Shear Strength of Rock

THE SHEAR STRENGTH OF ROCK MASSESby Kurt John Douglas BE(Hons) USyd A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy School of Civil and Environmental Engineering The University of New South Wales Sydney, Australia December 2002 Thesis/Project Report Sheet Surname or Family Name: DOUGLAS First Name: Kurt Other name/s: John Abbreviation for degree as given in the University calendar: PhD School: Civil and Environmental Engineering Faculty: Engineering Title: The Shear Strength of Rock Masses Declaration relating to disposition of project report/thesis I am fully aware of the policy of the University relating to the retention and use of higher degree project reports and theses, namely that the University retains the copies submitted for examination and is free to allow them to be consulted or borrowed. Subject to the provisions of the Copyright Act 1968, the university may issue a project report or thesis in whole or in part, in photostate or microfilm or other copying medium. I also authorise the publication by the University Microfilms of a 350 word abstract in Dissertations Abstracts International (applicable to doctorates only) ...................................................................... ...................................................................... ...................................................................... Signature Witness Date The university recognise that there may be exceptional circumstances requiring restrictions on copying or conditions on use, Requests for restriction for a period of up to 2 years must made in writing to the Registrar. Requests for a longer period of restriction may be considered in exceptional circumstances if accompanied by a letter of support from the Supervisor or Head of School. Such requests must be submitted with the thesis/project report. FOR OFFICE USE ONLY Date of completion of requirement for Award: Registrar and Deputy Principal THIS SHEET IS TO BE GLUED TO THE INSIDE FRONT COVER OF THE THESIS Abstract 350 words maximum: The first section of this thesis (Chapter 2) describes the creation and analysis of a database on concrete and masonry dam incidents known as CONGDATA. The aim was to carry out as complete a study of concrete and masonry dam incidents as was practicable, with a greater emphasis than in other studies on the geology, mode of failure, and the warning signs that were observed. This analysis was used to develop a method of very approximately assessing probabilities of failure. This can be used in initial risk assessments of large concrete and masonry dams along with analysis of stability for various annual exceedance probability floods. The second and main section of this thesis (Chapters 3-6) had its origins in the results of Chapter 2. It was found that failure through the foundation was common in the list of dams analysed and that information on how to assess the strength of the foundations of dams on rock masses was limited. This section applies to all applications of rock mass strength. Methods used for assessing the shear strength of jointed rock masses are based on empirical criteria. As a general rule such criteria are based on laboratory scale specimens with very little, and often no, field validation. The Hoek-Brown empirical rock mass failure criterion was developed in 1980 for hard rock masses. Since its development it has become almost universally accepted and is now used for all types of rock masses and in all stress regimes. This thesis uses case studies and databases of intact rock and rockfill triaxial tests collated by the author to review the current Hoek-Brown criterion. The results highlight the inability of the criterion to fit all types of intact rock and poor quality rock masses. This arose predominately due to the exponent, a, being restrained to approximately 0.5 to 0.6 and using rock type as a predictor of m i . Modifications to the equations for determining the Hoek-Brown parameters are provided that overcome these problems. In the course of reviewing the Hoek-Brown criterion new equations were derived for estimating the shear strength of intact rock and rockfill. Empirical slope design curves have also been developed. Abstract Page i ABSTRACT The first section of this thesis (Chapter 2) describes the creation and analysis of a database on concrete and masonry dam incidents known as CONGDATA. The aim was to carry out as complete a study of concrete and masonry dam incidents as was practicable, with a greater emphasis than in other studies on the geology, mode of failure, and the warning signs that were observed. This analysis was used to develop a method of very approximately assessing probabilities of failure. This can be used in initial risk assessments of large concrete and masonry dams along with analysis of stability for various annual exceedance probability floods. The second and main section of this thesis (Chapters 3-6) had its origins in the results of Chapter 2 and the general interests of the author. It was found that failure through the foundation was common in the list of dams analysed and that information on how to assess the strength of the foundations of dams on rock masses was limited. This section applies to all applications of rock mass strength such as the stability of rock slopes. Methods used for assessing the shear strength of jointed rock masses are based on empirical criteria. As a general rule such criteria are based on laboratory scale specimens with very little, and often no, field validation. The Hoek-Brown empirical rock mass failure criterion was developed in 1980 for hard rock masses. Since its development it has become virtually universally accepted and is now used for all types of rock masses and in all stress regimes. This thesis uses case studies and databases of intact rock and rockfill triaxial tests collated by the author to review the current Hoek-Brown criterion. The results highlight the inability of the criterion to fit all types of intact rock and poor quality rock masses. This arose predominately due to the exponent a being restrained to approximately 0.5 to 0.62 and using rock type as a predictor of m i . Modifications to the equations for determining the Hoek-Brown parameters are provided that overcome these problems. In the course of reviewing the Hoek-Brown criterion new equations were derived for estimating the shear strength of intact rock and rockfill. Empirical slope design curves have also been developed for use as a preliminary tool for slope design. Acknowledgements Page iii ACKNOWLEDGEMENTS The support of the sponsors of the research project - Dams Risk Project - Estimation of the Probability of Failure, the Australian Research Council, and the Faculty of Engineering at the University of New South Wales is acknowledged. The sponsors of the Dams Risk Project were: • ACT Electricity and Water; • Australian Water Technologies, Sydney Water Corporation; • Dams Safety Committee of NSW; • Department of Land and Water Conservation; • Department of Land and Water Conservation - Dams Safety; • Electric Corporation of New Zealand (ECNZ); • Goulburn Murray Water; • Gutteridge Haskins and Davey (GHD); • Hydro-Electric Commission, Tasmania; • Melbourne Water; • NSW Department of Public Works and Services; • Pacific Power; • Queensland Department of Natural Resources; • Snowy Mountains Engineering Corporation (SMEC); • Snowy Mountains Hydro-Electricity Authority. • South Australia Water Corporation; • Water Authority of Western Australia; The access to, and assistance with collection of data provided by the United States Bureau of Reclamation and BC Hydro is also acknowledged. Thanks are made to Pells Sullivan Meynink Pty Ltd who provided the data for most of the case studies for the rock mass component of this thesis. Thanks also to their staff who were always available to provide assistance and encouragement. Particular thanks to Alex Duran who worked with the author on the creation of the slope design curves. Acknowledgements Page iv A general acknowledgement is made to the organisations that provided data on various mine slopes and test results that have been used in the development of this thesis, yet for the purposes of confidentiality their contributions cannot be properly referenced. Marcus Helgstedt and Anna Tarua are acknowledged for their assistance with computer analysis of some of the rock mass strength case studies. To my fellow PhD comrades: Mark Foster, James Glastonbury and Gavan Hunter, a major thankyou for your encouragement through example and your friendship. To my friends, who have not only provided support but also nagging questions e.g. “Are you finished yet?” … “Yes”. To my parents, thanks for your values, your encouragement and your genes. To my supervisor and co-supervisor Garry Mostyn and Robin Fell respectively, thankyou not only for your invaluable assistance but also for the invaluable practical experience you gave me in the areas of rock and dam engineering. Finally, to my fiancée, Rebecca: thanks for hanging in all these years waiting for (and putting up with) me. Table of contents Page v TABLE OF CONTENTS CHAPTER 1: INTRODUCTION 1.1 THESIS OBJECTIVES.......................................................................................... 1.1 1.2 THE BACKGROUND TO THIS THESIS ............................................................ 1.2 1.3 THE CHAPTERS IN THIS THESIS ..................................................................... 1.3 1.3.1 The analysis of concrete and masonry dam incidents.......................................... 1.3 1.3.2 The shear strength of rock masses ....................................................................... 1.4 1.4 PUBLISHED PAPERS/REPORTS ....................................................................... 1.6 CHAPTER 2: THE ANALYSIS OF CONCRETE AND MASONRY DAM INCIDENTS 2.1 OUTLINE OF THIS CHAPTER........................................................................... 2.1 2.2 STRUCTURE AND ASSEMBLY OF CONGDATA DATABASE..................... 2.4 2.2.1 Sources of Data .................................................................................................... 2.4 2.2.2 CONGDATA Layout ............................................................................................ 2.9 2.2.3 Data Entered into CONGDATA......................................................................... 2.12 2.2.3.1 Definitions of Failures/Accidents............................................................... 2.12 2.2.3.2 Types of Dams............................................................................................ 2.14 2.2.3.3 Failure Types............................................................................................. 2.14 2.2.3.4 Incident Time.............................................................................................. 2.15 2.2.3.5 Type of Foundation.................................................................................... 2.15 2.2.3.6 Dam Height ................................................................................................ 2.15 2.2.3.7 Detection Methods..................................................................................... 2.16 2.2.3.8 Classification of Causes of Incidents of Dams And Reservoirs................. 2.17 2.2.3.9 Classification of Remedial Measures......................................................... 2.22 2.2.4 Selection of Additional Variables...................................................................... 2.24 2.2.4.1 Time of Incidents........................................................................................ 2.24 2.2.4.2 Foundation Incident Mode......................................................................... 2.25 2.2.4.3 Dam Incident Mode.................................................................................... 2.26 2.2.4.4 Comments on Incidents.............................................................................. 2.26 Table of contents Page vi 2.2.4.5 Description of the Failure or Accident ...................................................... 2.26 2.2.4.6 Additional Geological Information............................................................ 2.26 2.2.4.7 Dam Dimensions........................................................................................ 2.28 2.2.4.8 Valley Shape............................................................................................... 2.29 2.2.4.9 Radius of Curvature................................................................................... 2.29 2.2.4.10 Monitoring and Surveillance Data ............................................................ 2.31 2.2.4.11 Warning Rating.......................................................................................... 2.32 2.2.4.12 Warning Time............................................................................................. 2.32 2.2.4.13 Other Design Factors................................................................................. 2.32 2.2.5 Assumptions Made in Assembling the Database............................................... 2.33 2.2.6 Data on the Population of Dams ........................................................................ 2.36 2.3 RESULTS OF ANALYSIS OF THE DATABASE ............................................ 2.40 2.3.1 Summary of Incidents ........................................................................................ 2.40 2.3.2 Year Commissioned of Dams Experiencing Incidents ...................................... 2.45 2.3.3 Height................................................................................................................. 2.54 2.3.4 Age at Failure..................................................................................................... 2.60 2.3.5 Incident Causes.................................................................................................. 2.78 2.3.6 Monitoring and Surveillance Data ..................................................................... 2.85 2.3.6.1 Using ICOLD Terms .................................................................................. 2.85 2.3.6.2 Details of Warnings ................................................................................... 2.89 2.3.7 Remedial Measures............................................................................................ 2.98 2.3.8 Geology............................................................................................................ 2.101 2.3.8.1 Geology of Dam Foundations Experiencing Incidents............................ 2.101 2.3.8.2 Geology of the Population of Dams......................................................... 2.106 2.3.9.3 Geology - Comparison Between Incidents and Population..................... 2.112 2.3.9 Other Design Factors in Failed Dams .............................................................. 2.123 2.4 METHOD OF FIRST ORDER PROBABILITY ASSESSMENT .................... 2.132 2.4.1 Probability of Failure....................................................................................... 2.132 2.4.1.1 Introduction.............................................................................................. 2.132 2.4.1.2 Population of Dams ................................................................................. 2.133 2.4.1.3 Dam Year ................................................................................................. 2.135 2.4.1.4 Probabilities of Failure............................................................................ 2.135 2.4.1.5 Gravity Dams - Separation of Concrete and Masonry Dams.................. 2.146 Table of contents Page vii 2.4.2 General Approach for Estimating the Probability of Failure for Individual Gravity Dams ................................................................................................... 2.153 2.4.3 Details of the Method for Estimating the Probability of Failure for Individual Gravity Dams ................................................................................. 2.154 2.4.4 Gravity Dam Probability Multiplication Factors............................................. 2.158 2.4.4.1 Soil/Rock Foundation Factor, f SF and f PF ................................................ 2.158 2.4.4.2 Geology Types - Sliding on Rock, f SG ....................................................... 2.161 2.4.4.3 Geology Type - Piping on Rock, f GE ......................................................... 2.164 2.4.4.4 Height on Width Ratio, f H/W ...................................................................... 2.164 2.4.4.5 Other Observations, f O ............................................................................. 2.169 2.4.4.6 Surveillance, f S ......................................................................................... 2.169 2.4.5 Results.............................................................................................................. 2.170 2.5 DISCUSSION AND CONCLUSIONS.............................................................. 2.172 CHAPTER 3: THE SHEAR STRENGTH OF INTACT ROCK 3.1 INTRODUCTION.................................................................................................. 3.1 3.2 FAILURE CRITERIA FOR INTACT ROCK....................................................... 3.2 3.3 LABORATORY TEST DATABASE FOR INTACT ROCK............................. 3.12 3.4 AN ANALYSIS OF THE ANALYSIS OF DATA ............................................. 3.14 3.5 HOEK-BROWN CRITERION FOR INTACT ROCK........................................ 3.24 3.6 GENERALISED CRITERION FOR INTACT ROCK ....................................... 3.32 3.7 GLOBAL PREDICTION..................................................................................... 3.49 3.8 COMPARISON OF CRITERIA.......................................................................... 3.60 3.9 SYSTEMATIC ERROR IN HOEK-BROWN CRITERION............................... 3.64 3.10 APPLICATION TO SLOPE ENGINEERING.................................................... 3.73 3.11 CONCLUSION.................................................................................................... 3.77 CHAPTER 4: THE SHEAR STRENGTH OF ROCKFILL 4.1 OUTLINE OF THIS CHAPTER........................................................................... 4.1 4.2 FACTORS AFFECTING THE SHEAR STRENGTH OF ROCKFILL ............... 4.2 Table of contents Page viii 4.2.1 Confining Pressure............................................................................................... 4.2 4.2.2 Particle Strength................................................................................................... 4.6 4.2.3 Uniformi ty Coefficient ........................................................................................ 4.8 4.2.4 Density............................................................................................................... 4.10 4.2.5 Maximum Particle Size...................................................................................... 4.12 4.2.5.1 Increasing d max with Constant D.................................................................. 4.13 4.2.5.2 Increasing d max with Constant d max /D.......................................................... 4.13 4.2.6 Silt and Sand Fines versus Gravel and Larger Particle Content ........................ 4.14 4.2.7 Particle Angularity............................................................................................. 4.16 4.2.8 Other Factors...................................................................................................... 4.17 4.2.9 Summary of Factors Affecting the Secant Friction Angle ................................ 4.18 4.3 SHEAR STRENGTH CRITERIA ....................................................................... 4.19 4.4 DATABASE OF TRIAXIAL SHEAR TESTS.................................................... 4.26 4.5 DATABASE ANALYSIS.................................................................................... 4.29 4.5.1 Analysis Methodology....................................................................................... 4.29 4.5.2 Secant Friction Angle, φ sec , Versus Normal Stress, σ n ...................................... 4.30 4.5.2.1 General Assessment of Database............................................................... 4.30 4.5.2.2 Statistical Analysis of Database................................................................. 4.40 4.5.3 Maximum Principal Stress, σ′ 1 , versus Minimum Principal Stress, σ′ 3 ............ 4.41 4.5.3.1 Secant Friction Angle Versus Normal Stress............................................. 4.58 4.5.4 Hoek-Brown Criterion....................................................................................... 4.61 4.6 CONCLUSION.................................................................................................... 4.64 CHAPTER 5: EMPIRICAL ROCK SLOPE DESIGN 5.1 INTRODUCTION.................................................................................................. 5.1 5.2 REVIEW OF THE ROCK MASS RATING SYSTEMS ...................................... 5.2 5.2.1 Methods for Estimating the Basic Rock Mass Rating......................................... 5.3 5.2.1.1 The Rock Mass Rating, RMR, and Geological Strength Index, GSI............ 5.3 5.2.1.2 Mining Rock Mass Rating, MRMR.............................................................. 5.6 5.2.1.3 Rock Mass Strength, RMS............................................................................ 5.9 5.2.1.4 Slope Rock Mass Rating, SRMR................................................................ 5.11 5.2.1.5 Modified Rock Mass Classification, M-RMR............................................. 5.14 Table of contents Page ix 5.2.1.6 Basic Quality, BQ...................................................................................... 5.17 5.2.2 Adjustment Factors to basic rock mass ratings.................................................. 5.19 5.3 A REVIEW OF SLOPE DESIGN METHODS WHICH ARE BASED ON ROCK MASS RATINGS .................................................................................... 5.25 5.3.1 Correlations with Shear Strength Parameters and Slope Angles....................... 5.25 5.3.2 Available Slope Performance Curves................................................................ 5.30 5.3.3 Pells Sullivan Meynink Slope Performance Curves.......................................... 5.36 5.4 ANALYSIS OF CASE STUDY DATA.............................................................. 5.39 5.4.1 Case Studies Used.............................................................................................. 5.39 5.4.2 Correlations of MRMR, SRMR and RMS with GSI......................................... 5.40 5.4.3 General Assessment of the Parameters in GSI .................................................. 5.51 5.4.4 Development of Generalised Slope Design Curves........................................... 5.54 5.4.4.1 Use of MRMR in Haines and Terbrugge Method...................................... 5.54 5.4.4.2 Revised Method Using MRMR................................................................... 5.54 5.4.4.3 Method Based on the Use of the Geological Strength Index, GSI ............. 5.55 5.5 CONCLUSION.................................................................................................... 5.62 CHAPTER 6: THE SHEAR STRENGTH OF ROCK MASSES 6.1 INTRODUCTION.................................................................................................. 6.1 6.2 ESTIMATING THE SHEAR STRENGTH OF A ROCK MASS......................... 6.3 6.2.1 Predicting Rock Mass Strength from Discontinuities.......................................... 6.3 6.2.2 Predicting Rock Mass Strength using Empirical Formulae................................. 6.8 6.2.3 Predicting Rock Mass Strength using the Hoek-Brown Criterion....................... 6.8 6.3 A DISCUSSION OF THE HOEK-BROWN CRITERION WITH PARTICULAR REFERENCE TO SLOPES....................................................... 6.16 6.3.1 Calculation of GSI ............................................................................................. 6.16 6.3.1.1 Intact Strength............................................................................................ 6.16 6.3.1.2 RQD ........................................................................................................... 6.17 6.3.1.3 Defect spacing............................................................................................ 6.18 6.3.1.4 Joint condition............................................................................................ 6.18 6.3.1.7 GSI from published figures........................................................................ 6.20 6.3.1.8 A Note on Schistose Rocks......................................................................... 6.20 Table of contents Page x 6.3.2 Estimation of Parameters from GSI................................................................... 6.26 6.3.2.1 The Rock Mass Disturbance Factor, D...................................................... 6.26 6.3.2.2 The Variation of the Hoek-Brown Parameters with GSI........................... 6.27 6.4 VALIDATION OF THE HOEK-BROWN CRITERION ................................... 6.30 6.4.1 Chichester Dam.................................................................................................. 6.30 6.4.2 Nattai North Escarpment Failure ....................................................................... 6.30 6.4.3 Katoomba Escarpment Failure........................................................................... 6.35 6.4.4 Aviemore Dam Insitu Shear Tests ..................................................................... 6.39 6.4.5 Discussion of the Results of the Analysis.......................................................... 6.43 6.5 A NEW ESTIMATION OF ROCK MASS STRENGTH ................................... 6.46 6.5.1 Development of a Modified Criterion ............................................................... 6.46 6.5.1.1 Exponent ‘α’ .............................................................................................. 6.47 6.5.1.2 Parameter ‘m’............................................................................................ 6.47 6.5.1.3 Parameter ‘s’ ............................................................................................. 6.48 6.5.2 Development of the Equations to Estimate the Parameters in the Hoek- Brown Criterion................................................................................................. 6.49 6.5.2.1 A New Equation for ‘m b ’............................................................................ 6.50 6.5.2.2 A New Equation for ‘s b ’ ............................................................................. 6.54 6.5.2.3 A New Equation for ‘α b ’ ............................................................................ 6.56 6.5.2.4 The Overall Equation................................................................................. 6.61 6.5.3 Summary of Method.......................................................................................... 6.69 CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS 7.1 CONCLUSIONS....................................................................................................7.1 7.1.1 The Analysis of Concrete and Masonry Dams .................................................... 7.1 7.1.2 The Shear Strength of Intact Rock....................................................................... 7.3 7.1.3 The Shear Strength of Rockfill ............................................................................ 7.4 7.1.4 Empirical Slope Design ....................................................................................... 7.4 7.1.5 The Shear Strength of Rock Masses.................................................................... 7.5 7.2 RECOMMENDATIONS FOR FURTHER RESEARCH.....................................7.7 7.2.1 The Analysis of Concrete and Masonry Dams .................................................... 7.7 7.2.2 The Shear Strength of Rock Masses.................................................................... 7.7 Table of contents Page xi REFERENCES APPENDICES APPENDIX A – CONGDATA DATABASE ................................................... CD-ROM APPENDIX B – DAM LIST - FAILURES .................................................................. A.1 APPENDIX C – POPULATION OF DAMS................................................................ A.3 APPENDIX D – CAUSES OF INCIDENTS.............................................................. A.11 APPENDIX E – SHEAR STRENGTH OF INTACT ROCK DATABASE ...... CD-ROM APPENDIX F – SHEAR STRENGTH OF ROCKFILL DATABASE ............. CD-ROM Table of contents Page xii TABLE OF FIGURES Figure 1.1. Thesis structure.......................................................................................... 1.2 Figure 2.1. Definition of dimensions in CONGDATA............................................... 2.30 Figure 2.2. Definition of dimensions in CONGDATA - section across river............. 2.31 Figure 2.3. The distribution of reported dam incidents vs country............................ 2.43 Figure 2.4. Reported incidents as percentage of country’s dam population from ICOLD (1984) ......................................................................................... 2.44 Figure 2.5. Year commissioned vs concrete gravity dam incidents .......................... 2.47 Figure 2.6. Year commissioned vs masonry gravity dam incidents .......................... 2.48 Figure 2.7. Year commissioned vs all dam incidents ................................................ 2.49 Figure 2.8. Year commissioned for world population data obtained from ICOLD (1979) ...................................................................................................... 2.50 Figure 2.9. Year commissioned vs percentage of gravity dams constructed in the USA......................................................................................................... 2.51 Figure 2.10. Year commissioned - failures/population per period .............................. 2.52 Figure 2.11. CONGDATA - height ranges for all dam significant incidents ............... 2.55 Figure 2.12. CONGDATA - Height ranges for concrete gravity dam significant incidents................................................................................................... 2.56 Figure 2.13. CONGDATA - height ranges for masonry gravity dam significant incidents................................................................................................... 2.57 Figure 2.14. Height of failed dams - failures/population (%)...................................... 2.59 Figure 2.15. World dams - height ranges for all concrete & masonry dams ............... 2.60 Figure 2.16. Age at incident - all dams ........................................................................ 2.64 Figure 2.17. Age at incident - concrete gravity dams .................................................. 2.65 Figure 2.18. Age at incident - masonry gravity dams .................................................. 2.66 Figure 2.19. Time to significant incident - gravity dam incidents/population (%)...... 2.67 Figure 2.20. Time to significant incident - all dam incidents/population (%)............. 2.67 Figure 2.21. Failure mode: age at failure versus year commissioned (all dams)......... 2.73 Figure 2.22. Over topping: age at failure versus year commissioned (all dams)......... 2.74 Figure 2.23. Dam type: age at failure versus year commissioned ............................... 2.75 Figure 2.24. Age at significant incident versus year commissioned............................ 2.76 Figure 2.25. Age at significant incident versus year commissioned............................ 2.77 Figure 2.26. Causes of significant incidents (rock & unknown foundations) ............. 2.84 Table of contents Page xiii Figure 2.27. Causes of significant incidents (soil foundations)................................... 2.85 Figure 2.28. Warning types - gravity dams ................................................................. 2.86 Figure 2.29. Warning Types - All Dams ..................................................................... 2.87 Figure 2.30. Most common remedial measures - all dam incidents ............................ 2.99 Figure 2.31. Foundation incidents age, type and year commissioned - all dams ...... 2.104 Figure 2.32. Foundation incidents geology - all incidents......................................... 2.105 Figure 2.33. Geology for incidents in the foundation and dam population – all dams....................................................................................................... 2.115 Figure 2.34. Geology for incidents in the foundation and dam population – concrete gravity dams............................................................................ 2.116 Figure 2.35. Geology for incidents in the foundation and dam population – masonry gravity dams ........................................................................... 2.117 Figure 2.36. Foundation geology type as a percentage of the geology population – all dams.................................................................................................. 2.118 Figure 2.37. Foundation geology type as a percentage of the geology population – gravity dams .......................................................................................... 2.119 Figure 2.38. Foundation geology type as a percentage of geology population – arch dams ............................................................................................... 2.120 Figure 2.39. Foundation geology type as a percentage of geology population – buttress dams ......................................................................................... 2.121 Figure 2.40. Foundation incident geology and population – mode of failure/accident ...................................................................................... 2.122 Figure 2.41. Average failure stresses for dams with failure through the foundation. 2.131 Figure 2.42. Average failure stresses for Bhandardara Dam..................................... 2.131 Figure 2.43. h d /W versus year commissioned............................................................ 2.166 Figure 2.44. h d /W versus h d ....................................................................................... 2.167 Figure 2.45. h d /W factors........................................................................................... 2.168 Figure 2.46. Range of annual probability of failure for concrete gravity dams ......... 2.170 Figure 2.47. Range of annual probability of failure for masonry gravity dams ........ 2.171 Figure 3.1. Generalised failure criterion...................................................................... 3.2 Figure 3.2. Comparison of test results with theoretically based failure criteria (Johnston & Chiu, 1984) ........................................................................... 3.3 Figure 3.3. Comparison of Hoek-Brown criterion (solid) and Johnston criterion (dashed) for Melbourne mudstone (Johnston, 1985)................................. 3.4 Table of contents Page xiv Figure 3.4. Fits to artificial data (a) full range (b) low stress range .......................... 3.20 Figure 3.5. m i from literature against m i from test results and Hoek-Brown Equation................................................................................................... 3.26 Figure 3.6. Rock type against m i from test results and Hoek-Brown equation.......... 3.28 Figure 3.7. Unconfined compressive strength against that predicted by the Hoek- Brown equation ....................................................................................... 3.30 Figure 3.8. Uniaxial tensile strength against that predicted by the Hoek-Brown equation................................................................................................... 3.31 Figure 3.9. m i from literature against m i from test results and generalised equation................................................................................................... 3.34 Figure 3.10. m i from literature against α m i from test results and generalised equation................................................................................................... 3.36 Figure 3.11. Rock type against α m i from test results and generalised equation......... 3.37 Figure 3.12. Unconfined compressive strength against that predicted by generalised equation................................................................................ 3.39 Figure 3.13. Uniaxial tensile strength against that predicted by generalised equation................................................................................................... 3.41 Figure 3.14. α against m i .............................................................................................. 3.43 Figure 3.15. α against m i categorised by σ c ................................................................. 3.45 Figure 3.16. Family of failure envelopes..................................................................... 3.46 Figure 3.17. Results showing failure envelopes crossing............................................ 3.47 Figure 3.18. Residuals for global fit with α constant against σ′ 3 /σ c categorised by -σ c /σ t ........................................................................................................ 3.50 Figure 3.19. Residuals for global fit with variable α against σ′ 3 /σ c categorised by - σ c /σ t ......................................................................................................... 3.52 Figure 3.20. Three dimensional plot of global fit ........................................................ 3.54 Figure 3.21. σ′ 1 /σ c with fits for variable α against σ′ 3 /σ c categorised by -σ c /σ t for high stress................................................................................................ 3.56 Figure 3.22. σ′ 1 /σ c with fits for variable α against σ′ 3 /σ c categorised by -σ c /σ t for low stress ................................................................................................. 3.57 Figure 3.23. α against m i showing cases with measured or reported σ′ 3 and σ t ......... .3.59 Figure 3.24. σ′ 1 /σ c with fits for published m I against σ′ 3 /σ c categorised by m I for high stress................................................................................................ 3.62 Table of contents Page xv Figure 3.25. σ′ 1 /σ c with fits for published m I against σ′ 3 /σ c categorised by m I for low stress ................................................................................................. 3.63 Figure 3.26. Pattern of residuals for Hoek-Brown fits ................................................ 3.64 Figure 3.28. Hoek-Brown fits to artificial data............................................................ 3.67 Figure 3.29. Hoek-Brown fits to actual data................................................................ 3.69 Figure 3.30. Residuals for Hoek-Brown fits for weak rock against σ′ 3 /σ′ 3max categorised by α ...................................................................................... 3.71 Figure 3.31. Residuals for generalised fits for weak rock against σ′ 3 /σ′ 3max categorised by α ...................................................................................... 3.72 Figure 3.32. Residuals against σ′ 3 for various fits ....................................................... 3.75 Figure 4.1. Methods for representing the shear strength envelope.............................. 4.4 Figure 4.2. Variation of secant friction angle, φ sec , with respect to cell confining stress, σ′ 3 , for (a) dense and (b) medium dense crushed basalt from triaxial tests (Al-Hussaini, 1983)............................................................... 4.5 Figure 4.3. Average strength of rockfills from large-scale direct shear tests (Anagnosti & Popovic, 1982).................................................................... 4.5 Figure 4.4. Variation of secant friction angle, φ sec , with normal stress σ n (Indraratna et al., 1993) ............................................................................. 4.6 Figure 4.5. Shear strength and grain size curves for crushed (a) limestone and (b) marble (Anagnosti and Popovic, 1982)..................................................... 4.7 Figure 4.6. Shear strength and grain size curves for crushed flysch sandstone- marl rockfill (Anagnosti and Popovic, 1982)............................................ 4.7 Figure 4.7. Shear strength and grain size curves for different gradings of limestone gravel (Anagnosti and Popovic, 1982) ..................................... 4.9 Figure 4.8. Shear strength and grain size curves for (a) crystalline schist and (b) sandstone gravels (Anagnosti and Popovic, 1982).................................... 4.9 Figure 4.9. Scalped rockfill gradings (Marachi et al, 1969)...................................... 4.11 Figure 4.10. Strength porosity relationships with σ 3 = 88kPa (Marachi et al, 1969) .. 4.11 Figure 4.12. Void ratio vs angle of friction (modified from Nakayama et al., 1982).. 4.12 Figure 4.13. Friction angle vs ma ximum particle size (Thiers & Donovan, 1981) ..... 4.13 Figure 4.14. Effect of gravel content on φ for silty gravel based on USBR (1966) .... 4.15 Figure 4.15. Effect of gravel content on φ for clayey gravel based on USBR (1961) ...................................................................................................... 4.15 Table of contents Page xvi Figure 4.16. –4.76mm content vs secant angle of friction (Nakayama et al., 1982) ... 4.16 Figure 4.17. Gonzalez (1985) shear strength of rockfill equations.............................. 4.22 Figure 4.18. Friction angle, φ, vs normal stress, σ n . .................................................... 4.23 Figure 4.19. Frequency distributions for coefficients B versus porosity (Sarac & Popovic, 1985)......................................................................................... 4.23 Figure 4.20. Dependence between coefficient A and gravel unit weight (Sarac & Popovic, 1985)......................................................................................... 4.24 Figure 4.21. Dependence between coefficient A and mean grain diameter, d 50 (Sarac & Popovic, 1985) ......................................................................... 4.24 Figure 4.22. Secant friction angle, φ sec vs normal stress, σ n ........................................ 4.33 Figure 4.23. Secant friction angle, φ sec vs normal stress, σ n , sorted on angularity rating........................................................................................................ 4.34 Figure 4.24. Secant friction angle, φ sec vs normal stress, σ n , sorted on rock type = basalt........................................................................................................ 4.35 Figure 4.25. Secant friction angle, φ sec vs normal stress, σ n , sorted on coefficient of uniformity, c u ...................................................................................... 4.36 Figure 4.26. Secant friction angle, φ sec vs normal stress, σ n , sorted on maximum particle size, d max ..................................................................................... 4.37 Figure 4.27. Secant friction angle, φ sec vs normal stress, σ n , sorted on percent fines (passing 0.075mm) content ..................................................................... 4.38 Figure 4.28. Secant friction angle, φ sec vs normal stress, σ n , sorted on unconfined compressive strength of the rock substance, UCS (MPa) ....................... 4.39 Figure 4.29. RFI e versus void ratio.............................................................................. 4.43 Figure 4.30. RFI UCS versus unconfined compressive strength..................................... 4.43 Figure 4.31. RFI FINES versus percent fines................................................................... 4.44 Figure 4.32 Residuals versus unconfined compressive strength of intact rock ........... 4.46 Figure 4.33. Residuals versus d max ............................................................................... 4.47 Figure 4.34. Residuals versus void ratio...................................................................... 4.48 Figure 4.35. Residuals versus angularity rating........................................................... 4.49 Figure 4.36. Residuals versus fines content................................................................. 4.50 Figure 4.37. Residuals versus sample diameter........................................................... 4.51 Figure 4.38. Effect of unconfined compressive strength on σ′ 1 .................................. 4.52 Figure 4.39. Effect of angularity on σ′ 1 (7 = sub-angular to angular; 8 = angular)..... 4.52 Table of contents Page xvii Figure 4.40. Effect of fines content on σ′ 1 ................................................................... 4.53 Figure 4.41. Effect of maximum particle size on σ′ 1 ................................................... 4.53 Figure 4.42. Effect of initial void ratio on σ′ 1 ............................................................ .4.54 Figure 4.43. σ′ 1 vs σ′ 3 showing data used in analysis and RFI relationship................ 4.55 Figure 4.44. σ′ 1 vs σ′ 3 showing all data and RFI relationship..................................... 4.56 Figure 4.45. σ′ 1 vs σ′ 3 showing all data and RFI relationship (σ′ 3 up to 1.5MPa)...... 4.57 Figure 4.46. Effect of unconfined compressive strength on φ sec .................................. 4.59 Figure 4.47. Effect of angularity on φ sec (7 = sub-angular to angular; 8 = angular).... 4.59 Figure 4.48. Effect of fines content on φ sec .................................................................. 4.60 Figure 4.49. Effect of maximum particle size on φ sec .................................................. 4.60 Figure 4.50. Effect of initial void ratio on φ sec ............................................................. 4.61 Figure 4.51. Statistical analysis results using Hoek-Brown formula and for a = 0.6 and a = 0.95............................................................................................. 4.63 Figure 5.1. Estimate of GSI based on geological descriptions. (Hoek, 2000)............. 5.7 Figure 5.2. SRMR strength correlation (a) Island Copper Mine (b) Getchell Mine (Robertson, 1988).................................................................................... 5.14 Figure 5.3. Example of Planar Failure Case with High SMR.................................... 5.21 Figure 5.4. Slope height, H, vs slope height factor, ξ (after Chen, 1995) ................. 5.22 Figure 5.5. RMR versus slope angle (Orr, 1996)....................................................... 5.27 Figure 5.6. Observed cases (ESMR) vs (a) SMR, (b) CSMR (Chen, 1995) ............. 5.29 Figure 5.7. Upper bound slope height versus slope angle curve for rock masses (Hoek & Bray, 1981)............................................................................... 5.31 Figure 5.8. Slope angle versus slope height with regression curves (modified after McMahon, 1976)............................................................................. 5.33 Figure 5.9. Slope height vs slope angle for MRMR (Haines & Terbrugge, 1991).... 5.34 Figure 5.10. Haines & Terbrugge (1991) slope design replotted on basis of slope angle versus slope height showing Haines & Terbrugge (1991) slope data. ......................................................................................................... 5.35 Figure 5.11. Slope performance curves for case studies (Duran & Douglas, 1999).... 5.37 Figure 5.12. Correlations of GSI with MRMR, SRMR, RMS rating (mod. Duran and Douglas, 2002).................................................................................. 5.42 Figure 5.13. GSI versus slope height for failed and stable slopes............................... 5.51 Table of contents Page xviii Figure 5.14. GSI defect spacing rating versus slope height for failed and stable slopes....................................................................................................... 5.52 Figure 5.15. GSI defect condition rating versus slope height for failed and stable slopes....................................................................................................... 5.52 Figure 5.16. GSI RQD rating versus slope height for failed and stable slopes ........... 5.53 Figure 5.17. GSI UCS rating versus slope height for failed and stable slopes............ 5.53 Figure 5.18. Haines & Terbrugge (1991) slope design curves & slope data (Figure 5.10) with additional case studies (Duran & Douglas, 1999)................. 5.56 Figure 5.19. Suggested slope design curves for MRMR (Duran & Douglas, 1999)... 5.57 Figure 5.20. Slope height vs slope angle case study data and the author’s proposed design curves for a dry slope................................................................... 5.58 Figure 5.21. Slope height vs slope angle case study data and a comparison of design curves for a dry slope................................................................... 5.59 Figure 5.22. Slope height vs slope angle case study data and the author’s proposed design curves for moderate pressures...................................................... 5.60 Figure 5.23. Slope height vs slope angle case study data and a comparison of design curves for moderate pressures...................................................... 5.61 Figure 6.1. Heavily jointed rock mass ......................................................................... 6.1 Figure 6.2. Example of shear failure through rock mass at the toe of a slope - Nattai Escarpment Failure ......................................................................... 6.2 Figure 6.3. Assessment of Barton and Bandis (1982) JRC 0 vs JRC n .......................... 6.7 Figure 6.4. Values of the parameter m i for intact rock (Hoek, 1999) ........................ 6.11 Figure 6.5. Estimation of GSI (Hoek, 1997).............................................................. 6.12 Figure 6.6. History of the Hoek-Brown criterion (Hoek, 2002) ................................ 6.13 Figure 6.7. Scale effect of Intact Rock (Hoek and Brown, 1980) ............................. 6.17 Figure 6.8. Slope failure block size ........................................................................... 6.19 Figure 6.9. Effect of scale on defect properties ......................................................... 6.19 Figure 6.10. GSI Table (Hoek et al, 1998) .................................................................. 6.22 Figure 6.11. E d versus GSI case study data and Hoek et al (1995) equation for σ c ≥ 100MPa and σ c = 10MPa ..................................................................... 6.24 Figure 6.12. E d test from case studies versus E d pred from Hoek et al (1995) equation................................................................................................... 6.25 Figure 6.13. Variation of a, s and m b /m i with GSI....................................................... 6.28 Figure 6.14. Typical section of the Nattai North failure (Pells et al, 1987)................. 6.31 Table of contents Page xix Figure 6.15. Illustration of the failure mechanism at Nattai North (Helgstedt, 1997)........................................................................................................ 6.32 Figure 6.16. Katoomba Escarpment Failure ................................................................ 6.36 Figure 6.17. Katoomba Escarpment Failure, column prior to collapse....................... 6.37 Figure 6.18. Direct Shear Test Set up (Foster & Fairless, 1994)................................. 6.41 Figure 6.19. Example of mesh used (Helgstedt, 1997)................................................ 6.44 Figure 6.20. Close up of the simulated jack (Helgstedt, 1997) ................................... 6.44 Figure 6.21. Back analysis results using Figure 6.5 for GSI ....................................... 6.45 Figure 6.22. Test results for tectonised quartzitic sandstone (Habimana et al, 2002)........................................................................................................ 6.52 Figure 6.23. The author’s statistical fits to Habimana et al (2002) data...................... 6.53 Figure 6.24. m b versus GSI .......................................................................................... 6.54 Figure 6.25. GSI for an intact or massive rock structure (Hoek, 1999)....................... 6.55 Figure 6.26. s b versus GSI ........................................................................................... 6.56 Figure 6.27. α b versus GSI .......................................................................................... 6.57 Figure 6.28. Graphical representation of the equations for α and m........................... 6.58 Figure 6.29. Transition of α and m from intact rock to rock mass .............................. 6.59 Figure 6.30. Original and modified relationships for α i and m i ................................... 6.60 Figure 6.31. Shear strength curves for tectonised quartzitic sandstone (Habimana et al, 2002)............................................................................................... 6.61 Figure 6.32. Results of analysis of Habimana et al (2002) data using the new equation and parameters from equations ................................................. 6.63 Figure 6.33. Results of global analysis of Habimana et al (2002) data using new equations.................................................................................................. 6.64 Figure 6.34. Non-dimensionalised plot of new shear strength curves for m i = 40 and varying GSI....................................................................................... 6.65 Figure 6.35. Non-dimensionalised plot of new shear strength curves for m i = 4 and varying GSI....................................................................................... 6.66 Figure 6.1. Comparison of the author’s criterion and the Hoek-Brown criterion (Hoek, 2002) for m i = 40 ......................................................................... 6.67 Figure 6.2. Comparison of the author’s criterion and the Hoek-Brown criterion (Hoek, 2002) for m i = 4 ........................................................................... 6.68 Table of contents Page xx TABLE OF TABLES Table 2.1. Bibliography for failed dams in CONGDATA .......................................... 2.6 Table 2.2. CONGDATA parameters........................................................................ 2.10 Table 2.3. Causes of incidents of concrete dams ...................................................... 2.18 Table 2.4. Causes of incidents of masonry dams ..................................................... 2.19 Table 2.5. Causes of incidents to appurtenant works ............................................... 2.20 Table 2.6. Causes of incidents of reservoirs............................................................. 2.21 Table 2.7. Causes of incidents downstream of dam................................................. 2.21 Table 2.8. Classification of remedial measures........................................................ 2.23 Table 2.9. Number of dam incidents in database by type ........................................ 2.40 Table 2.10. Number of significant dam incidents in database by type....................... 2.40 Table 2.11. Number of dam incidents reported in each country................................ 2.42 Table 2.12. Year commissioned - failures vs population per period.......................... 2.53 Table 2.13. Year commissioned - accidents vs population per period....................... 2.54 Table 2.14. Percent of concrete & masonry dam fails vs population for height ........ 2.58 Table 2.15. Percent of concrete & masonry accidents vs population for height ........ 2.58 Table 2.16. No. of dam foundation sliding & piping failures vs age at failure.......... 2.62 Table 2.17. No. of structural (shear or tensile) failures vs age at failure ................... 2.63 Table 2.18. Time to significant incident - incident/population of dams surviving period (%)................................................................................................ 2.68 Table 2.19. Time to significant incident..................................................................... 2.69 Table 2.20. Details of dam failure water levels.......................................................... 2.70 Table 2.21. Failure types ............................................................................................ 2.78 Table 2.22. Main causes of incidents in all dams ....................................................... 2.79 Table 2.23. Main causes of incidents in concrete gravity dams ................................. 2.80 Table 2.24. Main causes of incidents in masonry gravity dams ................................. 2.80 Table 2.25. Main failure causes for dams with soil foundations ................................ 2.81 Table 2.26. Main significant incident causes for dams with rock or unknown foundations .............................................................................................. 2.82 Table 2.27. Warning types vs dam type - failures...................................................... 2.88 Table 2.28. Warning types vs dam type - accidents ................................................... 2.88 Table 2.29. Warning types vs dam type - major repairs............................................. 2.89 Table 2.30. Warning ratings for failed dams .............................................................. 2.90 Table of contents Page xxi Table 2.31. Details of dam failures and descriptions of warnings ............................. 2.91 Table 2.32. Details of dam significant accidents and descriptions of warnings......... 2.95 Table 2.33. Remedial measures - all dam incidents ................................................. 2.100 Table 2.34. Geology for dams with failure in the foundation.................................. 2.102 Table 2.35. Geology for dams with accidents in the foundation.............................. 2.103 Table 2.36. Foundation geology for Australia, New Zealand, Portugal and USBR (percent and number for each group) .................................................... 2.109 Table 2.37. Foundation geology for Australia, New Zealand, Portugal & USBR dams - totalled Figures .......................................................................... 2.111 Table 2.38. Failed dams with grouted foundation.................................................... 2.123 Table 2.39. Crest length/height for failed dams and population .............................. 2.125 Table 2.40. Upstream and downstream slopes for failed dams ................................ 2.126 Table 2.41. H d /W for failed dams ............................................................................. 2.128 Table 2.42. Back analysed shear strengths for failed dams (mod. from Rich, 1995)...................................................................................................... 2.129 Table 2.43. Calculated normal stresses along the failure plane of back analysed gravity dams .......................................................................................... 2.130 Table 2.44. Number of dams as at 1992................................................................... 2.133 Table 2.45. Population of dams by dam type and year commissioned .................... 2.134 Table 2.46. Number of dams (excluding China) in the population.......................... 2.134 Table 2.47. Annual probability of failure (1992, exc. China) - all failure types...... 2.136 Table 2.48. Probability of failure (as at 1992, exc. China, non-annualised) - all failure types ........................................................................................... 2.137 Table 2.49. Annual probability of failure (as at 1992, excluding China) - sliding failures................................................................................................... 2.138 Table 2.50. Probability of failure (as at 1992, excluding China, non-annualised) - sliding failures ....................................................................................... 2.139 Table 2.51. Annual probability of failure (as at 1992, excluding China) - piping failures................................................................................................... 2.140 Table 2.52. Probability of failure (as at 1992, excluding China, non-annualised) - piping failures........................................................................................ 2.141 Table 2.53. Annual probability of failure (as at 1992, excluding China) - tension/shear failures through dam body............................................... 2.142 Table of contents Page xxii Table 2.54. Probability of failure (as at 1992, excluding China, non-annualised) - tension/shear failures through dam body............................................... 2.143 Table 2.55. Number of failures during overtopping where the failure mode was unknown................................................................................................ 2.144 Table 2.56. No. of failures where the failure mode was unknown (no overtopping) .......................................................................................... 2.145 Table 2.57. Distribution of concrete and masonry gravity dams in the USA........... 2.146 Table 2.58. Distribution of concrete and masonry gravity dams chosen for analysis .................................................................................................. 2.148 Table 2.59. Summary of annualised probabilities of failure for gravity dams (exc. China) .................................................................................................... 2.148 Table 2.60. Suggested values for annualised probabilities of failure for gravity dams (excluding China)......................................................................... 2.149 Table 2.61. Annualised probabilities of failure for gravity dams - all failures ........ 2.150 Table 2.62. Annualised probabilities of failure for gravity dams - sliding failures . 2.150 Table 2.63. Annualised probabilities of failure for gravity dams - piping failures .. 2.151 Table 2.64. Annualised probabilities of failure for gravity dams - dam body tension/shear failures............................................................................. 2.151 Table 2.65. Number of failures during overtopping where failure mode was unknown................................................................................................ 2.152 Table 2.66. Number of failures where failure mode was unknown......................... 2.152 Table 2.67. Foundation types - USBR...................................................................... 2.158 Table 2.68. Foundation types - Australia/New Zealand........................................... 2.158 Table 2.69. Foundation types - Portugal .................................................................. 2.159 Table 2.70. Gravity dam foundation types - combined............................................ 2.159 Table 2.71. Foundations for gravity dam failures by sliding or piping.................... 2.159 Table 2.72. Gravity dam factors for piping and sliding failure on soil and rock, f SF and f PF ............................................................................................... 2.160 Table 2.73. Foundation types - accidents ................................................................. 2.160 Table 2.74. Weighting factors used for weighted average (ICOLD (1984) dam population)............................................................................................. 2.161 Table 2.75. Adopted gravity dam factors for sliding on a rock foundation, f SG ....... 2.162 Table 2.76. Gravity dam factors for sliding on a rock foundation........................... 2.163 Table of contents Page xxiii Table 2.77. Multiplication factors for structural height/width ratio of gravity dams, f H/W ............................................................................................... 2.165 Table 2.78. Monitoring and surveillance multiplication factors, f S .......................... 2.169 Table 3.1. Various intact rock failure criteria............................................................. 3.6 Table 3.2. Empirical estimates of exponents for the equations in Table 3.1............ 3.10 Table 3.3. Suggested values of constant k (Yudhbir et al, 1983 and Bieniawsi, 1974)........................................................................................................ 3.10 Table 3.4. Values of M and B for a range of materials (Johnston, 1991) ................ 3.10 Table 3.5. Intact rock database descriptors .............................................................. 3.13 Table 3.6. Results of different regression methods on artificial data....................... 3.19 Table 3.7. Error in approximating σ ut as -σ c /(m i +1)................................................. 3.42 Table 3.8. Comparison of predictions ...................................................................... 3.60 Table 3.9. Errors in fitting Hoek-Brown criterion to materials with α ≠ 0.5 ........... 3.65 Table 3.10. Variation of σ c and m i with σ 3max for exact simulated results ................. 3.66 Table 3.11. Variation of σ c and m i with σ′ 3max for data set 434.................................. 3.68 Table 3.12. Triaxial component of strength ............................................................... 3.73 Table 3.13. Comparison of predictions for weak rocks at low stress......................... 3.74 Table 4.1. Increase in φ with d max /D from Marsal (1973) data for different σ n ........ 4.13 Table 4.2. Reduction in φ with particle size, d max , from Marsal (1973) data ........... 4.13 Table 4.3. Summary of factors affecting the secant friction angle........................... 4.18 Table 4.4. Parameters obtained using De Mello (1977) (Charles, 1991)................. 4.19 Table 4.5. Various shear strength criteria for rockfill .............................................. 4.20 Table 4.6. List of parameters in triaxial shear strength database ............................. 4.27 Table 4.7. Summary of basic statistics from the rockfill database........................... 4.28 Table 4.8. Changes in φ sec on Figure 4.46 to Figure 4.50 for σ n =1MPa and σ n = 0.5MPa .................................................................................................... 4.58 Table 4.9. Results from the statistical analysis of the rockfill database using the Hoek-Brown equation ............................................................................. 4.62 Table 5.1. Comparison of weightings for various rock mass rating methods ............ 5.2 Table 5.2. Rock mass rating (Bieniawski, 1989)........................................................ 5.5 Table 5.3. Geological strength index, GSI (Hoek et al, 1995) ................................... 5.6 Table 5.4. MRMR (Laubscher, 1977) ........................................................................ 5.8 Table 5.5. Defect condition rating for MRMR (Laubscher, 1977)............................. 5.8 Table of contents Page xxiv Table 5.6. RMS Classification and Ratings (mod. Selby, 1980).............................. 5.10 Table 5.7. SRK Geomechanics Classification or Slope Rock Mass Rating (SRMR) ................................................................................................... 5.13 Table 5.8. SRMR strength correlation (Robertson, 1988)........................................ 5.14 Table 5.9. Joint condition index I JC (Ünal, 1996)..................................................... 5.16 Table 5.10. Ratings for joint condition parameters (Ünal, 1996)............................... 5.17 Table 5.11. The basic quality, BQ, rock mass classes (Lin, 1998) ............................ 5.18 Table 5.12. Adjustment rating for joints (after Romana, 1985) ................................. 5.20 Table 5.13. Adjustment Rating for methods of excavation of slopes (after Romana, 1985) ........................................................................................ 5.20 Table 5.14. Tentative description of SMR classes (after Romana, 1985).................. 5.21 Table 5.15. Discontinuity condition factor λ (Chen, 1995)........................................ 5.22 Table 5.16. Blasting adjustment, A b (Ünal, 1996) ...................................................... 5.23 Table 5.17. Major plane of weakness adjustment, A w (Ünal, 1996)........................... 5.23 Table 5.18. Rock mass properties for RMR 76 (Bieniawski, 1976)............................. 5.25 Table 5.19. Stable slope angle versus MRMR (Laubscher, 1977) ............................. 5.26 Table 5.20. Case records for SMR (after Romana, 1985) .......................................... 5.28 Table 5.21. Parameters for McMahon’s (1976) slope relationship............................ 5.32 Table 5.22. Summary of slope data from case studies ............................................... 5.39 Table 5.23. Correlation between rating methods – author’s case studies................... 5.41 Table 5.24. Summary of best estimate GSI data for mine cases ................................ 5.43 Table 5.25. Summary of defect condition for GSI ..................................................... 5.44 Table 5.26. Summary of best estimate of Laubscher’s MRMR data for mine cases......................................................................................................... 5.45 Table 5.27. Summary of best estimate of SRMR data for mine cases ....................... 5.47 Table 5.28. Summary of best estimate of RMS data for mine cases.......................... 5.49 Table 6.1. Estimation of Hoek-Brown co-efficients .................................................. 6.9 Table 6.2. Rock mass deformability case studies..................................................... 6.23 Table 6.3. Guidelines for estimating disturbance factor D (Hoek et al, 2002)......... 6.26 Table 6.4. Maximum and minimum values of Hoek-Brown parameters using Figure 6.10............................................................................................... 6.29 Table 6.5. Joint orientation, spacing and persistence for Nattai North .................... 6.34 Table 6.6. Summary of parameters used for the Nattai North Escarpment Failure...................................................................................................... 6.34 Table of contents Page xxv Table 6.7. Summary of Hoek-Brown parameters for Nattai using RMR and the Hoek-Brown chart ................................................................................... 6.35 Table 6.8. UDEC output: average shear and normal stresses along the predicted failure plane ............................................................................................. 6.35 Table 6.9. Summary of parameters used for the Katoomba Escarpment Failure..... 6.38 Table 6.10. Summary of Hoek-Brown parameters for the Claystone in the Katoomba Escarpment Failure using RMR and the Hoek-Brown chart ......................................................................................................... 6.38 Table 6.11. Summary of the Joint Properties from the Joint Survey carried out by Read et al (1996) ..................................................................................... 6.40 Table 6.12. Hoek Parameters for Aviemore Shear Tests using RMR, and the Hoek-Brown Chart .................................................................................. 6.40 Table 6.13. Intact material parameters ....................................................................... 6.43 Table 6.14. Defect and Interface Material Parameters ............................................... 6.43 Table 6.15. Results of statistical analysis of Habimana et al (2002) test data............ 6.50 Introduction Page 1.1 1 INTRODUCTION 1.1 THESIS OBJECTIVES The overall objective of this thesis was to improve design procedures for large-scale structures constructed on or in rock. The first objective of this thesis was the development of a comprehensive database and analysis of concrete and masonry dam incidents world-wide, with a view to developing methods of assessing the risk of failure of existing dam structures and as a consequence of this, identifying possibilities for improvement in design. The results from this work showed that a large proportion of dams had incidents associated with the strength of their foundations, which indicated a need for a better understanding of the strength of rock masses. The second and major objective of this thesis was to provide a detailed assessment of the applicability of the Hoek-Brown criterion to estimating the shear strength of jointed rock masses and to improve upon any deficiencies found in the criterion. A particular focus was placed on low stress situations (e.g. dams and slopes) in weak materials. This work also included the development of methods for assessing the strength of intact rock and rockfill and new methods for estimating the stability of rock slopes using rock mass rating systems. To achieve the first objective the author collated and analysed the largest and most comprehensive database of world-wide concrete and masonry dam incidents using both published literature and unpublished records personally obtained from the dam industry. Results were presented on what factors have led to a higher chance of a dam incident occurring. These results were then used to develop an approximate method of assessing probabilities of failure. The process for assessing the Hoek-Brown criterion had several components. Firstly, large databases of triaxial tests on intact rock and rockfill were statistically analysed to assess the applicability of the Hoek-Brown criterion at the limits of intact rock and very poor rock mass. Secondly, analyses of the failures of large scale rock masses were Introduction Page 1.2 carried out to assess how well the Hoek-Brown criterion predicted the insitu rock mass strength. Finally, high quality triaxial tests on rock mass were obtained from the literature and used together with the results of the previous steps and plausibility checks to create new equations for estimating the parameters in the Hoek-Brown criterion. 