Guidelines for the Design of High Mast Pole Foundation

Guidelines for the Design of High MastPole Foundations Fourth Edition Ministry of Transportation Engineering Standards Branch BRO - 009 Technical Report Documentation Page Publication Title GUIDELINES FOR THE DESIGN OF HIGH MAST POLE FOUNDATIONS Fourth Edition Author(s) Walter Kenedi, Mike Gergely, Raymond Haynes Originating Office Bridge Office, Engineering Standards Branch, Ontario Ministry of Transportation Report Number BRO – 009 Publication Date May 2004 Ministry Contact Bridge Office, Engineering Standards Branch, Ontario Ministry of Transportation 301 St. Paul Street, St. Catharines, ON L2R 7R4 Tel: (905) 704-2406; Fax: (905) 704-2060 Abstract These guidelines present procedures for the design of the Ontario Ministry of Transportation’s High Mast Pole Foundations subject to wind loads, including characteristics such as frost depth, layered soils, socketing to or embedding into rock. This third edition of design guidelines is based on the recently released Canadian Highway Bridge Design Code, and is in response to revised pole cross-sections and anchorage details for all five standard pole heights. Considered as ‘short’ piles, the design principles and included examples have a strong theoretical basis, which has been modified only to allow a greater simplicity in practical application. Key Words High mast pole; caisson foundations; wind pressure Distribution Unrestricted technical audience Ministry of Transportation Engineering Standards Branch BRO - 009 Guidelines for the Design of High Mast Pole Foundations Fourth Edition May 2004 Prepared by Bridge Office Ontario Ministry of Transportation 301 St. Paul Street St. Catharines, Ontario, L2R 7R4 Tel: (905) 704-2406; Fax: (905) 704-2060 April 2003 Although the contents of this guideline have been checked no warranty, expressed or implied, is made by the Ministry of Transportation as to the accuracy of the contents of this guideline, nor shall the fact of distribution constitute any such warranty, and no responsibility is assumed by the Ministry of Transportation in any connection therewith. It is the responsibility of the user to verify its currency and appropriateness for the use intended, to obtain the revisions, and to disregard obsolete or inapplicable information. May 2004 PREFACE The Structural Office issued the first edition of these procedures in January 1993, and the design was based on the 1983 Ontario Highway Bridge Design Code (OHBDC). (Note that the Third Edition of the OHBDC sometimes referred to as the 1991 OHBDC was not available at that time.) In June 1994 the Structural Office issued the second edition that added a section for foundations in rock, design aids and design to the Third edition of OHBDC. For the third edition of this manual changes were necessary for the following reasons: 1) Changes in April 2002 to the shape and diameters of the High Mast Lighting Poles used by the Ministry of Transportation prior to this date. 2) Replacement of the Ontario Highway Bridge Design Code (OHBDC) Third Edition with the Canadian Highway Bridge Design Code CAN/CSA-S6-00 (CHBDC) in May 2002. A summary of the changes to the poles that affect the design of their foundations is as follows: a) The pole diameters, at the base, have increased significantly. b) Circular pole cross-sections are no longer an option. The 25, 30 and 35 metre poles are 8-sided, and the 40 and 45 metre poles now have 12 sides instead of 8. c) The diameters of the base plate have changed and a single base plate replaces the double base plate. d) The bolt circle diameter on the anchorage assembly has increased except for the 25-metre pole, which has decreased. e) The number of anchor rods for the 40 and 45 metre poles has increased from 8 to 12. f) The unfactored moments at the base of the poles have increased for the 25, 30 and 35 metre poles and slightly decreased for the 40 and 45. g) The unfactored shears at the base of the poles have increased for the 25, 30 and 35 metre poles but no significant change for the 40 and 45. Details of these changes may be found on the following ministry standards and should be used when designing high mast pole foundations for the Ministry of Transportation: OPSD 2450.0110 HMLP 25m, 30m and 35m 8-Sided Pole Nov. 2003 OPSD 2450.0210 HMLP 40m and 45m 12-Sided Pole Nov. 2003 OPSD 2456.0110 HMLP Anchorage Assembly Details Nov. 2003 In addition the following standards are also available for use: SS116-50 HMLP Footing - Ground Mounted SS116-51 HMLP Footing - Top Barrier Wall Mounted (Symmetrical) SS116-52 HMLP Footing - Top Barrier Wall Mounted (Asymmetrical) Differences between the two codes do not have any significant effect on the contents of this manual as the load factors and wind load equations to be applied in the design of high mast lighting foundations are similar. In general, the philosophy used for design and many parts of the guidelines are still applicable, however there were some critical parts of the manual that required revision. For the fourth edition of this manual the Report Number was changed, MTOD standards were replaced by OPSD standards, and some typographical errors corrected. April 2003 Table of Contents 1.0 INTRODUCTION........................................................................................1 2.0 NOTATION ................................................................................................3 3.0 LOADING...................................................................................................7 3.1 LOADING ON MTOD POLES ............................................................................................ 7 4.0 COHESIVE SOILS.....................................................................................9 4.1 EXACT SOLUTION.......................................................................................................... 10 4.2 APPROXIMATE SOLUTION............................................................................................ 10 4.2.1 SOLUTION IN TERMS OF FOUNDATION LENGTH.................................................. 11 5.0 COHESIONLESS SOILS.........................................................................12 5.1 EXACT EQUATIONS ....................................................................................................... 13 5.2 APPROXIMATE EQUATIONS ......................................................................................... 14 5.2.1 APPROXIMATE EQUATIONS IN TERMS OF FOUNDATION LENGTH.................... 14 6.0 FOUNDATIONS IN ROCK.......................................................................16 6.1 CAISSON FOUNDATION EMBEDDED IN ROCK........................................................... 16 6.1.1 EXACT SOLUTIONS ................................................................................................... 16 6.1.1.1 SOLUTION IN TERMS OF FOUNDATION LENGTH.............................................. 17 6.2 FOUNDATION ANCHORED TO ROCK........................................................................... 17 7.0 FOUNDATIONS WITH TIP SOCKETED IN ROCK.................................19 7.1 COHESIVE SOIL WITH PILE TIP SOCKETED IN ROCK............................................... 19 7.1.1 EXACT SOLUTIONS ................................................................................................... 19 7.2 COHESIONLESS SOIL WITH PILE TIP SOCKETED IN ROCK..................................... 20 7.2.1 EXACT SOLUTIONS ................................................................................................... 21 7.2.2 APPROXIMATE SOLUTIONS ..................................................................................... 21 8.0 FOUNDATIONS IN LAYERED SOIL.......................................................22 8.1 APPROXIMATE SOLUTION............................................................................................ 22 9.0 CAISSON REINFORCEMENT.................................................................23 9.1 CALCULATE FACTORED APPLIED MOMENT.............................................................. 23 9.1.1 COHESIVE SOILS....................................................................................................... 23 9.1.2 COHESIONLESS SOILS ............................................................................................. 23 9.1.3 CAISSONS EMBEDDED IN ROCK............................................................................. 24 9.1.4 FOUNDATIONS ANCHORED TO ROCK.................................................................... 24 9.1.5 LAYERED SOILS......................................................................................................... 24 9.2 CALCULATE FACTORED RESISTING MOMENT.......................................................... 