cause perceptible change in the river slope which in turn causes large scale cutting or deposition in the channel, widening of the channel, meander cut-offs and such other changes. Such changes have occurred in the Mississippi river during 19th century and in the case of the Diyala river, a major tributary of the Tigris river in Iraq. A progressive uplift over 6000 years caused the Diyala to incise about 15 m, see Schumm (1977). Hence, such tendencies need to be noted in the region under consideration and its probable effect assessed. Various fluvial anomalies such as local development of meanders or braided pattern, local narrowing or widening of channel, anomalous ponds, alluvial marshes or alluvial fills, variation of levee width, discontinuous levees, or variation in sinuosity are possible indications of neo-tectonics. 15.4 VEGETAL COVER The information on land use and vegetal cover is required for hydrologic studies as well as for the estimation of erosion rates. This information can be obtained from State Departments of Irrigation, satellite imageries and also from Irrigation Atlas maps prepared by the Government of India. Vegetal cover can be classified as arable area, scrub and grass lands, forest area and waste lands, their percent area found out and vegetal cover map for the area can also be prepared. Changes in land use will change the vegetal cover and affect discharge and erosion rate. Hence historical data on vegetal cover can be extremely useful in explaining change in erosion rate with time. 15.5 GEOMORPHIC MAP Geomorphic map is a map which includes relevant landforms, materials, and processes. Such a map is prepared using a set of efficient symbols, which are recommended by technical committees, and use of colour systems. Such a geomorphological map which may contain a lot of unwanted information can be converted into a purpose oriented map carrying only that information which is necessary for a specific use. Geomorphic maps are extensively used in planning and economic development related to regional and territorial planning, agriculture and forestry, civil engineering, and prospecting and exploitation of the natural resources. Geomorphological mapping as it is known today was first used in Poland in 1950’s and has been extensively used in Europe, USA and other countries. Information that can be included on a geomorphic map for river development can be changes in land slope and sharp junctions; if necessary contours can be shown by different colour. Depending on the requirement the mapping scale can be 1:10000 to 1:75000. Bedrock as well as geologic structure and superficial material can be shown. The symbols used for slopes, rocks, geologic structure, and superficial unconsolidated materials are shown in Fig. 15.1. Forms of fluvial origin such as streams, channels, point bars and oxbow lakes can also be shown. Slope instability features are also shown in the map using brown colour. In addition, symbols are also recommended for showing geologic structure etc. These symbols are shown in Fig. 15.2. Such a map can be of immense use in the initial stages of planning of the project. Cook and Doornkamp (1978) have shown a typical geomorphic map for an area in South Africa, see Fig. 15.3. 447 Angular convex break of slope Angular concave break of slope Smoothly convex change of slope Smoothly concave change of slope Angle of slope degrees River Morphology Cliffs (bedrock 40 or more) Break of slope concave & convex too close together Change of slope Convex slope unit Convex slope unit to allow use of separate symbols Morphological mapping symbols Sedimentary Chalk Limestone Dotomite Igneous Granite Diorite Metamorphic quartzite State phyllite C Snale Mudstone Siltstone Gabbro Rhyolite Schist Gneiss Sandstone Breccia Conglomerate Andesite Basalt Migmatite Marble Symbols for bed-rock lithology Duricrust Boulders angular Boulders rounded Gravel Sand Silt Clay Shells Peat Fig. 15.1 Symbols for superficial unconsolidated material 448 Stream River channel Dry river channel Later fall (rapids) Spring Erosion terrace Accumulation terrace Alluvial fan Delta Lovees River Morphology Permanent lake Point bars Temparary lake Area susceptible to flooding FLUVIAL EROSION OF SLOPES Rill Gully Sheet Sand bar Cut-off meander Oxbow lake Swamp Badlands Symbols of fluvial origin (usually shown in blue) Landslide (type undetermined) Rotational slide (with back tilt) Flow slide Mud slide Rock fall Solifluction lobe Non circular rotational slide with graben Sand run Soil creep Slope instability features (usually shown in brown) Faults 3 3 Showing relative movement of the two sides 1 Tick on downthrown side, made in degrees throw (T) in metres T 150 20 Horizontal strata Dip and strike (dip in degrees) Vertical strata (long axis is strike) Overturned strata Anticlinal axis (plunge in degrees) Synclinal axis (plunge in degrees) Joints (lines show true or ientation) 1 1 1 Symbols for geological structure (usually shown in purple) Fig. 15.2 Geomorphic symbols Data Requirements for Morphological Studies 449 Ws Ws Sc Sc Sc Sc Sc Sc Gr Gr Gr Sc Slope movement Talus slope-grass covered Slump Lithology Gr+ +Sc Ws Q Granite Igneous complex (mainly schist) WIthwater sand system (quartzite and shale) Quartz vein Strike of dipping beds Fault Fault (inferred) Morphology Angular crest of residual hill Crest of residual hill Residual hill Structure Group of small slumps Planation surface Superfical creep Rock wall-quartzile Drainage Rock wall-granite Narrow out crop of quartzite Permanent water course Ridge Impermanent water Major river incision Rill erosion Accumulation terrance Gullery erosion Spring Fig. 15.3 Typical geomorphic map (Cook and Doornkamp 1978) 15.6 BASIN CHARACTERISTICS AND MORPHOMETRY River processes are largely controlled by the topography of the drainage basin. A river tends to shift towards the position of topographic minimum, as observed in the case of the river Kosi in North India. Such topographic minimum occurs commonly due to subsidence. Topography also affects the manner in which the deposition takes place on the flood plain. Overbank deposits preferentially occur in low areas where the velocity is small, increasing the rate of aggradation at these sites and producing variation in the thickness and facies. The catchment characteristics that should be studied are catchment area, its shape, average catchment slope, vegetal cover characteristics, average drainage density and such other characteristics which affect the erosion rate in the catchment and determine the nature and magnitude of flood hydrograph. The morphometric parameters of a river basin assume great importance since they influence a number of hydrologic processes operating in the basin. Horton initiated the work of characterisation of 450 River Morphology river networks and then significant contributions were made Strahler, Shreve and Schumm. Among these parameters the area of the catchment A plays an important role since flood discharge is related to A by many investigators e.g. Dicken, Ryve, Inglis, Emmett and others by equations of the form Q = const An -1 ...(15.1) Other morphometric parameter is drainage density Dd km , which depends on lithology, geologic structure and soil characteristics of the basin. Drainage density will be higher in hard rock terrain which has low permeability. Greater amount of vegetation reduces the drainage density. Since drainage channels convey water and sediment from catchment area to the stream, importance of drainage density in the river processes can be appreciated. Along with other parameters erosion rate from the catchment depends on the drainage density and average catchment slope. Slope as a relief parameter not only affects velocity and sediment transport, but also affects the planform. Hypsometric curve that shows percentage of total elevation plotted against percent of total area, provides a representation of the erosional development of the drainage basin and should be prepared. The morphometric parameters are also useful in constructing the geomorphic instantaneous unit hydrograph (GIUH) in which the peak discharge and time to peak are related to Horton’s numbers RA, RB, RL and internal scale parameter LW and mean velocity of stream flow U-, see Rodriguez-Iturbe and Valdes (1979). 