1.2 THE BACKGROUND TO THIS THESIS This thesis is divided into two sections: the risk assessment of concrete and masonry dam failures and accidents and their causes, and the shear strength of rock masses as shown in Figure 1.1. The analysis of concrete and masonry dam incidents Chapter 2 The shear strength of intact rock Chapter 3 The shear strength of rockfill Chapter 4 Empirical rock slope design Chapter 5 The shear strength of rock masses Chapter 6 The shear strength of rock masses Thesis Figure 1.1. Thesis structure The dams community as part of the Dams Risk Project (together with the ARC and The Faculty of Engineering at the University of New South Wales) provided initial funding for this research. Details of the specific contributors are provided in the acknowledgement section. The first section of the thesis (Chapter 2) was carried out in response to the specific needs of the research project and its sponsors. The aim of the project was to provide a guide as to which types of dams were more likely to experience incidents (failures and accidents) based on a statistical analysis of the historical performance of dams. The author’s role on the project was to study concrete and masonry gravity dams. The second section of this thesis (Chapters 3-6) had its origins in the results of Chapter 2 and the general interests of the author and the project sponsors. It was found that failure through the foundation was common in the list of dams analysed. Furthermore, it was Introduction Page 1.3 found that information on how to assess the strength of the foundations of dams on rock masses was limited. For example, the ANCOLD (1991) guidelines on design criteria for concrete gravity dams suggest using references such as McMahon (1985) and Hoek (1983) to assess the strength of the foundation. The guidelines also state that “in the absence of more reliable data, preliminary analysis of foundations on sound jointed hard rock where sub-horizontal joints are not continuous, the following peak effective shear strength parameters are suggested:” c peak = 0.14σ c or 1.4MPa whichever is the lesser, where σ c is the unconfined compressive strength of the rock substance. φ peak = 45° This approach is very misleading and in many cases would over-estimate the strength. The authors aim for this section was to assess how good the methods for estimating rock mass strength were and to suggest possible changes to existing methods or new methods if required The work on rock mass strength was extended from looking at the foundations of dams to looking at the strength of rock masses in slopes and other works. This was mainly in an attempt to find better case studies to analyse, to cover a wider stress range and to provide a work on rock mass strength that had applicability wherever an assessment of rock mass strength was required. The different sections of the thesis given in Figure 1.1 are described in more detail below. 1.3 THE CHAPTERS IN THIS THESIS 1.3.1 The Analysis of Concrete and Masonry Dam Incidents Many attempts have been made at compiling and assessing statistics of dam failures. The main attempts at assessing dam incidents on a world-wide scale have been by ICOLD (1974, 1983 and 1995). ICOLD (1974) analysed previous dam failures and accidents based on questionnaires provided by the National Committees on Large Dams. ICOLD Introduction Page 1.4 (1983) attempted to improve the completeness of the information with further questionnaires. An existing dam population was also developed by ICOLD for comparison with failures. The population comprised a sample of dams from the ICOLD World Register of Dams (ICOLD 1973, 1976 and 1979). ICOLD (1995) was an attempt to update the statistics on failures of dams with particular emphasis on comparisons with dam types, heights and years commissioned of existing dams. Although an extensive analysis, the ICOLD attempt lacks depth in some key areas. Most notably in information on the foundation conditions and the geometry of the dams where failures have occurred. The accuracy and consistency of the ICOLD data has also come into question during this current research. Various other attempts have been made to compile data on failures and accidents, all of which either suffer from a lack of detail or from a limited data set. Most of the statistical analyses of failures and accidents and attempts to determine probabilities of failure (Von Thun (1985), da Silveira (1984, 1990), Fell (1996), Blind (1983), and Schnitter (1993)) tend not to go into much detail, generally assessing only height, year commissioned and type of dam structure. Most of the emphasis in the analysis of dam incidents has been on embankment dams. This section of the thesis (Chapter 2) describes the creation and analysis of a database on concrete and masonry dam incidents known as CONGDATA. The aim was to carry out as complete a study of concrete and masonry dam incidents as was practicable, with a greater emphasis than in other studies on the geology, mode of failure, and the warning signs that were observed. The study assessed the characteristics of the population of dams, and compared these with the characteristics of those dams that had experienced incidents. This helped to provide a guide as to which dams were more likely to experience incidents. This analysis was used to develop an approximate method of assessing probabilities of failure. This can be used in initial risk assessments of large concrete and masonry dams along with analyses of stability for various annual exceedance probability floods. Introduction Page 1.5 1.3.2 The shear strength of rock masses Methods used for assessing the shear strength of jointed rock masses are based on empirical criteria (Hoek and Brown, 1980, Yudhbir et al, 1983, Ramamurthy et al, 1994 and Sheorey, 1997). As a general rule such criteria are based on laboratory scale specimens with very little, and often no, field validation. The most commonly used strength criterion, having received widespread interest and use over the last two decades, is the Hoek-Brown empirical rock mass failure criterion, the most general form of which is given in Equation 1.1. Hoek and Brown (1980) developed this rock mass criterion as they “found that there were really no suitable criteria for the purpose of underground excavation design” (Hoek, 2001). The equation, which has subsequently been updated by Hoek and Brown (1988), Hoek et al. (1992), Hoek et al. (1995) and Hoek et al (2002), was based on their criterion for intact rock. The only ‘rock mass’ tested and used in the original development of the Hoek-Brown criterion was 152mm core samples of Panguna Andesite from Bougainville in Papua New Guinea (Hoek and Brown, 1980). Hoek and Brown (1988) later noted that it was likely this material was in fact ‘disturbed’. The validation of the updates of the Hoek-Brown criterion have been based on experience gained whilst using this criterion. To the author’s knowledge the only data published supporting this experience has been two mine slopes cited in Hoek et al (2002). a c b c s m         + ′ + ′ = ′ σ σ σ σ σ 3 3 1 (1.1) This thesis assesses the Hoek-Brown criterion in detail and modifies it into a more generalised form to account for various inconsistencies in the current version. The assessment of the criterion is carried out by looking at several of its bounds including intact rock (Chapter 3) and rockfill (Chapter 4). Case studies of various failures and highly stressed rock masses are used, together with published laboratory test results on rock mass samples, to assess the Hoek-Brown criterion and to develop new equations that can be used to estimate the parameters of the Hoek-Brown equation (Chapter 6). Introduction Page 1.6 The individual chapters in this section of the thesis not only provide a basis for modifying the Hoek-Brown criterion (discussed in Chapter 6) but also have their own individual results including: • Chapter 3 - A statistical analysis of a database of over 4500 triaxial tests on intact rock and the subsequent development of new shear strength criterion for intact rock. • Chapter 4 - A review of current criteria for the shear strength of rockfill and the development of a new shear strength criterion for compacted rockfill based on a database of over 550 rockfill triaxial tests gathered from the literature and sponsors. • Chapter 5 - An analysis of current empirical slope design methods and the development of new slope design curves based on the author’s database of mine pit slopes. 1.4 PUBLISHED PAPERS/REPORTS The following papers and reports were published during the period of this thesis. Douglas, K.J. (1998) Case studies in the assessment of rock mass criteria. 3rd Young Geotechnical Professionals Conference, Melbourne. Douglas, K.J. and Mostyn, G. (1999) Strength of large rock masses – field verification. Rock Mechanics for Industry, Proceedings of the 37 th U.S. Rock Mechanics Symposium, Vail, Colorado, USA. 1:271-276. Balkema, Rotterdam, ISBN 90 5809 099 X0. Douglas, K., Spannagle, M. and Fell, R. (1998a) Estimating the probability of failure of concrete and masonry gravity dams. 1998 ANCOLD-NZSOLD Conference on Dams, Sydney. Douglas, K., Spannagle, M. and Fell, R. (1998b) Report on Analysis of Concrete and Masonry Dam Incidents. UNICIV, The School of Civil and Environmental Engineering, The University of New South Wales. Introduction Page 1.7 Douglas, K., Spannagle, M. and Fell, R. (1999a) Analysis of Concrete and Masonry Dam Incidents. The International Journal on Hydropower & Dams. 6(4):108-115. Aqua~Media, Surrey, ISSN 1352-2523. Douglas, K., Spannagle, M. and Fell, R. (1999b) Estimating the probability of failure of concrete and masonry gravity dams. ANCOLD Bulletin. No. 112:53-63. Australian National Committee on Large Dams, ISSN 0045-0731. Duran, A. and Douglas, K. (1999) “Do slopes designed with empirical rock mass strength criteria stand up?” Proceedings ISRM 9 th International Congress on Rock Mechanics, Paris, France, 1, pp. 87-90. Balkema, Rotterdam, ISBN 90 5809 070 1. Duran, A. & Douglas, K.J. (2000) Experience with empirical rock slope design. GeoEng2000: An International Conference on Geotechnical & Geological Engineering, 19-24 November, Melbourne, Australia, 2, pp. 41 and CD-Rom paper no. SNES1186, Technomic Publishing, Pennsylvania, ISBN 1-58716-068-4. Glastonbury, J. & Douglas, K.J. (2000) Catastrophic rock slope failures. GeoEng2000: An International Conference on Geotechnical & Geological Engineering, 19-24 November, Melbourne, Australia, Vol. 2 pp. 21 and CD-Rom paper no. SNES0507, Technomic Publishing, Pennsylvania, ISBN 1-58716-068-4. Helgstedt, M.D., Douglas, K.J. and Mostyn, G. (1997) A re-evaluation of in-situ direct shear tests at Aviemore Dam, New Zealand. Australian Geomechanics, 37 (June), pp. 56-65. Mostyn, G. & Douglas, K.J. (2000) Issues Lecture: The shear strength of intact rock and rock masses. GeoEng2000: An International Conference on Geotechnical & Geological Engineering, 19-24 November, Melbourne, Australia, Vol. 1, pp. 1389-1421, Technomic Publishing, Pennsylvania, ISBN 1-58716-067-6. Mostyn, G., M.D. Helgstedt and K.J. Douglas (1997) “Towards field bounds on rock mass failure criteria”. International Journal of Rock Mechanics and Mining Sciences, Vol. 34 (3-4): Paper No. 208. Analysis of Concrete and Masonry Dam Incidents Page 2.1 2 ANALYSIS OF CONCRETE AND MASONRY DAM INCIDENTS 2.1 OUTLINE OF THIS CHAPTER This chapter comprises a component of the research project on the risk assessment of dams. 17 sponsors comprising major dam owners and consultants from Australia and New Zealand support the project. The United States Bureau of Reclamation (USBR) and BC Hydro from Canada also assisted with the project. The aim of this component of the research was to provide a guide as to which dams were more likely to experience incidents based purely on a statistical analysis of historical incidents. The chapter describes the analysis of historical concrete and masonry dam incidents. For comparative purposes a compilation of data from a sample of existing concrete and masonry dams from Australia, New Zealand, Portugal and the USA is also presented for comparison with the incident database. A large portion (4168 dams from 22 countries) of the ICOLD (1973 and 1979) World Register was entered into a computer for further comparative purposes. The source for the analysis was a database developed by the author on failures and accidents in concrete and masonry dams known as CONGDATA. Many attempts have been made at compiling and assessing statistics of dam failures. The main attempts at assessing dam incidents on a worldwide scale have been by ICOLD (1974, 1983 and 1995). ICOLD (1974) analysed previous dam failures and accidents based on questionnaires provided by the National Committees on Large Dams. ICOLD (1983) attempted to improve the completeness of the information with further questionnaires. The presentation of the data and analyses was improved with the use of tables. An existing dam population was also developed for comparison with failures. The population comprised a sample of dams from the ICOLD World Register of Dams (ICOLD 1973, 1976 and 1979). ICOLD (1995) was an attempt to update the statistics on failures of dams with particular emphasis on comparisons with dam types, heights and years commissioned of existing dams. Although an extensive analysis, the ICOLD attempt lacks depth in some key areas. Most notably in information on the foundation conditions and the geometry of the dams where failures have occurred. The Analysis of Concrete and Masonry Dam Incidents Page 2.2 accuracy and consistency of the ICOLD data has also come into question during this current research (see Section 2.2.5). Vogel (1980, with updates to 1994) and Babb and Mermel (1968) have compiled lists of dam incidents with some limited comments and dimensions. Their main value is in providing a large source of references. USCOLD (1976 and 1988) collated a large amount of information on incidents in the USA. Other attempts at collecting data on historical incidents have been made by Jorgensen (1920), Jansen (1980), Varshney and Raheem (1971), USCOLD (1996) and Rao (1960). All of these either suffer from a lack of detail or from a limited data set. Smaller country scale data collections have been made for: • Spanish accidents and failures (Gomez Laa et al, 1979); • the deterioration of Italian Dams (Paolina et al, 1991); • South African dam incidents (Olwage & Oosthuizen, 1984); • Swedish accidents (Graham & Bartsch, 1995); • failures and accidents in the United Kingdom (Charles, 1985); • incidents in Australia (Ingles, 1984); and • failures and accidents in the USA (Hatem, 1985). Von Thun (1985) made an assessment of USA dams and their probability of failure based on a calculation of dam years. The parameters assessed were generally similar to those of ICOLD. Others who have attempted to analyse probabilities of failure include: da Silveira (1984, 1990); Fell (1996); Blind (1983); and Schnitter (1993) who generally based their analysis on ICOLD data and experience. Serafim (1981a, 1981b); Tavares and Serafim (1983); Smith (1972); Biswas and Chatterjee (1971); Gruner (1963, 1967); Kaloustian (1984) analysed incidents using ICOLD data and their own selected databases. These analyses tend not to go into much detail, generally assessing only Analysis of Concrete and Masonry Dam Incidents Page 2.3 height, year commissioned and type of dam structure. Most of the emphasis in the analysis of dam incidents has been on embankment dams. This study set out to carry out as complete a study of concrete and masonry dam failures and accidents as was practicable, with a greater emphasis than in other studies on the geology, mode of failure, and the warning signs that were observed. The study also sets out to assess the characteristics of the population of dams, and compares the characteristics of the failures and accidents with the population of dams, so a probability of failure or accident can be assigned. This data provides the basis for initial risk assessments of dams. The basic definitions used in CONGDATA and the subsequent analyses have been taken from ICOLD and are given in Section 2.2.3.1. The term incident has been used for both accidents and failures. Section 2.2 of this chapter describes the methods used in compiling and assessing the incident statistics. The results have been presented in Section 2.3. A method of first order probability assessment for gravity dams is provided in Section 2.4. Analysis of Concrete and Masonry Dam Incidents Page 2.4 2.2 STRUCTURE AND ASSEMBLY OF CONGDATA DATABASE 2.2.1 Sources of Data CONGDATA began with the information from the three ICOLD compilations of failures and accidents: • ICOLD (1995) Dam Failures Statistical Analyses. • ICOLD (1983) Deterioration of Dams and Reservoirs. • ICOLD (1974) Lessons From Dam Incidents. Where practicable ICOLD (1995) definitions were used. ICOLD (1995) was the main reference for the failures whilst accidents were principally from ICOLD (1983). ICOLD (1974) was used for further details when adding information into CONGDATA. The information in CONGDATA was then checked and updated using other existing databases including: • USCOLD (1976) Lessons from dam incidents, USA. • USCOLD (1988) Lessons from dam incidents. USA-II. • Vogel (1980) Bibliography of the History of Dam Failures. • Babb and Mermel (1968) Catalogue of Dam Disasters, Failures and Accidents. A large literature review was then conducted to gather as much information on dam failures and accidents as possible. References cited in the databases above were sought and then further references were obtained from journals; conference proceedings; reports; theses; and Internet pages. Published and unpublished reports were also accessed through sponsors and dam organisations. All references were followed to their origins as far as practically possible. The literature review was far more extensive than those previously reported for the development of other databases. Table 2.1 shows the bibliography for the failed dams contained in CONGDATA. Data from several additional dams was added to the database during the data gathering process. The additions are described in detail in Section 2.2.4. Analysis of Concrete and Masonry Dam Incidents Page 2.5 The sponsors of the research project, who are listed below, also provided access to information on their dams. • Australian Water Technologies, Sydney Water Corporation; • Department of Land and Water Conservation; • NSW Department of Public Works and Services; • SA Water Corporation; • ACT Electricity and Water; • Hydro-Electric Commission; • Dams Safety Committee of NSW; • Department of Land and Water Conservation - Dams Safety; • Snowy Mountains Engineering Corporation (SMEC); • Queensland Department of Natural Resources; • Goulburn-Murray Water; • Gutteridge Haskins and Davey; • Melbourne Water; • Pacific Power; • Sydney Water Corporation; • Water Authority of Western Australia; • Electric Corporation of New Zealand; • Snowy Mountains Hydro-Electricity Authority. The United States Bureau of Reclamation (USBR) in Denver allowed access to the information on their dams. This information was collected over two, three-week periods by the author together with Professor Robin Fell and Mark Foster. Other organisations that allowed access to data included: • BC Hydro; and the • Alberta Dam Safety Association. The data collected from the sponsors and other assisting organisations was used as a source of information on failures and more notably to assist in a collation of information on dam populations. Page 2.6 Table 2.1. Bibliography for failed dams in CONGDATA Dam References Angels, USA Babb and Mermel (1968); ICOLD (1974, 1995); USCOLD (1975); Vogel (1994) Ashley, USA Babb and Mermel (1968); Engineering News (1909); ICOLD (1974, 1984, 1995); Jorgensen (1920); Rao (1960); Scott and Von Thun (1993); Vogel (1994) Austin (Texas), USA Babb and Mermel (1968); Blanton (1915); Bowers (1928); Engineering News (1900a-e, 1901, 1902, 1908a-b, 1910b, 1915, 1916a-b); Engineering News Record (1911, 1918, 1911f); Engineering Record (1900a-b, 1911a-c, 1915a-b); Freeman and Alsop (1941); Hatton (1912); Hill (1902); Hornaday (1899); ICOLD (1974, 1995); Jorgensen (1920); King and Huber (1993); Leger et al (1997); McDonough (1940); Parker (1900); Patterson (1900); Rao (1960); Rosenberg (1900); Sawyer (1911); Schuyler (1908); Smith (1972); Taylor (1915); Taylor (1900); USCOLD (1975) Bacino di Rutte, Italy Fry (1996); Vogel (1984, 1994) Bayless, USA Babb and Mermel (1968); Bartholomew (1989); Bowers (1928); Engineering News (1910b, 1911); Engineering Record (1911d-e); ICOLD (1974, 1995); Jansen (1980); Leger et al (1997); Rao (1960); Scott and Von Thun (1993); Smith (1972) Bouzey, France Babb and Mermel (1968); Baker (1897); Courtney (1897); Engineering News (1897?); Fry (1996); ICOLD (1969, 1974, 1995); Institute of Civil Engineering (1897?); Jansen (1980); Jorgensen (1920); Leger et al (1997); Mary (1968); Rao (1960); Schuyler (1908); Smith (1972, 1995); The Engineer (1896, 1942); Vogel (1984, 1994); Wegmann (1889) Cheurfas, Algeria Babb and Mermel (1968); Benassini and Barona (1962); ICOLD (1969, 1974, 1995); Schuyler (1908); Smith (1972); Vogel (1994); Wegmann (1889) Chickahole, India ICOLD (1995); Lempérière et al (1997); Lempérière (1993); Murthy et al (1979); Vogel (1994) El Gasco, Spain Babb and Mermel (1968); Berga (1997); Gomez Laa et al (1979); ICOLD (1984); Jorgensen (1920); Schnitter (1994); Schuyler (1908); Smith (1972) Elmali I, Turkey Babb and Mermel (1968); ICOLD (1974, 1995); Vogel (1994); Yildiz and Üzücek (1994) Elwha River, USA Babb and Mermel (1968); Engineering Record (1912); ICOLD (1974, 1984, 1995); Reineking. (1914); USCOLD (1975); Vogel (1994) Fergoug I & II, Algeria Babb and Mermel (1968); ICOLD (1969, 1974, 1995); Lempérière (1993) Gallinas, USA Babb and Mermel (1968); Engineering News Record (1957); ICOLD (1974, 1984, 1995); Lempérière (1993); Sherman (1910); USCOLD (1975); Vogel (1994) Page 2.7 Dam References Gleno, Italy Babb and Mermel (1968); Bowers (1928); Coutinho Rodrigues (1987); Engineering News Record (1924a-c); Gruner (1963); ICOLD (1974, 1984, 1995); ITCOLD (1967); Mary (1968); Smith (1972); Vogel (1984, 1994) Granadillar, Spain Berga (1997); Gomez Laa et al (1979); ICOLD (1984) Habra, Algeria Babb and Mermel (1968); Gruner (1963); Gurtu (1925); Jansen (1980); Jorgensen (1920); Leger et al (1997); Rao (1960); Schuyler (1908); Smith (1972); Vogel (1994); Wegmann (1889) Hauser Lake II, USA Bowers (1928); ICOLD (1974, 1995); Jorgensen (1920); Rouve et al (1977); Sizer (1908); USCOLD (1975) Idbar, Yugoslavia ICOLD (1974, 1984, 1995); Mary (1968); Milovanovitch (1958) Khadakwasla, USA Babb and Mermel (1968); Biswas and Chatterjee (1971); Gruner (1967); Hunter (1964); ICOLD (1969, 1974, 1995); INCOLD (1967); Inglis (1962); Jansen (1980); Lempérière (1993); Murthy et al (1979); Murti (1967); Rao (1967); Vogel (1994) Kohodiar, India ICOLD (1995) Komoro, Japan Babb and Mermel (1968); ICOLD (1974, 1984, 1995); Vogel (1994) Kundli, India Babb and Mermel (1968); ICOLD (1969, 1974, 1984, 1995); Rao (1960); Vogel (1994) Lake Lanier, USA Babb and Mermel (1968); Bowers (1928); Coutinho Rodrigues (1987); Engineering News Record (1926a-b); Feld (1968); ICOLD (1974, 1984, 1995); Mary (1968); Rao (1960); Schnitter (1994); Scott and Von Thun (1993); USCOLD (1975); Veltrop, J.A. (1988); Vogel (1994) Leguaseca, Spain Berga, L. (1997); Fry, J. (1996); Guerreiro et al (1991); ICOLD (1995); Lempérière et al (1997) Lower Idaho Falls, USA ICOLD (1984, 1995); USCOLD (1988); Vogel (1994) Lynx Creek, USA Babb and Mermel (1968); ICOLD (1974); Vogel (1994) Malpasset, France Babb and Mermel (1968); Bellier et al (1976); Biswas and Chatterjee (1971); Carlier (1974); Commission Administrative d'Enquête - France (1965a-b); Commission de Contre-Expertise - France (1966); Coutinho Rodrigues (1987); Engineering News Record (1959, 1960a-b, 1962, 1963, 1964a-b, 1967); Flagg; Gosselin (1960); Gruner (1963, 1967); ICOLD (1974, 1984, 1995); Jansen (1988); Londe (1977); Mary (1968); Rao (1960); Scott and Von Thun (1993); Smith (1972); Stapleton (1976); Steger and Unterberger (1990); Terzaghi (1962); Vogel (1984,1994) Meihua, China Coutinho Rodrigues (1987); ICOLD (1995) Mohamed V, Morocco ICOLD (1984) Moyie River, USA Babb and Mermel (1968); Bowers (1928); Coutinho Rodrigues (1987); Engineering News Record (1926b); Feld (1968); ICOLD (1974, 1984, Page 2.8 Dam References 1995); Mary (1968); Rao (1960); Schnitter (1994); Scott and Von Thun (1993); USCOLD (1975); Veltrop (1988); Vogel (1994) Overholser, USA ICOLD (1974, 1984, 1995) Pagara, India Babb and Mermel (1968); ICOLD (1969, 1974, 1984, 1995); Rao (1960); Vogel (1994) Puentes, Spain Anderson and Trigg (1976); Babb and Mermel (1968); Berga (1997); Gomez Laa et al (1979); Hinds (1953); ICOLD (1974, 1984, 1995); Jansen (1980); Jorgensen (1920); Mary (1968); Schnitter (1994); Schuyler (1908); Smith (1972); Vogel (1984, 1994); Wegmann (1889) Santa Catalina, Mexico Babb and Mermel (1968); Lempérière (1993); Schuyler (1906); Vogel (1994) Selsford, Sweden ICOLD (1974, 1984, 1995) Sig, Algeria Babb and Mermel (1968); ICOLD (1969, 1974, 1995); Vogel (1994) St Francis, USA ASCE (1929); Babb and Mermel (1968); Bowers (1928); Clements (1969); David Rogers (1995); David Rogers and McMahon (1993); Engineering News Record (1928a-j, 1929a-b); Feld (1968); Gruner (1963); Grunsky and Grunsky (1928); ICOLD (1974, 1984, 1995); Jansen (1980, 1988); Jorgensen (1928); Leger et al (1997); Outland (1963); Ransome (1928); Rao (1960); Scott and Von Thun (1993); Smith (1972); Stapleton (1976); The Engineer (1928a-b); USCOLD (1975); Veesaert, C. (198?); Vogel (1994) Stony River, USA Bowers (1928); Engineering News (1914a-c); Engineering Record (1914); Finch (1914); ICOLD (1974); Jorgensen (1920); Rao (1960) Tigra, India Babb and Mermel (1968); Gurtu (1925); ICOLD (1969); ICOLD (1974); ICOLD (1984); ICOLD (1995); Jansen (1980); Lempérière (1993); Rao (1960); Vogel (1994) Torrejon Tajo, Spain Gomez Laa et al (1979); ICOLD (1984) Vega de Tera, Spain Babb and Mermel (1968); Berga (1997); Bollo (1965); Engineering News Record (1959b, 1960c); Gomez Laa et al (1979); Gruner (1963, 1967); ICOLD (1974, 1984, 1995); Rao (1960); Vogel (1984, 1994) Xuriguera, Spain Berga (1997); Fry (1996); ICOLD (1995) Zerbino, Italy Babb and Mermel (1968); Engineering News Record (1935); Fry, J. (1996); ICOLD (1974, 1984, 1995); ITCOLD (1967); Lempérière (1993); Vogel (1984, 1994) Analysis of Concrete and Masonry Dam Incidents Page 2.9 2.2.2 CONGDATA Layout The database was created using Microsoft Access for Windows 95 Version 9.0 (Access). The information was grouped under the following categories: • General description; • incident Details; • dimensions; • geology; • hydrology; and • references. A list of the parameters entered into the database is given in Table 2.2. Queries were developed in Access to analyse the data. Tables were then linked to Microsoft Excel for Windows 95 (Excel) spreadsheets for further analysis and interpretation. Excel was used to graph the various parameters. Analysis of Concrete and Masonry Dam Incidents Page 2.10 Table 2.2. CONGDATA parameters Variable Description Codes ID Identification number Significant Incident? (Y/N) Whether incident is significant Dam Name Name of dam Country Country dam is in Alternate Name 1 Other name Dam Type Type of dam Section 2.2.3.2 Year Commissioned Year dam commissioned Fail Acc Year of incident Failure/Accident Incident Category Section 2.2.3.1 Fail-Time Time to incident Section 2.2.3.3 CDR Time Time to incident Section 2.2.4.1 Fail-Type Where incident occurred Fail-Mode How incident occurred Cause A-E Causes of incident Tables 2.2-2.6 Detection Method Method of detecting incident Fail-Comments Comments about incident Remedial Measures A-D Methods of remediation Table 2.7 Concrete/ Masonry Type of concrete/masonry Foundation Whether foundation soil/rock Section 2.2.3.5 Geology A-C Types of foundation geology Section 2.2.4.4 Geology Comments Comments about foundation H lf (m) Height above lowest foundation Figure 2.1 H d (m) Structural height Figure 2.1 h wu (m) Height of water upstream - FSL Figure 2.1 h wt (m) Height of water at toe Figure 2.1 H f (m) Height to failure plane Figure 2.1 h wf (m) Height of water at failure Figure 2.1 W (m) Width of dam base Figure 2.1 W f (m) Width at failure plane Figure 2.1 Width of Spillway (m) Length of spillway Width of Non-Overflow Section (m) Crest length - spillway Width of Failed Section Length of failed section Where Failed Location of failure Upstream (xH:1V) Upstream slope of dam Figure 2.1 Downstream (yH:1V) Downstream slope of dam Figure 2.1 Valley Shape, L1 (m) Crest length Figure 2.2 L2 Left abutment length Figure 2.2 Analysis of Concrete and Masonry Dam Incidents Page 2.11 Table 2.2. CONGDATA parameters Variable Description Codes L3 Main valley width Figure 2.2 L4 Right abutment length Figure 2.2 Radius of Curvature (m) Radius of curvature of dam Warning Type 1-3 Type of warning given Section 2.2.4.11 Warning Time (weeks) Time from warning to incident Post-Tensioned? (Y/N) Whether post-tensioned Gallery (Y/N) Whether there is a gallery Gallery Elevation Height to gallery from dam base Drain Depth (m) Depth of drains into foundation Drain Spacing (m) Spacing of drains along dam Shear Key (Y/N) Whether there is a shear key Grouting Type Type of grouting Grout Depth Depth of grouting into foundation No. of victims Number of deaths due to incident References: Main references Analysis of Concrete and Masonry Dam Incidents Page 2.12 Analysis of Concrete and Masonry Dam Incidents Page 2.13 2.2.3 Data Entered into CONGDATA Details of dam incidents are given in CONGDATA. The following sections describe the coding used for input into Access. 2.2.3.1 Definitions of Failures/Accidents ICOLD(1995) define failure as ‘collapse or movement of part of a dam or part of its foundation, so that the dam cannot retain water. In general, a failure results in the release of large quantities of water, imposing risks on the people or property downstream’. ICOLD(1974) give the following definitions for failures and accidents. F1 - A major failure involving the complete abandonment of the dam F2 - A failure which at the time may have been severe, but yet has permitted the extent of damage to be successfully repaired and the dam again brought into use A1 - An accident to a dam which has been in use for some time but which has been prevented from becoming a failure by immediate remedial measures, including possibly drawing down the water A2 - An accident to a dam which has been observed during the initial filling of the reservoir and which has been prevented from becoming a failure by immediate remedial measures, including possibly drawing down the water A3 - An accident to a dam during construction, i.e. by settlement of foundations, slumping of side slopes etc., which have been noted before any water was impounded and where the essential remedial measures have been carried out, and the reservoir safely filled thereafter. The term incident is used to describe failures, accidents and major repairs. USCOLD(1988) give the following definitions for other accidents and deteriorations. These have been adopted for the database. Analysis of Concrete and Masonry Dam Incidents Page 2.14 AR - Accidents or unusual problems encountered in the reservoir upstream of the dam, which have occurred during operation of the project, but which have not caused failure or major accident to the dam structure. MR - Extensive or important repairs to a dam that were required because of deterioration or to update certain features. Refacing of deteriorated concrete, repair of deteriorated riprap, or replacement of gates are examples under this definition. DDC - Damage to partially constructed dam or to temporary structure required for construction prior to the dam being essentially completed. Failure of cofferdam or unplanned overtopping of partially completed dam are examples under this definition. Where the exact definition of the failure or accident is uncertain an ‘F’ or an ‘A’ has been used respectively. The term significant incident has been introduced to describe failures, accidents and major repairs where the incident has directly affected the dam stability. Cases where the dam has been repaired due to a ‘theoretical danger’, such as the updating of design standards, or due to minor damage to the dam or spillways have not been included under this term. Analysis of Concrete and Masonry Dam Incidents Page 2.15 2.2.3.2 Types of Dams Coding for the types of dams in CONGDATA are: PG CB VA MV PG(M) CB(M) VA(M) MV(M) - Concrete gravity - Concrete buttress - Concrete arch - Concrete multi-arch - Masonry gravity - Masonry buttress - Masonry arch - Masonry multi-arch 2.2.3.3 Failure Types Codes for the failure types were obtained from ICOLD(1983) and are: Ff Fm Fb Fa Ffb Ffa Fba Fbm - Failure due to the dam foundation - Failure due to the dam materials - Failure due to the structural behaviour of the dam body - Failure due to the appurtenant works - Failure due to the foundation and to the structural behaviour of the dam body - Failure due to the foundation of the dam and to the appurtenant works - Failure due to the structural behaviour of the dam body and to the appurtenant works - Failure due to the structural behaviour of the dam body and to the dam materials Analysis of Concrete and Masonry Dam Incidents Page 2.16 2.2.3.4 Incident Time The times at which the incident took place (or was detected) are indicated by the codes below. These codes were obtained from ICOLD(1983). In Section 2.2.4.1 the incident time is further discussed and T4 and T5 are redefined. T1 T2 T3 T4 T5 - During construction - During the first filling - During the first five years - After five years - Not available 2.2.3.5 Type of Foundation The foundation type was split into two categories as shown below. R S - Rock mass - Soil mass This was further differentiated as discussed in Section 2.2.4.6. 2.2.3.6 Dam Height Where the height of the dam (from lowest foundation) is uncertain the following definitions from ICOLD(1983) have been used. In other cases the actual height has been added. H1 5m ≤ H1 < 15m H2 15m ≤ H2 < 30m H3 30m ≤ H3 < 50m H4 50m ≤ H4 < 100m H5 100m ≤ H5 H6 Not available Analysis of Concrete and Masonry Dam Incidents Page 2.17 2.2.3.7 Detection Methods The methods for detecting incidents and the need for major repairs were obtained from ICOLD(1983) and are: D01 D02 D03 D04 D05 D06 D07 D08 D09 D10 D11 D12 D13 - Direct observation - Sampling and laboratory test - Water flow measurements - Phreatic level measurements - Uplift measurements - Pore pressure measurements - Turbidity measurements - Chemical analysis of water - Seepage path investigations - Joint and crack measurements - Horizontal displacement measurements - Vertical displacement measurements - Angular displacement measurements D14 D15 D16 D17 D18 D19 D20 D21 D22 D23 D24 D25 - Strain measurements - Stress measurements - Water level measurements - Temperature measurements - Hydrometric measurements - Rainfall measurements - Seismicity control - Sounding investigation - Water pressure measurements - Silting measurements - Design revision (new criteria) - Not available Analysis of Concrete and Masonry Dam Incidents Page 2.18 2.2.3.8 Classification of Causes of Incidents of Dams And Reservoirs The following tables show the codes defining the types and causes of incidents and the need for major repairs that occurred at the dams. The tables were obtained from ICOLD(1983) with some additions from ICOLD(1995). The codes used are followed in the database by a letter that determines their origin. • x - ICOLD(1983) • y - Not from ICOLD • - ICOLD(1995) It will be noted that the causes are an unfortunate mi xture of physical and human factors. They have been adopted for consistency with ICOLD data. Analysis of Concrete and Masonry Dam Incidents Page 2.19 Table 2.3. Causes of incidents of concrete dams 1.1 1.1.1 1.1.2 1.1.3 1.1.4 1.1.5 1.1.5.1 1.1.5.2 1.1.6 1.1.7 1.1.8 1.1.9 1.1.10 1.1.11 1.1.12 1.1.13 1.1.14 1.2 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.6 1.2.7 1.2.8 1.2.9 1.2.10 1.2.11 1.2.12 1.2.13 1.3 1.3.1 - Due to foundation - Inadequacy of site investigation - Deformation and land subsidence - Shear strength - Seepage - Internal erosion - in foundation - in abutment - Degradation (including swelling) - Initial state of stress - Tensile stresses at the upstream toe - Preparation of the foundation surface - Strengthening treatment - Grout curtains and other watertight systems - Drainage systems - Sealing of galleries, shafts and boreholes used for investigation - Leak of drainage system - Due to concrete - Reactions of concrete constituents (including alkali-aggregate reaction) - Reaction between concrete constituents and the environment (including dissolution of calcium hydroxide) - Resistance to freezing and thawing - Attack by bacteria - Compressive strength - Shear strength - Tensile strength - Permeability - Concreting (including order of casting of monoliths) - Cooling - Structural joints (including watertight systems) - Arrangement of reinforcements and anchorages - Ageing of concrete - Due to unforeseen actions or to actions of exceptional magnitude (as a principle, when the case does not fall under other headings) - Hydrostatic pressure and from accumulated silt (including pressure and impact of ice in the reservoir) 1.3.2 1.3.3 1.3.4 1.3.5 1.3.6 1.3.7 1.3.7.2 1.3.7.3 1.3.8 1.4 1.4.1 1.4.2 1.4.3 1.4.4 1.4.5 1.4.6 1.4.7 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1.5.5 1.5.6 1.6 1.6.1 1.7 1.7.1 1.7.2 1.7.3 1.7.4 1.7.5 2.3.9 - Uplift - Earthquakes (natural or man-made) - External temperature variation - Temperature variation due to the heat of hydration - Moisture variation - Overtopping - of abutment - of main section - Deterioration of concrete-rock interface - Due to structural behaviour of the arch and multiple arch dams (including the construction period) - Shape of the dam and its position in the valley - Tensile stresses - Stress concentration due to shape discontinuities in the foundation surface - Stress concentration at openings and shape discontinuities - Artificial abutments and foundation - Distribution and types of joints - Facings - Due to structural behaviour of gravity and buttress dams - shape of the dam and its position in the valley - Tensile stresses - Stress concentration due to shape discontinuities in the foundation surface - stress concentration at openings and shape discontinuities - Distribution and types of joints - Facings - Due to monitoring - Inadequacy of instrumentation - Due to maintenance - Periodic inspections - Cleaning of drains - Control of seepage - Pumping of seepage water - Deterioration of instrumentation - Failure due to an upstream dam collapse Analysis of Concrete and Masonry Dam Incidents Page 2.20 Table 2.4. Causes of incidents of masonry dams 3.1 3.1.1 3.1.2 3.1.3 3.1.4 3.1.5 3.1.6 3.1.7 3.1.8 3.1.9 3.1.10 3.1.11 3.1.12 3.1.13 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 3.2.8 3.2.9 3.2.10 3.3 3.3.1 3.3.2 - Due to foundation - Inadequacy of site investigation - Deformation and land subsidence - Shear strength - Seepage - Internal erosion - Degradation (including swelling) - Initial state of stress - Tensile stresses at the upstream toe - Preparation of the foundation surface - Strengthening treatment - Grout curtains and other watertight systems - Drainage systems - Sealing of galleries, shafts and boreholes used for investigation - Due to mortar - Reactions of masonry constituents (including alkali-aggregate reaction) - Reaction between masonry constituents and the environment (including dissolution of calcium hydroxide) - Resistance to freezing and thawing - Attack by bacteria - Compressive strength - Shear strength - Tensile strength - Permeability - Masonry construction (including order of placement) - Structural joints (including watertight systems) - Due to stone - Weathering - Joints between stones 3.4 3.4.1 3.4.2 j3.4.3 3.4.4 3.4.5 3.4.6 3.5 3.5.1 3.5.2 3.5.3 3.5.4 3.5.5 3.6 3.6.1 3.7 3.7.1 3.7.2 3.7.3 3.7.4 3.7.5 - Due to unforeseen actions or to actions of exceptional magnitude (as a principle, when the case does not fall under other headings) - Hydrostatic pressure and from accumulated silt (including pressure and impact of ice in the reservoir - Uplift - Earthquakes (natural or triggered) - External temperature variation - Variations due to changes of moisture content - Overtopping - Due to structural behaviour of masonry dams (including the construction period) - Shape of the dam and its position in the valley - Tensile stresses - Stress concentration due to shape discontinuities in the foundation surface - Distribution and types of joints - Facings - Due to monitoring - Inadequacy of instrumentation - Due to maintenance - Periodic inspections - Cleaning of drains - Control of seepage - Pumping of seepage water - Deterioration of instrumentation Analysis of Concrete and Masonry Dam Incidents Page 2.21 Table 2.5. Causes of incidents to appurtenant works 4.0 4.0.1 4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.1.5 4.1.6 4.1.7 4.1.8 4.1.9 4.1.10 4.1.11 4.1.12 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6 4.2.7 4.2.8 4.2.9 4.2.10 4.2.11 4.2.12 4.2.13 4.3 4.3.1 4.3.2 4.4 4.4.1 4.4.2 4.4.3 4.4.4 - I nadequate design - Tunnels and canals - Due to foundations (when they don’t have good dam characteristics) - Inadequacy of site investigations - Deformation and land subsidence - Shear strength - Percolation - Internal erosion - Degradation (including swelling) - Initial state of stress - Preparation of foundation surface - Strengthening treatment - Grout curtains and other watertight systems - Drainage systems - Sealing of galleries, shafts and boreholes used for investigation - Due to concrete - Reactions of concrete constituents (including alkali-aggregate reaction) - Reactions between concrete constituents and the environment (including dissolution of calcium hydroxide) - Resistance to freezing and thawing - Attack by bacteria - Mechanical strength (including tensile strength) - Permeability - Concreting (cooling included) - Cracking - Surface finishing (facing included) - Structural joints (including watertight systems) - Arrangement of reinforcements and anchorages - Erosion by abrasion - Erosion by cavitation - Due to riprap - Disintegration of blocks - Removal of blocks - Due to steel and other materials - Chemical and biological agents - Erosion by abrasion - Erosion by cavitation - Mechanical strength 4.5 4.5.1 4.5.2 4.5.3 4.5.4 4.5.5 4.5.6 4.6 4.6.1 4.6.2 4.6.3 4.6.4 4.6.4.2 4.7 4.7.1 4.7.2 4.7.3 4.7.4 4.7.5 4.7.6 4.7.7 4.7.8 4.7.9 4.7.10 4.8 4.9 4.9.1 4.9.2 4.10 4.10.1 4.11 4.11.1 4.11.2 4.11.3 4.11.4 4.11.5 4.11.6 4.11.7 - Due to unforeseen actions or actions of exceptional magnitude (when the case doesn’t fall under other headings) - Hydrostatic pressure and pressure due to silt accumulation - Pressure and impact of ice - Uplift - Earthquakes (natural or triggered) - Temperature and moisture variations - Delay in construction at the time of flood - Due to structural behaviour - Structural behaviour of spillways - Insufficient capacity of spillway - Erosion of spillway basement - Inadequate design of spillway - of canal or tunnel - Due to water flow, water level and water-borne debris (including construction periods) - Excessive rates of flow - Turbulence - Vortices - Waves - Abnormal pressures - Entrapped air - Inaccurate discharge curves - Solid materials carried by water flow - Discharge of floating materials - Piping outside inserted conduit - Due to local scour - Due to operation - Sudden opening of the discharge equipment - Inadequate instructions for operating the discharge equipment - Due to monitoring - Inadequacy of instrumentation - Due to maintenance - Periodic inspections - Cleaning of drains - Control of seepage - Pumping of seepage water - Deterioration of measurement instrumentation - Malfunction of discharge equipment - Debris in stilling basins Analysis of Concrete and Masonry Dam Incidents Page 2.22 Table 2.6. Causes of incidents of reservoirs 5.1 5.2 5.3 5.4 5.5 - Slope sliding - Overturning of rock blocks - Permeability - Silting - Ecological balance Table 2.7. Causes of incidents downstream of dam 6.1 6.2 6.3 - Equilibrium of river bed - Slope stability - Ecological balance Analysis of Concrete and Masonry Dam Incidents Page 2.23 2.2.3.9 Classification of Remedial Measures Table 2.8 shows the coding used for remedial measures. The codes used were obtained from ICOLD(1983).The codes used are followed by a letter which determines their origin. • x - ICOLD(1983) • y - Not from ICOLD • - ICOLD(1995) Analysis of Concrete and Masonry Dam Incidents Page 2.24 Table 2.8. Classification of remedial measures R101 R102 R103 R104 R105 R106 R107 R108 R109 R201 R202 R203 R204 R205 R301 R302 R303 R304 R305 R306 R307 R308 R309 R401 R402 R403 R404 R405 R406 R407 R408 - Of a general nature - Investigation - Monitoring - Lowering of reservoir level - Raising of dam crest - Overall reconstruction (same design - Reconstruction with new design - None - Not available - Scheme abandoned - I n foundations - Water tightening treatment - Drain & filter construction or repair - Strengthening by grouting or other methods (excluding anchoring) - Filling in of fractures and cavities - Anchoring - I n concrete and masonry dams - Water tightening treatment - Drain construction or repair - Thermal protection (excluding facing) - Facing - Reconstruction of deteriorated zones - Execution of joints - Strengthening by grouting - Strengthening by anchoring - Strengthening by shape correction - I n earth and rockfill dams - Impervious core repair - Construction or repair of other watertight systems - Drain & filter construction or repair - Slope protection construction or repair - Filling in of cracks and cavities - Reconstruction of deteriorated zones - Upstream slope flattening, construction of upstream berm or other stabilisation methods - Downstream slope flattening, construction of downstream berm or other stabilisation methods R501 R502 R503 R504 R505 R506 R507 R508 R509 R510 R511 R512 R513 R514 R515 R601 R602 R603 R604 R605 R606 R607 R701 R702 - I n appurture works - Discharge increase - Construction of additional appurtenant work - Overall reconstruction of appurtenant works - Partial reconstruction with strengthening or structural changes - Shape correction of surfaces contacting flow - Aeration devices: construction or increase of capacity - Repair of surfaces contacting flow (including facings and special treatments) - Joint water tightening treatment - Construction & repair of drains - Slope protection & stabilisation - Sediment discharge removal from surfaces contacting flow - Construction, modification and repair of valves and gates - Establishment and updating of rules for gate and valve operations - Reconstruction of deteriorated zones and other correcting measures - Abandon of appurtenant work - I n reservoir - Reforestation - Torrent training - Sediment discharge diversion - Slope regularisation, protection and strengthening - Draining - Water tightening - Dredging - Downstream of dam - Draining - Slope regularisation, protection and strengthening Analysis of Concrete and Masonry Dam Incidents Page 2.25 2.2.4 Selection of Additional Variables As the ICOLD (1974, 1983 and 1996) databases were limited in their scope it was decided to add additional variables to CONGDATA. The additional variables were generally proposed by the author and reviewed by the sponsors. Further variables were added where requested by the sponsors. Some potential variables were rejected due to limited information in the literature, reports etc. Following is a description of the additional data variables including a discussion of why each was chosen. 2.2.4.1 Time of Incidents It is important to understand at what age dams are more likely to fail or experience accidents. This can give dam owners a guide as to what intensity of monitoring they need to have throughout the life of a dam. ICOLD (1983) have analysed the time to failure and grouped their data into categories T1 to T5 as shown in Section 2.2.3.4. The oldest group is T4, which indicates an incident occurred after five years. It is clear that this is a large category that cannot adequately indicate potential deterioration effects in dams. The following grouping was used to allow for a better distribution, and hence understanding, of times to failure. T1 - During construction T2 - During first fill T3 - 0-5 years T4 - 5-10 years T5 - 10-20 years T6 - 20-30 years T7 - 30-40 years T8 - 40-50 years T9 - >50 years T10 - >5 years (else unknown) T11 - Unknown Analysis of Concrete and Masonry Dam Incidents Page 2.26 2.2.4.2 Foundation Incident Mode Where the foundation has played a part in the incident of the dam further codes have been added. This allows for a better understanding of the foundation parameters affecting different incident modes. The codes are: S - Sliding - where failure has occurred by the dam sliding on the foundation. Sliding can be along the dam-foundation interface or along a foundation discontinuity. P - Piping - of materials within soil foundations or rock discontinuities (generally joints). SC - Scour - of the foundation or the abutment. U - Uplift - in the foundation. D - Deformation - settlement or other movements of the foundation not including sliding. L - Leakage - beneath the dam or through the abutments. Analysis of Concrete and Masonry Dam Incidents Page 2.27 2.2.4.3 Dam Incident Mode Where the incident occurred in the dam the following codes have been used to define the incident mode. SH - Shear (sliding) within the dam. T - Tensile (overturning) within the dam. C - Compressive failure within the dam. CR - Cracking (due to concrete hydration etc.) ST - Structural damage to appurtenant structure such as spillway gates. LD - Leakage - through dam. EQ - Earthquake damage. 2.2.4.4 Comments on Incidents The causes of incidents as given in Section 2.2.3.8 are often too general to explain the type of incident. A brief description of the incident has been included in the database to allow for a better understanding of the causes of the incident. 2.2.4.5 Description of the Failure or Accident Brief descriptions of the failure or accident and warning are included in the database. 2.2.4.6 Additional Geological Information Previous dam failure databases have only listed the foundation as soil, rock or both. The dam geology has been included in the database in an attempt to determine whether certain foundation geology types are more susceptible to incidents and vice-versa. The geology of each dam was categorised into the following categories: Analysis of Concrete and Masonry Dam Incidents Page 2.28 Foundation Geology Categories - Rock Sedimentary Metamorphic Igneous Conglomerate Gneiss Granite Sandstone Schist Gabbro Mudstone Phyllite Rhyolite Shale Slate Andesite Siltstone Marble Basalt Claystone Quartzite Limestone Hornfels Dolomite Chalk Agglomerate Volcanic Breccia Tuff Saline Rocks Coal Lignite Foundation Geology Categories - Soil Alluvial Aeolian Marine Lacustrine Colluvial Volcanic (ash) Glacial Residual Unfortunately this detail is often not available, so the database is incomplete. Analysis of Concrete and Masonry Dam Incidents Page 2.29 2.2.4.7 Dam Dimensions The databases that have been developed previously included the height of the dam (taken as above the lowest foundation for ICOLD) and crest length. These are insufficient to fully describe the dam. To allow for the determination of gradients and performing simple analyses of some of the dam incidents, further dimensions were included in the database. The height to full supply level (FSL), tailwater height and the water height at failure were included. These are shown in Figure 2.1 and listed below. All heights, excluding H lf , have the general foundation level of the dam as their reference level. H lf - Height of dam above lowest foundation h d - Structural height h wu - Reservoir height at full supply level (FSL) h wt - Height of the tail water W - Base width of dam section h f - Height to failure plane (=0 if in foundation) h wf - Reservoir height at failure W f - Width of failure plane xH:1V - Upstream slope yH:1V - Downstream slope The drain depth, gallery height and length of spillway were also included in the database. The extent of each failure was also seen as important and so the length of the failed section and where the dam failed (spillway section/non-overflow section/both) were also included in the database. Analysis of Concrete and Masonry Dam Incidents Page 2.30 2.2.4.8 Valley Shape Stress concentrations and differential movements can occur at changes of section. This is particularly important with sharp section changes in the foundation. For this reason a method was developed to assess the valley shape. The parameters given below are shown in Figure 2.2. L1 - Crest length L2 - Left abutment length L3 - Length of valley section L4 - Right abutment length 2.2.4.9 Radius of Curvature A dam will have increased stability where there is some curvature in the dam and load is transferred to the dam abutments. The database includes the radius of curvature of the dam. For dams with straight axes the radius is shown as straight. Analysis of Concrete and Masonry Dam Incidents Page 2.31 Figure 2.1. Definition of dimensions in CONGDATA h f H lf h w h d W f h wt Drain Depth Gallery Height W 1V yH xH 1V Full Supply Level Dam Crest Failure Surface (where applicable) Gallery Dam Foundation Drain Holes Grout Holes Normal Tailwater Level Shear Key Water Level at Failure h wf Analysis of Concrete and Masonry Dam Incidents Page 2.32 Figure 2.2. Definition of dimensions in CONGDATA - section across river 2.2.4.10 Monitoring and Surveillance Data In some cases there have been signs of displaceme nt, cracking, seepage and other factors prior to the incident, giving some warning. These have been included in the database as: 0 - None observed 1 - Foundation piping 2 - Foundation leakage 3 - Dam leakage 4 - Horizontal displacements 5 - Vertical displacements 6 - Cracking 7 - Expansion & cracking 8 - Concrete deterioration 9 - Scour of the foundation 11 - Overtopping 12 - Slide downstream of dam 13 - Abnormal uplift development 14 - Unknown A brief description of the warning is also included. This allows some quantification of the warning e.g. the amount of leakage, and time before failure. L1 L2 L3 L4 Dam Crest Slope Change Slope Change Dam Foundation Analysis of Concrete and Masonry Dam Incidents Page 2.33 2.2.4.11 Warning Rating The following qualitative codes were used to show whether there was sufficient warning prior to the failure to allow for preventative measures and/or warning of people downstream. Y - Yes M - Maybe N - No F - Flood DF - Dam failure upstream ? - No data 2.2.4.12 Warning Time The time from when a warning was given to when the dam failed or when an accident occurred and the dam was remediated was recorded as the warning time. 2.2.4.13 Other Design Factors (a) Post-Tensioning Whether the dam was post-tensioned was included to assess the effects of post- tensioning dams. (b) Gallery The presence of a gallery allows for better maintenance and uplift pressure relief and the provision or otherwise of a gallery is included in the database. (c) Drain Depth and Spacing Drain depths and spacing were included in the database to assess the effects of reducing uplift pressure on dam stability. Analysis of Concrete and Masonry Dam Incidents Page 2.34 (d) Shear Key A shear key may increase the resistance of a dam to sliding and the presence of the key is included. (e) Grouting Type and Depth Consolidation and/or grout curtains can be used to improve the stability of dam foundations and to reduce uplift pressures. The presence of, depth and spacing are included in the database. (f) Number of Victims of Dam Failures This was included to crudely assess the hazard of the dam. It is possible that high hazard dams may have a lower chance of failure as they have better maintenance and higher factors of safety in design. 2.2.5 Assumptions Made in Assembling the Database The majority of the information in CONGDATA has been derived from ICOLD (1974,1983 and 1995). The ICOLD data was collated by sending questionnaires to the various National Committees. This method of data collection caused several problems (ICOLD, 1995). • Some failures were not reported due to a lack of response from some National Committees. • Replies from National Committees were not consistent with each other - some committees calling incidents failures where others would call them accidents. • Gate failure was included by some committees whilst others did not include them. It was ICOLD (1995) policy not to include gate failures. • The data from China was inconsistent with the rest of the world. China has the same amount of dams as the rest of the world put together yet has only reported 3 dam failures as opposed to 180 for the world. When comparing similar construction periods (post-1955) this becomes 3 failures as opposed to 50. It was ICOLD (1995) Analysis of Concrete and Masonry Dam Incidents Page 2.35 policy to ignore China when performing their statistical analyses. This policy has also been adopted here. When assessing the ICOLD data more specific inconsistencies were found in the following: • Dam type - Where failures occurred in composite structures (e.g. embankment/concrete gravity) some National Committees listed the dam as a composite structure (TE/PG) whereas others listed only the section of the dam that failed (e.g. TE). It is important when analysing dam failures that the section that failed be identified so that misleading conclusions are not made. Dams where failure occurred only through the embankment section were discarded in the preparation of CONGDATA. • Height - When comparing ICOLD data to that of other reports/papers/drawings etc. inconsistencies became apparent in the assigning of heights to each dam. Where possible the data was changed to what was understood to be the accurate height. Where corroborating information was not available the ICOLD heights were assumed. • Length - Similar inconsistencies to the height category were found here. Attempts were also made to determine the crest length of the failed section. • Year - generally the years of construction and incident were found to be accurate. Some small inconsistencies (1-2 years) were found in old dams. There were some errors found in the accidents. • Foundation - In ICOLD some dams are noted as having soil/rock foundations. Where possible it was determined where the failure occurred and which foundation type played a part. Where there was no other information the ICOLD foundation was assumed. • Failure type and cause - It appears that most of the ICOLD causes were chosen by the individual National Committees (and potentially smaller dam owners that the questionnaires were passed on to). There appears to be a bias as to which failure categories each country chooses. This has resulted in marked inconsistencies in the ICOLD causes. It is also often difficult to assess how a dam failed by the failure category alone. An attempt has been made to assess all the dams in CONGDATA Analysis of Concrete and Masonry Dam Incidents Page 2.36 independently. However, often the ICOLD data is the only available. Failure types were found to be misleading in several dams and have been corrected. • Remediation measures - Similar problems arise here as for failure type. However, many of the failed dams have been abandoned and so the effects are minimal. Many of the causes of incidents in CONGDATA are subjective but they have been chosen with as much care as possible from the references available. Where several sources have been found with conflicting information an attempt has been made to select the most ‘credible’ source. Most of the dams with most uncertainty are the older dams (prior-1950s). It should be remembered that many of the failures occurred a long time ago and hence information is scarce. Analysis of Concrete and Masonry Dam Incidents Page 2.37 2.2.6 Data on the Population of Dams The assessment of dam incident statistics is of value to the dam engineering community. With these statistics engineers can see which dams have had more dam incidents than other types. This method of analysis however can lead to incorrect conclusions. For example, from a cursory assessment of the failure statistics for concrete and masonry and embankment dams it is shown that there is many more embankment failures compared with concrete and masonry dams. This could lead to the assumption that an embankment dam is much more likely to fail than a concrete dam. If the analysis is continued by comparing the failure statistics to the total population of existing dams then it is shown that the percentage of failures for each dam type is roughly the same (ICOLD, 1995). ICOLD (1995) was the first to attempt to produce statistics on failures taking into account the number and type of existing dams. The population data was taken from the ICOLD World Register of Dams (1984 edition and 1988 updating). ICOLD (1995) compared statistics on existing and failed dams for their type, height and year commissioned. The results of the analyses assisted in qualifying many assumptions that were made on the basis of incident statistics alone. The assessment of the incidents in CONGDATA needed to be qualified with dam population data. ICOLD (1995) used a computerised version of the World Register of Dams that was unavailable to the author. To overcome this, the populations of dams in countries where either a failure had occurred or there was a large number of concrete/masonry dams were entered into a database to use for basic comparisons with the incident data. The table below shows the breakdown of the 4168 dams from 22 countries that were used. Analysis of Concrete and Masonry Dam Incidents Page 2.38 Population of Dams from World Register of Dams used for Analysis Country Gravity Arch Buttress Multi- Arch Total Algeria 5 1 4 10 Australia 69 39 10 3 121 Austria 23 15 38 Brazil 86 3 9 4 102 Canada 190 6 19 2 217 France 130 85 11 12 238 Great Britain 95 11 14 1 121 India 146 146 Italy 208 65 24 8 305 Japan 536 44 17 3 600 Mexico 101 6 3 1 111 Morocco 11 4 15 Norway 26 38 42 3 109 New Zealand 13 19 2 34 Portugal 27 19 4 1 51 South Africa 95 59 7 15 176 Spain 546 30 23 4 603 Sweden 12 5 27 44 Switzerland 51 48 3 102 Turkey 12 1 1 14 USA 717 169 46 25 957 Yugoslavia 30 19 1 4 54 CONGDATA included many more variables for each dam incident than is included in the World Register. A major component of this chapter is an assessment of the foundation geology type that ICOLD does not assess. It was therefore assessed that the population of dams needed to come from sources other than the World Register. The ideal statistical analysis would be made on the total population of dams however this would be impossible to collect. A compromise was made where large subsets of the world population were chosen. The populations chosen and the reasons why are given below. Analysis of Concrete and Masonry Dam Incidents Page 2.39 • Australia/New Zealand - This population was chosen for a number of reasons. The dam population is large and covers numerous geology and topography types. The sponsors of the project comprised the major dam owners in the two countries and hence access to data was made easier. It was also important to make sure the project produced results that could be used by the sponsors in Australia and New Zealand. Appendix C provides a listing of the dams used. • USBR - The USBR has been involved with a large number of dams that cover the western half of the USA. This population covers a wide area and hence a wide range of geology and topography. It was also seen as important to include a population from the country with the highest number of reported incidents. Another major factor was the free access to data that the USBR gave the author. Information on the dams was also available from USBR(1996). The list of dams used for the population is given in Appendix C. • US National Inventory of Dams - This computerised database comprised 1049 large concrete and masonry dams. Such statistics as foundation geology were not included. The inventory instead allowed assessment of the basic variables of dam type, age and height in the country with the greatest number of reported failures. • Portugal - Due to the easy access to the LNEC(1992) report on the Internet this population was also assessed. An attractive feature of this population was the inclusion of foundation geology types in a country with a much different geological environment (generally igneous and metamorphic). This population is shown in Appendix C. The populations of dams from the US National Inventory of Dams and Portugal were collated directly from the CD-ROM and the Internet respectively. The author also collected information from the USBR offices in Denver. Further information was taken from the Internet, personal communication with USBR staff, journal papers and various dam compilation reports published by the USBR and the United States Committee on Large Dams (USCOLD). The information on the Australia/New Zealand population was collected in person by the author and by using questionnaires sent to the sponsors Analysis of Concrete and Masonry Dam Incidents Page 2.40 and several other dam owners. Where required additional information was collected from journal papers and conference proceedings. The populations’ chosen above have several limitations including: • Limited extent - Using subsets of the world population can limit the extent to which the information is used. The information can be expected to be as accurate as possible in the areas surveyed but may not be typical of other areas. Countries where geological environments and dam design and construction methods are different to those assessed are likely to have led to different results. It is believed that the use of populations that cover a wide area of land and are located in the areas of most failures has reduced potential inaccuracies. • Errors/omissions - Where data has been collected second hand there is always a chance of inconsistencies. Attempts to limit these were made by providing extensive information with the questionnaires and checking data against other references. This problem was also limited by personal collection of a large amount of the population data. Analysis of Concrete and Masonry Dam Incidents Page 2.41 2.3 RESULTS OF ANALYSIS OF THE DATABASE 2.3.1 Summary of Incidents This chapter describes the main results obtained from the analysis of the database CONGDATA. A total of 485 dams comprising: 46 failures; 174 accidents; and 265 major repairs were entered into CONGDATA for 29 countries. Table 2.9 shows the number of incidents by dam type in the database. Table 2.10 shows the number of significant incidents as defined in Section 2.2.3.1. Figure 2.3 and Table 2.11 show the distribution of reported incidents by country. Table 2.9. Number of dam incidents in database by type Type Failures Accidents Major Repairs Total Population (1) PG 10 44 165 219 3434 PG(M) 21 17 39 77 VA 3 85 22 110 808 VA(M) 3 0 0 3 CB 4 8 30 42 316 CB(M) 3 1 2 6 MV 2 17 6 25 105 MV(M) 0 2 1 3 Total 46 174 265 485 4663 Note (1) ICOLD (1984) world population excluding China. Table 2.10. Number of significant dam incidents in database by type Type Failures Accidents Major Repairs Total Population (1) PG 10 38 52 100 3434 PG(M) 21 15 19 55 VA 3 85 1 89 808 VA(M) 3 0 0 3 CB 4 8 11 23 316 CB(M) 3 1 0 4 MV 2 15 0 17 105 MV(M) 0 2 0 2 Total 46 164 83 293 4663 Note (1) ICOLD (1984) world population excluding China. Analysis of Concrete and Masonry Dam Incidents Page 2.42 Figure 2.4 shows the dam incidents as a percentage of the total population of dams in each country. Algeria shows a large proportion of failures to their dams. The population in Algeria was taken as 14 (those in existence in 1983 plus those that failed). Due to their small populations Morocco and Turkey show high percentages of failures. India (5%) is noticeable particularly for its larger population. The USA has a failure rate of approximately 2%. Unfortunately many of the variables for each dam remained unknown due to a lack of published information. This was often due to insufficient reporting of old dam incidents. To simplify the analysis, and improve the quality, the nature of the accidents and major repairs to dams were initially assessed to see if the incident was likely to lead to failure of the dam. These incidents were then denoted as ‘significant’, a term which is used in some of the results in this chapter. It would appear likely that the few numbers of major repairs in some countries might be due to inadequate data rather than the absence of major repairs. Analysis of Concrete and Masonry Dam Incidents Page 2.43 Table 2.11. Number of dam incidents reported in each country Country Failures Accidents Major Repairs Total Population (1) (No. of Cases) (No. of Cases) (No. of Cases) (No. of Cases) (No. of Dams) Algeria 7 1 0 8 14 Australia 0 4 21 25 121 Austria 0 5 3 8 89 Brazil 0 2 2 4 121 Cameroon 0 1 0 1 2 Canada 0 1 9 10 219 Chin (2) 1 2 1 4 1290 Czechoslovakia 0 0 3 3 47 Finland 0 0 1 1 13 France 2 18 24 44 296 Germany 0 1 2 3 53 Great Britain 0 2 1 3 121 India 6 12 1 19 128 Ireland 0 0 1 1 8 Italy 3 21 57 81 327 Japan 1 4 11 16 703 Mexico 1 0 0 1 159 Morocco 1 0 0 1 18 New Zealand 0 0 1 1 38 Norway 0 1 0 1 108 Portugal 0 4 3 7 47 Rhodesia 0 6 3 9 19 South Africa 0 8 2 10 180 Spain 6 16 11 33 568 Sweden 1 0 0 1 45 Switzerland 0 10 4 14 106 Turkey 1 0 0 1 14 USA 16 56 102 174 754 Yugoslavia 0 1 2 3 58 TOTAL 46 176 265 487 5662 Note (1) Population from ICOLD (1984). (2) Chinese dams excluded in statistical analysis. Analysis of Concrete and Masonry Dam Incidents Page 2.44 0 5 10 15 20 25 30 35 40 Algeria Australia Austria Brazil Cameroon Canada China Czechoslovakia Finland France Germany Great Britain India Italy Japan Mexico Morocco New Zealand Norway Portugal Rhodesia South Africa Spain Sweden Switzerland Turkey USA Yugoslavia Percent of Total Failure Accident Major Repair Figure 2.3. The distribution of reported dam incidents vs country Analysis of Concrete and Masonry Dam Incidents Page 2.45 0 10 20 30 40 50 Algeria Austria Cameroon China Finland Germany India Japan Morocco Norway Rhodesia Spain Switzerland USA Percentage of Total Failure Accident Major Repair Figure 2.4. Reported incidents as percentage of country’s dam population from ICOLD (1984) Analysis of Concrete and Masonry Dam Incidents Page 2.46 2.3.2 Year Commissioned of Dams Experiencing Incidents Figure 2.5 and Figure 2.6 show the year dams were commissioned (broken into decades) for concrete gravity dam and masonry gravity dam incidents respectively. There were a total of 10 failures, 44 accidents and 165 major repairs for concrete gravity dams and 21 failures, 17 accidents and 39 major repairs for masonry gravity dams. Due to their age, it is considered likely that masonry gravity dam accidents and major repairs are less likely to have been reported to ICOLD. Concrete gravity dam failures occurred in dams commissioned in the 1900’s through to the 1920’s. No failures occurred in dams commissioned between 1926 and 1963. Three concrete gravity dam failures occurred in the 1960’s. There was a similar lack of failures in masonry gravity dams commissioned between 1930 and 1966. These periods of no failures are likely to be a function of the number of dams built and improvement in the understanding and construction of dams. Figure 2.7 shows the year commissioned for all dam incidents. This shows failures and accidents to dams commissioned in the 1930’s and 1940’s dropping off. This follows a similar trend to the world population shown in Figure 2.8. The ICOLD World Register data does not allow for the separation of concrete and masonry gravity dams. The USA population of dams (FEMA, 1995) was used to give a rough estimate of this separation. Figure 2.9 shows the year commissioned for concrete and masonry gravity dams in the USA. It should be noted that the USA data has been collated from dam owner responses and there is the chance that some dams have been denoted as concrete where in fact they were masonry. The peak in construction of masonry dams correlates reasonably with the peak in masonry gravity dam incidents (Figure 2.6). Peaks in dam commissioning were noted in the 1880’s and 1910’s. Peaks in failures of masonry gravity dams are noted in dams commissioned in the 1870’s to 1890’s and 1910’s to 1920’s. The graphs show that there were more incidents to dams commissioned in the 1910’s, 1920’s, 1950’s and 1960’s. However this appears to follow the trend in construction of dams. The incident numbers are likely to be partly a function of the number of dams Analysis of Concrete and Masonry Dam Incidents Page 2.47 built as well as design or construction deficiencies in these periods. The number of accidents and major repairs drops off prior to 1920 but this is very likely to