25 9.3 HIGH MAST POLE ANCHORAGE AND CAISSON REINFORCEMENT DETAILS........ 25 9.4 ROCK ANCHORS ............................................................................................................ 26 April 2003 10.0 EQUATION SUMMARY...........................................................................28 11.0 PROCEDURES AND EXAMPLES ..........................................................30 11.1 EXAMPLE 1: HOMOGENEOUS COHESIVE SOIL ........................................................ 33 11.2 EXAMPLE 2: HOMOGENEOUS COHESIONLESS SOIL .............................................. 35 11.3 EXAMPLE 3: CAISSON WITH TIP SOCKETED IN ROCK ............................................ 38 11.4 EXAMPLE 4: CAISSON EMBEDDED IN ROCK............................................................. 42 11.5 EXAMPLE 5: FOUNDATION ANCHORED TO ROCK ................................................... 44 11.6 EXAMPLE 6: CAISSON DESIGN USING EXACT EQUATIONS.................................... 47 12.0 APPENDICES..........................................................................................50 12.1 APPENDIX A: PROPERTIES OF SOILS........................................................................ 50 12.1.1 COHESIVE SOILS....................................................................................................... 50 12.1.2 COHESIONLESS SOILS ............................................................................................. 50 12.2 APPENDIX B: DESIGN AIDS.......................................................................................... 52 12.2.1 COHESIVE SOILS....................................................................................................... 52 12.2.2 COHESIONLESS SOILS ............................................................................................. 52 12.2.3 FOUNDATIONS ANCHORED TO ROCK.................................................................... 53 12.2.4 REINFORCEMENT REQUIRED FOR CAISSON FOUNDATIONS ............................ 53 April 2003 1 1.0 INTRODUCTION These guidelines present procedures for the design of High Mast Pole Foundations subject to wind loads. This comprehensive guide for caisson foundations accounts for the effects of frost depth, socketing in bedrock, layered soils and foundations entirely in bedrock, some of which were not fully elaborated on in previous reports. (Ma, S., "Proposed Design Guide For High Mast Lighting Foundations By Broms Method, OHBDC Loadings.", Structural Office, Procedures Section, 19**) (Wong, Dennis, "High Mast Pole Foundation", Central Region Structural Section Procedures Manual, Ontario Ministry of Transportation, 1985) Earlier design guidelines specified an absolute ½” or 12 mm lateral deflection at ground surface. The methodology proposed in this guide is based on a foundation rotation limit of 0.005 radians. The theoretical basis of this report is based on two papers published by Bengt Broms on cohesive (Broms, B. B., "Lateral Resistance of Piles in Cohesive Soils", Soil Mechanics and Foundations Division, ASCE, 1964) and cohesionless (Broms, B. B., " Lateral Resistance of Piles in Cohesionless Soils", Soil Mechanics and Foundations Division, ASCE, 1964.) soils. Broms papers present a series of graphs for piles which become very difficult to interpolate for the ranges of design parameters relevant to High Mast Poles and so these guidelines were developed. The foundations for high mast poles are made of reinforced, cast in place concrete and are classified as caisson type piles. The caissons are made using the following method: a hole is augured to the required depth, and the reinforcing cage is lowered into the hole; the top part of the hole (and the part above the ground surface) is formed using a circular sono tube and the anchorage assembly is positioned in place; concrete is then placed into the hole to the desired elevation. In this document, the term "pile" is meant to mean caisson. The caissons used for High Mast Poles are described as free-headed piles by Broms since they are able to rotate and translate at the ground surface. For the purposes of this document, piles are classified into three categories in accordance with Brom's findings, depending on the relative stiffnesses between the soil and the pile. Short piles are those considered infinitely stiff relative to the soil around them and thus deflect as a rigid body. Long piles subject to lateral load bend; develop adequate soil resistance near the ground surface such that the tip of the pile remains at a low stress. Intermediate length piles fall between the other two where the bending of the pile is significant and the full length of the pile is stressed by the soil. Typically, caissons for high mast pole foundations fall into the short pile category. If the short pile criteria are not met then the caisson diameter should be increased, since analysis of intermediate length piles is beyond the scope of this document. Lateral deflections are calculated using the concept of lateral subgrade reaction where the soil pressure on the pile varies with the deflection of the soil. Broms proposed reducing this lateral reaction by varying amounts for cohesive and cohesionless soil under sustained and repetitive loading. However, the design wind load is not a sustained load and thus the reductions are not used. This guide makes several conservative assumptions to simplify the procedures for calculating the caisson lengths. The overturning moments are obtained solely from the wind force acting on the pole and luminaries and resisting effects from the self-weight of the pole and the concrete caisson have been ignored. Also, the soil April 2003 2 resistance within the entire frost depth zone has been ignored even though the thawing does not affect this entire layer of soil at the same time. Previous guides limited the deflections at ground surface to 0.5 inch or 12mm. The half-inch limit is a serviceability criterion. Applying this limit to short piles as opposed to longer piles will lead to considerably larger deflections of the mast tip due to foundation movement that could degrade the performance and life expectancy of the light assembly. Likewise, using the arbitrarily set 0.5 inch deflection limit, alone, might be conservative for weaker soils but is could be unsafe for stiffer soils. Zubacs (Zubacs, Victor, "Report on Design Procedures for High Mast Lighting Foundations", Internal Report SO 92-06, Structural Office, Ontario Ministry of Transportation, 1991) found that a limit on the pile rotation, as opposed to the pile deflection, led to consistent mast behaviour for all pile lengths. Using a 0.005 radian rotation limit gives acceptable mast tip deflections and more consistent foundation behaviour than the deflection limit. Zubacs modelled the piles using a linear elastic analysis program, which took into account the interaction between the pile and soil and allows for bending of the pile. Comparing program results to a manual method that assumes rigid pile behaviour shows that the rigid pile assumption is in error by about 5%. High mast poles placed on cut and fill slopes and fill embankments are not covered in this report. If the pole is to be placed on a slope then the geotechnical engineer should be consulted in determining the required depth of foundation. Enquiries regarding the contents of this report may be directed to the Bridge Office. May 2004 3 2.0 NOTATION A s Area of steel reinforcement or rock anchors, mm 2 C e Wind exposure coefficient C g Wind gust effect coefficient C h Horizontal wind drag coefficient c u Undrained shear strength, kPa D Diameter of caisson or foundation, m e Distance from equivalent horizontal wind load on pole to bottom of base plate, m E Distance from equivalent horizontal wind load on pole to the ground, m E p Modulus of elasticity of caisson, MPa Equivalent lateral resistance parameter, an approximation of the coefficient of lateral subgrade reaction, kN/m 3 F Depth of frost penetration in soil, m f’ c Compressive strength of concrete in the foundation, MPa F h Horizontal design pressure due to wind, kPa f horiz Allowable horizontal bearing capacity of sound rock at ULS, kPa F q Resistance factor on unconfined compressive strength of cohesive soil Frost susceptible depth for situations with rock near or at the surface (the geotechnical engineer may specify a smaller value for F if the rock is competent) f vert Allowable vertical bearing capacity of sound rock at ULS, kPa f y Yield strength of reinforcing steel, MPa k Coefficient of lateral subgrade reaction, depends on soil-caisson interaction K p Rankine passive earth pressure coefficient L Length of foundation below depth ‘V’ for caisson, m L lim The minimum length of foundation allowed for foundation