15.7 SEA-LEVEL FLUCTUATIONS, CLIMATIC AND OTHER CHANGES The relative sea level changes over a period of time can occur either on global scale or on regional scale. Global changes occur because of the mechanisms affecting the sea level worldwide; on the other hand the regional changes are caused because of uplift or subsidence of the land. On global scale the sea levels rose rapidly during 5000 B.C. and 3000 B.C. when the former ice sheets of the ice age melted. According to Gribben and Lamb (1978) between 2000 B.C. and the present the sea levels may have dropped by about three meters, while at present times the sea level is rising at the rate of 1 mm per year. Similarly significant changes in sea levels were observed on the east and west coast, and the Cauveri, the Mahanadi and the Godavari deltas in India during 5000–10000 years B.C. Even though these changes over a span of few decades may not be important, they would play an important role in river geometry, plan-form and aggradation/degradation over a period of centuries. The climatic changes have been discussed in the chapter on Palaeo hydrology. The changes in precipitation and temperature affect the vegetation, and runoffs as well as the sediment yield from the catchment. As these parameters control the river behaviour, they directly influence the channel planform and geometry. Therefore a river morphologists needs to collect the data on palaeo climatic and palaeo hydrologic changes, along with long term changes in the sea level and carefully assess their effect on the historical changes in the river. In addition detailed information be obtained on human activity in the catchment such as mining, road and other construction activity and deforestation or reforestation, which can directly influence the river flows and sediment load. Data Requirements for Morphological Studies 451 15.8 CROSS-SECTIONS, LONGITUDINAL SECTION AND PLAN-FORM The cross-sections and the longitudinal section for the river reach and its tributaries under investigation constitute the basic information required for hydraulic calculations. The cross-sections should preferably be taken at regular intervals along the reach and in addition at important places such as gauging stations, bridges, sharp contractions and at hydraulic structures. The cross-section should cover the entire width of the channel and flood plains on both sides up to permanent banks (khadirs). One should mark on each section the lowest, mean and maximum water levels along with point of minimum elevation, and also record information about the nature its occupancy of flood plain. An average crosssection in a given reach is often required for hydraulic and sediment local calculations. Sliding the cross-sections so that the average bed levels of the sections coincide and then tracing the average section can obtain this. The longitudinal section should be prepared from the average bed levels of the main channel at each section and on it one should show where the tributaries join as well as the locations of important places and gauging stations. Mean annual discharges of tributaries and main river can also be shown at critical sections. Similarly the bed slope in different reaches can be shown on the longitudinal section. The locations of important structures such as dams should also be depicted. The cross-sectional and longitudinal section data are useful in the calculation of water surface profiles as well as in assessing aggradation or degradation in subsequent periods. The knowledge of low water levels at a few sections over a period of time can be utilised to determine the changes in bed levels. A map or maps showing the plan-form of the river in the river-reach under consideration is also essential. Such a map shows plan-form of the river in different reaches, acute bends and meander loops, ox-bow lakes, unstable reaches of river, location of bridges, barrages and proposed locations of structures, and the talweg. Such information about cross-sections, longitudinal section and map showing plan-form is needed not only for main river but for the tributaries also. A preliminary study should also be made as average bend radius to channel width ratio as well as its minimum values. This information is useful in design of guide bunds and cut offs. The river plan-form is classified into straight, meandering and braided. One parameter often used in river plan-form analysis is sinuosity. Normally sinuosity is defined as the ratio talweg length to the length along the valley. However, Friend and Sinha (1993) have proposed that instead of talweg length, one should use mid-channel length in defining sinuosity. According to them the revised definition can be used for a single or multiple channels; in the case of multiple channels mid-channel length of the widest channel in each reach of the channel belt can be taken. For braided rivers, normally some form of a braiding index is used; however its definition varies from one investigator to other. Brice (1964) defined it as Braiding Index = Sum of length of all islands or bars in a reach Length of reach measured midway between banks of channel belt According to Rust (1978) Braiding Index = Sum of length from u / s divergence to d / s convergence of surrounding talwegs Mean of meander wave length for each channel belt 452 River Morphology Another parameters used for describing channel is its width/depth ratio. This ratio is related to characteristic discharge by Leopold and Maddock (1953), while it is related to Q and bank silt/clay percentage by Schumm (1977). The entrenchment of river can be quantified by the ratio Entrenchment Ratio = width of flood plain width of main channel While collecting data on river reaches of a dynamic river system for the purpose of its management, it is necessary to classify the reach on the basis of ordering of river network as done first by Horton (see Chapter 2), on the basis of plan-form and river sinuosity into straight, meandering or braided, according to channel size, or for management purposes based on lateral erosion or deposition, aggradation, degradation or armouring, susceptibility to disturbance, etc. If repeated river channel cross sections and plan-form surveys are not available, it is difficult to ascertain river channel adjustment that may take place over a period of 10 to 100 years especially if changes in channel depth are needed which cannot be obtained from aerial surveys. For this purpose the National River Authority of U.K. (NRA 1990) has developed a system to classify river channel susceptibility to disturbance. The site visit utilises the following scheme to classify the susceptibility of reach to disturbance and entered in GIS. Table 15.1 NRA (1990) Classification of river channel susceptibility to disturbance Susceptibility to change High Moderate Low Channelised Navigable Score 8-10 5-7 2-4 1 0 Description Channel conforms to natural state, exhibits signs of free meandering and has fully developed point bars, pools–riffles Shows signs of previous alterations but has many natural features and shows tendency towards recovering to higher state Substantially modified by previous works, likely to possess artificial cross-section, no bank-side vegetation. Channels where bed and banks are provided with hard protection High level of flow regulation, bank protection and needing strategic dredging Based on the experience of river channel adjustments in the Thames basin, U.K., the following classification for lateral and vertical adjustments is evolved (Downs 1992, 1995). Stable Depositiond Lateral migration Enlargement S D m e Stable R C Deposition migration M U Lateral Enlargement E Data Requirements for Morphological Studies 453 Channel Adjustment Categories SStable DDeposition MLateral migration EEnlargement dLess severe deposition meRUC- Less severe lateral migration Less severe enlargement Recovery reach Undercutting reach Compound reach Here category C represents channel-indicating aggradation with erosion of channel banks; category U represents continuous erosion and migration of full width channel with coarse inner bank deposits. Similarly, Rosgen (1996) has provided a scheme for management of rivers. This is based on the developments since 1973 and makes use of extensive data dominant bed material, river slope, width to depth ratio, sinuosity and entrenchment ratio. This is briefly discussed in Chapter VII. 15.9 BED AND BANK MATERIAL Information about the size distribution of bed and bank material is required in determining the resistance to flow, estimation of sediment load, channel adjustment processes and in the analysis of problems related bank stability and lateral erosion. If adequate time and resources are available the bed material should be sampled at all the sections along the channel in order to find out how the characteristics of bed material change along the river length; otherwise a few representative sections be chosen. Due to non-uniform flow across the channel width and change in lithology along the channel length, a large variation in size distribution can be found across the channel at a given section and along the river length. Hence, it is necessary to take enough number of samples in a cross section and along the length. A core sample is preferred especially if dunes are present, the core depth should be approximately equal to the dune height. Such samples in a cross section can be mixed to form a composite sample, whose size analysis is carried out. For reliable size distribution, the sample mass M used for the size analysis is related to d84 in mm as 3. 