be due to the way the data was collected. There is a much higher chance of having details of failures, from the period prior to 1900, than accidents. Figure 2.10, Table 2.12 and Table 2.13 compare the failure and accident statistics with those of the population of dams as at 1983. The percentages refer to each subset (year commissioned and dam type). Generally there was a reduction in the number of failures per population with time. A small rise in the failure rate can be seen in the 1950’s and 1960’s. There are a number of various peaks in the percentage of failures for buttress and multi-arch dams, but there are too few incidents to make definitive judgements on this. Analysis of Concrete and Masonry Dam Incidents Page 2.48 To 1983 only 0 5 10 15 20 25 30 35 40 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 Decade Beginning Percentage of Total Incidents Failure Accident Major Repair Figure 2.5. Year commissioned vs concrete gravity dam incidents Analysis of Concrete and Masonry Dam Incidents Page 2.49 To 1983 only 0 5 10 15 20 25 30 35 40 45 <1800 1800-1859 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 Decade Beginning Percentage of Total Incidents Failure Accident Major Repair Figure 2.6. Year commissioned vs masonry gravity dam incidents Analysis of Concrete and Masonry Dam Incidents Page 2.50 To 1983 only 0 5 10 15 20 25 30 <1800 1800-1849 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 Decade Beginning Percentage of Total Incidents Failure Accident Major Repair Figure 2.7. Year commissioned vs all dam incidents Analysis of Concrete and Masonry Dam Incidents Page 2.51 Population to 1978 0 5 10 15 20 25 30 35 <1800 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 Decade Beginning Percent of Total for Dam Type Gravity Arch Buttress Multi-Arch Figure 2.8. Year commissioned for world population data obtained from ICOLD (1979) Analysis of Concrete and Masonry Dam Incidents Page 2.52 0 5 10 15 20 25 30 35 <1850 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s >1990 Decade % Concrete Gravity Masonry Gravity All Gravity Figure 2.9. Year commissioned vs percentage of gravity dams constructed in the USA Analysis of Concrete and Masonry Dam Incidents Page 2.53 0 5 10 15 20 25 <1900 1900-1909 1910-1919 1920-1929 1930-1939 1940-1949 1950-1959 1960-1969 1970-1979 Failures/Population (%) All Gravity Arch Buttress Multi-Arch Figure 2.10. Year commissioned - failures/population per period Analysis of Concrete and Masonry Dam Incidents Page 2.54 Table 2.12. Year commissioned - failures vs population per period Years Gravity Arch Buttress Multi-Arch All NUMBER OF FAILURES <1900 14 0 0 0 14 1900-1909 4 0 1 0 5 1910-1919 4 1 2 0 7 1920-1929 4 2 2 1 9 1930-1939 1 0 0 0 1 1940-1949 0 0 1 0 1 1950-1959 0 2 1 1 4 1960-1969 4 0 0 0 4 1970-1979 0 0 0 0 0 1980-1983 0 1 0 0 1 FAILURES/POPULATION (%) <1900 11.2 - - - 10.3 1900-1909 3.5 - 22.4 - 3.6 1910-1919 1.9 3.1 8.9 - 2.5 1920-1929 1.1 2.0 7.2 5.3 1.7 1930-1939 0.3 - - - 0.2 1940-1949 - - 3.4 - 0.2 1950-1959 - 1.2 1.1 5.6 0.4 1960-1969 0.5 - - - 0.4 1970-1979 - - - - - 1980-1989 - 1.8 - - 0.2 Analysis of Concrete and Masonry Dam Incidents Page 2.55 Table 2.13. Year commissioned - accidents vs population per period Years Gravity Arch Buttress Multi-Arch All NUMBER OF SIGNIFICANT ACCIDENTS <1900 2 1 1 0 4 1900-1909 3 2 0 0 5 1910-1919 8 6 2 4 20 1920-1929 6 11 1 3 21 1930-1939 4 6 0 2 12 1940-1949 2 6 0 3 11 1950-1959 7 28 3 4 42 1960-1969 15 21 2 0 38 1970-1979 5 4 0 1 10 1980-1983 1 0 0 0 1 ACCIDENTS/POPULATION (%) <1900 1.6 12.8 no pop - 2.9 1900-1909 2.6 11.2 - - 3.5 1910-1919 3.7 18.5 8.9 35.8 7.1 1920-1929 1.6 11.0 3.6 15.8 4.0 1930-1939 1.2 7.6 - 17.9 2.6 1940-1949 0.6 9.2 - 24.4 2.5 1950-1959 0.9 16.1 3.4 22.3 4.0 1960-1969 1.9 9.6 2.7 - 3.4 1970-1979 1.4 5.7 - 11.2 2.2 2.3.3 Height Figure 2.11 shows the height range distribution for all the significant incidents in CONGDATA. The last two ranges were chosen as ‘150-199m’ and ‘>200m’. The few dams higher than 150m were spread over a large range of heights. The failures appear to be more prevalent in the 15-50m height range (a total of 39). There are seven reported failures for dams of height 50-70m. No reported failures have occurred in dams higher than 70m. Most accidents occurred in the dams in the height range 15-60m. The same numbers of major repairs have generally taken place per 10m height range between 15m and 80m. There is a marked drop off from 80m onwards. The number of major repairs per 10m peaks at a height range of 40-49m. Figure 2.12 and Figure 2.13 show the height versus number of dams for significant incidents in concrete gravity and masonry gravity dams respectively. Proportionally Analysis of Concrete and Masonry Dam Incidents Page 2.56 more failures, accidents and major repairs have occurred in higher dams for concrete gravity dams than masonry gravity dams but this may simply reflect the fact that there are fewer high masonry gravity dams. There were no accidents reported in the range 120-199m for concrete gravity dams. No incidents were reported for masonry gravity dams higher than 100m. 0 5 10 15 20 25 15-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 100-109 110-119 120-129 130-139 140-149 150-199 >200 Unknown (m) Number of Dams Failures Accidents Major Repairs Figure 2.11. CONGDATA - height ranges for all dam significant incidents (Insert: Figure 2.14 Failures/Population (%) for comparison) Note: No failures for dams 70m or higher 0 1 2 3 4 5 6 15-19 20-29 30-39 40-49 50-59 60-69 (m) Failures/Population (%) All Gravity Arch Buttress Multi-Arch Analysis of Concrete and Masonry Dam Incidents Page 2.57 0 2 4 6 8 10 15-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 100-109 110-119 120-129 130-139 140-149 150-199 >200 Unknown (m) Number of Dams Failures Accidents Major Repairs Figure 2.12. CONGDATA - Height ranges for concrete gravity dam significant incidents (Insert: modified Figure 2.14 Failures/Population (%) for comparison) Note: No failures for dams 70m or higher 0 1 2 3 4 15-19 20-29 30-39 40-49 50-59 60-69 (m) Failures/Population (%) Gravity Analysis of Concrete and Masonry Dam Incidents Page 2.58 0 1 2 3 4 5 6 7 8 15-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 Unknown (m) Number of Dams Failures Accidents Major Repairs Figure 2.13. CONGDATA - height ranges for masonry gravity dam significant incidents Table 2.14, Table 2.15 and Figure 2.14 show the percentage of failures and accidents of concrete and masonry dams as a percentage of the population created from ICOLD (1979 and 1984). The database was created from the ICOLD (1979) dam population and extrapolated to the population in ICOLD (1984). The data shows the ratio of failures to population does not exhibit any major trend. There appears to be a higher percentage of failures to population in the 40-49m and 60- 69m height ranges. There is a slight trend of increasing percentage of gravity dam failures with height. Arch, buttress and multi-arch dams are shown to be more likely to have failures in the 15-39m height range. Analysis of Concrete and Masonry Dam Incidents Page 2.59 Table 2.14. Percent of concrete & masonry dam fails vs population for height Dam Height (m) Type 15-19 20-29 30-39 40-49 50-59 60-69 Unknown ALL NUMBER OF FAILURES PG 3 - 1 2 1 3 - 10 PG(M) 3 6 3 7 - 1 1 21 VA 2 - - - - 1 - 3 VA(M) 1 1 1 - - - - 3 CB 3 1 - - - - - 4 CB(M) 1 1 1 - - - - 3 MV - 1 1 - - - - 2 MV(M) - - - - - - - - All concrete 8 2 2 2 1 4 - 19 All masonry 5 8 5 7 - 1 1 27 NUMBER OF FAILURES/POPULATION (1) (%) Gravity 0.7 0.6 0.7 2.5 0.4 2.6 N/A 0.9 Arch 3.4 0.6 1.0 - - 1.7 N/A 0.8 Buttress 4.6 2.7 1.9 - - - N/A 2.4 Multi- Arch - 4.5 5.6 - - - N/A 2.0 All 1.2 0.8 0.9 1.9 0.3 2.2 N/A 1.0 Note (1) Population height ranges from ICOLD(1979) extrapolated to population in ICOLD(1984). Table 2.15. Percent of concrete & masonry accidents vs population for height Dam Height (m) Type 15-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 100-149 150-199 >200 Unknown NUMBER OF SIGNIFICANT ACCIDENTS PG 4 7 3 3 3 2 1 2 2 3 - 2 6 PG(M) - 4 3 1 3 1 - 2 1 - - - - VA - 2 13 9 12 5 6 3 4 16 5 6 4 VA(M) - - - - - - - - - - - - - CB 1 1 - - 1 - - 1 - 1 1 - 2 CB(M) - - - - 1 - - - - - - - - MV 1 2 2 4 1 1 1 2 - - - - 1 MV(M) - - 2 - - - - - - - - - - All concrete 6 12 18 16 17 8 8 8 6 20 6 8 13 All masonry - 4 5 1 4 1 8 2 1 - - - - NUMBER OF ACCIDENTS/POPULATION (1) (%) Gravity 0.5 1.1 1.0 1.1 2.5 2.0 1.2 6.7 7.1 4.7 - 35.8 N/A Arch - 1.2 12.5 11.8 18.8 8.3 15.3 7.9 12.8 22.5 24.8 76.6 N/A Buttress 1.1 1.4 - - 8.9 - - 11.2 - 25.0 no pop - N/A Multi-Arch 3.0 8.9 22.3 35.8 22.3 89.4 29.8 44.7 - - - - N/A All 0.6 1.3 2.9 3.6 6.3 3.9 6.0 9.0 9.3 14.4 21.5 55.0 N/A Note (1) Population height ranges from ICOLD(1979) extrapolated to population in ICOLD(1984). Analysis of Concrete and Masonry Dam Incidents Page 2.60 Figure 2.15 shows the height distribution for the world population at 1984. There appears to be an exponential like drop in numbers of dams per 10m height range. There were 26.8% of large dams in the range 20-29m; dropping to 0.6% at 110-119m; and to 0.4% at 140-149m. Note that the range 15-19m had 22.7% due to the smaller height range (5m c.f. 10m). Note: No failures for dams 70m or higher 0 1 2 3 4 5 6 15-19 20-29 30-39 40-49 50-59 60-69 (m) Failures/Population (%) All Gravity Arch Buttress Multi-Arch Figure 2.14. Height of failed dams - failures/population (%) Analysis of Concrete and Masonry Dam Incidents Page 2.61 22.7 26.8 16.7 10.2 7.1 4.9 2.9 2.4 1.6 0.9 0.6 0.5 0.6 0.4 0.6 0.3 0.8 0.0 5.0 10.0 15.0 20.0 25.0 30.0 15-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 100-109 110-119 120-129 130-139 140-149 150-199 >200 Unknown (m) Percent of Dams Figure 2.15. World dams - height ranges for all concrete & masonry dams 2.3.4 Age at Failure Figure 2.16 to Figure 2.18 show the age at failure for all, concrete gravity and masonry gravity dams. T2 (during first filling) is the most common time for failure to occur. Concrete gravity dams do appear to have proportionally fewer failures during first filling than do masonry gravity dams. The term first filling may be misinterpreted and as such a further analysis was carried out. All failed dams were assessed to see whether they had failed at their maximum water level, and whether this was the first time such a level had been reached. The results of this analysis are given in Table 2.20. Of the 46 dams assessed 29 had failed at their highest level ever recorded; four were not at the highest level recorded; and there were 13 cases with insufficient information. For Analysis of Concrete and Masonry Dam Incidents Page 2.62 the unknown cases four were during a flood and can be assumed to be at or near the highest water level. Of the four that did not fail at their highest recorded water level: • Bayless (B) had been at the same level the year prior when sliding had also occurred (Bayless (A)); • Bouzey (B) had been 0.1m higher for over a year; • Meihua had overtopped by 0.3m previously (0.8m higher than during failure); and • Leguaseca failed at a low reservoir storage. This multi-arch structural failure was due to concrete deterioration in the acidic reservoir water. From this analysis it is clear that the majority of failures have occurred when the reservoir was at its highest recorded level (which could be defined as ‘first fill’). Note however, that several of these dams failed at water levels the same or slightly higher than those previously recorded. The water levels were often reached during a rapid stage of first filling or during flood. Of those dams where information was available, most failed within two days of reaching their final water level and several failed within six hours. Table 2.16, Table 2.17 and Figure 2.21 show the age at failure versus year commissioned for various failure modes. Foundation piping failures generally occurred in the first three years. Exceptions to this were Puentes, Bacino di Rutte and Austin (A). Puentes, which was commissioned in 1790, failed in first fill which took 11 years. Bacino di Rutte failed due to piping in the foundation. During first fill a crack appeared under the dam which was filled. The dam was emptied and the silt removed 13 years later. The dam failed during refilling of the reservoir. Austin (A) failed due to a combination of scour, piping and sliding during overtopping at the highest water level the dam had experienced. Foundation sliding occurred in less than five years in all but two cases. Zerbino dam failed after ten years due to scour and sliding during overtopping. Xuriguera failed after 42 years, unfortunately no further details on the failure were available. Structural sliding was more evenly distributed with five failures occurring after ten years. One structural tensile/shear failure occurred after 80 years (Khadakwasla Dam Analysis of Concrete and Masonry Dam Incidents Page 2.63 that failed during overtopping due to an upstream dam failure). There are a number of dams with unknown failure modes. Most of these failed during overtopping events (see Figure 2.22). Most of the failures that occurred after five years were due to overtopping (12 compared to 6 non-overtopping). Prior to five years of age non-overtopping failures were more prevalent (21 compared to 4). Figure 2.23 shows the age at failure versus year commissioned for different dam types. Masonry dams appear to have failed at all ages. Concrete dams, with the exception of the three below, have failed within ten years of commissioning. There is insufficient information on the exceptions to determine why they failed at a later time. Kohodiar (India) - Combined concrete gravity/earthfill dam, unknown failure mode. Xuriguera (Spain) - Concrete gravity dam apparently failed by foundation sliding. Hauser Lake II (USA) - Concrete gravity dam with no failure information. Table 2.16. No. of dam foundation sliding & piping failures vs age at failure Sliding Piping Age at Failure Grav . Arch Butt. Total Grav . Arch Butt. Total T1 During construction - - - - - - - - T2 During first fill 3 1 - 4 4 1 3 8 T3 0-5 years 1 - 1 2 - - - - T4 5-10 years 1 - - 1 - - - - T5 10-20 years - - - - - 1 - 1 T6 40-50 years 1 - - 1 - - - - ALL 6 1 1 8 4 2 3 9 Analysis of Concrete and Masonry Dam Incidents Page 2.64 Table 2.17. No. of structural (shear or tensile) failures vs age at failure Age at Failure Grav. Arch Butt. Multi-Arch Total T1 During construction 1 - - - 1 T2 During first fill 1 - 2 1 4 T3 0-5 years - 1 - - 1 T4 5-10 years 2 - - - 2 T5 10-20 years 2 - - - 2 T6 20-30 years - - - 1 1 T7 30-40 years - - - - - T8 40-50 years 1 - - - 1 T9 >50 years 1 - - - 1 ALL 8 1 2 2 13 Analysis of Concrete and Masonry Dam Incidents Page 2.65 0 5 10 15 20 25 30 35 40 45 T1 (during const'n) T2 (first fill T3 (<5 yrs) T4 (5-10yrs) T5 (10-20yrs) T6 (20-30yrs) T7 (30-40yrs) T8 (40-50yrs) T9 (>50yrs) T10 (>5yrs, time unknown) T11 (unknown) Percent of Dams Failure Accident Major Repair Figure 2.16. Age at incident - all dams Analysis of Concrete and Masonry Dam Incidents Page 2.66 Figure 2.24 and Figure 2.25 show age at significant incident versus year commissioned for different dam types. As expected the accidents/major repairs tend to occur mostly after 1915. Older incidents are less likely to be recorded. Accidents and major repairs appear to occur at a later stage than that of failures. The distribution of ages to incident for both masonry and concrete dams appears to be similar. Table 2.18 gives the breakdown of incidents in all types of concrete and masonry dams. 0 5 10 15 20 25 30 35 T1 (during const'n) T2 (first fill T3 (<5 yrs) T4 (5-10yrs) T5 (10-20yrs) T6 (20-30yrs) T7 (30-40yrs) T8 (40-50yrs) T9 (>50yrs) T10 (>5yrs, time unknown) T11 (unknown) Percent of Dams Failure Accident Major Repair Figure 2.17. Age at incident - concrete gravity dams Analysis of Concrete and Masonry Dam Incidents Page 2.67 0 5 10 15 20 25 30 35 40 45 T1 (during const'n) T2 (first fill T3 (<5 yrs) T4 (5-10yrs) T5 (10-20yrs) T6 (20-30yrs) T7 (30-40yrs) T8 (40-50yrs) T9 (>50yrs) T10 (>5yrs, time unknown) T11 (unknown) Percent of Dams Failure Accident Major Repair Figure 2.18. Age at incident - masonry gravity dams Figure 2.19, Figure 2.20 and Table 2.18 show the time to significant incidents for dams. The data is presented as the number of incidents in a time period divided by the population of dams that had survived that time period. The population was taken from ICOLD (1979) and extrapolated to 1983 dam numbers. First filling is still the predominant failure time. There appears to be a slight rise in the rate of failures with time (ignoring T2). After 40 years of age there is a jump in the failure rate. It should be noted that the older age groups are represented by a small population Analysis of Concrete and Masonry Dam Incidents Page 2.68 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 Time to Significant Incident I n c i d e n t s / P o p u l a t i o n ( % ) Failures Accidents Major Repairs Figure 2.19. Time to significant incident - gravity dam incidents/population (%) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 Time to Significant Incident I n c i d e n t s / P o p u l a t i o n ( % ) Failures Accidents Major Repairs Figure 2.20. Time to significant incident - all dam incidents/population (%) Analysis of Concrete and Masonry Dam Incidents Page 2.69 Table 2.18. Time to significant incident - incident/population of dams surviving period (%) Failures Grav Arch Butt MA Total Tot 0.90 0.75 2.24 1.87 0.99 T1 0.09 - - - 0.07 T2 0.32 0.25 1.60 0.93 0.41 0-5 0.03 0.13 0.66 - 0.09 5-10 0.16 - - - 0.12 10-20 0.13 0.19 - - 0.13 20-30 0.12 - - 1.52 0.14 30-40 - - - - - 40-50 0.32 0.53 - - 0.32 >50 0.32 - - - 0.24 T10 - - - - - T11 - 0.13 - - 0.02 Accidents Grav Arch Butt MA Total Tot 1.54 10.69 2.88 14.02 3.47 T1 0.14 0.63 0.64 - 0.26 T2 0.41 2.39 0.32 5.61 0.86 0-5 0.27 1.16 0.99 0.95 0.49 5-10 0.03 - - - 0.02 10-20 0.22 0.19 - - 0.19 20-30 0.25 - - - 0.19 30-40 0.08 0.38 1.09 - 0.18 40-50 0.11 0.53 - - 0.16 >50 0.32 0.53 - - 0.32 T10 0.21 2.06 0.33 3.81 0.62 T11 0.09 4.03 0.32 5.61 0.90 Major Repairs Grav Arch Butt MA Total Tot 2.06 0.13 3.53 - 1.78 T1 0.06 - 0.64 - 0.09 T2 0.12 - 0.32 - 0.11 0-5 0.18 - - - 0.13 5-10 0.10 - - - 0.07 10-20 0.39 - - - 0.29 20-30 0.37 - 0.87 - 0.33 30-40 0.31 - - - 0.24 40-50 0.43 - 1.49 - 0.41 >50 0.64 0.53 1.49 - 0.65 T10 0.72 - 1.32 - 0.62 T11 0.09 - 0.32 - 0.09 T1: During construction; T2: During first fill; T10: >5 years, else unknown; T11: Unknown. Page 2.70 Table 2.19. Time to significant incident No. Failures Accidents Major Repairs PG PG(M) CB CB(M) VA VA(M) MV ALL PG PG(M) CB CB(M) VA MV(M) ALL PG PG(M) CB VA ALL TOTAL T1 2 1 - - - - - 3 4 1 1 1 5 - 12 2 - 2 - 4 21 T2 3 8 3 2 2 - 1 19 11 3 1 - 19 - 40 2 2 1 - 5 63 T3 1 - 1 1 - 1 - 4 6 3 3 - 9 - 22 6 - - - 6 32 T4 1 4 - - - - - 5 1 - - - - - 1 2 1 - - 3 9 T5 1 2 - - - 1 - 4 4 1 - - 1 - 6 7 2 - - 9 19 T6 - 2 - - - - 1 3 1 3 - - - - 4 5 1 1 - 7 14 T7 - - - - - - - 0 1 - 1 - 1 - 3 3 1 - - 4 7 T8 1 2 - - - 1 - 4 - 1 - - 1 - 2 3 1 1 - 5 11 T9 1 2 - - - - - 3 1 2 - - 1 - 4 3 3 1 1 8 15 T10 - - - - - - - 0 6 1 1 - 16 2 28 16 8 4 - 28 56 T11 - - - - 1 - - 1 3 - 1 - 32 - 42 3 - 1 - 4 47 10 21 4 3 3 3 2 46 38 15 8 - 85 2 164 52 19 11 1 83 294 Page 2.71 Table 2.20. Details of dam failure water levels Dam Name Dam Type Year Com. Year Fail Fail Type Fail Mode MWL (m) Height at fail (m) Highest record level? Height above previous Time (hrs) Comments Torrejon-Tajo PG 1967 1965 Fa SH DNA Zerbino PG 1925 1935 Faf S/SC 10 15 Y ≈5m >FSL Large flood caused overtopping. Mohamed V PG 1966 1963 Fb ? DNA Elwha River PG 1912 1912 Ff P 31 31 Y 1 st fill 240 Failure occurred 10 days after pond was first filled. Xuriguera PG 1902 1944 Ff S Bayless (A) PG 1909 1910 Ff S 12.5 12.5 Y 1 st fill 48 Failed 2 days after spillway began discharging. Bayless (B) PG 1909 1911 Ff S 12.5 12.5 N <6 Was at this level previous year when failure A occurred. Failed at 2-2:30 on day the reservoir filled. St Francis PG 1926 1928 Ff S 61 61 Y 1 st fill 170 Gradual first fill. Hauser Lake II PG 1911 1969 ? ? DNA Kohodiar PG/TE 1963 1983 ? ? DNA Fergoug I PG(M) 1871 1881 Fa SC >43 Y Flood due to failure of Habra dam. Fergoug II PG(M) 1885 1927 Fa SC? >43 Y Flood due to failure of Habra dam. Sig PG(M) 1858 1885 Fa SC? Y Flood due to failure of Cheurfas dam. Santa Catalina PG(M) 1900 1906 Fa ? Cheurfas PG(M) 1884 1885 Fb ? Y 1 st fill Granadillar PG(M) 1930 1933 Fb ? Bouzey PG(M) 1881 1895 Fb T 19.7 19.6 N 0.1m >1 year Had been at 19.7m for over a year previously. Khadakwasla PG(M) 1879 1961 Fb T/SH 28 32.7 Y* 3.9m 4 Flood due to failure of Panshet dam. Page 2.72 Dam Name Dam Type Year Com. Year Fail Fail Type Fail Mode MWL (m) Height at fail (m) Highest record level? Height above previous Time (hrs) Comments * Overtopped by 2.7m and failed when overtopping had receded to 1.8m. Habra (B) PG(M) 1872 1881 Fba T/SH 33 36.9 Y Overtopping. Angels PG(M) 1895 1895 Ff P Tigra PG(M) 1917 1917 Ff S 27.1 26.7 Y 1.1m 0.5 Spillway section overtopped by 1.1m. Whole dam overtopped by 0.15m. Austin (A) PG(M) 1893 1900 Ff SC/P/S 20.7 24.1 Y 0.4m Flood overtopped dam by 3.4m. Puentes PG(M) 1791 1802 Ffb P >47 47 Y 1 st fill* *1 st fill took 11yrs. Dam filled from 22-47m in final 4 mths. Kundli PG(M) 1924 1925 Fm ? Y 1 st fill Rapid 1 st fill due to floods. Chickahole PG(M) 1966 1972 Fm T 27.4 26 ? Flood rise of 1.5m immediately prior to failure. Gallinas PG(M) 1910 1957 Fm/Fa ? Y Overtopped by record flood. Lynx Creek PG(M) 1891 1891 Fm ? Flood. Pagara PG(M) 1927 1943 Fmb T? 28.7 30 Y 1.3m <12 Overtopped by 0.4m in flood. Habra (A) PG(M) 1871 1872 Fmb T/SH 33 Y Flood after 1 st fill. Habra (C) PG(M) 1881 1927 Fmb T/SH 33 37 Y Flood overtopped, largest since repair. Elmali I PG(M)/TE 1892 1916 Fa ? Overtopped. Lower Idaho Falls ER/PG(M) 1914 1976 Fa ? Y Overtopped from upstream failure of Teton. Vaughn Creek VA 1926 1926 Ff P 17 17 Y 1 st fill 48 Malpasset VA 1954 1959 Ff S 66 65.7 Y* 3 * Just previously exceeded this by ≈ 0.1m for 3 hours. Moyie River VA 1924 1926 Ffa SC 14 16-18 Y 2-4m Storm and upstream dam failure flood overtopped dam. Page 2.73 Dam Name Dam Type Year Com. Year Fail Fail Type Fail Mode MWL (m) Height at fail (m) Highest record level? Height above previous Time (hrs) Comments Meihua VA(M) 1981 1981 Fb 21.5 N Previously overtopped by 0.3m (0.8m > than at failure). Bacino di Rutte VA(M) 1952 1965 Ff D/P 12 Y* <48 * Highest since sediment removed. Dam had been filling for 2 days. Ashley CB 1908 1909 Ff P 17 17 Y 1 st fill >1 Just spilling when pipe failed. Stony Creek CB (Ambursen) 1913 1914 Ff P 13 13 ? Unsure how long at this level or if it had been higher. Dam in service 6 months. Komoro CB 1927 1928 Ff S/P No suggestion of high water level. Overholser CB (Ambursen) 1920 1923 Ffa SC Y Overtopped in flood. Austin (B) CB(M) 1915 1915 Fba SH Y 3 Highest since rebuilt. Vega de Tera CB(M) 1956 1959 Fm T/C 33 33 Y 1.75m <0.5 Previous year was at 31.25m. Flood had just completed 1 st fill. “The dam reportedly was breached at the moment of topping of the crest” Selsfors CB/TE 1943 1943 Ff P 20 18.2 Y 1 st fill ≈ 6 Gleno MV 1923 1923 Fb T/C 32 32 Y 1 st fill 1 month Had been at full supply level for ≈ 1 month. Leguaseca MV 1958 1987 Fb T/C N “low reservoir storage” Page 2.74 T3 T4 T5 T6 T7 T8 T9 0 10 20 30 40 50 60 70 80 90 100 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 Year Commissioned A g e ( y e a r s ) Structural Structural (T1 or T2) Fndn Sliding Fndn Sliding (T1 or T2) Fndn Piping Fndn Piping (T1 or T2) Unknown Unknown (T1 or T2) T1- During construction T2- First Fill Figure 2.21. Failure mode: age at failure versus year commissioned (all dams) Page 2.75 T9 T8 T7 T6 T5 T4 T3 0 10 20 30 40 50 60 70 80 90 100 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 Year Commissioned A g e ( y e a r s ) ? Over Topping Non-Over Topping T1- During construction T2- First Fill Figure 2.22. Over topping: age at failure versus year commissioned (all dams) Page 2.76 T9 T8 T7 T6 T5 T4 T3 0 10 20 30 40 50 60 70 80 90 100 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 Year Commissioned A g e ( y e a r s ) Concrete Gravity Masonry Gravity Concrete Buttress Masonry Buttress Concrete Arch Masonry Arch Concrete Multi-Arch T1- During construction T2- First Fill Figure 2.23. Dam type: age at failure versus year commissioned Page 2.77 0 10 20 30 40 50 60 70 80 90 100 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 Year Commissioned A g e ( y e a r s ) Fail - Concrete Gravity Fail - Masonry Gravity Fail - Other Acc/MR - Concrete Gravity Acc/MR - Masonry Gravity Acc/MR - Other Figure 2.24. Age at significant incident versus year commissioned Page 2.78 0 10 20 30 40 50 60 70 80 90 100 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Year Commissioned A g e ( y e a r s ) Fail - Concrete Gravity Fail - Masonry Gravity Fail - Other Acc/MR - Concrete Gravity Acc/MR - Masonry Gravity Acc/MR - Other Figure 2.25. Age at significant incident versus year commissioned Analysis of Concrete and Masonry Dam Incidents Page 2.79 2.3.5 Incident Causes Table 2.21 shows that failures in the foundation are much more common in concrete dams than in masonry dams (47% compared to 19% and 68% compared to 22% when combined failure types, F f , F fa and F fb , are included). Failures due to the dam body or materials are more common in masonry dams. Table 2.21. Failure types Dam Type Ff Fb Fa Fm Ffa Ffb Fbm Fba Unknown PG 5 1 1 1 2 PG(M) 3 4 5 4 1 3 1 VA 1 2 VA(M) 1 1 1 CB 3 1 CB(M) 1 1 1 MV 2 Total Concrete 9 (47) 3 (16) 1 (5) - 4 (21) - - - 2 (11) Total Masonry 5 (19) 5 (19) 5 (19) 6 (22) - 1 (4) 3 (11) 2 (7) - Total All 14 (30) 8 (17) 6 (13) 6 (13) 4 (9) 1 (2) 3 (7) 2 (4) 2 (4) NOTE: Figures in brackets are percentages for each dam type. Tables D1 to D3 in Appendix D give the incident causes for all dams, concrete gravity dams and masonry gravity dams respectively. These have been derived from the ICOLD failure causes terminology shown in Section 2.2.3.8. Table 2.22 to Table 2.24 show the most common causes of incidents to all dams, concrete gravity dams and masonry gravity dams respectively. It should be noted that the ‘percentage of dams’ column can total more than 100% since there can be more than one cause for each incident. Analysis of Concrete and Masonry Dam Incidents Page 2.80 Table 2.22. Main causes of incidents in all dams Rank Code Description No % of Dams FAILURES 1 3.4.6 Overtopping 10 22 2 3.4.2 Uplift 8 17 3 1.1.4 seepage in the foundation 7 15 4 1.1.5 piping through the foundation 6 13 5 4.7.1 excess rates of flow 6 13 ACCIDENTS 1 1.1.4 seepage in the foundation 16 9 2 4.8 local scour 16 9 3 1.1.5 piping through the foundation 13 7 4 4.7.1 excess rates of flow 13 7 5 4.11.6 discharge equipment malfunction 10 6 MAJOR REPAIRS 1 1.2.3 freezing and thawing 53 20 2 1.3.4 external temperature variation 28 11 3 1.2.2 reaction between concrete & environment 22 8 4 1.2.8 concrete permeability 22 8 5 3.2.2 reaction between masonry & environment 22 8 Overtopping, uplift and foundation seepage and piping are the most common causes of failure for all dams combined. Foundation problems (shear and seepage) are the major cause of failures for concrete gravity dams. Masonry gravity dams have more failures due to overtopping. Seepage and flow problems are the main causes of accidents whilst concrete reactions, temperature and freeze-thaw cause the most major repairs. These types of major repairs tend to cause only surficial damage. Analysis of Concrete and Masonry Dam Incidents Page 2.81 Table 2.23. Main causes of incidents in concrete gravity dams Rank Code Description No % of Dams FAILURES 1 1.1.3 shear strength in the foundation 4 40 2 1.1.4 seepage in the foundation 4 40 3 1.3.2 Uplift 2 20 4 4.7.1 excess rates of flow 2 20 ACCIDENTS 1 1.1.5 piping through the foundation 8 18 2 1.1.4 seepage in the foundation 7 16 3 4.6 due to structural behaviour 7 16 4 4.7.1 excess rates of flow 5 11 5 4.11.6 discharge equipment malfunction 5 11 MAJOR REPAIRS 1 1.2.3 freezing and thawing 40 24 2 1.2.2 reaction between concrete & environment 15 9 3 1.2.8 concrete permeability 15 9 4 1.3.2 Uplift 15 9 5 4.2.12 concrete erosion by abrasion 13 8 Table 2.24. Main causes of incidents in masonry gravity dams Rank Code Description No % of Dams FAILURES 1 3.4.6 Overtopping 8 38 2 3.4.2 Uplift 7 33 3 2.3.9 upstream dam collapse 5 24 4 3.5.2 tensile stresses 5 24 ACCIDENTS 1 3.4.2 Uplift 6 35 2 3.5.2 tensile stresses 3 18 3 3.1.4 seepage in foundation 2 12 4 3.2.8 mortar permeability 2 12 5 3.2.9 masonry construction (including order) 2 12 MAJOR REPAIRS 1 3.2.2 reaction between masonry & environment 20 51 2 3.2.8 mortar permeability 10 26 3 3.1.4 seepage in foundation 8 21 4 3.2.3 freezing and thawing 8 21 5 3.4.1 hydrostatic, silt and ice pressure 5 13 Analysis of Concrete and Masonry Dam Incidents Page 2.82 When all the dams were analysed together, similar incident codes were grouped together to better distinguish the main causes of incidents. Only ‘significant incidents’ were included. The incidents were separated into those with soil foundations and those with rock or unknown foundations. Figure 2.26, Table 2.25 and Table 2.26 show the results of this analysis. Table 2.25 only shows results for failures of dams with soil foundations. There were only three dam accidents where the dam was known to have a soil foundation. The results show that piping was the predominant cause of failure for dams with soil foundations. For dams with rock or unknown foundations, the major cause of failure was overtopping followed by shear strength of the foundation. Piping was the sixth most common cause of failure with five cases noted. The causes of accidents for dams with rock or unknown foundations were seepage, scour, piping, permeability in the concrete and tensile stresses in the dam body. Major repairs were caused by reactions of the masonry/concrete with the environment, concrete/masonry permeability and construction methods. Table 2.25. Main failure causes for dams with soil foundations Rank ICOLD Codes Description No % of Dams 1 1.1.5, 3.1.5, 4.1.5 internal erosion in the foundation (piping) 6 67 2 1.1.4, 3.1.4, 4.1.4 seepage in the foundation 2 22 2 1.1.9, 3.1.9, 4.1.8 foundation preparation 2 22 Analysis of Concrete and Masonry Dam Incidents Page 2.83 Table 2.26. Main significant incident causes for dams with rock or unknown foundations Rank ICOLD Codes Description No % of Dams FAILURES 1 1.3.7, 3.4.6 overtopping 12 32 2 1.1.3, 3.1.3, 4.1.3 shear strength in the foundation 8 22 3 1.1.4, 3.1.4, 4.1.4 seepage in the foundation 7 19 3 1.4.2, 1.5.2, 3.5.2 tensile stresses in the concrete/masonry 7 19 5 4.7.1 excess rates of flow (3 due to overtopping) 6 16 6 1.1.5, 3.1.5, 4.1.5 internal erosion in the foundation (piping) 5 14 6 1.2.6, 1.3.6 shear strength of concrete/masonry 5 14 ACCIDENTS 1 1.1.4, 3.1.4, 4.1.4 seepage in the foundation 18 11 2 4.8 local scour 15 9 3 1.1.5, 3.1.5, 4.1.5 internal erosion in the foundation (piping) 13 8 3 1.2.8, 3.2.8, 4.2.6 permeability in the concrete/masonry 13 8 3 1.4.2, 1.5.2, 3.5.2 tensile stresses in the concrete/masonry 13 8 MAJOR REPAIRS 1 1.2.2, 3.2.2, 4.2.2, 4.4.1 reaction between concrete/masonry & environment 21 26 2 1.2.8, 3.2.8, 4.2.6 permeability in the concrete/masonry 16 20 2 1.2.9, 1.2.10, 3.2.9, 4.2.7 method of construction (including cooling) 16 20 4 1.2.3, 3.2.3, 4.2.3 freezing and thawing 12 15 5 1.2.11, 3.2.10, 3.3.2, 4.2.10 structural joints in concrete/masonry 10 12 6 1.1.4, 3.1.4, 4.1.4 seepage in the foundation 9 11 Analysis of Concrete and Masonry Dam Incidents Page 2.84 Failure modes for incidents involving the foundation will be discussed further in Section 2.3.8. For the failures in the dam structure the following was noted: • The numbers of structural failures attributed to ‘poor construction’ and ‘design flaws’ were similar. There was difficulty in separating design and construction problems as, in many cases, both contributed to the failure. • Only one concrete gravity dam failed due to an inadequacy in the structure. The dam (Torrejon-Tajo, Spain) failure cause was traced to organics present in the aggregate, and filling of the dam by a flood during construction before the concrete had fully set. • Overtopping preceded 5 of the failures. • The majority of the failure cases were masonry gravity dams, probably reflecting the quality of construction and materials. Analysis of Concrete and Masonry Dam Incidents Page 2.85 0 5 10 15 20 25 30 35 fndn shear strength fndn seepage fndn piping overtopping excess flow rates local scour upstream dam fail tensile stresses structural joints mat shear strength mat tensile strength compressive strength construction method mat permeability enviro & mat reaction freeze/thaw Percent of Incidents Failure Accident Major Repair Figure 2.26. Causes of significant incidents (rock & unknown foundations) Analysis of Concrete and Masonry Dam Incidents Page 2.86 0 1 2 3 4 5 6 7 fndn seepage fndn piping fndn preparation uplift overtopping shape of dam structural joints mechanical strength discharge malfunction Number of Incidents Failure Accident Figure 2.27. Causes of significant incidents (soil foundations) 2.3.6 Monitoring and Surveillance Data 2.3.6.1 Using ICOLD Terms Overtopping was the most common failure warning type followed by dam leakage and no warning. However, as can be seen from Table 2.27 it is masonry dams which are most susceptible to overtopping. Dam leakages followed by cracking were the most prevalent warning in accidents. Major repairs tended to have been prompted by dam leakage or concrete deterioration. It appears that the accidents and major repairs tend to have a ‘structural’ warning that can be noticed, whereas the failure warnings are more difficult to notice. Figure 2.28 and Figure 2.29 show the warning types for concrete gravity dam and all dam incidents respectively. Analysis of Concrete and Masonry Dam Incidents Page 2.87 Table 2.27 to Table 2.29 show the warning types for failures, accidents and major repairs for each dam type. It should be noted here that there can be more than one warning type per dam failure. From Section 2.3.5, it appears that the accidents and major repairs generally occur where there has been obvious signs of distress (e.g. surficial damage, uplift records, seepage monitoring). Whether these problems may signal potential instability in the dam is questionable. For example, it is unlikely that cavitation damage in a spillway will lead to failure of the dam. Failures have occurred where it is likely that little warning was given or where the least amount was known, that is, in the foundation. 0 5 10 15 20 25 30 35 40 45 None Foundation piping Foundation leak Dam leak Move, horizontal Move, vertical Cracking AAR Conc. deterioration Scour Overtopping Downstream slide Uplift develop Percent of Incidents Failure Accident Major Repair Figure 2.28. Warning types - gravity dams Analysis of Concrete and Masonry Dam Incidents Page 2.88 0 5 10 15 20 25 30 35 40 None Foundation piping Foundation leak Dam leak Move, horizontal Move, vertical Cracking AAR Conc. deterioration Scour Overtopping Downstream slide Uplift develop Percent of Incidents Failure Accident Major Repair Figure 2.29. Warning Types - All Dams Analysis of Concrete and Masonry Dam Incidents Page 2.89 Table 2.27. Warning types vs dam type - failures Warning Type PG PG(M) CB CB(M) VA VA(M) MV Total None 1 3 - 1 - - 1 6 Foundation piping - 2 1 - 2 - - 5 Foundation leak 1 1 1 - 3 - - 6 Dam leak 3 2 2 - - 1 1 9 Move, horizontal 2 2 - - 1 - - 5 Move, vertical - - 1 - - - - 1 Cracking 2 - 1 - 1 1 1 6 AAR - - - - - 1 - 1 Conc deteriorate - - - - - - 2 2 Scour - 2 - - - - - 2 Overtopping 1 11 1 1 1 1 - 16 Downstream slide - - - - - - - - Uplift develop - - - - - 1 - 1 Unknown 4 2 - 1 - - - 7 Total 14 25 7 3 8 5 5 67 Table 2.28. Warning types vs dam type - accidents Warning Type PG PG(M) CB CB(M) VA MV MV(M) Total None 1 - 1 - 2 - - 4 Foundation piping 5 - 1 - 1 - - 7 Foundation leak 7 1 1 - - - - 9 Dam leak 6 9 1 - 2 - - 18 Move, horizontal 3 1 - - 3 - - 7 Move, vertical 2 2 - - 4 - - 8 Cracking 3 5 2 - 4 - - 14 AAR - - - - - - - 0 Conc deteriorate - - 1 - - - - 1 Scour 3 1 - - - - - 4 Overtopping 2 2 - 1 - - - 5 Downstream slide 3 - - - - - - 3 Uplift develop 2 1 - - 1 - - 4 Unknown 20 4 4 - 77 17 2 124 Total 57 26 11 1 94 17 2 208 Analysis of Concrete and Masonry Dam Incidents Page 2.90 Table 2.29. Warning types vs dam type - major repairs Warning Type PG PG(M) CB CB(M) MV MV(M) Total None - - - - - - - Foundation piping 1 1 - - - - 2 Foundation leak 7 4 - - - - 11 Dam leak 17 10 4 - - - 31 Move, horizontal 1 - 1 - - - 2 Move, vertical - - - - - - - Cracking 9 1 6 - - - 16 AAR 4 - 1 - - - 5 Conc deteriorate 18 7 2 - - - 27 Scour 2 - - - - - 2 Overtopping 2 - - - - - 2 Downstream slide 4 - - - - - 4 Uplift develop 3 1 - - - - 4 Unknown 110 21 21 2 6 1 161 Total 178 45 35 2 6 1 267 2.3.6.2 Details of Warnings Warnings prior to dam failures are very important as they allow for the possibility of either preventing the failure if detected early enough or, importantly, they allow time for people downstream to be notified and evacuated. A warning, even a few hours prior to failure, can have a major effect on loss of life. Table 2.31 was created to describe each of the failures and their warnings. A subjective warning rating was given to each failure. The ratings were taken as to whether a dam failure had a sufficient warning which could have led to people downstream being advised of the impending failure. Table 2.31 also includes information on the failure type and failure mode. Many of the dam failures had limited information and as such could not be given a warning rating. Table 2.30 shows the results for this analysis. Analysis of Concrete and Masonry Dam Incidents Page 2.91 Table 2.30. Warning ratings for failed dams Warning Rating Number of Dams Yes 10 No 1 Maybe 9 Dam failure upstream 5 Flood 5 Unknown 16 Ashley Dam was the only dam where the failure signs were deemed insufficient to allow a warning to be given. There was some seepage 1.5 to 2 hours prior to failure but, the time was insufficient to allow for a warning to be given. Failure occurred through the alluvial foundation. Selsfors Dam had a small seepage 4.25 hours prior to collapse. The seepage increased slowly for 0.5 hour and then rapidly. The signs may have been enough to give a limited warning. An important note to come from this analysis is that most of the warnings comprised a rapid increase in flow prior to failure. Quantity of flow appears not to be as critical. Table 2.32 shows a similar analysis for significant accidents. Most of the accidents gave signs of problems developing. Blackbrook II did not, as the accident was caused by an earthquake. Bhandardara Dam which went close to failure through the dam body had insufficient warning. Cracking occurred quickly at a flood level slightly higher than that recorded previously. Page 2.92 Table 2.31. Details of dam failures and descriptions of warnings Dam Name Dam Type Fail Type Fail Mode Failure Description Warning Description Warning Rating Torrejon-Tajo PG Fa SH Failure of outlet gate. No details available ? Zerbino PG Faf S/SC Scour due to overtopping, followed by foundation failure (sliding or overturning) No details available, but some warning issued - “Despite warnings, the flood drowned 100 people”. Large scour occurred in power plant tunnel in 1928 (same rock). M Mohamed V PG Fb ? No details available No details available ? Elwha River PG Ff P Piping through alluvial sand and gravel during construction of cutoff. Dam was completed and reservoir part filled before cutoff construction. Leakage into caisson for cutoff. Failed in 1.5 hours. M Xuriguera PG Ff S No details available No details available ? Bayless (A) PG Ff S Left half of dam moved 450mm downstream at base, 790mm at top by sliding on foundation. Landslide left abutment downstream, large leakage 4.5-15m downstream of dam 12 days before dam failed. Y Bayless (B) PG Ff S Rapid failure of most of dam by sliding and overturning. Previous failure 8 months before. No remedial action taken. Y St Francis PG Ff S Sudden failure in foundation due to “softening of conglomerate” or sliding on existing landslide or foliation surface in schist. Foundation seepage measured as reservoir rose to 1-2ft 3 /sec (30-60l/sec) or 6-9hrs before failure water level recorder dropped 0.1m in ½ hour before failure. (There is a suggestion that this was due to the tilting of the dam, but in any case it would have acted as a warning.) Some evidence of cracking in foundation 2 months before failure (due to landslide in abutment). Y/M Hauser Lake II PG ? ? No details available. No details available. ? Kohodiar PG/TE ? ? No details available. No details available. ? Fergoug I PG(M) Fa SC 50m spillway section scoured by flood and failed. Flood caused by failure of Habra dam upstream. DF Page 2.93 Dam Name Dam Type Fail Type Fail Mode Failure Description Warning Description Warning Rating Fergoug II PG(M) Fa SC? 125m section failed during flood. Flood caused by failure of Habra dam upstream. DF Sig PG(M) Fa SC? Overtopped in flood. Founded on gravel. Flood caused by failure of Cheurfas dam upstream 2 hours before. DF Santa Catalina PG(M) Fa ? Overtopping. No details available. No details available. ? Cheurfas PG(M) Fb ? No details available. ICOLD cite piping in foundation as cause, but failure in dam, which is inconsistent. No details available. ? Granadillar PG(M) Fb ? Failure of dam due to inadequate cross section. No data available. ? Bouzey (B) PG(M) Fb T Sudden tensile/compressive and overturning failure. Failure surface slope gently 3.5m from upstream face, then steeply. Crush and shear marks near downstream face. Dam had leaked badly in foundation and moved up to 0.34m downstream 11 years before failure. Repairs had been carried out 3 years before, and crest deflection 25mm observed. No warning immediately before failure. Y Khadakwasla PG(M) Fb T/SH Failure in masonry. Tensile/compression probably enhanced by stress concentration due to sudden change in foundation elevation. Dam was overtopped for 4 hours prior to failure, and was vibrating. Flood due to failure of Panshet dam upstream 7 hours prior to breach. DF Habra (B) PG(M) Fba T/SH Sudden failure in masonry during flood. No warning immediately before failure (flood). F Angels PG(M) Ff P Piping in (soil?) foundation. No data available. ? Puentes PG(M) Ffb P Piping failure through alluvium in foundation. Leakage from fndn noted just over 0.5hr prior to failure. Just prior to failure there was a large explosion from the discharge wells and a large increase in leakage. It is said that the dam emptied in 1hr. A messenger was sent to warn the town of Lorca when the leakage was first noted (by bike) but was overtaken by the flood wave. M Tigra PG(M) Ff S Sliding on weak shale (?) seam in foundation under flood level. Dam overtopped by 0.15m only so overtopping itself unlikely to be critical re scour, but may have affected uplift inside dam. Dam went overtopped ½ hour before failure. F Austin (A) PG(M) Ff SC/P/ S Sliding on weak seam in foundation of two 80m long sections of the spillway, moved downstream 20m. Whirlpools in storage 1 year before, 2m scour at toe of spillway section of dam. Failed in 3 minutes Y Page 2.94 Dam Name Dam Type Fail Type Fail Mode Failure Description Warning Description Warning Rating during flood of record. Kundli PG(M) Fm ? Failure attributed to “green” uncured lime mortar masonry. No data available. ? Chickahole PG(M) Fm T Sudden tensile/overturning failure. Flood rise of 1.5m immediately prior to failure. No warning immediately prior to failure. Cracking of dam occurred during consolidation grouting of foundation. M Gallinas PG(M) Fm/Fa ? Overtopped and “washed out” (no details). No data available. “Early warnings … credited with preventing loss of life”. M Lynx Creek PG(M) Fm ? Failure in masonry in flood. No details available. ? Pagara PG(M) Fmb T? Overtopping. No additional details. No data available. ? Habra (A) PG(M) Fmb T/SH Sudden failure in foundation or masonry during overtopping by flood. No warning immediately before failure (“large leakage” in dam on first filling but had reduced). Y Habra (C) PG(M) Fmb T/SH Sudden failure in masonry during flood. Flood no details about any warnings but, “reportedly did not result in a loss of human lives because of adequate advance warnings”. F Elmali I PG(M)/T E Fa ? Overtopped. No data available. No data available. ? Lower Idaho Falls ER/PG( M) Fa ? Overtopped due to failure of Teton dam upstream. Failure of Teton dam 96km upstream. DF Vaughn Creek VA Ff P Foundation piping and arch concrete failure. Considerable flow below west abutment, followed by settlement and sliding of abutment and in a short time, its overturning. Some seepage in abutment on first filling. Very large and serious leakage just before failure through abutment. Y Malpasset VA Ff S Sudden shear failure in foundation controlled by geology and uplift. Failure very rapid. Seepage in abutment on first filling 15 days, and more 2 days before failure. 17mm displacement of dam base compared to estimated 10mm. M Moyie River VA Ffa SC Spillway scoured and undermined left abutment dam left standing. No details available, but scour should have been evident. F Meihua VA(M) Fb ? Page 2.95 Dam Name Dam Type Fail Type Fail Mode Failure Description Warning Description Warning Rating Bacino di Rutte VA(M) Ff D/P Foundation seepage and movement causing crack to open upstream of dam on first filling. Crack sealed. Dam operated for 13 years, but failed when sediment removed from reservoir and dam refilled. Failure was piping initiated along crack, giving breach 12m by 2m into which dam collapsed. Prior seepage, observation of cracks in foundation, and displacement. Y Ashley CB Ff P Piping failure in fine sand with a little clay and gravel, 6m deep below cutoff. Seepage in foundation noted 1.5-2 hours before piping failure. N Stony Creek CB Ff P Piping in foundation followed by settling of dam, cracking and collapse of dam. Large leakage through weep holes in floor of the dam 24 hours before flow developed rapidly in last 20 minutes before failure. Y Komoro CB Ff S/P Failure due to softening of volcanic ash in foundation. Unclear whether piping, sliding or both. No details available. ? Overholser CB Ffa SC Overtopping. Scour of abutment. No details available. ? Austin (B) CB(M) Fba SH Flood destroyed 20 gates of masonry dam, and filled tailrace and draft tubes with debris. Flooding F Vega de Tera CB(M) Fm T/C Structural failure of masonry buttress. No warning noted. “Heavy leakage” occurred through masonry but may have been unrelated. M Selsfors CB/TE Ff P Piping in foundations fluvioglacial sand, followed by collapse of dam into void. Small seepage into abutment 4.25 hours prior to failure, increased slowly for 0.5 hour, then rapidly. M/N Gleno MV Fb T/C Rapid structural failure of multiple buttress arch dam attributed to weakness in poor quality supporting masonry. Leakage through dam and on the cut off between dam and foundation during and after construction. Leakage increased markedly in the days before failure up to 50l/sec. Y Leguaseca MV Fb T/C Structural failure of an arch due to concrete deterioration in acidic reservoir water. No details available (concrete deterioration). M Page 2.96 Table 2.32. Details of dam significant accidents and descriptions of warnings Dam Name Dam Type Fail Type Fail Mode H d / W Failure Description Warning Description Warning Rating Bingham PG Fa SC ? Spillway failed by overturning due to piping and erosion of the weathered foundation rock. No details available. ? Wilbur PG Fa ST ? Overtopping of dam caused damage to power station downstream. Dam was not damaged. Flood F Upper Glendevon PG Ff/Fb P 1.32 Leakage of 25l/sec on first filling, giving high uplift. Leakage through foundation of 25l/sec on first filling. Y Mequinenza PG Ff S 0.6 Weak bedding surfaces in limestone, lignite and marl exposed during construction, led to strengthening works being built before the dam was completed. Horizontal and vertical movements anticipated but did not occur because dam was strengthened before completion. Y Aguilar PG Ff P 1.25 Piping of clay filled joint in limestone foundation giving leakage of 50l/sec. Leakage in joint in foundation of 50l/sec. Y Villagarcia PG Ff P ? Leakage and piping through rock foundation of up to 100l/sec on first filling. Leakage up to 100l/sec in foundations Y Hales Bar PG Ff P 1.61 Leakage through karst limestone foundation, reaching 47600l/sec (47.6m 3 /sec) 27 years after construction. Many attempts to stop leakage failed, dam abandoned 51 years after construction. Leakage up to 47600l/sec, whirlpools in reservoir, boils downstream. Y Woodbridge (A) PG Ff P ? Piping of alluvial foundation. No details available. ? Zardezas PG Ff S ? Foundation slide during construction. No details available. ? Don Marco PG Ff S 1.44 Scour of foundations due to spillway, and sliding of dam on weak zone in foundation rock. Sliding of dam, erosion of downstream foundation. Y Castrelo PG Ff S ? Landslide from abutment onto power station outlet. Landslide in abutment. Y Burrinjuck (C) PG Ffa S 1.57 Rock slide in spillway channel partly damaged outlet works. No details available. ? Page 2.97 Dam Name Dam Type Fail Type Fail Mode H d / W Failure Description Warning Description Warning Rating Great Falls Generating Station (A) PG Ff P ? Leakage through a narrow ridge in reservoir which increased from 560l/sec on first filling, to 12600l/sec over 20 years. Leakage was through limestone interbedded with shale. Leakage began at 560l/sec, increasing steadily each year at 640l/sec/year to 14 years after filling, and 840l/sec/year to 12600l/sec, 24 years after filling. Leakage was from 19 areas. Y Dworshak PG Fm CR/L 1.25 Thermal cracking which developed to give up to 380l/sec leakage into the drainage gallery. Cracking prior to initial filling, remained small for 9 years, then suddenly opened to give 380l/sec leakage. M Jandula PG(M) Fa T/SH ? Overtopped by flood to a depth of 0.15m. Flood overtopping. F New Croton PG(M) Fa CR 1.5 Cracking of spillway concrete due to vibration by floodwater over flashboards on top of the dam. Flood, cracking in spillway, vibration and leakage up to 9l/sec. F Blackbrook II PG(M) Fb CR 1.25 Earthquake caused cracking of parapit wall. Temporary increase in foundation seepage. Cracking of dam, increased foundation seepage and earthquake itself. N Mulshi PG(M) Fb L/SH ? Leakage through dam increased to 42l/sec, analysis showed inadequate stability. Mortar quality was an issue. Leakage through dam increased from 3.6l/sec 28 years after construction to 42l/sec 11 years later. Y Thokarwadi PG(M) Fb L/SH ? Fine cracks right through dam on abutments. 200l/sec leakage from weep holes drilled low down on downstream face. Fine cracks through dam on abutments. 200l/sec flow from weep holes drilled in downstream face near foundation. Y Walman PG(M) Fb L/SH ? Leakage at many places, maximum 280l/sec. Leakage at many places up to 280l/sec. Y Bhandardara PG(M) Fb T/SH 1.15 Cracking of dam due to tensile failure of masonry under slightly higher flood level from previously. Also greatly increased leakage in dam. Dam must have gone very close to collapse. Leakage through dam for 43 years less than 1.8l/sec. Suddenly increased to 870l/sec at dam/foundation interface and 150mm diameter hole in dam “as a powerful jet” (1 day after flood level reached). Cracking of dam located from upstream to downstream face. N Gela (A) PG(M) Fb L/SH ? “Considerable seepage” through dam into inspection gallery. “Considerable seepage” through dam into inspection gallery. Y Page 2.98 Dam Name Dam Type Fail Type Fail Mode H d / W Failure Description Warning Description Warning Rating El Gasco (A) PG(M) Fba ? Flood overtopped dam, saturated clay and rock filling between two outer masonry walls. No data available. ? Bouzey (A) PG(M) Ff S 1.66 135m length of dam slid up to 0.34m downstream. Foundations disturbed up to 3m below dam. Spring discharges in foundation 50-75l/sec 2 ¼ years before accident, increasing to 230l/sec after accident. Y Shirawata PG(M) Fmb L/SH ? Leakage through dam increased to 600l/sec 10 years after construction. Mortar quality was an issue. Leakage through dam increased from first filling to 600l/sec 10 years after construction. Y Olef CB Fbm CR Tensile cracking of buttress dam during curing of concrete in construction. Cracking of concrete. Y Estremera CB Ff P “High leakage” through alluvial foundation with solution of gypsum. “High leakage” through foundation. Y Ayers Islands CB Fm CR/L Concrete deterioration by freeze-thaw until a hole formed in buttress slab concrete. Concrete deterioration, hole formed, leakage of dam. M Austin (C) CB(M)/ PG(M) Fa ST Spillway piers destroyed during flood and hollow concrete dam section partly destroyed. Flood. Dam previously damaged and foundations scoured. F Austin (D) CB(M)/ PG(M) Faf SC/P Scour and piping of foundation of hollow concrete dam caused collapse of 60m of dam. Flood. Dam previously damaged and foundations scoured. Y Umberumba VA Fa SC/L Overtopped by flood, scour of downstream toe, leakage under dam. No details available. (Flood) F Idbar VA Ff P High seepage and piping of limestone foundation which had not been grouted. Dam was abandoned. Leakage, piping of foundation. Y Vajont VA Fa S Massive landslide in reservoir caused overtopping of dam by many metres (>100m). Dam remained intact. Movements in landslide accelerating with time. M Analysis of Concrete and Masonry Dam Incidents Page 2.99 2.3.7 Remedial Measures ‘Abandonment of the dam’ and ‘reconstruction with a new design’ were the most common remedial measures for failures. For accidents, reconstruction of deteriorated zones in appurtenant works and water tightening treatment in the foundations were the most common. Repairing concrete/masonry facing or reconstructing the deteriorated concrete/masonry was the most frequent remedial method for major repairs. Figure 2.30 shows the most common remedial measures vs incident type. shows the number of dams within each remedial measure category. Table 2.33 shows the number of dams within each remedial measure category. Analysis of Concrete and Masonry Dam Incidents Page 2.100 0 5 10 15 20 25 30 35 Reconstruction (same design) Reconstruction (same design) Not available Scheme abandoned Foundation watertightening Drain and filter construction Concrete watertightening Concrete facing Reconstruction (deteriorated zones) Grouting Dam shape correction Appurtenant surface repair Appurtertenant Reconst. (deteriorated zones) Percent of Incidents with Remedial Measure Failure Accident Major Repair Figure 2.30. Most common remedial measures - all dam incidents Analysis of Concrete and Masonry Dam Incidents Page 2.101 Table 2.33. Remedial measures - all dam incidents Failures Accidents Major Repairs All Incidents Remedial Measure Number %* Number %* Number %* Number %* Of a general nature: Investigation 1 2 8 5 19 7 28 6 Monitoring 0 0 9 5 14 5 23 5 Lowering of reservoir level 1 2 10 6 11 4 22 5 Overall reconstruction (same design)_ 5 11 0 0 0 0 5 1 Reconstruction with new design 10 22 3 2 2 1 15 3 None 1 2 8 5 7 3 16 3 Not available 1 2 11 6 8 3 20 4 Scheme abandoned 15 33 5 3 1 0 21 4 In foundations: Water tightening treatment 0 0 20 11 24 9 44 9 Drain & filter construction or repair 0 0 15 9 23 9 38 8 Strengthening by grouting or other methods 0 0 10 6 6 2 16 3 Filling in of fractures & cavities 1 2 2 1 1 0 4 1 Anchoring 1 2 0 0 2 1 3 1 In concrete and masonry dams: Water tightening treatment 1 2 15 9 28 11 44 9 Drain construction or repair 1 2 1 1 14 5 16 3 Thermal protection (exc. facing) 0 0 0 0 7 3 7 1 Facing 0 0 9 5 56 21 65 13 Reconstruction of deteriorated zones 5 11 10 6 35 13 50 10 Execution of joints 0 0 3 2 5 2 8 2 Strengthening by grouting 0 0 9 5 21 8 30 6 Strengthening by anchoring 2 4 7 4 11 4 20 4 Strengthening by shape correction 4 9 8 5 3 1 15 3 In appurtenant works: Discharge increase 1 2 8 5 7 3 16 3 Construction of additional appurtenant work 1 2 2 1 1 0 4 1 Overall reconstruction of appurtenant works 0 0 2 1 6 2 8 2 Partial reconstruction with strengthening 0 0 5 3 6 2 11 2 Shape correction of surfaces contacting flow 0 0 3 2 5 2 8 2 Aeration devices: construction or capacity inc. 0 0 0 0 2 1 2 0 Repair of surfaces contacting flow 0 0 8 5 19 7 27 6 Slope protection & stabilisation 0 0 2 1 1 0 3 1 Const., modification & repair of valves & gates 0 0 10 6 4 2 14 3 Establish. & update rules for gate & valve ops 0 0 0 0 2 1 2 0 Reconstruction of deteriorated zones 1 2 19 11 8 3 28 6 Abandonment of appurtenant work 0 0 0 0 1 0 1 0 In reservoir: Reforestation 0 0 2 1 0 0 2 0 Torrent training 0 0 5 3 0 0 5 1 Sediment discharge diversion 0 0 1 1 0 0 1 0 Slope regularisation, protection & strengthening 0 0 2 1 0 0 2 0 Water tightening 0 0 4 2 1 0 5 1 Dredging 0 0 2 1 2 1 4 1 Downstream of Dam: Draining 0 0 2 1 0 0 2 0 Slope regularisation, protection & strengthening 0 0 2 1 2 1 4 1 TOTAL 52 242 365 659 Note: (*) Percent of dams (of particular incident type) with particular remedial measure Analysis of Concrete and Masonry Dam Incidents Page 2.102 2.3.8 Geology 2.3.8.1 Geology of Dam Foundations Experiencing Incidents In previous databases and analyses the dam foundation geology has been simply described using categories of soil and/or rock. Since a large proportion of failures have occurred due to deficiencies in the foundation, an improved analysis would be to classify what type of soil or rock the dam was founded on, and then assess whether certain foundation types are more susceptible to failure. The aim of this section is to assess the geology of the foundations of dams that have failed with particular reference to those that have undergone failure due to sliding or piping in the foundation. There are 65 dams in the database that have experienced foundation incidents, of which there are 19 failures 25 accidents and 25 (16 of which were ‘significant’) major repairs. Table 2.34 and Table 2.35 list the dams that have had failures or accidents (respectively) due to deficiencies in the foundation. Figure 2.31 shows the age to failure for dams with failure in the foundation. Times to failure and accidents in the foundation tend to be confined to less than five years. Major repairs have occurred up to 45 years after commissioning. Failures due to the foundation have occurred mainly in dams constructed prior to 1940. Figure 2.32 shows the foundation geology types for incidents occurring in the foundation. Limestone, shale, granite and alluvium are the most common foundation geology types for dam foundations that have had accidents. Shale, limestone, sandstone and alluvium are the most common for major repairs. However, there are a large number of foundation major repairs (27%) with unknown foundation geologies. The two main foundation failure modes are: (a) Sliding on/in the Foundation Table 2.34 and Table 2.35 show that sliding is most prevalent in interbedded sedimentary sequences particularly with shale, and in schistose metamorphic where weaknesses could be expected. The tuff and conglomerate (and shale for Bayless Dam) were noted to have softened when wet. In the case of Malpasset the rock type played Analysis of Concrete and Masonry Dam Incidents Page 2.103 some role in the failure but it was predominately due to uplift pressure and a fault zone. In the case of Zerbino Dam the failure occurred along the foliations of the schist. There are no cases of dam sliding associated with igneous rocks. Overtopping preceded four of the foundation sliding cases. Table 2.34. Geology for dams with failure in the foundation Dam Name Dam Type Year Failed Failure Mode * Fndn Material ** Geology FAILURES Bayless (A) PG 1910 Slide R Shale Sandstone Bayless (B) PG 1911 Slide R Shale Sandstone St Francis PG 1928 Slide R Conglomerate Schist Xuriguera PG 1944 Slide R Unknown Austin (A) PG(M) 1900 Slide R Shale Limestone Dolomite Tigra PG(M) 1917 Slide R Shale Sandstone Malpasset VA 1959 Slide/Uplift R Gneiss Komoro CB(M) 1928 Slide/Piping R Tuff Elwha River PG 1912 Piping S/R Fluvioglacial Conglomerate Angels PG(M) 1895 Piping S Unknown Puentes PG(M) 1802 Piping S Alluvium Sandstone Vaughn Creek VA 1926 Piping (abt) S/R Residual Conglomerate Ashley CB 1909 Piping S Fluvioglacial Selsfors CB 1943 Piping S/R Fluvioglacial Stony River CB 1914 Piping S Alluvial Shale Bacino di Rutte VA(M) 1965 Deformation/Piping R Dolomite Zerbino PG 1935 Scour/Slide R Schist Hornfeld Moyie River VA 1926 Scour R Unknown Overholser CB 1923 Scour R Unknown * Piping failure through abutment denoted by (abt). ** Note: S= Soil; R= Rock Analysis of Concrete and Masonry Dam Incidents Page 2.104 Table 2.35. Geology for dams with accidents in the foundation Dam Name Dam Type Year Failed Failure Mode * Fndn Material ** Geology Castrelo PG - Slide R Granite Don Marco PG 1975 Slide R Unknown Mequinenza PG 1966 Slide R Limestone Lignite Zardezas PG 1932 Slide R Sandstone Limestone Conglomerate Bouzey (A) PG(M) 1884 Slide R Sandstone Dobra VA 1954 Slide R Unknown Aguilar PG 1963 Piping R Limestone Great Falls (A) PG 1945 Piping R Shale Limestone Hales Bar PG 1964 Piping R Limestone Shale Kawamata PG 1966 Piping ? Unknown Upper Glendevon PG 1956 Piping R Andesite Agglomerate Siltstone Villagarcia PG 1961 Piping R Granite Woodbridge (A) PG - Piping S Alluvial Idbar VA 1959 Piping R Limestone Schist Estremera CB 1955 Piping S Alluvial Logan Martin PG/TE 1964 Piping R Dolomite Limestone Koshibu PG 1969 Piping/Leakage R Granite Bingham PG - Piping/Scour R Unknown Austin (D) CB(M) 1937 Scour/Piping R Limestone Shale Dolomite Saulspoort PG 1988 Scour R Sandstone Siltstone Dolerite Albigna PG - Deformation R Granite Santa Maria VA 1968 Deformation R Granite Gerlos VA 1964 Deformation R Unknown Kariba VA 1958 Leakage R Unknown Kolnbrein VA 1978 Uplift/Tension/Leakage R Gneiss * Piping failure through abutment denoted by (abt). ** Note: S= Soil; R= Rock Analysis of Concrete and Masonry Dam Incidents Page 2.105 (b) Piping through the Foundation Piping has tended to occur in soils namely alluvium, fluvioglacial and residual. Although large concrete dams are generally not built on soil foundations, smaller structures such as weirs are. Where foundations were rock, piping failure was through the abutment of the dam. The abutment is defined by ICOLD(1978) as ‘that part of the valley side against which the dam is constructed’ (i.e. zones L2 and L4 of Figure 2.2 in Section 2.2.4.9). A disproportionately high number of piping failures occurred in buttress and arch dams. This is likely to be due to the high hydraulic gradients in the foundations/abutments of these types of dams. Note, the scouring associated with Overholser Dam was also through the abutment. When accidents are included limestone becomes notably more prevalent. 0 10 20 30 40 50 60 1880 1900 1920 1940 1960 1980 2000 Year Commissioned Age Fail - Slide Fail - Piping Fail - Other Acc - Slide Acc - Piping Acc - Other Xuriguera Austin (A) Bacino di Rutte Zerbino Figure 2.31. Foundation incidents age, type and year commissioned - all dams Analysis of Concrete and Masonry Dam Incidents Page 2.106 (45%) 0 5 10 15 20 25 Sandstone Shale Siltstone Conglomerate Sedimentary Limestone Agglomerate Gneiss Schist Hornfeld Lignite Dolomite Dolerite Andesite Basalt Granite Volcanic Ash Alluvial Residual Unknown Percent of Dams FAIL (19) ACC (25) MR* (16) Note(*) Significant incidents only Figure 2.32. Foundation incidents geology - all incidents Analysis of Concrete and Masonry Dam Incidents Page 2.107 2.3.8.2 Geology of the Population of Dams As discussed above a large proportion of concrete dam failures have occurred in the foundation. ICOLD (1974, 1983 and 1995) and USCOLD (1975 and 1988) have only assessed the foundation of dams as soil or rock. Little work has been done in attempting to compare foundation geology to likelihood of failure. This would allow comparison of the geology of those dams experiencing incidents to the geology of the population of dams allowing identification of those with disproportionately high or low number of incidents. To gain a better understanding of which foundation geology is likely to cause problems a population of dams was required. The difficulty in doing this was finding populations of concrete and masonry dams where the geology of dams could reasonably be attained. The following populations were chosen: • USBR; • Australia/New Zealand; and • Portugal. Descriptions of the populations are given below. The results of the analysis are shown in Table 2.36 and Table 2.37. It should be noted that where a dam has two foundation geology types both are included in the tables. This results in the total number of dams being less than the total number of foundation geology types in Table 2.36 and Table 2.37. The percentage figures are calculated as the number of occurrences of a particular geology type divided by the number of dams (and not the total number of geology types). The figures therefore represent the percentage of dams with a particular geology type. Analysis of Concrete and Masonry Dam Incidents Page 2.108 (a) USBR Large Concrete Dams The USBR large concrete dam population was chosen for its good information on geologies. The main sources being: • USBR (1996) Large Concrete Dams Online Database; • USBR SEED Reports; • USBR database Dam Safety Information System; and • personal communication with USBR personnel. The results of the analysis on the dams are shown in Table 2.36. The results are in percent per dam type. The number of dams is given in italics. The predominant foundation types were granite (25%) and sandstone (22%). The total number of unknowns was six. (b) Australian and New Zealand Dams The Australia/New Zealand population of dams was taken primarily from the ANCOLD dam register with more detailed information provided by the sponsors of the research project. Other information was taken from ICOLD Congresses, the ANCOLD Bulletin and other journals. The major New Zealand dam owners (besides ECNZ who were a sponsor) were contacted and the following companies provided information: • Contact Energy Ltd • Central Electric Ltd • Egmont Electricity Ltd • Marlborough Electric Ltd Table 2.36 gives the breakdown of foundation geology types. The most common foundation geology types were sandstone (26%) and granite (14%). Analysis of Concrete and Masonry Dam Incidents Page 2.109 (c) Portuguese Dams The Portuguese population was taken from LNEC (1996). The results are given in Table 2.36 in a similar method to above. There were 52 dams on rock foundations; 1 on a soil/rock foundation and 1 unknown. The most common geology types were granite (50%), schist (30%) and sandstone (19%). The populations from Australia, New Zealand, the USBR and the Portuguese population have been added into one population, which is presented in Table 2.37. Sandstone (24%) and granite (24%) were the most common foundation geology types. 2% of the dam population had soil, namely alluvium, foundations. Page 2.110 Table 2.36. Foundation geology for Australia, New Zealand, Portugal and USBR (percent and number for each group) AUSTRALIA/NEW ZEALAND PORTUGAL USBR Grav Arch Butt MA ALL Grav Arch Butt MA ALL Grav Arch Butt ALL Total Dams 97 42 10 3 152 28 20 4 2 54 21 7 31 59 Sandstones 24 23 36 15 20 2 26 40 21 6 15 3 25 1 19 10 24 5 43 3 16 5 22 13 Shale 8 8 5 2 7 10 0 10 2 14 1 3 1 7 4 Siltstone 5 5 14 6 20 2 9 13 0 0 Conglomerate 10 4 3 4 0 5 1 14 1 10 3 8 5 Limestone 5 2 1 2 50 1 2 1 5 1 13 4 8 5 Claystone 3 3 7 3 4 6 0 0 Mudstone 4 4 10 1 3 5 0 0 Chert 2 2 2 1 2 3 0 0 Breccia 2 2 1 2 0 0 Dolomite 5 1 3 1 3 2 Tillite 2 1 1 1 0 0 Marl 5 1 2 1 Schist 7 7 7 3 7 10 21 6 30 6 75 3 50 1 30 16 14 3 6 2 8 5 Quartzite 7 7 12 5 10 1 33 1 9 14 4 1 5 1 4 2 14 1 6 2 5 3 Gneiss 7 7 5 7 5 1 2 1 3 1 2 1 Phylitte 2 2 2 1 2 3 7 2 5 1 25 1 7 4 0 Slate 3 3 7 3 4 6 0 0 Hornfels 0 5 1 2 1 5 1 2 1 Argillite 1 1 1 1 0 0 Granite 21 20 5 2 14 22 43 12 65 13 50 2 50 27 24 5 14 1 29 9 25 15 Basalt 4 4 5 2 10 1 5 7 50 1 2 1 14 3 29 2 10 3 14 8 Tuff 9 9 5 2 20 2 9 13 0 5 1 3 1 3 2 Page 2.111 AUSTRALIA/NEW ZEALAND PORTUGAL USBR Grav Arch Butt MA ALL Grav Arch Butt MA ALL Grav Arch Butt ALL Dolerite 8 8 5 2 7 10 0 0 Rhyolite 4 4 5 2 4 6 0 5 1 10 3 7 4 Andesite 3 3 5 2 10 1 4 6 0 0 Porphyry 2 2 1 2 0 6 2 3 2 Diorite 1 1 2 1 1 2 0 5 1 3 1 3 2 Granodiorite 2 2 1 2 4 1 2 1 0 Greenstone 1 1 1 1 0 5 1 3 1 3 2 Agglomerate 1 1 1 1 0 3 1 2 1 Pumice 1 1 1 1 0 0 Volcanic Ash 0 0 0 Alluvium 2 2 1 2 0 5 1 14 1 3 2 Glacial 5 1 2 1 Residual 1 1 1 1 0 0 Unknown 20 19 14 6 50 5 67 2 21 14 18 5 9 5 0 Grav - Gravity; Butt - Buttress; MA - Multi-Arch Analysis of Concrete and Masonry Dam Incidents Page 2.112 Table 2.37. Foundation geology for Australia, New Zealand, Portugal & USBR dams - totalled Figures Gravity Arch Buttress Multi-Arch ALL Total Dams 125 93 21 5 265 Sandstone 27 34 25 23 29 6 24 63 Shale 8 10 3 3 5 1 5 14 Siltstone 4 5 6 6 10 2 5 13 Conglomerate 1 1 8 7 5 1 3 9 Limestone 1 1 6 6 20 1 3 8 Claystone 2 3 3 3 2 6 Mudstone 3 4 5 1 2 5 Chert 2 2 1 1 1 3 Breccia 2 2 1 2 Dolomite 1 1 1 1 1 2 Tillite 1 1 0 1 Marl 1 1 0 1 Schist 13 16 12 11 14 3 20 1 12 31 Quartzite 6 8 9 8 10 2 20 1 7 19 Gneiss 6 7 2 2 3 9 Phylitte 3 4 2 2 5 1 3 7 Slate 2 3 3 3 2 6 Hornfels 1 1 1 1 1 2 Argillite 1 1 0 1 Granite 30 37 26 24 14 3 24 64 Basalt 6 7 5 5 14 3 20 1 6 16 Tuff 8 10 3 3 10 2 6 15 Dolerite 6 8 2 2 4 10 Rhyolite 4 5 5 5 4 10 Andesite 2 3 2 2 5 1 2 6 Porphyry 2 2 2 2 2 4 Diorite 2 2 2 2 2 4 Granodiorite 2 3 1 3 Greenstone 2 2 1 1 1 3 Agglomerate 1 1 1 1 1 2 Pumice 1 1 0 1 Alluvium 2 3 5 1 2 4 Glacial 1 1 0 1 Residual 1 1 0 1 Unknown 19 24 6 6 24 5 40 2 14 37 Analysis of Concrete and Masonry Dam Incidents Page 2.113 2.3.9.3 Geology - Comparison Between Incidents and Population The following assesses the foundation geology more likely to cause foundation piping and stability problems. This has been based on the statistics of failures and accidents and the “population” assumed in Table 2.37. Due to the limited number of foundation failures that have occurred and the potential inaccuracies introduced by adopting Table 2.37 as a world population, care should be exercised here and the information taken as qualitative only. Figure 2.33 to Figure 2.35 gives the number of incidents in each geology type for: all dams; concrete gravity dams; and masonry gravity dams respectively. From these figures it becomes evident that soil foundations - most particularly alluvial soils are over represented in the foundation incidents. The alluvial soils have a tendency to pipe under the high gradients imposed. No dam has been reported to have failed by sliding on alluvial soils. Normally a large concrete or masonry dam would not be built on a soil foundation. It is interesting that sandstone does not appear to be over represented when the population is taken into account. Failures tend not to occur in sandstone alone but only when the sandstone is interbedded with shales. Shale and limestone (often interbedded) have a high incidence for failing. The limestone has a high proportion of accidents generally due to excessive leakage through dissolution. Another point of note is that no incidents have occurred in basalt foundations. Figure 2.36 to Figure 2.39 give the number of incidents in each geology type over the population of dams in the same geology. The population was estimated using the figures from Table 2.37 and the estimated world population of dams at 1983 (the available ICOLD world population data cutoff). For gravity dams conglomerate, limestone, dolomite and alluvium foundations stand out. Dams with limestone foundations appear to be very susceptible to accidents. The figures for arch and buttress dams are based on small failure populations and should therefore be looked at with caution. Dolomite and gneiss stands out for arch dams whilst alluvium and shale are notable in buttress dams. Figure 2.40 gives a clear indication of which foundation geology types have a tendency to slide or pipe fail. Soils (particularly alluvial and fluvioglacial) and limestones are more likely to have piping problems. Shale (interbedded with other sedime ntary units) has a greater tendency to be involved with sliding failure because of the likely presence Analysis of Concrete and Masonry Dam Incidents Page 2.114 of weaknesses in the bedding such as bedding surface shears. These conclusions agree with the general knowledge regarding the geology types (e.g. as described in Fell et al, 1992). Page 2.115 0 5 10 15 20 25 30 S a n d s t o n e S h a l e S i l t s t o n e C o n g l o m e r a t e L i m e s t o n e D o l o m i t e S c h i s t G n e i s s H o r n f e l s G r a n i t e B a s a l t D o l e r i t e A n d e s i t e A g g l o m e r a t e A l l u v i u m R e s i d u a l U n k n o w n P e r c e n t o f P o p u l a t i o n . 0 1 2 3 4 5 6 7 8 9 N u m b e r o f D a m s . ALL - FAIL ALL - ACC ALL - POP Note: Population based on Australia, New Zealand, Portugal and USBR Figure 2.33. Geology for incidents in the foundation and dam population – all dams Page 2.116 0 5 10 15 20 25 30 35 S a n d s t o n e S h a l e S i l t s t o n e C o n g l o m e r a t e L i m e s t o n e D o l o m i t e S c h i s t G n e i s s H o r n f e l s G r a n i t e B a s a l t D o l e r i t e A n d e s i t e A g g l o m e r a t e A l l u v i u m R e s i d u a l U n k n o w n P e r c e n t o f P o p u l a t i o n . 0 1 2 3 4 5 6 7 N u m b e r o f D a m s . PG - FAIL PG - ACC Gravity - POP Note: Population based on Australia, New Zealand, Portugal and USBR Figure 2.34. Geology for incidents in the foundation and dam population – concrete gravity dams Page 2.117 0 5 10 15 20 25 30 35 S a n d s t o n e S h a l e S i l t s t o n e C o n g l o m e r a t e L i m e s t o n e D o l o m i t e S c h i s t G n e i s s H o r n f e l s G r a n i t e B a s a l t D o l e r i t e A n d e s i t e A g g l o m e r a t e A l l u v i u m R e s i d u a l U n k n o w n P e r c e n t o f P o p u l a t i o n . 