anchored to rock due to the size of the anchorage assembly, m L REQ The required foundation length based on rotation, ultimate lateral load capacity and “too short” pile limits. M f Factored applied bending moment on the foundation at ULS, kN.m M r The factored flexural resistance of the foundation, kN.m M unf Unfactored moment due to wind at the level of the base plate, kN.m N Standard penetration number n h Coefficient of horizontal subgrade reaction of cohesionless soil, a property of in-situ soil, kN/m 3 P sls SLS wind load on the foundation, kN P uls ULS wind load on the foundation, kN P ult The ultimate lateral resistance of the caisson, kN P unf Unfactored wind load on the pole, kN q 50 50 year reference wind pressure, Pa q u Unconfined compressive strength of cohesive soil = 2c u , kPa S Depth of socket into rock, m T i Thickness of soil layer, m T w Thickness of very weak top layer of soil, or the thickness of soil atop rock, m U Distance above caisson tip to point of rotation, m May 2004 4 V Depth to resisting soil or rock (given in table below), m Application Caisson in Cohesive Soil Caisson in Cohesionless Soil Caisson Embedded in Rock Foundation Anchored to Rock Rotation Larger of F or T W Larger of F or T W N.A. N.A. Ultimate Resistance Larger of F or T W , or 1.5D Larger of F or T W Larger of F or (W+T W ) Larger of F or (W+T W ) or (L lim - ∆ drainage ) Bending Moment in Caisson Larger of F or T W , or 1.5D Larger of F or T W Larger of F or (W+T W ) Larger of F or (W+T W ) or (L lim - ∆ drainage ) W Depth of weathered rock, m y Lateral deflection of caisson due to wind, m z Depth below grade, m β Parameter for determining relative length of pile in cohesive soils ∆ Additional eccentricity due to levelling (typ. 0.1m), drainage (typ. 0.2m), concrete median barrier wall or construction staging (see Figure 2.1 (a) and 2.1 (b)), m ∆ drainage Portion of additional eccentricity due to drainage, i.e. the distance from the ground surface to the top of concrete footing (minimum of 0.2m), m γ Unit weight of soil, taken as submerged unit weight if soil is below water table and wet unit weight if the soil is above the water table, kN/m 3 η Parameter for determining relative length of pile in cohesionless soils θ Calculated rotation of caisson, rad. θ allow Allowable rotation of caisson at SLS loading = 0.005 rad. φ Angle of internal friction of cohesionless soil ρ Reinforcement ratio of steel reinforcement or rock anchors -L Equation denoted with “-L” are rearranged equation to directly give the Length of Caisson required * Equations denoted with an asterisk are approximate equations with some restrictions on the range of applicability April 2003 5 Figure 2.1 (a): Notation for High Mast Poles and Foundations April 2003 6 Figure 2.1 (b): Notation for High Mast Poles and Foundations April 2003 7 3.0 LOADING The loading on High Mast Light Poles is calculated from the Canadian Highway Bridge Design Code (Canadian Highway Bridge Design Code, CSA S6-00) (CHBDC). The wind load per unit frontal area is calculated by CHBDC Clause 3.10.2.2 as: h g e h C C C q F 50 = Eq. 3.1 where: q 50 is the 50 year return reference wind pressure (3.10.1.1). C e is the exposure coefficient (3.10.1.3) and the value depends on the height of each component above the ground. C g is the gust effect coefficient (3.10.1.2) = 2.5. C h is the horizontal drag coefficient (A3.2.2) and depends on the shape of each component in the pole. This equation is to be used for all components of the pole including the pole and the entire luminaire assembly. 3.1 LOADING ON MTOD POLES The wind loading has been determined for the poles described in OPSD 2450.0110 & OPSD 2450.0210. This includes the unfactored wind load on the poles and the unfactored moment on the poles caused by the wind. The eccentricity of the wind load above the pole base plate is what produces to the moment. An allowance is also made for an increase in this moment due to the P- delta effect; the base moment caused by the weight of the pole and luminaire assembly in their deflected position. This allowance amounts to 5%. Table 3.1 summarizes the unfactored wind force and the equivalent eccentricity, including for the P-delta effect. Table 3.1: Unfactored wind load and eccentricity of load. Pole Height Wind Force, P unf (kN) M unf (kN.m) | | . | \ | = unf unf P M e 05 . 1 (m) # 25 m 29 380 13.8 30 m 38 570 15.8 35 m 50 815 17.1 40 m 48 895 19.6 45 m 56 1155 21.7 # - Note: Add to this value the total additional eccentricity (Δ ). The eccentricity of the wind load above the pole base plate is calculated such that a concentrated lateral load applied at the specified location produces the equivalent effect about the base as the sum of the wind loads. The location of the wind load above the ground must also include an allowance for the height of the pole base plate above the ground surface. Typically the bottom of the base plate April 2003 8 is no more than 0.1 m above the top of the concrete foundation, which is in turn about 0.2 m above the level of the finished grade. Frequently, high mast poles are erected before the local topography is finished to the final grade. This may result in a portion of the foundation being exposed above ground level for some period of time. The high mast pole may also be erected on a median barrier wall creating an extra distance to the ground. These extra lengths must be treated as additional eccentricity. For various calculations, the serviceability and ultimate limit states loads are required. From CHBDC Clause A3.2.1, the SLS and ULS factors can be obtained as 0.7 and 1.3 respectively. Since the tabulated values were obtained for the highest wind pressure in Ontario, the wind at each specific location is adjusted by the local wind pressure. Thus the equations become: | . | \ | = 595 7 . 0 50 q P P unf sls Eq. 3.1 | . | \ | = 595 3 . 1 50 q P P unf uls Eq. 3.2 Although all high mast poles are designed for 595 Pa, the design of caissons is site-specific; they are designed for the reference wind pressure of the specific site. April 2003 9 4.0 COHESIVE SOILS The coefficient of lateral subgrade reaction, k, for cohesive soils is assumed to be independent of the depth of soil. An equivalent lateral resistance parameter, k, (which, for most high mast pole foundations, is a conservative approximation of the coefficient of lateral subgrade reaction) is given in the Canadian Foundation Engineering Manual (Canadian Geotechnical Society, "Canadian Foundation Engineering Manual", 2nd ed., Canadian press & pub. Vancouver, 1985) as: . 2 67 D q k u = Broms suggests separating the deflection into two components, one due to translation and one due to rotation of the pile. To calculate this, two separate lateral resistance parameters are needed, one for translation and one for rotation. When these are combined an approximate (and conservative) single value for the equivalent lateral resistance parameter, k, can be obtained as: LD q k u 103 = . At SLS loads, the pile rotates about a point above the tip leading to the soil reactions shown in Figure 4.1 (a). The soil resistance is calculated as the product of k, and y, the deflection. The strength of the frost-affected layer cannot be counted on to provide resistance and thus it is considered as additional eccentricity. Figure 4.1 (a): Distribution of soil stresses in cohesive soil at SLS In order for the pile to remain rigid at the SLS load it must be "short" as defined by Broms. Broms gives the limit on pile length as β L<2.25, which becomes: ( ) D q E L u p 7 1 2 2 3 2 12 8 2 10 103 4 9 ( ( ¸ ( ¸ < π . Substituting in for ( ) 5 . 1 ' 2300 6900 3000 | . | \ | + = c c p f E γ , with γ c = 2400 kg/m 3 , the equation becomes: ( )7 2 55 u q D L < . Eq. 4.1 April 2003 10 At ULS the deflections in the soil are large enough to develop the full plastic resistance of the soil. The top layer of soil, 1½ times the pile diameter or the frost depth, whichever is larger, is assumed to have no resistance since the soil is being pushed upwards as the pile moves laterally. Below this point the soil is assumed to have a constant resistance of 4½ times the unconfined compressive strength of the soil regardless of the pile shape. The resulting soil stress distribution is shown in Figure 4.1 (b). Figure 4.1 (b): Stress distribution in cohesive soil at ULS At ULS, the CHBDC resistance factor of Fq=0.5 (CHBDC 6.6.2.1) shall be applied to the unconfined compressive strength. 4.1 EXACT SOLUTION The exact solutions are obtained based on the soil stress distributions given in Figures 4.1 (a) and (b). The foundation rotation can be determined from: ( ¸ ( ¸ | . | \ | + + = L V L E kDL P sls 2 1 6 2 θ . When LD q k u 103 = , the equation becomes: ( ¸ ( ¸ | . | \ | + + = L V L E L D q P u sls 2 1 103 6 5 . 