0 M = 0.02 d84 ...(15.2) where M is in Kg. For high accuracy the coefficient can be changed to 0.20 (see Jansen et al. (1979). Drag bucket or grab bucket sampler can be used for collecting the sample. These samplers have been discussed in detail by Garde and Ranga Raju (2000), Jansen et al. (1979) and Van Rijn (1986). In a few cases especially at bends and point bars, the coarse surface material should also be sampled. Size distribution of the sediment samples should be determined and it should be seen whether it follows normal or log-normal distribution. From the size distribution curves d90, d84.1, d65, d50, d35 and d15.9 should be listed at all the cross sections since these sizes appear in resistance and sediment transport calculations. Also geometric standard deviation sg and Kramer’s uniformity coefficient be determined. The median size of bed material decreases in the downstream direction due to abrasion and sorting. In the absence of other perturbations such as joining of the tributaries, d50 decreases with increasing in L as d50 ~ const e–a L where the constant = size of d50 when L = 0 and a is a coefficient. ...(15.3) 454 River Morphology As regards the bank material, it may be mentioned that in addition to the size distribution, other soil properties may be also important since bank material is usually cohesive. The presence of clay minerals plays an important role in the process of bank erosion. Water content, salt content and ion exchange affect the strength of clays. Leaching of salts from clay is found to reduce its strength to 1/100 to 1/1000th of its original value. In general cohesive soils offer greater resistance to erosion and hence there will be less sediment load in the case of cohesive banks. Assessment of the bank material can be done with the help of Table 15.2. The shear strength of the soil, its effective cohesion, and plasticity index are some other soil properties of interest when bank stability is considered. Table 15.2 gives the Field Engineering Estimates of Plasticity Index. Table 15.2 S1 S2 S3 S4 S5 R1 R2 R3 R4 R5 Very soft Soft Firm Stiff Very stiff Very soft rock Soft rock Hard rock Very hard rock Very very hard rock Field assessment of material (Cook and Doornkamp 1978) Easily moulded in fingers; shows distinct heel marks Moulds in fingers with strong pressure; faint heel marks Very difficult to mould in fingers; difficult to cut with hand spade Cannot be moulded in fingers; requires hand-picking for excavation Very tough and difficult to move with hand-pick requires great effort for excavation Material crumbled under firm blows with sharp pick Can be scraped and peeled with knife Can be broken if hand specimen is hammered Table 15.3 Term Non plastic Slightly plastic Medium plastic Highly plastic Field engineering estimates of plasticity index (Cook and Doornkamp 1978) Plasticity index 0-3 4-15 15-30 31 + Dry strength Very low Slight Medium High Field test Falls apart easily Easily crushed with fingers Difficult to crush Impossible to crush with fingers 15.10 HYDROLOGIC DATA A map showing the distribution of average annual rainfall over the catchment as well as average monthly rainfall distribution in the wettest month are always useful. In addition the rainfall distribution in the most severe storm that has occurred on the catchment is useful to the hydrologist. For meaningful estimation of flood hydrographs, data of spatial and temporal distribution of rain in the catchment is essential. Hourly rainfall data for all stations in catchment is generally preferred. But for large Data Requirements for Morphological Studies 455 catchments daily or ten-day average rainfall data for period of 25 to 30 years is generally preferred. In absence of such data Isopluvial maps of IMD giving rainfall distribution over catchment for average and severe conditions can be used. From these data the maximum, minimum, and average annual precipitation over the catchment as well as its standard deviation can be obtained. At the selected gauging stations along the river and at its tributaries, stage discharge relations should be available. In the absence of such a curve, the same can be prepared by using one of the resistance relationships discussed in Chapters 5 and 7. In addition, at a few selected gauging stations one should have yearly hydrographs from which water availability can be assessed. Flow duration curve at the gauging site is required in assessing yearly sediment transport and hence it should be prepared from all available data. From these data maximum, minimum and mean discharge can be obtained along with the corresponding stages or depths of flow. Annual flood discharge series at critical gauging stations should be analysed, appropriate probability distribution function fitted to the data and design flood discharges of known return period should be determined. The flood marks or flood levels during highest observed floods be obtained from local enquires; these are very useful for extrapolation of water levels for design or higher discharges. In the analysis of hydraulic geometry and related aspects of river morphology, various discharges are used. The Indian practice is to use the bankful discharge and relate channel width, depth, meander length and meander width to it. Since in many situations the bankful discharge is not well defined, mean annual discharge which has a return period of 2.33 years has been used by Schumm (1977) and Leopold and Maddock (1953). Some investigators also use average daily discharge for the whole year. Another discharge which is often used in Europe is the bed generative discharge. This is a constant discharge flowing through out the year that would carry the same amount of sediment load as carried by the varying discharge. These discharges should be evaluated. Knowledge of low discharge of a known dependability is useful in problems related to navigation, water supply, degradation of water quality, changes in water temperature, recreational use, and recreation of water. The information usually required is 7-day low flow of 10 year return period. Given a stream flow record of 15 or 20 years, or more, the annual minimum flow for 1, 3, 7, 14, 30, 60, 90, 120, 150 and 273 days can be obtained and a frequency curve prepared for each n – day flow. The frequency curve can be defined graphically or mathematically. For navigation studies along with the low discharge of known dependability, the width and the depth of flow in the reach are also needed to assess use of the river for navigation, and to plan river training works at low flows. The variation of low water level along the river length with time gives tendency of the river to aggrade or degrade. 15.11 SEDIMENT LOAD DATA Usually suspended load concentrations are measured at the gauging station along with the discharge measurement. If these measurements are not adequate, arrangements should be made to collect data with increased frequency especially during the high flows. Before the suspended sediment data are subjected to further analysis it is necessary to remove wash load from it since the rate of wash load transport is related to supply of sediment from the drainage basin whereas the rate of bed material transport is related to flow condition. Arbitrarily it is assumed that sediment load, finer than 10% size of 456 River Morphology bed material constitutes wash load. Thus knowing size distribution of suspended sediment concentration, the wash load can be estimated and removed. Knowing the average suspended load concentration and water discharge, the rate of suspended load transport can be obtained. Except in small rivers it is not possible to measure the rate of bed-load transport even though some bed-load samplers are available. For preliminary study it is prudent to assume that the bed-load is a certain percent of suspended load, its actual value depending on the sediment size etc. Otherwise one of the bed-load equations e.g., Meyer-Peter and Müller can be used. Some procedures are available for computing fraction wise bed-load transport. However, for preliminary analysis, such refinement may not be warranted. The suspended or total sediment transport rate thus obtained can be related to water discharge Q, by a relation of the type Qs or QT = const Qm ...