0 1 2 3 4 N u m b e r o f D a m s . PG(M) - FAIL PG(M) - ACC Gravity - POP Note: Population based on Australia, New Zealand, Portugal and USBR Figure 2.35. Geology for incidents in the foundation and dam population – masonry gravity dams Page 2.118 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 S a n d s t o n e S h a l e S i l t s t o n e C o n g l o m e r a t e L i m e s t o n e D o l o m i t e S c h i s t G n e i s s H o r n f e l s G r a n i t e B a s a l t D o l e r i t e A n d e s i t e A g g l o m e r a t e A l l u v i u m R e s i d u a l U n k n o w n I n c i d e n t s / P o p u l a t i o n ( % ) . ALL - Fail ALL - Acc Note: Population based on Australia, New Zealand, Portugal and USBR Figure 2.36. Foundation geology type as a percentage of the geology population – all dams Page 2.119 0.0 5.0 10.0 15.0 20.0 25.0 30.0 S a n d s t o n e S h a l e S i l t s t o n e C o n g l o m e r a t e L i m e s t o n e D o l o m i t e S c h i s t G n e i s s H o r n f e l s G r a n i t e B a s a l t D o l e r i t e A n d e s i t e A g g l o m e r a t e A l l u v i u m R e s i d u a l U n k n o w n I n c i d e n t s / P o p u l a t i o n ( % ) Gravity - Fail Gravity - Acc Note: Population based on Australia, New Zealand, Portugal and USBR Figure 2.37. Foundation geology type as a percentage of the geology population – gravity dams Page 2.120 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 S a n d s t o n e S h a l e S i l t s t o n e C o n g l o m e r a t e L i m e s t o n e D o l o m i t e S c h i s t G n e i s s H o r n f e l s G r a n i t e B a s a l t D o l e r i t e A n d e s i t e A g g l o m e r a t e A l l u v i u m R e s i d u a l U n k n o w n I n c i d e n t s / P o p u l a t i o n ( % ) . Arch - Fail Arch - Acc Note: Population based on Australia, New Zealand, Portugal and USBR Figure 2.38. Foundation geology type as a percentage of geology population – arch dams Page 2.121 0.0 5.0 10.0 15.0 20.0 25.0 S a n d s t o n e S h a l e S i l t s t o n e C o n g l o m e r a t e L i m e s t o n e D o l o m i t e S c h i s t G n e i s s H o r n f e l s G r a n i t e B a s a l t D o l e r i t e A n d e s i t e A g g l o m e r a t e A l l u v i u m R e s i d u a l U n k n o w n I n c i d e n t s / P o p u l a t i o n ( % ) . Buttress - Fail Buttress - Acc Note: Population based on Australia, New Zealand, Portugal and USBR Figure 2.39. Foundation geology type as a percentage of geology population – buttress dams Page 2.122 0 1 2 3 4 5 6 7 G r a n i t e S a n d s t o n e S c h i s t B a s a l t S h a l e S i l t s t o n e C o n g l o m e r a t e G n e i s s L i m e s t o n e A n d e s i t e D o l o m i t e H o r n f e l s A g g l o m e r a t e A l l u v i a l R e s i d u a l U n k n o w n N u m b e r o f D a m s 0 5 10 15 20 25 30 P e r c e n t o f P o p u l a t i o n o f D a m s Fail - Piping Fail - Sliding Acc - Piping Acc - Sliding Population Note: Population based on Australia, New Zealand, Portugal and USBR Figure 2.40. Foundation incident geology and population – mode of failure/accident Analysis of Concrete and Masonry Dam Incidents Page 2.123 2.3.9 Other Design Factors in Failed Dams Due to the limited information no conclusions could be drawn for the following factors. (a) Post-Tensioning No dam that failed was found to have been post-tensioned. The dams where there is no information tend to be older dams (generally masonry) where post-tensioning is unlikely. (b) Gallery and Drains Of the 46 dam failures, information could be found on the gallery and drains for 21 dams. Of these, only Zerbino Dam had drains present. The gallery was 4m above the base of the dam with drains to the concrete-rock interface. Zerbino overtopped by 3m causing erosion of the weak foundation rock at the toe, which resulted in foundation sliding. It is not known what effect, if any, the drains had on the failure. (c) Foundation Grouting Of the 46 dam failures, information could be found on the foundation grouting for 20 dams. Of these, 2 dams had curtain grouting; three dams had consolidation grouting; and one (Vega de Tera) had both. These dams are shown in Table 2.38. The foundations of the other 14 failed dams were not grouted. Table 2.38. Failed dams with grouted foundation Dam Name Dam Type Grout Type Foundation Geology Failure Comments Cheurfas PG(M) curtain limestone Failed in dam body Austin (B) PG(M) curtain limestone/shale/ dolomite Seepage softened fndn prior to sliding - grouting inadequate Zerbino PG consolidation hornfeld/schist Overtopped by 3m with toe erosion then sliding Chickahole PG(M) consolidation gneiss Failed in dam body Bacino di Rutte VA(M) consolidation dolerite Concrete failure due to fndn movement Vega de Tera CB(M) both gneiss/schist Failed in dam body Analysis of Concrete and Masonry Dam Incidents Page 2.124 (d) Shear Key Bouzey Dam was the only failed dam found to have a shear key. The failure occurred within the body of the dam. (e) Radius of Curvature Where information on the radius of curvature for failed gravity dams was available (15), all but two dams had straight sections. Tigra Dam and St Francis Dam had radii of curvature of 1000m and 152m respectively. (f) Valley Shape 18 failed dams were found with information on the valley shape. The gradient of the valley sides ranged from 0.06 to 2.0 (H/L) for gravity dams and 0.6 to 1.3 for arch dams. The averages were 0.72 and 0.84 respectively. Table 2.39 shows the ratio of crest length to dam height for both failed dams (where information was available) and the population of dams. The structural height, H d , was used for the failed dams. The population from ICOLD as described in Section 2.2.6 was used for the comparison. Dams with composite embankment sections were omitted from both the failure and population analyses. The data shows that the failures were in relatively wide valleys (L 1 /H d ≥3.1 for gravity dams) where three-dimensional effects are unlikely to make a significant impact to the strength of the dams. Elwha River Dam, a gravity dam which pipe failed, had a very narrow valley (11m) with reasonably steep sides. However the failure was likely to be mainly due to the alluvial foundation. No conclusive results were attained from this analysis. Analysis of Concrete and Masonry Dam Incidents Page 2.125 Table 2.39. Crest length/height for failed dams and population DAM FAILURES POPULATION TYPE Number Range Mean Number Range Mean Gravity 27 3.1-53 13.2 2887 0.3-182 (1) 10.1 Arch 5 2.9-4.3 3.6 663 0.2-29 3.8 Buttress 6 6.0-26 13.2 232 1.0-131 10.1 Multi-Arch 2 3.5-6.8 5.1 82 2.0-47 9.2 Note (1) 80% of the population of gravity dams has a crest length/height greater than 3.1. Analysis of Concrete and Masonry Dam Incidents Page 2.126 (g) Upstream/Downstream Slopes Table 2.40 shows the upstream and downstream slopes for the failed dams where the information was available. Of the 15 gravity dams in the table, 13 had vertical or near vertical upstream slopes. On the downstream face the concrete gravity dams ranged from 0.55:1 (H:V) to 1:1. The masonry gravity dams ranged from 0.38:1 to 3:1. The arch dams ranged from near vertical to 0.32:1. Table 2.40. Upstream and downstream slopes for failed dams Failure Mode Dam Name Dam Type Upstream (xH:1V) Downstream (yH:1V) Foundation Dam Bayless (A) PG 0 1 S Bayless (B) PG 0 1 S Elwha River PG 0 0.75 P St. Francis PG 0 1 S Zerbino PG 0.05 0.55 S/SC Angels PG(M) 0 0.6 P Austin (A) PG(M) 0 0.38 SC/P/S Bouzey PG(M) 0 1 T Chickahole PG(M) 0.1 0.7 T Habra (A) PG(M) 0.3 0.8 T/SH Habra (B) PG(M) 3 1 T/SH Habra (C) PG(M) 3 1 T/SH Khadakwasla PG(M) 0.05 0.4 T/SH Puentes PG(M) 0 0.6 P Tigra PG(M) 0 0.67 S Malpasset VA 0 0 S Moyie River VA 0 0.06 SC Vaughn Creek VA 0 0.2 P Bacino di Rutte VA(M) 0.12 0.12 D/P Gallinas VA(M) 0 0.32 ? Meihua VA(M) 0 0 SH Ashley CB 1 0.5 P Stony Creek CB 1 0.15 P Vega de Tera CB(M) 0.05 0.75 T/C Austin (B) CB(M) 0 1 SH Gleno MV 0.85 0.1 T/C Analysis of Concrete and Masonry Dam Incidents Page 2.127 (h) Dam Height/Base Width (H d /W) Table 2.41 shows the dam structural height and height of water at failure over base width (H d /W and h wf /W respectively) for the failed dams where the information was available. Figure 2.1 in Section 2.2.4.9 shows the definition of these terms. The H d /W and/or h wf /W ratios give an indication of the stability and hydraulic gradient of the dams. A high H d /W or h wf /W indicates a slender dam with potentially a high hydraulic gradient. These are common for arch dams. The definitions for the failure modes are given in Sections 2.4.2 and 2.4.3. Dams that failed by piping generally had soil foundations. Those with alluvial foundations had h wf /W ratios of 0.6 to 1.1. Vaughn Creek, an arch dam which pipe failed through its extremely to highly weathered conglomerate abutment, had a ratio of 3.0. Austin (A), the only dam to have pipe failure through rock (weathered) had a h wf /W of 1.2. Gravity dams that failed by sliding had h wf /W ratios of 1.2 to 2.1. Of these, Zerbino Dam (h wf /W=2.1) was the only dam known to have drainage. Malpasset Dam, an arch dam, had a h wf /W of 5.8. Analysis of Concrete and Masonry Dam Incidents Page 2.128 Table 2.41. H d /W for failed dams Dam Name Dam Type H d /W h wf /W Failure Mode Foundation Dam Bayless (A) PG 1.6 1.6 S Bayless (B) PG 1.6 1.6 S Elwha River PG 1.4 0.6 P St. Francis PG 1.2 1.2 S Zerbino PG 1.7 2.1 S/SC Austin (A) PG(M) 1.0 1.2 SC/P/S Bouzey PG(M) 1.7 1.7 T Cheurfas PG(M) 1.0 ? Chickahole PG(M) 1.3 1.0 ? Fergoug I PG(M) 1.3 ? Fergoug II PG(M) 1.3 Habra (A) PG(M) 1.3 T/SH Habra (B) PG(M) 1.3 1.2 T/SH Habra (C) PG(M) 1.3 1.4 T/SH Khadakwasla PG(M) 1.8 2.0 T/SH Puentes PG(M) 1.1 1.1 P Tigra PG(M) 1.5 1.5 S Malpasset VA 6.0 5.8 S Moyie River VA 7.0 SC Vaughn Creek VA 4.3 3.0 P/D Gallinas VA(M) 3.1 3.2 ? Meihua VA(M) 18.3 17.5 SH Ashley CB 1.2 1.1 P Stony River CB 1.0 0.9 P Vega de Tera CB(M) 2.0 1.8 T/C Austin (B) CB(M) 0.7 1.2 SH Gleno MV 1.1 1.1 T/C (i) Stability Analyses Gulan (1995) and Rich (1995) collated information for 13 concrete gravity dams that had failed by either sliding or overturning through their foundations or the concrete mass. Of the 13 cases, nine failures were back analysed to determine the shear strength properties of either the foundation or concrete. Table 2.42 shows the results from the analyses, which have been checked and some adjustments to the cohesion results made. The results are quoted as c=0, φ or c, φ=0. Actual strengths are between these limits. The results for Khadakwasla Dam have been omitted as the analysis technique was not Analysis of Concrete and Masonry Dam Incidents Page 2.129 valid for the failure mode. The failure plane for Khadakwasla Dam was 6m below the base of the dam. An additional analysis was carried out for Bhandardara Dam, an 82m high gravity dam in India. The dam suffered extensive cracking, from an elevation of 39m at the upstream face to the toe, and came close to failure. The dam has been extensively investigated and several papers describe the accident including: Murthy et. al. (1976 & 1979); and Kulkarni & Kulkarni (1994). Two simple analyses were carried out: the first assuming a horizontal failure at the elevation where the cracking initiated; and the second assuming an angled crack from the location of crack initiation to the toe. The results from the analyses have been included in the tables and figures below. Table 2.43 shows the reanalysed stresses along the failure planes. As can be seen seven of the dams had tensile stresses, up to -280KPa at the heel of the dam. Bhandardara Dam, a concrete gravity structure, experienced up to -440kPa tension. Table 2.42. Back analysed shear strengths for failed dams (mod. from Rich, 1995) Name Dam Type Failure φ′ (°) C′ (KPa) Foundation Concrete Austin (A) PG(M) Foundation sliding 49 0 0 120 limestone rubble limestone in portland cement- mortar Bouzey (1 st ) PG(M) Foundation sliding 40 0 0 110 sandstone & schist masonry in lime- mortar Bouzey (2 nd ) PG(M) Through concrete 34 0 0 75 sandstone & schist masonry in lime- mortar El Habra (3 rd ) PG(M) Foundation sliding 46 0 0 605 int. sandstone & clay rubble masonry in lime-mortar Tigra PG(M) Foundation sliding 48 0 0 195 stratified sandstone rubble masonry in lime-mortar Bayless PG Foundation sliding 43 0 0 300 int. sandstone & shale cyclopean concrete St. Francis PG Foundation sliding 41 0 0 155 mica schist & conglomerate portland cement Bhandardara (horizontal) PG Severe cracking - tension & shear >46 0 0 >1015 basalt rubble masonry Bhandardara (angled) PG severe cracking - tension & shear >71 0 0 >480 basalt rubble masonry Analysis of Concrete and Masonry Dam Incidents Page 2.130 Table 2.43. Calculated normal stresses along the failure plane of back analysed gravity dams Name Dam Type σ n Upstream (KPa) σ n Downstream (KPa) Austin PG(M) -20 +210 Bouzey (1 st ) PG(M) -20 +265 Bouzey (2 nd ) PG(M) -10 +220 El Habra (3 rd ) PG(M) -280 +735 Tigra PG(M) +25 +355 Bayless PG -155 +425 St. Francis PG +35 +355 Bhandardara (horizontal) PG -440 +1085 Bhandardara (angled) PG -50 +320 The average stresses acting along the failure planes have been calculated using the forces on each dam provided by Rich (1995). Figure 2.41 and Figure 2.42 compare the ANCOLD guidelines (ANCOLD, 1991) to the failure stresses of the nine failure cases. It was assumed that shear strength only acted in the region of compression along the failure plane. The figures show that the failure stresses were much lower than those recommended by ANCOLD for initial assessments. The likely reason for this is the existence of continuous defects through or below the dam. The friction angle and cohesion suggested by ANCOLD assumes no continuous defects. The results show the importance of having a good geotechnical model for the dam and a good bond at the dam/foundation interface. Analysis of Concrete and Masonry Dam Incidents Page 2.131 0 200 400 600 800 1000 1200 1400 1600 1800 0 100 200 300 400 500 600 σ n (kPa) τ(kPa) ANCOLD Bayless Austin Bouzey I Habra St Francis Tigra Figure 2.41. Average failure stresses for dams with failure through the foundation 0 500 1000 1500 2000 2500 0 200 400 600 800 1000 σ n (kPa) τ (kPa) ANCOLD Bhandardara (horizontal) Bhandardara (angled) Figure 2.42. Average failure stresses for Bhandardara Dam Analysis of Concrete and Masonry Dam Incidents Page 2.132 2.4 METHOD OF FIRST ORDER PROBABILITY ASSESSMENT 2.4.1 Probability of Failure 2.4.1.1 Introduction This section describes an attempt to develop a ‘first’ estimate of the annual probability of failure of concrete and masonry dams based on the history of dam failures. ‘Average’ annual probabilities of failure have been assessed for all concrete and masonry dam types. These probabilities have been further refined for concrete and masonry gravity dams. The initial or ‘average’ annual probability of failure was calculated as the number of dam failures, using the history of failures, over an estimate of the population of dams. The cut off year for the population of dams was taken as 1992 as the latest ICOLD statistics on failures (ICOLD, 1995) go up to this time. Dams were separated using the following categories: (a) Dam type: gravity, arch, buttress, multi-arch; (b) year commissioned; (c) age at failure (0-5 years and >5 years); and (d) Concrete or masonry (gravity dams). Analysis of Concrete and Masonry Dam Incidents Page 2.133 2.4.1.2 Population of Dams The total number of concrete and masonry dams as at 1992 (excluding China) is shown in Table 2.44. Since the ICOLD world population data for post 1983 was not available, the population for the period 1983-1992 was estimated as shown in the table below. Table 2.44. Number of dams as at 1992 Year Commissioned Number of Dams Reference 1700-1799 37 ICOLD (1983) 1800-1899 167 ICOLD (1983) up to 1977 4446 ICOLD (1984) 1978-1982 217 ICOLD (1984) 1983-1992 434 estimated as 2 x 1978-82 Total 5097 Dams were divided into gravity, arch, buttress and multi-arch dams. Where a dam was described as a composite section an assessment of the category best describing the dam was made. The population was also split according to age (year commissioned) to account for progress in the methods used for dam construction. The breakdown of the population of dams into dam types and year commissioned was performed using a computer database created by the author using ICOLD (1979). The database comprised the concrete and masonry dams from the 26 countries with the largest dam populations. These countries included all those that had experienced failures (excluding China). Table 2.45 shows the percentage split for population of dams according to dam type and year commissioned. Analysis of Concrete and Masonry Dam Incidents Page 2.134 Table 2.45. Population of dams by dam type and year commissioned Year Commissioned Gravity (%) Arch (%) Buttress (%) Multi-Arch (%) <1900 2.7 0.2 0.0 0.1 1900-1909 2.5 0.4 0.1 0.1 1910-1919 4.7 0.7 0.5 0.2 1920-1929 8.3 2.2 0.6 0.4 1930-1939 7.5 1.7 0.5 0.2 1940-1949 7.4 1.4 0.6 0.3 1950-1959 16.9 3.8 1.9 0.4 1960-1969 17.3 4.8 1.6 0.3 1970-1977 7.8 1.5 0.4 0.2 1977-1983 (1) 81.1 12.0 6.0 0.9 Note (1) Data from ICOLD (1983) For dams commissioned during the period 1978 to 1982 the distribution of concrete and masonry dam types was taken from ICOLD (1983). Dams commissioned between 1983 and 1992 were assumed to have a similar distribution of dam types. Table 2.46 shows the number of dams as at 1992 calculated from Table 2.44 and Table 2.45. Table 2.46. Number of dams (excluding China) in the population Year Commissioned Gravity Arch Buttress Multi-Arch Total 1700-1799 34 2 0 1 37 1800-1899 152 10 1 4 167 1900-1909 109 17 4 3 133 1910-1919 205 31 21 11 267 1920-1929 362 94 27 18 501 1930-1939 327 75 20 11 433 1940-1949 321 62 28 12 422 1950-1959 738 164 85 17 1004 1960-1969 757 208 71 13 1049 1970-1977 339 67 18 8 433 1978-1982 176 26 13 2 217 1983-1992* 352 52 26 4 434 Total 3872 808 314 103 5097 Note (1) Estimated as 2 x 1977-1982 Analysis of Concrete and Masonry Dam Incidents Page 2.135 2.4.1.3 Dam Year As most failures occur prior to five years after commissioning (Douglas et al, 1998) the failure probabilities were broken into: less than or equal to five years of age; and greater than five years of age. Equations 1 and 2 were used to calculate the number of dam years for dams less than or equal to five years, and for dams greater than five years of age respectively. Y n ≤ = × 5 5 (2.1) ( ) Y y i > = − ∑ 5 5 (2.2) where, n = total number of dams y i = age of individual dam in years 2.4.1.4 Probabilities of Failure Annual probabilities (number of failures/number of dam years) and straight probabilities of failure (number of failures/number of dams) were calculated from the database of failures and the population of dams. A distinction was made between dams commissioned prior to, and those commissioned after 1930. This represents the historical change to a better understanding of uplift pressures and materials properties for dams. Categories without failures have been denoted as ‘NF’. The probabilities were recalculated for the various failure modes. The following failure modes were used: • All modes (Table 2.47 and Table 2.48) • Sliding (Table 2.49 and Table 2.50) • Piping (Table 2.51 and Table 2.52) • Through the dam body (Table 2.53 and Table 2.54) Table 2.55 and Table 2.56 show the number of failures with unknown failure modes. Table 2.55 shows those unknowns where failure during overtopping was known to have occurred. Analysis of Concrete and Masonry Dam Incidents Page 2.136 Table 2.47. Annual probability of failure (1992, exc. China) - all failure types Year Gravity Arch Comm. 0-5 years (1) >5 years Total 0-5 years (1) >5 years Total 1700-1799 5.9E-03 NF 1.2E-04 NF NF NF 1800-1899 6.6E-03 3.8E-04 6.0E-04 NF NF NF 1900-1909 3.7E-03 2.2E-04 4.2E-04 NF NF NF 1910-1919 2.0E-03 1.4E-04 2.5E-04 NF 4.5E-04 4.2E-04 1920-1929 1.1E-03 8.9E-05 1.7E-04 4.2E-03 NF 3.2E-04 1930-1939 6.1E-04 NF 5.4E-05 NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF 1.2E-03 1.9E-04 3.3E-04 1960-1969 5.3E-04 1.2E-04 2.0E-04 NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF 7.7E-03 NF 3.2E-03 1983-1992 (3) NF NF NF NF NF NF 1700-1929 2.8E-03 1.9E-04 3.3E-04 2.6E-03 8.9E-05 2.5E-04 1930-1992 (3) 2.0E-04 2.6E-05 5.5E-05 6.2E-04 5.8E-05 1.5E-04 Total (3) 7.9E-04 1.1E-04 1.8E-04 1.0E-03 7.0E-05 1.8E-04 Year Buttress Multi-Arch Comm. 0-5 years (1) >5 years Total 0-5 years (1) >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF NF NF 1900-1909 4.7E-02 NF 2.7E-03 NF NF NF 1910-1919 1.9E-02 NF 1.2E-03 NF NF NF 1920-1929 1.5E-02 NF 1.1E-03 1.1E-02 NF 8.3E-04 1930-1939 NF NF NF NF NF NF 1940-1949 7.3E-03 NF 7.7E-04 NF NF NF 1950-1959 2.4E-03 NF 3.2E-04 NF 1.8E-03 1.6E-03 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 (3) NF NF NF NF NF NF 1700-1929 1.9E-02 NF 1.2E-03 5.4E-03 NF 3.2E-04 1930-1992 (3) 1.6E-03 NF 2.5E-04 NF 5.1E-04 4.3E-04 Total (3) 4.5E-03 NF 5.8E-04 2.0E-03 2.0E-04 3.7E-04 Year All Concrete & Masonry Comm. 0-5 years (1) >5 years Total 1700-1799 5.4E-03 NF 1.1E-04 1800-1899 6.0E-03 3.5E-04 5.5E-04 1900-1909 4.5E-03 1.8E-04 4.3E-04 1910-1919 3.0E-03 1.6E-04 3.4E-04 1920-1929 2.8E-03 6.4E-05 2.7E-04 1930-1939 4.6E-04 NF 4.1E-05 1940-1949 4.7E-04 NF 5.0E-05 1950-1959 4.0E-04 6.2E-05 1.1E-04 1960-1969 3.8E-04 8.7E-05 1.4E-04 1970-1977 NF NF NF 1978-1982 9.2E-04 NF 3.8E-04 1983-1992 (3) NF NF NF 1700-1929 3.6E-03 1.6E-04 3.6E-04 1930-1992 (3) 3.6E-04 3.9E-05 9.0E-05 Total (3) 1.1E-03 9.7E-05 2.1E-04 Notes (1) Assumes dam years = number of dams * five years life (2) NF - No Failure (3) Assumes number of dams constructed in 1983-1992 = 2 * number of dams in 1978-1982 Analysis of Concrete and Masonry Dam Incidents Page 2.137 Table 2.48. Probability of failure (as at 1992, exc. China, non-annualised) - all failure types Year Gravity Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 3.0E-02 NF 3.0E-02 NF NF NF 1800-1899 3.3E-02 5.3E-02 8.5E-02 NF NF NF 1900-1909 1.8E-02 1.8E-02 3.7E-02 NF NF NF 1910-1919 9.8E-03 9.8E-03 2.0E-02 NF 3.3E-02 3.3E-02 1920-1929 5.5E-03 5.5E-03 1.1E-02 2.1E-02 NF 2.1E-02 1930-1939 3.1E-03 NF 3.1E-03 NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF 6.1E-03 6.1E-03 1.2E-02 1960-1969 2.6E-03 2.6E-03 5.3E-03 NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF 3.8E-02 NF 3.8E-02 1983-1992 NF NF NF NF NF NF 1700-1929 1.4E-02 1.6E-02 3.0E-02 1.3E-02 6.5E-03 2.0E-02 1930-1992 1.0E-03 6.6E-04 1.7E-03 3.1E-03 1.5E-03 4.6E-03 Total 3.9E-03 4.1E-03 8.0E-03 5.0E-03 2.3E-03 7.3E-03 Year Buttress Multi-Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF NF NF 1900-1909 2.4E-01 NF 2.4E-01 NF NF NF 1910-1919 9.4E-02 NF 9.4E-02 NF NF NF 1920-1929 7.5E-02 NF 7.5E-02 5.5E-02 NF 5.5E-02 1930-1939 NF NF NF NF NF NF 1940-1949 3.6E-02 NF 3.6E-02 NF NF NF 1950-1959 1.2E-02 NF 1.2E-02 NF 5.9E-02 5.9E-02 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 9.3E-02 NF 9.3E-02 2.7E-02 NF 2.7E-02 1930-1992 7.7E-03 NF 7.7E-03 NF 1.5E-02 1.5E-02 Total 2.2E-02 NF 2.2E-02 9.7E-03 9.7E-03 1.9E-02 Year All Concrete & Masonry Comm. 0-5 years >5 years Total 1700-1799 2.7E-02 NF 2.7E-02 1800-1899 3.0E-02 4.8E-02 7.8E-02 1900-1909 2.2E-02 1.5E-02 3.7E-02 1910-1919 1.5E-02 1.1E-02 2.6E-02 1920-1929 1.4E-02 4.0E-03 1.8E-02 1930-1939 2.3E-03 NF 2.3E-03 1940-1949 2.4E-03 NF 2.4E-03 1950-1959 2.0E-03 2.0E-03 4.0E-03 1960-1969 1.9E-03 1.9E-03 3.8E-03 1970-1977 NF NF NF 1978-1982 4.6E-03 NF 4.6E-03 1983-1992 NF NF NF 1700-1929 1.8E-02 1.4E-02 3.2E-02 1930-1992 1.8E-03 1.0E-03 2.8E-03 Total 5.3E-03 3.7E-03 9.0E-03 Analysis of Concrete and Masonry Dam Incidents Page 2.138 Table 2.49. Annual probability of failure (as at 1992, excluding China) - sliding failures Year Gravity Arch Comm. 0-5 years (1) >5 years Total 0-5 years (1) >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 1.3E-03 NF 4.6E-05 NF NF NF 1900-1909 3.7E-03 1.1E-04 3.2E-04 NF NF NF 1910-1919 9.8E-04 NF 6.3E-05 NF NF NF 1920-1929 5.5E-04 4.5E-05 8.3E-05 NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF 1.2E-03 NF 1.6E-04 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 (3) NF NF NF NF NF NF 1700-1929 1.2E-03 2.7E-05 8.8E-05 NF NF NF 1930-1992 (3) NF NF NF 3.1E-04 NF 4.9E-05 Total (3) 2.6E-04 1.3E-05 4.1E-05 2.5E-04 NF 3.1E-05 Year Buttress Multi-Arch Comm. 0-5 years (1) >5 years Total 0-5 years (1) >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 NF NF NF NF NF NF 1920-1929 7.5E-03 NF 5.6E-04 NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 (3) NF NF NF NF NF NF 1700-1929 3.7E-03 NF 2.5E-04 NF NF NF 1930-1992 (3) NF NF NF NF NF NF Total (3) 6.5E-04 NF 8.3E-05 NF NF NF Year All Concrete & Masonry Comm. 0-5 years (1) >5 years Total 1700-1799 NF NF NF 1800-1899 1.2E-03 NF 4.2E-05 1900-1909 3.0E-03 9.1E-05 2.6E-04 1910-1919 7.5E-04 NF 4.9E-05 1920-1929 8.0E-04 3.2E-05 8.9E-05 1930-1939 NF NF NF 1940-1949 NF NF NF 1950-1959 2.0E-04 NF 2.7E-05 1960-1969 NF NF NF 1970-1977 NF NF NF 1978-1982 NF NF NF 1983-1992 (3) NF NF NF 1700-1929 1.1E-03 2.2E-05 8.1E-05 1930-1992 (3) 5.1E-05 NF 8.2E-06 Total (3) 2.8E-04 1.0E-05 4.1E-05 Notes (1) Assumes dam years = number of dams * five years life (2) NF - No Failure (3) Assumes number of dams constructed in 1983-1992 = 2 * number of dams in 1978- 1982 Analysis of Concrete and Masonry Dam Incidents Page 2.139 Table 2.50. Probability of failure (as at 1992, excluding China, non-annualised) - sliding failures Year Gravity Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 6.6E-03 NF 6.6E-03 NF NF NF 1900-1909 1.8E-02 9.2E-03 2.7E-02 NF NF NF 1910-1919 4.9E-03 NF 4.9E-03 NF NF NF 1920-1929 2.8E-03 2.8E-03 5.5E-03 NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF 6.1E-03 NF 6.1E-03 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 5.8E-03 2.3E-03 8.1E-03 NF NF NF 1930-1992 NF NF NF 1.5E-03 NF 1.5E-03 Total 1.3E-03 5.2E-04 1.8E-03 1.2E-03 NF 1.2E-03 Year Buttress Multi-Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 NF NF NF NF NF NF 1920-1929 3.8E-02 NF 3.8E-02 NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 1.9E-02 NF 1.9E-02 NF NF NF 1930-1992 NF NF NF NF NF NF Total 3.2E-03 NF 3.2E-03 NF NF NF Year All Concrete & Masonry Comm. 0-5 years >5 years Total 1700-1799 NF NF NF 1800-1899 6.0E-03 NF 6.0E-03 1900-1909 1.5E-02 7.5E-03 2.2E-02 1910-1919 3.7E-03 NF 3.7E-03 1920-1929 4.0E-03 2.0E-03 6.0E-03 1930-1939 NF NF NF 1940-1949 NF NF NF 1950-1959 1.0E-03 NF 1.0E-03 1960-1969 NF NF NF 1970-1977 NF NF NF 1978-1982 NF NF NF 1983-1992 NF NF NF 1700-1929 5.4E-03 1.8E-03 7.2E-03 1930-1992 2.5E-04 NF 2.5E-04 Total 1.4E-03 3.9E-04 1.8E-03 Analysis of Concrete and Masonry Dam Incidents Page 2.140 Table 2.51. Annual probability of failure (as at 1992, excluding China) - piping failures Year Gravity Arch Comm. 0-5 years (1) >5 years Total 0-5 years (1) >5 years Total 1700-1799 5.9E-03 NF 1.2E-04 NF NF NF 1800-1899 1.3E-03 NF 4.6E-05 NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 9.8E-04 NF 6.3E-05 NF NF NF 1920-1929 NF NF NF 2.1E-03 NF 1.6E-04 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF 1.9E-04 1.6E-04 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 (3) NF NF NF NF NF NF 1700-1929 7.0E-04 NF 3.8E-05 1.3E-03 NF 8.3E-05 1930-1992 (3) NF NF NF NF 5.8E-05 4.9E-05 Total (3) 1.6E-04 NF 1.8E-05 2.5E-04 3.5E-05 6.1E-05 Year Buttress Multi-Arch Comm. 0-5 years (1) >5 years Total 0-5 years (1) >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF NF NF 1900-1909 4.7E-02 NF 2.7E-03 NF NF NF 1910-1919 9.4E-03 NF 6.1E-04 NF NF NF 1920-1929 NF NF NF NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 7.3E-03 NF 7.7E-04 NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 (3) NF NF NF NF NF NF 1700-1929 7.5E-03 NF 4.9E-04 NF NF NF 1930-1992 (3) 7.8E-04 NF 1.2E-04 NF NF NF Total (3) 1.9E-03 NF 2.5E-04 NF NF NF Year All Concrete & Masonry Comm. 0-5 years (1) >5 years Total 1700-1799 5.4E-03 NF 1.1E-04 1800-1899 1.2E-03 NF 4.2E-05 1900-1909 1.5E-03 NF 8.6E-05 1910-1919 1.5E-03 NF 9.7E-05 1920-1929 4.0E-04 NF 3.0E-05 1930-1939 NF NF NF 1940-1949 4.7E-04 NF 5.0E-05 1950-1959 NF 3.1E-05 2.7E-05 1960-1969 NF NF NF 1970-1977 NF NF NF 1978-1982 NF NF NF 1983-1992 (3) NF NF NF 1700-1929 1.1E-03 NF 6.1E-05 1930-1992 (3) 5.1E-05 9.8E-06 1.6E-05 Total (3) 2.8E-04 5.1E-06 3.6E-05 Notes (1) Assumes dam years = number of dams * five years life (2) NF - No Failure (3) Assumes number of dams constructed in 1983-1992 = 2 * number of dams in 1978- 1982 Analysis of Concrete and Masonry Dam Incidents Page 2.141 Table 2.52. Probability of failure (as at 1992, excluding China, non-annualised) - piping failures Year Gravity Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 3.0E-02 NF 3.0E-02 NF NF NF 1800-1899 6.6E-03 NF 6.6E-03 NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 4.9E-03 NF 4.9E-03 NF NF NF 1920-1929 NF NF NF 1.1E-02 NF 1.1E-02 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF 6.1E-03 6.1E-03 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 3.5E-03 NF 3.5E-03 6.5E-03 NF 6.5E-03 1930-1992 NF NF NF NF 1.5E-03 1.5E-03 Total 7.7E-04 NF 7.7E-04 1.2E-03 1.2E-03 2.5E-03 Year Buttress Multi-Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF NF NF 1900-1909 2.4E-01 NF 2.4E-01 NF NF NF 1910-1919 4.7E-02 NF 4.7E-02 NF NF NF 1920-1929 NF NF NF NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 3.6E-02 NF 3.6E-02 NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 3.7E-02 NF 3.7E-02 NF NF NF 1930-1992 3.8E-03 NF 3.8E-03 NF NF NF Total 9.5E-03 NF 9.5E-03 NF NF NF Year All Concrete & Masonry Comm. 0-5 years >5 years Total 1700-1799 2.7E-02 NF 2.7E-02 1800-1899 6.0E-03 NF 6.0E-03 1900-1909 7.5E-03 NF 7.5E-03 1910-1919 7.5E-03 NF 7.5E-03 1920-1929 2.0E-03 NF 2.0E-03 1930-1939 NF NF NF 1940-1949 2.4E-03 NF 2.4E-03 1950-1959 NF 1.0E-03 1.0E-03 1960-1969 NF NF NF 1970-1977 NF NF NF 1978-1982 NF NF NF 1983-1992 NF NF NF 1700-1929 5.4E-03 NF 5.4E-03 1930-1992 2.5E-04 2.5E-04 5.0E-04 Total 1.4E-03 2.0E-04 1.6E-03 Analysis of Concrete and Masonry Dam Incidents Page 2.142 Table 2.53. Annual probability of failure (as at 1992, excluding China) - tension/shear failures through dam body Year Gravity Arch Comm. 0-5 years (1) >5 years Total 0-5 years (1) >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 2.6E-03 2.4E-04 3.2E-04 NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 NF NF NF NF NF NF 1920-1929 NF 4.5E-05 4.1E-05 NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 2.6E-04 6.0E-05 9.8E-05 NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF 7.7E-03 NF 3.2E-03 1983-1992 (3) NF NF NF NF NF NF 1700-1929 4.6E-04 8.0E-05 1.0E-04 NF NF NF 1930-1992 (3) 6.8E-05 1.3E-05 2.2E-05 3.1E-04 NF 4.9E-05 Total (3) 1.6E-04 4.6E-05 5.9E-05 2.5E-04 NF 3.1E-05 Year Buttress Multi-Arch Comm. 0-5 years (1) >5 years Total 0-5 years (1) >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 9.4E-03 NF 6.1E-04 NF NF NF 1920-1929 NF NF NF 1.1E-02 NF 8.3E-04 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 2.4E-03 NF 3.2E-04 NF 1.8E-03 1.6E-03 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 (3) NF NF NF NF NF NF 1700-1929 3.7E-03 NF 2.5E-04 5.4E-03 NF 3.2E-04 1930-1992 (3) 7.8E-04 NF 1.2E-04 NF 5.1E-04 4.3E-04 Total (3) 1.3E-03 NF 1.7E-04 2.0E-03 2.0E-04 3.7E-04 Year All Concrete & Masonry Comm. 0-5 years (1) >5 years Total 1700-1799 NF NF NF 1800-1899 2.4E-03 2.2E-04 3.0E-04 1900-1909 NF NF NF 1910-1919 7.5E-04 NF 4.9E-05 1920-1929 4.0E-04 3.2E-05 6.0E-05 1930-1939 NF NF NF 1940-1949 NF NF NF 1950-1959 2.0E-04 3.1E-05 5.4E-05 1960-1969 1.9E-04 4.3E-05 7.1E-05 1970-1977 NF NF NF 1978-1982 9.2E-04 NF 3.8E-04 1983-1992 (3) NF NF NF 1700-1929 7.2E-04 6.5E-05 1.0E-04 1930-1992 (3) 1.5E-04 2.0E-05 4.1E-05 Total (3) 2.9E-04 4.0E-05 6.8E-05 Notes (1) Assumes dam years = number of dams * five years life (2) NF - No Failure (3) Assumes number of dams constructed in 1983-1992 = 2 * number of dams in 1978- 1982 Analysis of Concrete and Masonry Dam Incidents Page 2.143 Table 2.54. Probability of failure (as at 1992, excluding China, non-annualised) - tension/shear failures through dam body Year Gravity Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 1.3E-02 3.3E-02 4.6E-02 NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 NF NF NF NF NF NF 1920-1929 NF 2.8E-03 2.8E-03 NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 1.3E-03 1.3E-03 2.6E-03 NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF 3.8E-02 NF 3.8E-02 1983-1992 NF NF NF NF NF NF 1700-1929 2.3E-03 7.0E-03 9.3E-03 NF NF NF 1930-1992 3.3E-04 3.3E-04 6.6E-04 1.5E-03 NF 1.5E-03 Total 7.7E-04 1.8E-03 2.6E-03 1.2E-03 NF 1.2E-03 Year Buttress Multi-Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 4.7E-02 NF 4.7E-02 NF NF NF 1920-1929 NF NF NF 5.5E-02 NF 5.5E-02 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 1.2E-02 NF 1.2E-02 NF 5.9E-02 5.9E-02 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 1.9E-02 NF 1.9E-02 2.7E-02 NF 2.7E-02 1930-1992 3.8E-03 NF 3.8E-03 NF 1.5E-02 1.5E-02 Total 6.4E-03 NF 6.4E-03 9.7E-03 9.7E-03 1.9E-02 Year All Concrete & Masonry Comm. 0-5 years >5 years Total 1700-1799 NF NF NF 1800-1899 1.2E-02 3.0E-02 4.2E-02 1900-1909 NF NF NF 1910-1919 3.7E-03 NF 3.7E-03 1920-1929 2.0E-03 2.0E-03 4.0E-03 1930-1939 NF NF NF 1940-1949 NF NF NF 1950-1959 1.0E-03 1.0E-04 2.0E-03 1960-1969 9.5E-04 9.5E-04 1.9E-03 1970-1977 NF NF NF 1978-1982 4.6E-03 NF 4.6E-03 1983-1992 NF NF NF 1700-1929 3.6E-03 5.4E-03 9.0E-03 1930-1992 7.5E-04 5.0E-04 1.3E-03 Total 1.4E-03 1.6E-03 2.9E-03 Analysis of Concrete and Masonry Dam Incidents Page 2.144 Table 2.55. Number of failures during overtopping where the failure mode was unknown Year Gravity Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 NF 3 3 NF NF NF 1900-1909 NF 1 1 NF NF NF 1910-1919 NF 1 1 NF 1 1 1920-1929 NF NF NF 1 NF 1 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 NF 5 5 1 1 2 1930-1992 NF NF NF NF NF NF Total NF 5 5 1 1 2 Year Buttress Multi-Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 NF NF NF NF NF NF 1920-1929 1 NF 1 NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 1 NF 1 NF NF NF 1930-1992 NF NF NF NF NF NF Total 1 NF 1 NF NF NF Year All Concrete & Masonry Comm. 0-5 years >5 years Total 1700-1799 NF NF NF 1800-1899 NF 3 3 1900-1909 NF 1 1 1910-1919 NF 2 2 1920-1929 2 NF 2 1930-1939 NF NF NF 1940-1949 NF NF NF 1950-1959 NF NF NF 1960-1969 NF NF NF 1970-1977 NF NF NF 1978-1982 NF NF NF 1983-1992 NF NF NF 1700-1929 2 6 7 1930-1992 NF NF NF Total 2 6 8 Analysis of Concrete and Masonry Dam Incidents Page 2.145 Table 2.56. No. of failures where the failure mode was unknown (no overtopping) Year Gravity Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 1 NF 1 NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 NF 1 1 NF NF NF 1920-1929 1 NF 1 NF NF NF 1930-1939 1 NF 1 NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 1 1 2 NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1960-1982 NF NF NF NF NF NF 1960-1992 1 1 2 NF NF NF 1700-1929 2 1 3 NF NF NF 1930-1992 2 1 3 NF NF NF Total 4 2 6 NF NF NF Year Buttress Multi-Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 NF NF NF NF NF NF 1920-1929 NF NF NF NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1960-1982 NF NF NF NF NF NF 1960-1992 NF NF NF NF NF NF 1700-1929 NF NF NF NF NF NF 1930-1992 NF NF NF NF NF NF Total NF NF NF NF NF NF Year All Concrete & Masonry Comm. 0-5 years >5 years Total 1700-1799 NF NF NF 1800-1899 1 NF 1 1900-1909 NF NF NF 1910-1919 NF 1 1 1920-1929 1 NF 1 1930-1939 1 NF 1 1940-1949 NF NF NF 1950-1959 NF NF NF 1960-1969 1 1 2 1970-1977 NF NF NF 1978-1982 NF NF NF 1983-1992 NF NF NF 1960-1982 NF NF NF 1960-1992 1 1 2 1700-1929 2 1 4 1930-1992 2 1 2 Total 4 2 6 Analysis of Concrete and Masonry Dam Incidents Page 2.146 2.4.1.5 Gravity Dams - Separation of Concrete and Masonry Dams The ICOLD(1984) population for gravity dams does not distinguish between dams made of concrete and those made of masonry. An estimate was made for the population taking into account the history of dam building and the USA population of dams. Dams of cyclopean concrete construction were assumed to be concrete. According to Smith (1972), Schnitter (1994) and Lewis (1988) the first concrete dams were completed in the 1870’s in Australia and the USA; the 1890’s in India; and the 1900’s in Great Britain. The distribution of concrete and masonry gravity dams in the USA was taken from the 567 concrete and masonry dams in the US Inventory of dams (1994) and is presented in Table 2.57. Table 2.57. Distribution of concrete and masonry gravity dams in the USA Year Commissioned Concrete (%) Masonry (%) Pre 1900 68.4 31.6 1900-1909 76.5 23.5 1910-1919 93.7 6.3 1920-1929 96.3 3.7 1930-1939 98.3 1.7 1940-1949 100 0 1950-1959 98.9 1.1 1960-1969 100 0 1970-1979 100 0 1980-1989 100 0 1990-1992 100 0 Table 2.57 was not used directly as this was likely to be biased towards concrete dams due to the modern nature of USA dams compared to much of the rest of the world. It is also possible that some dams denoted as ‘gravity’, and therefore assumed to be concrete, in the US database are masonry. Some countries such as India, which has approximately 3.2% of the world concrete and masonry dam population (ICOLD, 1994), commonly use masonry to construct their dams due to material availability and expense. Table 2.58 shows the distribution chosen for the analysis. It was found that the probabilities of failure were not sensitive to the assumptions in the concrete/masonry distribution for the post 1960 period. Analysis of Concrete and Masonry Dam Incidents Page 2.147 Table 2.61 to Table 2.64 show the annualised probabilities of failure for concrete and masonry dams for the various failure modes. Table 2.65 and Table 2.66 show the number of failures with unknown failure modes. Table 2.65 shows those unknowns where failure during overtopping was known to have occurred. A distinction was made between dams commissioned prior to, and those commissioned after 1930. This represents the historical change to a better understanding of uplift pressures and materials properties for gravity dams. Table 2.59 summarises the annualised probabilities of failure using this distinction. As there were a number of categories without failures (denoted ‘NF’) a ‘maximum’ annual probability (assuming one failure to have occurred over the number of dam years) has been calculated and included in the last row of Table 2.59. Table 2.51 gives suggested average annualised probabilities of failure for concrete and masonry gravity dams based on Table 2.59. Unknowns were accounted for by distributing them evenly through the three dam failure modes (foundation sliding and piping and failure within the dam body). This allowed for the total probability to be equal to the sum of the three modes. The probabilities have been rounded down (to one decimal place) to account for the assumptions in the analysis. In particular, the population used was that in existence as at 1992 and many dams are likely to have been decommissioned prior to this time or omitted from the ICOLD database and hence not included in the population. A larger population would result in lower probabilities of failure. This was checked for validity by assuming a larger population and re-running the analysis. Where no failures have occurred the suggested value is lower than that for the case where one failure had occurred. Analysis of Concrete and Masonry Dam Incidents Page 2.148 Table 2.58. Distribution of concrete and masonry gravity dams chosen for analysis Year Commissioned Concrete (%) Masonry (%) Pre 1900 0/30 100/70 1900-1909 60 40 1910-1919 75 25 1920-1929 90 10 1930-1939 90 10 1940-1949 95 5 1950-1959 95 5 1960-1969 97.5 2.5 1970-1979 97.5 2.5 1980-1989 97.5 2.5 1990-1992 97.5 2.5 Note (1) 1700-1799/1800-1899 Table 2.59. Summary of annualised probabilities of failure for gravity dams (exc. China) Concrete Gravity Masonry Gravity Failure Mode Year Commissioned 0-5 years >5 years Total 0-5 years >5 years Total 1700-1929 1.0E-03 9.3E-05 1.5E-04 5.2E-03 3.4E-04 5.4E-04 All Modes 1930-1992 1.4E-04 1.4E-05 3.5E-05 1.6E-03 2.4E-04 4.2E-04 1700-1929 6.7E-04 7.0E-05 1.1E-04 1.5E-03 NF 6.0E-05 Foundation Sliding 1930-1992 NF NF NF NF NF NF 1700-1929 3.4E-04 NF 2.2E-05 1.5E-03 NF 6.0E-05 Foundation Piping 1930-1992 NF NF NF NF NF NF 1700-1929 NF NF NF 7.3E-04 1.6E-04 1.8E-04 Within Dam Body 1930-1992 7.1E-05 NF 1.1E-05 NF 2.4E-04 2.1E-04 1700-1929 3.3E-04 2.3E-05 2.2E-05 7.3E-04 3.1E-05 3.0E-05 Max. No Fails (1) 1930-1992 7.0E-05 1.4E-05 1.1E-05 1.6E-03 2.4E-04 2.1E-04 1700-1929 - - - - 6 6 Unknown (O/T) 1930-1992 - - - - - - 1700-1929 - 1 1 3 - 3 Unknown 1930-1992 2 2 4 2 - 2 Note (1) Assuming 1 failure (for where no failures have occurred) Analysis of Concrete and Masonry Dam Incidents Page 2.149 Table 2.60. Suggested values for annualised probabilities of failure for gravity dams (excluding China) Concrete Gravity Masonry Gravity Failure Mode Year Commissioned 0-5 years >5 years 0-5 years >5 years pre 1930 N/A 6.4E-05 2 N/A 3.2E-04 2 All Failures 1930-present 1.3E-04 2 1.2E-05 2 1.5E-03 2 2.4E-04 2 pre 1930 N/A 5.0E-05 2 N/A 6.0E-05 1 Foundation Sliding P SA 1930-present 2.0E-05 1 4.0E-06 1 5.0E-04 1 2.0E-05 1 pre 1930 N/A 7.0E-06 1 N/A 6.0E-05 2 Foundation Piping P PA 1930-present 2.0E-05 1 4.0E-06 1 5.0E-04 1 2.0E-05 1 pre 1930 N/A 7.0E-06 1 N/A 2.0E-04 2 Within Dam Body P BA 1930-present 9.0E-05 2 4.0E-06 1 5.0E-04 1 2.0E-04 2 Note: (1) No failures, probability estimated lower than that for one failure. (2) Probability rounded down to account for smaller than actual population used in the analysis. Analysis of Concrete and Masonry Dam Incidents Page 2.150 Table 2.61. Annualised probabilities of failure for gravity dams - all failures Concrete Gravity Masonry Gravity Year Commissioned 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 NF NF NF 5.9E-03 NF 1.2E-04 1800-1899 NF NF NF 7.5E-03 5.5E-04 7.9E-04 1900-1909 3.0E-03 3.7E-04 5.2E-04 NF 2.7E-04 2.6E-04 1910-1919 1.3E-03 8.9E-05 1.7E-04 3.8E-03 2.7E-04 5.0E-04 1920-1929 6.0E-04 4.9E-05 9.0E-05 5.4E-03 4.4E-04 8.1E-04 1930-1939 NF NF NF 6.0E-03 NF 5.3E-04 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 5.3E-04 6.1E-05 1.5E-04 NF 2.4E-03 1.9E-03 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 1.0E-03 9.2E-05 1.5E-04 5.1E-03 3.4E-04 5.4E-04 1930-1992 1.4E-04 1.4E-05 3.4E-05 1.6E-03 2.4E-04 4.2E-04 Total 2.9E-04 4.3E-05 7.5E-05 4.0E-03 3.3E-04 5.2E-04 Table 2.62. Annualised probabilities of failure for gravity dams - sliding failures Concrete Gravity Masonry Gravity Year Commissioned 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF 1.9E-03 NF 6.6E-05 1900-1909 3.0E-03 3.7E-04 5.2E-04 NF NF NF 1910-1919 NF NF NF 3.8E-03 NF 2.5E-04 1920-1929 6.0E-04 4.9E-05 9.0E-05 NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 6.7E-04 6.9E-05 1.1E-04 1.5E-03 NF 6.0E-05 1930-1992 NF NF NF NF NF NF Total 1.2E-04 2.6E-05 3.7E-05 1.0E-03 NF 5.2E-05 Analysis of Concrete and Masonry Dam Incidents Page 2.151 Table 2.63. Annualised probabilities of failure for gravity dams - piping failures Concrete Gravity Masonry Gravity Year Commissioned 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 NF NF NF 5.9E-03 NF 1.2E-04 1800-1899 NF NF NF 1.9E-03 NF 6.6E-05 1900-1909 NF NF NF NF NF NF 1910-1919 1.3E-03 NF 8.3E-05 NF NF NF 1920-1929 NF NF NF NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 3.3E-04 NF 2.2E-05 1.5E-03 NF 6.0E-05 1930-1992 NF NF NF NF NF NF Total 5.8E-05 NF 7.5E-06 1.0E-03 NF 5.2E-05 Table 2.64. Annualised probabilities of failure for gravity dams - dam body tension/shear failures Concrete Gravity Masonry Gravity Year Commissioned 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF 1.9E-03 2.7E-04 3.3E-04 1900-1909 NF NF NF NF NF NF 1910-1919 NF NF NF NF NF NF 1920-1929 NF NF NF NF 4.4E-04 4.1E-04 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 2.7E-04 NF 4.9E-05 NF 2.4E-03 1.9E-03 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1960-1982 1.6E-04 NF 3.6E-05 NF 1.8E-03 1.4E-03 1960-1992 1.3E-04 NF 3.4E-05 NF 1.8E-03 1.3E-03 1700-1929 NF NF NF 7.3E-04 1.6E-04 1.8E-04 1930-1992 7.0E-05 NF 1.1E-05 NF 2.4E-04 2.1E-04 Total 5.8E-05 NF 7.5E-06 5.0E-04 1.6E-04 1.8E-04 Analysis of Concrete and Masonry Dam Incidents Page 2.152 Table 2.65. Number of failures during overtopping where failure mode was unknown Concrete Gravity Masonry Gravity Year Commissioned 0-5 years >5 years Total 0-5 years >5 years Total 1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF 4 4 1900-1909 NF NF NF NF 1 1 1910-1919 NF NF NF NF 1 1 Total NF NF NF NF 6 6 Table 2.66. Number of failures where failure mode was unknown Concrete Gravity Masonry Gravity Year Commissioned 0-5 years >5 years Total 0-5 years >5 years Total 1800-1899 NF NF NF 2 NF 2 1910-1919 NF 1 1 NF NF NF 1920-1929 NF NF NF 1 NF 1 1930-1939 NF NF NF 1 NF 1 1960-1969 1 1 2 NF NF NF 1930-1992 1 1 2 1 NF 1 Total 1 2 3 4 NF 4 Analysis of Concrete and Masonry Dam Incidents Page 2.153 2.4.2 General Approach for Estimating the Probability of Failure for Individual Gravity Dams Not all dams can be considered as ‘average’. Corrections can be made to the average probabilities so that they can be used for particular dams. The following describes a method to assess multiplication factors for concrete and masonry gravity dams that can be applied to the ‘average’ probabilities from the previous section for better or worse than ‘average’ dams. The method is for gravity dams that have a straight axis (no curvature) and are not post-tensioned. Where a dam is constructed of masonry but can be shown to be of a quality comparable to that of a good concrete gravity dam, the average annual probability may be taken as somewhere between that for masonry and that for concrete. Where a dam has been raised and the full supply level (FSL) increased, the dam should be treated as a ‘new’ dam and the age of the dam calculated from this time. That is, the dam should fall back into the 0-5 years category. This stems from the Section 2.3.4 that showed that dams have generally failed at or just above their highest recorded water level. If the dam is of good design, is very well drained, has good uplift monitoring AND the dam foundation has been assessed by a suitably qualified rock mechanics practitioner and found to easily satisfy present day standards then a reduction factor, f red , of between 0.9 and 0.1 can be used. This factor should be applied to the annual probability of failure in Equation 2.6. This factor can NOT be applied to dams with soil foundations and should NOT be used for initial dam screening assessments where the data available and the level of investigation and analysis are limited. Analysis of Concrete and Masonry Dam Incidents Page 2.154 2.4.3 Details of the Method for Estimating the Probability of Failure for Individual Gravity Dams The following summarises the suggested procedure for estimating the annual probability of failure of a concrete or masonry gravity dam. The annual probability of failure of the dam, P, should be calculated as the sum of the probabilities of failure for sliding, piping and through the dam body. • Sliding through the foundation: Step (1) Determine the average annual probability of failure, P SA , from Table 2.51 in Section 2.4.1.5. (2) Determine the multiplication factor for sliding on a soil or rock foundation, f SF , from Table 2.72 in Section 2.4.4.1. (3) If the foundation is rock go to Step (4), if it is soil go to Step (5). (4) Determine the geology type factor, f SG, from Analysis of Concrete and Masonry Dam Incidents Page 2.155 Table 2.75 in Section 2.4.4.2, then go to Step (6) (5) f SG = 1.0 (6) Determine the structural height/width factor, f H/W , from Table 2.77 in Section 2.4.4.4. (7) Determine the other observations factor, f O , from Section 2.4.4.5. (8) Determine the surveillance factor, f S , from Table 2.78 in Section 2.4.4.6. (9) Calculate the probability of a foundation sliding failure as: P P f f f f f S SA SF SG H W O S = × × × × × / (2.3) Analysis of Concrete and Masonry Dam Incidents Page 2.156 • Piping through the foundation: Step (1) Determine the average annual probability of failure, P PA , from Table 2.51 in Section 2.4.1.5. (2) Determine the multiplication factor for piping on a soil or rock foundation, f PF , from Table 2.72 in Section 2.4.4.1. (3) If the foundation is rock go to Step (4), if it is soil go to Step (5). (4) Determine the geological environment, f GE, factor from Section 2.4.4.3, then go to Step (6). (5) f GE = 1.0 (6) Determine the structural height/width factor, f H/W , from Table 2.77 in Section 2.4.4.4. (7) Determine the other observations factor, f O , from Section 2.4.4.5. (8) Determine the surveillance factor, f S , from Table 2.78 in Section 2.4.4.6. (9) Calculate the probability of a foundation piping failure as: P P f f f f f P PA PF GE H W O S = × × × × × / (2.4) Analysis of Concrete and Masonry Dam Incidents Page 2.157 • Failure through the dam body: Step (1) Determine the average annual probability, P BA, of failure from Table 2.51 in Section 2.4.1.5. (2) Determine the structural height/width factor, f H/W , from Table 2.77 in Section 2.4.4.4. (3) Determine the other observations factor, f O , from Section 2.4.4.5. (4) Determine the surveillance factor, f S , from Table 2.78 in Section 2.4.4.6. (5) Calculate the probability of a failure through the dam body as: P P f f f B BA H W O S = × × × / (2.5) • Total annual probability of failure: ( ) B P S red P P P f P + + = (2.6) where, f red = Reduction factor, only applied when conditions described in Section 2.4.2 are satisfied. Analysis of Concrete and Masonry Dam Incidents Page 2.158 2.4.4 Gravity Dam Probability Multiplication Factors The following outlines the basis for assigning the multiplication factors. The factors, where possible, have been based on the failure statistics in the previous sections. Where necessary the accident statistics have been used to assist in developing the multiplication factors. It should be noted however, that most of the dam accidents were ‘theoretical’ (eg. a calculation was performed that indicated the dam was unsafe and it was anchored) and as such of little value to this exercise. 2.4.4.1 Soil/Rock Foundation Factor, f SF and f PF The probability of a dam failing through the foundation is highly dependent on whether the foundation is soil and/or rock. An estimation of the multiplication factors for sliding and piping of gravity dams on soil and rock foundations is outlined below. The percentage of soil and rock foundations in the world population was estimated from the USBR, Australia/New Zealand, and Portugal populations (Table 2.67 to Table 2.69) and is shown in Table 2.70. It is recognised that this may be a somewhat biased sample but there was no way of practically obtaining data for a larger population. Table 2.67. Foundation types - USBR Foundation Gravity Arch Buttress Multi-Arch Total Rock 18 31 6 - 55 Soil 1 - 1 - 2 Soil and Rock 2 - - - 2 Total 21 31 7 - 59 Table 2.68. Foundation types - Australia/New Zealand Foundation Gravity Arch Buttress Multi-Arch Total Rock 84 40 6 1 131 Soil - - - - 0 Soil and Rock 3 - - - 3 Total 87 40 6 1 134 Analysis of Concrete and Masonry Dam Incidents Page 2.159 Table 2.69. Foundation types - Portugal Foundation Gravity Arch Buttress Multi-Arch Total Rock 26 20 4 2 52 Soil - - - - 0 Soil and Rock 1 - - - 1 Unknown 1 - - - 1 Total 28 20 4 2 54 Table 2.70. Gravity dam foundation types - combined Foundation Number % Rock 128 94.1 Soil 1 0.7 Soil and Rock 6 4.4 Unknown 1 0.7 Total 136 100 The number of failures (both sliding and piping) in a particular foundation type is shown below. Table 2.71. Foundations for gravity dam failures by sliding or piping Foundation Piping Sliding PG PG(M) PG PG(M) Rock 5 2 Soil 2 Soil and Rock 1 Total 1 2 5 2 To determine the factors for soil and rock the following assumptions were made: • All piping failures occurred through the soil section of the foundation. • Combined soil/rock (S/R) foundations are taken as soil. • Unknown foundation types are rock. Analysis of Concrete and Masonry Dam Incidents Page 2.160 The factors were calculated as: f percent of failures percent of population = (2.7) For example, the factor for piping through soil foundations is: f PF = = 100% 51% 196 . . (2.8) Where there are no failures (0%) the factor is zero. To overcome this problem it was assumed that 1% of all foundation failures would occur on this particular foundation type. The results of this analysis are shown in Table 2.72. Table 2.72 shows that the factor for sliding on rock is greater than that for soil. This can be justified by the fact that no sliding failures have occurred on soil. It is likely that engineers have taken the soil into account in the dam design whereas, there may be defects which drastically reduce the foundation strength, in a rock foundation that may be overlooked in the design. Historically no gravity dam piping failures have occurred in rock foundations. A number of accidents have occurred as shown in Table 2.73. It is likely that there is sufficient warning of the progression of piping through rock foundations to allow for action to be taken to prevent failure. Table 2.72. Gravity dam factors for piping and sliding failure on soil and rock, f SF and f PF Foundation Piping, f PF Sliding, f SF Rock 0.01* 1.1 Soil or Soil and Rock 19.6 0.2* * These values were derived by assuming 1% failures. Table 2.73. Foundation types - accidents Piping Sliding Foundation PG PG(M) PG PG(M) Rock 9 1 5 1 Soil 1 Soil and Rock Unknown 1 Total 11 1 5 1 Analysis of Concrete and Masonry Dam Incidents Page 2.161 2.4.4.2 Geology Types - Sliding on Rock, f SG Some rock types are more likely to have weaknesses in the foundation (Fell et al, 1992), so a geology type factor has been included. The geology population was calculated from a weighted average of the representative populations from the USBR, Australia/New Zealand and Portugal. The population for the whole of the USA was assessed by considering the overall geology map of the USA and comparing the distribution of geology types west of longitude 100°W (where the USBR population lies) with that east of longitude 100°W. A weighted average population was created using the number of gravity dams in the respective countries as given in ICOLD (1984) as weighting factors. Equation 2.9 shows the method used. Table 2.74 gives the weighting factors used in the analysis. Table 2.76 shows the weighted population and the number of sliding failures in each foundation. The calculated and adopted sliding factors are also included. Table 2.75 shows a summary of the factors adopted. Where there is a high chance of a through going defect beneath the dam a factor of 3 should be used. The following points should be noted: • There were three failures in sandstone/shale foundations and none in sandstone alone. • There was one failure in a combined limestone/dolomite foundation. G G G G G G G = + + 1 1 2 2 3 3 1 2 3 α α α (2.9) where, G is the weighted geology type population G 1 , G 2 and G 3 are the geology type populations for each region α 1 , α 2 and α 3 are the weighting factors Table 2.74. Weighting factors used for weighted average (ICOLD (1984) dam population) Population α Australia/ New Zealand 81 Portugal 27 USA 528 Analysis of Concrete and Masonry Dam Incidents Page 2.162 Table 2.75. Adopted gravity dam factors for sliding on a rock foundation, f SG Geology Type Multiplication Factor Comments shale, claystone sandstone with shale interbeds limestone with shale interbeds default for sandstone 3 Where a dam is known to be on sandstone but it can not be proved that no shale/claystone exists then the default of 3 should be taken. Mudstone, siltstone, Conglomerate Schist, gneiss, phyllite, slate Hornfels, limestone, dolomite 1.5 Mudstone and siltstone represent a transition from shale to sandstone. Others based on failure statistics. Granite Granodiorite 0.3 A low factor has be deemed appropriate as there have been no sliding failures on granite yet there exists a large population of dams. Others 0.9 Where it can be proved that the dam foundation comprises ONLY sandstone 0.9 can be used else, a factor of 3 should be taken Analysis of Concrete and Masonry Dam Incidents Page 2.163 Table 2.76. Gravity dam factors for sliding on a rock foundation Failures Factors Geology Type Population % No. % Calculated Adopted Comments Total 100 13 100 Sandstones 21.1 3 23.1 1.1 0.9 No sandstone only failures so treated as no failures Shale 8.0 4 30.8 3.9 3 Based on failure data, includes shale & sandstone Siltstone 0.5 0.0 0.0 1.5 Assumed transitional between shale & sandstone Conglomerate 3.6 1 7.7 2.1 1.5 Based on failure data Limestone 3.6 1 7.7 2.1 1.5 Based on failure data Claystone 0.3 0.0 0.0 3 Similar properties to shale Mudstone 0.4 0.0 0.0 1.5 Assumed transitional between shale & sandstone Chert 0.2 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1 Breccia 0.2 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1 Dolomite 3.6 1 7.7 2.1 1.5 Based on failure data Marl 3.6 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1 Schist 11.4 2 15.4 1.4 1.5 Based on failure data Quartzite 0.8 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1 Gneiss 0.7 0.0 0.0 1.5 Similar properties to schist Phylitte 0.5 0.0 0.0 1.5 Similar properties to schist Slate 0.3 0.0 0.0 1.5 Similar properties to schist Hornfels 3.3 1 7.7 2.4 1.5 Based on failure data Argillite 0.1 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1 Granite 20.1 0.0 0.0 0.3 Factor would be 0.4 assuming 1 failure Basalt 5.0 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1 Tuff 2.4 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1 Dolerite 0.8 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1 Rhyolite 1.9 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1 Andesite 0.3 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1 Porphyry 0.2 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1 Diorite 3.4 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1 Granodiorite 0.3 0.0 0.0 0.3 Similar properties to granite Greenstone 3.4 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1 Agglomerate 0.1 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1 Pumice 0.1 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1 Analysis of Concrete and Masonry Dam Incidents Page 2.164 2.4.4.3 Geology Type - Piping on Rock, f GE As there have been no piping failures of concrete dams on rock foundations it was decided to take all factors as unity. Another factor, which takes account of problem geological environments, was used as a better indicator of variations of likelihood of failure from the average. The environments considered for this were those that allowed for the possibility of open joints and include: • Granitic foundations with sheet joints; • very steep sided narrow valleys with likely stress relief joints parallel to the ground surface; • sedimentary sequences with stress relief effects; • very weak erodible volcanics; and • limestone or dolomite. (Reference Fell, MacGregor and Stapledon, 1992) The factor should be chosen on a site by site basis but should not exceed 2. The minimum multiplication factor should be 1. The default value (where the environment is unknown) should also be taken as 1. 2.4.4.4 Height on Width Ratio, f H/W The structural height to width ratio (h d /W) is used to take account of the stockiness/slenderness of the gravity dam. Hence the h d /W ratio offers a first order guide to the relative likelihood of failure by sliding and within the body of the dams. A database of h d /W ratios was collected from the Australia/New Zealand, USBR populations and from selected ICOLD international conferences (Questions 26, 30, 45, 52, 56, 59, 65). Where found, dams with any curvature were excluded. Figure 2.43 and Figure 2.44 show scatter plots of h d /W versus year commissioned and h d respectively for the population and failed dams. Failures are scattered amongst the population, although the majority appear to be more concentrated above the average h d /W ratio. The h d /W population does not show any correlation with year commissioned. However, as h d increases h d /W approaches approximately 1.2. It was decided to apply factors as shown in Table 2.77 and Figure 2.45. These factors have been derived by dividing the percentage of failures (due to sliding or in the dam body) by the percentage of the Analysis of Concrete and Masonry Dam Incidents Page 2.165 population in each h d /W range, in a similar manner to those for sliding and piping in Section 2.4.4.1. Table 2.77. Multiplication factors for structural height/width ratio of gravity dams, f H/W h d /W <1.0 1.0-1.19 1.2-1.39 1.4-1.59 1.6-1.79 1.8-1.99 Factor 0.1 0.5 0.9 1.3 3 6 Page 2.166 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 Year Commissioned h d / W . Population - Concrete Gravity Population - Masonry Gravity Population - Unknown Gravity Failure - Sliding Failure - Body Figure 2.43. h d /W versus year commissioned Page 2.167 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 0 20 40 60 80 100 120 140 160 180 200 hd h d / W . Population - Concrete Gravity Population - Masonry Gravity Population - Unknown Gravity Failure - Sliding Failure - Body Figure 2.44. h d /W versus h d Page 2.168 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 hd/W F a c t o r ( % F a i l u r e s / % P o p u l a t i o n ) . Sliding Body Combined Suggested Figure 2.45. h d /W factors Analysis of Concrete and Masonry Dam Incidents Page 2.169 2.4.4.5 Other Observations, f O This section allows for a multiplication factor to be applied for observed conditions or special features of the dam. These features will vary with each dam and must be assessed on a dam by dam basis. The minimum value for any dam should be 0.9 (no signs of distress, no or very little leakage). The default value should be 1.0. Conditions, which would warrant a higher multiplication factor (up to a maximum of 10), include: • Sudden increases in seepage through the dam or foundation • Cracking (of a nature that could effect the dam’s stability) • High or non-linear uplift pressures (also blocked drains) • Alkali aggregate reaction (AAR) or alkali silica reaction (ASR) • Extensive calcite deposits • Large/non-linear dam movements 2.4.4.6 Surveillance, f S Historically, unlike embankment dams, most gravity dams have failed with only a short amount of warning. This warning may be enough to warn people downstream but, is usually insufficient to enable the dam to be saved from failure. However dams will sometimes begin to show some signs of problems developing, allowing intervention (eg by controlling the water level, or by remedial works). Hence it is considered reasonable to apply a factor to allow for the quality of monitoring and surveillance. Table 2.78 shows the multiplication factors recommended. The multiplication factors have been modified from those given by Foster et al (1998) for embankment dams. Table 2.78. Monitoring and surveillance multiplication factors, f S Surveillance Embankment Dam Factor Factor f S Inspections annually 2.0 1.5 Inspections monthly 1.2 1.1 Irregular seepage observations, inspections weekly 1.0 1.0 weekly seepage monitoring, weekly inspections 0.8 0.9 Daily monitoring of seepage, daily inspections 0.5 0.8 Analysis of Concrete and Masonry Dam Incidents Page 2.170 2.4.5 Results Figure 2.46 and Figure 2.47 show the potential ranges for the annual probabilities of failure for various cases. The ‘average’ dam has been taken as a dam that has: a geology type factor, f SG , of 0.9; a height to width ratio, h d /W, of 1.3; and the remaining multiplication factors as unity. A number of dams that have failed have been plotted together with dams from the Australia/New Zealand population and USBR population of concrete and masonry gravity dams. None of the dams plotted have the f red reduction factor, as it could not be proven that they satisfied the criteria described above. Where unknown, multiplication factors were taken as their default or unity. For the most common type of dam (commissioned after 1930, greater than five years in age and on a rock foundation) the potential average probabilities using the method range from 4 x 10 - 8 to 1 x 10 -3 . ANZ dam failed dam min USBR dam maximum 'average' 1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 post 1930/<5 years/soil fndn post 1930/<5 years/rock fndn post 1930/>5 years/soil fndn post 1930/>5 years/rock fndn pre1930/>5 years/soil fndn pre1930/>5 years/rock fndn Probability of Failure Figure 2.46. Range of annual probability of failure for concrete gravity dams Analysis of Concrete and Masonry Dam Incidents Page 2.171 1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 post 1930/<5 years/soil fndn post 1930/<5 years/rock fndn post 1930/>5 years/soil fndn post 1930/>5 years/rock fndn pre1930/>5 years/soil fndn pre1930/>5 years/rock fndn min 'average' failed dams maximum Probability of Failure Figure 2.47. Range of annual probability of failure for masonry gravity dams Analysis of Concrete and Masonry Dam Incidents Page 2.172 2.5 DISCUSSION AND CONCLUSIONS Most of the results have been discussed in Section 2.3. Below is a brief discussion of the major components of CONGDATA. • Year commissioned The data shows a distinct increase in incidents for all concrete/masonry dam types in the 1920’s. Another peak occurred in the 1960’s for concrete gravity and concrete arch dams. There were no failures in gravity dams commissioned between 1930 and 1963. Based on the population data there appears to be a reduction in the failure rate with time. Buttress and multi-arch dams show some various peaks due to their limited populations. • Height No concrete or masonry dams greater than 70m are reported to have failed. Failures in masonry gravity dams appear to be concentrated below 50m in height. Concrete gravity dams tend to be spread out more. Accidents and more particularly major repairs are more evident in greater height concrete dams than masonry gravity dams. This however, is likely to be due to the lower height at which masonry dams are constructed. The ratio of failures to population does not exhibit any major trend. There appears to be a higher percentage of failures to population in the 40-49m and 60-69m height ranges. Arch, buttress and multi-arch dams are shown to be more likely to have failures in the 15-39m range. • Age at failure There is a large proportion of dams that have failed during first filling. An analysis of the water levels at failure show most dams failed at their highest recorded water level. Several of these were only slightly higher than that recorded previously. There appears to be a slight rise in the rate of failures with time (ignoring first filling). After 40 years of age there is a jump in the failure rate. It should be noted that the older age groups are Analysis of Concrete and Masonry Dam Incidents Page 2.173 represented by a small population. Concrete gravity dams of less than five years age appear to have a greater chance of failure compared to older concrete gravity dams. Masonry gravity dams are more evenly distributed throughout the ages. A noticeable problem with the accident/major repair data is its bias to the post 1920’s whereas failures occur much further back. This can be put down to a lack of detailed dam information in the period prior to 1920. Large dam failures would still have been published during these times. Piping tends to occur early in a dams life (<5 years, with one exception). Sliding of the foundation also tends to occur early but is not as restricted as piping. Structural problems seem to be more likely than foundation problems with age. Concrete dams have a tendency to fail at younger ages than masonry dams. Most older (masonry) dam failures have overtopping as a component. Unfortunately there is usually little information as to the actual mode of failure. • Incident causes Foundation problems (sliding, leakage and piping) are the main causes of failure to concrete dams, overtopping tends to play a bigger part in the failure of masonry dams. Accidents and major repairs are more likely to come about due to surficial damage to the dam structure or noticeable uplift or leakage in the foundation. Piping is the main cause of failure for dams with soil foundations. Overtopping and foundation shear strength are the main causes of failure for dams with rock or unknown foundations. • Warning types Overtopping was the most common failure warning type. This was mainly due to the masonry gravity dams which are more susceptible to overtopping failure. This could be due to the poorer quality downstream face of masonry dams which can be eroded during overtopping events and/or the higher permeability of masonry dams which results in a Analysis of Concrete and Masonry Dam Incidents Page 2.174 more rapid increase in uplift pressures. For accidents, and even more so for major repairs, the warning signs tend to be visual damage of the dam or excessive leakage. An analysis of all dam failures showed that, where information was available, most had some warning which could have resulted in the warning and evacuation of residents downstream. Often the warning was a sudden increase in the amount and rate of leakage. • Remedial measures Where a dam has failed it is usually abandoned or reconstructed with a new design. In the case of accidents and major repairs it is most common that the damaged section is replaced with no effect to the dam structure as a whole. • Geology Soils and limestones are more likely to have piping problems. The alluvial soils have a tendency to pipe under the high gradients imposed. No dam has been reported to have failed by sliding on alluvial soils. Normally a large concrete or masonry dam would not be built on a soil foundation. Shale (interbedded with other sedimentary units) has a greater tendency to be involved with sliding failure because of the likely presence of weaknesses in the bedding such as bedding surface shears. It is interesting that sandstone does not appear to be over represented when the population is taken into account. Failures tend not to occur in sandstone alone but only when the sandstone is interbedded with shale. Shale and limestone (often interbedded) have a high incidence for failing. The limestone has a high proportion of accidents generally due to excessive leakage through dissolution. Another point of note is that no incidents have occurred in basalt foundations. These conclusions agree with the general knowledge regarding the geology types (e.g. as described in Fell et al, 1992 11 ). Analysis of Concrete and Masonry Dam Incidents Page 2.175 • Other design factors The factors in Section 2.3.9 suffered from a lack of information. Generally these could only be obtained if a dam’s cross section was available. From the data collected it appears that the failed dams suffered from a lack of ‘good engineering’. Very few dams were found with galleries (1 dam); drainage (1 dam); grout curtains (4 dams);and shear keys (1 dam). The downstream slopes appeared to be too steep. Six gravity failures had downstream slopes of 0.6:1 (H:V) or less. Failed dams, particularly gravity dams, were usually located in relatively wide valleys or were composite sections with earthfill dams. Three dimensional effects are unlikely to have contributed any strength in these cases. h wf /W ratios ranged from 0.6 to 2.1 with an average of 1.35. Generally, unlike embankment dams, concrete and masonry dams are analysable and hence can readily be checked for stability. The major unknowns for these dams lie in the foundation where sliding and piping failures can occur. Section 2.4 gives a method for assessing the first order probability of failure of masonry or concrete gravity dams. The method accounts for dam age, year commissioned and type; failure mode; foundation geology; height to width ratio; and monitoring and surveillance. General probabilities of failure for arch, buttress and multi-arch dams, based on failure and population statistics, are included. The author cautions that this approach should only be used as a first order approximation of the annual probabilities of failure. It is clearly very approximate, and suffers from being based on small numbers of failures, and limited quality data. Where significant decisions on dam safety are being made, detailed deterministic and/or probabilistic methods should be used. The results from the analysis of CONGDATA are subject to the limitations mentioned earlier. Whilst all care has been taken in compiling data, it should be remembered that the information in CONGDATA has come from numerous sources, not all of which could be validated. The analysis of dams in CONGDATA does not take into account such things as: surveillance; quality of construction; and quality of geological Analysis of Concrete and Masonry Dam Incidents Page 2.176 description. It is therefore recommended that this work be used in a qualitative sense only. The Strength of Intact Rock Page 3.1 3 THE SHEAR STRENGTH OF INTACT ROCK 3.1 INTRODUCTION The application of the Hoek-Brown criterion (Hoek & Brown, 1980) to intact rock and rock masses is common in slope engineering, so it is important that it is validated in both applications, and that the uncertainty of its predictions are well understood. This chapter presents a detailed analysis of the application of the criterion to laboratory test data on intact rock and suggests modifications that provide improved predictions of triaxial strength based on easily measured material properties. The data consists of 4507 test results from 511 sets obtained from the literature and original laboratory test reports. The Strength of Intact Rock Page 3.2 3.2 FAILURE CRITERIA FOR INTACT ROCK Equation 3.1 presents a generalised criterion where a 1 , a 2 , etc are material properties. Figure 3.1 presents a generalised failure criterion in the σ′ 1 -σ′ 3 plane and shows the locations of the unconfined compressive strength, σ c , Brazillian strength, σ Bt , uniaxial tensile strength, σ ut and pure tensile strength,σ pt . ,....) , , , , ( fn 0 2 1 3 2 1 a a σ σ σ · (3.1) Sigma 3 / Sigma C S i g m a 1 / S i g m a C -1 0 1 2 3 -0.25 0.00 0.25 0.50 σ c σ pure t σ uniaxial t σ Brazillian t Figure 3.1. Generalised failure criterion There are two approaches to the selection of a failure criterion for intact rock, theoretical and empirical. The base of the most commonly adopted theoretical approaches are those of Coulomb: φ σ τ tan n c + · (3.2) or Griffith’s (1924) criterion for fracture initiation: ( ) ( ) 3 1 2 3 1 8 σ σ σ σ σ + − · − t (3.3) σ′ 3 /σ c σ′ 1 /σ c The Strength of Intact Rock Page 3.3 Most practical engineering relies on a linear Mohr’s envelope being fitted to experimental data or to the relevant portion of a theoretical or empirical criterion. Notwithstanding this it is becoming increasingly common for computer software to be able to deal directly with one or more non-linear criteria. Thus while the limits and pitfalls of linearisation are well understood, it is now important to assess the accuracy of non-linear criteria. It is well known that the theoretical criteria do not accurately predict the failure strength of rock and often rely on parameters that are difficult to measure (Ramamurthy et al, 1988, Andreev, 1995, Parry, 1995). Figure 3.2 by Johnston & Chiu (1984) shows that equations based on the work by Griffith provide poor fits to Melbourne mudstone. For these reasons many criteria have been developed that seek to capture the important elements of measured rock strengths or seek to modify theoretical approaches to accommodate experimental evidence, several of these empirical criteria are listed in Table 3.1. Most of these share a reasonably similar structure and all have elements that are likely to fail at the extremes. Figure 3.2. Comparison of test results with theoretically based failure criteria (Johnston & Chiu, 1984) The requirements of a good rock shear strength criterion are: that the criterion is a good predictor of strength at the stresses of interest (if not all confining stresses); that it is mathematically simple and preferably based on dimensionless parameters; and that it The Strength of Intact Rock Page 3.4 can also be used for rock mass (Hoek, 1983). Many of these criteria have been developed with high (underground) stresses and hard rocks in mind. As such many do not acurately predict shear strengths at low (or negative) stresses. For example, Mogi (1966) states Equation 3.6 “is applicable to the middle part of curves, but it deviates from observed values at an initial part and later ductile part of curves”. This is a problem where estimates of the strength of rock at low stresses (say slopes or dams) are required. Figure 3.3 shows that the Hoek-Brown shear strength criterion provides a poor fit to Melbourne mudstone. This is mainly due to the exponent being set at 0.5 in the Hoek- Brown equation. This is likely a direct result of the equation being created for hard rocks. Figure 3.3. Comparison of Hoek-Brown criterion (solid) and Johnston criterion (dashed) for Melbourne mudstone (Johnston, 1985) An inspection of Table 3.1 shows that equations (3.6), (3.9), (3.12), (3.14) and (3.15) do not algebraically reduce to the unconfined compressive strength, σ c , when the minor principal stress, σ′ 1 , is zero. Similarly, (3.6), (3.7), (3.9), (3.10), (3.14) and (3.15) fail to predict strengths in the tensile range (some completely and others at particular reasonably expected constant values) whilst (3.5) recommends a tensile cutoff due to it overestimating σ t . The Strength of Intact Rock Page 3.5 Equations (3.6), (3.7), (3.10) and (3.14) indicate ∞ → ′ ′ →0 3 1 3 σ σ σ d d which implies a friction angle of 90° at σ′ 3 = 0. Equation 3.8 represents straight line (Coulomb type) fits to lab data. As the rock strength envelope is known to be curved this equation could only be expected to predict the correct shear strengths over very narrow ranges. As is discussed elsewhere in this thesis, (3.4) is unsuitable for rock mass as it does not allow for a tensile strength of zero and hence can not be sensibly extended into the strength of rock mass or rockfill. The unconfined compressive strength, σ c , is widely used and is a useful index for rock strength. Only Equations (3.8), (3.10), (3.11) and (3.15) can be non-dimensionalised by σ c . This aids in the presentation and grouping of data with various unconfined compressive strengths. Table 3.2 shows the various exponents suggested (or obtained by regression) by the authors for their particular criterion. A power function of unity would imply a straight line (Coulomb). Smaller power functions will generally imply that the criterion has a higher curvature at very low stresses. Page 3.6 Table 3.1. Various intact rock failure criteria Reference Equation Constants Development UCS Tensile strength 3.4 Balmer (1952) Sheorey et al (1989) b t c , _ ¸ ¸ ′ + · ′ σ σ σ σ 3 1 1 b = 0.411 to 0.828 (ignoring samples controlled by defects orientated 15-75° to the load axis) Sheorey et al used tests on sandstone and shale plus literature. 