1 θ . Eq. 4.2 The ultimate lateral load capacity can be determined from: | . | \ | | . | \ | | . | \ | | . | \ | | . | \ | | . | \ | | . | \ | + + − + + + + + = 2 1 9 81 81 162 2 81 2 81 2 81 L V L E L V L E L V L E L V L E DL u q q F ult P Eq. 4.3 4.2 APPROXIMATE SOLUTION The above equation for ultimate lateral load is very complicated and can be simplified for the ranges of eccentricity, pile length, pile diameter and frost depths that are commonly encountered in Ontario. To use the approximate equation it is required that the following two limits be met: 7 75 . 1 < | . | \ | < L E and 4 . 0 05 . 0 < | . | \ | < L V . April 2003 11 The approximate ultimate lateral load capacity of the foundation may be calculated from: | . | \ | + + = L V L E DL q F P u q ult 2 1 2 . 2 Eq. 4.3* 4.2.1 SOLUTION IN TERMS OF FOUNDATION LENGTH The previous exact equation can be rewritten to yield the approximate length of caisson required. To determine the foundation length, L, based on limiting rotation, the following equation must be solved iteratively: 3 2 12 | . | \ | + + = V E L kD P L allow sls θ . When LD q k u 103 = , and substituting in θ allow =0.005, the equation becomes: 4 . 0 2 3 . 23 ( ( ¸ ( ¸ | . | \ | + + = V E L D q P L u sls . Eq. 4.2-L To determine the foundation length, L, based on the ultimate soil capacity, the following equation may be used to solve directly for L: ( ) V E D q F P D q F P D q F P L u q uls u q uls u q uls + | | . | \ | + | | . | \ | + | | . | \ | = 9 8 81 8 9 2 2 . Substituting in for F q , the equation becomes: ( ) V E D q P D q P D q P L u uls u uls u uls + | | . | \ | + | | . | \ | + | | . | \ | = 9 16 81 16 9 4 2 Eq. 4.3-L May 2004 12 5.0 COHESIONLESS SOILS The coefficient of lateral subgrade reaction, k, of the in-situ soil is assumed to increase linearly with the depth below grade, inversely with the diameter of the pile and directly with the coefficient of horizontal subgrade reaction, n h , (a coefficient which varies with soil properties and not with the soil-pile interaction). Approximate values of n h were found by Terzaghi (Terzaghi, K., "Evaluation of Coefficients of Subgrade Reaction", Gotechnique, Institution of Civil Engineers, Vol. V, London, 1955, pp. 297-326). The equivalent lateral resistance parameter, k, can be found by substituting these values of n h into the equation: D z n k h = . Broms did not address the problem of frost susceptible soils and it has become common to ignore the soil resistance from the frost susceptible layer and treat that thickness of soil as additional eccentricity. However, for cohesionless soils the equivalent lateral resistance parameter and the ultimate soil strength both increase with depth because of the weight of the overburden. Thus the weight of the soil affected by frost can be counted on to improve the resistance of the soil below. At SLS loads the pile is assumed to rotate about a point above the tip of the pile. The resistance is calculated by multiplying the equivalent lateral resistance parameter, k, by the deflection of the soil, y. Both these quantities vary with depth of soil and are shown in Figure 5.1 (a). Also shown are the soil stresses. Figure 5.1 (a): Distribution of stresses in cohesionless soil at SLS. In order for the pile to remain rigid at the SLS load it must be "short" as defined by Broms. Broms gives the limit on pile length as ηL<2, which becomes: 5 4 5 1 3 2 10 D n E L h p ( ¸ ( ¸ < π . Substituting in for ( ) 5 . 1 ' 2300 6900 3000 | . | \ | + = c c p f E γ , with γ c = 2400 kg/m 3 , the equation becomes: 5 1 4 33 | | . | \ | < h n D L . Eq. 5.1 April 2003 13 In order to prevent high local stresses from developing at the tip of the pile it is recommended by Broms that the equations only be applied when the pile length is at least 4 times the pile diameter. At the ultimate load the movement of the pile is large enough to develop the full passive pressure of the soil on the pile over its entire length. The active pressures that develop as the pile moves away from the soil are neglected. Passive pressure is calculated by the Rankine theory | | . | \ | − + = ϕ ϕ sin 1 sin 1 p K . Tests studied by Broms found that regardless of pile cross section the actual passive pressures on the piles can safely be taken as 3 times the Rankine pressure. This is because the pile has a rough surface and a finite size enabling a larger wedge of soil to provide resistance. However, most tests that Broms studied involved driven piles in which the soil around the pile benefited from compaction due to the driving process. High Mast Pole Foundations are drilled caisson foundations. This procedure is therefore based on the use a factor of 2 on the Rankine pressure. Again at the ULS load, the pile rotates about a point and the full resistance of the soil is developed. The resulting stresses on the pile are shown in Figure 5.1 (b). This differs from the soil pressure distribution given by Broms, who shows the lower part of the soil pressure as an equivalent concentrated force located at the pile tip. Figure 5.1 (b): Distribution of stresses in cohesionless soil at ULS. 5.1 EXACT EQUATIONS The exact solutions are obtained based on the soil stress distributions given in Figures 5.1 (a) and (b). The foundation rotation can be determined from: ( ( ( ( ( ¸ ( ¸ ) ` ¹ ¹ ´ ¦ | . | \ | + ¦ ) ¦ ` ¹ ¦ ¹ ¦ ´ ¦ | . | \ | + | . | \ | + | . | \ | + | . | \ | | . | \ | + | . | \ | + | . | \ | + | . | \ | | . | \ | + | . | \ | + = L V L V L V L V L V L E L V L V L V L E L E L n P h sls 3 2 6 6 1 18 18 30 18 21 6 4 12 2 3 2 2 3 θ April 2003 14 The ultimate lateral load capacity from: ( ( ( ( ( ¸ ( ¸ + | . | \ | + | . | \ | + | . | \ | − | . | \ | | . | \ | − | . | \ | + = L V L E L u L u L u L V L V L DK P p ult 1 3 4 2 2 3 1 3 2 2 2 γ where u is the distance to the point above the caisson tip about which the caisson rotates. It is calculated from: 2 2 2 2 1 1 L DK P L V L V L V L u p ult γ + + | . | \ | + | . | \ | − | . | \ | + = 5.2 APPROXIMATE EQUATIONS The above equations for rotation and ultimate load are very complicated and can be simplified for the ranges of eccentricity, pile length, pile diameter and frost depths that are commonly encountered in Ontario. To use the approximate equations it is required that the following two limits be met: 7 75 . 1 < | . | \ | < L E and 4 . 0 05 . 0 < | . | \ | < L V . Hence, the approximate foundation rotation can be determined from: ( ( ( ( ¸ ( ¸ + | . | \ | + | . | \ | = 35 . 0 8 . 0 12 3 L V L E L n P h sls θ Eq. 5.2* The ultimate lateral load capacity can be approximated as: ( ( ( ( ¸ ( ¸ + | . | \ | | . | \ | + | . | \ | = 9 . 0 7 3 3 2 2 L E L V L DK P p ult γ Eq. 5.3* 5.2.1 APPROXIMATE EQUATIONS IN TERMS OF FOUNDATION LENGTH The previous approximate solutions can be rewritten to give directly the length of caisson required. However, these must be solved iteratively. The foundation length, L, based on limiting the rotation may be determined from: 3 35 . 0 8 . 0 12 | . | \ | + + = L V L E n P L allow h sls θ . Substituting in for θ allow gives: 3 35 . 0 8 . 0 2400 | . | \ | + + = L V L E n P L h sls Eq. 5.2-L* April 2003 15 The foundation length, L, based on the ultimate soil capacity may be determined from: | | | | . | \ | + + = L V L E DK P L p uls 7 3 9 . 0 2 3 γ Eq. 5.3-L* April 2003 16 6.0 FOUNDATIONS IN ROCK This section discusses high mast light pole foundations in rock. The two foundation types discussed are caisson type foundations embedded in rock and foundations anchored to the surface of sound rock with reinforcement. 6.1 CAISSON FOUNDATION EMBEDDED IN ROCK The rotation of caissons embedded in sound rock will be insignificant owing to the high stiffness of the rock. Thus, caissons in rock need only to be proportioned based on the ultimate lateral resistance. The ultimate lateral resistance of the foundation will be reached when the resisting rock first reached its allowable horizontal bearing resistance. The rock forces at the ultimate load are shown in Figure 6.1 Figure 6.1: Stresses in rock at ULS. The geotechnical engineer must be consulted to determine the location of the sound rock (and thus the depth of weathered rock (W) and the value of V to be used. For caisson type foundations a minimum length of caisson embedment in sound rock of 2.5m is suggested below the bottom of frost penetration. The lateral bearing resistance must be taken as the lesser of the strength of the rock or the compressive strength of the concrete in the caisson (f horiz <f ’ c ). 