(15.4) where m may vary from 1.2 to 3.0. The sediment rating curve for Qs or QT can be prepared for different sizes or different seasons. Such analysis is required to know the amount of sediment transported by the river every year. It is also useful in aggradation/degradation studies. One can also obtain the bed generative discharge by combining the flow duration curve and QT vs Q relationship. If any reservoirs have been built either on the main river or on its tributaries, their survey reports should be studied to obtain their rates of sedimentation. These give an idea about yearly sediment loads carried by the tributary or main stream. In the same manner catchment erosion rates under the present land use and urbanisation, as well as in the earlier times when human activity did not affect the catchment characteristics. On the basis of these estimates, along with changes in the river channel and flood plain levels, the sediment balance in the river system should be studied. This may involve relatively large time span of few decades to hundred years. This type of analysis involving sediment budget, and channel and flood plain accretion or erosion has been modelled by Trimble (1995) who has identified five conceptual models of valley storage fluxes depending on the time variation of the process (quasi steady or unsteady), climatic region (arid or humid) and perturbations in it, human activity, and amount of energy available. Such analysis enhances our understanding of the fluvial processes and throws light on the magnitude and time-scales of sediment storage fluxes under different environmental conditions. 15.12 STRATIGRAPHIC STUDIES The relationship between geomorphic processes and sediment is also important in understanding the history of rivers. Sediment on the surface is easily visible and can be easily studied as discussed earlier. The subsurface deposits in reservoirs, lakes, fans and deltas can be studied using techniques such as sinking deep bore holes and examining the cores, using seismic reflection data from different layers or electric log records. One can also see sediment exposed in sections in stream banks. Much information can be obtained from their studies. The basic rules followed by the geologists and geomorphologists in studying sediment in sections are (Kale and Gupta 2001): 1. Law of superposition: An underlying layer or strata is older than the overlying layer unless the strata have been disturbed. 2. Any disturbance to a layer of sediment is post-deposition in time, for example faults. 3. A vertical sequence of strata usually indicates a lateral continuing for the same strata. Data Requirements for Morphological Studies 457 These layered strata tell us about the operating process and the depositing environment. If the surface of contact between the two neighbouring strata is smooth, it implies that the higher or upper one was deposited over the lower one in an environment of small velocity without disturbing the lower strata. If the interface is wavy or uneven, it indicates erosion between two events of deposition. This sequence can occur in two ways. A high velocity event such as rising flood may cause erosion while the recession of flood may cause deposition. The other way would be one event of high velocity would cause erosion of sediment and then another event may cause deposition. However, it is usually difficult to tell the extent of scouring of the lower layer. If a soil (palaeosol) occurs between two layers, it can be concluded that considerable time has elapsed when neither erosion nor deposition occurred. Geologists normally study the following properties of each stratum: Size class Colour Thickness Internal structure Bounding surface Special characteristics Size class in general would be related to size of deposited material e.g., clay, silt, sand, gravel, pebbles or boulder. Larger size of sediment will indicate higher velocity while finer size would indicate a smaller velocity. Colour is an indication of the source of material from which the sediment is derived. It is also related to the environment in which the sediment is deposited or environment after its deposition. Presence of oxidised iron gives reddish tint while presence of organic material gives greyish tint. Thickness of the stratum is proportional to the amount of sediment carried by the flow. Further, if the sediment deposited is coarser, it suggests a high discharge event. The internal structure refers to the pattern in which the particles are deposited in the stratum. This is related to the flow velocity and particle size. In the lower regime i.e. ripples and dunes in finer material, different types of cross bedding are observed. When the flow is near critical and material is coarse sand, horizontal lamination is obtained. Thus by examining the change in structure inside a single stratum one can get information about the flow regime. The bounding surfaces of the stratum can also be interpreted in terms of erosion and deposition as related to the flow velocity. As mentioned earlier an erosional bottom surface indicates a relatively higher velocity which could erode the previously deposited sediment. If mud cracks are present in the upper bounding surface along with rootlets, this is indicative of shallow flow condition of low velocity. Special features to be noted in deposited material are the presence of animal and plant remains and carbonate concretions (Kankars). Similarly sorting of coarse deposited material and their roundness can also be noted. Exposed vertical section should be logged and graphical presentation be made. Also the size distribution of deposited material in each stratum can be prepared and whether it is coarsening upwards or fining upwards be noted. Such analysis provides valuable information about the processes causing deposition. Some diagnostic characteristics of fluvial deposition are: erosion, sorting, stratification, shallow water features e.g. mud cracks and repetition of units in the vertical. A facies is a body of sediment with a specific characteristic of its own. The characteristic can be based on composition, structure, texture, fossil content, etc. The depositional facies have been classified by Miall (1977, 1996) and are shown in Table 15.3. In the same manner sediment deposits in braided 458 River Morphology Table 15.4 Description of deposition facies (Adapted from Miall 1977, 1996) Facies notation Gmm Gmg Gm Sediment texture Matrix– supported gravel Matrix–supported gravel Predominantly massive gravel with weak bedding, some sand or fines or fences Stratified gravel Stratified gravel Very coarse to fine sand, pebbles may be present Very coarse to fine sand, pebbles may be present Coarse to very fine sand Coarse to fine sand, pebbles may be present Very coarse to fine sand, pebbles may be present Major sediment structure Massive Vertical change in clast size Imbricated or horizontal gravel Morphological identification Pebris flow (plastic) Debris flow Channel bed deposits, longitudinal bars Small channel fill Bars Dunes Bars and sand waves Ripples Plane beds Small channel depression fills or scoured Gt Gp St Sp Sr Sh Ss Trough cross bedding Planar cross bedding Trough cross bedding Planar cross bedding Ripple marks, cross lamination Horizontal laminations and lineations of different types Shallow, broad scours Ft Fsm Fra Fine sand, silt and clay silt and clay Silt, clay Carbonate deposits Very small ripples, rootlets bioturbation, calcrete etc. Massive Massive, dessication cracks, rootlets Nodules, linear forms in palaeosols Shallow deposition: in waning floods abandoned channels, or overbank Backswamp, abandoned channel fills Deposits draped around pools of water in abandoned channels or over bank Palaeosols P and meandering streams have been studied and models built for variation in the texture and structure of deposits. 