23 sets in total of which 11 had no UCS recorded, 6 of which were also defect controlled. σ c -σ t 3.5 Fairhurst (1964) ( ) ( ) 3 1 2 3 1 σ σ σ σ ′ + ′ + · ′ − ′ B A 1 1 ] 1 ¸ − , _ ¸ ¸ − · 1 2 1 2 2 m A t σ ( ) 2 1 2 − · m B t σ 1 + · t c m σ σ Based on an empirical generalisation of Griffith allowing for all n = σ c /σ t possibilities. b b a t + 2 4 2 b b a t + 2 4 2 Note a tensile cut-off is recommended 3.6 Hobbs (1966) Mogi (1966) n c 3 3 1 σ α σ σ σ ′ + ′ + · ′ α - f(rock type) n – 0.38 to 0.73 (Mogi) Developed using triaxial tests on intact rock and literature results. σ c (n>0) undefined 3.7 Murrel (1965) Hobbs (1970) A c F 3 1 σ σ σ ′ + · ′ F, A Non-linear empirical adjustment to Coulomb. Hobbs (1970) found that his earlier equation (3.6) did not fit new test data. σ c (A>0) − ¸ ¸ _ , σ c A F 1 (undefined for most A) Page 3.7 Reference Equation Constants Development UCS Tensile strength 3.8 Bodonyi (1970) 3 1 σ σ σ ′ + · ′ a c or c c a σ σ σ σ 3 1 1 ′ + · ′ A Straight line fit to lab test data σ c −σ c a 3.9 Franklin (1971) ( ) b a 3 1 3 1 σ σ σ σ ′ + ′ + ′ · ′ a, b 0 Undefined Page 3.8 Reference Equation Constants Development UCS Tensile strength 3.10 Bieniawski (1974) Yudhbir et al (1983) α σ σ σ σ , _ ¸ ¸ ′ + · ′ c c k 3 1 1 412 triaxial samples used to determine constants: α ≈ 0.75 (Bieniawski) α ≈ 0.65 (Yudhbir et al) k - varies with rock type from 2 to 5(see Table 3.2. Empirical estimates of exponents for the equations in Table 3.1 Equation Parameter Exponent for rock 3.4 b 0.411 to 0.828 3.6 n 0.38 to 0.73 3.8 N/A 1 3.10 α 0.75 (Bieniawski, 1974) 0.65 (Yudhbir et al., 1983) 3.11 α 0.5 3.12 β 0.38 (tuff only) 3.13 B 0.5 – 0.81 (Johnston & Chiu, 1984) ( ) 2 log 0172 . 0 1 c σ − (Johnston, 1985) 3.14 α 0.8 Non-dimensional form of Murrell (1965). Note that k has become dependent on σ c as ( ) 1 − · A c F k σ σ c (α>0) α σ 1 1 , _ ¸ ¸ − k c (undefined for most α) Page 3.9 Reference Equation Constants Development UCS Tensile strength 3.11 Hoek & Brown (1980a) ( ) 2 1 2 3 3 1 c c i s m σ σ σ σ σ + ′ + ′ · ′ or 2 1 3 3 1 , _ ¸ ¸ + ′ + ′ · ′ s m c i c c σ σ σ σ σ σ m i – depends on rock type s = 1 Developed using curve fitting to extensive triaxial data on hard rock. s 0.5 σ c = σ c (s=1) 2 4 2 s m m i c c i + −σ σ 3.12 Adachi et al (1981) q p p p ′ · ′ ′ ¸ ¸ _ , 0 0 α β or ( ) β β σ σ α σ σ , _ ¸ ¸ ′ + ′ · ′ − ′ − 3 2 3 1 1 0 3 1 p q = (σ 1 -σ 3 ) p = (σ 1 +2σ 3 )/3 p o = 0.1MPa (unit stress) α,β = strength parameters tuff: α = 1.76 and β = 0.38. Based on triaxial test results plotted on a log-log graph. The equation is from Hobbs (1966). Porous tuff was used to represent soft rock. β β α − , _ ¸ ¸ 1 1 3 1 . 0 (MPa) 01 2 3 1 1 . − ¸ ¸ _ , ¸ ¸ _ , − α β β (MPa) 3.13 Johnston & Chiu (1984) Johnston (1985) B c c B M 1 ] 1 ¸ + ′ · ′ 1 3 1 σ σ σ σ M = f(rock type and σ c ) B = f(rock type) – 1984 see Table 3.4. ( ) 2 log 0172 . 0 1 c B σ − · (Johnston, 1985) Developed empirically for soft rocks after Hoek & Brown was shown to give a poor fit. σ c − B M c σ Page 3.10 Reference Equation Constants Development UCS Tensile strength 3.14 Ramamurthy et al (1985) Ramamurthy et al (1988) Rao et al (1988) α σ σ σ σ σ , _ ¸ ¸ ′ ′ + ′ · ′ 3 3 3 1 c B B - function of rock type/quality ≈ 1.8 to 3.54 α - slope of log-log curve of (σ′ 1 -σ′ 3 )/σ′ 3 and σ c /σ′ 3 ≈ 0.75 to 0.85 (0.8 usually taken) Modified Mohr-Coulomb to become non-linear. Empirical work done using testing on 4 sandstones plus 100 sets from literature. Extended for anisotropy and rock mass in 1988. 0 (α<1) Bσ c (α=1) Undefined (α>1) 0 (α<1) ( )α σ 1 B c − ( ) K 7 1 5 1 3 1 , , 1, · α else undefined 3.15 Yoshida et al (1990) b c c s a 1 3 3 1 , _ ¸ ¸ + ′ + ′ · ′ σ σ σ σ σ or b c c c s a 1 3 3 1 , _ ¸ ¸ + ′ + ′ · ′ σ σ σ σ σ σ a = 1.3 to 8.3 s = 0.01 to 0.78 b = 1 to 3.3 (tuff = 7.2) 1/b = 0.3 to 1 (tuff = 0.14) Proposed for geologic materials exhibiting time dependent softening e.g. soft rocks. Data came from 16 rock sets from the literature. aσ c s b The Strength of Intact Rock Page 3.11 Table 3.2. Empirical estimates of exponents for the equations in Table 3.1 Equation Parameter Exponent for rock 3.4 b 0.411 to 0.828 3.6 n 0.38 to 0.73 3.8 N/A 1 3.10 α 0.75 (Bieniawski, 1974) 0.65 (Yudhbir et al., 1983) 3.11 α 0.5 3.12 β 0.38 (tuff only) 3.13 B 0.5 – 0.81 (Johnston & Chiu, 1984) ( ) 2 log 0172 . 0 1 c σ − (Johnston, 1985) 3.14 α 0.8 3.15 1/b 0.3 – 1.0 (tuff = 0.14) Table 3.3. Suggested values of constant k (Yudhbir et al, 1983 and Bieniawsi, 1974) Rock Type k Norite, granite, quartzdiorite, chert 5 Quartzite, sandstone, dolerite 4 Siltstone, mudstone 3 Tuff, shale, limestone 2 Table 3.4. Values of M and B for a range of materials (Johnston, 1991) Material UCS (MPa) M B Soft clay 0.02 2.5 0.97 Stiff clay 0.2 3.5 0.91 Soft rock 2.0 5.1 0.81 Soft rock 20 7.2 0.68 Hard rock 100 9.0 0.57 Hard rock 200 9.8 0.52 The Strength of Intact Rock Page 3.12 Given the variability typical of rock test results it is likely that any one criteria is as suitable overall as any of the alternatives. The Hoek-Brown empirical failure criterion (Hoek & Brown, 1980) was developed in the early 1980s for intact rock and rock masses, it has been subject to continual refinement for rock masses. For intact rock its form has not changed and is given in Equation 3.16. 5 . 0 3 3 1 1 , _ ¸ ¸ + ′ + ′ · ′ c i c m σ σ σ σ σ (3.16) In common with most of the empirical failure criteria, the Hoek-Brown criterion is formulated in terms of σ′ 1 and σ′ 3 and is independent of σ′ 2 . The author does not consider this a major impediment for practical purposes. It is the author’s experience that the Hoek-Brown criterion forms the basis of virtually all the non-linear criteria now used by practising engineers. Further it forms the basis for the almost universal extension into rock mass strength. It thus has been adopted as the basis of examination for the rest of this Chapter. Further, for these reasons it is important to establish that the criterion does accurately represent actual intact rock behaviour. The Strength of Intact Rock Page 3.13 3.3 LABORATORY TEST DATABASE FOR INTACT ROCK A large database of test results has been assembled for a wide variety of rocks; tests include uniaxial tensile strength, Brazilian tensile strength, unconfined compressive strength and triaxial compression and tension. Many of the results were sourced from Sheorey (1997), Hoek and Brown (1980), Shah (1992) and Johnston (1985) and checked against original sources where possible. Further test information from other sources was obtained. Full details of the data are contained in the Appendix. At present, the data consists of 4507 test results forming 511 sets. In addition to the principal stresses, and to aid in the examination of the data, the information in Table 3.5, about the rock samples, was obtained where possible. The Strength of Intact Rock Page 3.14 Table 3.5. Intact rock database descriptors Database heading Description Set Set number (1-511) Test Test number within set D? "*" denotes σ′ 1 <4.4σ′ 3 – from Sheorey (1997) method of denoting ductile behaviour R G – good range of σ′ 3 ( c σ σ σ 3 . 0 min 3 max 3 ≥ ′ − ′ ); P – poor range σ′ 3 ( c σ σ σ 3 . 0 min 3 max 3 < ′ − ′ ) s3 Minimum principal stress, σ′ 3 (MPa) s1 Maximum principal stress, σ′ 1 (MPa) Name/location Specific rock name or location of source Rock type General geological group term m i98 Published Hoek et al (1998) m i value for the rock type orientation: BP/weak Orientation relative to bedding or planes of weakness (if any) moisture Sample moisture condition diam Sample diameter (mm) h/d Sample height to diameter ratio poros Porosity of sample (%) grain size Sample mean grain size (mm) B/T/D Comment on behaviour of sample under load based on an observation of the stress-strain curves, options were:.Brittle/Transitional/Ductile strain rate Test strain rate (%/second) comments Other comments on test, sample or test type Reference Quoted original reference for data Source Source of data for database:: - original - original reference used - SH_A.1. - Sheorey (1997) Table A1 - SH_A.2.- Sheorey (1997) Table A2 - Doruk - Doruk (1991) - Shah - Shah (1992) The Strength of Intact Rock Page 3.15 3.4 AN ANALYSIS OF THE ANALYSIS OF DATA When confronted with a set of data, there are a number of questions that have to be addressed: • What data should be included in the analysis? • What equation should be fitted? • What method of fitting should be adopted? It is of little value undertaking a comprehensive test program or detailed analysis of the results if the methodology is flawed. In fact, parameters determined can vary from very conservative to quite the opposite, both situations have consequences in analysis and design. Turning to the first question, the data included is that described in the previous section. It has been common practice for researchers fitting empirical failure criterion to intact rock to exclude results thought to exhibit ductile behaviour; this approach has been adopted by Hoek and Brown (1981), Shah (1992), Johnston (1985) and Sheorey (1997). In general these researchers have adopted the brittle-ductile transition suggested by Mogi (1966). The Equation is given by: 3 4 . 3 σ′ · C (3.17) There is some confusion in the literature regarding Equation 3.17. Sheorey (1997) has assumed C to be the difference in the maximum and minimum principal stresses (i.e. 3 1 σ σ ′ − ′ ) whilst the other authors have assumed C to be the maximum principal stress, 1 σ ′ . Mogi (1966) defined C as the ‘compressive strength’ but did not define it in relation to principal stresses. Mogi (1973) however, defines C as 3 1 σ σ ′ − ′ . Therefore it is assumed that the brittle-ductile transition, given by Mogi (1966), is: 3 3 1 4 . 3 σ σ σ ′ · ′ − ′ or 3 1 4 . 4 σ σ ′ · ′ (3.18) The Strength of Intact Rock Page 3.16 The exclusion of ductile data would be appropriate if (i) only brittle behaviour was of interest, (ii) the boundary was clear and (iii) the failure criterion was disjoint across the transition. In the case of a criterion based solely on Griffith’s theory, exclusion of ductile tests results would be appropriate. It is not necessary, is counter productive and is arbitrary, for an empirical criterion. Research (Evans et al., 1990, Mogi, 1966 and 1973, Scott & Nielsen, 1991, Rutter & Hadizadeh, 1991, Hoshino et al, 1972) shows that the transition is not well defined for all rocks, is often curved and certainly occurs over a wide range of stresses. Gustkiewicz (1985) found that “the value of [the brittle ductile transition] pressure cannot be seen distinctly on the curve of strength versus confining pressure”. Research by others (Evans et al., 1990) also showed that the failure envelope is not necessarily disjoint at the brittle-ductile transition. Thus an appropriate criterion can model strength on both sides of the transition. Triaxial tests with stresses around the brittle-ductile transition should be checked to ascertain that they actually reached their maximum stress. Often the triaxial apparatus (or sample) will not allow sufficient strain for this to happen and thus the result should be ignored. Sheorey (1997) only uses data points where σ′ 1 >4.4σ′ 3 and data sets where there are at least 5 data points. Doruk (1991) uses the following criteria to decide whether a data set is acceptable: • Each data set must have major and minor principal stresses at failure. • Only the results of effective or drained uniaxial and triaxial compression tests at room temperature are used. • Each data set must contain at least three triaxial test results. • Only results in the brittle range (defined as σ′ 1 ≥ 3.4σ′ 3 and σ′ 3 ≤ σ c ) were used. Doruk (1991) divides the data sets used into the following classes: The Strength of Intact Rock Page 3.17 • Class 1: ≥ 5 ‘well fitted’ data points with c σ σ σ 3 . 0 min 3 max 3 ≥ ′ − ′ • Class 2: ≥ 5 ‘scattered’ data points with c σ σ σ 3 . 0 min 3 max 3 ≥ ′ − ′ • Class 3: ≥ 5 ‘well fitted’ data points with c σ σ σ 3 . 0 min 3 max 3 < ′ − ′ • Class 4: < 5 ‘well fitted’ data points with c σ σ σ 3 . 0 min 3 max 3 ≥ ′ − ′ • Class 5: < 5 ‘scattered’ data points with c σ σ σ 3 . 0 min 3 max 3 ≥ ′ − ′ • Class 6: < 5 ‘well fitted’ data points with c σ σ σ 3 . 0 min 3 max 3 < ′ − ′ • Class 7: Data sets which contain ‘very scattered’ data points In the current work as many test results as possible have been included and only results for which there is true ductile behaviour (no ma ximum definable σ′ 1 or where there is significant doubt as to their accuracy) have been excluded. Columns in the rock strength database show the number of points and whether the data has a good range of σ 3 (i.e. c σ σ σ 3 . 0 min 3 max 3 ≥ ′ − ′ ) or a poor range of σ′ 3 (i.e. c σ σ σ 3 . 0 min 3 max 3 < ′ − ′ ). The effect of the number of tests in a data set is investigated in the analysis. There are several forms of the Hoek-Brown criterion that can be adopted for data analysis, these include Equation 3.16 and: ¹ ¹ ¹ ; ¹ − ≤ ′ ′ · ′ − > ′ , _ ¸ ¸ + ′ + ′ · ′ i c i c c i c m m m σ σ σ σ σ σ σ σ σ σ σ 3 3 1 3 5 . 0 3 3 1 for for 1 (3.19) ( ) 2 3 2 3 1 c c i m σ σ σ σ σ + ′ · ′ − ′ (3.20) ( ) ( ) 2 3 3 1 log 5 . 0 log c c i m σ σ σ σ σ + ′ · ′ − ′ (3.21) Equation 3.16 is strictly the Hoek-Brown criterion, but is undefined for σ′ 3 less than approximately -σ c /m i . Equation 3.19 ensures that the criterion is defined over the full range of σ′ 3 . Equations 3.20 and 3.21 are linearisations of the criterion. The impact of adopting these different forms is discussed at the end of this section. The Strength of Intact Rock Page 3.18 The method of least squares is very widely adopted in fitting models to data; there are often very sound statistical reasons to so do. Shah (1992) suggests that the simplex method with the function (observed-predicted) 2 is a better method than least squares. In fact, the method presented by Shah is least squares, the simplex is purely a numerical method to optimise some function, in this case minimising the sum of squared differences (ie errors). It has been verified that the resulting parameter estimates are the same as those from other robust least squares procedures. If the departure of the measured σ′ 1 from the predicted σ′ 1 (ie the error) is normally distributed with a variance that is independent of the predictor variables (here σ′ 3 ), then the predictions obtained with least squares, either with a simplex or otherwise, will be uniform minimum variance unbiased estimators; this is highly desirable. But consideration of data with multiple measurements of σ ut or σ Bt will indicate that straight least squares is not appropriate for fitting the Hoek-Brown criterion. Consider an experimental program with multiple measurements of σ ut , it is clear that if a failure criterion is to be fitted to the test data it is desirable that the estimated tensile strength should be the average of these measurements (ie the fitted curved should pass through the middle of the measured values). Equation 3.16 is not defined for measured values of σ ut less than the fitted value (ie larger tensile strengths) and this forces many fitting methods to fit the maximum measured (ie most negative) tensile strength as the estimated tensile strength. Equation 3.19 overcomes this problem, but reference to Figure 3.1 shows that the slope of the equation to the left of the estimated σ ut is much less than that to the right; the figure is drawn for an m i of 8 and the slope to the right is much steeper for higher m i . Given that a general least squares approach assesses the error as the observed σ′ 1 (ie zero) minus the predicted σ′ 1 , then data a given distance to the right of the estimated σ ut will have a much larger “error” than data the same distance to the left. Thus a standard least squares procedure will result in a very poor fit at low stresses and force a small σ ut and high m i , ie the opposite effect to adopting Equation 3.16. A resolution of the above problem comes about by recognising that in a uniaxial tensile strength test, the controlled variable is σ′ 1 and the measured variable is σ′ 3 , thus the real The Strength of Intact Rock Page 3.19 error is observed σ′ 3 minus the predicted σ′ 3 . But this error is scaled in σ′ 3 and needs to be adjusted if it is to have equal status with measurements in σ′ 1 . It is suggested that scaling by m i is a convenient and accurate approach. Given this it is recommended that a least squares procedure be used where the error is defined as: ( ) ( ) ¹ ; ¹ ′ − ≤ ′ × ′ − ′ ′ − > ′ ′ − ′ 3 1 3 3 3 1 1 1 3 for predicted measured 3 for predicted measured σ σ σ σ σ σ σ σ i m (3.22) This has been found to provide very good fits for a wide variety of data. It is the author’s experience that the method of parameter estimation can, and often does, have a large impact on parameters derived from experimental data but the effect is often camoflaged by the variability of test data. Table 3.6 and Figure 3.4 show the results of analysis of a simulated test program with results generated for a material with a Hoek-Brown failure criterion, σ c and m i are both normally distributed with mean/standard deviation of 10/2 MPa and 12/2 respectively. Results generated were 10 uniaxial tensile strength tests, 20 unconfined compressive strength tests, and 4 each triaxial strength tests at confining pressures of 1, 2, 5, 10, 20, 40 and 80 MPa. Thus there were 58 data points in all, simulating a very comprehensive test program from which it should be possible to determine accurate estimates of material properties. The entire generated data and selected fits are shown on Figure 3.4a. It can be seen that, with two exceptions, the methods provide a reasonable fit for the majority of the data. But reference to Figure 3.4b shows that most methods provide a very poor fit to the data at low stresses, that is over the stress range of interest in slope analysis. Page 3.20 Table 3.6. Results of different regression methods on artificial data Case Equation Fitting method Number σ c (MPa) m i r 2 (%) 1 Actual data 58 10.0 12.0 na 2 Normal equation 3.16 Least squares 58 14.9 7.75 97.88 3 Extended equation 3.19 Least squares 58 8.46 15.6 99.12 4 Extended equation 3.19 Modified least squares, Eqn 3.22 58 10.7 12.0 99.00 5 Adopting known σ c and normal equation 3.16 Least squares 58 na 5.21 91.69 6 Excluding σ t results and normal equation 3.16 Least squares 48 9.53 13.7 99.06 7 Excluding σ c & σ t results and normal equation 3.16 Least squares 28 6.20 21.4 98.80 8 Stress difference squared 3.20 Least squares 58 3.97 35.2 95.53 9 Stress difference squared and known σ c 3.20 Least squares 58 na 13.8 95.47 10 Stress difference squared 3.20 Least sum of absolute differences 58 9.18 15.4 95.45 11 Logarithms 3.21 Least squares 58 8.09 4.12 55.97 12 Logarithms and excluding σ t results 3.21 Least squares 48 9.67 12.2 95.00 The Strength of Intact Rock Page 3.21 Sigma 3 (MPa) S i g m a 1 ( M P a ) 0 50 100 150 200 250 -10 10 30 50 70 UCS mi Artificial data 10.012.0 Normal eqn & LS14.97.75 Extended eqn & LS 8.4615.5 Ext eqn & mod LS 10.712.0 Fix UCS & LS 10.05.21 Excl Sc or St & LS 6.1921.4 DS^2 & LS 3.9735.2 Log & LS 8.094.12 Not shown Excl St & LS 9.5213.7 DS^2 with UCS fixed 10.013.8 DS^2 & Least abs sum 9.1815.4 Log with excl St 9.6712.2 Sigma 3 (MPa) S i g m a 1 ( M P a ) 0 10 20 30 40 -2 0 2 4 6 UCS mi Artificial data 10.012.0 Normal eqn & LS14.97.75 Extended eqn & LS 8.4615.5 Ext eqn & mod LS 10.712.0 Fix UCS & LS 10.05.21 Excl Sc or St & LS 6.1921.4 DS^2 & LS 3.9735.2 Log & LS 8.094.12 Not shown Excl St & LS 9.5213.7 DS^2 with UCS fixed 10.013.8 DS^2 & Least abs sum 9.1815.4 Log with excl St 9.6712.2 Figure 3.4. Fits to artificial data (a) full range (b) low stress range UCS m i Artificial data 10.0 12.0 Normal eqn & least squares 14.9 7.75 Extended eqn & least squares 8.46 15.5 Extended eqn & modified least squares 10.7 12.0 Fixed UCS and least squares 10.0 5.21 Excluding σ c or σ t and least squares 6.2 21.4 (σ 1 - σ 3 ) 2 and least squares 3.97 35.2 Logarithm and least squares 8.09 4.12 UCS m i Artificial data 10.0 12.0 Normal eqn & least squares 14.9 7.75 Extended eqn & least squares 8.46 15.5 Extended eqn & modified least squares 10.7 12.0 Fixed UCS and least squares 10.0 5.21 Excluding σ c or σ t and least squares 6.2 21.4 (σ 1 - σ 3 ) 2 and least squares 3.97 35.2 Logarithm and least squares 8.09 4.12 The Strength of Intact Rock Page 3.22 The following comments are offered on the various analyses undertaken, listed in the same order as in Table 3.6. 1. The generated data, the author considers that this is a reasonable representation of a comprehensive test program in a moderately variable unit. 2. The strict application of least squares to Equation 3.16, ie the usual form of the Hoek-Brown criterion, results in the uppermost curve in Figure 3.4b. The criterion cannot be evaluated for σ′ 3 less than the estimated tensile strength. This results in large estimates of σ ut and σ c and thus a low m i . From 5 to 80 MPa the curve passes through the middle of the data. Below 1 MPa the estimated strength is nearly 50% higher than the true strength even though the regression r 2 is nearly 98%. This problem could be partially fixed by including only the average measured tensile strength in the analysis but this ignores considerable readily obtained and economic data and disguises the true variability. 3. Least squares applied to Equation 3.19 results in vastly improved parameter estimation but the lower slope to the left of the estimated σ ut produces a low estimate of σ ut and thus somewhat low estimated σ c and high estimated m i . A good fit overall with the highest r 2 , but approximately 15% underestimate of true strength for low σ 3 . 4. Modified least squares, Equation 3.22, applied to Equation 3.19 results in accurate estimation of the parameters and does so in almost all circumstances. The fact that r 2 is slightly less than for method 3 is a necessary consequence of the treatment of variability of the measured tensile strengths. 5. Least squares applied to Equation 3.16 with σ c fixed at the average of the test results. It might be thought that knowing one property should help with estimating a second unknown property, this is not the case here. The problem in 2 above is now magnified to produce almost the worst fit imaginable. It shows that an r 2 of over 90% can be obtained with a fit that bears only a passing relationship to the data. The Strength of Intact Rock Page 3.23 6. Least squares applied to either Equation 3.16 or 3.19, with the tensile strength test results excluded, results in a good fit. Again the problem is that good economic data is ignored and the fit at low stress will be more variable. 7. Least squares applied to either Equation 3.16 or 3.19 with both the tensile and unconfined compression test results excluded. In this case more than half the data is ignored and, in the present case, the fit at low σ′ 3 is more than 30% out. This is a random error and the fit could be low or high. The problem with this approach is that it is poorly controlled at the stresses of interest in slope analysis. 8. Least squares applied to Equation 3.20. This is a common form of fitting the Hoek-Brown criterion to data and estimating σ c and m i . This method virtually minimises “errors” to the fourth power, hence the lowish r 2 , and dramatically overweights the larger values of σ′ 1 . Errors in parameter estimates are not predictable, but in this example, estimated σ c and m i are 40% and 300% of the true values respectively, even though the corrupted r 2 is over 95%. Over most of the range of the test results it is a very good fit but not over that portion of interest in slope design. It is not recommended. 9. As for 8 above but with σ c fixed at the mean value, in contrast to 5 above this results in a good fit across the range but relies on a good estimate of σ c and increased faith that this accurately represents triaxial behaviour. 10. Least sum of absolute differences applied to Equation 3.20. This in large measure compensates for the overweighting of large σ′ 1 values of method 8. The resulting estimates are good. 11. Least squares applied to Equation 3.21, again a common form of fitting the Hoek-Brown criterion. As for Equation 3.16 this equation is not defined for σ′ 3 less than σ pt . This method has major problems fitting any data which includes a moderate spread of tensile testing. The Strength of Intact Rock Page 3.24 12. Least squares applied to Equation 3.21 with the tensile strength test results excluded. A robust method weighted to low stress results and good for slope analysis but unable to take advantage of economic and readily available data. From Table 3.6 it can be seen that r 2 is not a useful indicator of accuracy of estimates of the parameters and that these estimates can vary widely depending on the method of analysis. Methods with r 2 in excess of 95% and that model the data very well over most of the range have estimates of σ c varying from 3.97 to 14.9 MPa and m i from 7.75 to 35.2 and this is for artificial data that follows exactly the criterion with only test variability. Thus many of these methods are very poor estimators of strength in the low stress region that is of interest in slope analysis. The Strength of Intact Rock Page 3.25 3.5 HOEK-BROWN CRITERION FOR INTACT ROCK Modified least squares, Equation 3.22, was combined with the extended formulation of the Hoek-Brown criterion, Equation 3.19, to estimate σ c and m i for all test data in the database. Discussion in the previous section indicates that the fit is poorly controlled at low stresses for sets with little data, particularly σ c and σ t . Small changes in the data can lead to wildly varying estimates of both σ c and m i , in general with σ c becoming very small and m i very high but with the fit being almost identical over the range of the test results. In fact for many data sets σ c and m i are not independent but σ c →0 as m i →∞. The best solution to this issue is to place plausibility limits on the parameters. A number of limits were considered and the following ones adopted: • As all the test results were taken from materials described as rock, σ c was limited to be not less than 1 MPa. • Published values of m i fall in the range of 4 to 33 (Hoek & Brown, 1998). As will be discussed later m i is very closely related to the ratio -σ c /σ ut , reference to the figures in Lade (1993) indicates that this ratio varies from less than 2 to over 50. This limits m i to the range 1 to 50. Further m i is related to the angle of friction at σ′ 3 =0 (ie φ 0 ), which is of great interest in slope analysis. It was considered that φ 0 should be limited to the range of 15 to 65°, which for the Hoek-Brown criterion further limits m i to the range 1.4 to 40. The process was completed for 475 data sets involving 3779 test results. The results of the analysis are provided in Figure 3.5 to Figure 3.8. Figure 3.5 shows a “box and whisker” plot of the values of m i estimated from the data, m itest , against the values of m i provided in Hoek & Brown (1998) and Hoek et al (1995), m ipub . Several such figures are presented in this chapter, the whiskers show the range of test results, the box shows the upper and lower quartiles and the bar the median value. Also shown on this figure is a linear regression between published m ipub and m itest weighted for the number of data points supporting each estimate. The regression equation is: ipub itest m m 441 . 0 58 . 7 + · (3.23) The Strength of Intact Rock Page 3.26 This is a very poor relation, r 2 =16.4%, between m i determined on the basis of actual testing and that obtained from the literature. Page 3.27 m i from literature, m ipub m i f r o m f i t t i n g H B e q u a t i o n , m i t e s t 0 10 20 30 40 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Figure 3.5. m i from literature against m i from test results and Hoek-Brown Equation The Strength of Intact Rock Page 3.28 Figure 3.6 presents m itest against rock type ordered in increasing m ipub , it can be seen that it is difficult to ascribe a single or even small range to m i on the basis of rock type. It should be remembered that 50% of the test data falls outside the range indicated by the box for each rock type, thus for example 50% of the values for sandstone fall below 11 or above 19, and for granite below 19 or above 31. Page 3.29 m i t e s t 0 10 20 30 40 C l a y s t o n F i r e c l a y G r e e n s t o M u d s t o n e S e r p e n t i S c h i s t S h a l e C h a l k C h l o r i t i L i m e s t o n M a r b l e S i l t s t o n S l a t e B i o c a l c a D o l o m i t e A n h y d r i t S a l t C o a l T u f f P y r o c l a s R h y o l i t e A p l i t e B a s a l t L a m p r o p h T r a c h i t e A g g t u f f G r e y w a c k W h i n s t o n A n d e s i t e D i a b a s e D o l e r i t e Q u a r t z d o S a n d s t o n G r a n i t e 1 N o r i t e Q u a r t z i t D u n i t e E c l o g i t e G a b b r o P e r i d o t i A m p h i b o l D i o r i t e Q u a r t z d i G r a n o d i o G n e i s s G r a n i t e Figure 3.6. Rock type against m i from test results and Hoek-Brown equation The Strength of Intact Rock Page 3.30 Figure 3.7 presents the σ c determined from fitting the Hoek-Brown equation against the σ c determined from σ c testing or, at least, as reported in the literature from which the data was obtained. Several figures in this chapter are presented in this style. The upper and lower dashed lines represent 1.5 and 0.67 times the reported σ c values. Further, the symbols represent the number of test results used to determine the fit, a small cross is 4 or less data points, a small circle is 7 or less, large circle is 12 or less and a square is more than 12 data points. It can be seen that virtually all the data lies in a very narrow band, such that the fitted σ c is quite close to the reported σ c . Figure 3.8 is a similar presentation to Figure 3.7 except that it presents fitted tensile strength versus reported tensile strength. It can be seen that the fitting method adopted provides a very good estimate of σ t for those data sets which do have reported tensile strengths. Most of the other methods fail for such data, so much so that often practitioners are forced to ignore the valuable information available from inexpensive tensile testing. This is particularly a problem as such data forms a good control on the failure envelope over the low stress range (Lade, 1993). In summary the proposed method results in good fits of the Hoek-Brown criterion to the data and, in particular, results in good fits in the low stress region. It appears that published values of the parameter m i might be quite misleading as m i does not appear to be related to rock type. Page 3.31 Unconfined compressive strength (MPa) U C S f r o m H B e q u a t i o n ( M P a ) 1 4 7 10 40 70 100 400 700 1000 1 4 7 10 40 70 100 400 7001000 Figure 3.7. Unconfined compressive strength against that predicted by the Hoek-Brown equation Page 3.32 Tensile strength (MPa) T e n s i l e s t r e n g t h f r o m H B e q u a t i o n ( M P a ) 0.1 0.4 0.7 1.0 4.0 7.0 10.0 40.0 70.0 100.0 0.1 0.4 0.7 1.0 4.0 7.0 10.0 40.0 70.0 100.0 Figure 3.8. Uniaxial tensile strength against that predicted by the Hoek-Brown equation The Strength of Intact Rock Page 3.33 3.6 GENERALISED CRITERION FOR INTACT ROCK There are a number of concerns regarding the formulation of the Hoek-Brown criterion: • Several authors, including Johnston (1985), note that soil, soft rock, and brittle rock form a continuum and thus a failure criterion should be able to accommodate the linear or near linear behaviour observed in soils and soft rocks. Fixing the exponent at a half means that at best the criterion is a poor model of soft rocks. This is not surprising as it was developed for brittle rocks but it is a limitation which is often overlooked by practitioners who apply it to all rocks. Further it is a severe limitation on the extension of the criterion to rock mass strength. • Lade (1993) in comparing the theories and the evidence regarding rock strength criteria finds that an appropriate criterion should have three independent characteristics – the opening angle, the curvature and the tensile strength. The fixed exponent on the Hoek-Brown criterion limits it to modelling only two of these characteristics. In fact as often used, m i is varied to model the curvature over the stress range of the test results and neither the opening angle nor the tensile strength are modelled. Lade also states that it may be an advantage to include the tensile strength in determination of material parameters as it stabilises the fit at low stresses. This is particularly important for slope analysis. If the exponent, α, is allowed to vary the Hoek-Brown criterion can model widely varying curvatures and opening angles. It is also able to include an accurate representation of the tensile strength. This “generalised” Hoek-Brown criterion for intact rock has been applied to the full data set. As would be expected, adding an extra parameter or property always improves the fit but has many other benefits as well. The equation becomes: ¹ ¹ ¹ ; ¹ − ≤ ′ ′ · ′ − > ′ , _ ¸ ¸ + ′ + ′ · ′ i c i c c i c m m m σ σ σ σ σ σ σ σ σ σ σ α 3 3 1 3 3 3 1 for for 1 (3.24) The Strength of Intact Rock Page 3.34 The modified least squares, Equation 3.22, is adopted. The limits, given above for fitting the Hoek-Brown criterion, are also placed on the parameters. For the generalised criterion these become, σ c >1, m i in the range 1 to 50, and α m i in the range 0.7 to 20 (this is the equivalent limit on φ 0 ). In addition, α is limited to the range 0.2 to 1. Allowing α to vary provides the ability to obtain a much better fit over the low stress range which is of greatest interest in slope analysis. The results of the analysis are presented in a series of figures. Figure 3.9 presents a box and whisker plot of m i determined from the data against the published values of m i . Again it can be seen that there is little relationship between the two. Likewise, there was found to be no relationship between m i and rock type. Page 3.35 m i from literature m i f r o m f i t t i n g e q u a t i o n 0 10 20 30 40 50 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Figure 3.9. m i from literature against m i from test results and generalised equation The Strength of Intact Rock Page 3.36 The slope of the generalised criterion at σ′ 3 =0 is 1+α m i , and is related to φ 0 by: ( ) ( ) ( ) 45 1 atan 2 5 . 0 0 − + · i m α φ (3.25) If a classification of samples, say by m i or rock type, is predictive of the triaxial envelope at low stresses then it will be apparent on a plot of that classification against α m i . Figure 3.10 and Figure 3.11 present plots of α m i against published m i and rock type respectively. From Figure 3.10 it can be seen that published m i is not a good predictor of the triaxial envelope at low stress. Examination of Figure 3.11 shows that there is a weak correlation of rock type with α m i in that fine grained rocks tend to have the lowest values, medium to coarse grained higher and rocks with tightly interlocked crystals the highest. It is not believed that the relationship is strong enough to be used predictively. Page 3.37 m i from literature a l p h a * m i f r o m f i t t i n g e q u a t i o n 0 5 10 15 20 25 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Figure 3.10. m i from literature against α m i from test results and generalised equation Page 3.38 A l p h a * m i 0 5 10 15 20 C l a y s t o n F i r e c l a y G r e e n s t o M u d s t o n e S e r p e n t i S c h i s t S h a l e C h a l k C h l o r i t i L i m e s t o n M a r b l e S i l t s t o n S l a t e B i o c a l c a D o l o m i t e A n h y d r i t S a l t C o a l T u f f P y r o c l a s R h y o l i t e A p l i t e B a s a l t L a m p r o p h T r a c h i t e A g g t u f f G r e y w a c k W h i n s t o n A n d e s i t e D i a b a s e D o l e r i t e Q u a r t z d o S a n d s t o n G r a n i t e 1 N o r i t e Q u a r t z i t D u n i t e E c l o g i t e G a b b r o P e r i d o t i A m p h i b o l D i o r i t e Q u a r t z d i G r a n o d i o G n e i s s G r a n i t e Figure 3.11. Rock type against α m i from test results and generalised equation The Strength of Intact Rock Page 3.39 Figure 3.12 presents the σ c obtained from fitting the generalised equation against the reported σ c . It can be seen that virtually all the data lies in a very narrow band, such that the fitted σ c is quite close to the reported σ c . As would be expected the overall correlation is better than that shown on Figure 3.7. Page 3.40 Unconfined compressive strength (MPa) U C S f r o m f i t t i n g e q u a t i o n ( M P a ) 1 4 7 10 40 70 100 400 700 1000 1 4 7 10 40 70 100 400 7001000 Figure 3.12. Unconfined compressive strength against that predicted by generalised equation The Strength of Intact Rock Page 3.41 Figure 3.13 presents the fitted tensile strength versus reported tensile strength. It can be shown that the uniaxial tensile strength σ ut is bound as: ( ) 1 + − ≤ < − i c ut i c m m σ σ σ (3.26) Page 3.42 Tensile strength (MPa) T e n s i l e s t r e n g t h f r o m H B e q u a t i o n ( M P a ) 0.1 0.4 0.7 1.0 4.0 7.0 10.0 40.0 70.0 100.0 0.1 0.4 0.7 1.0 4.0 7.0 10.0 40.0 70.0 100.0 Figure 3.13. Uniaxial tensile strength against that predicted by generalised equation The Strength of Intact Rock Page 3.43 Table 3.7 presents the errors involved in adopting –σ c /(m i +1) as σ t . For simplicity the lower bound has been adopted in plotting Figure 3.8 and Figure 3.13, the error in doing this is quite small. It should be noted that it is likely that many of the reported σ t are likely to be Brazilian tensile strengths. Table 3.7. Error in approximating σ ut as -σ c /(m i +1) α m i Error (%) 1 All 0 0.8 All <7.6 0.5 1 19 0.5 >8 <10 0.4 1 23 0.4 >9 <10 The fit in Figure 3.13 is extremely good. Figure 3.12 and Figure 3.13 provide considerable confidence that the fitted curves provide a very good model of triaxial strength at low stresses. In both cases the unexplained variance of the generalised fits is about half that of the Hoek-Brown fits. Figure 3.14 presents a plot of α against m i as determined for each data set from the generalised criterion. Also shown on the figure are hyperbolae showing lines of constant α m i , ie φ 0 , for 15° to 65°. Inspection of the figure shows that the constraints on m i , α and α m i did not often limit the regression procedure. Page 3.44 mi A l p h a 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 10 20 30 40 50 φ 0 15 25 35 45 55 65 φ 0 Figure 3.14. α against m i The Strength of Intact Rock Page 3.45 An interesting and useful observation from Figure 3.14 is that there appears to be a relationship between α and m i . Such a relationship is derived in the next section and is shown on Figure 3.14. It is often thought that the curvature of the strength envelope, ie α against m i in the current context, should be greater for strong rocks than weak rocks. The data set and analysis do not support this contention. Figure 3.15 shows the relationship between α and m i plotted for the data divided into four categories depending on the σ c . It can be seen that the relationship is independent of strength. High strength rocks can have linear flat failure envelopes and low strength rocks can have steep curved envelopes. Thus σ c is a truly independent parameter in a rock failure criterion. Page 3.46 mi a l p h a UCS<= 40 0.0 0.5 1.0 0 20 40 40<UCS<=100 0 20 40 100<UCS<=200 0.0 0.5 1.0 0 20 40 200<UCS 0 20 40 Figure 3.15. α against m i categorised by σ c The Strength of Intact Rock Page 3.47 A consequence of allowing α to vary at all, is that a failure envelope with a high φ 0 can have a low φ at high stresses and thus failure envelopes for different rocks normalised on σ c , can cross at high stresses. This cannot happen with α fixed at 0.5 in which case all envelopes cross only once at σ c . Figure 3.16 shows a family of curves, normalised by σ c , for various m i and the α typical of the relationship shown on Figure 3.14. It can be seen that the m i equals 40 curve crosses the m i equal 10 and 3 curves at 1.4 and 2.5 times σ c respectively. This implies that high frictional strength at low stresses is often associated with low frictional strength at higher stresses. Figure 3.17 shows some examples of test data that illustrate this point. Sigma 3 / Sigma C S i g m a 1 / S i g m a C -2 0 2 4 6 8 10 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 mi 40 10 3 1 Figure 3.16. Family of failure envelopes Page 3.48 Sigma 3 / Sigma C S i g m a 1 / S i g m a C 0 2 4 6 8 10 12 14 16 18 20 -1 0 1 2 3 4 5 Set 382 Sandstone Set 305 Granite Set 425 Gabbro Figure 3.17. Results showing failure envelopes crossing The Strength of Intact Rock Page 3.49 A relationship between α and m i implies that the triaxial failure envelope can be estimated from σ c and either m i or σ t , with α being determined by the relationship. Thus there are no more parameters to be determined than for the usual Hoek-Brown criterion. The parameters can be based on simple testing and provide a more accurate prediction of strength than published m i values, particularly in the low stress region typical of slopes. The Strength of Intact Rock Page 3.50 3.7 GLOBAL PREDICTION A single equation could be fitted to the entire database on the following assumptions: • The value of σ c obtained from fitting the generalised Hoek-Brown criterion is the best estimate of σ c for each data set. • A reasonable estimate of |σ t | is obtained for each data set by dividing σ c by the value of m i obtained by fitting the generalised Hoek-Brown criterion. Figure 3.12 and Figure 3.13 show that the above assumptions are quite reasonable for those cases where there is data to confirm them. On this basis m i can be set to –σ c /σ t and Equations 3.19 and 3.24 can be rewritten as: α σ σ σ σ σ σ , _ ¸ ¸ ′ − + ′ · ′ t c c 3 3 1 1 (3.27) , _ ¸ ¸ , _ ¸ ¸ , _ ¸ ¸ , _ ¸ ¸ − + + , _ ¸ ¸ ′ − + ′ · ′ c m b a t c c t c σ σ σ σ σ σ σ σ 0 exp 1 3 3 1 1 (3.28) Equation 3.27 is equivalent to the Hoek-Brown criterion but with an exponent not necessarily equal to 0.5. Equation 3.28 is equivalent to the generalised Hoek-Brown criterion. The exponent of Equation 3.28 is a general function that varies from a to b with a midpoint at –m 0 and a variable length of step. These equations can be fitted to the entire data set using Equation 3.22. Two of the data sets produced extremely large residuals and were ignored in reanalysis. Fitting Equation 3.27, ie a constant exponent, resulted in α being estimated as 0.439 and an r 2 of 83.5%. This is a reasonable fit when the range of rocks to which it applies is considered. Examination of the residuals reveals that a better fit will be possible as the residual is a function of m i . This is illustrated on Figure 3.18, for m i <10 the residuals are positive and increase with σ′ 1 . The residuals gradually reduce until for m i greater than 40 they are predominantly negative. This is strong evidence that α is not constant. Page 3.51 Sigma 1 / Sigma c R e s i d u a l f o r g l o b a l r e g r e s s i o n w i t h c o n s t a n t a l p h a <= 5 -10 -5 0 5 10 0 5 10 15 20 (5,10] 0 5 10 15 20 (10,20] 0 5 10 15 20 (20,30] -10 -5 0 5 10 0 5 10 15 20 (30,40] 0 5 10 15 20 > 40 0 5 10 15 20 Number under graph is estimated ratio of -Sigma c / Sigma t Figure 3.18. Residuals for global fit with α constant against σ′ 3 /σ c categorised by -σ c /σ t The Strength of Intact Rock Page 3.52 Fitting Equation 3.28 resulted in the following estimate for the exponent: ( ) ( ) 455 . 7 exp 1 08585 . 1 4032 . 0 i m + + · α (3.29) This equation is shown on Figure 3.14 and models the results of the analysis of the individual data sets very well. This analysis resulted in an r 2 of 94.8%, which is extremely good for such a global fit. The residuals are plotted on Figure 3.19, there is no or little trend with m i or σ 1 and it can be seen that this is a much better fit than Equation 3.27 and Figure 3.18. Page 3.53 Sigma 1 / Sigma c R e s i d u a l f o r g l o b a l r e g r e s s i o n w i t h v a r i a b l e a l p h a <= 5 -10 -5 0 5 10 0 5 10 15 20 (5,10] 0 5 10 15 20 (10,20] 0 5 10 15 20 (20,30] -10 -5 0 5 10 0 5 10 15 20 (30,40] 0 5 10 15 20 > 40 0 5 10 15 20 Number under graph is estimated ratio of -Sigma c / Sigma t Figure 3.19. Residuals for global fit with variable α against σ′ 3 /σ c categorised by -σ c /σ t The Strength of Intact Rock Page 3.54 Figure 3.20 shows a three dimensional plot of the failure criterion described by Equations 3.28 and 3.29, ie σ′ 1 as a function of σ′ 3 and m i (ie –σ c /σ t ). It can be seen that for m i <8 the failure envelope is close to linear and then becomes more curved. The ridge at m i equals 8 is well supported in the data and may reflect “more” or “less” than Griffith behaviour. Page 3.55 Figure 3.20. Three dimensional plot of global fit The Strength of Intact Rock Page 3.56 Figure 3.21 and Figure 3.22 show slices through the model for high and low stress ranges respectively with the equation for the midrange of each slice also shown. Thus the upper left subgraph on Figure 3.21 presents all the σ 1 versus σ 3 data, normalised by σ c , for sets with σ c /|σ t |<=5 together with the equation for σ c /|σ t |=3. Figure 3.21 provides the data for σ′ 3 up to three times σ c and Figure 3.22 for σ′ 3 to half of σ c . It can be seen that the fits are very good. The ridge at high stress and m i =8 are apparent on Figure 3.21 with uniform behaviour at low stress seen on Figure 3.22. Page 3.57 Sigma 3 / Sigma c S i g m a 1 / S i g m a c <= 5 0 5 10 15 0 1 2 3 (5,10] 0 1 2 3 (10,20] 0 1 2 3 (20,30] 0 5 10 15 0 1 2 3 (30,40] 0 1 2 3 > 40 0 1 2 3 Number under graph is estimated ratio of -Sigma c / Sigma t Figure 3.21. σ′ 1 /σ c with fits for variable α against σ′ 3 /σ c categorised by -σ c /σ t for high stress Page 3.58 Sigma 3 / Sigma c S i g m a 1 / S i g m a c <= 5 0 1 2 3 4 5 0.0 0.1 0.2 0.3 0.4 0.5 (5,10] 0.0 0.1 0.2 0.3 0.4 0.5 (10,20] 0.0 0.1 0.2 0.3 0.4 0.5 (20,30] 0 1 2 3 4 5 0.0 0.1 0.2 0.3 0.4 0.5 (30,40] 0.0 0.1 0.2 0.3 0.4 0.5 > 40 0.0 0.1 0.2 0.3 0.4 0.5 Number under graph is estimated ratio of -Sigma c / Sigma t Figure 3.22. σ′ 1 /σ c with fits for variable α against σ′ 3 /σ c categorised by -σ c /σ t for low stress The Strength of Intact Rock Page 3.59 Figure 3.23 presents α against m i including Equation 3.29 and showing those data for which there is actual, not estimated, values for both σ c and σ t . It can be seen that these sets are distributed similarly to those for which at least one of these parameters has been estimated by fitting the generalised Hoek-Brown criterion. Page 3.60 mi A l p h a 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 10 20 30 40 50 Data with compressive and tensile strengths Other data Figure 3.23. α against m i showing cases with measured or reported σ′ 3 and σ t The Strength of Intact Rock Page 3.61 3.8 COMPARISON OF CRITERIA A comparison of the various criterion as fitted to the database is provided in Table 3.8. The variance explained approximates r 2 . As would be expected, the generalised Hoek- Brown criterion provides by far the best fit, r 2 of 99.5%, as it has three parameters and is fitted to the individual data sets. None the less, the fit obtained is considerably better than the fit obtained by the Hoek-Brown criterion (ie with α fixed at 0.5) , r 2 of 98.9%. The unexplained variance for the generalised criterion is less than half that of the Hoek- Brown criterion with α of 0.5. Table 3.8. Comparison of predictions Variable/prediction Variance Variance explained σ′ 1 /σ c 16.93 0 Global regression with α constant 2.78 83.6 Hoek-Brown with published m i 2.00 88.2 Global regression with α variable 0.846 95.0 Hoek-Brown fitted to individual sets 0.186 98.9 Generalised Hoek-Brown fitted to individual sets 0.077 99.5 The above methods compare different ways of fitting triaxial data, ie different criteria applied to actual triaxial data. Table 3.8 also allows a comparison of three methods of prediction of triaxial strength that are not based on having actual data but are based on parameters estimated in some other manner. The methods are discussed in the following points: • Prediction based on global equation with variable α. This method is based on Equations 3.28 and 3.29 and estimates of σ c and σ t . It has an r 2 of 95.0% when used to predict the test results in the database. The accuracy of the predictions are illustrated on Figure 3.21 and Figure 3.22. • Prediction based on global equation with constant α. This method, based on Equation 3.27, is the least accurate of the three and is not discussed further. The Strength of Intact Rock Page 3.62 • Prediction based on published values of m i . This method is based on Equation 3.19 with values of m i estimated from those widely published in the literature. The method has an r 2 of 88.2% when used to predict the test results in the database. On average this method predicts the strengths well but with considerably more scatter than that from the global equation. Figure 3.24 and Figure 3.25 present the data categorised by published m i , these figures are in a similar form and can be compared to Figure 3.21 and Figure 3.22. It is clear from the figures that at low published m i the triaxial strength is under predicted and at high published m i it is over predicted. In effect what this means is that triaxial strength is poorly predicted by published m i values and the method is predicting the average strength for all tests. Page 3.63 Sigma 3 / Sigma c S i g m a 1 / S i g m a c <= 7 0 5 10 15 0 1 2 3 (7,9] 0 1 2 3 (9,18] 0 1 2 3 (18,19] 0 5 10 15 0 1 2 3 (19,24] 0 1 2 3 > 24 0 1 2 3 Categorised by published values of mi Figure 3.24. σ′ 1 /σ c with fits for published m I against σ′ 3 /σ c categorised by m I for high stress Page 3.64 Sigma 3 / Sigma c S i g m a 1 / S i g m a c <= 7 0 1 2 3 4 5 0.0 0.1 0.2 0.3 0.4 0.5 (7,9] 0.0 0.1 0.2 0.3 0.4 0.5 (9,18] 0.0 0.1 0.2 0.3 0.4 0.5 (18,19] 0 1 2 3 4 5 0.0 0.1 0.2 0.3 0.4 0.5 (19,24] 0.0 0.1 0.2 0.3 0.4 0.5 > 24 0.0 0.1 0.2 0.3 0.4 0.5 Categorised by published values of mi Figure 3.25. σ′ 1 /σ c with fits for published m I against σ′ 3 /σ c categorised by m I for low stress The Strength of Intact Rock Page 3.65 3.9 SYSTEMATIC ERROR IN HOEK-BROWN CRITERION If α for a particular rock is not equal to 0.5 then there is a systematic error in fitting the Hoek-Brown criterion to any triaxial test results obtained on that rock. The error is illustrated on Figure 3.26, two data sets are shown, the upper one is for σ c , m i and α of 30 MPa, 24 and 0.4 respectively and the lower one for 8 MPa, 5 and 0.8. The different σ c were chosen to separate the curves, and the m i and α are typical combinations determined in the analysis of the entire database. The solid lines represent the Hoek- Brown fits to these data. The residuals are shown on the bottom graph, if α is less than 0.5 then there are negative residuals at both the low and high end of the range of σ′ 3 tested with positive residuals in the middle range. The sign of the residuals is reversed if α is greater than 0.5. While the fits in the upper graph might look satisfactory for engineering purposes, the errors in estimates of σ c and m i can be significant. Table 3.9 shows the parameters estimated from fitting the Hoek-Brown criterion to these data, it can be seen that errors in the estimates vary from one half to five times the correct values. Thus the parameters of this model cannot be considered material properties. These errors are discussed in more detail below. Sigma 3 (MPa) S i g m a 1 ( M P a ) 0 20 40 60 80 100 120 140 160 0 5 10 15 20 25 30 35 R e s i d u a l ( M P a ) -20 -10 0 10 20 0 5 10 15 20 25 30 35 Figure 3.26. Pattern of residuals for Hoek-Brown fits The Strength of Intact Rock Page 3.66 Table 3.9. Errors in fitting Hoek-Brown criterion to materials with α ≠ 0.5 Actual parameters Material σ c m i α r 2 (%) Upper 30.0 24.0 0.4 100.0 Lower 8.0 5.0 0.8 100.0 Parameters determined by fitting Hoek-Brown criterion Material Estimated σ c Estimated m i r 2 (%) Upper 33.0 11.7 99.65 Lower 3.94 48.5 97.47 Consider programs of triaxial testing on rocks with σ c equal to 3 MPa, and m i and α of (a) 40 and 0.4 and (b) 4 and 0.8. Both are weak rocks and their triaxial strength could be of interest in design of a large rock slope. Further consider that different test programs are undertaken in which the maximum σ′ 3 is determined by the capacity of the triaxial apparatus. The following test programs could result: • Program A - 12 stages to a maximum σ′ 3 of 10 MPa, • Program B - 10 stages to 5 MPa (ie omitting the last two stages), • Program C - 8 stages to 3 MPa, • Program D - 6 stages to 1.5 MPa, and • Program E - 4 stages, including UCS, to 0.7 MPa. If there was no variability in the test apparatus or material, and measurement was perfect, the test results would be as shown on Figure 3.27, that is there is no sample or test error. Quite different envelopes result if the Hoek-Brown criterion is fitted to these test programs. The estimated σ c and m i are given in Table 3.10. Estimated σ c varies from 1.66 to 4.20 MPa and m i from 8.0 to 29.6 with very high r 2 . The Strength of Intact Rock Page 3.67 Table 3.10. Variation of σ c and m i with σ 3max for exact simulated results Material (a) σ c = 3 MPa, m i = 40 and α = 0.4 Program σ′ 3max (MPa) Stages Estimated σ c Estimated m i r 2 (%) A 10 12 4.20 11.5 99.43 B 5 10 3.77 14.2 99.41 C 3 8 3.47 16.9 99.38 D 1.5 6 3.22 20.3 99.52 E 0.7 4 3.07 23.4 99.74 Material (b) σ c = 3 MPa, m i = 4 and α = 0.8 Program σ′ 3max (MPa) Stages Estimated σ c Estimated m i r 2 (%) A 10 12 1.66 29.6 97.96 B 5 10 2.23 17.5 98.65 C 3 8 2.59 12.6 98.96 D 1.5 6 2.85 9.60 99.46 E 0.7 4 2.96 8.01 99.85 Page 3.68 Sigma 3 S i g m a 1 0 5 10 15 20 25 30 35 40 -2 0 2 4 6 8 10 12 Artificial data for sc=3 MPa, mi=40 and alpha=0.4 Sigma 3 S i g m a 1 0 5 10 15 20 25 30 35 40 -2 0 2 4 6 8 10 12 Artificial data for sc=3 MPa, mi=4 and alpha=0.8 Figure 3.27. Hoek-Brown fits to artificial data The Strength of Intact Rock Page 3.69 The dashed lines on Figure 3.27 show the envelopes fitted to cases A, C and E. It is emphasised that while the upper line for material (a) and the lower line for material (b) (ie Case E) do not look like good fits, they are in fact very good fits for the 4 test results, below σ′ 3 equal 0.7 MPa, that form their basis with r 2 of 99.74% and 99.85% respectively. Such results might erroneously be taken to support the contention that the material was well modelled by the Hoek-Brown criterion. It can be concluded that the estimated parameters are as much a function of the test program as of the material tested. These errors would generally be obscured by the material variability but they are still present. Figure 3.28 and Table 3.11 present the results of analysis of data set 434, a sandstone, in which the analysis has assumed different maximum possible σ′ 3 . This further illustrates the errors that can occur if a Hoek-Brown envelope is fitted to material for which α does not equal 0.5. Depending on the test program, estimates of σ c obtained by fitting the generalised criterion vary from 85.4 to 57.7 MPa and of m i from 6.35 to 13.1, variations of 150% and 205%. If the Hoek-Brown criterion is fitted, the estimates vary from 23.8 to 55.5 MPa (230%) and 31 to 138 (445%). Again the r 2 determined for the fits are very good. Table 3.11. Variation of σ c and m i with σ′ 3max for data set 434 For generalised Hoek-Brown criterion σ′ 3max (MPa) N Estimated σ c Estimated m i Estimated α r 2 (%) All data 20 85.4 6.71 0.75 99.70 400 16 59.2 13.1 0.65 99.63 200 9 57.7 13.0 0.66 99.50 100 5 64.1 6.35 0.87 98.18 For Hoek-Brown criterion σ′ 3max (MPa) N Estimated σ c Estimated m i r 2 (%) All data 20 23.8 138 97.00 400 16 35.1 75.2 98.49 200 9 44.9 49.7 98.20 100 5 55.5 31.0 93.99 Page 3.70 Sigma 3 S i g m a 1 0 500 1000 1500 2000 2500 0 100 200 300 400 500 600 700 Sigma 3 S i g m a 1 0 500 1000 1500 2000 2500 0 100 200 300 400 500 600 700 Figure 3.28. Hoek-Brown fits to actual data The Strength of Intact Rock Page 3.71 Figure 3.29 shows the residuals from fitting the Hoek-Brown criterion to data sets with σ c less than 20 MPa plotted against σ′ 3 divided by the maximum test σ′ 3 . There are four graphs showing cases where the estimated α from fitting the generalised criterion is (a) less than 0.4, (b) between 0.4 and 0.6, (c) between 0.6 and 0.8 and (d) greater than 0.8. On each graph the residuals have been fitted with a quadratic relationship. It can be seen that these residuals conform almost perfectly to those predicted on Figure 3.26. This is very strong evidence that the Hoek-Brown model is not appropriate. Figure 3.30 shows the residuals obtained from fitting the generalised Hoek-Brown criterion. It can be seen that these show little or no trend. The Strength of Intact Rock Page 3.72 Data with estimated UCS less than 20 MPa Sigma 3 / Maximum test sigma 3 R e s i d u a l f r o m f i t t i n g H B e q u a t i o n Alpha <= .4 -30 -20 -10 0 10 20 30 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 Alpha (.4,.6] -0.2 0.0 0.2 0.4 0.6 0.8 1.0 Alpha (.6,.8] -30 -20 -10 0 10 20 30 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 Alpha > .8 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 Figure 3.29. Residuals for Hoek-Brown fits for weak rock against σ′ 3 /σ′ 3max categorised by α The Strength of Intact Rock Page 3.73 Data with estimated UCS less than 20 MPa Sigma 3 / Maximum test sigma 3 R e s i d u a l f r o m f i t t i n g g e n e r a l e q u a t i o n Alpha <= .4 -30 -20 -10 0 10 20 30 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 Alpha (.4,.6] -0.2 0.0 0.2 0.4 0.6 0.8 1.0 Alpha (.6,.8] -30 -20 -10 0 10 20 30 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 Alpha > .8 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 Figure 3.30. Residuals for generalised fits for weak rock against σ′ 3 /σ′ 3max categorised by α The Strength of Intact Rock Page 3.74 3.10 APPLICATION TO SLOPE ENGINEERING In general the triaxial strength of intact rock is not particularly important in the analysis or design of rock slopes, even large rock slopes. The maximum depth of the failure surface for even a 500 m high slope is generally only 100 to 150 m deep, and thus the maximum σ′ 3 of interest is around 4 MPa. The relative contribution of the triaxial component of strength for various rocks (ie σ c , m i and α) and overburden stresses is given in Table 3.12. It can be seen that for high φ 0 rocks triaxial strength is generally significant, even for quite low slopes and high strength, but for most of these situations intact rock strength will not be critical except in forming the basis of rock mass strength. For low φ 0 rocks triaxial strength is important for low strength or high stress conditions and it is these situations for which intact strength may be critical in design. Table 3.12. Triaxial component of strength σ c σ′ 3 High φ 0 case m i = 50, α = 0.4 % Low φ 0 case m i = 0.8, α = 0.9 % 300 4.0 24 2.3 100 4.0 59 6.9 30 4.0 140 23 10 4.0 280 68 3 4.0 570 230 300 0.5 3.4 0.3 100 0.5 9.8 0.9 30 0.5 29 2.9 10 0.5 70 8.6 3 0.5 160 29 Table 3.13 and Figure 3.31 provide a comparison of different methods of predicting the triaxial strength of low strength rocks at low stress. The predicted strengths are compared with the measured strengths for all cases in the database for which σ c is less than 20 MPa and σ′ 3 is between 0 and 5 MPa (excluding UCS test results). The variances of the residuals scaled on σ c are given in Table 3.13 and the scaled residuals The Strength of Intact Rock Page 3.75 plotted on Figure 3.31. In general the order of accuracy of the various prediction methods is the same as discussed for the overall predictions. It is of interest to note that the global generalised equation (r 2 of 88.6%) is almost as accurate a prediction of the triaxial strength of these rocks as that obtained by fitting the Hoek-Brown criterion directly to triaxial test data (r 2 of 90.3%). This reflects the fact that there is abundant evidence that α does not equal 0.5 for a large proportion of the rocks tested – see Figure 3.14 and thus there will be systematic errors at low stress. Table 3.13. Comparison of predictions for weak rocks at low stress Variable/prediction Variance Variance explained % σ′ 1 /σ c 7.69 0 Global regression with α constant 1.91 75.1 Hoek-Brown with published m i 1.99 74.1 Global regression with α variable 0.88 88.6 Hoek-Brown fitted to individual sets 0.74 90.3 Generalised Hoek-Brown fitted to individual sets 0.12 98.5 The above situation arises because the range of σ′ 3 over which the tests were performed hardly ever corresponded to 5 MPa and thus there were almost always systematic errors at the lower stresses tested. It is sometimes argued that the solution to this is to test over a range of σ′ 3 that represents the field conditions, but this is hardly ever possible as generally the one set of testing is used to design low and high slopes. Further for a given slope different portions of the failure surface are at different stresses. Another solution is to determine the parameters as a function of stress, but this virtually defeats the purpose of adopting a non-linear failure envelope and confirms they are not a material property. The Strength of Intact Rock Page 3.76 Sigma 3 G e n e r a l i s e d H B -5 0 5 10 0 2 4 Sigma 3 H B -5 0 5 10 0 2 4 Sigma 3 G l o b a l -5 0 5 10 0 2 4 Sigma 3 G l o b a l w i t h f i x e d a l p h a -5 0 5 10 0 2 4 Sigma 3 H B a n d p u b l i s h e d m i -5 0 5 10 0 2 4 Figure 3.31. Residuals against σ′ 3 for various fits The Strength of Intact Rock Page 3.77 A useful approximation of the effective stress parameters, c 0 and φ 0 , at low stress can be obtained in the following manner. Equation 3.26 can be rearranged to provide an estimate of m i based on σ c and σ t as: t c i t c m σ σ σ σ < ≤ −1 (3.30) In addition, α can be estimated from Equation 3.29, φ o is given by Equation 3.25 and: ( ) ( ) 5 . 0 0 1 2 i c m c α σ + · (3.31) The writers do not argue that this approximation is a substitute for triaxial testing but, in the absence of such testing, the approximation should be more accurate than other methods of estimation such as using σ c and published values of m i . Further it results in a linear failure envelope which is exact at the origin and as such is convenient to use in many slope stability programs. The Strength of Intact Rock Page 3.78 3.11 CONCLUSION This chapter presented an overview of the strength of intact rock. It was demonstrated that the method of fitting the criterion to the test data has a major effect on the estimates obtained of the material properties. The results of a recent analysis of a large database of test results demonstrated that there are inadequacies in the Hoek-Brown empirical failure criterion as currently proposed for intact rock and, by inference, as extended to rock mass strength. The parameters m i and σ c are not material properties if the exponent is fixed at 0.5. Published values of m i can be misleading as m i did not appear to be related to rock type. The Hoek-Brown criterion can be generalised by allowing the exponent to vary. This change resulted in a better model of the experimental data. The most accurate method of estimating m i and α is through using triaxial tests on intact rock. The recommended method for regression of the data is modified least squares, Equation 3.22, combined with the extended formulation of the generalised criterion, Equation 3.24. The equations are repeated below. ( ) ( ) ¹ ; ¹ ′ − ≤ ′ × ′ − ′ ′ − > ′ ′ − ′ 3 1 3 3 3 1 1 1 3 for predicted measured 3 for predicted measured σ σ σ σ σ σ σ σ i m (3.22) ¹ ¹ ¹ ; ¹ − ≤ ′ ′ · ′ − > ′ , _ ¸ ¸ + ′ + ′ · ′ i c i c c i c m m m σ σ σ σ σ σ σ σ σ σ σ α 3 3 1 3 3 3 1 for for 1 (3.24) Analysis of individual data sets indicated that the exponent, α, is a function of m i which is, in turn, closely related to the ratio of σ c /σ t . A regression analysis of the entire database provided a model to allow the triaxial strength of an intact rock to be estimated from a reliable measurement of its uniaxial tensile and compressive strengths. The method proposed is the most accurate of those methods that do not require triaxial testing and is adequate for preliminary analysis. An analysis was presented that showed applying the Hoek-Brown criterion to most rocks results in systematic errors. Simple relationships for triaxial strength that are adequate for slope design were presented. The Shear Strength of Rockfill Page 4.1 4 THE SHEAR STRENGTH OF ROCKFILL 4.1 OUTLINE OF THIS CHAPTER The work by Marsal (1973) on the shear strength of rockfill showed that the strength of rockfill may vary directly with normal effective stress, dry density, particle roughness, particle crushing strength and inversely with grain size, uniformity of grading, and particle shape. The aim of this Chapter is to verify and extend this work using an extensive literature review and an analysis of a triaxial shear strength database which has been collected from the literature, and from organisations who have carried out testing for dams and other projects. In the context of this Chapter the term rockfill encompasses both material of alluvial origin and that of blasted quarry origin. The differentiation between the two can be made by looking at parameters such as angularity. This Chapter also comprises part of the larger study that is investigating rock mass strength. The author believes that it is reasonable to assume that a compacted rockfill is representative of a poor quality rock mass as defined by Hoek and Brown (1980). The author has therefore used the data collected in this report to create a lower bound for the Hoek-Brown criterion. This Chapter presents a summary of the main factors affecting rockfill strength from the literature; the triaxial shear strength database; statistical results from the database; and several shear-strength criteria for rockfill using Hoek-Brown and other methods. The Shear Strength of Rockfill Page 4.2 4.2 FACTORS AFFECTING THE SHEAR STRENGTH OF ROCKFILL The author believes that the shear strength of rockfill at a particular confining stress may be seen as the combination of a basic friction angle (shearing between rock surfaces), φ b , plus a dilation component less an amount caused by asperity or particle crushing/shearing and reorientation of particles. In terms of friction angle: crush φ φ φ − + = i b (4.1) Dilation ceases to occur at the critical confining pressure as defined by Seed and Lee (1967). Marsal (1973) found that the shear strength of rockfill may vary directly with normal effective stress, dry density, particle roughness, particle crushing strength and inversely with grain size, uniformity of grading, and particle shape. The following discussion centres on what factors have been found to affect the shear strength of rockfill. An attempt is made to relate these factors to the equation above. 4.2.1 Confining Pressure Several authors have shown the shear strength curve for rockfill is non-linear, particularly at low confining pressures (triaxial: Leslie, 1963, Marachi et al, 1969, Leps, 1970, Bertacchi & Bellotti, 1970, Penman et al., 1982 and Indraratna et al., 1993; direct shear: Dobr & Rozsypal, 1974 and Anagnosti & Popovic, 1982; plane strain: Al- Hussaini, 1983). This would be consistent with the theory that as normal stress is increased dilation is suppressed and therefore shear strength increase is reduced. Indeed, Boughton (1970) found “some indication … that the limiting value of φ as σ′ 3 increases is the value for the surfaces of the individual rock pieces” or φ b in Equation 4.1. The effect of a curved strength envelope has a large impact on the stability analysis of rockfill dams where shallow slip surfaces are shown by the analysis to be critical using traditional average c-φ analysis. These failure surfaces are not found in practice and this The Shear Strength of Rockfill Page 4.3 is likely to be due to the high frictional strength of rockfill at the low confining pressures acting near the surface. Figure 4.1 shows a curved envelope together with various c-φ representations. The tangent friction angle, φ t , is defined as the slope of the tangent to the curved shear strength envelope at a given normal stress. The secant friction angle, φ sec , is defined as the slope of the tangent from the origin to the Mohr’s circle for a particular normal stress (Equation 4.2). It is this secant friction angle that is most commonly quoted when test results are published.         + − = − 3 1 3 1 1 sec sin σ σ σ σ φ (4.2) Where the Mohr-Coulomb parameters are taken as c = 0 and φ = φ sec the shear strength will be underestimated for normal stresses less than σ n2 and over estimated for stresses greater than σ n2 . Where the Mohr-Coulomb parameters are taken as c = c t and φ = φ t the strength will be overestimated at confining pressures less than the normal stress at the tangent point. Where c t is taken as zero, and φ = φ t , as sometimes is done by designers, the strength will be significantly underestimated. This shows the importance of using a non-linear strength criterion or stress dependent parameters e.g. a bi-linear strength envelope. The Shear Strength of Rockfill Page 4.4 φ sec φ t σ n2 τ σ n τ 0 <τ env <τ t Failure envelope τ t =τ env <τ 0 τ env <τ t <τ 0 Assumes φ = φ t and c = 0 Tangent to circle through origin = secant to failure envelope Tangent to failure envelope Figure 4.1. Methods for representing the shear strength envelope As is typical in the literature, this report uses φ = φ sec in its discussion unless otherwise stated. Marachi et al (1969) carried out large scale triaxial tests on highly angular argillite, crushed basalt and rounded amphibolite and found that φ does not appear to decrease significantly beyond σ n = 4.5MPa. Note that they did not perform tests beyond a confining pressure of 4.5MPa. Figure 4.2 and Figure 4.3 show curved strength envelopes from triaxial and direct shear tests respectively which support this. Indraratna and his co-workers (Indraratna et al., 1993, 1998, Indraratna, 1994) performed tests on greywacke rockfill and basalt ballast. They found that the shear strength of the failure envelope was highly curved for confining stresses of less than 500kPa. Penman et al (1982) found a similar result for confining stresses below 400kPa. Indraratna found that the shear strength could be approximated by a linear Mohr- Coulomb criterion at stresses higher than 1.5MPa (as compared to the Marachi value of 4.5MPa above). Figure 4.4 shows the variation of φ sec with σ n on a log scale presented by Indraratna et al. (1993). The figure also shows a lower limit to the shear strength of rockfill proposed by Indraratna et al (1993). The Shear Strength of Rockfill Page 4.5 Figure 4.2. Variation of secant friction angle, φ sec , with respect to cell confining stress, σ′ 3 , for (a) dense and (b) medium dense crushed basalt from triaxial tests (Al-Hussaini, 1983) 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 σ n (MPa) τ/σ n 1 1 2a 2b 4 5 6 7 3 2b 2b crushed quarry rockfill gravel rockfill 1 marble 2a limestone (0.15 x 0.15m) 2b limestone (0.07 x 0.07m) 3 mica & phyllite 4 sandstone-claystone-marl flysch 5 claystone-marl flysch 6 crystalline schist 7 sandstone Figure 4.3. Average strength of rockfills from large-scale direct shear tests (Anagnosti & Popovic, 1982) The Shear Strength of Rockfill Page 4.6 Figure 4.4. Variation of secant friction angle, φ sec , with normal stress σ n (Indraratna et al., 1993) 4.2.2 Particle Strength The strength of the individual particles could be expected to have some effect on the shear strength of rockfill. Where the confining pressure, σ′ 3 , is low compared to the particle (or unconfined compressive) strength, σ c , it could be expected that variations in particle strength would have minimal effect on the shear strength. The only exception to this is if it could be shown that σ c affects φ b . It has been shown however that φ b generally falls within a narrow range for defects in rocks which have not been tectonically sheared. As σ′ 3 /σ c decreases, dilation will be the main contributor to increased shear strength. As σ′ 3 /σ c increases, failure of particles could be expected through crushing shearing and/or splitting, and thus a reduction in dilation would take place leading to lower shear strength. Particle strength should therefore play a major role with higher strength particles generally leading to higher strength rockfill. Hirshfeld et al (1973) found the curvature of the shear strength envelope to be more distinct for weak particles. This would be due to the rapid reduction in dilation with increase in confining stress. A reduction in dilation for high strength particles could be expected at much higher stresses than weak particles. The Shear Strength of Rockfill Page 4.7 Anagnosti and Popovic (1982) found for crushed rocks, there is a large drop in shear strength up to normal stresses of 1MPa for strong rockfills (Figure 4.5) with a much smaller drop for weaker flysch materials (Figure 4.6). It is likely that tests were not carried out at low enough confining pressures to capture the curvature in the flysch material. Figure 4.5. Shear strength and grain size curves for crushed (a) limestone and (b) marble (Anagnosti and Popovic, 1982) Figure 4.6. Shear strength and grain size curves for crushed flysch sandstone-marl rockfill (Anagnosti and Popovic, 1982) The Shear Strength of Rockfill Page 4.8 4.2.3 Uniformity Coefficient Generally, it could be expected that a poorly-graded rockfill (low uniformity coefficient, c u , Equation 4.3), would have a higher strength than a well-graded rockfill assuming a constant void ratio for both. A well-graded material would be more likely to reduce the amount of dilation required due to the ‘gaps’ in the gravel matrix being filled with smaller particles. However, Marachi et al (1969) claim that if both rockfills were compacted to their maximum density then the well graded material could be expected to be stronger as it would have the greater density. 10 60 d d c u = (4.3) Where, d 60 is the particle size for which 60% is finer. Chiu (1994) using data by Marsal (1967) found that the effect of c u on the shear strength of rockfill was more pronounced for low σ′ 3 , with little effect at high σ′ 3 . c u affects dilation however, at higher σ′ 3 that dilation may have been retarded. Sarac & Popovic (1985) found that the failure envelope was more curved for narrowly graded materials. Al-Hussaini (1983) found strength increased with c u but felt it may also have been affected by maximum particle size. Anagnosti & Popovic (1982) found for gravels there is a marked drop in strength for the high strength limestone below σ′ 3 =1MPa possibly due to dilational effects below σ′ 3 =0.4MPa caused by the uniform grading (Figure 4.7). The well-graded and weaker material does not show this effect (Figure 4.8). The Shear Strength of Rockfill Page 4.9 Figure 4.7. Shear strength and grain size curves for different gradings of limestone gravel (Anagnosti and Popovic, 1982) Figure 4.8. Shear strength and grain size curves for (a) crystalline schist and (b) sandstone gravels (Anagnosti and Popovic, 1982) The Shear Strength of Rockfill Page 4.10 4.2.4 Density When comparing the degree of compaction of rockfill relative density or void ratio can be used. Where materials of the same rock type and grading characteristics are tested dry density may be used as it will be related to relative density. Dry density or void ratio will not be a good parameter to use where different types and gradings of rockfills are compared. Rockfill with a higher relative density has been found to have a higher shear strength (Boughton, 1970, Leps, 1970, Marsal, 1973, Williams & Walker, 1984, Sarac & Popovic, 1985, Tosun et al., 1999). The shape of the Mohr-Coulomb failure envelope is also affected. Initially dense rockfill shows a marked curvature showing a distinct drop in the friction angle whereas an initially loose sample shows minimal curvature and drop in friction. The two curves tend to merge at very high confining pressures. This is consistent with the behaviour of granular soils which reach the critical state or constant volume/void ratio at large strains. Marachi et al (1969) indicate that the curves continue as a straight line whose projection passes through the origin. This is likely due to the dense material requiring dilation at low stresses to fail. At higher confining stresses dilation is restrained and particle shearing/crushing occurs resulting in a lower angle of friction. Initially loose material will require much less dilation as particles have more freedom to move (e.g. rotation) during shearing. Thus without the dilation there will be a minimal drop in the friction angle. Al-Hussaini (1983) found that dense crushed basalt has a higher strength than medium dense crushed basalt. Dobr & Rozsypal (1974) tested basalt at different dry densities in direct shear. They found that the strength increases with density but, the strength difference reduces with confining pressure. Chui (1994) also found little difference at high confining pressures. Alva-Hurtado et al. (1981) found the opposite with the difference in strengths increasing with confining pressure. Zeller et al (1957), as reported in Marachi et al (1969), performed triaxial tests on scalped rockfill samples for Goscheoenalp Dam in Switzerland. The confining pressure for all tests was 88kPa. It should be noted that the scalping method used did not result in parallel gradations. Zeller’s results (Figure 4.9 and Figure 4.10) show a decrease in The Shear Strength of Rockfill Page 4.11 friction angle of approximately 50° to 40° for an initial porosity increase of 8% for all dry rockfill samples (d max of 10mm to 100mm). Figure 4.9. Scalped rockfill gradings (Marachi et al, 1969) Figure 4.10. Strength porosity relationships with σ 3 = 88kPa (Marachi et al, 1969) Marachi et al (1969) tested rockfill material from Pyramid Dam. They found a drop in friction angle of approximately 4° for an increase in void ratio of 0.3. Nakayama et al. (1982) found that the friction angle was reduced with an increase in the void ratio (Figure 4.11). There is no indication in the paper as to what the confining pressure or method of assessing φ was. Boughton (1970) and Anagnostic & Popovic (1985) found a similar result although, as might be expected, Anagnostic & Popovic (1985) found the effect was more noticeable at low confining pressures and low C u . The Shear Strength of Rockfill Page 4.12 40 41 42 43 44 45 0.25 0.3 0.35 0.4 0.45 0.5 e φ triaxial - green schist - 12% -4.76mm triaxial - green schist - 18% -4.76mm triaxial - quartz schist - 13% -4.76mm triaxial - quartz schist - 20% -4.76mm direct shear - quartz schist - 18% -4.76mm direct shear - quartz schist - 25% -4.76mm direct shear - green schist - 17% -4.76mm Figure 4.11. Void ratio vs angle of friction (modified from Nakayama et al., 1982) 4.2.5 Maximum Particle Size There is some conjecture as to the effect of the maximum particle size on the shear strength of rockfill. It is generally accepted that the shear strength decreases with particle size (Marachi et al., 1969 & 1972, Marsal, 1973, Chui, 1994). However, some researches claim no effect (Charles et al., 1980) or the opposite effect (Anagnosti & Popovic, 1981). Some data from Marsal is tabulated below. The effect of maximum particle size should be considered as two issues: (I) the effect of increasing maximum particle diameter, d max with constant sample diameter, D; and (II) the effect of increasing d max with constant d max /D ratio. (both assuming constant sample height to sample diameter, H/D ratio) The Shear Strength of Rockfill Page 4.13 4.2.5.1 Increasing d max with Constant D Marsal (1973) performed tests on basalt rockfill (the results of the tests are tabulated below). The results show an increase in friction angle of 3-4% for a change in d max /D from 0.07 to 0.18. At high normal stresses (3.9MPa) the effect is more limited (0.3°). Table 4.1. Increase in φ with d max /D from Marsal (1973) data for different σ n Source Rock Type D (mm) C u C c σ n (MPa) d max1 /D d max2 /D (φ 2 - φ 1 )/φ 2 (%) Marsal (1973) Basalt 1130 A 11 - 18 5.21 – 0.55 0.8 0.07 0.18 3 Marsal (1973) Basalt 1130 A 11 - 18 5.21 – 0.55 1.6 0.07 0.18 4 Marsal (1973) Basalt 1130 A 11 - 18 5.21 – 0.55 3.9 0.07 0.18 0.3 Note: d max1 , φ 1 and d max2 , φ 2 are the maxi mum particle sizes and secant friction angle for sample one and sample two respectively. 4.2.5.2 Increasing d max with Constant d max /D Thiers & Donovan (1981) present Figure 4.12 to estimate the shear strength of rockfill at field scale. The figure plots the angle of internal friction versus maximum particle size. It should be noted that all the samples tested had a constant d max /D ratio. Table 4.2. Reduction in φ with particle size, d max , from Marsal (1973) data Source Rock Type d max /D C u C c σ n (MPa) d max1 (mm) d max2 (mm) (φ 1 - φ 2 )/φ 2 (%) Marsal (1973) Silicified conglomerate .18 A 10 1.72 3.92 38.1 200 7 Marsal (1973) Granitic-gneiss .18 SA 14 1.30 3.92 38.1 200 20 Note: d max1 , φ 1 and d max2 , φ 2 are the maximum particle sizes and secant friction angle for sample one and sample two respectively. Figure 4.12. Friction angle vs maximum particle size (Thiers & Donovan, 1981) The Shear Strength of Rockfill Page 4.14 4.2.6 Silt and Sand Fines versus Gravel and Larger Particle Content The percent of material passing 2mm is believed to affect the shear strength of rockfill. At the point where the failure shear surface does not incorporate gravel to gravel contact it could be expected that the shear strength of the finer particles would be the sole control on the shear strength of the material. Large triaxial tests for silty gravels were carried out by the USBR (1966). Tests were carried out at 0, 35, 50 and 65% gravel content. Shear strengths were found to be similar for the 0 and 35% gravel content tests. Shear strengths increased considerably at 50% and 65% gravel content. Further tests on clayey gravels found that the shear strength increased considerably between 42 and 50% gravel content. Other conclusions that were reached included: • Clayey and silty gravel show the shear strength is unaffected by gravel contents below 35%. • Sandy gravel shows an increase in gravel gives an increase in strength up to a maximum of 50% gravel • At 50% gravel content, silty gravel and clayey gravel strengths significantly increase. • At 65% gravel content the silty gravel has similar shear strength to the sandy gravel. Data from USBR (1966) and USBR (1961) for silty gravel and clayey gravel are plotted on Figure 4.13 and Figure 4.14 respectively. Trend lines (logarithmic) have been plotted on the curves to show the general trends of the data. They should not be used for design. Marsal (1976) reports two triaxial tests each on rockfill-silt and rockfill-sand mixtures and compares these to a test on rockfill only. The clean rockfill and 10% sand-rockfill mixtures had a φ of 34.1° whilst the 30% sand-rockfill had a φ of 39°. Marsal (1976) attributes the difference to the lower initial void ratio in the 30% sand-rockfill mixture. The 10% silt-rockfill mixture showed a decrease in φ to 28.8° whilst the 30% silt- rockfill mixture had the strength properties of the silt. Nakayama et al. (1982) performed triaxial and direct shear tests on schist gravels (quartz schist and green schist) with maximum particle size of 63.5mm at Inamura Rockfill Dam. It was found that the friction angle was reduced with an increase in the percent of –4.76mm particles (Figure 4.15). The Shear Strength of Rockfill Page 4.15 30 35 40 45 50 55 60 65 70 75 80 0.0 0.2 0.4 0.6 0.8 1.0 σ′ 3 (MPa) φ 38% gravel 53% gravel 67% gravel Figure 4.13. Effect of gravel content on φ for silty gravel based on USBR (1966) 30 32 34 36 38 40 42 44 46 48 50 0.0 0.1 0.2 0.3 0.4 σ′ 3 (MPa) φ 26% gravel 42% gravel 55% gravel 68% gravel Log. (26% gravel) Log. (42% gravel) Log. (55% gravel) Log. (68% gravel) Figure 4.14. Effect of gravel content on φ for clayey gravel based on USBR (1961) The Shear Strength of Rockfill Page 4.16 35 40 45 50 10 15 20 25 30 -4.76mm content (%) φ direct shear - quartz schist - e=0.28 direct shear - quartz schist - e=0.39 Figure 4.15. –4.76mm content vs secant angle of friction (Nakayama et al., 1982) 4.2.7 Particle Angularity The strength of highly angular rockfill could be expected to be higher than that for a rounded rockfill at similar relative density and low confining pressures. This is due in some part to the interlocking effect of the angular particles and also increased dilation. At high stresses the effect may not be as prominent and may be the opposite. An angular rockfill may allow for stress concentrations that cause breakage of the particles at high confining pressures reducing dilation and leading to a lower overall rockfill strength than the rounded particles with less stress concentrations. The shape co-efficient, C f , is often used to describe the shape of particles and is given in Equation 4.4. The shape coefficient is the volume of n particles of gravel over the equivalent volume of n spheres of diameter D. ∑ ∑ = n n f D V C 0 3 0 6 π (4.4) Bertacchi & Berlotti (1970) found that serpentinite (UCS = 100-150MPa, laminar surfaces, sharp edges, C f = 0.11) gives higher friction angles than tonalite (UCS = 150MPa, irregular rough surfaces, C f = 0.17) due to the irregularity in the shape of the serpentinite particles. Sarac & Popovic (1985) found a similar result but the effect was less with higher confining pressures. The Shear Strength of Rockfill Page 4.17 4.2.8 Other Factors The type of shear test is believed to have an influence over results. Generally plane strain tests in the literature (Al-Hussaini, 1983 – dense crushed basalt, Barton & Kjærnsli, 1981, Charles & Watts, 1980) give higher friction angles, φ′ ps , than triaxial shear tests, φ′ ax . Tests by Marsal et al (1967) and Marsal (1973) discussed by Charles (1991) showed φ′ at failure is greater in the plane strain tests by up to 8° for the same minor principal stress. The Danish Code of Practice (Steensen-Bach, 1989) gave: ax ps φ φ ′ = ′ 1 . 1 (4.5) Whilst Wroth (1984) gives: ax ps φ φ ′ = ′ 9 8 (4.6) McWilliam (2001), working with the author, used published data to show that the ratio between φ′ ps and φ′ ax varied from 1.02 to 1.1 (c.f. 1.125 from equation 4.6). The ratio varied with material type and confining pressure. The triaxial test provides a correct value of φ as it incorporates the intermediate principal stress, σ′ 2 (=σ′ 3 ). In a plain strain test, strain is prevented in the direction of σ′ 2 . Where the popular Mohr-Coulomb criterion is used the intermediate stress is ignored which leads to a miscalculation of φ. It is a common misconception that using the Mohr-Coulomb derived φ from plain strain tests gives a better correlation to field values and should therefore be used in preference to the φ from triaxial tests. The backanalysis of failures have traditionally been carried out in two dimensions. This procedure ignores σ′ 2 in the same manner as in the derivation of φ from the plane strain lab tests. Thus, the plain strain φ and the back calculated φ are both incorrect but, as they have similar errors in their derivation they tend to give similar results. The author recommends the use of the φ derived from triaxial tests for design. The shear strength of rockfill may decrease with moisture content (Frassoni et al., 1982, Chui, 1994, Marsal, 1967). This is probably related to the drop in unconfined compressive strength for some intact rocks. The Shear Strength of Rockfill Page 4.18 4.2.9 Summary of Factors Affecting the Secant Friction Angle Table 4.3 shows a summary of the factors affecting the secant friction angle discussed in this section. The most significant effects on the secant friction angle appear to be caused by confining pressures, density and maximum particle size. There is also a substantial effect on φ sec at high percentages of material finer than gravel. Minor effects on the secant friction angle are caused by angularity and the uniformity coefficient. Table 4.3. Summary of factors affecting the secant friction angle Parameter Effect on φ sec with increase in parameter Comment Confining pressure Decrease Significant effect. The rate of decrease in φ sec will drop with increasing confining pressure Unconfined compressive strength of intact rock Increase Effect will depend on the ratio of confining stress to compressive strength Uniformity coefficient Decrease Minor effect and may reverse if samples are compacted to their maximum density prior to testing Density Increase Maximum particle size (assuming the ratio of maximum particle size to sample diameter is constant) Decrease Ratio of maximum particle size to sample diameter Increase Angularity Increase The effect will be most noticeable with highly angular material Percent finer than gravel size in sample Decrease The effect will not be significant at low percentages. At high percentages strength will approach that of the finer material. The Shear Strength of Rockfill Page 4.19 4.3 SHEAR STRENGTH CRITERIA Table 4.5 shows a number of rockfill shear strength equations from the literature. The equations are numbered in the first column of the table. The criteria are empirical having been based on laboratory tests of rockfill. De Mello (1977) proposed Equation 4.8 as suitable for representing the curved strength envelope. Charles & Watts (1980) also used this form of equation. Indraratna et al. (1993) developed a non-dimensional form of Equation 4.8 for both shear stress and principal stress plots (Equations 4.9 and 4.11). Charles (1991) gives values for the constants A and B in the De Mello (1977) equation (Table 4.4). Table 4.4. Parameters obtained using De Mello (1977) (Charles, 1991) I D A B Sandy gravel .95 4.4 .81 Soft rockfill .95 4.2 .75 Soft rockfill .70 1.4 .90 Indraratna et al. (1998) also uses Equation 4.12 to describe the shear strength of basalt ballast. Doruk (1991) created a modified version of the Hoek-Brown criterion by removing the s component and thus rendering the unconfined compressive strength of the rock mass to zero. (Equation 4.13) Sarac & Popovic (1985) analysed a large number of large scale (0.7x0.7x0.4 to 1.9x2.9x1.5m) direct shear tests carried out at the Institute for Geotechnics and Foundation Engineering, Sarajevo (Equation 4.10). The materials tested were generally limestone, sandstone, serpentinite and slate and were from a mixture of sources including: natural; rock debris; and quarry rockfill. The tests were generally carried out for materials for embankment dams over stress ranges between 0.05 to 2.0MPa. Figure 4.17 shows the test results. Page 4.20 Table 4.5. Various shear strength criteria for rockfill Eq Reference Equation Parameters Development 4.8 De Mello (1977) Charles & Watts (1980) B n Aσ τ = A, B see Table 4.4 Empirical curved envelope. 4.9 Indraratna et al (1993) Indraratna (1994) b c n c a         = σ σ σ τ a,b = 0.25,0.83 (lower bound, σ n =0.1-1MPa) a,b = 0.71,0.84 (upper bound, σ n =0.1-1MPa) a,b = 0.75,0.98 (lower bound, σ n =1-7MPa) a,b = 1.80,0.99 (upper bound, σ n =1-7MPa) Non-dimensionalised form of (4.8). Note that if A in (4.8) is independent of σ c then a is not independent of σ c . 4.10 Sarac & Popovic (1985) ( ) B n A 0 max σ σ τ = A increases with σ c ↑, C u ↑, γ ↑, d 50 ↑ ≈ 0.7 to 1.5 (Figure 4.19,Figure 4.20) B increases with σ c ↑, C u ↑, γ ↓ ≈ 0.419 to 0.911 ( Figure 4.18) σ 0 = 1MPa Developed from large-scale direct shear tests (up to σ n = 2MPa) on quarry rockfill and natural gravels. Various sedimentary rocks were used.(Figure 4.17) 4.11 Indraratna et al (1993) Indraratna (1994) β σ σ α σ σ         ′ = ′ c c 3 1 α,β = 0.4,0.62 (lower bound, 0.1 to 1MPa) α,β = 0.78,0.65 (upper bound, 0.1 to 1MPa) α,β = 2.71,0.96 (lower bound, 1 to 7MPa) α,β = 3.58,0.90 (upper bound, 1 to 7MPa) Alternative of (4.9) for principal stresses 4.12 Indraratna et al (1998) b a 3 3 1 σ σ σ ′ = ′ ′ a, b = 84.98,-0.49 (gradation A) a, b = 125.17,-0.56 (gradation B) Developed empirically for two gradations of ballast Undefined at σ′ 3 = 0 4.13 Doruk (1991) c a c m σ σ σ σ σ         ′ + ′ = ′ 3 3 1 m, a Developed from Hoek-Brown by setting the rockfill compressive strength to zero (i.e. s = 0). The Shear Strength of Rockfill Page 4.26 4.4 DATABASE OF TRIAXIAL SHEAR TESTS The author has collated a database of large-scale triaxial shear tests. The database has over 989 individual triaxial shear tests from 307 sets of data. The information in the database has been collected from selected quality published papers and reports and from unpublished laboratory reports from organisations that have carried out high quality testing for dams and other projects. There is an assumption inherent in collating a large amount of data that all data sets are of equal quality. The dangers of making this assumption were mitigated to some degree by using the quality sources stated above. Although virtually all tests were accepted, there were some that were rejected. Tests that were carried out at a very high strain rate were rejected. As were results where the strength of the sample was estimated due to the test reaching the strain limit of the testing apparatus prior to attaining the maximum strength of the sample. Table 4.6 shows the parameters recorded in the database. The complete database is contained in Appendix F on a CD-ROM that is appended to this thesis. Table 4.7 summarises the basic statistics of the data. The triaxial cells used for tests ranged from a diameter of 50.8mm to a diameter of 1130mm. The maximum particle size in the tests ranged from 4.8mm to 200mm. The minimum particle size in the tests ranged from 0.0035mm to 40mm. Note that many tests recorded a minimum particle size of ‘less than’ a particular diameter. 40% of tests had zero fines (% passing 0.075mm) content whilst 80% of the tests had a fines content of no more than 5%. 10% of the triaxial tests had fines contents in excess of 20%. The largest fines content for a test in the database was 45%. Note that the uniformity coefficient and the coefficient of curvature are very high for tests where fines have been added to a large diameter rockfill. 18.7% of the triaxial tests were on basalt material whilst 14.9% were on granite, 8.2% sandstone and 3.9% limestone. Many tests did not give the rock type of the material tested. 49% of the samples tested were considered angular (with an angularity rating = 8). The Shear Strength of Rockfill Page 4.27 Table 4.6. List of parameters in triaxial shear strength database Parameter Description Case Test number within database Reference Data source Data set Identifying number given for each set of tests performed. Taken from reference where given. Test Test number within data set Site Place of origin of material or location (e.g. dam name) Origin Source of gravel size particles (e.g. crushed, blasted, alluvial etc.) Type Rock particle type (e.g. sandstone etc) UCS (MPa) Unconfined compressive strength of individual particles UCS * (MPa) Includes UCS estimated where not given (see Section 4.5.1) Ang Angularity of particles from: angular; sub-angular; sub-rounded; rounded Ang rat A value from 1 (rounded) to 8 (angular) based on a description of the rockfill given in reference. (0 = not given) Ds (mm) Sample diameter Hs (mm) Sample height Fines (%) Percent of material finer than 0.075mm Fines * (%) Includes estimated fines where not given (see Section 4.5.1) d min (mm) Minimum particle size d 10 (mm) Diameter corresponding to 10% finer d 30 (mm) Diameter corresponding to 30% finer d 50 (mm) Diameter corresponding to 50% finer d 60 (mm) Diameter corresponding to 60% finer d 90 (mm) Diameter corresponding to 90% finer d max (mm) Maximum particle size c u Coefficient of uniformity: 10 60 d d c u = c c Coefficient of curvature: 60 10 2 30 d d d c c = Grav (%) Gravel content (defined as percent of material greater than 2mm diameter) r d Relative density γ d (kN/m 3 ) Dry unit weight e min Minimum void ratio e max Maximum void ratio e i Initial void ratio e i * Includes estimated void ratio where not given (see Section 4.5.1) n Porosity B g Breakage co-efficient (Marsal) G S Specific gravity w (%) Moisture content S (%) Degree of saturation σ′ 3 Minimum principal effective stress σ′ 1 Maximum principal effective stress ε af Axial strain at failure ε vf Volumetric strain at failure Brit Type of failure (B-brittle, T-transitional, D-ductile). Qualitative term based on the stress-strain curves (if given) presented in the reference. φ sec Secant friction angle (calculated) σ n Normal stress on failure plane (calculated) σ 1 -σ 3 Principal stress difference (calculated) σ 1 /σ 3 Principal stress ratio (calculated) The Shear Strength of Rockfill Page 4.28 Table 4.7. Summary of basic statistics from the rockfill database Parameter Minimum Average Maximum Sample diameter (mm) 50.8 332 1130.3 Minimum particle size (mm) 0.0035 3.6 40 d 10 (mm) 0.001 4.3 53 d 30 (mm) 0.01 9 90 d 50 (mm) 0.09 16 100 d 60 (mm) 0.22 20 110 Maximum particle size (mm) 4.8 59 200 Fines content (%) 0 4.1 45 Uniformity coefficient, c u 1.3 81 3243 Coefficient of curvature, c c 0.04 2 16.9 Unconfined compressive strength of intact rock particles (MPa) 25 153 761 The Shear Strength of Rockfill Page 4.29 4.5 DATABASE ANALYSIS This section describes the qualitative and quantitative (using statistical methods) analysis of the rockfill database. Analyses using both the secant friction angle and principal stresses were carried out. A final analysis using the Hoek-Brown criterion was performed as part of the development of a criterion for rock mass strength. 4.5.1 Analysis Methodology The database contained missing information for some of the test results. If a parameter used in the statistical analysis was missing for a particular test, that test result was generally ignored. However, to increase the number of tests, certain assumptions were made prior to the analysis. These are: Where an unconfined compressive strength of the intact rock was not given and reasonable estimates could be made, it was estimated into three groupings of 40, 100 and 200MPa rocks based on a description of the rock type, degree of weathering and also the origin of the material. These samples were placed. The effect of including these data sets was evaluated during the statistical analysis. Where the minimum particle size, d min , was recorded as ‘less than’ a particular diameter the following table was used to estimate d min for the analysis. Minimum particle size given, d min Minimum particle size used, d minhat <0.075 (and d 10 >0.075) 0.01 <0.075 (and d 10 ≤0.075) 0.005 <0.02 0.005 <0.005 (and d 10 >0.003) 0.001 <0.005 (and d 10 ≤0.003) 0.0005 Where an initial void ratio was not given it was calculated from one of the following equations (in order of preference): n n e − = 1 (4.17) The Shear Strength of Rockfill Page 4.30 ( ) min max max e e D e e r − − = (4.18) 1 − = d w s G e γ γ (4.19) where e = void ratio n = porosity e max = maximum void ratio e min = minimum void ratio D r = relative density (%) γ w = unit weight of water (kN/m 3 ) γ d = dry unit weight (kN/m 3 ) G s = specific gravity (assumed = 2.7 if not given) 4.5.2 Secant Friction Angle, φ sec , Versus Normal Stress, σ n Relationships between secant friction angle, φ sec , and normal stress, σ n , were investigated using the rockfill shear strength database. This relationship was chosen as it is commonly used in the literature and practice to present and analyse data. The results are discussed in detail below however, it should be noted at the outset that the fits obtained using this statistical analysis were inferior to those obtained using a relationship of maximum principal stress, σ′ 1 , versus minor principal stress, σ′ 3 . This is of particular importance at both low and high confining stress, σ′ 3 . 4.5.2.1 General Assessment of Database Figure 4.21 to Figure 4.27 show plots of φ sec vs σ n with σ n plotted on a logarithmic scale. These plots are discussed in turn below. Note that these analyses were carried out for the complete data sets. No parameter (e.g. σ c ) was estimated for these plots. Where a specific parameter has been investigated a small ‘+’ symbol on a figure represents a test result where the parameter is unknown (except for Figure 4.21). The Shear Strength of Rockfill Page 4.31 q Figure 4.21 φ sec vs σ n : This figure shows that φ sec has a range of approximately 25° for any given value of σ n . This shows that the bounds given by Indraratna et al (1993) (equating to a range of about 15°) for this type of plot do not indicate the full range of φ sec possible. Their upper bound appears to be too conservative whilst the lower bound, although providing a better fit, has several test results below it. The gradient of the bounds does not appear to be steep enough to adequately describe the variation in φ sec relative to σ n . q Figure 4.22 φ sec vs σ n sorted on angularity rating: The addition of angularity rating does not assist greatly with improving the prediction of φ sec vs σ n . The figure shows that angular rockfill (angrat = 7 or 8) generally lies above sub-angular material (angrat = 5 or 6). However, rounded material (angrat = 1 or 2) lies roughly in the centre of the data with angular material lying both above and below the data. q Figure 4.23 φ sec vs σ n sorted on rock type = basalt: This was plotted to see the amount of variability there was within one class of rock type. Basalt is used as railway ballast, road base and dam rockfill. A basalt rockfill might be expected to lie at the higher strength end of all rockfills. Although the figure shows this to be true there is still a 10°-15° range in φ sec for the material for any given σ n . q Figure 4.24 φ sec vs σ n sorted on coefficient of uniformity, c u : The figure shows that c u does not appear to be a very good additional predictor with data for each c u range generally being well and evenly spread. It could be argued that the lower strength rockfills predominately have high c u values (>12). However, these types of rockfills are spread throughout the full strength range. q Figure 4.25 φ sec vs σ n sorted on maximum particle size, d max : This data is also quite scattered although there appears to be a tendancy for high d max rockfills to result in a higher strength than small d max rockfills. q Figure 4.26 φ sec vs σ n sorted on percent fines content: The rockfills with a high fines content (>20%) generally have a lower φ sec . Much of the other data, particularly with fines less than 10% is well scattered. The Shear Strength of Rockfill Page 4.32 q Figure 4.27 φ sec vs σ n sorted on unconfined compressive strength, σ c : Rockfills with a σ c of less than 100MPa appear to have lower strengths than those greater than 100MPa. It is difficult to discern any real difference in the results for rockfills with strengths of 100-200MPa and greater than 200MPa. A general conclusion from the analysis of the graphs may be made that the factors described above do have some effect on the shear strength of rockfill, although none of them stands out as being substantially better than the others as a predictor. It is unwise to estimate strength based solely on these graphs due to the interrelationship between the various factors in the tests. A better statistical analysis is to perform a global analysis of the data using all these factors and assessing whether they are statistically significant. This is performed in the next section. Page 4.33 Sigma n (kPa) P h i s e c a n t ( d e g ) 20 30 40 50 60 70 80 10 40 70 100 400 700 1000 4000 7000 Figure 4.21. Secant friction angle, φ sec vs normal stress, σ n Approximate location of bounds from Indraratna et al (1993) - see Figure 4.4. Page 4.34 Sigma N (kPa) P h i s e c ( d e g ) 20 30 40 50 60 70 80 1 0 4 0 7 0 1 0 0 4 0 0 7 0 0 1 0 0 0 4 0 0 0 7 0 0 0 1 0 0 0 0 angrat=1 or angrat=2 angrat=3 or angrat=4 angrat=5 or angrat=6 angrat=7 or angrat=8 Figure 4.22. Secant friction angle, φ sec vs normal stress, σ n , sorted on angularity rating Note a ‘+’ symbol indicates the angularity rating is unknown for that particular test Page 4.35 Sigma n (kPa) P h i s e c ( d e g ) 20 30 40 50 60 70 80 1 0 4 0 7 0 1 0 0 4 0 0 7 0 0 1 0 0 0 4 0 0 0 7 0 0 0 1 0 0 0 0 type="basalt" type="basalt r" type="basalt1" Figure 4.23. Secant friction angle, φ sec vs normal stress, σ n , sorted on rock type = basalt Note a ‘+’ symbol indicates the material is not basalt or is unknown for that particular test Page 4.36 Sigma n (kPa) P h i s e c ( d e g ) 20 30 40 50 60 70 80 10 40 70 100 400 700 1000 4000 7000 10000 cu<=2 cu<=6 cu<=12 cu>12 Figure 4.24. Secant friction angle, φ sec vs normal stress, σ n , sorted on coefficient of uniformity, c u Note a ‘+’ symbol indicates the coefficient of uniformity is unknown for that particular test Page 4.37 Sigma N (kPa) P h i s e c ( d e g ) 20 30 40 50 60 70 80 1 0 4 0 7 0 1 0 0 4 0 0 7 0 0 1 0 0 0 4 0 0 0 7 0 0 0 1 0 0 0 0 dmax<=20 dmax<=50 dmax<=100 dmax>100 Figure 4.25. Secant friction angle, φ sec vs normal stress, σ n , sorted on maximum particle size, d max Note a ‘+’ symbol indicates d max is unknown for that particular test Page 4.38 Sigma n (kPa) P h i S e c ( d e g ) 20 30 40 50 60 70 80 1 0 4 0 7 0 1 0 0 4 0 0 7 0 0 1 0 0 0 4 0 0 0 7 0 0 0 1 0 0 0 0 fines<=0 fines<=5 fines<=10 fines<=20 fines>20 Figure 4.26. Secant friction angle, φ sec vs normal stress, σ n , sorted on percent fines (passing 0.075mm) content Note a ‘+’ symbol indicates the fines content is unknown for that particular test Page 4.39 Sigma n (kPa) P h i s e c ( d e g ) 20 30 40 50 60 70 80 1 0 4 0 7 0 1 0 0 4 0 0 7 0 0 1 0 0 0 4 0 0 0 7 0 0 0 1 0 0 0 0 ucs>=200 ucs>=100 ucs>0 Figure 4.27. Secant friction angle, φ sec vs normal stress, σ n , sorted on unconfined compressive strength of the rock substance, UCS (MPa) Note a ‘+’ symbol indicates the UCS of the intact particles is unknown for that particular test The Shear Strength of Rockfill Page 4.40 4.5.2.2 Statistical Analysis of Database A non-linear statistical analysis was carried out on the database. The estimation method used was least squares. An analysis of the form shown below was found to be the most effective for relating φ to σ n . c n b a σ φ ′ + = ′ (4.20) The analysis resulted in the following constants: ( ) ( ) 150 0459 . 0 2 756 . 0 172 . 0 267 . 0 43 . 36 − + − + − − = UCS c FINES ANG a c (4.21) ( ) ( ) 150 408 . 0 2 105 . 5 549 . 0 27 . 10 51 . 69 − − − − + + = UCS c FINES ANG b c -0.408 (4.22) 3974 . 0 − = c (4.23) where, ( ) 5 − = rating angularity ANG for angularity rating >5.5; otherwise 0 FINES = percentage of fines passing 0.075mm (%) c c = coefficient of curvature UCS = unconfined compressive strength of the rock substance (MPa) This function resulted in a variance explained of just 61.7%. It should be noted that the addition of the uniformity coefficient, c u , and the maximum and minimum particle sizes, d max and d min , did not result in a better fit to the data. As the φ vs σ n curve is unconstrained at both low and high σ n it is unlikely that a reasonable fit will be found regardless of the function used. Due to the relatively poor statistical results it was decided to proceed with an analysis using principal stresses. The Shear Strength of Rockfill Page 4.41 4.5.3 Maximum Principal Stress, σ′ 1 , versus Minimum Principal Stress, σ′ 3 The analysis using φ sec vs σ n gave poor results. In this section principal stresses are used. These are constrained at σ′ 3 =0, σ′ 1 =0. A non-linear statistical analysis was carried out on the database. The estimation method used was least squares. An analysis of the form shown in Equation 4.24 was found to be the most effective for relating σ′ 1 to σ′ 3 . α σ σ 3 1 ′ = ′ RFI (4.24) An initial analysis on the whole database (988 data sets) found (Variance explained = 97.13%): RFI = 4.7002 α = 0.8972 To determine which parameters affected RFI, the analysis was carried out iteratively. The analysis was carried out using a parameter in the database as a predictor of RFI (e.g. σ c ). After each analysis the residuals were plotted against the parameters in the database. Where a trend was noted for a particular parameter another analysis was carried out using that additional parameter. The analysis resulted in the following equations (based on 869 data sets and with a variance explained = 98.82%): 8726 . 0 = α UCS FINES d ANG e RFI RFI RFI RFI RFI RFI 30598 . 0 1568 . 1 0027 . 0 48763 . 0 3491 . 6 max + − − + = (4.25) i e e RFI + = 1 1 (4.26) 0 otherwise angular, if 1 = = ANG RFI (4.27) max max d RFI d = (mm) (4.28) ( ) ( ) 20 Fines 20 Fines 1 − − + = e e RFI FINES where fines is in % (4.29) ( ) ( ) 110 UCS 110 UCS 1 − − + = e e RFI UCS where UCS is in MPa (4.30) The Shear Strength of Rockfill Page 4.42 Equation 4.29 and 4.30 are effectively smooth “step” functions that are ameniable to equation solving routines. Figure 4.28 shows the variation of RFI e with initial void ratio. This shows that an increase in initial void ratio will lead to a decrease in σ′ 1 and shear strength. Highly angular rockfill (angularity rating = 8) showed an increase in strength. There was no noticeable trend for less angular rockfill (angularity rating ≤ 7) and hence Equation 4.27 was chosen. The strength of the rockfill (σ′ 1 ) was found to be proportional to the maximum particle size (Equation 4.28). The unconfined compressive strength, σ c , was found to have a limited effect on the strength of the rockfill. Generally strengths below a σ c of 100MPa had similar strengths, as did those with σ c greater than 120MPa. Equation 4.30 acts as a switch at a σ c around 110MPa. Below a σ c of 110MPa the function rapidly approaches zero and above a σ c of 110MPa the function rapidly approaches unity (Figure 4.29). The fines content was found to only affect the strength of the rockfill where the fines content was greater than approximately 20%. Equation 4.29 acts as a switch at a fines content around 20%. Below a fines content of 20% the function rapidly approaches zero and above a fines content of 20% the function rapidly approaches unity (Figure 4.30). The Shear Strength of Rockfill Page 4.43 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 Void Ratio RFI e Figure 4.28. RFI e versus void ratio 0 0.2 0.4 0.6 0.8 1 50 60 70 80 90 100 110 120 130 140 150 UCS (MPa) RFI UCS Figure 4.29. RFI UCS versus unconfined compressive strength The Shear Strength of Rockfill Page 4.44 0 0.2 0.4 0.6 0.8 1 0 5 10 15 20 25 30 35 40 FINES (%) RFI FINES Figure 4.30. RFI FI NES versus percent fines The residuals versus unconfined compressive strength, maximum particle size, initial void ratio, angularity and fines content are shown on Figure 4.31 to Figure 4.35 respectively. These figures shown no discernible trend from which it can be assumed that the equations provided above are reasonable over the range of the data. Figure 4.36 shows the residuals plotted against sample diameter. The lack of any major trend in the data suggests that sample diameter does not have a large effect on rockfill strength at least up to diameters of about 1.2m. This suggests that the process of scaling using parallel grading lines when testing rockfill for use in the field is valid and should not affect the results. Note however, that if fines are increased due to the scaling strength (σ′ 1 ) may be reduced. Figure 4.37 to Figure 4.41 show the effect that a change in unconfined compressive strength, angularity, fines content, maximum particle size and initial void ratio have on σ′ 1 respectively. The Shear Strength of Rockfill Page 4.45 Figure 4.42 shows the data used in the analysis together with lines representing RFI=7 (approximate upper bound), RFI=4.7 (approximate best estimate) and RFI=3 (approximate lower bound). Figure 4.43 shows the same plot with all the data in the database plotted. It shows that the bounds are still reasonable and that the data left out of the analysis (due to insufficient information) would not have changed the results significantly. Figure 4.44 shows the same plot for a stress range (σ′ 3 ) up to 1.5MPa. Page 4.46 -3 -2 -1 0 1 2 3 0 100 200 300 400 500 600 700 800 UCS (MPa) R e s i d u a l s ( M P a ) Figure 4.31 Residuals versus unconfined compressive strength of intact rock Page 4.47 -3 -2 -1 0 1 2 3 0 50 100 150 200 250 Dmax (mm) R e s i d u a l s ( M P a ) Figure 4.32. Residuals versus d max Page 4.48 -3 -2 -1 0 1 2 3 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Void Ratio R e s i d u a l s ( M P a ) Figure 4.33. Residuals versus void ratio Page 4.49 -3 -2 -1 0 1 2 3 0 1 2 3 4 5 6 7 8 9 Angularity Rating R e s i d u a l s ( M P a ) 2 - Rounded 4 - Sub-rounded 6 - Sub-angular 8 - Angular Figure 4.34. Residuals versus angularity rating Page 4.50 -3 -2 -1 0 1 2 3 0 5 10 15 20 25 30 35 40 Fines (%) R e s i d u a l s ( M P a ) Figure 4.35. Residuals versus fines content Page 4.51 -3 -2 -1 0 1 2 3 0 200 400 600 800 1000 1200 Sample diameter (mm) R e s i d u a l s ( M P a ) Figure 4.36. Residuals versus sample diameter The Shear Strength of Rockfill Page 4.52 0 5 10 15 20 0 1 2 3 4 5 σ 3 (MPa) σ1 (MPa) UCS = 50MPa UCS = 110MPa UCS = 200MPa Angularity = 7 Fines = 0% d max = 60 Void ratio = 0.4 Figure 4.37. Effect of unconfined compressive strength on σ′ 1 0 5 10 15 20 0 1 2 3 4 5 σ 3 (MPa) σ1 (MPa) Angularity = 7 Angularity = 8 UCS = 100 MPa Fines = 0% d max = 60 Void ratio = 0.4 Figure 4.38. Effect of angularity on σ′ 1 (7 = sub-angular to angular; 8 = angular) The Shear Strength of Rockfill Page 4.53 0 5 10 15 20 0 1 2 3 4 5 σ 3 (MPa) σ1 (MPa) Fines = 40% Fines = 20% Fines = 0% UCS = 100 MPa Angularity = 7 d max = 60 Void ratio = 0.4 Figure 4.39. Effect of fines content on σ′ 1 0 5 10 15 20 0 1 2 3 4 5 σ 3 (MPa) σ1 (MPa) dmax = 200 dmax = 100 dmax = 5 UCS = 100 MPa Angularity = 7 Fines = 0% Void ratio = 0.4 Figure 4.40. Effect of maximum particle size on σ′ 1 The Shear Strength of Rockfill Page 4.54 0 5 10 15 20 0 1 2 3 4 5 σ 3 (MPa) σ1 (MPa) e = 0.8 e = 0.5 e = 0.2 UCS = 100 MPa Angularity = 7 Fines = 0% d max = 60 Figure 4.41. Effect of initial void ratio on σ′ 1 Page 4.55 0 5 10 15 20 25 30 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 σ 3 (MPa) σ 1 (MPa) RFI = 7 RFI = 3 RFI = 4.7 Figure 4.42. σ′ 1 vs σ′ 3 showing data used in analysis and RFI relationship Page 4.56 0 5 10 15 20 25 30 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 σ 3 (MPa) σ 1 (MPa) RFI = 7 RFI = 3 RFI = 4.7 Figure 4.43. σ′ 1 vs σ′ 3 showing all data and RFI relationship Page 4.57 0 2 4 6 8 10 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 σ 3 (MPa) σ 1 (MPa) RFI = 7 RFI = 3 RFI = 4.7 Figure 4.44. σ′ 1 vs σ′ 3 showing all data and RFI relationship (σ′ 3 up to 1.5MPa) The Shear Strength of Rockfill Page 4.58 4.5.3.1 Secant Friction Angle Versus Normal Stress Figure 4.37 to Figure 4.41 are replotted as curves for φ sec vs σ n by using the following equations:         ′ + ′ ′ − ′ = − 3 3 3 3 1 sec sin σ σ σ σ φ α α RFI RFI (4.31) 1 3 sec cos + ′ = α σ φ σ RFI n (4.32) Table 4.8 shows the variation in φ sec due to changes in various parameters for σ n =1MPa and 0.5MPa. These give some idea of the influence of different parameters on the secant friction angle. Note that these friction angles are based on assumptions as shown on Figure 4.45 to Figure 4.49. The values chosen for the parameters are realistic upper and lower bounds from the database. Table 4.8. Changes in φ sec on Figure 4.45 to Figure 4.49 for σ n =1MPa and σ n = 0.5MPa σ n = 0.1MPa σ n = 0.5MPa σ n = 1MPa Parameter Value φ sec (°) Change in φ with increase in parameter φ sec (°) Change in φ with increase in parameter φ sec (°) Change in φ with increase in parameter 50 46.8 42.2 40.3 σ c (MPa) 200 48.1 +1.3 43.6 +1.4 41.8 +1.5 1-7 46.7 42.2 40.3 Angularity rating 8 48.8 +2.1 44.4 +2.2 42.6 +2.3 0 46.7 42.2 40.3 Fines content (%) 20 43.9 -2.8 39.1 -3.1 36.9 -3.4 50 47.0 42.4 40.4 Maximum particle size (mm) 200 44.8 -2.2 40.3 -2.1 38.3 -2.1 0.2 49.9 45.5 43.7 Initial void ratio 0.6 43.5 -6.4 36.4 -9.1 34.2 -9.5 The Shear Strength of Rockfill Page 4.59 30 35 40 45 50 0 2 4 6 8 σ n (MPa) φ sec UCS = 50MPa UCS = 200MPa Angularity = 7 Fines = 0% d max = 60 Void ratio = 0.4 Figure 4.45. Effect of unconfined compressive strength on φ sec 30 35 40 45 50 0 2 4 6 8 σ n (MPa) φ sec Angularity = 7 Angularity = 8 UCS = 100MPa Fines = 0% d max = 60 Void ratio = 0.4 Figure 4.46. Effect of angularity on φ sec (7 = sub-angular to angular; 8 = angular) The Shear Strength of Rockfill Page 4.60 20 25 30 35 40 45 50 0 2 4 6 8 σ n (MPa) φ Fines = 0% Fines = 20% Fines = 40% UCS = 100MPa Angularity = 7 d max = 60 Void ratio = 0.4 Figure 4.47. Effect of fines content on φ sec 30 35 40 45 50 0 2 4 6 8 σ n (MPa) φ dmax = 5 dmax = 100 dmax = 200 UCS = 100MPa Angularity = 7 Fines = 0% Void ratio = 0.4 Figure 4.48. Effect of maximum particle size on φ sec The Shear Strength of Rockfill Page 4.61 20 25 30 35 40 45 50 0 2 4 6 8 σ n (MPa) φ e = 0.2 e = 0.4 e = 0.6 UCS = 100MPa Angularity = 7 Fines = 0% d max = 60 Figure 4.49. Effect of initial void ratio on φ sec 4.5.4 Hoek-Brown Criterion The author considers that rockfill could represent a very poor quality rockmass. As such an analysis of the database using the Hoek-Brown criterion was performed. The results from this analysis could then be used as a lower bound rock mass strength estimator. The statistical analysis was carried out for data where the UCS was known. This resulted in a sample of 409 triaxial tests. Two approaches were used: one where the variables are σ′ 3 and the dependent variable σ′ 1 ; and the other where the variables are σ′ 3 /σ c and the dependent variable σ′ 1 /σ c . Similar analyses to those discussed previously were carried out i.e. non-linear, quasi-Newton with a loss function of (observed – predicted) 2 . A further analysis was carried out where the estimated values of the UCS of the intact rock were used where no UCS was recorded for the sample. The ability of the Hoek-Brown criterion to estimate the shear strength of rockfill (and subsequently poor quality rock mass) was performed by assuming typical Hoek-Brown parameters of s = 0 and a = 0.6. This was compared with a further analyses where a was defined as a parameter. The results from the analyses are shown in Table 4.9. The Shear Strength of Rockfill Page 4.62 Table 4.9 and Figure 4.50 show that if the recommended Hoek-Brown parameters are used a poor fit results. Due to the enforced curvature (a = 0.6), σ′ 1 is overpredicted at low σ′ 3 and under predicted at high σ′ 3 . Much better fits (Table 4.9 and Figure 4.50) are obtained where a was a parameter. These analyses showed that an a of 0.90 to 0.95 was much more suitable for rockfill. Similarly to intact rock, the interrelation between a and m b is also illustrated by the results in Table 4.9. The conclusion from the point of view of rock masses is that a is too constrained in the current Hoek-Brown criterion. Modifications need to be made such that the exponent, a, towards a value of 0.90-0.95 for poor quality rockfill. A look at the forms of the equations used shows that the method of fitting is very important to the results obtained. In this case, non-dimensionalising the equations resulted in a better variance explained. Table 4.9. Results from the statistical analysis of the rockfill database using the Hoek-Brown equation Form of equation Data sets m b a Variance explained 6 . 0 3 3 1 0         + ′ + ′ = ′ c b c m σ σ σ σ σ 405 σ ci known 0.42929 0.6 (input) 88.95% a c b c m         + ′ + ′ = ′ 0 3 3 1 σ σ σ σ σ 405 σ ci known 2.40706 0.89999 97.40% 6 . 0 3 3 1 0         + ′ + ′ = ′ c b c c m σ σ σ σ σ σ 405 σ ci known 0.75486 0.6 (input) 90.93% a c b c c m         + ′ + ′ = ′ 0 3 3 1 σ σ σ σ σ σ 405 σ ci known 2.71833 0.94877 98.73% a c b c m         + ′ + ′ = ′ 0 3 3 1 σ σ σ σ σ 988 σ ci estimated where unknown 2.39551 0.8954 97.42% Page 4.63 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 σ 3 /σ c σ 1 /σ c 6 . 0 3 3 1 75486 . 0         + = c c c σ σ σ σ σ σ 94877 . 0 3 3 1 71833 . 2         + = c c c σ σ σ σ σ σ Figure 4.50. Statistical analysis results using Hoek-Brown formula and for a = 0.6 and a = 0.95 Page 4.64 4.6 CONCLUSION This chapter presented an overview of the strength of rockfill. An analysis of a large database of test results was used to develop two new shear strength equations, one relating the secant friction angle and normal stress and the other the principal stresses. The equation for principal stresses provided a much better fit to the data and is recommended. Of the parameters statistically investigated, the unconfined compressive strength, particle angularity, fines content, maximum particle size and void ratio were found to have the most significant effect on the shear strength of rockfill. An analysis using the database and the Hoek-Brown criterion demonstrated that the criterion provided a poor fit to the rockfill data due to the restrictions placed on the exponent a of approximately 0.6. A good fit was obtained where a was free to vary up to unity (a value of 0.9 to 0.95 was obtained). This has important implications for the use of the Hoek-Brown criterion for very poor quality rock masses. Empirical Rock Slope Design Page 5.1 5 EMPIRICAL ROCK SLOPE DESIGN 5.1 INTRODUCTION Due to the complexity of rock masses, a number of researchers have attempted to correlate rock slope design with rock mass parameters. Many of these methods have been subsequently modified by others and are now currently being used in practice for preliminary and sometimes final design. This chapter presents a review of the more commonly used empirical rock slope design methods. The historical development of these methods and the data used to support them is discussed. A number of case studies are assessed using the different methods. Finally, a new relationship between the Geological Strength Index, GSI, slope height and stable slope angle is presented for use in the design of cuts in rock masses in dry conditions or under moderate water pressures. Empirical Rock Slope Design Page 5.2 5.2 REVIEW OF THE ROCK MASS RATING SYSTEMS There are several empirical rock mass rating techniques that can be utilised in the design of slopes. These include: • RMR - Rock mass rating (Bieniawski, 1976 & 1989) • MRMR - Mining rock mass rating (Laubscher, 1977 & 1990) • RMS - Rock mass strength (Selby, 1980) • SMR - Slope mass rating (Romana, 1985) • SRMR - Slope rock mass rating (Robertson, 1988) • CSMR - Chinese system for SMR (Chen, 1995) • GSI - Geological strength index (Hoek et al. 1995) • M-RMR - Modified rock mass classification (Ünal, 1996) • BQ - Index of rock mass basic quality (Lin, 1998) The majority of methods require the determination of a basic rock mass rating. The rating is usually calculated as the summation of a number of rating values that account for intact rock strength, block size, defect condition and possibly groundwater. A number of the methods then adjust this value based on such factors as defect orientation, excavation method, weathering, induced stresses and the presence of major planes of weakness. Table 5.1 compares a number of these methods. The numbers show the range of weightings possible for each component of the rating system, whilst an asterix, ‘*’, shows which parameters are taken into account in each method. It should be noted that the different rock mass rating systems use varying methods to account for each parameter. The MRMR and M-RMR adjustment factors are multipliers whilst the adjustment factors for the other methods are added to the basic rock mass rating. The maximum value of 141 for CSMR assumes a slope height of 50m. The numbers shown in brackets, ‘( )’, in Table 5.1 represent negative values. Table 5.1. Comparison of weightings for various rock mass rating methods Empirical Rock Slope Design Page 5.3 Method RMR 76 RMR 89 MRMR RMS SMR CSMR M-RMR SRMR GSI Intact strength 0-15 0-15 0-20 5-20 0-15 0-15 0-15 0-30 0-15 Block size 8-50 8-40 0-40 8-30 8-40 8-40 0-40 8-40 8-50 - Spacing * * * * * * * * * - RQD * * * * * * * * Defect condition 0-25 0-30 0-40 3-14 0-30 0-30 0-30 0-30 0-25 - Persistence * * * * * * * * * - Aperture * * * * * * * * * - Roughness * * * * * * * * - Infilling * * * * * * * * - Weathering * * * * * * * Ground water 0-10 0-15 * 1-6 0-15 0-15 0-15 - 10 Defect orientation (60)-0 (60)-0 63-100% 5-20 (60)-0 (60)-0 (12)-(5) - Strike * * * * * - Dip * * * * * * - Slope dip – defect dip * * Excavation method - - 80-100% - (8)-15 (8)-15 80-100% - - Weathering - - 30-100% 3-10 - - 60-115% - - Induced stresses - - 60-120% - - - - - - Major plane of weakness - - - - - - 70-100% - - TOTAL RANGE (52)-100 (52)-100 0-120 25-100 (60)-115 (63)-141 (7)-105 8-100 18-100 B A S I C R O C K M A S S R A T I N G A D J U S T M E N T S - - Note values in brackets are negative 5.2.1 Methods for Estimating the Basic Rock Mass Rating The basic rock mass rating attempts to capture the main features of a rock mass that, in the context of this report, affect the shear strength of the rock mass and subsequently the stability of slopes in that rock mass. 5.2.1.1 The Rock Mass Rating, RMR, and Geological Strength Index, GSI Bieniawski’s (1973, 1975, 1976, 1989) rock mass rating (RMR) is probably the most commonly used rock mass rating system for estimating rock mass strength. Initially created to assess the stability and support requirements of tunnels, it has been found to be useful in assessing the strength of rock masses for slope stability. Table 5.2 shows the rating method of Bieniawski (1989). It should be noted that the weighting of the parameters has changed slightly over the years since its development. Wherever the RMR is referred to in this document, the subscript will refer to the year of publication of that version. For example, RMR 76 , refers to the RMR published by Bieniawski (1976). Hoek et al (1995) modified the RMR so as to make it more applicable to assessing the strength of rock masses. The result of this was the Geological Strength Index (GSI). Table 5.3 shows the components and ratings from the GSI. Empirical Rock Slope Design Page 5.4 The GSI is based on RMR 76 and is calculated by summing the ratings for each parameter and adding 10. A rating value of 10 is added as the GSI assumes water conditions to be dry. No corrections are made for joint orientation as it is assumed to be favourable. Hoek et al. (1995) believe that joint orientation and water conditions should be assessed during the analysis. Hoek et al. (1995) allow for the use of RMR 89 to estimate the GSI by using GSI = RMR 89 – 5. The author warns that RMR 89 should be used with caution as it can lead to a GSI difference of up to 10 when compared with the GSI derived as above. Hoek (2000) provides another method of estimating GSI using Figure 5.1. This chapter is primarily concerned with the estimate of the strength of large rock masses and the subsequent correlation with slope angles. The GSI is made up of several components: intact rock strength; rock quality designation (RQD); defect spacing; and joint condition (water is already set to dry). All these components can be affected by scale and thus must be considered carefully when designing for very large rock masses. A larger discussion of the applicability of using the GSI for rock slopes is contained in Chapter 6. Empirical Rock Slope Design Page 5.5 Table 5.2. Rock mass rating (Bieniawski, 1989) Empirical Rock Slope Design Page 5.6 Table 5.3. Geological strength index, GSI (Hoek et al, 1995) 5.2.1.2 Mining Rock Mass Rating, MRMR Laubscher (1977, 1984 and 1990) developed a classification system, based on Bieniawski (1973), that gave a basic rating from 0 (very poor) to 100 (very good) (Table 5.4 and Table 5.5). The system changes some of the weightings of parameters and alters the method of determining joint spacing and condition compared to Bieniawski (1973). Laubscher assesses the rock joint spacing for one, two or three “continuous” joint systems. “A joint is continuous if its length is greater than one diameter of the excavation or 3m. It is also continuous if it is less than 3m but it is displaced by another joint – that is, the joints are features that define blocks of ground.” Joints logged from boreholes are placed in three 30° dip ranges. “Experience” is used to divide these ranges into further joint sets. MRMR was specifically developed for use in the assessment of support for underground openings and there is ambiguity in the assessment of MRMR when dealing with slopes. For poor and very poor quality rock masses (MRMR<40) the MRMR can be largely influenced by the evaluation of joint spacing and joint/water conditions. The appropriate evaluations are very difficult to assess when only borehole data is available and clearly requires a large degree of judgement even when exposures are available. Empirical Rock Slope Design Page 5.7 Figure 5.1. Estimate of GSI based on geological descriptions. (Hoek, 2000) Empirical Rock Slope Design Page 5.8 Table 5.4. MRMR (Laubscher, 1977) RQD (%) 100-91 90-76 75-66 65-56 55-46 45-36 35-26 25-16 15-6 5-0 Rating 20 18 15 13 11 9 7 5 3 0 IRS (MPa) 141-136 135-126 125-111 110-96 95-81 80-66 65-51 50-36 35-21 20-6 5-0 Rating 10 9 8 7 6 5 4 3 2 1 0 Defect spacing Depends on number of defect sets and spacing Rating 30.................................................................................................................................. 0 Defect condition 45° .......................................................See Table ........................................................5° Rating 30.................................................................................................................................. 0 Groundwater Inflow/10m length 0 25 l/min 25 – 125 l/min 125 l/min Joint water pressure/σ 1 0 0.0 - 0.2 0.2 - 0.5 0.5 Description dry moist Moderate pressure Severe problems Rating 10 7 4 0 Table 5.5. Defect condition rating for MRMR (Laubscher, 1977) Parameter Description Percentage adjustment to maximum rating of 30 Joint expression (Large-scale) Wavy unidirectional 90-99 Curved 80-89 Straight 70-79 Joint surface (Small-scale) Striated 85-99 Smooth 60-84 Polished 50-59 Alteration zone Softer than wall rock 70-99 Joint filling Coarse hard-sheared 90-99 Fine hard-sheared 80-89 Coarse soft-sheared 70-79 Fine soft-sheared 50-69 Gouge thickness < irregularities 35-49 Gouge thickness > irregularities 12-23 Flowing materials > irregularities 0-11 Empirical Rock Slope Design Page 5.9 5.2.1.3 Rock Mass Strength, RMS Selby (1980, 1982, 1987, 1993 and Moon & Selby, 1983) developed the RMS system based on correlations between RMS and stable slope angles of natural rock outcrops. The slopes were located in New Zealand, Antarctica, the Namib Desert and the margins of the Central plateau of southern Africa. The geology included sedimentary sequences and metamorphic (quartzite, gneiss, schist and marble) and igneous (dolerite, basalt and granite) rock masses. The RMS is calculated in a similar way to RMR with a summation of rating parameters for intact rock strength, weathering, defect spacing, aperture, defect orientation relative to the slope, defect continuity and groundwater flow (Table 5.6). Orr (1992) found an approximate (r 2 = 0.88) correlation between RMS and RMR 88 : 130 2 . 2 88 − = RMS RMR (5.1) Selby uses natural slopes in his database, and thus the slopes have been exposed over geological time. These slopes could therefore be seen to be conservative when compared to slopes in a pit with a limited design life. Selby breaks the natural slopes into small sections (generally bedding layers) and assesses the slope angle of these. The slope angles of these segments of limited height are generally structurally controlled (slaking mudstones may be an example of an exception) in practice and thus not applicable to correlations with rock mass. Schmidt and Montgomery (1996) modified the RMS for application to deep-seated bedrock landsliding in sedimentary rocks. They examined a total of 61 slopes, of which 17 were rockslides. The slopes were in the Eocene Chuckanut Formation, which comprises a fluvial sequence of interbedded sandstone and siltstone/mudstone. Schmidt and Montgomery note that there were distinct planes of weakness at lithological contacts. The sandstone and siltstone/mudstone layers showed distinct differences in strength. Table 5.6. RMS Classification and Ratings (mod. Selby, 1980) Intact strength (N-type Schmidt 100-60 60-50 50-40 40-35 35-10 Empirical Rock Slope Design Page 5.10 Hammer ‘R’) Rating 20 18 14 10 5 Weathering unweathered slightly weathered moderately weathered highly weathered completely weathered Rating 10 9 7 5 3 Defect spacing >3m 3-1m 1-0.3m 0.3-0.05m <0.05m Rating 30 28 21 15 8 Defect orientation very favourable steep dips into slope, cross defects interlock favourable moderate dips into slope fair horizontal dips, or nearly vertical (hard rocks only) unfavourable moderate dips out of slope very unfavourable steep dips out of slope Rating 20 18 14 9 5 Defect aperture <0.1mm 0.1-1mm 1-5mm 5-20mm >20mm Rating 7 6 5 4 2 Defect continuity none continuous few continuous continuous, no infill continuous, thin infill continuous, thick infill Rating 7 6 5 4 1 Groundwater outflow none trace slight <25 l/min/10m 2 moderate 25-125 l/min/10m 2 great >125 l/min/10m 2 Rating 6 5 4 3 1 The main changes to the RMS were in the defect orientation parameter. Schmidt and Montgomery (1996) state that defects with moderate dips into the slope should have a higher rating than those with steep dips into the slope. Steep dips into the slope are more likely to cause toppling and so this change appears reasonable. They also give steep dips out of the slope a higher rating than moderate dips out of the slope. This appears to contradict what would be expected. An important point to note is that Schmidt and Montgomery’s data appears to be based on translational slides and hence structurally controlled rather than on rotational rock mass slides. This would be backed up by their statement that “the vast majority of deep-seated rockslides … occur on hillslopes inclined at 15° to 35°”. Schmidt and Montgomery also state that the low RMS values associated with rockslides are due to the intact rock and defect orientation parameters. Empirical Rock Slope Design Page 5.11 Based on their data, Schmidt and Montgomery claim that the RMS “successfully discriminates localised areas of low rock mass strength within a landscape exhibiting deep-seated rockslides”. However, as this data appears defect controlled it is not considered to be reliable for use with a rock mass rating and hence this author cannot come to the same conclusion. Also, the method could only apply in bedded rocks given its database. 5.2.1.4 Slope Rock Mass Rating, SRMR Robertson et al (1987), using back analysis of slopes at Island Copper Mine in British Columbia, found that the RMR and MS (Hoek-Brown correlation to RMR) were poor predictors of the strength of rock masses for weak rock masses. They developed the Island Copper Rock Mass Rating (ILC-RMR) which modified RMR for RMR values less than 40. As this method did not allow for consistency in strength assessment (i.e. different rock mass rating methods above and below RMR = 40), Robertson (1988) proposed the SRK Geomechanics Classification of rock masses (SRMR), shown in Table 5.7. Robertson (1988) defines weak rock masses as those with shear strength parameters less than: c′ = 0.2 MPa φ′ = 30° This being equivalent to a jointed specimen having an unconfined compressive strength, UCS, of less than 0.7MPa. Robertson gives three cases where rock mass strength can be this low (or combinations of these). 1. Where the intact rock is very weak or soil-like. 2. Where there is an intense number of defects that allow the material to fail along random stepped surfaces. Empirical Rock Slope Design Page 5.12 3. Where there is sufficient freedom of rotation in the mass to allow intact material to rotate to allow for the formation of a failure surface. Note, rotation/freedom increases with equidimensional, rounded intact particles with weak infill or voids. The SRMR varies from RMR 74 in the following ways: • Groundwater is ignored as it is assumed that groundwater is a destabilising force and does not influence the rock mass strength. The maximum groundwater factor (15) has been added to the intact rock factor. • For material in the ‘soil strength’ range additional classes and ratings have been added (S1-S5). • The RQD has been replaced with a ‘handled’ RQD (HRQD). This is in effect a disturbed RQD where the material has been “firmly twisted and bent but without substantial force or use of any tools or instruments”. High RQD values will therefore not be assigned for weak or weakly cemented rock. Note that the RQD should only be applied to hard rock masses and as such, if properly recorded, should be equivalent to HRQD. The HRQD suffers from the same problems as RQD when using it for large slopes. • Discontinuity spacing is substituted with ‘handled’ discontinuity spacing in a similar manner to HRQD. • The discontinuity condition parameters stay unchanged except that the rating is limited to less than or equal to ten for mat1erial with intact rock strength less than or equal to R1. This is to stop weak rock being given a high discontinuity condition rating. Table 5.7. SRK Geomechanics Classification or Slope Rock Mass Rating (SRMR) PARAMETER RANGES OF VALUES I s50 (MPa) > 10 4 - 10 2 - 4 1 – 2 For this low range UCS test is preferred <1 Strength of intact rock material UCS (MPa) R5 >250 R4 100-250 R3 50-100 R2 25-50 R1 5-25 R1 1-5 S5 S4 S3 S2 S1 Empirical Rock Slope Design Page 5.13 Rating 30 27 22 19 17 15 10 6 2 1 0 Handled RQD (%) 90-100 75-90 50-75 25-50 <25 Rating 20 17 13 8 3 Handled (mm) discontinuity spacing >2000 600-2000 200-600 60-200 <60 Rating 20 15 10 8 5 Condition of discontinuities Rock > R1 Very rough surfaces Not continuous No separation Unweathered rock wall Rock > R1 Slightly rough surfaces Separation < 1mm Slightly weathered walls Rock > R1 Slightly rough surfaces Separation < 1mm Highly weathered walls Rock ≥ R1 Slickensided surfaces OR Gouge < 5mm OR Separation 1 – 5mm Continuous Rock < R1 Soft gouge > 5mm thick OR Separation > 5mm Continuous Rating 30 25 20 10 0 The SRMR system was found to give similar rating values as the ILC-RMR for the Island Copper Mine. Therefore, Robertson (1988) concludes that Robertson et al (1987) correlations with rock strength can be used with the SRMR. The SRMR or SRK-RMR system was also checked using Getchell Mine, Nevada. Table 5.8 shows the correlations given by Roberston (1988). Figure 5.2 shows these correlations as Mohr-Coulomb strength curves. It can be seen that for SRMR = 20-25 the results seem invalid for normal stresses less than about 700kPa (for values less than this it implies that higher SRMR values give lower strengths). The author does not know the normal stresses acting on the Island Copper Mine Slopes. Table 5.8 and Figure 5.2 show that the correlations vary a considerable amount with sites and thus the rating system may need refining. Robertson cautions that more case histories are required before the data in Table 5.8 can be used with confidence. Table 5.8. SRMR strength correlation (Robertson, 1988) Strength Parameters Island Copper Mine Getchell Mine Rock Mass Class SRMR c′ (kPa) φ′ c′ (kPa) φ′ IVa 35-40 86 40 - - Empirical Rock Slope Design Page 5.14 30-35 72 36 - - 25-30 69 34 48 30 IVb 20-25 138 30 48 26 Va 15-20 62 27.5 48 24 Vb 5-15 52 24 14 21 0 200 400 600 800 1000 0 200 400 600 800 1000 σ n (kPa) τ ( k P a ) 35-40 30-35 25-30 20-25 15-20 5-15 0 200 400 600 800 1000 0 200 400 600 800 1000 σ n (kPa) τ ( k P a ) 35-40 30-35 25-30 20-25 15-20 5-15 Figure 5.2. SRMR strength correlation (a) Island Copper Mine (b) Getchell Mine (Robertson, 1988) 5.2.1.5 Modified Rock Mass Classification, M-RMR Ünal (1996) developed the M-RMR from the RMR method with additional features for better characterisation of weak, stratified, anisotropic and clay bearing rock masses. The method was based on investigations carried out at a borax mine and two coal mines. The geology at the borax mine comprised laminated and bedded limestone with continuous beds (varying from 2m to 9m in thickness) of consolidated clay. Stability was affected by the presence of water. The coal mines consisted of lignite with associated coal measure rocks (marl, claystone, mudstone) and clayey limestone. The rating is given below. I UCS , I RQD , I JC , I JS , I GW and I JO are the ratings for σ c , RQD, joint condition, joint spacing, groundwater and joint orientation respectively. Table 5.9 and Table 5.10 show the ratings for I JC . The tables appear very extensive however, as they are based on a very limited database the author believes these should not be used for general application. F c is the weathering coefficient and A b and A w are the adjustment factors for blasting and major planes of weakness respectively. The factors are discussed further in the rating adjustment section. Empirical Rock Slope Design Page 5.15 ( ) ( ) JO GW JS JC RQD UCS c w b I I I I I I F A A RMR M + + + + + = - (5.2) 515 . 0 856 . 0 c UCS I σ = (5.3) For RQD>10: RQD I RQD 173 . 0 7 . 2 + = (5.4) For RQD≤10: RQD I RQD 443 . 0 = (5.5) 187 . 0 93 . 3 S JS J I = (5.6) W GW e I 03 . 0 15 − = (5.7) Where, w = Inflow of groundwater per 10m of tunnel length (lt/min) (Note, damp = 0-10; wet = 10-20; dripping = 20-35; flowing >35) For ICR≤5: 12 − = JO I (5.8) Where, ICR = Intact core recovery (%) For 5<ICR<25: 75 . 13 35 . 0 − = ICR I JO (5.9) For ICR≥25: 5 − = JO I (5.10) ( ) 2 00515 . 0 2 6 . 0 0015 . 0 − + = − d I d C e I F (5.11) Where, I d-2 = Slake durability index Empirical Rock Slope Design Page 5.16 Table 5.9. Joint condition index I J C (Ünal, 1996) Intact core recovery Condition J JC No filling 10 ICR < 5 Filling 0 No filling, RQD = 0 13 No filling, 0 < RQD < 10 17 No filling, RQD ≥ 10 22 Filling ≥ 5mm (soft) 0 Filling ≥ 5mm (hard) 4 Filling 1 - 5mm (soft) 8 Filling 1 - 5mm (hard) 11 5 ≤ ICR ≤ 25 Filling < 1mm 14 No filling ( ) D A C R W × × + + Filling ≥ 5mm (soft) 0 Filling ≥ 5mm (hard) ( ) D C× + 2 Filling 1 - 5mm (soft) ( ) D C× + 4 Filling 1 - 5mm (hard) ( ) D C× + 6 ICR > 25 Filling < 1mm ( ) D C × + 8 It is interesting to note that I JO is calculated from the intact core recovery from boreholes. Ünal (1996) indicates that Bieniawski’s (1989) adjustments should be used where field surveys are available. Empirical Rock Slope Design Page 5.17 Table 5.10. Ratings for joint condition parameters (Ünal, 1996) Parameter Condition Rating Parameter Condition Rating Unweathered 8 Very low 3.5 Slightly weathered 7 Low 3 Moderately weathered 6 Medium 2 Highly weathered 4 High 1.5 Very highly weathered 2 Continuity C Very high 1 Weathering W Decomposed 0 0.0 - 0.01mm 4 Undulating, very rough 8 0.01 - 1.0mm 3 Undulating, rough 6 1.0 - 5.0mm 2 Undulating, slightly rough 4 Aperture A >5mm 0 Undulating, smooth 2 None 1 Undulating, slickensided 1 0 - 1mm 4 Planar, very rough 4 1-5mm, hard 3.5 Planar, rough 3 1-5mm, soft 3 Planar, slightly rough 2 >5mm, hard 2 Planar, smooth 1 Filling F >5mm, soft 0 Roughness R Planar, slickensided 0 5.2.1.6 Basic Quality, BQ The BQ system was introduced as a “forced standard” in China in 1995 (Lin, 1998). It was developed using an extensive database of projects around China. A number of numerical analysis techniques were used to assess the data including: reliability analysis; stepwise regression (dynamic cluster analysis and expert system); and stepwise discriminative analysis (dynamic cluster analysis and expert system). The final equation chosen to represent a rock mass is shown below. 