6.1.1 EXACT SOLUTIONS The exact solution is obtained based on the soil stress distribution given in Figure 6.1. The ultimate lateral load capacity can be obtained from: | . | \ | + + = L V L E DLf P horiz ult 6 4 Eq. 6.1 April 2003 17 6.1.1.1 SOLUTION IN TERMS OF FOUNDATION LENGTH The previous equation can be rewritten to give the length of foundation required in the rock. The length required based on the ultimate rock capacity can be determined from: ( ) ( ( ¸ ( ¸ + + + = ULS horiz horiz uls P V E D f Df P L 6 4 2 Eq. 6.1-L For the typical case where the lateral bearing resistance of rock is greater than 300 kPa, this equation can be simplified to become: ( ) horiz uls Df V E P L + = 7 , must be >2.5m Eq. 6.1-L* 6.2 FOUNDATION ANCHORED TO ROCK Caisson foundations shall be anchored to rock when sound bedrock is encountered at a relatively shallow depth below grade, and embedment into rock is uneconomical because it would require a very long caisson. Neglecting the relatively small axial load in the caisson, the Anchorage shall be designed to transfer the factored applied moment from the base of the caisson to the rock. Figure 6.2: Foundation Anchored to Rock The calculation for determining the rock anchor area of steel is analogous to that required for calculating the resisting moment (M r ) of a reinforced concrete section. Using the compressive strength of the sound bedrock (f vert , given in the Foundation Report), and the yield strength and location of the anchorage reinforcing, the A s can be designed generally according to CHBDC 8.8.4. The difference is that the material resistance factor, φ c , should be replaced with the geotechnical resistance factor for rock as obtained from clause 6.6.2.1. The minimum reinforcement requirement of clause 8.8.4.3 does not need to be checked because the interface between the concrete and rock is already considered “cracked”, and the massive sound bedrock itself won’t crack. The allowable vertical bearing capacity of the rock must be taken as the lesser of the strength of the rock or the compressive strength of the concrete in the caisson (f vert < f’ c ) April 2003 18 Instead of doing the above calculations, reference can be made to Table 6.2. This Table gives, for all pole heights, the required caisson diameters at top and bottom (for D top and D, see Figure 9.3), and the required number and size of rock anchors, with corresponding resisting moments (M r ). Note that the caisson diameters (D) are one size larger for all caissons when compared to Table 11.1. This is required in order to accommodate the rock anchor reinforcing such that they do not interfere with the HMP anchorage. For the caissons to be safely anchored to rock, the rock must be sound, but it could have a relatively low compressive strength. Because the strength of rock can vary over a large range, this table conservatively neglects the contribution of the rock, which could crush if it is a relatively weak rock; the tabulated Mr considers only the contribution of the rock anchor reinforcing. Table 6.2: Rock Anchors Caisson Diameter (m) Rock Anchor Pole Height (m) D top D Number Size Circle Dia. (m) Hole Dia. (m) Mr (kNm) (rebar only) 25 1.22 1.37 8 35M 1.01 100 730. 30 1.37 1.52 10 35M 1.16 100 1040. 35 1.37 1.52 10 45M 1.16 110 1560. 40 1.52 1.83 8 45M 1.47 110 1560. 45 1.52 1.83 10 45M 1.47 110 1990. The resisting moments listed in the above Table are well in excess of the factored moments encountered in most calculations, based on M f = P uls (E+V). The required embedment length of the anchorage can be determined based on the ultimate bond strength given in the Foundation Investigation Report and the resistance factors for rock in tension, as given in Clause 6.6.2.1. If rock anchors are considered, it is recommended that a test program should be carried out to determine the allowable bond stress. It is recommended that the foundation be socketed into the rock to a depth equal to the depth of the weathered rock. The rock/concrete interface should also be located below the frost susceptible depth to ensure sound rock conditions. It is also required that the total length of the concrete foundation be at least L lim (= 1.75 m for 25, 30, and 35 m high poles, and = 2.0 m for 40 and 45 metre poles). This requirement is to allow adequate room for the anchorage assembly (see Fig. 9.3). These conditions can be met by choosing the socket depth as the larger of: S = W Eq.6.2(a) S = F - T w or, S = L lim - ∆ drainage - T w April 2003 19 7.0 FOUNDATIONS WITH TIP SOCKETED IN ROCK When there is an insufficient depth of soil overlying bedrock to provide adequate resistance, then "socketing" the bottom of the foundation into the bedrock may prove to be adequate. 7.1 COHESIVE SOIL WITH PILE TIP SOCKETED IN ROCK The soil resistances for the socket in rock case are identical to the standard cohesive soil case, however the deflected shape of the pile changes since the point about which the pile rotates is forced down to the level of the rock. Shown below are the soil stresses on the pile at SLS (Figure 7.1 (a)) and ULS loads (Figure 7.1 (b)). Figure 7.1 (a): Stresses in Figure 7.1 (b): Stresses in cohesive soil cohesive soil at SLS at ULS The ultimate lateral resistance is determined by equating the overturning moment caused by the applied load to the resisting moment from the soil. When horizontal equilibrium is considered then it is seen that a large horizontal force must exist in the rock to maintain equilibrium. The depth of the socket must be enough to resist this horizontal force. The total socket depth specified should be based on a uniform distribution of the horizontal bearing capacity of the rock over this depth, plus an allowance for the presence of weathered rock at the soil/rock interface (W). The value of W should be obtained from the geotechnical engineer. The socket depth should not be taken as less than one half the pile diameter and the lateral bearing resistance of the rock must be taken as less than the strength of concrete in the caisson ( ) ' c horiz f f < . 7.1.1 EXACT SOLUTIONS The exact solutions are obtained based on the soil stress distributions given in Figures 7.1 (a) and (b). The rotation of the foundation can be calculated from: ( ¸ ( ¸ | . | \ | + + = L V L E kDL P sls 1 3 2 θ , When LD q k u 103 = , the equation becomes: ( ¸ ( ¸ | . | \ | + + = L V L E L D q P u SLS 1 103 3 5 . 1 θ Eq. 7.1.1 April 2003 20 The ultimate lateral load capacity can be determined from: | | | | . | \ | + + = L V L E DL q F P u q ult 1 1 4 9 Eq. 7.1.2 The required depth of socketing into rock can be obtained from: W L V L E f L q F S horiz u q + | | | | . | \ | + + − = 1 1 2 4 9 Eq. 7.1.3 where: W = the depth of weathered rock, and S must be 2 D ≥ . 7.2 COHESIONLESS SOIL WITH PILE TIP SOCKETED IN ROCK The soil resistances for the socket in rock case are identical to the standard cohesionless soil case, however the deflected shape of the pile changes since the point about which the pile rotates is forced down to the level of the rock. Shown below are the equivalent lateral resistance parameter, k, the deflection, y, and resulting soil stresses at SLS loads (Figure 7.2(a)) and soil stresses at ULS loads (Figure 7.2(b)). Figure 7.2 (a): Stresses in cohesionless Figure 7.2 (b): Stresses in soil at SLS cohesionless soil at ULS The ultimate lateral resistance of the pile is determined by equating the overturning moment caused by the applied load to the resisting moment from the soil. When horizontal equilibrium is checked then it is seen that a large force must exist in the rock. A socket depth must be provided to resist this force based on a uniform distribution of the horizontal bearing capacity of rock over this depth, plus an allowance for the presence of weathered rock at the soil/rock interface (W). The value of W should be obtained from the geotechnical engineer. The socket depth should not be taken as less than one half the pile diameter and the lateral bearing resistance of the rock must be taken as less than the strength of concrete in the caisson ( ) ' c horiz f f < . April 2003 21 7.2.1 EXACT SOLUTIONS The exact solutions are obtained based on the soil stress distributions given in Figures 7.2 (a) and (b). The rotation of the foundation can be calculated from: ( ( ( ( ¸ ( ¸ | . | \ | + | . | \ | + | . | \ | + = L V L V L E L n P h sls 4 1 1 12 3 θ Eq. 7.2.1 The ultimate lateral load resistance at ULS is obtained from: ( ( ( ( ¸ ( ¸ + | . | \ | + + | . | \ | = L V L E L V L DK P p ult 1 1 3 3 2 γ Eq. 7.2.2 The required socket depth can be obtained from: ( ( ( ( ¸ ( ¸ + | . | \ | + + | . | \ | + | . | \ | + | . | \ | | . | \ | + | . | \ | = L V L E L V L V L V L E L E f L K S horiz p 1 2 6 6 6 3 3 2 2 γ Eq. 7.2.3 7.2.2 APPROXIMATE SOLUTIONS The above equation for socket depth is complicated and can be simplified for the ranges of eccentricity, pile length, pile diameter and frost depths that are commonly encountered in Ontario. To use the approximate equations it is required that the following two limits be met: 7 75 . 1 < | . | \ | + < L V L E and 4 . 0 05 . 