15.13 WATER QUALITY RELATED DATA Since river water is used for domestic, industrial, recreational purposes as well as for irrigation, cooling water and water power generation, it becomes necessary to collect relevant data on water quality to assess its suitability for specific uses. The water quality standards depend on type of water use as well as on the degree of development of the nation, and hence water quality standards vary from one country to other. The type of data deeded and its frequency of collection have to be, therefore, decided depending Data Requirements for Morphological Studies 459 on water usage. These aspects will be decided by an expert on water quality and the engineers. However, certain general comments can be made. For drinking water purposes the chlorides content, concentration of heavy metals such as chromium, copper, zinc, cadmium, mercury and lead need to be measured. Varying percentages of heavy metal bond with sediment particles and can be transferred to agricultural land, and can eventually be absorbed by crops, grass, cattle and sheep. Non-biodegradable organic substances such as chlorinated hydrocarbons from pesticides and herbicides, and industrial processes such as paper mills also need to be measured. When water has to be used for thermal power plants for cooling purposes, temperature variation and limits on it become important. For water used for irrigation purposes, the salt content is the main parameter for determining suitability of water. It is known that large human settlements such as those in Mesopotamia have disappeared in the past because of salinization of irrigation fields. Plants vary considerably in their sensitivity to a number of substances that are toxic (e.g., beryllium) or they have a range within which they are beneficial to plant growth and beyond which they have detrimental effect. The important sources of pollution of stream water are municipal sewage, urban runoff, industrial wastes, agricultural runoff and natural pollution due to minerals and detritus from watershed entering the stream. Hence, some of the parameters commonly measured to assess water quality include BOD (biological oxygen demand), COD (chemical oxygen demand), TOC (total organic carbon), fixed and volatile dissolved and suspended solids, chlorides, alkalinity, organic and inorganic phosphorus and nitrogen. For water used for water power generation, the most important parameters are size, concentration and composition of sediment entering turbines. 15.14 CATALOGUE OF INFORMATION ON MORPHOLOGICAL STUDIES When one is entrusted with morphological studies of a given reach of the river with some specific objectives, it is always beneficial to collect data on the river under consideration and adjoining similar rivers and prepare a catalogue or information listing the problem, how was it solved, how did the river respond to the changes made, what were the consequences of the river response? Such analysis of a few situations done with an objective approach, always gives valuable clues, albeit qualitative, about the possible alternatives for managing the river under consideration. This can also suggest if certain aspects need to be studied on physical or mathematical model and the additional data that need to be collected. References ASCE (1980) Characteristics of Low Flows – Task Committee Report. JHD, Proc. ASCE, Vol. 106, No. HY5, May, pp. 717-731. Brice J.E. (1994) Channel Patterns and Terraces of the Loup River in Nebraska. U.S. Geological Survey Prof. Paper 422-D, D1-D41. Colby B.R., (1957). Relationship of Unmeasured Sediment Discharge to Mean Velocity. Trans. AGU, Vol. 38, No. 5, Oct. Cook R.V. and Doornkamp J.C. (1978) Geomorphology in Environmental Management. Clarendons Press, Oxford (U.K.), Chapter 14. 460 River Morphology Downs P.W. (1992) Spatial Variations in River Channel Adjustments : Implications for management in South- East England. Ph.D Thesis, University of Southampton, 340 p. Downs P.W. (1995) River Channel Classifications for Channel Management Purpose. In Changing River Channels (Eds. Gurnell A. and Petts G.) John Willey & Sons, Chichester, 16 – 347-365. Friend P.F. and Sinha R. (1993) Braiding and Meandering Parameters. In Braided River (Ed. Best, J.L. and Baristow C.S.) Geological Society Special Publication, No. 75, London, pp. 105-111. Garde R.J. and Dattatri J. (1963) Investigations of Total Sediment discharge of Alluvial Streams. Roorkee University Res. Journal, vol. 6, No. 2, pp. 65-78. Garde R.J. and Ranga Raju K.G. (2000) Mechanics of Sediment Transportation and Alluvial Stream Problems. New Age International Ltd. Publishers, New Delhi. Gregory K.J.(Ed) (1977) River Channel Changes. A Wiley Interscience Publication. John Wiley and Sons, New York, 450 p. Gribben J. and Lamb H.H. (1978) Climatic change in Historic times : In climatic Changes (Ed. J. Gribben) Cambridge University Press, Cambridge, London, pp. 68-82 Jansen P. ph., Bendigo L. Van, de Vries M., and Zanen A. (1979) Principles of River Engineering – The Non-tidal Alluvial River. Pitman, London. Kale V.S. and Gupta A. (2001). Introduction to Geomorphology. Oriental Longmans Ltd., Calcutta. 264 p. Kellerhals R. Neill C.R. and Bray D.I. (1972). Hydraulic and Geomorphic Characteristics of Rivers in Alberta. Research Council of Alberta, River Engineering and surface Hydrology Report 72-1, 54 p. Lane E.W. and Borland W.M. (1951). Estimating Bed-Load. Trans AGU, Vol. 32, No. 1, April. Leopold L.B. and Maddock T. (1953). The Hydraulic Geometry of River Channels and Some Physiographic Implications – USGS Professional Paper 252, 57 p. Lillesand T.M. and Kiefer R.W. (1994) Remote Sensing and Image Interpretation. John Wiley and Sons, Inc., New Yor. Chapters 1 and 7. Miall A.D. (1977). A Review of the Braided River Depositional Environment. Earth Science Reviews, Vol. 13, pp. 1-62. Miall A.D. (1996). The Geology of fluvial Deposits: Sedimentary Facies, Basin analysis and Petroleum Geology. Springer Verlag, Berlin. Münault A.V. (1986). Dendrochronology Applied to Mire Environments. In Handbook of Holocene Palaeoecology and Palaeohydrology. (Ed. Berglund B.E.) John Wiley and Sons Inc., New York. Chapter 18, pp. 371-385. NRA (1990) River Stort Morphological Survey: Appraisal and Watercourse Summaries. Compiled by Brookes A. and Long H., National River Authority, U.K. Olsson I.U. (1986). Radiometric Dating. In Handbook of Holocene Palaeoecology and Palaeohydrology (Ed. Berglund B.E.). John Wiley and Sons Inc., New York. Chapter 14, pp. 273-312. Rodriguez–Iturbe and Valdes J.B. (1979) The Geomorphic Structure of Hydrologic Response. W.R. Research, Vol. 15, No. 6, pp. 1409-1420. Rosgen D. (1996) Applied River Morphology, U.S.A. Rust B.R. (1978). A Classification of Alluvial Channel Systems. Canadian Society of Petroleum Geologists, Memoir 5, 187-198. Schumm, S.A. (1977). The Fluvial System. A Wiley Interscience Publication. John Wiley and Sons Inc., New York. Trimble S.W. (1995) Catchment Sediment Budget and Change. In Changing River Channels (Ed. Grunnel A. and Petts G.) John Willey & Sons Ltd., Chichester, U.K. Data Requirements for Morphological Studies 461 Van Rijn L.C. (1982). Sediment Transport – Part II : Suspended Load Transport. JHE, Proc. ASCE, Vol. 110, No. 11, pp. 1613-1641 Van Rijn L.C. (1986). Manual : Sediment Transport Measurement. Delft Hydraulics Laboratory, Delft (Netherlands), March. Appendix A Outline of Report on River Morphology 1. OBJECTIVE Discuss general and specific objectives in undertaking the specific morphological study. Detail out any specific information sought. Mention about the agency sponsoring the study and the terms of reference. 2. GENERAL DESCRIPTION OF THE CATCHMENT Give general description of the location of the catchment, climatic conditions, description of the terrain, catchment area and shape, relief, average slope, surface geology, land-use, drainage density, tectonic and neotectonic activities, land slides. Annual rainfall and its variation, storm distribution of rainfall and other rainfall characteristics, temperature ranges. 3. VALLEYS AND STREAM Approximate width of the valley at the bottom and the top, depth, vegetation on valley walls, presence of rapids, falls, oxbow lakes and rock-outcrops; valley slope and its variation along length, terraces—are they present? How many? Their approximate widths, wide mountainous valley or stream cut valley, underfit or overfit stream and probable reasons for it. Present condition of the stream-incised or flood-plain, flood marks, water level marks on hydraulic structures and their use in discharge and water level estimates, approximate depth during floods, channel slope and its variation, qualitative description of bed and bank material and their size distribution, study of other engineering properties of bank material, analysis of bore hole data, variation of median size of bed-material and its standard deviation along length, presence of boulders and large Outline of Report on River Morphology 463 material on the bed, tendency toward armouring, general description of bed features, their average height and length and three dimensionality. Analysis and interpretation of data from archaeological studies, historical and travel records, aerial photographs, old and new cartographic maps and satellite imageries about changes in river plan forms, river course, avulsion, channel slope and its variation; palaeo studies on palaeo channels, palaeo floods etc. 4. HYDRAULICS OF THE STREAMS Collection of hydraulic data from other agencies; analysis of discharge and sediment load data of the past-ascertaining their reliability and consistency; study of Qs vs Q curve, estimation of 10-daily flood and sediment load graph; estimation of bankful discharge and bed-generative discharge; bed-load and wash load estimation; stage-discharge relationship, estimation of Manning’s n and its variation. Analysis of width, depth, area of stream, and meander characteristics and plan forms and comparison with results from established methods to identify any anomalies. Analysis of floods and low flows: flood records, maximum, minimum and mean annual flood; analysis of flood series to estimate floods of different return periods used by engineers in the design, map of area of flooded, analysis of low flows. Estimation of average erosion rate of catchment and its discussion, variation of plan-forms as a function of distance and time; such information is useful in the location of bridges, barrages etc. Study of longitudinal profile of the stream as a function of time to see in which regions bed levels are changing and find reasons for the same; estimate approximate rates of aggradation and degradation; similarly study reaches in which excessive erosion of bank line and bends is taking place. Study of bed-level variation at existing bridges, spurs, barrages, guide banks and embankments and methods used to control it. Water-quality studies taking into account the general and specific requirement of morphological studies. 