2 2 9786 . 276 0492 . 1 0064 . 0 1130 . 546 9212 . 1 0451 . 41 v v c c v c K K K BQ − + − + + − = σ σ σ (5.12) where, velocity seismic intact velocity seismic insitu = v K σ c = unconfined compressive strength of the intact rock Empirical Rock Slope Design Page 5.18 Although this equation is called “precise” it should be noted that other parameters were found to have some importance including rock unit weight and average defect spacing. There is also no statistical data presented to support the formula. Table 5.11 shows the rock classes. There are no correlations to rock mass properties provided in the paper. Table 5.11. The basic quality, BQ, rock mass classes (Lin, 1998) Empirical Rock Slope Design Page 5.19 5.2.2 Adjustment Factors to basic rock mass ratings Most of the empirical rating methods apply adjustment factors to their basic rock mass rating. These adjustment factors account for such things as defect orientation, excavation method, weathering, induced stresses and major planes of weakness. Bieniawski (1976 and 1989) applies the adjustments by subtracting them from the rock mass rating. Table 5.1 shows that the defect orientation adjustment can dominate the RMR. If the defect orientations are deemed “very unfavourable” an adjustment of -60 is required to the basic rock mass rating. Even for defect orientations denoted as “fair” this adjustment is -25. There is no guideline as to what “very unfavourable” means. Bieniawski (1989) recommends the use of the Romana (1985) SMR corrections for slopes. Romana used the same basic rock mass rating as RMR 89 but developed new adjustment factors for joint orientation and blasting to account for the lack of guidelines in the RMR methods. The equation for SMR is shown below. The joint orientation weighting includes a factor for the difference between joint dip and slope angle, F 3 . This requires an iterative approach for design. Table 5.12 and Table 5.13 show the adjustment ratings. 4 3 2 1 89 F F F F RMR SMR + − = (5.13) Romana (1985) developed his factors not only for rock mass failures but also for wedge and planar failure. A rock mass rating method should not be used for these two cases as they are defect controlled and can be assessed using such measures as stereographic projection. Even if the method was applicable, the ratings for planar failure are questionable. F 2 depends on defect dip and must account for the defect shear strength however, the method seems to assume that friction angles are quite high. For example, bedding surface shears may attain strengths of φ′ below 12° yet these would be given a ‘very favourable’ rating of 0.15. Empirical Rock Slope Design Page 5.20 Table 5.12. Adjustment rating for joints (after Romana, 1985) Case Very Favourable Favourable Fair Unfavourable Very unfavourable P s j α α − T o 180 − − s j α α >30° 30°-20° 20°-10° 10°-5° <5° P/T ( ) 2 1 sin 1 s j F α α − − = 0.15 0.4 0.7 0.85 1.00 P j β <20° 20°-30° 30°-35° 35°-45° >45° P j F β 2 2 tan = 0.15 0.4 0.7 0.85 1.00 T F 2 1.00 1.00 1.00 1.00 1.00 P s j β β − >10° 10°-0° 0° 0°-(-10°) <-10° T s j β β − <110° 110°-120° >120° - - P/T F 3 0 -6 -25 -50 -60 P - Planar failure α s - Slope dip direction α j - Defect dip direction T - Toppling failure β s - Slope dip β j - Defect dip Table 5.13. Adjustment Rating for methods of excavation of slopes (after Romana, 1985) Method Natural Slope Presplitting Smooth Blasting Blasting or Mechanical Defficient Blasting F 4 +15 +10 +8 0 -8 Figure 5.3 shows the problem with attempting to predict structurally controlled failures with rock mass ratings. The example shows a defect dipping out of the slope at 60°. The dip direction is within 15° of the dip direction of the slope. The intact rock has a high strength and there are no other defects. The defect shown is unweathered, fairly tight and slightly rough. By inspection, this is an unstable slope however, the SMR rates it as ‘II Good’ (Table 5.14). Empirical Rock Slope Design Page 5.21 Table 5.14. Tentative description of SMR classes (after Romana, 1985) SMR 0-20 21-40 41-60 61-80 81-100 Class V IV III II I Description Very Bad Bad Normal Good Very Good Stability Completely Unstable Unstable Partially Stable Stable Completely Stable Failures Big planar or soil like Planar or big wedges Some joints or many wedges Some blocks None Support Reexcavation Important/ Corrective Systematic Occasional None Figure 5.3. Example of Planar Failure Case with High SMR The CSMR method (Chen, 1995) is based on the SMR method. The CSMR applies a discontinuity condition factor, λ, that describes the conditions of the controlling discontinuity on which the ratings F 1 , F 2 and F 3 are based (Table 5.15). This factor ranges from 0.7 to 1.0. The CSMR method also assumes that the SMR method is applicable for a slope height of 80m but must be adjusted for other slope heights, H, using the slope height factor, ξ. The relationship for ξ, based on an extensive survey and rigorous analysis of slopes in China, is shown in Figure 5.4. With the addition of the two new factors, the equation for CSMR is defined as: 4 3 2 1 76 F F F F RMR CSMR + × − × = λ ξ (5.14) 60° UCS rating = 15 (300MPa) RQD rating = 20 (100%) Spacing rating = 20 (> 2m) Condition rating = 25 Groundwater rating = 15 (dry) F 1 = 0.7 (15°) F 2 = 1.0 F 3 = -60 F 4 = +10 (presplitting) SMR = 63 Empirical Rock Slope Design Page 5.22 H 4 . 34 57 . 0 + = ξ (5.15) where, H = Slope height in metres Table 5.15. Discontinuity condition factor λ (Chen, 1995) λ Defect Condition 1.0 Faults, long weak seams filled with clay 0.8 to 0.9 Bedding planes, large scale joints with gouges 0.7 Joints, tightly interlocked bedding planes 0 2 4 6 8 10 1 10 100 1000 H (m) ξ Figure 5.4. Slope height, H, vs slope height factor, ξ (after Chen, 1995) The CSMR has been based on the SMR and thus has similar problems. CSMR acknowledges the affect of slope height. It is the authors view that height should not be grouped with the rock mass rating (a defacto strength estimate) but should be addressed during the stability analysis where it will contribute to the stresses acting. Laubscher (1977) adjusts his MRMR for weathering; field and induced stresses; change in stress due to mining; orientation and type of excavation with respect to geological structures; and blasting effects. The multipliers were developed primarily for underground excavations but are also used for slopes. Empirical Rock Slope Design Page 5.23 Ünal (1996) uses corrections for weathering, blasting and major planes of weakness. Table 5.16 and Table 5.17 show the adjustment factors A b and A w for blasting and major planes of weakness respectively. ( ) ( ) JO GW JS JC RQD UCS c w b I I I I I I F A A RMR M + + + + + = - (5.16) Table 5.16. Blasting adjustment, A b (Ünal, 1996) No blasting 1.0 Smooth blasting 0.95 Fair blasting 0.90 Poor blasting 0.85 Very poor blasting 0.80 Table 5.17. Major plane of weakness adjustment, A w (Ünal, 1996) No major weakness zones 1.0 Stiff dykes 0.90 Soft ore zones 0.85 Host rock/ore contact zones 0.80 Folds; synclines; anticlines 0.75 Discrete fault zones 0.70 It is not understood why the RQD rating is adjusted for weathering whilst the joint spacing rating is not. It is felt that ideally A w should not be used in a rock mass classification system for slopes. If major planes of weakness exist they should be considered individually during the analysis phase. MRMR, RMS and M-RMR contain an adjustment for weathering. The author believes that weathering should not be used as an adjustment factor in the estimation of rock mass strength. The effect of weathering is to alter the intact strength and defect condition parameters over geological time. ‘Present day’ weathering condition should already have been accounted for in the strength of the rock substance. Where further weathering may be expected within the design life of a slope, the parameters for intact strength and defect condition could be adjusted. However, the extent of these effects needs to take into account the scale of influences versus the scale of the slope. That is, surficial weathering Empirical Rock Slope Design Page 5.24 may not extend into the slope to such a degree as to affect the strength of the rock mass along the shear failure surface. The excavation method adjustment (MRMR, SMR, CSMR and M-RMR) was originally designed for support of underground excavations where it has obvious implications. The method of excavation may affect low height slopes, however large slopes are unlikely to be affected by blasting (with regard to rock mass failure). The author believes that the rock mass involved in the failure is usually remote to the region affected by blasting. Blasting may affect the stability of benches. However, failures of slopes of this scale can be expected to be caused by failure along structure and not through rock mass due to the low stresses acting. Hoek et al (2002) suggest that destressing can have a significant affect on the strength of rock masses for slopes. Where blasting or destressing is believed to have affected the rock mass to a large degree, then these affects should be accounted for in the assigning of weightings for block size (smaller) and joint condition (persistence and aperture) and not as an adjustment factor. The author believes that the best currently available rock mass rating for slope design is the GSI (Hoek et al, 1995). The GSI is relatively simple to use and accounts for the major factors that affect rock mass strength (block size and strength and defect condition). Reducing the GSI can incorporate affects due to destressing and blasting. The effect of groundwater should be included in the analysis as a stress and the effect of major structures should be analysed separately. Empirical Rock Slope Design Page 5.25 5.3 A REVIEW OF SLOPE DESIGN METHODS WHICH ARE BASED ON ROCK MASS RATINGS 5.3.1 Correlations with Shear Strength Parameters and Slope Angles Bieniawski (1976) and Robertson (1988) provided estimates of cohesion and friction angle values for different RMR and SRMR ranges respectively that could be used for slope stability analysis. Robertson’s (1988) shear strength correlations (Table 5.8) were based on the back analysis of failed slopes in weak rock masses at two mine sites. Bieniawski’s (1976) shear strength correlations (Table 5.18) were based on experience working with underground excavations, slopes and foundations. Cited published case studies included: a cable jacking test in highly weathered to friable gneiss and schist bedrock (Pells, 1975); a 50m high toppling slope failure induced by base shearing through weak decomposed amphibolite; and slopes (stable and one failure) consisting of dolerite, shale and melaphyre (Bieniawski, 1975). The cases reported comprised failures in very poor quality rock masses. Table 5.18. Rock mass properties for RMR 76 (Bieniawski, 1976) RMR 76 <20 21-40 41-60 61-80 81-100 Rock mass cohesion (kPa) <100 100-150 150-200 200-300 >300 Rock mass friction angle (°) <30 30-35 35-40 40-45 >45 Laubscher (1977) presents a table of stable slope angles versus MRMR independent of slope height (Table 5.19). These slope angles were based on Laubscher’s 20 years of experience working predominately in metamorphic and volcanic rocks of varying quality, taking in the whole range of possible MRMR values. Laubscher (1977) mentions an example of a pit slope with MRMR of 12 that failed at a slope angle of 45°. A stable slope angle was found at 35°, which corresponds with the value in Table 5.19. No information with regard to the slope’s height, geology or failure mode was provided. Empirical Rock Slope Design Page 5.26 Table 5.19. Stable slope angle versus MRMR (Laubscher, 1977) MRMR 81-100 61-80 41-60 21-40 0-20 Slope Angle ±75 ±65 ±55 ±45 ±35 Abrahams and Parsons (1987) performed a statistical analysis of Selby’s RMS data and developed the following relationship: ( ) 072 . 141 681 . 2 degrees − = RMS Angle Slope Stable (5.17) The data has a narrow spread of RMS (approximately 55 to 90) and yet, the slope angles predicted by the equation range from approximately 5° to 90° for their RMS data. The line of best fit to Selby’s data indicates a slope angle of -74° for a “very weak” rock mass (RMS=25). This is not meaningful and is likely due to the lack of “weak” and “very weak” rock masses (RMS<50) in the data. Selby (1980) divided the slopes he assessed into sections of similar geology, generally with slope heights less than 40m. This resulted in short lengths of slopes under different stresses being compared. Slope angles for low slope heights are likely to be governed by the dip of defects and less so the strength of rock mass where the intact rock strength is high enough to prevent intact rock failure. These aspects may account for some of the scatter in the data and subsequent poor statistical results. Orr (1992) proposed the following relationship between RMR (converted from RMS) and slope angle as the limit of long term stability, using the data on Figure 5.5. Orr (1992) states that the equation is for slopes up to 50m high and with RMR values of between 20 and 77. ( ) 71 ln 35 angle Slope − = RMR (5.18) Empirical Rock Slope Design Page 5.27 Figure 5.5. RMR versus slope angle (Orr, 1996) Romana (1985) correlated SMR with stability class. Of the 28 slopes (ignoring the six toppling failures) presented by Romana (1985) only six had failed and only one of those was a rock mass failure (“soil like failure”), the others were planar or wedge failures (Table 5.20). The highest known slopes tested against SMR by Romana were up to 62m in calcareous slopes and all were stable or partially stable (Jordá et al., 1999). Slope heights less than 40m are invariably controlled by structure (Duran and Douglas, 1999) and hence there is very little if any published rock mass failure data supporting the Romana (1985) SMR correlation. Empirical Rock Slope Design Page 5.28 Table 5.20. Case records for SMR (after Romana, 1985) Rock Excavation method SMR Failures Limestone Presplitting 85 None Sandy marl Natural slope 84 None Limestone Presplitting 77 3 small blocks Gneiss Presplitting 72-75 Small wedges during construction Limestone Blasting 74 None Dolestone Blasting 64-76 Small planes during construction Limestone Smooth blasting 61-73 None Marl Smooth blasting 71 None Limestone Blasting 70 Small blocks Sandstone/Siltstone Natural slope 68 Small blocks Limestone Deficient blasting 59 Many blocks Marl/Limestone Mechanical excavation 55 “Local problems” Gypsum rock Natural slope 52 Some wedges (1m 3 ) Claystone/Sandstone Blasting 47 Big wedge (15m 3 ) Claystone Mechanical excavation 46 Surface erosion Sandstone/Marl Blasting 43 Many wedges Limestone Deficient blasting 40 Many failures Gypsum Rock Natural slope 31-43 Big wedge (100m 3 ) Sandy marl Mechanical excavation 32 Blocks, mud flows Sandstone/Marl Blasting 30 Big planar failure during construction Limestone Blasting 29 Several wedges (50m 3 ) Marl Smooth blasting 36 Almost total planar failure after weathering Volcanic tuff/Diabase Blasting 30 Big planar failure Marl Blasting 16 Total planar failure after weathering Marl Blasting 42 Small wedges Marl Blasting 17 Total planar failure after weathering Marl Blasting 43 Small wedges Slate/Greywacke Mechanical excavation 17 Soil like failure The CSMR uses the same stability class correlation as SMR. Figure 5.6 shows correlations between observed behaviour (ESMR) and SMR and CSMR for 44 slopes with heights ranging from 8 to 42m. Chen (1995) uses a similar method proposed by Collado and Gili (1988) to determine ESMR. The ESMR is derived from estimates of the factor of safety from field engineers and the following empirical equation: Empirical Rock Slope Design Page 5.29 15 . 0 5 . 52 100 − − = F ESMR where, F = Factor of safety All points falling on the 45° line would represent a good correlation. Although the CSMR has slightly less scatter than the SMR, both methods can be seen to have a poor correlation. Figure 5.6. Observed cases (ESMR) vs (a) SMR, (b) CSMR (Chen, 1995) Moon et al (2001) found that rock mass classification techniques (RMR, SMR and RMS), used for slope angle estimation, perform poorly for weak rock masses where failure occurs through intact rock, rather than solely along defects. Empirical Rock Slope Design Page 5.30 Tsiambaos & Telli (1991) compare the RMR and SMR systems for limestone slopes. They found that the RMR system leads to an underestimation of the stability conditions (i.e. the actual rock conditions are better than predicted) of limestone cuts whilst the SMR was a better predictor. It should be noted that the only stability problems the slopes had were rock falls that were structurally controlled. Of the methods presented, Robertson’s (1988) approach has the most merit as it was developed specifically for slopes and is based on slope failures in weak rock masses. Unfortunately, only two slopes have been used and hence c′ and φ′ values are only available for two specific rock masses. Other methods presented have limited value as they are based on either long-term natural slopes that are often structurally controlled; stable slopes; or slopes of only limited height. 5.3.2 Available Slope Performance Curves Slope performance curves provide a valuable tool in the design process where rock mass failure plays a strong control in the stability of slopes. The curves are derived from the performance of stable and unstable slopes plotted on a slope angle versus slope height plot. The curves are often site specific and take into account the impact of existing failures, the remaining time frame for mining and the acceptable risks to the mining operation. Extending slope design curves from being a site specific tool to a general tool must be treated with caution. Early attempts at doing this include Lane (1961) and Fleming et al (1970 for slopes in shale, Coates et al (1963) for “incompetent rock” slopes, Shuk (1965) for natural slopes, Lutton (1970) and Hoek (1970) for general rock excavations. Hoek and Bray (1981) present a collection of data, from mines, quarries, dam foundation excavations and highway cuts, on stable and unstable slopes in hard rock (Figure 5.7). The plot also shows a curve representing the highest and steepest slopes that have successfully been excavated in hard rock (note that many failures have occurred in flatter slopes). This line can therefore be used as a guide as to the upper bound heights and slope angles that can be considered in slope design. Empirical Rock Slope Design Page 5.31 McMahon (1976) attempted to group similar rock masses together and came up with correlations (based on log-log graphs) relating slope length, L, with slope height, H (Equations 5.19 and 5.20 and Table 5.21). b aL H = (5.19) ( ) angle slope tan H L = (5.20) Figure 5.7. Upper bound slope height versus slope angle curve for rock masses (Hoek & Bray, 1981) Empirical Rock Slope Design Page 5.32 Table 5.21. Parameters for McMahon’s (1976) slope relationship Rock mass type a B Massive granite with few joints 139 0.28 Horizontally layered sandstone 85 0.42 Strong but jointed granite and gneiss 45 0.47 Jointed partially altered crystalline rocks 16 0.58 Stable shales 8.5 0.62 Swelling shales 2.4 0.75 Figure 5.8 shows the data from McMahon (1976) replotted on a slope height versus slope angle curve. The relationships from Table 5.21 are also plotted on the graph. It can be seen from the figure that the relationships provide a poor fit to a lot of the data, particularly the stronger rock masses. The curves also tend toward about 10° which is not supported by the data. It should also be noted that only the data for shale was near limit equilibrium and so the curves for the other rock mass types represent conservative (by an unknown amount) boundaries. Haines and Terbrugge (1991) took this technique further and tried to correlate slope design curves with rock mass ratings. The Haines and Terbrugge (1991) slope design methodology makes use of the MRMR empirical rock mass strength assessment as presented by Laubscher (1977 and 1990). The slope design methodology is presented in Figure 5.9 and again in Figure 5.10, replotted on the basis of slope angle versus slope height and with contours of MRMR presented. Haines & Terbrugge (1991) divide the graph into three design zones where: (1) classification alone may be adequate; (2) marginal on classification alone; and (3) slopes require additional analysis. Empirical Rock Slope Design Page 5.33 0 500 1000 1500 2000 2500 3000 0 10 20 30 40 50 60 70 80 90 Slope angle H e i g h t ( m ) . Massive granite with few joints Horizontally bedded sandstones Strong but jointed granite and gneiss Jointed partially altered rocks Horizontally bedded stable shales Swelling shales Clay shale Jointed & altered Sandstone and shale strong granite and gneiss Figure 5.8. Slope angle versus slope height with regression curves (modified after McMahon, 1976) Case studies were utilised by Haines & Terbrugge (1991) to evaluate the design curves. It is noted that several of the cases presented related to slopes for feasibility studies that had at the time not been excavated. The cases of excavated slopes have been presented in Figure 5.10. The MRMR values, grouped into intervals, are presented by the use of different symbols. Three aspects of the Haines & Terbrugge (1991) design curves are of concern: Empirical Rock Slope Design Page 5.34 Firstly, the data does not appear to indicate the validity of the design curves presented. Vertical design lines could have been equally appropriate, i.e. independent of slope height. This is in keeping with the use of MRMR for open pit slopes, as originally proposed by Laubscher (1977), shown in Table 5.19. Secondly, the shape of the interpreted design curves does not appear valid. The curves are broadly convex in shape and nearly linear for slope heights of up to 100m. This is at odds with the wide body of experience, which suggests a concave shape is appropriate. In addition, the experience presented in Figure 5.11 suggests a predominant curvature would be expected for slope heights up to 100m. Finally, the curves are not asymptotic and indicate a continuing reduction in slope angle with slope height is required. Thirdly, none of the case studies presented by Haines & Terbrugge (1991) related to unstable slopes. Moreover, a third of the cases related to road cuttings where typically a high degree of conservatism is utilised. As such the design curves have a large element of conservatism built into them. Figure 5.9. Slope height vs slope angle for MRMR (Haines & Terbrugge, 1991) Empirical Rock Slope Design Page 5.35 20 40 60 80 100 0 50 100 150 200 250 20 30 40 50 60 70 Slope angle (deg) S l o p e H e i g h t ( m ) . 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Classification alone may be adequate Marginal on classification alone Slopes require additional analysis MRMR MRMR Values Figure 5.10. Haines & Terbrugge (1991) slope design replotted on basis of slope angle versus slope height showing Haines & Terbrugge (1991) slope data. Empirical Rock Slope Design Page 5.36 5.3.3 Pells Sullivan Meynink Slope Performance Curves Through the utilisation of aggressive designs within interim pits and documentation of stable and failed slopes, slope performance curves have been established at several mining operations by Pells Sullivan Meynink Pty Ltd, consulting geotechnical engineers and engineering geologists, to aid in the slope design process. They indicate that the methodology has been of enormous benefit in slope design for mining operations where multiple open pits are developed in similar geotechnical conditions, a poor rock mass is present and rock mass failures have been the predominant control on slope stability. Figure 5.11 presents six case studies where slope performance curves were developed on the basis of the site specific stability. Pells Sullivan Meynink (pers. com. Alex Duran) indicate that the methodology has been of particular use in operations where multiple shallow pits have been developed and where no geotechnical studies were available. Although these curves are not presented the shapes of the curves are in keeping with those presented in Figure 5.11. Three key regions can be defined on the slope performance curves in Figure 5.11. The three regions and the division within the slope angle versus slope height plot are in keeping with typical rock mass strengths for poor quality rock masses and the concept of a curved strength envelope. Region 1: Typically negligible rock mass failures occur for slope heights of less than 40m. This is in keeping with findings of a survey of 54 mining operations which indicated generally stable pits for slope heights less than 45m (Swindells, 1990). This is anticipated since for these heights, i.e. low stress levels, rock mass strengths typically have a high friction angle. Typical slip-circle analyses indicate steep slopes can be achieved for these slope heights. The experience of the author and that of Pells Sullivan Meynink personnel indicates unstable slopes in Region 1 are invariably controlled by structure except where very poor rock mass conditions are encountered. Empirical Rock Slope Design Page 5.37 Figure 5.11. Slope performance curves for case studies (Duran & Douglas, 1999) 0 50 100 150 200 250 20 30 40 50 60 70 Slope angle (deg) S l o p e H e i g h t ( m ) . Case 1 Case 2 Case 3 Case 4 Case 6 Case 9 1 2 3 4 6 9 After Figure 7, Hoek & Bray (1981) Numbers refer to cases in Table 2 Solid symbols represent unstable slopes Upper bound from Hoek & Bray (1981) – see Figure 5.7 Slope performance curves Numbers refer to cases in Table 5.22 Solid symbols represent unstable slopes as does the symbol x Empirical Rock Slope Design Page 5.38 Region 2: For slopes above 40m in height rock mass failures become apparent in poor quality rock masses. The design curves display a pronounced concave curvature with a reduction in the overall slope angle for increasing slope height. This curvature is in keeping with that indicated by Hoek & Bray (1981) and with typical slip circle analyses. The curvature of the design curves conform to a curved rock mass strength envelope. Back analyses indicate the use of a fixed friction angle and cohesion provides a poor fit. Whilst back analyses using a decreasing friction angle and increasing cohesion, with increasing slope height (i.e. increasing stress level), provides a better fit to the curves. It should be noted the design curves are roughly sub-parallel and with curves further to the right representing better rock mass conditions. Region 3: For slope heights above 90m the curves show a trend of becoming asymptotic to a given slope angle. This is in keeping with the fact that at higher stress levels the curved envelope approaches a straight line and a constant friction angle is implied. Empirical Rock Slope Design Page 5.39 5.4 ANALYSIS OF CASE STUDY DATA 5.4.1 Case Studies Used Table 5.22 summarises the case studies that were made available to the author by Pells Sullivan Meynink Pty Ltd. Each ‘case’ represents a particular open pit mine. Each mine may have several stable/unstable slopes in the database. Where this situation exists the different slopes are denoted a, b, c etc. Case 5 was obtained separately from Glastonbury (2002). A total of 13 cases with 37 slopes, of which 21 were stable and 16 had failed, was made available. All failures were considered to have had a rock mass failure component. Table 5.22. Summary of slope data from case studies Geology Mine Case Height (m) Slope angle (°) MRMR interval GSI interval Water Stable Saprolite/Basalt 1a 70 49 20-30 40-50 none yes Saprolite/Basalt 1b 41 50 20-30 40-50 none no Saprolite/Basalt 1c 41 55 20-30 40-50 none no Saprolite/Basalt 1d 46 55 20-30 40-50 none no Saprolite/Basalt 1e 57 49 20-30 40-50 none no Saprolite/Basalt 2a 58 50 30-40 50-60 none yes Saprolite/Basalt 2b 60 48 30-40 50-60 none yes Saprolite/Basalt 2c 60 52 30-40 50-60 none yes Volcanoclastics 3a 20 39 10-20 30-40 mod no Volcanoclastics 3b 40 32 10-20 30-40 mod yes Volcanoclastics 3c 60 31 10-20 30-40 mod yes Talc chlorite schist 4a 70 44 30-40 40-50 mod no Talc chlorite schist 4b 120 35 30-40 40-50 mod no Talc chlorite schist 4c 120 38 30-40 40-50 mod no Talc chlorite schist 4d 150 31 30-40 40-50 mod yes Talc chlorite schist 4e 150 35 30-40 40-50 mod yes Argillite 5a 250 42 30-40 50-60 mod no Empirical Rock Slope Design Page 5.40 Table 5.22. Summary of slope data from case studies (cont.) Geology Mine Case Height (m) Slope angle (°) MRMR interval GSI interval Water Stable Argillite 5b 107 37 30-40 50-60 mod yes Argillite 5c 80 38 30-40 50-60 mod yes Schist 6a 70 45 20-30 40-50 mod no Schist 6b 95 45 20-30 40-50 mod no Mudstone/siltstone 7 38 39 40-50 50-60 none yes Breccia 8 200 65 60-70 70-80 none yes Faulted breccia 9a 78 32 20-30 40-50 high yes Faulted breccia 9b 50 34 20-30 40-50 high yes Faulted breccia 9c 77 37 20-30 40-50 high no Faulted breccia 9d 60 40 20-30 40-50 high no Sheared siltstone 10a 97 36 20-30 40-50 mod yes Siltstone 10b 157 48 50-60 60-70 none yes Siltstone 10c 60 53 50-60 60-70 none yes Siltstone 11 110 48 30-40 40-50 none no Shale 12a 29 39 10-20 30-40 mod yes Shale 12b 37 28 10-20 30-40 mod yes Shale 12c 30 40 10-20 30-40 mod no Shale 12d 45 26 10-20 30-40 mod no Granodiorite breccia 13a 40 75 50-60 70-80 none yes Granodiorite breccia 13b 90 80 50-60 70-80 none yes 5.4.2 Correlations of MRMR, SRMR and RMS with GSI Data from 12 of the case studies have been used to provide correlation’s between three rating methods (MRMR, SRMR and RMS) and GSI (Table 5.23 and Figure 5.12). The data from Selby (1980) has also been used for the correlation between RMS and GSI and is plotted on Figure 5.12. Table 5.24 and Table 5.25 show the data used to determine the GSI for the case studies. Table 5.26, Table 5.27 and Table 5.28 show the data used to determine the MRMR, Empirical Rock Slope Design Page 5.41 SRMR, and RMS for the case studies respectively. Best estimate data was used for all case studies and interpolation used to choose ratings for each parameter. Some assumptions were made in assessing SRMR for the author’s case studies, based on the intact strength and character of borehole core, to assess handled RQD and spacing. Table 5.23. Correlation between rating methods – author’s case studies MINE CASE Rock Unit GSI MRMR SRMR RMS 1 Saprolite/Basalt 41 22 42 58 2 Saprolite/Basalt 52 36 49 74 3 Volcanoclastics 37 15 35 59 4 Talc chlorite schists 45 30 47 69 6 Schist 44 22 45 51 7 Mudstone/Siltstone 57 43 49 76 8 Breccia 76 65 97 98 9 Faulted breccia 49 24 57 71 10a Sheared siltstone 48 24 51 54 10c Siltstone 68 54 63 80 11 Siltstone 46 35 55 63 12 Shale 39 18 41 52 13 Granodiorite breccia 73 55 83 85 GSI was chosen since it provides a measure of the basic rock mass quality. Correlation with the other rating systems was not considered appropriate in view of the rating adjustments required. The correlations exhibit a good fit, even though there is limited data for the correlations with MRMR and SRMR. Empirical Rock Slope Design Page 5.42 GSI = 0.78MRMR + 25.22 R 2 = 0.94 GSI = 0.67SRMR + 15.10 R 2 = 0.84 GSI = 1.07RMS - 22.39 R 2 = 0.82 0 20 40 60 80 100 0 20 40 60 80 100 Rating G S I MRMR SRMR RMS Figure 5.12. Correlations of GSI with MRMR, SRMR, RMS rating (mod. Duran and Douglas, 2002). Empirical Rock Slope Design Page 5.43 Table 5.24. Summary of best estimate GSI data for mine cases MINE CASE Rock Unit UCS RQD Spacing Defect Condition GSI value 3MPa 46% 0.6m Table 5.25 1 a-e Saprolite/ Basalt rating 1.3 9.3 11.2 9.8 41 value 5MPa 56% 2m Table 5.25 2 a-c Saprolite/ Basalt rating 1.5 11 20 9.7 52 value 13MPa 45% 0.1m Table 5.25 3 a-c Volcanoclastics rating 2.2 9.1 6.1 9.6 37 value 30MPa 25% 1m Table 5.25 4 a-e Talc chlorite schists rating 3.8 6.1 14.6 11.1 45 value 12MPa 65% 0.1m Table 5.25 6 a-b Schist rating 2.1 12.6 6.1 12.6 44 value 5MPa 75% 1m Table 5.25 7 Mudstone/ Siltstone rating 1.5 14.6 14.6 16.7 57 value 150MPa 98% 5m Table 5.25 8 Breccia rating 11.4 19.5 11.8 23.3 76 value 60MPa 50% 0.5m Table 5.25 9 a-d Faulted breccia rating 6.4 9.9 10.3 12.8 49 value 23MPa 90% 2m Table 5.25 10 a Sheared siltstone rating 3.1 17.7 20 16.7 68 value 23MPa 70% 0.5m Table 5.25 10 b-c Siltstone rating 3.1 13.6 10.3 10.8 48 value 11 Siltstone rating RMR from Q = 1.3 and 44 ln 9 + = Q RMR 46 value 18MPa 40% 0.1m Table 5.25 12 a-d Shale rating 2.7 8.3 6.1 12.1 39 Empirical Rock Slope Design Page 5.44 Table 5.25. Summary of defect condition for GSI MINE CASE Rock Unit Length (m) Separation (mm) Roughness Infilling Weathering 1 Saprolite/Basalt 5 0-1 smooth soft High 2 Saprolite/Basalt 5 0-1 smooth soft High 3 Volcanoclastics 20 0-1 slickensided soft moderate 4 Talc chlorite schists 10 1-5 smooth soft fresh 6 Schist 20 1-5 smooth hard fresh 7 Mudstone/Siltstone 5 0-1 smooth hard fresh 8 Breccia 2 <1 rough hard fresh 9 Faulted breccia 15 1-5 slightly rough soft fresh 10a Sheared siltstone 15 1-5 smooth soft fresh 10c Siltstone 5 0-1 smooth hard fresh 11 Siltstone 12 Shale 10 1-5 slightly rough hard moderate Page 5.45 Table 5.26. Summary of best estimate of Laubscher’s MRMR data for mine cases Adjustments Mine Case UCS RQD Defect set spacing Defect condition * RMR Weathering Orientation Blasting MRMR 3MPa 46% 0.6m/0.8m/5m wavy/smooth undulose/soft medium slight 1 year poor good conventional 1 1 8 15 13 37 0.9 0.75 0.9 22 5MPa 56% 2m/5m/10m curved/smooth undulose/soft medium slight 4 years good good conventional 2 2 10 22 11 45 0.96 0.9 0.92 36 13MPa 45% 0.1m/2m/5m straight/smooth planar/soft medium slight 1 year topple poor 3 3 8 12 8 31 0.9 0.65 0.85 15 30MPa 25% 1m/2m/5m slight undulating/slickensided undulose/soft fine nil poor fair 4 4 12 18 9 43 1 0.8 0.88 30 12MPa 65% 0.1m/2m/2m slight undulating/smooth-rough planar/non soft med nil very poor fair conventional 6 3 10 11 11 35 1 0.7 0.9 22 5MPa 75% 1m/5m/5m straight/rough planar/no filling nil good good conventional 7 1.5 12 21 17 51 1 0.9 0.94 43 150MPa 98% 5m/5m/5m slight undulating/rough undulose/non soft medium nil good good conventional 8 16 15 25 20 76 1 0.9 0.94 65 60MPa 50% 0.5m/2m/5m straight/smooth to rough/gouge nil fair poor 9 6 8 16 3 33 1 0.85 0.85 24 Page 5.46 Table 5.26. Summary of best estimate of Laubscher’s MRMR data for mine cases (cont.) Adjustments Mine Case UCS RQD Defect set spacing Defect condition * RMR Weathering Orientation Blasting MRMR 23MPa 70% 0.5m/0.8m/1m curved/slickensided undulose/non soft medium nil very poor poor 10a 3 10 11 16 40 1 0.7 0.85 24 23MPa 90% 2m/2m/5m curved/smooth stepped/non soft coarse nil very good pre-split 10b,c 3.5 14 20 22 59 1 0.95 0.97 54 nil fair fair conventional 11 RMR from Q = 1.3 and 44 ln 9 + = Q RMR 46 1 0.85 0.9 35 18MPa 40% 0.1m/2m/5m slight undulating/smooth-rough, planar/hard med. nil topple poor 12 3 6 12 11 32 1 0.65 0.85 18 * large scale/small scale/infilling Page 5.47 Table 5.27. Summary of best estimate of SRMR data for mine cases Mine Case Rock unit UCS Handled RQD Spacing Defect Condition SRMR value 3MPa 34.50% 0.3 to 0.4m R1 1 Saprolite/Basalt rating 15 7 10 10 42 value 5MPa 28% 1 to 2m R1 2 Saprolite/Basalt rating 15 8.5 15 10 49 value 13MPa 22.50% 0.08m schist R1 3 Volcanoclastics rating 15 3 7 10 35 value 30MPa 25% 1 to 2m R2, Slickensided surfaces 4 Talc chlorite schists rating 19 3 15 10 47 value 12MPa 48.75% 0.08m schist R1 6 Schist rating 17 10.5 7 10 45 value 5MPa 37.50% 0.5 to 2m R1 7 Mudstone/Siltstone rating 16 8 15 10 49 value 150MPa 98% 5 R4, rough, not continuous 8 Breccia rating 27 20 20 30 97 value 60MPa 40% 0.5 to 2m R3, slightly rough - gouge 9 Faulted breccia rating 22 8 15 12 57 Page 5.48 Table 5.27. Summary of best estimate of SRMR data for mine cases (cont.) Mine Case Rock unit UCS Handled RQD Spacing Defect Condition SRMR value 23MPa 52.50% 0.4 to 0.6m R1 10a Sheared siltstone rating 19 10.5 11 10 51 value 23MPa 90% 2 R1 10b,c Siltstone rating 19 18.5 15 10 63 value 11 Siltstone rating SRMR estimated using MRMR and multiplying by average SRMR/MRMR ratio for all cases (=1.2) 55 value 18MPa 30% 0.08 to 0.5m R1 12 Shale rating 17 6 8 10 41 Page 5.49 Table 5.28. Summary of best estimate of RMS data for mine cases Defect Mine Case Rock unit UCS Weathering Spacing Orientation Aperture Length Water RMS value 3MPa high 0.6m unfavourable 0-1mm 5m none 1 Saprolite/Basalt rating 5 5 21 9 6 6 6 58 value 5MPa high 2m favourable 0-1mm 5m none 2 Saprolite/Basalt rating 5 5 28 18 6 6 6 74 value 13MPa moderate 0.1m favourable 0-1mm 20m slight 3 Volcanoclastics rating 5 7 15 18 6 4 4 59 value 30MPa fresh 1m unfavourable 1-5mm 10m slight 4 Talc chlorite schists rating 10 10 25 9 5 6 4 69 value 12MPa fresh 0.1m unfavourable 1-5mm 20m mod 6 Schist rating 5 10 15 9 5 4 3 51 value 5MPa fresh 1m very favourable 0-1mm 5m trace 7 Mudstone/Siltstone rating 5 10 25 20 6 5 5 76 value 150MPa fresh 5m very favourable <1mm 2m none 8 Breccia rating 18 10 30 20 7 7 6 98 value 60MPa fresh 0.5m fair 1-5mm 15m moderate 9 Faulted breccia rating 14 10 21 14 5 4 3 71 Page 5.50 Table 5.28. Summary of best estimate of RMS data for mine cases (cont.) Defect Mine Case Rock unit UCS Weathering Spacing Orientation Aperture Length Water RMS value 23MPa fresh 0.5m very unfavourable 1 to 5mm 15m slight 10a Sheared siltstone rating 5 10 21 5 5 4 4 54 value 23MPa fresh 2m very favourable 0 to 1mm 5m trace 10b,c Siltstone rating 5 10 28 20 6 6 5 80 value 25MPa fresh 0.05-0.3m fair <1mm few none 11 Siltstone rating 5 10 15 14 7 6 6 63 value 18MPa moderate 0.1m favourable 1 to 5mm 10m mod 12 Shale rating 5 7 10 18 5 4 3 52 Empirical Rock Slope Design Page 5.51 5.4.3 General Assessment of the Parameters in GSI The GSI calculated from RMR (GSI RMR ) contains ratings for UCS, RQD, defect spacing and defect condition. This section uses the case study data to assess how well these individual ratings differentiate rock mass strength. Figure 5.13 shows GSI versus slope height for both failed and stable slopes from the case studies. A general observation shows that the failed slopes are gathered at the lower end of the ratings. Figure 5.14 to Figure 5.17 show the same graph as Figure 5.13 with defect spacing rating, defect condition rating, RQD rating and UCS rating substituted for GSI respectively. The RQD and spacing ratings (which essentially are both substitutions for block size) both appear to differentiate between the rock masses well and have the failed slopes toward the lower rating values. The defect condition rating appears to group most rock masses in the case studies together. The UCS rating does not appear to differentiate between the failed and stable slopes. This is not suprising as slope failure will generally occur along defects unless the intact rock strength is very low due to the low stress environment. 0 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 GSI Rating H ( m ) . Failed Stable Figure 5.13. GSI versus slope height for failed and stable slopes Empirical Rock Slope Design Page 5.52 0 50 100 150 200 250 0 5 10 15 20 25 30 Spacing Rating H ( m ) . Failed Stable Figure 5.14. GSI defect spacing rating versus slope height for failed and stable slopes 0 50 100 150 200 250 0 5 10 15 20 25 Defect Rating H ( m ) . Failed Stable Figure 5.15. GSI defect condition rating versus slope height for failed and stable slopes Empirical Rock Slope Design Page 5.53 0 50 100 150 200 250 0 2 4 6 8 10 12 14 16 18 20 RQD Rating H ( m ) . Failed Stable Figure 5.16. GSI RQD rating versus slope height for failed and stable slopes 0 50 100 150 200 250 0 2 4 6 8 10 12 14 UCS Rating H ( m ) Failed Stable Figure 5.17. GSI UCS rating versus slope height for failed and stable slopes Empirical Rock Slope Design Page 5.54 5.4.4 Development of Generalised Slope Design Curves 5.4.4.1 Use of MRMR in Haines and Terbrugge Method Table 5.22 shows the MRMR’s that have been evaluated for the case studies. Each case has been allotted into a MRMR interval owing to the uncertainties in assessing a rigorous value. The data presented by Haines & Terbrugge (1991) and the new case studies (Figure 5.10 and Table 5.22 respectively) have been combined into one database. The author (Duran & Douglas, 1999) presented cases 1-10 and the Haines & Terbrugge (1991) design methodology in Figure 5.18. Several of the cases do not confirm the Haines & Terbrugge design curves. For cases 1, 2, 6 and 8 the Haines & Terbrugge curves are conservative for these mining operations. In cases 4 and 9 however, the design curves would have indicated the use of steeper slopes. For these two latter cases there are additional factors which affected the overall stability of slopes. For case 4 structure made a significant contribution to the failure. Whilst for case 9, groundwater played a critical role. 5.4.4.2 Revised Method Using MRMR Figure 5.19 presents design curves that have been defined by the author (Duran & Douglas, 1999) on the basis of the available data. An upper bound design curve has been suggested which relates to MRMR values greater than 40. This is based on the experience of Duran & Douglas (1999) as no rock mass failures have been observed in slopes that are comprised of good, or better, rock mass quality. This observation was previously related by Robertson (1988) who indicated that stability was almost exclusively controlled by structure where MRMR was greater than 40. It must be stressed that these design curves are based on slopes in mi ning operations, where some instability is acceptable and slopes need only to stand up over short time frames of up to two years. Appropriate reductions in slope angles could be utilised where a conservative design is required. Empirical Rock Slope Design Page 5.55 It should be noted that cases 4 and 9 were treated as exceptions in defining the design curves. This clearly reinforces that in the design of rock slopes there needs to be a careful assessment of the influence of structure and groundwater in defining an acceptable design. 5.4.4.3 Method Based on the Use of the Geological Strength Index, GSI The case studies discussed above together with additional data from Haines and Terbrugge (1991) and Selby (1980) have been used to create slope design curves based on GSI. Slope height versus slope angle was plotted for two ground water conditions, dry and moderate pressures. Moderate water pressures are defined as where the piezometric surface reaches the surface at a distance of 4 x the slope height. This is taken from Hoek and Bray’s (1981) circular failure slope chart No. 3. Figure 5.20 and Figure 5.22 show the data and the author’s proposed design curves for dry and moderate water pressures respectively. Where failure occurred predominantly through the rock mass the data is presented as a solid symbol. Figure 5.20 does not contain a curve for GSI = 30 due to a lack of data. It could be assumed that this curve would lie 10-15° to the right of the curve for GSI = 40 based on the curves in Figure 5.22. The slope design curves for various ranges of MRMR presented in the previous section (Figure 5.19) have been used as the basis for deriving the GSI slope design curves. These curves have been assessed for GSI values of 40 and 50, utilising the author’s correlation. The author’s design curves provide a very good fit of the data. Slope designs using strength estimates estimated by Bieniawski (1976), assuming no rating adjustment for orientation, are presented on Figure 5.21 and Figure 5.23 based on stability charts from Hoek and Bray (1981) and assuming a Factor of Safety of one. As readily evident, Bieniawski’s strength estimates are too high. Robertson (1988) provided estimates of shear strength for back-analyses of failures. Using the correlation of SRMR with GSI presented earlier, Robertson’s rock mass strengths were assessed for GSI values of 30 and 40, Figure 5.21 and Figure 5.23. Robertson (1988) suggested rock mass failure in slopes was unlikely for an SRMR of greater than 35 (GSI≈40) and this is confirmed by the data presented in Figure 5.21 and Figure 5.23. The strengths estimated by Robertson (1988), if correlated to GSI, appear to overestimate slopes angles for dry slopes. For moderate water pressures the curves are similar to the author’s curves for Empirical Rock Slope Design Page 5.56 heights greater than 150m for lower heights, the author’s curves predict flatter stable slope angles. 20 40 60 80 100 0 50 100 150 200 250 20 30 40 50 60 70 Slope angle (deg) S l o p e H e i g h t ( m ) . 0-10 10-20 20-30 30-40 40-50 50-60 60-70 MRMR Solid symbols represent unstable slopes Solid symbols represent unstable slopes as do the symbols + x Haines & Terbrugge MRMR curves Figure 5.18. Haines & Terbrugge (1991) slope design curves & slope data (Figure 5.10) with additional case studies (Duran & Douglas, 1999) Empirical Rock Slope Design Page 5.57 0 50 100 150 200 250 20 30 40 50 60 70 Slope angle (deg) S l o p e H e i g h t ( m ) . 0-10 10-20 20-30 30-40 40-50 50-60 60-70 MRMR > 40 30 20 Solid symbols represent unstable slopes MRMR = Solid symbols represent unstable slopes as do the symbols + x S S H H =Significant contribution to failure from structure. =High water pressures in slope S H Figure 5.19. Suggested slope design curves for MRMR (Duran & Douglas, 1999) Empirical Rock Slope Design Page 5.58 0 50 100 150 200 250 10 20 30 40 50 60 70 80 90 Slope Angle (deg) S l o p e H e i g h t ( m ) . 20-30 30-40 40-50 50-60 60-70 70-80 80-90 GSI GSI ≈ 40 GSI ≈ 50 Solid symbols represent unstable slopes Figure 5.20. Slope height vs slope angle case study data and the author’s proposed design curves for a dry slope Empirical Rock Slope Design Page 5.59 0 50 100 150 200 250 10 20 30 40 50 60 70 80 90 Slope Angle (deg) S l o p e H e i g h t ( m ) . 20-30 30-40 40-50 50-60 60-70 70-80 80-90 GSI GSI≈30 GSI≈40 RMR≈30 RMR<20 Robertson (1988) RMR≈50 Bieniawski (1979) Author's curves GSI≈40 GSI≈50 Solid symbols represent unstable slopes Figure 5.21. Slope height vs slope angle case study data and a comparison of design curves for a dry slope Empirical Rock Slope Design Page 5.60 0 50 100 150 200 250 10 20 30 40 50 60 70 80 90 Slope Angle (deg) S l o p e H e i g h t ( m ) . 20-30 30-40 40-50 50-60 60-70 70-80 80-90 GSI S = Solid symbols represent unstable slopes = Significant contribution to failure from structure = High water pressures in slope S H H H S GSI ≈ 30 GSI ≈ 40 GSI ≈ 50 Figure 5.22. Slope height vs slope angle case study data and the author’s proposed design curves for moderate pressures Empirical Rock Slope Design Page 5.61 0 50 100 150 200 250 10 20 30 40 50 60 70 80 90 Slope Angle (deg) S l o p e H e i g h t ( m ) . 20-30 30-40 40-50 50-60 60-70 GSI GSI ≈ 30 GSI ≈ 40 RMR ≈ 30 RMR<20 Robertson RMR ≈ 50 Bieniawski = Solid symbols represent unstable slopes = Significant contribution to failure from structure = High water pressures in slope S H H H S S Author's curves GSI ≈ 40 GSI ≈ 50 GSI ≈ 30 Figure 5.23. Slope height vs slope angle case study data and a comparison of design curves for moderate pressures Empirical Rock Slope Design Page 5.62 5.5 CONCLUSION A rock mass rating system should provide a measure of the basic quality/strength of the rock mass. Aspects such as ground water, excavation method, slope height and orientation of structure should not be included in the rock mass rating and should be taken account of during analysis. Correlation of GSI with several other rock mass ratings indicates a good correlation and would suggest GSI is an adequate indicator of basic rock mass quality for rock slopes. Slope design curves have been developed based on a number of stable and unstable open pit mine slopes. Shear strength estimates for rock slopes that were proposed by Bieniawski (1976) are too high for values of GSI below 40. The design curves using strength estimates proposed by Robertson (1988) predict steeper angles than the author’s design curves. Most slopes will be structurally controlled and therefore a rock mass rating system will not be applicable for most slope design. Empirical slope design using rock mass rating systems should only be considered for slopes in rock masses with GSI values lower than about 45 and only after any potential structurally controlled failures have been investigated. The method should only be applied at the preliminary stage or as a site specific tool to complement detailed mapping and analysis. The Shear Strength of Rock Masses Page 6.1 6 THE SHEAR STRENGTH OF ROCK MASSES 6.1 INTRODUCTION This chapter contains a discussion of current methods of predicting rock mass strength and develops modifications to the Hoek-Brown strength criterion that account for the results in the previous chapters. The author has concentrated mainly on developing the criterion for use at low confining stresses (e.g. slopes) however, the resulting criterion should be applicable for the full stress range. A rock mass criterion should only be used where “there are a sufficient number of closely spaced discontinuities that isotropic behaviour involving failure on discontinuities can be assumed” (Hoek and Brown, 1997). Such a situation for slopes is illustrated on Figure 6.1, it should be noted that the concept of closely spaced should be defined in terms of the scale of the failure surface. Figure 30 : Heavily jointed rock mass Figure 6.1. Heavily jointed rock mass Slope failures in which the failure surface is entirely through the rock mass are not common. This is due to the low stresses typically acting in a slope. Failure through the rock mass usually requires large scale (relative to the slope in question) defects concentrating stresses into regions of weak rock mass. For example a long vertical joint or subvertical fault may lead to over stressing of weak material at the toe of the slope (Figure 6.2). In this case a rock mass criterion is only applicable to the region of rock mass at the toe of the slope. The Shear Strength of Rock Masses Page 6.2 ‘long’ subvertical joint Rock mass failure at toe of slope Figure 6.2. Example of shear failure through rock mass at the toe of a slope - Nattai Escarpment Failure The Shear Strength of Rock Masses Page 6.3 6.2 ESTIMATING THE SHEAR STRENGTH OF A ROCK MASS As mine slopes become larger (stresses increasing), the necessity to account for the strength of rock masses in design increases. This section discusses different techniques to determine the strength of a rock mass. 6.2.1 Predicting Rock Mass Strength from Discontinuities Initial methods of determining the shear strength of rock mass relied on using intact and rock joint strengths. This section briefly describes current methods for estimating rock joint strengths and the problems with extending these for use with rock masses. The two most commonly used approaches to estimating discontinuity strength are those by Patton (1966) and Barton and his co-workers (Barton, 1971a-c, 1973, 1976, Barton and Bandis, 1982, 1990, Barton and Choubey, 1977). Patton (1966) showed that the bi- linear equation presented below could be used to estimate the shear strength of discontinuities. ) tan( i b n + · φ σ τ (6.1) The problem with this equation is that the dilation angle, i, is stress dependent and also scale dependent. There is also some conjecture as to how the basic friction angle, φ b , should be measured. The author believes that the basic friction angle should not be measured on artificially polished or otherwise artificially modified samples. The reasoning for this is that φ b should represent the minimum friction angle that a discontinuity could reasonably be expected to attain in the field. Therefore the best way to determine φ b would be to measure the friction angle at high strain or to use the approach suggested by Hencher (1995) where the shear test results are corrected for dilation using the equations below and plotted to find the slope of the curve (φ b ). ( ) i i i n c cos sin cos σ τ τ − · (6.2) ( ) i i i n nc cos sin cos τ σ σ + · (6.3) The Shear Strength of Rock Masses Page 6.4 where, τ c and σ nc are the corrected shear strength and normal stresses respectively. There is, at present, no definitive way of measuring the dilation angle, i, for field scale discontinuities. The approach by McMahon (1985) or similar, where asperities are measured for a certain wavelength (or interlimb angle) of the defect are used to predict i, is probably the best current approach. Bandis et al (1981) developed the following shear strength criterion for discontinuities: 1 ] 1 ¸ + , _ ¸ ¸ · b n n JCS JRC φ σ σ τ 10 log tan (6.4) Where, JRC = Joint roughness coefficient JCS = Joint compressive strength This equation was developed based on 100mm long discontinuities and as such can be expected to resonably predict shear strengths on this scale. Barton and Bandis (1982) presented the following formulae to predict JRC and JCS for field scale samples. 0 02 . 0 0 0 JRC n n L L JRC JRC − , _ ¸ ¸ · (6.5) 0 03 . 0 0 0 JRC n n L L JCS JCS − , _ ¸ ¸ · (6.6) where, JRC n = Joint roughness coefficient for a discontinuity of length L n JCS n = Joint compressive strength for a discontinuity of length L n JRC 0 = Joint roughness coefficient for a discontinuity of length L 0 JCS 0 = Joint compressive strength for a discontinuity of length L 0 These equations are now widely used to predict the shear strength of discontinuities in the field. However, there appears to be a problem with the form of the equations. Figure The Shear Strength of Rock Masses Page 6.5 6.3 shows a plot of JRC n vs JRC 0 for discontinuity lengths varying from 1m to 100m. It is clear from this figure that the general trend of the equation must be incorrect. For example, for a discontinuity length of 100m a JRC 0 of 8 would imply a JRC n of approximately 2.65 whereas, a JRC 0 of 20 would imply a JRC n of 1.26. This implies that two discontinuities identical in every respect except small-scale roughness would have reversed larger scale roughness. Clearly this is wrong. It is understood that this equation was developed on small-scale models and therefore the author suggests that this equation may only be appropriate for joint lengths in the region of 1m. For larger joint lengths/block sizes, and high JRC 0 , the scaling equations are clearly unsuitable. This has important implications where at least part of the failure surface is controlled by long joints or where the block size of the rock mass is in excess of 1m. Some early studies (e.g. Bray, 1966) suggested that the strength of a rock mass could be estimated as the lowest strength envelope of the individual discontinuities in the rock mass (assuming that the strength of the intact material is relatively high). This could be true where the failure of the rock mass was purely due to sliding along discontinuities. However, this theory does not account for any interlocking or rotation of the intact rock blocks in the rock mass. Any interlocking of the rock mass would require a dilation of the mass to fail and hence an increase in strength. The shear strength of the individual discontinuities in the rock mass could therefore be seen only as a lower bound to the shear strength of the rock mass and not much use in design. Where failure is partly through intact rock it has been suggested that the strength of the rock mass could be estimated as a combination of the joint and intact rock strengths (e.g. John, 1962, 1969, Einstein et al, 1983). Brown (1970) showed that failure through a rock mass is more complex than the methods above suggest. Brown (1970) tested models of rock masses and found that: • At low confining stresses collapse was possible due to block movement involving the opening of joints and dilation of the mass. He found this mode “of probable practical significance in studying the behaviour of large masses of jointed rock in which the unit rock block is small compared with the dimensions of the mass as a whole as, for example, in deep open cut mines.” The Shear Strength of Rock Masses Page 6.6 • Axial cleavage of the rock blocks (gypsum plaster in the models) occurred at low confining stresses. • Where failure occurred at low confining pressures through the model material or as a combined shear and tension failure the strengths were lower than theories developed from intact rock and rock joints would suggest. The prediction of the strength of discontinuities on the field scale is, at best, approximate. When applied, the predicted strengths of these discontinuities can only be used to give a lower bound envelope to the shear strength of rock masses. Failure modes for rock masses are more complex than simple shearing along defects and through intact rock, particularly at low confining stresses. It is for these reasons that researchers have taken an empirical approach to estimating the shear strength of rock masses. Page 6.7 0 1 2 3 4 5 6 7 8 9 0 2 4 6 8 10 12 14 16 18 20 JRC 0 (for L 0 = 0.1m) J R C n JRC JRC L L n n JRC · ¸ 1 ] 1 − 0 0 0 02 0 . L n = 1m 2m 5m 10m 20m 50m 100m 65 . 2 m 100 8 m 1 . 0 0 0 · ¹ ¹ ¹ ; ¹ · · · n n JRC L JRC L 26 . 1 m 100 20 m 1 . 0 0 0 · ¹ ¹ ¹ ; ¹ · · · n n JRC L JRC L = Example point Figure 6.3. Assessment of Barton and Bandis (1982) JRC 0 vs JRC n The Shear Strength of Rock Masses Page 6.8 6.2.2 Predicting Rock Mass Strength using Empirical Formulae Yudhbir et al (1983), Ramamurthy et al (1994) and Sheorey (1997) (Equations 6.7 to 6.9 respectively) present rock mass criteria that have been developed as extensions of strength criteria for intact rock. The modification process has typically been based on model tests, small sample testing and limited experience. The criteria all assume a non- zero unconfined compressive strength, σ cm , and hence tensile strength, σ tm , for the rock mass. These criteria would therefore be expected to overpredict the strength for poor quality rock masses at the low stresses common to failure surfaces in slopes. α α σ σ σ σ σ σ σ σ , _ ¸ ¸ ′ + · ′ , _ ¸ ¸ ′ + · ′ c cm c m c b b a 3 1 3 1 or (6.7) m b cm m a , _ ¸ ¸ ′ ′ + ′ · ′ 3 3 3 1 σ σ σ σ σ (6.8) m b tm cm , _ ¸ ¸ ′ + · ′ σ σ σ σ 3 1 1 (6.9) where, α, a m , b m are constants 6.2.3 Predicting Rock Mass Strength using the Hoek-Brown Criterion The most commonly and almost exclusively used strength criterion for rock mass, over the last two decades, is the Hoek-Brown empirical rock mass failure criterion, the most general form of which is given in Equation 6.10. Hoek and Brown (1980) developed this criterion, as there was no suitable alternate empirical strength criterion. The equation, which has subsequently been updated by Hoek and Brown (1988), Hoek et al. (1992) and Hoek et al. (1995), was based on their criterion for intact rock discussed earlier in this paper. Although initially developed for hard rock masses, this criterion is now used for all types of rock masses and stress regimes. The only ‘rock mass’ tested and used in the original development of the Hoek-Brown criterion was 152mm core samples of Panguna Andesite from Bougainville in Papua New Guinea (Hoek and Brown, 1980) together with rock mass models (Brown, 1970). Hoek and Brown (1988) later noted that it was likely this material was in fact ‘disturbed’. The validation of the The Shear Strength of Rock Masses Page 6.9 updates of the Hoek-Brown criterion have been based on experience gained whilst using this criterion. To the author’s knowledge the only data published supporting this experience has been two slopes cited by Hoek et al (2002). a c b c s m , _ ¸ ¸ + ′ + ′ · ′ σ σ σ σ σ 3 3 1 (6.10) The parameters m i and m b are intact and mass material parameters; a and s are parameters that depend on the rock mass characteristics; and σ c is the uniaxial compressive strength of the intact rock. Estimating the parameters, m b , s and a in the Hoek-Brown criterion is done by correlation with rock mass rating parameters. The most current of these is the Geological Strength Index (GSI) (Hoek, 1994). The correlations with GSI were modified by Hoek et al (2002) to allow for a continuous transition at GSI=25 and to introduce a rock mass disturbance factor, D. These equations are given in Table 6.1. Table 6.1. Estimation of Hoek-Brown co-efficients Parameter Hoek et al (pre 2002) Hoek et al (2002) m b , _ ¸ ¸ − · 28 100 exp GSI m m i b , _ ¸ ¸ − − · D GSI m m i b 14 28 100 exp GSI>25 , _ ¸ ¸ − · 9 100 exp GSI s s GSI<25 0 · s , _ ¸ ¸ − − · D GSI s 3 9 100 exp GSI>25 5 . 0 · a a GSI<25 200 65 . 0 GSI a − · ( ) 3 20 15 6 1 2 1 − − − + · e e a GSI The Shear Strength of Rock Masses Page 6.10 A summary of all the changes to the equations for estimating the shear strength of rock masses using the Hoek-Brown criterion was presented by Hoek (2002) and is reproduced here as Figure 6.6. Hoek and Brown (1980) introduced the material parameter m i . Figure 6.4 gives an example from Hoek (1999) of how to estimate m i based on rock type. Hoek and his co- workers have presented numerous variations of this table. Chapter 3 on intact rock has shown that rock type is a poor predictor of m i and as such a discussion of these variations has not been provided here. Hoek (1997) provides Figure 6.5 to determine the GSI directly. The GSI tables have been modified several times up to Hoek et al (2002). These modifications will be discussed in the following sections. Hoek et al (1995) say that the GSI may also be calculated using Bieniawski’s (1976 and 1989) rock mass rating (RMR), GSI RMR , or Barton’s (1974) Q-system, GSI Q . The Shear Strength of Rock Masses Page 6.11 Figure 6.4. Values of the parameter m i for intact rock (Hoek, 1999) The Shear Strength of Rock Masses Page 6.12 Figure 6.5. Estimation of GSI (Hoek, 1997) The Shear Strength of Rock Masses Page 6.13 Figure 6.6. History of the Hoek-Brown criterion (Hoek, 2002) The Shear Strength of Rock Masses Page 6.14 Figure 6.6. History of the Hoek-Brown criterion (Hoek, 2002) (cont.) The Shear Strength of Rock Masses Page 6.15 Note 1: These are corrected Balmer equations. The original equations were incorrect. Figure 6.6. History of the Hoek-Brown criterion (Hoek, 2002) (cont.) The Shear Strength of Rock Masses Page 6.16 6.3 A DISCUSSION OF THE HOEK-BROWN CRITERION WITH PARTICULAR REFERENCE TO SLOPES 6.3.1 Calculation of GSI GSI RMR and GSI Q are derived from the rating parameters for several rock mass properties (Equations 6.11 and 6.12). ( ) ∑ + + + · condition defect spacing defect strength intact Ratings RQD GSI RMR (6.11) 44 log 9 + , _ ¸ ¸ · a r n e Q J J J RQD GSI (6.12) where J r = joint roughness number J n = joint set number J a = joint alteration number The RMR was derived for and on the basis of a data set of underground tunnels that were of the order of 10 to 20m in span (Bieniawski, 1989). The Q-system was developed in a similar way. It can be expected from this that the RMR and Q-system could be expected to be reasonable indicators of rock mass properties for underground tunnels and caverns. Where a slope is in the order of several hundred meters high, ranges of values for each parameter in the RMR system begin to lose meaning. This is discussed further below for each component of the GSI. 6.3.1.1 Intact Strength It is well known that intact rock exhibits a strength scale effect. This scale effect exists up to block sizes of at least one metre. Figure 6.7 shows this effect. The author suggests, that this should be considered when assigning a rating for intact rock strength. The Shear Strength of Rock Masses Page 6.17 Figure 6.7. Scale effect of Intact Rock (Hoek and Brown, 1980) 6.3.1.2 RQD Since the RQD is based on a fixed length of 100mm of drill core, the ability of the RQD to give meaningful information reduces as slopes get larger. Roof stability of a 10m diameter tunnel is likely to be affected by a reduction in RQD. However, for slopes several hundred meters high the RQD (particularly estimated from borehole data) has questionable value. On the scale of a large pit slope it is highly unlikely that all the defects encountered in boreholes would be of significance to the overall rock mass stability. The defect sets controlling stability for a large rock slope could be expected to have a spacing far in excess of 100mm because the closely spaced ones are unlikely to be persistent. If only these defects are taken into account in the GSI then a rating of 20 (the highest possible) will always apply for RQD. There is a general correlation between RQD and defect spacing and as such the need for both spacing and RQD in the method is questioned. The Shear Strength of Rock Masses Page 6.18 6.3.1.3 Defect spacing Most systems refer to the term ‘joint’. The author believes that the term ‘defect’ is more appropriate as all types of defects including bedding planes, shears, faults, lithological contacts (and not just joints) will interact to form blocks in a rock mass. The defect spacing suffers from a similar problem to that of the RQD. The maximum spacing interval is “greater than 3m” and “greater than 2m” for Bieniawski (1976) and Bieniawski (1989) respectively. A defect spacing of this size would result in large blocks which would have a much lower probability of forming blocks that would fall out of a 10m diameter tunnel roof. When assessing loading of rock mass around the tunnel, stress concentrations would generally be confined within single blocks and so a maximum GSI parameter would be applicable. However, for a large rock slope the region of over stressed rock can be expected to comprise several of these blocks. The critical defect spacing may be much larger than 3m. Thus, a maximum GSI parameter may not be suitable. Figure 6.8 shows blocks from a 400m high slope failure. A tunnel of 15m span is unlikely to have rock mass strength problems with a block size as big as those in the figure. 6.3.1.4 J oint condition The analyst must take into account the ‘large scale’ (i.e. scale of rock mass) defect characteristics as well as those on the small scale. This is similar to considering both the basic friction angle, φ b , and the field roughness, i, from Patton’s (1966) shear strength of defects formula. The thickness of defect infilling and defect roughness should be considered proportionately to the size of the rock blocks in the slope. Figure 6.9 shows two defects, on the small scale (borehole) defect A would have a high rating and defect B a low rating. However, when one looks at the large scale (large slope), defect A would be expected to have a lower strength. The Shear Strength of Rock Masses Page 6.19 Figure 6.8. Slope failure block size Very rough Smooth Very rough Smooth & infilled Defect A Defect B Figure 6.9. Effect of scale on defect properties 6.3.1.6 GSI from Bartons Q-System Hoek et al. (1995) also offer a method of using the Q-system developed by Barton et al. (1974) to estimate GSI. The system includes RQD, joint number, J n , joint roughness and joint alteration. RQD/J n represents block size. This system suffers in a similar way to RMR in its over reliance on RQD for large rock masses. The Shear Strength of Rock Masses Page 6.20 6.3.1.7 GSI from published figures Figure 6.5 shows estimates of GSI provided by Hoek (1997). The main components affecting the strength of the rock mass are covered (ie structure and surface conditions). It is not clear how scale is to be interpreted on this figure. The author believes that GSI should be interpreted as being on the scale of the rock mass under assessment. Using judgement the user can estimate the condition of their rock mass at the scale of their slope. For example, a ‘blocky’ rock mass at a scale of 10m is vastly different to a ‘blocky’ rock mass at the scale of 500m. Smaller relative block size leads to more freedom for block rotation and a greater chance for mass failure. Liao & Hencher (1997) showed that relative block size was critical in deciding the mode of failure. The smaller the block size (when compared to slope height) the more likely rock mass failure would be the dominant failure mechanism. The author recommends the use of Figure 6.5 for calculations of GSI for slopes. The use of GSI RMR and GSI Q from boreholes should only be used for preliminary strength estimates. It should be remembered that the key to the structure column is ‘degree of interlocking’. The degree of interlocking should be assessed on the scale of the slope under consideration. For example, the rock mass controlling the slopes for an ultimate pit may be considered interlocked whilst the rock mass may be considered as very well interlocked on the scale of individual benches of the same slope. It should also be remembered that “where block size is of the same order as that of the structure being analysed, the Hoek-Brown criterion should not be used. The stability of the structure should be analysed by considering the behaviour of blocks and wedges defined by intersecting structural features” (Hoek, 1997). 6.3.1.8 A Note on Schistose Rocks Hoek et al (1998) presented Figure 6.10 as a new version of the GSI estimation table (Figure 6.5). This new figure allows for the estimation of GSI for sheared rock masses. The author does not agree with this new extension to GSI. This extension to GSI contradicts the basic premise of a rock mass as defined in the Hoek-Brown criterion: The Shear Strength of Rock Masses Page 6.21 “The Hoek-Brown failure criterion is only applicable to intact rock or to heavily jointed rock masses which can be considered homogeneous and isotropic. In other words the properties of these materials are the same in all directions. The criterion should not be applied to highly schistose rocks such as slates…The strength of the discontinuities should be analysed in terms of a shear strength criterion such as that published by Barton (1976).” (Hoek et al, 1995) One reason that Hoek et al (1998) gave for extending the GSI table was that the empirical equation for estimating the modulus of deformation of the rock mass, E d , from the GSI and σ ci developed by Hoek and Brown (1997), overestimated E d in schistose rocks. , _ ¸ ¸ − · 40 10 10 10 GSI ci d E σ (6.13) The conclusion by Hoek et al (1998) was that GSI must therefore be lower for schistose rocks. The author has, together with his Kung (2001), collated a number of case studies from the literature where rock mass deformability has been measured. The results from the case studies, together with data presented by Bieniawski (1978) and Serafim and Pereira (1983) are shown in Figure 6.11 and Table 6.2. The error bars acknowledge the variation of E d in the test results. The uncertainty in GSI was due both to the variability of the rock masses and also the conversion from published RMR values to GSI. Figure 6.12 shows a plot of E d as measured in the field versus E d predicted from the equaton above using the published unconfined compressive strengths. Figure 6.11 and Figure 6.12 show that there is, not suprisingly, a large amount of scatter in the data. Also, a lot of the data is over predicted by the above equation. The Shear Strength of Rock Masses Page 6.22 Figure 6.10. GSI Table (Hoek et al, 1998) The Shear Strength of Rock Masses Page 6.23 Table 6.2. Rock mass deformability case studies Reference Rock type GSI Ed (GPa) Type of In-situ Testing Santiago J.L. (1986) Claystone 34 (30-63) 1.6 Pile Loading Test Georgiadis M. (1986) Mudstone 49 (40-49) 1.8 Dilatometer Test Gifford A.B. (1986) Claystone 53 (44-62) 4.40 (0.51-8.28) Plate Bearing Test Pavlakis M. (1980) Siltstone 39 (23-60) 0.11 (.05-.17) Pressuremeter Test Poulton M.M. (1986) Sandstone 67 (54-79) 0.3 (0.25-0.36) Plate Loading Test Schultz R.A. (1995) Basalt 60 (51-79) 25 (10-40) Jointed Block Test Sandstone 3.9 (2.2-5.6) Flat Jack Test Cheng Y. (1993) Sandstone 75 (55-87) 3.7 (2.3-5.1) Plate Loading Test Giovanni B. (1993) Limestone 79 (63-91) 37.5 (32.5-42.5) Plate Loading Test Mcdonald P. (1993) Basalt 39 (30-74) 1.39 (.2-4.6) Pressuremeter Test Granodiorite 52 3.8 Granite 55 2.5 Siltstone 60 14 Tuff 75 11 Marble 76 18 Goodman Jack Test Sandstone 46 (35-57) 7.5 (5-10) Granite 48 (41-55) 17.5 (15-20) Siltstone 68 (64-71) 25 (20-30) Littlechild B.D. (2000) Marble 78 (71-84) 15 (10-20) Cross-Hole Geophysics Test Sandstone 60 (55-65) 6.6 Shale 63 (58-68) 13.8 Shale 72 (67-77) 13.8 Mudstone 75 (70-80) 5 Bieniawski Z.T. (1990) Shale 75 (70-80) 12.4 MPBX 35 (30-40) 4 42 (37-47) 8 43 (38-48) 10 45 (40-50) 7 62 (58-68) 9 64 (59-69) 8 50 (45-55) 13 55 (50-60) 13 57 (52-62) 18 67 (62-72) 24 70 (65-75) 20 75 (70-80) 13 75 (70-80) 15 80 (75-85) 33 Ribacchi R. (1984) Granite 80 (75-85) 35 Plate Loading Test Page 6.24 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 80 90 100 GSI E d ( G P a ) . Bieniawski (1978) Serafim & Pereira (1983) Santiago (1986) Georgiadis (1986) Gifford (1986) Pavlakis (1980) Poulton (1986) Schultz (1995) Cheng (1993) Giovanni (1993) McDonald (1993) Littlechild (2000) Bieniawski (1990) Ribacchi (1984) UCS = 100MPa UCS = 10MPa ( ) 40 10 10 10 − · GSI c d E σ Figure 6.11. E d versus GSI case study data and Hoek et al (1995) equation for σ c ≥ 100MPa and σ c = 10MPa The Shear Strength of Rock Masses Page 6.25 The author believes that the fact that the modulus of a schistose rock is over predicted by an empirical equation does not justify the extension of GSI to these types of rocks. The manner in which Figure 6.10 has been extended is also questionable. The author does not believe that there is a continuum between “poorly interlocked, heavily broken rock mass” and “thinly laminated or foliated” rock masses with “closely spaced schistosity”. Therefore extrapolating the lines of equal GSI across this boundary can not be justified. The author has decided to adopt the Hoek et al (1995) position and omit highly schistose rock from the rock mass criterion. 