0 < | . | \ | < L V . The approximate socket depth can be calculated from: W L V f L K S horiz p + | . | \ | + = 5 . 9 . 1 2 γ , where S must be > 2 D . Eq. 7.2.3* April 2003 22 8.0 FOUNDATIONS IN LAYERED SOIL An exact solution for laterally loaded piles in layered soils is not available. At this time, the most accurate results for this type of analysis are achieved by the use of finite element computer programs. Zubacs describes a two dimensional linear elastic structural analysis, using a computer program. At SLS loads he modelled the soil as a series of springs where the spring constant (force per unit deflection) is calculated as the equivalent lateral resistance parameter (k) multiplied by the pile diameter (D) multiplied by the increment of soil depth used in the computer model. To avoid the complex analysis of foundations in layered soils, the various soil strata can sometimes be simplified into a single homogeneous soil type and thus analysed by manual methods. For example, if a relatively thin strong layer exists, or the tip of the pile just penetrates down into a stronger soil layer, then it is safe to take these layers as having the properties of the soil in the weaker, adjacent layer. 8.1 APPROXIMATE SOLUTION A simple procedure has been proposed by Wong to deal with layered soil cases. The "Percentage Contribution" method, as he calls it, has a weak theoretical basis and its agreement with other solutions (e.g. computer model) is not consistent (sometimes it is conservative, other times unconservative). Best results are achieved for cases were the soil strength is nearly constant or varies slightly with depth. Extreme caution must be exercised when using this method for layered soil conditions in which stronger layers of soil are sandwiched between weaker ones. This procedure is best suited for preliminary design, or when a computer is not available. This document proposes the use of a modified version of Wong's "Percentage Contribution" method, which states that the total percent contribution should be 120% as opposed to the 100% given by Wong. This equation becomes conservative for a larger range of layered conditions. 20 . 1 = | | . | \ | ∑ i REQ i L T Eq. 8.1 where: T i is the thickness of layer i, and i REQ L is the governing length obtained from the rotation and ultimate lateral capacity equations for the particular soil type in layer i. Some allowance is needed to ensure that the pile is "short", ensuring that the rigid pile assumption is valid. The "short" pile equation for each layer may be violated providing that the layers of soil where it is violated does not account for over a third of the total percent contribution. Also, too short of a pile is not desired as high stresses may develop at the tip of the pile. Thus i REQ L for each layer shall not be taken as less than 4D. April 2003 23 9.0 CAISSON REINFORCEMENT The proportions of the caisson are based on applied load, relative stiffness of caisson to soil, and minimum size restrictions to accommodate the pole anchorage. Reinforcement in the caisson is based on applied moment at ULS. 9.1 CALCULATE FACTORED APPLIED MOMENT The maximum bending moment in the pile occurs a small distance below the frost depth. This depth depends on the stiffness of the soil, the stiffness of the pile and the applied load. It must be remembered that the maximum bending moment must be determined using the loads at the ultimate limit state (ULS). 9.1.1 COHESIVE SOILS The maximum bending moment is calculated from the soil reaction distribution for cohesive soils at the ultimate load. The depth into the reacting soil (reacting soil begins at the larger of F or 1.5D below the ground surface) to the point of maximum moment can be found where the shear force in the foundation is zero. This is done by equating the soil resistance over this depth to the applied load. The maximum bending moment in the foundation can be found as: ( ) D q F P V E P M u q uls uls f 9 2 + + = Eq. 9.1.1 The final term is due to the extra distance to the point of maximum bending moment. It is found that this term is very small for typical cases. This term is at its largest (as a percent of the total) when P uls is large and V, D, E and q u are small. For a 45 m pole this term would rarely exceed 3.5% of the total while for a 25 m pole it would rarely exceed 4.0%. The approximate equation can then be written for the factored moment as: ( ) V E P M uls f + = 1 . 1 Eq. 9.1.1* The equations for the case of a pile in cohesive soils with the tip socketed in rock is identical to the above since the distance down to the point of maximum moment is smaller than the distance to the point of rotation of the foundation. 9.1.2 COHESIONLESS SOILS The maximum bending moment is calculated from the soil reaction distribution for cohesionless soils at the ultimate load. The depth into the reacting soil (reacting soil begins at the bottom of the frost depth) to the point of maximum moment can be found where the shear force in the pile is zero. This is done by equating the soil resistance over this depth to the applied ultimate load. April 2003 24 The maximum bending moment in the foundation at ULS can be found as: 3 3 2 2 2 3 2 2 3 5 F p DK F ULS P p DK ULS P F F p DK p DK ULS P F ULS P E ULS P f M γ γ γ γ − − + + + + = Eq. 9.1.2 This complicated equation can be approximated by a simpler equation which ignores all soil parameters. It was found that the same equation that is used for cohesive soils provides a reasonable approximation for this equation. The approximate equation is the least conservative when P uls is large and F, D, E and γ are small. For most cases the approximate equation ranges from 7% unconservative to 5% conservative. To ensure a conservative value, the equation can be rewritten: ( ) V E P M uls f + = 1 . 1 Eq. 9.1.2* The equations for the case of a pile in cohesive soils with the tip socketed in rock is identical to the above since the distance down to the point of maximum moment is smaller than the distance to the point of rotation of the foundation. 9.1.3 CAISSONS EMBEDDED IN ROCK The distance below the reacting soil (reacting soil begins at a distance V below the rock surface) to the point of no shear force (maximum bending moment) is very small due to the high strength of rock. Thus it is felt that ( ) V E P M uls f + = would be a good approximating equation. This equation is compared to the exact equation of maximum bending moment (which is very complex) and it is found to be virtually identical with the largest error of 0.6% for weak rock (with long pile length), with high P uls and low E and D values. The moment on the foundation at ULS can thus be written: ( ) V E P M uls f + = Eq. 9.1.3* 9.1.4 FOUNDATIONS ANCHORED TO ROCK The resistance of such a foundation is derived from the rock anchors. Therefore the applied moment should be that calculated at the foundation-rock interface. The moment at ULS thus becomes: ( ) V E P M uls f + = Eq. 9.1.4* 9.1.5 LAYERED SOILS The exact formula for the maximum bending moment in the foundation will be identical to the previously developed equation (cohesive or cohesionless soil) for April 2003 25 the top layer of soil, provided that the top soil layer is where the point of zero shear force (maximum bending moment) occurs. However since the same approximate equation is used for both cohesive and cohesionless soils, it can be used safely in layered soils. 9.2 CALCULATE FACTORED RESISTING MOMENT The resistances of reinforced caissons are given in Table 9.2. A resistance must be chosen so that it is larger than the applied factored (M f ) moment at ULS (as calculated in Section 9.1). M r > M f Table 9.2: Factored Resisting Moment (M r ) of caisson (kN.m) Caisson Diameter (m) Bar Size Number of Bars 1.22 1.37 1.52 1.83 12 1080 1250 1410 1760 14 1250 1440 1640 2030 25M 16 1400 1620 1850 2310 12 1460 1700 1930 2400 14 1670 1950 2230 2790 30M 16 1890 2200 2510 3150 12 - - 2680 3350 14 - - 3060 3880 35M 16 - - 3460 4360 The CHBDC requirement for Minimum Reinforcement [8.8.4.3] has been checked and is satisfied for all cases in the above Table. 