5. MAN-MADE INTERFERENCES Identify man-made interferences along the stream in the past and their effect on the river profile and plan-form; anticipate interferences of human beings that are likely to occur in future in order to fulfill the objectives; comments on the analysis that can be carried out to study these effects. 6. MORPHOLOGY OF STREAMS IN THE REGION Compare study of morphological problems in the stream under consideration and other streams in the region. Find if such study can throw light on some of the problems. 7. 8. RECOMMENDATIONS OF GENERAL AND SPECIFIC NATURE: REFERENCES This page intentionally left blank Author Index Abbott, M.B. 362 Acaroglu, E.R. 159 Ackers, P. 160, 164, 249 Adachi, S. 350 Adams, J. 231 Agarwal, A.K. 298 Agarwal, K.K. 430 Agarwal, V.C. 203, 211, 220, 230 Agnihotri, R. 274 Ahmad, M. 171 Aich, B.N. 393 Alam, A.M.Z. 141, 143 Albertson, M.L. 91, 126, 133, 172 Allen, J.R.L. 92, 129, 315, 316 Ali, K.A.S. 384 Ananian, A.K. 285 Anil Kumar 133 Ansari, S.A. 296 Anstey, R.K. 102 Apmann, R.P. 193 Armstrong, C.L., 67 Arora, M. 230 Asawa, G.L. 425 ASCE 163 Ashida, K. 118, 371 Ashmore, P.E. 198 Bagnold, R.A. 159, 194, 249 Bajpai, I.P. 32 Baker, V.R. 273 Banerjee, D. 273 Barbarossa, N.L. 139 Baruah, B. 424 Baruah, B.B. 405, 407 Basu, A.K. 441 Bathija, T.S. 67 Bathurst, J.C. 230, 248, 249 Bayazit, M. 371 Bechteler, W. 164 Belleudy, P.A. 384 Bendegom, L.Van 312 Benson, M.A. 264 Berg, J. Van den 312 Berglund, B.E. 258 Best, J.L. 198 Bettess, R. 227, 248 Bhalerao, A.R. 296 Bhandari, R.K. 432 Bharadwaj, R.C. 167 Bhatnagar, S. 312, 384 Bhowmik, N.G. 234 Blakely, B.D. 49 Blench, T. 91, 171 Bloom, A.L. 75 Bogardi, J.L. 115 Bolt, B.A. 297 Bondurant, D.C. 283, 437 Borah, D.K. 383 Borgohain, J.K. 419 Borland, W.M. 52, 306 Bradford, J.M. 69 Bray, D.I. 108, 225, 230, 233, 234, 242, 243, 264, 460 Breusers, H.N.C. 288 Briaud, J.L. 296 Brice, J.E. 200, 451 Bridge, J.S. 104 Bristow, C.S. 198 Brookes, A. 440 466 Brooks, N.H. 140, 156 Brown, L.R. 35 Brownlie, W.R. 141, 162 Bruijnzeel, L.A. 22 Bruk, S. 52 Brune, G.M. 303 Brush, L.M. Jr. 95 Buffington, J.M. 113 Bull, W.B. 102, 300 Burr, G.S. 274 Callander, R.A. 202, 212 Campbell, P.L. 255 Cao, H.H. 248, 249 Carey, W.C. 126 Carlson, C.W. 25, 231 Carlson, E.J. 231 Carslaw, H.S. 346 CBIP 288 Chandra, S. 366 Chang, H.H. 173, 175, 178, 205, 209, 218 Charlton, F.G. 233 Chatley, H. 327 Chatterjee, P.K 54 Cheetham, G.H. 256, 265 Chen, W.L. 385 Chen Yuaner 167 Chen,Y. H. 365 Chien, N. 147, 317 Chitale, S.V. 89, 101, 389, 391, 400 Chollet, J.P. 384 Chorely, R.J. 184 Chow, V.T. 264 Church, M. 108, 225, 230, 233, 238, 313 Coleman, N.L. 154, 200, 409, 415 Colosimo, C. 230, 242 Condolios, E. 121 Cook, R.V. 446 Copertino, V.A 230 Cornwell, D.A. 438 Correia, L.R.P. 384 Cotton, C.A. 85 Coyle, J.J. 67 Craig, R.C. 76 Cross, B.V. 70 Cui,Y. 364 Culling, W.E.H. 345, 346 Cunge, J.A. 360, 362, 366 Dalrymple, T. 264 Dangler, E.W. 67 Daniel, J.F. 323 Daniel, P. 121 Dattatri, J. 67, 159 David, J.K. 165 Davies, B.E. 72, 279 Davies, L.B. 313 Davies, T.R.H. 198 Davis, M.E. 274 Davis, M.L. 87, 438 Davis, W.M. 9 Dawdy, D.R. 132 Day, T.J. 248 de La Cruz, C.d. R. 99 de Vriend, H.J. 194 de Vries M. 312, 345, 347, 354, 357, 364 Dekov, A.P. 52 Dendy, F.E. 34 Deshmukh, D.N. 436 Dhanju, M.S. 425 Dhruva Narayana 64 Diegaard, R. 332 Dietrich, W.B. 58 Diette, S. 369 Doornkamp, J.C. 446 Downs, P.W. 452 Doyle, W.M. 300 Drinker, P.A. 193 Du Boys, P. 5, 145 Dunne, T. 58 Durand, R. 121 Dury, G.H. 89, 90, 258, 265, 323 Dutton, C.E. 8 Eaking, H.M. 209 Eden, E.W. 126 Edgar, D.E. 198 Egiazaroff, I.V. 118, 279 Einhellig, R. 384 Einstein, H.A. 6, 122, 139, 147, 149, 155 Author Index Author Index 467 Godbole, M.L. 395 Goel, R.S. 430 Gogoi, P.K. 424 Gohain, K. 392, 393, 400 Gole, C.V. 101, 389, 391 Golubstov, V.V. 242 Goncharov, G.N. 186 Goswami, D.C. 23, 407, 410, 413, 415, 416, 417, 423 Gottgen, J.F. 312 Graf, W.H. 159, 248, 249 Grass, A.J. 114 Gregory, K.J. 24, 257, 258, 315 Gribben, J. 450 Griffiths, G.A. 230 Griggs, R.F. 210 Grishanin, K.V. 246 Gudavali, R. 311 Gupta, A. 456 Gupta, R.D. 173 Gupta, H.K. 432, 433 Gurnell, A. 315 Hack, J.T. 76, 95 Handique, G.R. 419 Hansen, E. 133, 160 Haque, M.I. 126 Harbor, J.M. 312 Harrison, A.S. 156, 233, 369 Harvey, A.M. 323 Hasan, S.M. 369 Hathaway, G.A. 283 Hayashi, T. 118, 122, 203, 208, 212, 213, 219 Heede, B.H. 40 Heinemann, H.G. 303 Henderson, F.M. 217 Henderson, K.A. 274 Hey, R.D. 186, 230, 234, 241 Hickin, E.J. 204, 324 Hill, J.C. 365 Hines, W.G.S. 69 Hjulstorm, F.A. 210 Holeman, J.N. 35 Holly, F.M. 371, 384 Hong, L.B. 198 Eliassen, S. 284 Ellison, W.D. 48 El-Shami, F.M. 436 El-Swaify, S.A. 34 Elwell, H.A. 44 Ely, L. 273 Engelund, F. 133, 141, 160, 194, 196, 202, 212 Enzel, Y. 373 Esterbrook, D.J. 72 Ettema, R. 290 Evans, J.E. 300 Exner, F.M. 6, 356 F. A.O. 47, 57 Fargue, O. 5 Fergusson, R.I. 209, 335 FISRWG 439 Flemming, P.M. 227 Foster, G.R. 39 Fournier, F. 41, 47, 259 Fredsoe, J. 129, 202, 332 Friedkin, J.F. 203, 209, 327 Friend, P.F. 200, 202, 336, 451 Frisk, H.N. 316, 327 Fujita, Y. 221 Fullam, T.J. 126 Galay, V.J. 126, 283, 284 Gallagher, R.H. 385 Gandolfo, J.S. 180 Gangadharaiah, T. 165, 296 Garde, R.J. 4, 24, 64, 66, 86, 98, 115, 126, 133, 136, 140, 143, 153, 155, 157, 159, 178, 187, 233, 234, 242, 254, 282, 287, 296, 312, 303, 313, 318, 369, 394, 395, 411, 453 GARMIN 54 Garrel, R.M. 68 Gee, E.P. 4, 106, 410 Gessler, J. 113, 114, 279, 286, 299, 369 Ghosh, B. 271 Gilbert, G.K. 5, 9, 209 Gill, M.A. 129, 149, 347, 349, 351, 353 Gill, G.M. 312 Gladky, H. 230 Glock, W.S. 12 468 Hood, P. 385 Hooke, J.M. 324, 326 Horn, W.L. 311 Horton, R.E. 14, 17, 19, 26, 76 Hou, Z. 354, 356 Howard, A.D. 13 Hsia, C.S. 155 Hsu, S.H. 384 Hubbell, D.W. 122 Huber, E. 287 Hudson, N.W. 46 Hughes, H.J. 323 Hung, C.S. 161 Husain, Z. 273 Hutton, J. 8 Ichibashi, I. 166 Ikeda, S. 194, 220, 225, 239 Indiresan, P.V. 432 Inglis, C.C. 177, 204, 209, 233 Ippen, A.T. 193 IRTCES 301, 305, 310 Isaac, N. 126, 127 Ishizaki, T. 350 Islam, M.N. 294 Ismaghilov, H.A. 186 Ismail, H.M. 154 Itakura, T. 126 IWAI 424 Jackson II, R.G. 124, 237 Jaeger, J.C. 346 Jain, S.C. 210, 347, 351 Jain, V. 317, 388 Jakhade, G.S., 413 Janda, T. Dunne 68 Jansen, P. 276, 453 Jaramillo, W.F. 351 Jeffrey, H. 114 Jhonson, C.B. 70 Johnson, D. 83 Jones, D. 238 JSCE 143 Julien, P. 63 Jull, A.J.T. 274 Author Index Kale, V.S. 267, 268, 269, 456 Kalinske, A.A. 121, 153, 155, 157 Kamble, K.J. 441 Kand, C.V. 296 Kar, A. 273 Karahan, E. 113 Karim, M.F. 163, 371 Kawahita, R. 354, 356 Keefer, D.K. 10 Keller, E.A. 240 Keller, M.D. 126 Kellerhals, R. 91, 230, 233, 284, 443 Kennedy, J.F. 141, 143, 163, 194, 210, 356, 384 Khan, H.R. 329 Khanal, N.R. 31 Khosla, A.N. 38, 64 Kiefer, R.W. 443 Kikkawa, H. 194 King, L.C. 75 Kinnell, P.I.A. 45 Kinoshita, R. 203 Kishi, T. 202, 220, 222 Kitagawa, A. 194, 225 Klaassen, G.J. 276 Klingeman, P.C. 247 Knighton, A.D. 233 Kochel, R.C. 313 Kolhi, S. 432 Komura, S. 179 Kondap, D.M. 173 Kondratev, N.E. 207 Koster, E.H. 240 Kothyari, U.C. 24, 63, 64, 66, 231, 259, 287, 290, 411, 425, Krishnan, M.S. 79, 80 Krishnappen, B.G. 365 Kuenen, P.H. 68 Kumar, A. 224 Kumar, R. 313 Kumar, S. 126, 270 Kuroki, M. 202, 220, 222 Kusumagar, M.G. 273 Lacey, G. 6, 143, 170, 233 Lamb, H.H. 450 Lane, E.W. 52, 72, 85, 88, 96, 126, 153, 155, 157, 199, 216, 231, 240, 284, 297, 304 Author Index 469 Melhorn, W.N. 240 Melton, M.A. 26 Melville, B.W. 289 Meyer, L.D. 49 Meyer-Peter, E. 6, 146, 249 Miall, A.D. 199, 200, 457 Michalik, A.S. 230 Michiue, M. 118, 164, 371 Mikuni, N. 228 Milhaus, R.T. 230 Miller, C.R. 54, 306 Miller, J.P. 41, 68, 184, 226, 256, 335 Miller, V.C. 32 Milliman, J.D. 35 Mirkari, G.D. 309 Mishra, P.K. 273 Mishra, S. 273 Misri, R.L. 247 Mittal, M.K. 280, 347, 351 Mittal, R.S., 17 Mizuyama, T. 250 Mohan, J. 290 Molinas, A. 