0 10 20 30 40 50 60 0 10 20 30 40 50 60 E d test (MPa) E d p r e d Figure 6.12. E d test from case studies versus E d pred from Hoek et al (1995) equation The Shear Strength of Rock Masses Page 6.26 6.3.2 Estimation of Parameters from GSI 6.3.2.1 The Rock Mass Disturbance Factor, D The rock mass disturbance factor, D, was introduced by Hoek et al (2002) to account for the degree of disturbance to which the rock mass has been subjected by blast damage and stress relaxation. It varies from zero for undisturbed insitu rock masses to unity for very disturbed rock masses. Table 6.3 shows the suggested values for D for slopes. Table 6.3. Guidelines for estimating disturbance factor D (Hoek et al, 2002) Description of rock mass Suggested value for D Small scale blasting in civil engineering slopes results in modest rock mass damage, particularly if controlled blasting is used. However, stress relief results in some disturbance. D = 0.7 Good blasting D = 1.0 Poor blasting Very large open pit mine slopes suffer significant disturbance due to heavy production blasting and also due to stress relief from overburden removal. In some softer rocks excavation can be carried out by ripping and dozing and the degree of damage to the slopes is less. D = 1.0 Production blasting D = 0.7 Mechanical excavation The introduction of D was in response to published experience using the Hoek-Brown criterion. Sjöberg et al (2001) and Pierce et al (2001) stated that the Hoek-Brown criterion overestimated the strength of rock masses based on experience with mine slopes. The author (Douglas and Mostyn, 1999) agrees with these findings and discusses this further on in the chapter. Sjöberg et al (2001) claimed that the equations (6.14 and 6.15) presented by Hoek and Brown (1988) for ‘disturbed’ rock masses were more appropriate. Hoek et al (2002) in response modified their formulas for the parameters m b and s, using D such that they could reduce to the Hoek and Brown (1988) formulas (Table 6.1). , _ ¸ ¸ − · 14 100 exp RMR m m i b (6.14) The Shear Strength of Rock Masses Page 6.27 , _ ¸ ¸ − · 6 100 exp RMR s (6.15) Prior to excavation, the only tools available to the designer are boreholes and possibly surface exposures. The model that is developed can therefore only be considered as preliminary (see Section 6.3.1 for discussion). De-stressing and blasting of the rock mass may reduce the interlocking of the rock mass in the original model however, the author does not believe a ‘catch all’ parameter ‘D’ is appropriate. Different types of rock masses with different stress histories will be affected differently when subjected to blasting and destressing affects. Good quality blasting should not affect a large region of rock mass. This region is likely to be remote to the failure surface. If it is considered that this is not the case or that de-stressing will affect the rock mass the GSI can be reduced accordingly. The GSI is considered the appropriate parameter as it is meant to be a representation of the degree of interlocking of the rock mass as per Hoek et al (1995). The reduction of the GSI should follow an observational type approach. Changes to the rock mass (interlocking and defect surface conditions) due to blasting and de-stressing can be predicted using past experience in the particular rock mass under consideration. As excavation proceeds mapping of exposed surfaces should show whether these predictions are reasonable or whether they need to be modified. The author has not used the disturbance factor, D, in this thesis. Instead, where analysis is performed the GSI at the time of interest (i.e. the time of slope failure or pit wall completion) is used. 6.3.2.2 The Variation of the Hoek-Brown Parameters with GSI Figure 6.13 shows the variation of the Hoek-Brown parameters m b /m i , a and s with GSI based on Hoek et al (2002) and D = 0. It should be noted that if the Hoek (1997) table, Figure 6.5, is used then the minimum and maximum values of GSI are 5 and 80 respectively (Table 6.4). m b /m i , which mainly accounts for friction, varies gradually from unity as could be expected for a rock mass. The value of s (which mainly accounts for cohesion) dimi nishes rapidly with a reduction in GSI thus, indicating a rapid The Shear Strength of Rock Masses Page 6.28 reduction in compressive strength and an even more rapid reduction in tensile strength as the quality of the rock mass decreases. This is as expected. As rock mass defects become more cohesive it would be expected that s would be non-zero so as to avoid zero compressive strength. But GSI reduces for increasing cohesion and if s is predicted from GSI then s approaches zero not a finite value. This may be why the Hoek-Brown criterion will underpredict the shear strength of clayey bench slopes. It should be remembered at this point that the initial Hoek-Brown criterion was developed for hard rocks and has only recently been accepted for use with very poor quality rock masses by Hoek and Brown (1997). Thus, it could be expected that the experience with using the criterion for poor quality rock masses (particularly for slopes) would be limited. 0 0.2 0.4 0.6 0.8 1 0 20 40 60 80 100 GSI m b / m i ; s ; a mb/mi s a m b /m i s a Figure 6.13. Variation of a, s and m b /m i with GSI The Shear Strength of Rock Masses Page 6.29 Table 6.4. Maximum and minimum values of Hoek-Brown parameters using Figure 6.10 Parameter Minimum GSI = 5 Maximum GSI = 80 m b /m i 0.034 0.49 s 0.000026 0.11 a 0.62 0.50 The value of a remains relatively constant and has a maximum value of 0.62 (Table 6.4). This is not consistent with what is known about compacted rockfill strength (a material that could represent a lower bound to poor quality rock masses) where an a of 0.95 would be expected (Chapter 4). Chapter 3 on intact rock indicates that a actually varies from 0.2 to 1.0, with a reasonable estimate of 0.4 to 0.95 depending on m i . Thus it is not correct at two limits presented in this thesis. Where the intact rock approaches that of a soft rock or hard soil the curvature is much less pronounced than an exponent of 0.65 would suggest (Johnston & Chiu, 1984). As has been shown for intact rock (Chapter 3), fixing or limiting a has a very large impact on the estimation of the other parameters (m b and s) and therefore a cannot simply be changed without addressing the other parameters as well. The Shear Strength of Rock Masses Page 6.30 6.4 VALIDATION OF THE HOEK-BROWN CRITERION This section describes some analyses performed in order to assess the ability of the Hoek-Brown criterion to predict the shear strength of rock mass. 6.4.1 Chichester Dam The first case analysed was Chichester Dam, a 41m high concrete gravity dam constructed in the 1920’s. The dam was upgraded with drainage holes and post tensioning due to a perceived weakness in the foundation. The foundation consisted of interbedded tuffaceous sandstone and thin shale layers. The best estimate GSI for the foundation was 75. Unfortunately the analysis of the foundation (assuming no post tensioning and drainage) using the distinct element program UDEC found that the stresses beneath the dam were insufficient to give meaningful bounds on the Hoek- Brown criterion. Note that sliding of the dam along bedding surfaces was a potential failure mode. It was decided at this point to direct attempts at validating the criterion toward higher stressed rock mass such as large failed slopes. 6.4.2 Nattai North Escarpment Failure The Nattai North escarpment failure is located 80km south west of Sydney. The failure, with a total volume of 14 million cubic meters and height ranging between 200 and 300m, is one of the largest rock mass failures to have occurred in Australia in modern times. The failure has been well documented with studies in the area by Kotze & Pells (1980), McGregor (1980), Cunningham (1986) and Pells et al (1987). Figure 6.2 shows a photograph and diagram of the failure. Figure 6.14 shows the escarpment stratigraphy consists of Hawkesbury Sandstone overlying sandstones and claystones of the Narrabeen Group which in turn overlies the Illawarra Coal Measures. Of most interest to stability considerations are the weaker more fractured, and finer grained claystone and siltstone known as the Wombarra Claystone and the 2.7m thick Bulli Coal Seam. The Shear Strength of Rock Masses Page 6.31 Figure 6.14. Typical section of the Nattai North failure (Pells et al, 1987) Persistent vertical defects dipping at approximately 84° out of the slope together with bedding planes dipping 5° into the slope, resulted in large pillars that were prevented from sliding or toppling. The pillars were supported on the highly stressed weaker Wombarra Claystone. These conditions are believed to be sufficient to cause shearing through the claystone and failure of the escarpment under natural processes. It is believed that the failure was triggered by mining of coal seams beneath the escarpment. The mining is suspected to have caused further fracturing to the claystone and stress concentrations at the toe (Pells et al, 1987). Figure 6.15 gives a general illustration of the failure mode. Shearing occurs through the claystone at the base of the pillars. The base of the pillars slide out and the mass collapses (Cunningham, 1986). The failure of the escarpment at Nattai North is seen as predominately shear failure along defects (natural and mining induced) and through rock mass. The nature of the defects in the claystone lend themselves well to the description of rock mass by Hoek (1980) and hence the Hoek-Brown empirical rock mass failure criteria. The Shear Strength of Rock Masses Page 6.32 a) Pre-mining: failure may occur as a natural process if the vertical joints are continuous and the base rock is of poor quality. b) De-pillaring proceeds toward the escarpment. Vertical joints open and extend to form continuous joints. Fracturing of the Wombara claystone is occurring. c) Massive columns are formed. Yielding and shearing at the base is initiated. d) Shearing through of base and complete failure. Fracturing of Wombara Claystone due to high shear stress. Further fracturing due to tensile strain. Highly stressed Fractured due to high shear and tensile stresses. Coal seam shown exaggerated. Figure 6.15. Illustration of the failure mechanism at Nattai North (Helgstedt, 1997) The geometry and rock mass properties of the failure were estimated using data from Cunningham (1986), McGregor (1980), Kotze and Pells (1980) and Richmond and Smith (1979). The strength and deformation properties of the intact rock were estimated from Bhattacharya (1976) and Evans (1978) who had performed testing on similar rocks in a different area. The author validated as much of the information as possible during surface field mapping (both on top and at the toe) of the landslide. The properties used in the analysis are shown in Table 6.5 and Table 6.6. Table 6.7 shows the GSI estimated for the claystone where rock mass failure was deemed to have occurred. Helgstedt (1997) carried out numerical modelling of the failure under the supervision of the author and Garry Mostyn using the distinct element code UDEC. Two series of runs were made, with and without mining. The slope was modelled as two units comprising sandstones and claystones. The geometry of the slope and cliff line prior to failure was reconstructed using the Burragorang 1:25000 topographical map. The Shear Strength of Rock Masses Page 6.33 All parameters adopted for the model were ‘best estimate’ average values. Extreme but possible values were chosen for the sensitivity analysis. During modelling the material parameters (marked with an asterix in Table 6.6) were progressively reduced until failure occurred. The stresses at failure were then obtained along the shear surface through the claystone. Due to computational constraints, the actual spacing for the joint sets and bedding planes could not be implemented in UDEC in areas remote to the zone of shearing. However, the true spacing for most of the slope was not required to model the mechanism of slope failure. Three different areas needing different spacing were recognised and are outlined below. Stresses of 3.5+0.055z and 1.6+0.034z MPa were used as the upper and lower bounds respectively for σ 1 (horizontal stress). The base of the slope in the Wombarra Claystone and lower section of the Scarborough Sandstone (‘rough’ zone) required a spacing as close to actual as possible. Due to the failure mechanism being one of shear failure both along discontinuities and through intact rock, ‘randomly’ oriented fictitious joints having intact rock strength were added. It should be noted that although the ficticious joints are given intact rock strengths, once they fail UDEC assumes their strength to reduce to zero rather than that expected for a rock joint in claystone/sandstone. The section above the failing base required continuous vertical joints to permit the mechanism of failure to be modelled. The presence of these vertical joints was confirmed by the author during field mapping. For simplicity bedding plane spacing was made equal to the vertical joint spacing. Away from the failure the joint spacing was increased. The purpose of modelling this area was purely to reduce any edge effects in the model. The Shear Strength of Rock Masses Page 6.34 Table 6.5. Joint orientation, spacing and persistence for Nattai North Parameter Applied to Upper bound Adopted value Lower bound vertical joints 87.9 84 75.6 Apparent Dip (°) bedding - -5 - vertical joints 20,40,150,250 14,30,125,250 8,20,100,250 Apparent spacing (m) (finest to roughest) Bedding discontinuities 20,40,110,180 14,30,90,180 8,20,70,180 Discontinuity persistence all discontinuities - continuous - Table 6.6. Summary of parameters used for the Nattai North Escarpment Failure Adopted initial value Parameter Sandstone Claystone Density (kg/m 3 ) 2560 2650 Young’s modulus, E (GPa) 14.4 10.5 Shear modulus, G (GPa) 5.54 4.04 Bulk modulus, K (GPa) 12.00 8.75 Poissions ratio 0.3 Friction angle of intact material (°)* 40 35 Cohesion of intact material (MPa)* 6 5 Tensile strength of intact material, σ ti (MPa)* 0.75 0.6 Normal stiffness, K n (GPa/m) 50 Shear stiffness, K s (GPa/m) 25 Defect friction angle (°)* 32 28 Defect cohesion (MPa)* 0.025 0.03 In-situ in plane horizontal stress, σ 1 (MPa) 2.5+0.044z (where z = depth) In-situ out of plane horizontal stress, σ 2 (MPa) 1.2+0.026z In-situ vertical stress, σ 3 (MPa) 0.026z * Changed globally for sensitivity analysis. The Shear Strength of Rock Masses Page 6.35 Table 6.7. Summary of Hoek-Brown parameters for Nattai using RMR and the Hoek-Brown chart GSI source RMR 89 Hoek-Brown Chart (Hoek, 1997) Estimate LB BE UB LB BE UB GSI 55 61 69 49 45 55 m i 4 6.5 9 4 6.5 9 LB = Lower bound; BE = Best estimate; UB = Upper bound The results of the analysis using UDEC correlated well with the assumed failure mode. Average shear and normal stresses along the failure zone are presented in Table 6.8. The mode of failure did not change where mining was modelled however, the shear zone was found to extend deeper into the toe of the slope. Table 6.8. UDEC output: average shear and normal stresses along the predicted failure plane Average stress along failure zone (MPa) Case Strength parameters used Normal stress Shear stress Best estimate of all values, no mining 0.8 x best estimate 1.21 1.39 Lower bound in-situ stresses, no mining 0.7 x best estimate 1.16 1.32 Upper bound in-situ stresses, no mining 1.3 x best estimate 1.26 1.63 Best estimate of all values, mining 1.4 x best estimate 1.96 1.90 6.4.3 Katoomba Escarpment Failure The Katoomba (or Dogface Rock) escarpment failure is located at Katoomba in the Blue Mountains west of Sydney. The main failure occurred on the 28 th January 1931. Smaller failures have been recorded through to July 1977. The total volume of all failures comprises approximately 75000 to 100000m 3 . The depth to the failure surface was up to 280m. The failure has been documented by Pells et al (1987). Figure 6.16 shows a photograph from after the failure. The Shear Strength of Rock Masses Page 6.36 Figure 6.16. Katoomba Escarpment Failure (photo courtesy Mrs Gwen Silvey of the Blue Mountains Historical Society) The geology and mode of failure was similar to that of the Nattai Escarpment failure. The rocks were part of the Narrabeen Group with hard competent sandstones (Banks Wall Sandstone and Burramoko Head Sandstone) overlying weaker material (including The Shear Strength of Rock Masses Page 6.37 Hartley Vale Claystone, Victoria Pass Claystone, Beauchamp Falls Shale). Bedding planes were near horizontal and joints in the sandstones persistent and subvertical. Figure 6.17 shows an example of the vertical defects in the sandstone. Figure 6.17. Katoomba Escarpment Failure, column prior to collapse (photo courtesy Mrs Gwen Silvey of the Blue Mountains Historical Society) No site specific testing was carried out on the materials and so all parameters were estimated from testing on similar rocks in other areas (Evans, 1978 and Bhattacharyya, 1976). Table 6.9 shows the material properties used and Table 6.10 shows the estimation of the GSI. The Shear Strength of Rock Masses Page 6.38 Table 6.9. Summary of parameters used for the Katoomba Escarpment Failure Adopted initial value Parameter Sandstone Claystone Density (kg/m 3 ) 2560 2650 Young’s modulus, E (GPa) 14.4 10.5 Shear modulus, G (GPa) 5.9 3.86 Bulk modulus, K (GPa) 8.57 12.5 Poissions ratio 0.22 0.36 Friction angle of intact material (°)* 38 33 Cohesion of intact material (MPa)* 15 12.9 Tensile strength of intact material, σ ti (MPa)* 1.91 1.61 Defect friction angle (°)* 32 28 Defect cohesion (MPa)* 0.025 0.03 In-situ in plane horizontal stress, σ 1 (MPa) 2.5+0.044z (where z = depth) In-situ out of plane horizontal stress, σ 2 (MPa) 1.2+0.026z In-situ vertical stress, σ 3 (MPa) 0.026z Table 6.10. Summary of Hoek-Brown parameters for the Claystone in the Katoomba Escarpment Failure using RMR and the Hoek-Brown chart GSI source RMR 89 Hoek-Brown Chart (Hoek, 1997) Estimate LB BE UB LB BE UB GSI 28 50 69 48 53 58 m i 4 6.5 9 4 6.5 9 Tarua (1997) carried out the numerical modelling under the supervision of the author and Garry Mostyn using the distinct element code UDEC. As the mode of failure and geology/geometry was simlar, the analysis was carried out in the same manner as that for the Nattai Escarpment failure. The Shear Strength of Rock Masses Page 6.39 6.4.4 Aviemore Dam Insitu Shear Tests Aviemore Dam, constructed between 1963 and 1968, is located on the Waitaki river, 185km south west of Christchurch, New Zealand. The dam is comprised of both a 340m long, 57m high concrete gravity section and a 350m long, 49m high earth embankment section (Read et al, 1996). During construction eight large-scale in-situ shear tests were carried out on the foundation in order to determine the strength of the concrete/rock interface for stresses relevant to those induced by the proposed dam. The dam is founded on silty to sandy greywacke of Mesozoic age and coal measure sediments of Tertiary age. However all in-situ tests were carried out on greywacke rock. The rock mass is closely jointed, veined, and often is crushed and sheared. Read et al (1996) identified three semi -orthogonal joint sets as follows: • joints sub-parallel to bedding, 150°-190°/75°NE-75°SW (strike/dip) • joints striking approximately perpendicular to bedding, 100°-120°/70°NW-90° • joints striking approximately perpendicular to bedding, 080°-110°/30°-50°SW The range of the orientation for the joint sets is very wide and in addition several other randomly orientated joints are present. Read et al (1996) stated that a statistical analysis gives the impression that the overall jointing pattern at Aviemore was random. The most common spacing has been found to be between 60 and 200mm (Read et al, 1996). Most of the joints were found to have a slightly wavy profile, were rough to smooth and closed with a persistence of a few metres. Moreover sheared and crushed zones occur, although these are very widely spaced at the location of the in-situ shear tests. Read et al (1996) mapped approximately 350 defects on available outcrops. The outcrops were considered similar to the rock mass in the tests based on photos and other documents. By scrutinising old photos and documents Read et al (1996) concluded that the tested rock mass was of similar quality to that covered by the joint survey. A summary of this survey is shown in Table 6.11. The GSI was estimated using the results of this survey and is shown in Table 6.12. Figure 6.18 illustrates the setup and dimensions of the tests at Aviemore. One test block (0.76mx1.8m) and one reaction (anchor) block (0.9mx1.8m) were cast directly onto The Shear Strength of Rock Masses Page 6.40 clean rock foundations (Foster & Fairless, 1994). The vertical load was applied to the blocks using stressed bars anchored into the rock foundation. An ungrouted length of 4.9m was used for at least two of the tests. Freyssinet flat jacks were used to force the blocks apart as constant vertical load was maintained on the test blocks. Six tests were performed using a horizontally acting thrust and two using an inclined thrust acting at a downward angle through the centre of the blocks. The latter two test results were not used. Table 6.11. Summary of the Joint Properties from the Joint Survey carried out by Read et al (1996) Persistence of joints (m) 0-0.75 0.75-1.5 1.5-2.5 2.5-3.5 3.5-4.5 4.5-7 7-(15) % per metre interval 27 30 19 13 9 5 0.5 Defect types shear/ fault joint bedding schistosity /foliation % 10 84 6 0 Aperture (mm) >200 60-200 20-60 6-20 2-6 <2 tight % 0 0 0 1 2 97 0 Nature of infill clean surface stain. non-cohesive cemented % 12 72 1 12 Roughness polished slickensided smooth rough defined ridges small steps % 0 1 58 35 4 1 Table 6.12. Hoek Parameters for Aviemore Shear Tests using RMR, and the Hoek-Brown Chart GSI Source RMR Hoek-Brown Chart (Hoek, 1997) Estimate UB BE LB UE BE LB GSI 52 43 31 40 35 30 m i 15 12 10 15 12 10 σ c (MPa) 50 35 20 50 35 20 Foster & Fairless (1994) stated that all tests failed through the rock mass, approximately 50-100mm below the rock-concrete contact, involving failure of several defects. During the test both the test block and the reaction block failed at the same time. Foster & Fairless (1994) analysed the failures and proposed that both blocks failed at the same τ/σ N ratio and that the σ-ε curves should have been similar. Since the σ-ε curves were similar it was likely that vertical force had been transferred between the blocks via the stiff jack. The Shear Strength of Rock Masses Page 6.41 Foster and Fairless (1994) adjusted the vertical stresses on the test and reaction blocks assuming that vertical forces were transferred from the reaction block to the test block due to differential displacement. The values were adjusted to yield similar τ/σ N ratios for the reaction and the test blocks. Helgstedt (1997) carried out the numerical modelling under the supervision of the author and Mr Garry Mostyn using the distinct element code UDEC. The modelling was used to investigate whether the assumptions of Foster and Fairless (1994) were reasonable. The general model behaviour was studied to see if it agreed with observations from the real tests and to confirm the theory that vertical stress had been transferred between the blocks through the Freyssinet jack. The failure stresses from the model were not used. Figure 6.18. Direct Shear Test Set up (Foster & Fairless, 1994) The Shear Strength of Rock Masses Page 6.42 The defects in the rock mass were created by Monte Carlo generation. The joints were assumed to be randomly orientated with a negative exponentially distributed joint trace length. The distribution of the discontinuities in space was assumed to be random. These assumptions were verified against the data from the joint survey and data presented by Read et al (1995 and 1996). Figure 6.19 illustrates the mesh generated for one of the UDEC models. The actual true joint frequency was only modelled close to the simulated test and reaction blocks, joints were more widely spaced in the far field. The vertical load applied by stressed bars, anchored in the rock below the shear tests, at Aviemore was simulated in the UDEC model by applying vertical loads at the top of the blocks. This simplification is however not likely to influence the results. The horizontal load from the Freyssinet jack was simulated by four blocks as can be seen in Figure 6.20 (between the test and reaction block). The left and right blocks represent pressurised sides of the jack. A pressure was exerted in the vertical slot between these blocks. The upper and lower blocks represent the casing of the jack. The two horizontal cracks dividing the upper and lower blocks from the left and right blocks were given zero friction angle and cohesion, but very high tensile strength. This allows the left and right blocks to slide freely in a horizontal direction, while simultaneously, the simulated jack can act as a rigid device capable of transferring moment. The parameters that were used for the numerical model are given in Table 6.13 and Table 6.14. The general displacement (vertical and horizontal) behaviour matched the behaviour of the field tests. The assumptions of Foster and Fairless (1994) were validated as vertical stress was shown to be transferred through the jack and failure occurred simultaneously in the reaction and test blocks. The statistically generated models were run several times. All with results similar to that discussed above. The Shear Strength of Rock Masses Page 6.43 Table 6.13. Intact material parameters Material Tensile strength (MPa) Cohesion (MPa) Friction angle (°) Bulk Modulus (MPa) Shear Modulus (MPa) Density (t/m 3 ) Concrete blocks 5 15 45 25000 10400 2.4 Jack and stressed bars 200 400 0 133333 80000 7.6 Intact rock 3 8 45 20000 18000 2.2 Table 6.14. Defect and Interface Material Parameters Material Tensile strength (MPa) Cohesion (MPa) Friction angle (°) Normal Stiffness (MPa) Shear Stiffness (MPa) Conc-steel interface 0 0 45 50000 30000 Conc-rock interface 5 15 50 25000 15000 Jack casing interface 200 0 0 2500000 1500000 Press. void in jack 0 0 0 2500000 1500000 Defects in rock mass 0 0 44 15000 5000 6.4.5 Discussion of the Results of the Analysis The Hoek-Brown criterion, together with Figure 6.5 to estimate GSI, was used to estimate the shear strength of the rock mass. Balmer’s method was used to convert from principal stresses to shear and normal stresses. Figure 6.21 shows a plot of the ratio of calculated shear strength, τ in-situ , versus the shear strength estimated from GSI for the cases. The results show that the Hoek-Brown criterion provides a reasonable estimate of the strength at the Nattai Escarpment. The Aviemore insitu shear tests show the predicted strength using the Hoek-Brown criterion to range from 0.8 to 1.2 times the computed strength from the shear tests. The Hoek-Brown criterion predicts twice the strength as that calculated using UDEC for the Katoomba escarpment failure. However this may be due to the lack of site specific strength data at Katoomba. The GSI estimated from the RMR was noticeably higher than that estimated using Figure 6.5 for the Aviemore insitu shear tests and Nattai escarpment failure. Thus, the strengths estimated using RMR would lead to an overprediction of the strength of the rock mass The Shear Strength of Rock Masses Page 6.44 Figure 6.19. Example of mesh used (Helgstedt, 1997) Figure 6.20. Close up of the simulated jack (Helgstedt, 1997) The Shear Strength of Rock Masses Page 6.45 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 σ n (MPa) τ i n - s i t u / τ t a b l e Katoomba escarpment failure Aviemore shear tests Nattai escarpment Failure Figure 6.21. Back analysis results using Figure 6.5 for GSI The Shear Strength of Rock Masses Page 6.46 6.5 A NEW ESTIMATION OF ROCK MASS STRENGTH 6.5.1 Development of a Modified Criterion As discussed earlier the Hoek-Brown criterion is virtually universally accepted. It also appears to give reasonable results if used in conjunction with Figure 6.5 to estimate GSI. The current method of calculating the parameters m and a appears to be flawed at the limits of intact rock (Chapter 3) and rockfill (Chapter 4). It has therefore been decided to modify this criterion so that it incorporates some of the results presented in this thesis rather than to develop a completely new approach. The terminology used for the modified criterion is outlined below. α σ σ σ σ σ , _ ¸ ¸ + ′ + ′ · ′ s m ci ci 3 3 1 (6.15) For intact rock (GSI=100): s = s i m = m i α = α i For rock mass (GSI<100): s = s b m = m b α = α b In general, σ ci is the unconfined compressive strength, σ c , of the intact rock; unless the scale of the discontinuities affects the strength of the blocks in the rock mass under consideration. The author proposes to use the form of the Hoek-Brown criterion and to modify the method of calculating the parameters α, s and m. The basic assumption is that the rock mass parameters will be factored versions of the intact parameters developed in Chapter 3. The Shear Strength of Rock Masses Page 6.47 6.5.1.1 Exponent ‘α’ Hoek and Brown (1980) restricted α to 0.5. Hoek (1994) modified this for GSI<25 to allow α to vary up to a theoretical maximum of 0.65 (but actually 0.625 for a minimum GSI of 5) using the equation below. 200 / 65 . 0 GSI − · α (6.16) This equation resulted in a ‘step’ at GSI = 25 from 0.525 to 0.5. Hoek et al (2002) eliminated this step by modifying the equation for all GSI values to: ( ) 3 20 15 6 1 2 1 − − − + · e e GSI α (6.17) This equation results in a maximum α of 0.62 using a minimum GSI of 5. Chapter 3 has shown that α is not fixed at 0.5, and can vary considerably for intact rock. A rock mass can be considered a transitional material between intact rock and soil. At the soil limit it is expected that α would approach unity (Mohr-Coulomb material). A statistical analysis of 929 triaxial tests on rockfill given in Chapter 4 showed that α b for rockfill is approximately 0.9 and that m b ≈2.5. If the results of Chapter 3 are used for intact rock then a modification to the current Hoek-Brown equation is required where α b is not restricted to a range of 0.5 to 0.65, and is a function of m b and GSI. It is assumed that as the rock mass approaches a soil like material that α b will approach 0.9 and m b will approach 2.5. 6.5.1.2 Parameter ‘m’ Hoek and Brown provide estimates of m i based on rock type however, as discussed in Chapter 3, rock type is a poor predictor of m i . The parameter m i should be estimated using triaxial tests on intact rock samples or can be approximately estimated as σ ci /σ ti . This method may also be appropriate for intact soil-like materials (clays). Limited Al- Hussaini (1981) found that the “unconfined compression strength obtained was about 5 The Shear Strength of Rock Masses Page 6.48 to 10 times larger than the tensile strength” for samples of high and low plasticity clay and sandy clay. Fang and Fernandez (1981) found that the ratio of σ c /σ t was between 15-28 for clays at their optimum moisture content and 3-7 for air dried samples. These ratios from the literature fall within the authors suggested m i range. There is some limited information in the literature that shows that m i = σ c /σ t , for intact soil-like materials (clays), is within the range found for intact rock (between 4 and 40) (Al-Hussaini, 1981 and Fang and Fernandez, 1981). However, the information in the literature is insufficient for the author to make a definitive judgement on whether the author’s criterion can be applied to clays. As the criterion is empirical and has been developed for rock using triaxial tests on rock samples the author does not recommend the extrapolation and use of the criterion for clays. The parameter m (in association with the exponent α) predominately affects the friction angle of the rockmass. Therefore as GSI drops it can be expected that the rockmass will become less interlocked and the frictional strength of the rockmass will reduce (predominately through a reduction in dilation). The parameter m b should therefore reduce from m i to a limiting value as a function of GSI. The limiting value for a non- cohesive rockmass could be taken as 2.5 from the analyses of rockfill discussed earlier. 6.5.1.3 Parameter ‘s’ The parameter s contributes predominately to the cohesiveness of the rock mass. Thus, as GSI decreases s should also decrease as per the Hoek-Brown criterion. The limiting value should be zero where the ‘soil-like’ rock mass is non-cohesive. Once a rock mass no longer behaves as ‘intact’ it can be expected that cohesion and thus s should decrease rapidly with a decrease in GSI. Hoek and Brown use an exponential drop in s versus GSI as shown in the following equation. ( ) , _ ¸ ¸ − · 9 100 exp GSI s (6.18) Hoek and Brown consider a well-interlocked rock mass to have a GSI of 80. Therefore, s may be close to unity in the region of GSI equal to 80-100. The Shear Strength of Rock Masses Page 6.49 The Hoek-Brown criterion was developed for hard rock masses. As such, at the ‘soil limit’ (GSI→ 0) the parameter s in the Hoek-Brown equation approaches zero. This is reasonable for a non-cohesive or frictional rock mass. However, where the rock mass is controlled by cohesion (i.e. the rock mass is controlled by the clay in the mass) this assumption is incorrect. The author believes that where there is sufficient clay material in the rock mass such that there is no rock to rock contact during shearing the shear strength of the soil should be used. The Hoek-Brown criterion is inappropriate, as the properties of the intact rock (e.g. σ c ) will have at the most a minor effect on the strength of the mass. The cohesive soil limit is not considered in this thesis. 6.5.2 Development of the Equations to Estimate the Parameters in the Hoek-Brown Criterion The previous section discussed the development of modifications to the parameters of the Hoek-Brown criterion. These were based on the author’s work on intact rock, rockfill and rock masses. The bounds have been well quantified in this thesis however, due to the limited information available about failures and the addition of a variable α dependent on m, it meant good quality triaxial tests were needed to provide equations for intermediate rock masses. The analysis of triaxial testing on rock mases could also give confidence to the theory developed in the previous section. Habimana et al (2002) published four sets of triaxial tests on quartzitic sandstone. These were part of an extensive laboratory testing programme carried out by the rock mechanics laboratory of the Swiss Federal Institute of Technology Lausanne (EPFL) for the hydroelectric power plant of Cleuson-Dixence and the reconnaissaince gallery for the Lotschberg Tunnel in the Swiss Alps. New sampling techniques were developed to ensure as little disturbance as possible. To the author’s knowledge, these are the best set of published triaxial tests on rock mass available. The quartzitic sandstone had varying degrees of tectonic crushing. Habimana et al (2002) classified the rocks used into four GSI groupings (GSI = 15, 25, 50 and 80). Figure 6.22 shows the triaxial test results for each GSI data set. The samples were tested perpendicular to anisotropic planes (if any) to induce rock matrix failure. Habimana et al (2002) noted that the degree of anisotropy decreased with an increase in tectonic crushing. At a low GSI the material was considered isotropic. The Shear Strength of Rock Masses Page 6.50 Each data set was analysed statistically using the Hoek-Brown equation. Figure 6.23 shows the Habimana et al (2002) data together with the author’s statistical fits. During this analysis the loss function used in the statistical analysis had to be modified to allow the solution to converge and to avoid local minimums outside the bounds of the Hoek- Brown parameters i.e. 0 ≤ s ≤ 1 0 ≤ m ≤ 40 0 ≤ α ≤ 1 The results of the statistical analyses are shown in Table 6.15. Table 6.15. Results of statistical analysis of Habimana et al (2002) test data GSI m s α σ c (MPa) Variance explained (%) 15 2.46 0 0.84 16 93.4 25 3.9 0.016 0.65 16 99.3 50 14 0.10 0.62 16 99.996 80 20 0.7 0.55 16 93.3 Table 6.15 was used together with the discussion and models in the preceding section to develop equations for the parameters s b , α b and m b . 6.5.2.1 A New Equation for ‘m b ’ The results for the parameter m b showed that a linear equation gave the best fit to the data. The best-fit equation (variance explained = 95.5%) was: 4 GSI m b · (6.19) If this line was extrapolated to GSI = 100 then m b = 25. The equation was therefore rewritten as: The Shear Strength of Rock Masses Page 6.51 100 GSI m m i b · (6.20) Figure 6.24 shows this equation together with the data used. A lower limit of m b was set at 2.5 as indicated from the analysis of rockfill. Thus the equation becomes: ¹ ¹ ¹ ' ¹ · 5 . 2 100 max GSI m m i b (6.21) Page 6.52 0 20 40 60 80 100 0 5 10 15 20 σ′3 (MPa) σ′1 GSI = 15 0 20 40 60 80 100 0 5 10 15 20 25 σ′ 3 (MPa) σ′ 1 GSI = 25 0 20 40 60 80 100 0 5 10 15 20 σ′ 3 (MPa) σ′ 1 GSI = 50 0 20 40 60 80 100 0 5 10 15 20 σ′3 (MPa) σ′ 1 GSI = 80 Figure 6.22. Test results for tectonised quartzitic sandstone (Habimana et al, 2002) Page 6.53 0 20 40 60 80 100 0 5 10 15 20 σ′ 3 (MPa) σ′ 1 GSI = 15 0 20 40 60 80 100 0 5 10 15 20 σ′ 3 (MPa) σ′ 1 GSI = 25 0 20 40 60 80 100 0 5 10 15 20 σ′ 3 (MPa) σ′ 1 GSI = 50 0 20 40 60 80 100 0 5 10 15 20 σ′ 3 (MPa) σ′ 1 GSI = 80 Figure 6.23. The author’s statistical fits to Habimana et al (2002) data The Shear Strength of Rock Masses Page 6.54 The linear relationship is different in form to the exponential Hoek-Brown relationship: ( ) , _ ¸ ¸ − · 28 100 exp GSI m m i b (6.22) The author does not see this as a problem as: • Frictional strength may not decrease as rapidly with GSI as indicated by the Hoek- Brown equation for m b . • α is no longer almost constant and as it is directly related to m b , the Hoek-Brown equation will not be appropriate. • An exponential relationship is not supported by the data. 0 5 10 15 20 25 0 20 40 60 80 100 GSI m b Figure 6.24. m b versus GSI 6.5.2.2 A New Equation for ‘s b ’ The results from the statistical analysis of the Habimana et al (2002) data showed a rapid decrease of s with a decrease in GSI as predicted in the discussion in Section 6.5.1.3. Therefore an exponential relationship, similar to the Hoek-Brown relationship for s, was deemed appropriate. One issue raised from the test results was the relatively high value for s for a GSI of 80. This result was taken to indicate the possibility of a The Shear Strength of Rock Masses Page 6.55 plateau in the value of s at high GSI. This can be justified by the argument that at high GSI (>85) the rockmass is very strongly interlocked and thus the cohesive strength is similar to that of intact rock. This is supported by the GSI table by Hoek (1999) that includes a new row for ‘intact or massive’ rock that has a GSI ranging from 80 upwards for very good defect quality (Figure 6.25). Figure 6.25. GSI for an intact or massive rock structure (Hoek, 1999) A statistical analysis of the data in Table 6.15 using an exponential curve together with a plateau (maximum) of s = 1 for GSI>85 was performed and produced the following equation (variance explained = 99.97%): ( ) ¹ ¹ ¹ ¹ ¹ ' ¹ , _ ¸ ¸ − · 1 15 85 exp min GSI s b (6.23) This relationship is plotted on Figure 6.26 together with the data used. The Shear Strength of Rock Masses Page 6.56 0 0.2 0.4 0.6 0.8 1 0 20 40 60 80 100 GSI s b Figure 6.26. s b versus GSI 6.5.2.3 A New Equation for ‘α b ’ The exponent, α b , varies with GSI and m b . The limits, as discussed in Section 6.5.1.1, on α b are: GSI = 100, α b = α i GSI → 0, α b → 0.90 A statistical analysis of the data using these limits produced the following equation (variance explained = 83.3%). ( ) , _ ¸ ¸ − − + · i b i i b m m 30 75 exp 9 . 0 α α α (6.24) Figure 6.27 shows the relationship for α b together with the data. It should be noted that for this analysis m i was taken as that extrapolated from the equation derived earlier for m b . The exponent for intact rock, α i , was also estimated from the test data. The Shear Strength of Rock Masses Page 6.57 0 0.2 0.4 0.6 0.8 1 0 20 40 60 80 100 GSI α b Figure 6.27. α b versus GSI Figure 6.28 shows the relationship plotted on a m versus α curve (Figure 6.29 shows an example of the transition from intact rock to rock mass). Plotted on this curve is a relationship between m i and α i (Equation 6.25). This relationship is a slight modification to that derived in Chapter 3 (Equation 6.26). This was done to allow the curve to pass through α = 1 when m i = 0. , _ ¸ ¸ + + · 7 exp 1 2 . 1 4 . 0 i i m α (6.25) , _ ¸ ¸ + + · 455 . 7 exp 1 08585 . 1 4032 . 0 i i m α (6.26) Figure 6.30 shows that the modification does not affect the results significantly. Figure 6.27 and Figure 6.28 show that the increase in α occures rapidly over a short range of m b . This increase starts at approximately m i /4 or GSI ≈ 20-25. Interestingly this is very similar to the Hoek et al (1995) relationship for a where a remains constant for GSI approximately 25-100 and increases below a GSI of 25. Page 6.58 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 5 10 15 20 25 30 35 40 m α m i = 40 m i = 20 6 m i = 10 4 ( ) , _ ¸ ¸ − − + · i b i i b m m 30 75 exp 9 . 0 α α α , _ ¸ ¸ + + · 7 exp 1 2 . 1 4 . 0 i i m α Figure 6.28. Graphical representation of the equations for α and m Page 6.59 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 5 10 15 20 25 30 35 40 m α Intact sample GSI = 100 m i , α i Mass sample m b = function of GSI α i = function of m b (GSI) Transition curve from GSI =100 to GSI = 0 Rock mass limit GSI = 0 Relationship between m i and α i for intact rocks Figure 6.29. Transition of α and mfrom intact rock to rock mass Page 6.60 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 5 10 15 20 25 30 35 40 45 50 m i α i ai ainew α i α inew , _ ¸ ¸ + + · 455 . 7 exp 1 08585 . 1 4032 . 0 i i m α , _ ¸ ¸ + + · 7 exp 1 2 . 1 4 . 0 i inew m α Figure 6.30. Original and modified relationships for α i and m i The Shear Strength of Rock Masses Page 6.61 6.5.2.4 The Overall Equation Figure 6.32 shows the original plots of data together with curves developed using the preceding equations. These curves provide a good fit to the data. For a GSI of 50 there is a slight underestimation of the strength and for a GSI of 25 there is a slight overestimation of the strength. A look at the original test curves presented by Habimana et al (2002) (Figure 6.31) shows that there is a larger gap between GSI = 25 and 50 than could be expected for a regular transition from an intact rock to a weak rockmass. Habimana et al (2002) claim that their estimates of GSI are within t5. It may be that the gap is due to a slight error in the estimation of GSI. Figure 6.31. Shear strength curves for tectonised quartzitic sandstone (Habimana et al, 2002) A final global statistical analysis of all the data was performed using the general Hoek- Brown criterion together with the equations developed in this section. This was carried out to check whether any errors were introduced due to each parameter equation being derived seperately and then being recombined into the Hoek-Brown equation. Figure 6.33 shows the plots for GSI = 15, 25, 50 and 80 provide good fits to the data (variance explained 95.6%). Figure 6.34 and Figure 6.35 show non-dimensional example plots of the shear strength criterion for an m i of 40 and an m i of 4 respectively for GSI varying from 10 to 100. The Shear Strength of Rock Masses Page 6.62 Figure 6.36 and Figure 6.37 compare the author’s modified criterion with that of the current Hoek-Brown criterion for an m i of 40 and an m i of 4 respectively. The plots show that the modified criterion gives a higher strength in the compressive region for an m i of 4. For an m i of 40, the modified criterion gives a lower strength for a GSI of 100, a similar strength for a GSI of 80 and a higher strength for a GSI of 10. There is a larger relative drop in strength between GSI 100 and 80 for the Hoek-Brown criterion compared with the modified criterion. This is in accordance with the discussion in Section 6.5.2.2. It should be noted that the two criteria use different methods of approximating m i . Page 6.63 0 20 40 60 80 100 0 5 10 15 20 25 σ′ 3 (MPa) σ′ 1 GSI = 15 0 20 40 60 80 100 0 5 10 15 20 25 σ′ 3 (MPa) σ′ 1 GSI = 25 0 20 40 60 80 100 0 5 10 15 20 25 σ′ 3 (MPa) σ′ 1 GSI = 50 0 20 40 60 80 100 0 5 10 15 20 25 σ′ 3 (MPa) σ′ 1 GSI = 80 Figure 6.32. Results of analysis of Habimana et al (2002) data using the new equation and parameters from equations Page 6.64 0 20 40 60 80 100 0 5 10 15 20 25 σ′ 3 (MPa) σ′ 1 GSI = 15 0 20 40 60 80 100 0 5 10 15 20 25 σ′ 3 (MPa) σ′ 1 GSI = 25 0 20 40 60 80 100 0 5 10 15 20 25 σ′ 3 (MPa) σ′ 1 GSI = 50 0 20 40 60 80 100 0 5 10 15 20 25 σ′ 3 (MPa) σ′ 1 GSI = 80 Figure 6.33. Results of global analysis of Habimana et al (2002) data using new equations Page 6.65 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 σ′ 3 /σ c σ′ 1 /σ c GSI = 10 GSI = 40 GSI = 60 GSI = 80 GSI = 100 α σ σ σ σ σ σ , _ ¸ ¸ + ′ + ′ · ′ s m ci ci ci 3 3 1 Figure 6.34. Non-dimensionalised plot of new shear strength curves for m i = 40 and varying GSI Page 6.66 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 σ′ 3 /σ c σ′ 1 /σ c GSI = 10 GSI = 40 GSI = 60 GSI = 80 GSI = 100 α σ σ σ σ σ σ , _ ¸ ¸ + ′ + ′ · ′ s m ci ci ci 3 3 1 Figure 6.35. Non-dimensionalised plot of new shear strength curves for m i = 4 and varying GSI Page 6.67 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 σ′ 3 /σ c σ′ 1 /σ c Hoek 2002 Author's criterion α σ σ σ σ σ σ , _ ¸ ¸ + ′ + ′ · ′ s m ci ci ci 3 3 1 Figure 6.36. Comparison of the author’s criterion and the Hoek-Brown criterion (Hoek, 2002) for m i = 40 Page 6.68 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 σ′ 3 /σ c σ′ 1 /σ c Hoek 2002 Author's criterion α σ σ σ σ σ σ , _ ¸ ¸ + ′ + ′ · ′ s m ci ci ci 3 3 1 Figure 6.37. Comparison of the author’s criterion and the Hoek-Brown criterion (Hoek, 2002) for m i = 4 The Shear Strength of Rock Masses Page 6.69 6.5.3 Summary of Method The basic form of the shear strength equation remains unchanged from the Hoek-Brown criterion. α σ σ σ σ σ , _ ¸ ¸ + ′ + ′ · ′ s m ci ci 3 3 1 (6.27) For intact rock m = m i and α = α i . These should preferably be measured from triaxial tests on intact rock samples. Alternatively an approximation can be made using the uniaxial compressive strength, σ ci , and tensile strength, σ ti , of the intact rock and the equations below. ti ci i m σ σ · (6.28) , _ ¸ ¸ + + · 7 exp 1 2 . 1 4 . 0 i i m α (6.29) The estimation of m b , α b and s b can be made using the following equations: ¹ ¹ ¹ ' ¹ · 5 . 2 100 max GSI m m i b (6.30) ( ) , _ ¸ ¸ − − + · i b i i b m m 30 75 exp 9 . 0 α α α (6.31) ( ) ¹ ¹ ¹ ¹ ¹ ' ¹ , _ ¸ ¸ − · 1 15 85 exp min GSI s b (6.32) The equations presented by Hoek et al (2002) (Figure 6.6) can be used to estimate the cohesion, c, and friction angle, φ, of the rock mass, as the form of the Hoek-Brown equation has not been changed. Conclusions and Recommendations Page 7.1 7. CONCLUSIONS AND RECOMMENDATIONS 7.1 CONCLUSIONS This thesis is divided into two sections. The first section of this thesis (Chapter 2) describes the creation and analysis of a database on concrete and masonry dam incidents known as CONGDATA. The second and main section of this thesis (Chapters 3-6) had its origins in the results of Chapter 2 and the general interests of the author. It was found that failure through the foundation was common in the list of dams analysed and that information on how to assess the strength of the foundations of dams on rock masses was limited. This section applies to all applications of rock mass strength such as the stability of rock slopes. 7.1.1 The Analysis of Concrete and Masonry Dams The author has collected a far more extensive database on concrete and masonry dam incidents (CONGDATA) than has previously been attempted Generally, unlike some failure modes for embankment dams, e.g. internal erosion and piping, the stability of concrete and masonry dams is analysable and hence can readily be checked. The major unknowns for these dams lie in the foundation where sliding and piping failures can occur. It is for this reason that foundation problems (sliding, leakage and piping) are the main causes of failure to concrete dams. Overtopping tends to play a bigger part in the failure of masonry dams, possibly reflecting limited understanding of floods when they were built. It should be noted that the actual failure mode for ‘overtopping’ failures was often unknown. Foundation shear strength is the main cause of failure for dams with rock or unknown foundations. Shale (interbedded with other sedimentary units) has a greater tendency to be involved with sliding failure because of the likely presence of weaknesses in the bedding such as bedding surface shears. Shale and limestone (often interbedded) have a high incidence of failure. The limestone has a high proportion of accidents generally due to excessive leakage through dissolution. Conclusions and Recommendations Page 7.2 An analysis of the water levels at failure show most dams failed at their highest recorded water level (regardless of the age of the dam). Several of these were only slightly higher than that recorded previously. The database showed that, where information was available, most dam failures had some warning that could have resulted in the warning and evacuation of residents downstream. Often the warning was a sudden increase in the amount and rate of leakage. The actual volume of leakage was not as significant a guide. This indicates that although a dam may have performed satisfactorily in the past, increases in water level (above historical maxima) should be treated with caution and the dam sufficiently monitored as the water level rises. Piping is the main cause of failure for concrete and masonry dams with soil foundations. The alluvial soils have a tendency to pipe under the high gradients imposed. No gravity dam has been reported to have failed by sliding on alluvial soils. Piping tends to occur early in a dam’s life (<5 years, with one exception). From the data collected it appears that the failed dams suffered from a lack of ‘good engineering’. Very few dams were found with galleries (1 dam); drainage (1 dam); grout curtains (4 dams); and shear keys (1 dam). The downstream slopes appeared to be too steep. Six gravity failures had downstream slopes of 0.6:1 (H:V) or less. Failed dams, particularly gravity dams, were usually located in relatively wide valleys or were composite sections with earthfill dams. Three-dimensional effects are unlikely to have contributed any strength in these cases. h wf /W ratios ranged from 0.6 to 2.1 with an average of 1.35. The author has used the analysis of CONGDATA and a ‘population’ database to develop a method for assessing the first order probability of failure of masonry or concrete gravity dams. The method accounts for dam age, year commissioned and type; failure mode; foundation geology; height to width ratio; and monitoring and surveillance. General probabilities of failure for arch, buttress and multi-arch dams, based on failure and population statistics, are included. The author cautions that this approach should only be used as a first order approximation of the annual probabilities of failure. It is clearly very approximate, and suffers from being based on small numbers of failures, and limited quality data. Where Conclusions and Recommendations Page 7.3 significant decisions on dam safety are being made, detailed deterministic and/or probabilistic methods should be used. Whilst all care has been taken in compiling the data in CONGDATA, it should be remembered that the information in CONGDATA has come from numerous sources, not all of which could be validated. The analysis of dams in CONGDATA does not take into account such things as: surveillance; quality of construction; and quality of geological description. It is therefore recommended that this work be used in a qualitative sense only. 7.1.2 The Shear Strength of Intact Rock An overview of the strength of intact rock has been presented. It was demonstrated that the method of fitting the criterion to the test data has a major effect on the estimates obtained of the material properties. The results of a recent analysis of a large database of test results demonstrated that there are inadequacies in the Hoek-Brown empirical failure criterion as currently proposed for intact rock and, by inference, as extended to rock mass strength. The parameters m i and σ c are not material properties if the exponent is fixed at 0.5. Published values of m i can be misleading as m i is not related to rock type. The Hoek-Brown criterion can be generalised by allowing the exponent to vary. As expected, this change resulted in a better model of the experimental data. The most accurate method of estimating m i and α is through using triaxial tests on intact rock. The recommended method for regression of the data is modified least squares, Equation 7.1, combined with the extended formulation of the generalised Hoek-Brown criterion, Equation 7.2. The equations are repeated below. ( ) ( ) ¹ ; ¹ ′ − ≤ ′ × ′ − ′ ′ − > ′ ′ − ′ 3 1 3 3 3 1 1 1 3 for predicted measured 3 for predicted measured σ σ σ σ σ σ σ σ i m (7.1) ¹ ¹ ¹ ; ¹ − ≤ ′ ′ · ′ − > ′ , _ ¸ ¸ + ′ + ′ · ′ i c i c c i c m m m σ σ σ σ σ σ σ σ σ σ σ α 3 3 1 3 3 3 1 for for 1 (7.2) Conclusions and Recommendations Page 7.4 Analysis of individual data sets indicated that the exponent, α, is a function of m i which is, in turn, closely related to the ratio of σ c /σ t . A regression analysis of the entire database provided a model to allow the triaxial strength of an intact rock to be estimated from a reliable measurement of its uniaxial tensile and compressive strengths. The method proposed is the most accurate of those methods that do not require triaxial testing and is adequate for preliminary analysis. An analysis was presented that showed applying the Hoek-Brown criterion to most rocks results in systematic errors. Simple relationships for triaxial strength that are adequate for slope design were presented. 7.1.3 The Shear Strength of Rockfill A general overview of the shear strength of rockfill is presented. An analysis of a large database of test results was used to develop two new shear strength equations, one relating the secant friction angle and normal stress (Equation 7.3) and the other the principal stresses (Equation 7.4). The parameters can be found using equations 4.21- 4.23 and 4.25-4.30 in Chapter 4 respectively. The equation for principal stresses provided a much better fit to the data and is recommended. The equations presented effectively give the mean strengths of the data. Graphs are provided showing the range of strengths and the affect of various parameters on the shear strength of rockfill. Of the parameters statistically investigated, the unconfined compressive strength, particle angularity, fines content, maximum particle size and void ratio were found to have the most significant effect on the shear strength of rockfill. c n b a σ φ ′ + · ′ (7.3) α σ σ 3 1 ′ · ′ RFI (7.4) 7.1.4 Empirical Slope Design A review of current empirical methods of slope design using rock mass characterisation has also been presented. The findings highlighted the lack of well tested methods. Current slope design methods were based on limited databases with no failures and slopes of limited height. Many of the methods were incorrectly advocated for structurally controlled slopes. The author has presented new slope design curves, based Conclusions and Recommendations Page 7.5 on slopes that have had rock mass failure components, that can be used for preliminary slope design. 7.1.5 The Shear Strength of Rock Masses The Hoek-Brown criterion is the most commonly used strength criterion for rock mass and has thus been the main subject of this section of the thesis. The author has examined the appropriateness of the equation for predicting strengths at the two limits of rock mass (intact rock and rockfill). A study of the strength of intact rock using a large database of triaxial tests shows that the exponent, a, in the Hoek-Brown criterion should vary from about 0.2 to 0.9. The study of a database of 988 triaxial tests on rockfill shows that, if it is assumed a rockfill is representative of a very poor quality rock mass, the exponent, a, should approach 0.9 to 0.95 (with m i approximately 2.4-2.7) as GSI approaches zero. The current Hoek-Brown criterion assumes for most rock masses a is 0.5 and limits a to approximately 0.62 for a very poor quality rock mass. A problem with simply modifying a is that a and m i (or m b ) are interrelated. The author has developed a new method of determining the parameters in the Hoek- Brown criterion to overcome these problems. It is strongly suggested that the intact rock parameters m i & a i should be obtained using triaxial testing and statistical methods discussed in Chapter 3. The author has provided approximate methods of determining m i and a i where no triaxial test results are available. Equations have been derived for rock mass to address the limit (a b ≈0.95, m b ≈2.5, s b =0) of very poor quality rock masses. The equations developed allow for a reduction in m b from m i (and associated increase from a b from a i ) and s b from s i to this limit. A summary of the method is presented below. The basic form of the shear strength equation remains unchanged from the Hoek-Brown criterion. α σ σ σ σ σ , _ ¸ ¸ + ′ + ′ · ′ s m ci ci 3 3 1 (7.5) Conclusions and Recommendations Page 7.6 For intact rock m = m i and α = α i . These should preferably be measured from triaxial tests on intact rock samples. Alternatively an approximation can be made using the uniaxial compressive strength, σ ci , and tensile strength, σ ti , of the intact rock and the equations below. ti ci i m σ σ · (7.6) , _ ¸ ¸ + + · 7 exp 1 2 . 1 4 . 0 i i m α (7.7) The estimation of m b , α b and s b can be made using the following equations: ¹ ¹ ¹ ' ¹ · 5 . 2 100 min GSI m m i b (7.8) ( ) , _ ¸ ¸ − − + · i b i i b m m 30 75 exp 9 . 0 α α α (7.9) ( ) ¹ ¹ ¹ ¹ ¹ ' ¹ , _ ¸ ¸ − · 1 15 85 exp min GSI s b (7.10) The equations presented by Hoek et al (2002) can be used to estimate the cohesion, c, and friction angle, φ, of the rock mass, as the form of the Hoek-Brown equation has not been changed. Conclusions and Recommendations Page 7.7 7.2 RECOMMENDATIONS FOR FURTHER RESEARCH 7.2.1 The Analysis of Concrete and Masonry Dams The analysis of CONGDATA and the method for predicting probabilities of failure of concrete and masonry dams is based on field data of varying quality. Further detailed analysis of new incidents would improve the confidence in the conclusions presented in this thesis. Further detailed information on the geology of the foundations of dams would allow a better prediction of the likelihood of failure. Research into the effectiveness of monitoring and warning systems using the outcomes from this thesis would be of value. The author believes that it is better to do a probabilistic analysis of stability modelling uncertainty in the geology, shear strengths of the foundation and foundation pore pressures (uplift) as modified by grouting and drainage. Where large defects exist below a dam the shear strength in the foundation will be governed by these defects. As discussed in Section 7.2.2 the shear strength of field scale defects is still poorly understood. Further work in this area is required. Studies could examine large-scale failures, preferably with insitu shear tests and laboratory scale shear tests for comparison. However, these would be limited in number and quality. Alternatively studies could use numerical modelling to look at the effect of increasing the scale of defects. The use of the program PFC which models the movement and interaction of circular particles by the distinct element method has shown some promise in this area. 7.2.2 The Shear Strength of Rock Masses The methods presented for estimating the shear strength of intact rock and rockfill are based on substantial databases. These provide good bounds on the shear strength of rock masses. The development of the equations for estimating the strength of the transitional rock masses is based on a limited amount of field and laboratory data. Further analysis and reporting of well-documented failures and lab testing of rock masses of varying quality would improve the confidence in the results presented in this thesis and would also provide a better understanding of the degree of uncertainty in the results obtained Conclusions and Recommendations Page 7.8 by the equations presented in this thesis. The publishing of more data on failures would also assist in improving the slope design curves presented in this thesis. The equations for rock masses provided in this paper are principally for cohesionless rock masses. Further work could be carried out to assess cohesive rock masses. Modifications to the parameter s based on cohesive properties of the rock mass would allow the Hoek-Brown criterion to better model these types of rock masses at low confining stresses. This would be of value for predicting strengths for pit slope benches. The effect of the intermediate principal stress, σ′ 2 , could be incorporated into the equations for intact rock and ultimately rock masses. The use of Lade’s (1993) work would be of benefit here. Appendix Page A.1 APPENDIX A: CONGDATA DATABASE The full CONGDATA database is contained on the accompanying CD-ROM. APPENDIX B: DAM LIST - FAILURES Table B1. Dam list - failures Dam Name Country Dam Type Year Commissioned Year Failed Hlf (m) Kohodiar India PG/TE 1963 1983 36 Zerbino Italy PG 1925 1935 16 Mohamed V Morocco PG 1966 1963 62 Torrejon-Tajo Spain PG 1967 1965 62 Xuriguera Spain PG 1902 1944 42 Bayless (A) USA PG 1909 1910 17 Bayless (B) USA PG 1909 1911 17 Elwha River USA PG 1912 1912 51 Hauser Lake II USA PG 1911 1969 40 St Francis USA PG 1926 1928 62 Cheurfas Algeria PG(M) 1884 1885 42 Fergoug I Algeria PG(M) 1871 1881 43 Fergoug II Algeria PG(M) 1885 1927 43 Habra (A) Algeria PG(M) 1871 1872 40 Habra (B) Algeria PG(M) 1872 1881 40 Habra (C) Algeria PG(M) 1881 1927 40 Sig Algeria PG(M) 1858 1885 21 Bouzey France PG(M) 1881 1895 26 Chickahole India PG(M) 1966 1972 30 Khadakwasla India PG(M) 1879 1961 33 Kundli India PG(M) 1924 1925 45 Pagara India PG(M) 1927 1943 30 Tigra India PG(M) 1917 1917 28 Santa Catalina Mexico PG(M) 1900 1906 15 Granadillar Spain PG(M) 1930 1933 22 Puentes Spain PG(M) 1791 1802 69 Elmali I Turkey PG(M)/TE 1892 1916 23 Angels USA PG(M) 1895 1895 16 Austin (A) USA PG(M) 1893 1900 21 Lower Idaho Falls USA ER/PG(M) 1914 1976 15 Appendix Page A.2 Dam Name Country Dam Type Year Commissioned Year Failed Hlf (m) Lynx Creek USA PG(M) 1891 1891 15 Komoro Japan CB 1927 1928 16 Selsford Sweden CB/TE 1943 1943 21 Ashley USA CB 1908 1909 18 Overholser USA CB 1920 1923 17 Vega de Tera Spain CB(M) 1956 1959 35 Austin (B) USA CB(M) 1915 1915 20 Stony River USA CB(M) 1913 1914 15 Gleno Italy MV 1923 1923 35 Leguaseca Spain MV 1958 1987 20 Malpasset France VA 1954 1959 66 Moyie River USA VA 1924 1926 16 Vaughn Creek USA VA 1926 1926 20 Meihua China VA(M) 1981 1981 22 Bacino di Rutte Italy VA(M) 1952 1965 15 Gallinas USA VA(M) 1910 1957 32 Appendix Page A.3 APPENDIX C: DAM LIST - POPULATION OF DAMS Table C1. Dam list - USBR population Dam Name Type Year Commissioned Height (m) Altus PG 1945 33.5 American Falls PG 1927 31.5 Angostura PG 1949 58.8 Black Canyon PG 1924 55.8 Brantley PG 1988 33.5 Camp Dyer PG 1929 24.1 Canyon Ferry PG 1954 68.6 Elephant Butte PG 1916 91.7 Folsom PG 1956 103.6 Friant PG 1942 97.2 Grand Coulee PG 1942 167.6 Jackson Lake PG 1911 20 Keswick PG 1950 47.9 Kortes PG 1951 74.4 Marshall Ford PG 1942 84.7 Nimbus PG 1955 26.5 Olympus PG 1949 21.3 Savage Rapids Diversion PG 1921 13.1 Shasta PG 1945 183.5 Upper Stillwater PG 1988 88.4 Yellowtail Afterbay PG 1965 21.9 Bartlett CB/MV 1939 94 Coolidge (BIA) CB/MV 1928 75.9 Minidoka CB 1906 26.2 Pueblo CB 1975 76.2 Red Bluff Diversion CB 1963 15.8 Stony Gorge CB 1928 42.4 Thief Valley CB 1932 22.3 Anchor VA 1960 63.4 Arrowrock VA 1915 106.7 Buffalo Bill VA/PG 1910 106.7 Clear Creek VA 1914 25.6 Crystal VA 1976 98.5 Deadwood VA 1931 50.3 East Canyon VA 1966 79.2 Appendix Page A.4 Dam Name Type Year Commissioned Height (m) East Park VA 1910 42.4 Flaming Gorge VA 1964 153 Gerber VA 1925 26.8 Gibson VA 1929 60.7 Glen Canyon VA 1964 216.4 Hoover VA 1936 221.4 Horse Mesa VA 1927 93 Hungry Horse VA 1953 171.9 Monticello VA 1957 92.7 Mormon Flat VA 1926 68.3 Morrow Point VA 1968 142.6 Mountain Park VA 1975 40.5 Nambe Falls VA 1976 45.7 Owyhee VA/PG 1932 127.1 Parker VA 1938 97.5 Pathfinder VA(M) 1909 65.2 Santa Cruz VA 1929 46 Seminoe VA 1939 89.9 Stewart Mountain VA 1930 63.1 Swift VA 1967 62.5 Theodore Roosevelt VA(M) 1911 108.5 Warm Springs VA 1919 32.3 Wild Horse VA 1967 33.5 Yellowtail VA 1966 160 Appendix Page A.5 Table C2. Dam list - Australia/New Zealand population Dam Name Type Year Commissioned Height (m) Bendora VA 1961 47 Cotter PG 1915 31 Lower Molongolo PG 1994 32 Scrivener PG 1963 33 Wrights PG 1989 16 Avon PG 1927 72 Back Creek VA 1937 15 Borenore Creek VA 1928 18 Bundanoon VA 1960 35 Burrinjuck PG 1928 93 Captains Flat PG 1939 19 Carcoar VA 1970 58 Cataract PG 1907 56 Chichester PG 1923 44 Coeypolly Creek No I VA 1932 19 Cordeaux PG 1926 67 Crookwell PG 1937 16 Danjera CB 1971 36 Deep Creek PG 1961 21.3 Dunn Swamp VA 1930 16 Flat Rock Creek VA 1933 16 Fountaindale VA 1915 15 Glenquarry Cut PG 1974 18 Greaves Creek VA 1942 19 Guthega PG 1955 33.5 Happy Jack PG 1959 76.2 Hume PG 1936 Ingleburn MV 1933 16 Island Bend PG 1965 48 Junction Reefs MV 1897 19 Keepit PG 1960 55 Lake Medlow VA 1907 21 Lake Rowlands CB 1953 25 Lithgow No 2 VA 1907 26 Loyalty Road PG 1995 30 Maldon Weir PG 1968 20 Manly PG 1892 20 Medway VA 1964 25 Middle Cascade (No 1) VA 1915 15 Molong PG 1987 16 Appendix Page A.6 Dam Name Type Year Commissioned Height (m) Mooney Upper VA 1961 28 Moore Creek VA 1898 19 Murray 2 VA 1968 42.7 Nepean PG 1935 82 Oaky River PG 1956 18 Oberon CB 1949 35 Parramatta VA(M) 1857 15 Porters Creek PG 1968 18 Puddledock Creek VA 1928 19 Redbank Creek VA 1899 15 Rylstone VA 1953 20 Suma Park VA 1962 35 Tallowa PG 1976 43 Tantangara PG 1960 45.1 Timor VA 1961 22 Tumut 2 PG 1961 46.3 Tumut 3 Pipeline PG 1971 34.7 Tumut Pond VA 1959 86.3 Umberumberka PG 1914 41 Upper Cordeaux No 2 VA 1915 22 Warragamba PG 1960 142 Warragamba Weir PG 1940 21 Wellington VA 1933 15 Winburndale PG 1936 22 Woodford Creek VA 1928 16 Woronora PG 1941 74 Wyangla PG 1971 85 Atiamuri PG 1958 46 Aviemore PG 1968 57 Clyde PG 1993 105 Lake Onslow VA 1982 17 Mangahao No. 1 PG 1926 36 Mangahao No. 2 PG 1924 32 Marslin VA 1982 19 Roxburgh PG 1956 70 Waihopai VA 1927 34 Waitaki PG 1934 37 Whakamaru PG 1956 Beardmore PG 1972 17 Boggabilla Weir PG 1991 16 Burdekin Falls PG 1987 55 Burton Gorge PG 1992 34 Appendix Page A.7 Dam Name Type Year Commissioned Height (m) Cedar Pocket PG 1984 20 Chinaman PG 1993 19 Cooloolabin PG 1979 20 Copperfield PG 1984 40 Dumbleton PG 1992 15 Ibis PG 1906 16.5 Julius MV 1976 38 Koombooloomba PG 1961 52 Kroombit PG 1992 23 Lake Manchester PG 1916 38 Leslie PG 1965 33 Little Nerang PG 1961 47 Moogerah VA 1961 37 North Pine PG 1975 46 Rifle Creek VA 1929 21 Somerset PG 1955 50 Theresa Creek PG 1982 19 Tinaroo Falls PG 1958 47 Greenstone Ck Dam VA 1969 20 Wappa PG 1961 20 Wuruma PG 1969 46 Aroona PG 1955 26.2 Barossa VA 1902 36 Beetaloo PG 1890 31 Clarendon Weir PG(M) 1896 15 Middle River PG 1968 20 Mount Bold VA 1938 58 Myponga VA 1962 52 Sturt VA 1966 41 Ullabidinie PG 1914 22 Ulbana PG 1911 11.1 Warren PG 1916 26 Yeldulknie PG 1913 17 Bowden 1984 18 Catagunya PG 1962 49 Clark VA 1949 67 Cluny PG 1967 30 Craigbourne PG 1986 25 Devils Gate VA 1969 84 Gordon VA 1974 140 Henty PG 1988 23 Lake Margaret PG 1918 17 Appendix Page A.8 Dam Name Type Year Commissioned Height (m) Liapootah PG 1960 40 Meadowbank CB 1966 43 Mount Paris CB 1936 18 Pine Tier PG 1953 39 Repulse VA 1968 42 Ridgeway VA 1919 59 Trevallyn PG 1954 33 Clover CB 1956 20 Dartmouth PG 1980 25 Evansford PG 1887 17 Glenmaggie PG 1927 37 Goulburn Weir PG 1891 15 Hume Weir 1919 Junction CB 1945 26 Lauriston CB 1941 33 Lower Stoney Creek PG 1875 21 Maroondah PG 1927 46 Mt Cole PG 1903 28 Nicholson River CB 1976 16 Rocklands PG 1953 28 Swingler PG 1977 18 Yallourn Storage CB 1961 21 Canning PG 1940 70 Conjurunup PG 1992 Harvey PG 1916 24 Kununurra Diversion 1963 20 Mundaring PG 1902 71 New Victoria PG 1991 52 Serpentine Pipehead PG 1957 16 Wellington PG 1933 37 Appendix Page A.9 Table C3. Dam list - Portugal population Dam Name Type Year Commissioned Height (m) Alto Cavado PG 1964 29 Alem da Fazenda PG 1967 20 Carrapatelo PG 1972 57 Corgas PG 1991 25 Cova do Viriato PG 1962 28 Fratel PG 1973 43 Monte Novo PG 1982 30 Penha Garcia PG 1980 25 Pocinho PG 1982 49 Raiva PG 1981 36 Ranhados PG 1986 41 Regua PG 1973 42 Torrao PG 1988 70 Touvedo PG 1996 43 Valeira PG 1975 48 Gameiro PG/TE 1960 20 Andorinhas PG(M) 1945 25 Burgaes PG(M) 1940 30 Covao do Ferro PG(M) 1956 35 Freigil PG(M) 1955 17 Guilhofrei PG(M) 1938 49 Idanha PG(M) 1949 54 Lagoa Comprida PG(M) 1958 29 Poio PG(M) 1932 18 Povoa PG(M) 1928 32 Vale do Rossim PG(M) 1956 27 Penide PG(M) 1951 15 Caia CB/PG/TE 1967 52 Roxo CB/PG/TE 1968 49 Miranda CB 1961 80 Pracana CB 1951 60 Odivelas MV/TE 1972 55 Aguieira MV 1981 89 Alto Lindoso VA 1993 110 Bravura VA 1958 41 Cabril VA 1954 136 Caldeirao VA 1996 39 Appendix Page A.10 Dam Name Type Year Commissioned Height (m) Fagilde VA 1984 27 Fronhas VA 1984 62 Funcho VA 1991 49 Picote VA 1958 100 Varosa VA 1976 76 Vilarinho das Furnas VA 1972 94 Alto Rabagao VA/PG 1964 94 Bemposta VA/PG 1964 87 Castelo do Bode VA/PG 1951 115 Covao do Meio VA/PG 1953 25 Venda Nova VA/PG 1951 97 Alto Ceira VA 1949 36 Bouca VA 1955 65 Canicada VA 1955 76 Salamonde VA 1953 75 Santa Luzia VA 1942 76 Appendix Page A.11 APPENDIX D: CAUSES OF INCIDENTS Table D1. Causes of incidents - all dams Cause Fail Acc. Major Repairs Total Cause Fail Acc. Major Repairs Total 1.1.1 1 2 3 3.1.2 1 1 2 1.1.2 1 8 4 13 3.1.3 3 1 2 6 1.1.3 5 5 2 12 3.1.4 2 3 9 14 1.1.4 7 16 7 30 3.1.5 5 1 6 1.1.5 6 13 1 20 3.1.9 2 1 1 4 1.1.5.1 4 2 6 3.1.12 1 2 3 1.1.5.2 1 1 2 3.2 1 1 1.1.6 1 1 3.2.2 3 1 22 26 1.1.8 1 2 3 3.2.3 9 9 1.1.9 1 1 2 3.2.5 3 3 1.1.10 1 1 3.2.6 4 1 5 1.1.11 4 3 7 3.2.7 4 1 5 1.1.12 3 4 7 3.2.8 3 10 13 1.1.14 1 1 3.2.9 3 2 1 6 1.2.1 6 13 19 3.2.10 3 3 1.2.2 1 6 22 29 3.3.2 1 1 2 4 1.2.3 1 6 53 60 3.4.1 5 5 1.2.5 1 1 2 3.4.2 8 6 1 15 1.2.6 1 1 3.4.3 1 1 1.2.7 1 1 3.4.4 4 4 1.2.8 9 22 31 3.4.5 1 1 1.2.9 9 17 26 3.4.6 10 10 1.2.10 3 4 7 3.5.1 2 2 4 1.2.11 7 13 20 3.5.2 5 3 1 9 1.2.13 1 2 3 3.5.3 1 1 1.3.1 1 4 5 3.5.4 1 1 2 1.3.2 4 3 15 22 3.5.5 1 3 4 1.3.3 6 1 7 3.7.2 1 1 1.3.4 4 28 32 4.1.5 2 2 1.3.5 5 16 21 4.1.8 0 1.3.7 3 1 4 4.2.1 1 1 1.3.7.2 1 1 4.2.2 1 1 1.3.7.3 1 1 4.2.3 6 6 1.4.1 1 1 2 4.2.4 1 1 1.4.2 8 8 4.2.5 1 1 2 Appendix Page A.12 Cause Fail Acc. Major Repairs Total Cause Fail Acc. Major Repairs Total 1.4.3 1 1 2 4.2.6 1 1 1.4.4 1 1 2 4.2.7 1 2 3 1.4.6 1 2 3 4.2.8 4 1 5 1.4.7 2 3 5 4.2.9 1 2 3 1.5.1 1 2 2 5 4.2.10 1 1 1.5.2 2 4 6 12 4.2.12 3 13 16 1.5.4 2 3 5 4.2.13 2 12 14 1.5.5 2 2 4.4.2 1 1 1.5.6 1 1 4 6 4.4.3 1 1 1.6.1 2 2 4.4.4 3 1 4 1.7.1 1 1 4.5.1 1 1 1.7.2 8 8 4.5.5 4 4 2.3.9 5 5 4.6 1 10 5 16 4.6.1 1 1 4.9.1 2 2 4 4.6.2 1 1 2 4.9.2 2 2 4 4.6.3 1 1 4.11.1 1 1 4.7.1 6 13 10 29 4.11.6 10 6 16 4.7.2 4 1 5 4.11.7 1 4 5 4.7.3 1 1 4.12.6 1 1 4.7.4 1 1 5.1 5 5 4.7.6 1 1 2 5.3 4 1 5 4.7.7 1 1 5.4 9 2 11 4.7.8 4 9 13 6.1 1 1 4.7.9 1 3 4 6.2 5 2 7 4.8 2 16 6 24 Total 121 283 450 854 Appendix Page A.13 Table D2. Causes of incidents - PG dams Cause Fail Acc. Major Repairs Total Cause Fail Acc. Major Repairs Total 1.1.1 1 1 4.1.5 2 2 1.1.2 2 2 4 4.1.8 0 1.1.3 4 3 1 8 4.2.1 1 1 1.1.4 4 7 5 16 4.2.2 1 1 1.1.5 1 8 1 10 4.2.3 6 6 1.1.5.1 1 2 3 4.2.4 1 1 1.1.5.2 1 1 4.2.5 1 1 2 1.1.6 1 1 4.2.7 1 2 3 1.1.9 1 1 4.2.8 1 1 2 1.1.10 1 1 4.2.9 1 1 1.1.11 1 3 4 4.2.12 1 13 14 1.1.12 4 4 4.2.13 11 11 1.2.1 8 8 4.4.3 1 1 1.2.2 1 15 16 4.4.4 1 1 1.2.3 1 40 41 4.5.1 1 1 1.2.5 1 1 4.5.5 4 4 1.2.7 1 1 4.6 1 7 4 12 1.2.8 2 15 17 4.6.2 1 1 1.2.9 2 11 13 4.7.1 2 5 10 17 1.2.10 1 3 4 4.7.2 1 1 2 1.2.11 1 7 8 4.7.3 1 1 1.3.1 4 4 4.7.4 1 1 1.3.2 2 2 15 19 4.7.6 1 1 1.3.4 1 6 7 4.7.7 1 1 1.3.5 1 2 3 4.7.8 9 9 1.3.7 1 1 4.7.9 2 2 1.4.1 1 1 4.8 4 3 7 1.4.6 2 2 4.9.1 1 1 2 1.5.1 1 1 2 4 4.9.2 2 2 1.5.2 1 1 3 5 4.11.1 1 1 1.5.4 1 1 4.11.6 5 4 9 1.5.5 2 2 4.11.7 4 4 1.5.6 4 4 4.12.6 1 1 1.6.1 2 2 5.1 2 2 1.7.1 1 1 5.3 2 2 1.7.2 8 8 5.4 2 2 4 3.1.4 1 1 6.1 1 1 3.2.2 1 1 6.2 3 1 4 3.2.8 1 1 Total 19 82 263 364 Appendix Page A.14 Table D3. Causes of incidents - PG(M) dams Cause Fail Acc. Major Repairs Total Cause Fail Acc. Major Repairs Total 1.1.3 1 1 3.2.9 3 2 1 6 1.1.5 1 1 3.2.10 3 3 1.2.2 1 1 3.3.2 1 2 3 1.2.3 1 1 3.4.1 5 5 1.2.8 1 1 3.4.2 7 6 1 14 1.3.1 1 1 3.4.3 1 1 1.3.3 1 1 3.4.4 4 4 1.3.7 1 1 2 3.4.6 8 8 1.4.7 1 1 3.5.1 2 2 4 1.5.6 1 1 3.5.2 5 3 8 2.3.8 1 1 3.5.3 1 1 2.3.9 5 5 3.5.4 1 1 3.1.12 1 2 3 3.5.5 1 3 4 3.1.2 1 1 2 3.7.2 1 1 3.1.3 3 1 1 5 4.2.8 1 1 3.1.4 1 2 8 11 4.6 1 1 3.1.5 4 1 5 4.6.2 1 1 3.1.9 2 1 1 4 4.7.1 2 1 3 3.2 1 1 4.7.8 1 1 3.2.2 3 1 20 24 4.7.9 1 1 3.2.3 8 8 4.8 1 1 3.2.5 2 2 4.9.1 1 1 3.2.6 4 1 5 4.11.6 1 1 3.2.7 4 1 5 5.3 1 1 3.2.8 2 10 12 5.4 2 2 Total 62 39 80 181 References Page Ref.1 REFERENCES Abel, J.F. and Jowis, J.E. (1979) Concrete shaft lining design. Concrete Shaft Lining Design, 20th U.S. Symposium on Rock Mechanics, Austin, Texas, pp. 627-640. Abraham, T.J. (1970) Selection and Design of a Compacted Rock Fill Dam with a Slopin g Earth Core on Foundation Rock with Weak Horizontal Bedding Planes. 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