9.3 HIGH MAST POLE ANCHORAGE AND CAISSON REINFORCEMENT DETAILS The anchor rod sizes and placement are specified in OPSD 2456.0110. The number of anchor rods is eight or twelve, and the rod diameters and bolt circle diameters are shown in Table 9.3 (a). To ensure adequate room for the anchorage assembly it is required that the total length of the concrete foundation be at least (L lim = ) 1.75 m for 25, 30, and 35 metre high poles and at least 2.00 m for 40 and 45 metre poles. This condition is met by the latter part of Equation 6.2(a) (S > L lim – ∆ drainage – T w ). For cases with little or no soil overburden and with sound rock that is not frost susceptible ( F , T w ,W = 0 ), the above limit on the total length of the concrete foundation can cause some large socket lengths to be specified. However, this can sometimes be avoided by specifying a larger ∆ drainage to prevent this part of Equation 6.2(a) from governing. May 2004 26 Table 9.3 (a): Anchor Rod Dimensions Pole Height (m) Number of Anchor Rods Anchor Rod Diameter (mm) Bolt Circle Diameter (mm) 25 8 48 750 30 8 48 850 35 8 48 950 40 12 48 1075 45 12 48 1075 In addition to the plates shown in OPSD 2456.0110, the anchor rods shall be tied with 5 – 15 M rings at 100mm spacing. To conform with the CHBDC the clear cover to the reinforcement shall be 100±25mm to the spiral reinforcement. In addition, the longitudinal reinforcement should be tied with a 15M-spiral with a 300 mm pitch along its entire length. In order to minimize interference between the anchorage and the reinforcing cage, it is recommended that maximum size of bars is limited to that shown in Table 9.3 (b). Table 9.3 (b) Maximum Size of Caisson Reinforcement POLE HEIGHT (m) FOOTING DIAMETER (m) MAX. SIZE 25 1.22 30M 30 1.37 30M 35 1.37 30M 40 1.52 35M 45 1.52 35M The Standard drawing SS 116-50 should be used for ground mounted caisson type foundations and SS 116-51/52 for poles mounted on the tall wall mounted median barrier. 9.4 ROCK ANCHORS The rock anchors should be located inside the longitudinal reinforcement. Locating the centres of the rock anchors about 180 mm from the concrete surface is recommended. The method suggested in section 6.2 can be used to determine the longitudinal reinforcement required, for rock anchors. The typical layout of reinforcement is shown in Figure 9.3. April 2003 27 Caisson Type Foundation Foundation Anchored to Rock Figure 9.3: Reinforcement for foundations April 2003 28 10.0 EQUATION SUMMARY The equations below are taken from the previous chapters. For designing high mast pole foundations the maximum allowable rotation is limited to 0.005 radians. The approximate equations (marked with *) for L and S (but not M f ) must obey the following limits, otherwise the exact equations must be used: 7 75 . 1 < | . | \ | < L E and 4 . 0 05 . 0 < | . | \ | < L V . Eq. No. Loading SLS load | . | \ | = 595 7 . 0 50 q P P unf sls 3.1 ULS load | . | \ | = 595 3 . 1 50 q P P unf uls 3.2 Determining Caisson Length Cohesive Soils 4 . 0 2 3 . 23 ( ( ¸ ( ¸ | . | \ | + + = V E L D q P L u sls (rotation) ( ) V E D q P D q P D q P L u uls u uls u uls + | | . | \ | + | | . | \ | + | | . | \ | = 9 16 81 16 9 4 2 (ultimate) ( )7 2 55 u q D L < (“short pile” limit) 4.2-L 4.3-L 4.1 Cohesionless Soils 3 35 . 0 8 . 0 2400 | . | \ | + + = L V L E n P L h sls (rotation) | | | | . | \ | + + = L V L E DK P L p uls 7 3 9 . 0 2 3 γ (ultimate) 5 1 4 33 | | . | \ | < h n D L (“short pile” limit) 5.2-L* 5.3-L* 5.1 Caisson Embedded in Rock ( ) horiz uls Df V E P L + = 7 , must be >2.5m (ultimate) 6.1-L Caisson Anchored to Rock See Section 6.2 April 2003 29 Cohesive Soils with Base Socketed into Rock ( ¸ ( ¸ | . | \ | + + = L V L E L D q P u sls 1 103 3 5 . 1 θ , must be <0.005 | | | | . | \ | + + = L V L E DL q F P u q ult 1 1 4 9 , must be > P uls W L V L E f L q F S horiz u q + | | | | . | \ | + + − = 1 1 2 4 9 and S must be 2 D ≥ . 7.1.1 7.1.2 7.1.3 Cohesionless Soils with Base Socketed into Rock ( ( ( ( ¸ ( ¸ | . | \ | + | . | \ | + | . | \ | + = L V L V L E L n P h sls 4 1 1 12 3 θ , must be <0.005 ( ( ( ( ¸ ( ¸ + | . | \ | + + | . | \ | = L V L E L V L DK P p ult 1 1 3 3 2 γ , must be > P uls W L V f L K S horiz p + | . | \ | + = 5 . 9 . 1 2 γ and S must be 2 D ≥ . 7.2.1 7.2.2 7.2.3* Layered Soils 20 . 1 = | | . | \ | ∑ i REQ i L T 8.1 Reinforcement Design ULS Moment in Caisson (in Soil, Layered Soil, or with Tip Socketed in Rock) ( ) V E P M uls f + = 1 . 1 9.1.1* 9.1.2* ULS Moment in Caisson (Caisson Embedded or Anchored in Rock) ( ) V E P M uls f + = 9.1.3* 9.1.4* Resisting Moment See Table 9.2 April 2003 30 11.0 PROCEDURES AND EXAMPLES 1. Calculate P sls and P uls using equations 3.1 and 3.2. 2. Calculate the total eccentricity (E) for the pole above the ground. Take the eccentricity for the pole (e) from Table 3.1 and add the additional eccentricities (∆). 3. Select a Caisson diameter (D) from Table 11.1 below. These values are the minimum possible to allow for the size of the base plate, anchorage, and foundation reinforcement. Larger sizes of caisson are available in diameters of 1.83m and 2.13m. Increasing the caisson diameter above those specified in Table 11.1 is only required in cases with extremely weak soils. Table 11.1: Minimum allowable foundation diameters. Pole Height (m) Caisson Diameter (m) 25 30 35 40 45 1.22 1.37 1.37 1.52 1.52 4. Determine the required soil parameters by consulting the geotechnical engineer. For cohesive soils, q u (q u = 2c u ) is required. For cohesionless soils, the required values are n h , γ, and φ. The passive earth pressure coefficient can be calculated from: | | . | \ | − + = ϕ ϕ sin 1 sin 1 p K . Figure 12.1.2, relating n h to φ, has been supplied by the Foundation Design Section for typical soil conditions. Where socketing in rock is involved, then f horiz is required and for foundations anchored to rock, f vert is required. The value of V must be determined for both rotation and ultimate lateral resistance equations based on the ground material (see Section 2 – Notation). 5. Calculate the Length (L) of the caisson required using the appropriate method depending on the geology of the site: a. For homogeneous soils 1. Make an initial guess of L=4D. Iterate each of the equations for serviceability and ultimate resistance (4.2-L and 4.3-L for cohesive soils, 5.2-L* and 5.3-L* for cohesionless soils) about 3 times until they converge to obtain the required length of the caisson below V. 2. Choose the larger of the two overall caisson lengths (L+V) from the above serviceability and ultimate resistance equations. 3. Check if the pile is “short” using equations 4.1 or 5.1 for cohesive and cohesionless soils respectively. If the pile is not “short”, a larger D must be chosen. OR April 2003 31 4. From the soil strength and the frost depth and additional eccentricity (F and ∆), determine the caisson diameter and length required from Table 12.2.1 or 12.2.2 in Appendix B. b. For soil atop rock If the length calculated in 5a above is longer than the thickness of the soil layer above sound rock, then socketing the caisson tip into the rock may be adequate. 1. Calculate the rotation (using equation 7.1.1 for cohesive soils and equation 7.2.1 for cohesionless soils) and check that it is <0.005. 2. Calculate P ult (using equation 7.1.2 for cohesive soils and equation 7.2.2 for cohesionless soils 3. If the above equations are met, the design is adequate. If the above two equations are not met, then they may be met by choosing a larger D. However, this usually has little effect and generally the caisson should be designed by ignoring the resistance of the entire soil layer. Design the caisson as embedded in sound rock or as anchored to sound rock. Use the procedures listed in step 5c). 4. Check if the pile is “short” using equations 4.1 or 5.1 for cohesive and cohesionless soils respectively. If the pile is not “short”, a larger D must be chosen. The limit of L>4D does not need to be satisfied for the socketing in rock case. 5. Calculate the socket length using equations 7.1.3 for cohesive soils and 7.2.3* for cohesionless soils. c. For caisson in sound rock The caisson can either be embedded in the sound rock or it can be attached to the sound rock by means of rock anchors. 1. If the caisson is to be embedded in rock, calculate the required length using equation 6.1-L. This length must be taken as at least 2.5m. 2. If the foundation will be anchored to rock, the procedures given in Section 6.2 should be followed. d. For layered soils 1. Calculate the required length (L REQ ) of the caisson in each layer using the method of 5a) above. A separate soil layer occurs if q u , γ, φ, or n h changes. 2. If the layers are very thin, they can be grouped together such that the combined layer takes on the properties of the weakest soil in the group. 3. For each layer, the L>4D limit (to ensure that the pile is not too short) must be obeyed and for the equations of L REQ that are based on the approximate equations (denoted by “*”), the limits on E, V, and L must be satisfied in each layer (otherwise the exact equations must be used). 4. The “short” pile limit need not be met in all layers, however, the layers that violate the limit should not make up more than a third of the total contribution, otherwise a larger caisson diameter must be used. April 2003 32 5. Using the soil layer thicknesses and the required lengths, ensure that equation 8.1 is satisfied. 