164 Mookerjea, D. 393 Morgan, R.P.C. 39, 43, 50, 63 Morisawa, M.E. 18, 21, 24 Mosley, N.P. 109 Mosley-Thompson, E 274 Moss, A.J 232 Mozzherin, V.I. 52 Mukhamedov, A.M. 186 Mukherjee, S.K. 441 Muller, R. 6, 146, 249 Münault, A.V. 460 Muramoto, Y. 221 Murthy, A.S. 426 Murthy, B.N. 430 Murthy, B.S. 286 Mutchler, C.K. 47 N.I.H. 313, 393 Nagao, T. 228 Nakatoh, T. 350 Namjoshi, A.G. 296 Nanson, G.C. 204, 324 Langbein, W.B. 25, 30, 44, 181, 210, 233, 258 Lara, J.M. 310 Laursen, E.M. 154, 158 Laws, J.O. 45 Leeder, M.R. 273 Lehre, A.K. 58 Leliavsky, S. 210 Leopold, L.B. 30, 41, 52, 88, 97, 177, 180, 184, 198, 209, 210, 217, 230, 233, 240, 256, 315, 317, 329, 452, 455 Lewin, J. 209, 257, 315, 327 Lewis, G.W. 327 Li Guifen 320 Li, R.M. 69 Li, S.J. 385 Lidicker, A.C. 156 Lillesand, T.M. 443 Limerinos, J.T. 243 Lin, P.N. 274, 320 Little, W.C. 279, 281, 369 Livesey, R.H. 437 Lobeck, A.K. 321 Lovera, F. 141 Lu Jianyi 335 Lu, J.Y. 282, 369, 384 Lyell, C. 8 Lyn, D.A. 364 Macdonald, G.A. 311 Mackenzie, F.T. 68 Mackey, S.D. 312 Mackin, J.H. 2,84 Maddock, T. 52, 177, 180, 233, 310, 452, 455 Mahmood, K. 126, 303, 336 Maizels, J.K. 266 Malm, D.E.G. 31 Manandhar, I.N. 24 Mannering, J.V. 49 Mantz, P.A. 114, 126 Mathur, V.B. 441 Mayer, P.G. 279, 281, 369 Mazumder, S.K 325 McCool, D.K. 50 McLean, D.G. 255 Meade, R.H. 35 Mehta, P.J. 347, 350 470 NEDCO 179 Negev, M. 62 Neill, C.R. 115, 204, 233, 460 Neu, H.A. 209 Newson, M.D. 315 Nicholas, W.R. 441 Nicollet, G. 288 Nixon, M.A. 177, 180 Noble, E.L. 258, 259 Nomicos, G.N. 139 NRA 452 Odgaard, A.J. 194, 197, 231, 282, 369 Olsson, I.U. 460 Onishi, Y. 210 Osaki, S. 122 Osborn, J.F. 29 OSMG 429 Ouchi, S. 10, 106 Ozaki, S. 208, 212, 213, 219 Palaniappan, A.B. 362, 371 Panchang, G.M. 422 Pande, P.K. 157, 313, 425 Paris, W.E. 227 Park, C.C. 182 Park, L. 351 Parkash, B. 32, 392, 393, 400 Parker, G. 202, 203, 212, 220, 233, 234, 250, 384 Parola, C. 384 Parsons, D.A. 45 Patel, P.L. 118, 119, 150 Patil, B.M. 142, 145 Patton, P.C. 274 Pechinov, D. 69 Peltier, L.C. 26 Penck, W. 75 Perugu, S. 311 Pettijohn, F.J. 332 Petts, G. 315 Pickles, G.W. 327, 328 Piest, R.F. 40 Pitty, A.F. 98 Playfair, J. 8 Pogorzelski, H.A. 31 Powell, J.W. 8 Prakash, H. 230 Prasad, R.C. 24 Prashun, A.L. 370 Prus-Chacinski, T.M. 210 Quaraishy, M.S. 210 Quinton, J.N. 68 Author Index Rachocki, A. 101, 202 Raghuvanshi, A. 430 Rahman, A. 171 Rahuel, J.L. 365, 384 Rajagopal, H. 313 Rajesh Kumar 313 Rajguru, S.N. 273 Ram Babu 67 Ramesh, R. 274 Ramette, M. 209, 211, 220 Rana, S.A. 332 Ranga Raju, K.G. 118, 119, 136, 140, 143, 150, 153, 312, 425, 453 Rao, K.L. 413 Raudkivi, A.J. 149, 154 Rendard, K.G. 50 Reynolds, A.J. 212 Rhodes, C.C. 183 Rice, R.J. 74, 78, 81 Richards, K. 240, 316 Riggs, H.C. 178 Rikson, R.J. 68 Robinson, A.R. 40, 43 Rodriguez-Iturbe, I. 29 Roehl, J.E. 40, 57 Rohan, K. 86 Rojas, R. 63 Rook, R. 230 Root, T.L. 260 Rose, C.W. 45, 60 Rosgen, D. 87, 92 Rotnicki, K. 269 Rouse, H. 113, 153 Rozovskii, I.L. 190, 196 Ruane, R.J. 436 Rubey, W.W. 180 Author Index 471 Smart, J.S. 17 Smith, D.D. 46, 47 Smith, K.G. 14 Smith, N.D. 238 Smith, T.R. 181 Somayajulu, B.L. 274 Soni, J.P. 347 Sparks, B.W. 99 Speight, J.G. 209 Spomer, R.G. 69 Srivastava, R. 425 Stanley, E.H. 312 Steele, J.G. 67 Sternberg 86 Stevans, J.C. 283 Stevens, M.A. 69 Stocking, M.A. 44 Strahler, A.N. 14, 17, 25 Sukegawa, N. 203, 212, 220 Surya Rao, S. 312 Sutherland, A.J. 289 Swain, K.K. 441 Swamee, P.K. 303 Swanson, D.N. 68 Switsur, V. R. 426 Tamai, N. 227 Tangri, A.K. 317 TCEEHS 430, 433 TCPSM 52 Thomas, W.A. 370 Thompson, L.G. 270 Thompson, S.M. 255 Thornbury, W.D. 13, 82 Thorne, C.R. 186, 230, 257 Thornes, J.B. 273 Ting, F.C.K. 311 Tinkler, K.J. 7 Tiwari, A.K. 44, 68 Tiwari, S.K. 313 Tobes, G.H. 209 Todd, O.J. 284 Tricart, J. 53 Trimble, S.W. 59, 456 Tsuchiya, B. 350 Ruhe, R.V. 10 Rundquist, L.A. 227 Rust, B.R. 202 Rzhanitsyn, N.A. 15, 87 Sahay, A. 312, 384 Sahay, R.N. 298, 400 Sangeet, S. 67 Sanyal, N. 400 Sarkar, A. 271 Sato 350 Sayre, W.W. 122 Schaffernak, F. 179 Scheideggar, A.E. 15 Scheuernlein, H. 286 Schick, A.P. 10 Schneider, S.H. 260 Schoklitsch, A. 209, 249 Schumm, S.A. 11, 17, 19, 25, 27, 38, 44, 74, 91, 104, 105, 184, 198, 256, 258, 265, 315, 329, 330, 331, 452, 455 Schwarz, P. 384 Scott, C.H. 137 Scott, R.F. 311 Sethia, B. 312 Sethurathinam 426 Sharma, T.C. 64 Shen, H.W. 161, 210, 282, 288, 369 Sheshagiri Rao, R. 312 Shields, A. 111 Shimuzu, Y. 166 Shreve, R.L. 15, 30 Shukry, A. 193 Shulits, S. 86 Silva, J.M. 356 Silvester, R. 99 Simons, D.B. 62, 91, 172, 336 Singh, A.K. 224 Singh, I.R. 126 Singh, J. 369 Singh, R. 68 Singhvi, A.K. 273 Sinha, R. 200, 202, 317, 388, 451 Sinha, R.K. 400 Skovgaard, O. 202, 212 Smart, G.M. 249 472 U.N.E.P. 69 U.S. Govt. and IIHR 69 U.S.S.R. National Committee for I.H.D. 69 UNESCO 301, 305, 310 Vaidhankar, D.V. 436 Vaidya, S. 435 Valdiya, K.S. 411 Van Rijn, L.C. 69, 129, 157, 164, 241, 242, 453 Vanoni, V.A. 139, 140, 154 Verwey, A. 384 Vetri, M. 230 Vetter, C.P. 283 Vetter, M. 164 Vijander, S. 441 Vischer, G.S. 232 Vittal, N. 162, 347, 351 Vreugenhill, C.B. 345, 354 Wadia, D.N. 79, 80 Walling, D.E. 24, 35, 57, 58 Wallis, I.G. 209 Walters, W.H. Jr. 107 WAPCOS 407, 413, 422 Weaver, W.E. 109 Wei, G. 311 Weller, H.E. 420 Werner, P.W. 210 Wharton, G. 186 Whetten, J.T. 126 White, W.R. 160, 164, 175, 248, 249 Author Index Williams, G.P. 177, 264, 265 Williams, M.A. 45, 48 Winkely, B.R. 331 Wischmeier, W.H. 46, 47, 48 Wolman, M.G. 41, 88, 97, 184, 198, 209, 217, 230, 317, 323, 335 Woodyer, K.D. 227 Worcester, P.G. 1, 74, 321 Wõrman, A. 296, 329 Xu Fuling 320 Yalin, M.S. 113, 114, 126, 129, 149 Yamaguchi, H 166 Yang, C.T. 161, 164, 209 Yang, G. 384 Yang, J.C. 384 Yao, T. 274 Yearke, L.W.C. 285 Yen, K.C. 364 Young, A. 38 Zanen, N. 312 Zang, H. 354, 356 Zao Yun 167 Zernitz, E.R. 13 Zevenbergen, L.W. 230 Zhide, Z. 304 Zienkieveiz, J.C. 362 Zimmermann, C. 194 Zimpfer, G.L. 198 Subject Index ablation 81 actions causing disturbance in stream system 429 aggradation 276, 296 due to floods 300 due to increase in sediment load 297 due to change in water surface slope 298 due to withdrawal of clear water 298 at channel bifurcation 299 other occurrences 299 planned removal of dam 300 occurrence 297 allogenic changes 315 alluvium 58 alluvial fans 101 alluvial rivers hydraulic geometry and plan forms 169 hydraulic geometry 176 analytical models 337, 343 applications 346 one-dimensional equations 338 one-dimensional dynamic equation 340 analysis of w.s. and bed waves 342 hyoperbolic model 345, 354 parabolic model 344 wave model 345, 356 aquatic organisms 428 area of drainage basins 19 armouring models 369 assimilative capacity 428 autogenic changes 315 avulsion 315 of the Tigris 318 of the Yellow river 320 bars 199, 237 alternate 239 diagonal 238 longitudinal 200 point 200 transverse 200 base level 72 basin shape 21 bed-forms 124 antidunes 124, 131 bars 124 in unidirectional flow 124 distinction between ripples and dunes 126 dunes 124 ripples 124 stability analysis 127 transverse ribs 131 bed-load transport 145 DyBoy’s equation 145 Meyer-Peter and Mûller’s equation 146 Patel and Ranga Raju equation 150 bed-load equations for gravel-bed rivers 248 Ackers and White 248 Bagnold 250 Meyer Peter and Mûller 249 Mizuyama 250 Parker et al. 250 Schoklitsch 250 Smart 249 bed material load 123 bends 189 distribution of longitudinal velocity over width 192 entrenched 197 474 flow in rigid and alluvial bends 189 free bends 197 growth and decay of secondary circulation 192 head loss 194 shear distribution and topography 194 super elevation 192 velocity distribution in rigid bed bends 189 bifurcation ratio 16 biological integrity 428 biological oxygen demand (bod) 427 Brahmaputra 402 bank stability 409 climate and hydrology 411 development plans 423 drainage of hinterlands 420 flooding and flood protection 419 plan forms 416 resistance to flow and sediment transport 414 river bed changes 422 river characteristics 407 role of dredging 424 seismicity and landslides 410 braided rivers 198 types of bars 199 longitudinal 200 lingioid 200 lateral 200 point 200 side 200 causes of 198 parameters 200 modeling of 202 braiding indices 200 Brice index 200, 451 Rust index 202, 451 Braid channel ratio 202 channel pattern changes 329 channel slopes 28 characteristics of graded streams 85 characteristic discharges bankful discharge bed generative discharge 179 dominant discharge 177 mean annual discharge 177 CHARIMA 376 chars 391 chemoclinie 434 cirques 81 classification of models 364 coupled 364 fully unsteady 364 quasi-steady 364 uncoupled 364 climatic changes 260 causes 261 forecasts 262 colluvium 58 conceptual model of valley storage 59 consistency 366 continuity equation for flow 338 for sediment 339 convergence (of numerical scheme) 366 Courant condition 366 Courant–Friedrich–Levy condition 366 critical shear stress 111 for uniform materials 111 for non-uniform sediment 117 critical velocity approach 114 cut-off 326 artificial cutoff 327 chute cutoff 327 natural and artificial 326 neck cutoff 327 Subject Index dams–large vs small 432 dams and reservoirs 430 Darcy–Weisbach equation 5 data requirements for morphological studies 442 basin characteristics and morphometry 449 bed and bank material 453 catalogue of information 459 cross-sectional, longitudinal section, plan-form 451 digital image processing 444 geomorphic map 446 hydrologic data 454 Subject Index 475 drainage texture 13 dune dimensions 127 dunes 127 dynamic equation 340 dynamic simulation model 62 entrenchment ratio 93, 452 environmental effects 429 of hydraulic structures 429 dams and reservoirs 430 epilimnion 434 equilibrium in natural streams 84 erosion 34 equations 48 factor 65 factors affecting 41 gully erosion 24, 39, 40 modeling of 60 rates (global) 35 rates in Indian catchments 64 rill 29 sheet 44 types 39 erosion and depositional landforms 61 erosion at bends 323 erosivity indices 47 erosion models dynamic simulation 62 EUROCEM 63 process based 60 stochastic 64 erosional and depositional land-forms of glaciers 81 cirques 81 deltas 98 fans 101 glacial troughs 81 hanging valleys 82 fluvial hydraulics 1 fluvial morphology 82 fluvial palaeo hydrology 256 fluvial palaeo hydrologic studies in India 271 geomorphological instantaneous unit hydrograph (GIUH) 29, 450 geomorphology 7, 71 lithology and tectonics 445 maps, air photos, satellite imageries 442 remote sensing 443 sediment load data 455 stratigraphic studies 456 vegetative cover 446 water quality data 458 degradation 276, 277 at dams and barrages 282 at bifurcations 284 control of 286 downstream progressing 282, 285 effects of 285 gravel mining 284 increase in discharge 284 parallel 284 planned removal of dam 300 prediction of depth 286 rotational 278 storage of bed material 284 types 277 downstream progressing 282 upstream progressing 277 deltas 98 dhars 391 diastrophism 71 diffusion model 244 disturbances in stream system and their impacts 429 dissolved oxygen 434 dominant discharge 176 bankful discharge 177 drainage basin 11 drainage basin characteristics and hydrology 29 drainage density 24 drainage patterns 12 centripetal 13 dendritic 12 deranged 12 highly violent 13 parallel 12 radial 12 rectangular 12 trellised or lattice like 12 476 geologic time scale 77 geomorphic cycle (erosion cycle) 72 criticism 74 rejuvenation of cycle 74 geomorphic processes 71 endogenous 71 exogenous 71 glaciation 80 in India 80 glacial movements and erosion 81 glaciers 80 ice cap 80 ice streams 80 glacial troughs 81 valley glaciers 80 global warming 262 forecast 262 graded stream 2, 84 characteristics 85 gravel-bed rivers 229 bed material 230 bed-load equations 248 bed-features 237 bed-load sampling 247 data 230 hydraulic geometry 233 pavement 233 resistance to flow 241 resistance at bankful discharge 242 resistance at varying discharge 244 sediment transport 246 universal stage discharge curve 246 hanging valleys 82 healthy streams 428 HEC-6 372 applications to Kosi 378 reservoir sedimentation 382 Helly smith sampler 247 historical developments 4 in fluvial hydraulics 4 in geomorphology 7 Horton’s area ratio 20 length ratio 18 laws 16, 17 number 25 hydraulic geometry of alluvial streams 176 empirical relations 180 non-dimensional relations 186 hydropower plants 436 hypolimnion 434 hypsometric curves 27 ice-caps 80 ice-streams 80 incipient motion 110 critical velocity approach 114 empirical equations CTF 111 Shields’ analysis 111 for non-uniform sediments 117 Subject Index Kosi 388 catchment characteristics and geology 391 channel patterns 401 discharge and sediment measurements 393 flood embankments 400 geotectonics 392 hydrology 393 management of Kosi 398 morphology of Kosi 396 present day problems 402 sediment size and slope 345 landscape evolution non-cyclic concept 76 Lane’s balance analogy 259, 275 Lax theorem 366 Lithology 21 longitudinal grain sorting 331 Maddock’s classification (unmeasured load) 52 mass wasting 24 Manning’s equation 5 meander belt 97 length 97 free 98 meandering 202 meander bend migration 205 meander characteristics 206 relations for geometry 207 theories 209 Subject Index 477 physiography 2 plan-form 87 plan-form criteria 212, 216 problems in river morphology 2 randon walk model 29, 30 recreation 437 regimes of flow prediction 131 rehabilitation of stream 440 relief 26 relief aspects 26 relief ratio 26 remote sensing 443 restoration of stream 439 reservoir sedimentation 301 density current 305 empirical area redution method 306 method of preserving and Miraki’s method 309 modeling of sediment deposition 304 movement and sediment deposition 304 restoring capacity 310 shape and deposition profile 305 sediment inflow and trap efficiency 302, 303 upstream effects 301 reservoir induced seismicity 432 reservoir surveys 53 resistance equations 241 bank resistance 138 Darcy Waisbach equation 5, 137 Engelund’s method 141 general comments 139 in alluvial streams 137 Manning’s equation 5, 137 of undulations 139 Strickler’s equation 138 river action plans 438 rivers and environment 427 river morphology 2 river systems in India 386 ruggedness number 25, 26 Saraswati river 271 sea level fluctuations 450 measurement of sediment yield 50 mechanics of sheet erosion 44 modeling of armouring 369 HEC-6 372 CHARIMA 376 modes of sediment transport 119 bed load 120 bed material load 123 contact load 120 saltation load 120 suspended load 120 wash load 123 natural levees 98 neotectonics and earthquakes 105 non-cycle concept of land scaped evoluation 76 numerical model 360 numerical schemes 362 explicit method 362 finite difference 362 implicit method 363 one dimensional models boundary conditions 367 classification 363 equations 360 list of models 365 osage type stream 90 overland flow 60 oxbow lake 327 palaeo climatology 256 palaeo geomorphology 256 palaeo hydraulics 257 palaeo hydrology 256 palaeo hydrologic studies 257 palaeo peology 257 basis of analysis 258 estimation of Q and U 262, 264 in India 267 objectives 257 palaeo velocity determination 264 in gravel-bed rivers 266 pavement 233 peneplain 72 478 scour 276 around bridge piers 287 factors affecting 288 in cohesive soils 296 in gravelly materials 295 Kothyari’s equation 292 Lacey–Inglis method 292 Melville–Sutherland method 292 prediction of scour depth 296 protection of scour 291 verification of equations 293 secondary circulation 103 sediment budget concept 58 sediment delivery ratio 23, 56 sediment discharge 157 relations 157 sediment production and yield 23 sediment yield 23, 34, 35 computation 56 measurement 50 sheet erosion mechanics 44 sinusity 97 slack water deposits 267 soil erosion 34 gullies 39 rills 39 sheet 39 types of 39 soil loss equations 48 slope ratio 28 stable channels 170 carrying sediment 170 stable channel design Lacey’s method 170 Blench’s method 171 Chang’s method 174 Simon’s method 172 Kondap’s method 173 stability (numerical) 366 stability analysis 127 for bed-forms 127 for plan forms 202 Sternberg’s equation 86 stream action causing disturbances in 429 assimilative capacity 428 Subject Index biological integrity 428 capture 321 flow regime 23 habilitation 440 equilibrium 427 frequency 24 order 14 pollution 437 reclamation 440 restoration 439 sinuosity 97 terraces 95 stream classification boulder 92, 229 consequent 87 ephemeral 40, 87 flood plains 92 gravel bed 92, 229 insequent 87 intermittent 87 misfit 89 obsequent 87 osage 90 over fit 89 perennial 48, 87 resequent 87 subsequent 87 under fit 89 submergence of land and forests 431 suspended load transport 150 integration of sediment distribution equation 155 measurements 150 Rouse equation 153 sediment distribution 152 theories of meandering 209 conceptual model 210 disturbance 210 earth’s rotation 289 excess energy 209 helicoidal motion 210 Ramette’s theory 211 thermal and hydro power plants 436 topography 73 mature 73 old 73 Subject Index 479 trap efficiency 303 equations 303 universal soil loss equation 42, 48 unit weight of sediment 55 valley glaciers 80 variables in river morphology 104 variation in sediment size 86 vegetation 22 vortex bed-load sampler 247 water quality in reservoirs 433 dissolved oxygen 434 iron and manganese 435 nitrogen 435 pH 434 phosphorus 435 salinity 434 temperature 434 turbidity 434 wash load 123 wave model 356 old stage 83 youthful 73 topography produced by streams 94 alluvial fans 101 delta 98 flood plains 95 meanders 96 natural levees 98 point bars 103 stream terraces 95 valleys 94 total load transport 158 total load equations Ackers and White 160 Bagnold 159 Brownlie 162 Effective shear stress approach 162 Engelund and Hansen 160 Garde–Dattari 159 Graf–Acaroglu 159 Karim–Kennedy 163 Laursen 158 Shen and Hung 161 Yang 161