6. Check that the limits on E, L, and V are met for all approximate equation designated with a “*”. If the limits are not met, the exact equations must be used to check the results. a. Using the Exact Equations to Determine Length 1. Steps 1 through 4 remain the same. 2. The value of L obtained from step 5 should be used as a first guess for the caisson length. This value must be >4D. 3. Calculate the rotations and ultimate lateral resistance (and socket depth) using the exact equations from section 4, 5, 6, and 7. 4. If the rotation (θ) is <0.005, the chosen length is adequate for serviceability. If not, choose a larger length (possibly, choose a larger D). 5. If the ultimate lateral resistance (P ult ) is larger than the applied ultimate wind load (P uls ), the chosen length is adequate. If not, choose a larger length (possibly, choose a larger D). 6. If both the rotation and ultimate lateral resistance equations are obeyed then: • Ensure that the pile is “short” (using equations 4.1 and 5.1). If not, choose a larger diameter and recalculate the rotation and ultimate resistance. • If applicable, calculate the required socket depth (S) (using equation 7.1.3 for cohesive soils and 7.2.3 for cohesionless soils. 7. For layered soils, the above must be done for each layer and the resulting lengths become the L REQ values to be used in equation 8.1. 7. Design the reinforcement. 1. Determine the moment acting on the caisson at ULS from the appropriate equation in Section 9. 2. Obtained the required reinforcement from Table 9.2. April 2003 33 11.1 EXAMPLE 1: HOMOGENEOUS COHESIVE SOIL Given: A clay with an undrained shear stregth (cu) of 40 kPa. The frost depth (F) is 1.5m. Using a 45m pole in an area with q 50 of 595 Pa. 1. Calculate P sls and P uls using equations 3.1 and 3.2. From Table 3.1, P unf =56kN for a 45m pole. 2 . 39 595 595 56 7 . 0 595 7 . 0 50 = | . | \ | = | . | \ | = x x q P P unf sls kN 8 . 72 595 595 56 3 . 1 595 3 . 1 50 = | . | \ | = | . | \ | = x x q P P unf uls kN 2. Calculate E. From Table 3.1, e=21.7m for a 45m pole. Add 0.1m for levelling and 0.2m for drainage. There is no construction staging to consider. Thus: E=21.7+0.1+0.2=22.0m. 3. Select a caisson diameter from Table 11.1. For a 45m pole, use D=1.52m 4. Determine the required soil parameters. q u =2c u =2x40=80kPa. Calculate V, refer to Section 2 – Notation. For rotation, V=F=1.5m For ultimate resistance, V=larger of (F or 1.5D)=larger of (1.5 or 1.5x1.52)=2.28m 5. Calculate the required length. Make an initial guess of L=4D = 4x1.52 = 6.08m Calculate the required length based on rotation: 4 . 0 2 3 . 23 ( ( ¸ ( ¸ | . | \ | + + = V E L D q P L u sls Eq. 4.2-L m x L 04 . 9 5 . 1 0 . 22 2 08 . 6 52 . 1 80 2 . 39 3 . 23 4 . 0 = ( ¸ ( ¸ | . | \ | + + = m x L 24 . 9 5 . 1 0 . 22 2 04 . 9 52 . 1 80 2 . 39 3 . 23 4 . 0 = ( ¸ ( ¸ | . | \ | + + = m x L 25 . 9 5 . 1 0 . 22 2 24 . 9 52 . 1 80 2 . 39 3 . 23 4 . 0 = ( ¸ ( ¸ | . | \ | + + = The equation has converged to L=9.25m. Use L=9.3m, or L+V=9.3+1.5 = 10.8m Calculate the required length based on ultimate lateral capacity: ( ) V E D q P D q P D q P L u uls u uls u uls + | | . | \ | + | | . | \ | + | | . | \ | = 9 16 81 16 9 4 2 Eq. 4.3-L April 2003 34 ( ) m x x x L 36 . 5 28 . 2 0 . 22 52 . 1 80 8 . 72 9 16 52 . 1 80 8 . 72 81 16 52 . 1 80 8 . 72 9 4 2 = + | . | \ | + | . | \ | + | . | \ | = This is not an iterative equation. Thus, L=5.36m, or L+V=5.36+2.28 = 7.64mm The governing length is the one with the larger L+V. Thus, L=9.3m and V=1.5m Ensure that the caisson is “short” using equation 4.1. ( ) ( ) m x q D L u 9 . 23 80 52 . 1 55 55 7 2 7 2 = = < which is greater than L=9.4m. The pile is “short” 6. Since the lengths were based on the exact equations (the equation number did not contain an asterisk), there are no limits to check. Thus, the total length of the caisson is L+V = 9.3 + 1.5 = 10.8m 7. Determine the longitudinal reinforcing. M f = 1.1 P uls (E + V) Eq. 9.1.1 = 1.1 (72.8) (22.0 + 2.28) V uls = 2.28 m = 1944 kN.m from Table 9.2, for D = 1.52 m, required A s = 14 – 30M Thus, M r = 2230 kN.m > 1944 kN.m O.K. Thus, use 14 – 30M for longitudinal reinforcing. April 2003 35 11.2 EXAMPLE 2: HOMOGENEOUS COHESIONLESS SOIL Given: A sand with a density of 19 kN/m 3 and an internal friction angle of 36˚. The frost depth is 1.2m and the water table is located 7.0m below the surface. Use a 30m pole in an area with q 50 of 520 Pa. 1. Calculate P sls and P uls using equations 3.1 and 3.2. From Table 3.1, P unf =38kN for a 30m pole. 2 . 23 595 520 38 7 . 0 595 7 . 0 50 = | . | \ | = | . | \ | = x x q P P unf sls kN 2 . 43 595 520 38 3 . 1 595 3 . 1 50 = | . | \ | = | . | \ | = x x q P P unf uls kN 2. Calculate E. From Table 3.1, e=15.8m for a 30m pole. Add 0.1m for levelling and 0.2m for drainage. There is no construction staging to consider. Thus: E=15.8+0.1+0.2=16.1m. 3. Select a caisson diameter from Table 11.1. For a 30m pole, use D=1.37m 4. Determine the required soil parameters. γ= 19.0 kN/m 3 . φ= 36˚. n h =12,200 kN/m 3 (from Figure 12.1.2) . Calculate 85 . 3 36 sin 1 36 sin 1 sin 1 sin 1 = − + = − + = ϕ ϕ p K Calculate V, refer to Section 2 – Notation. For rotation and ultimate lateral resistance, V=F=1.2m 5. Calculate the required length. Make an initial guess of L=4D = 4x1.37 = 5.48m Calculate the required length based on rotation: 3 35 . 0 8 . 0 2400 | . | \ | + + = L V L E n P L h sls Eq. 5.2-L* m x x x L 11 . 3 48 . 5 35 . 0 2 . 1 48 . 5 8 . 0 1 . 16 200 , 12 2 . 23 2400 3 = | . | \ | + + = m x x x L 33 . 3 11 . 3 35 . 0 2 . 1 11 . 3 8 . 0 1 . 16 200 , 12 2 . 23 2400 3 = | . | \ | + + = m x x x L 31 . 3 33 . 3 35 . 0 2 . 1 33 . 3 8 . 0 1 . 16 200 , 12 2 . 23 2400 3 = | . | \ | + + = The equation has converged to L=3.31m. However, L>4D. Thus, Use L=5.5m, or L+V=5.5+1.2 = 6.7m April 2003 36 Calculate the required length based on ultimate lateral capacity: | | | | . | \ | + + = L V L E DK P L p uls 7 3 9 . 0 2 3 γ Eq. 5.3-L* m x x x x x x L 33 . 2 48 . 5 7 3 2 . 1 48 . 5 9 . 0 1 . 16 85 . 3 37 . 1 0 . 19 2 2 . 43 3 = | | | | . | \ | + + = m x x x x x x L 75 . 2 33 . 2 7 3 2 . 1 33 . 2 9 . 0 1 . 16 85 . 3 37 . 1 0 . 19 2 2 . 43 3 = | | | | . | \ | + + = m x x x x x x L 67 . 2 75 . 2 7 3 2 . 1 75 . 2 9 . 0 1 . 16 85 . 3 37 . 1 0 . 19 2 2 . 43 3 = | | | | . | \ | + + = The equation converges to about L=2.69m. However, L>4D. Thus, Use L=5.5m, or L+V=5.5+1.2 = 6.7m The governing length is the one with the larger L+V. Both are the same. Thus, L=5.5m and V=1.2m Ensure that the caisson is “short” using equation 5.1. m n D L h 5 . 6 200 , 12 37 . 1 33 33 5 1 4 5 1 4 = | | . | \ | = | | . | \ | < which is greater than L=5.5m. The pile is “short” 6. Since the lengths were based on approximate equations (the equation number contained an asterisk), the limits on E, L, and V are to be checked. 9 . 2 5 . 5 1 . 16 = | . | \ | = | . | \ | L E . This satisfies: 7 75 . 1 < | . | \ | < L E . 22 . 0 5 . 5 2 . 1 = | . | \ | = | . | \ | L V . This satisfies 4 . 0 05 . 0 < | . | \ | < L V Thus, the total length of the caisson is L+V = 5.5 + 1.2 = 6.7m April 2003 37 7. Determine the longitudinal reinforcing. M f = 1.1 P uls (E + V) Eq. 9.1.2 = 1.1 (43.2) (16.1 + 1.2) = 822 kN.m from Table 9.2, for D = 1.37m, required A s = 12 – 25M Thus, M r = 1250 kN.m > 822 kN.m O.K. Thus, use 12 – 25M for longitudinal reinforcing. April 2003 38 11.3 EXAMPLE 3: CAISSON WITH TIP SOCKETED IN ROCK Given: A sand with a submerged unit weight of 5.2 kN/m 3 and an internal friction angle of 28˚ exists for a depth of 8.7 m from ground surface. At a depth of 8.7 m begins 0.2 m of weathered rock and then rock with an allowable horizontal bearing resistance f horiz of 3000 kPa. The frost depth is 1.2 m and the water table 1.0 m below the surface. Use a 35 m pole. The wind in the area has a 50 year reference wind pressure of 595 Pa. It is also given that the caisson will be placed at the beginning of construction such that the temporary ground surface at the pole site will be 1.0 m below the elevation of the final ground. (i.e. only 7.7m of soil are present during the extended construction period). 1. Calculate P sls and P uls using equations 3.1 and 3.2. From Table 3.1, P unf =50kN for a 35m pole. 0 . 35 595 595 50 7 . 0 595 7 . 0 50 = | . | \ | = | . | \ | = x x q P P unf sls kN 0 . 65 595 595 50 3 . 1 595 3 . 1 50 = | . | \ | = | . | \ | = x x q P P unf uls kN 2. Calculate E. From Table 3.1, e=17.1m for a 35m pole. Add 0.1m for levelling and 0.2m for drainage and add 1.0m for construction staging (1.0m of fill not initially in place). Thus: E=17.1+0.1+0.2+1.0=18.4m. 3. Select a caisson diameter from Table 11.1. For a 35m pole, use D=1.37m 4. Determine the required soil parameters. γ= 5.2 kN/m3. φ= 28˚. n h =700 kN/m 3 (from Figure 12.1.2) . Calculate 77 . 2 28 sin 1 28 sin 1 sin 1 sin 1 = − + = − + = ϕ ϕ p K Calculate V, refer to Section 2 – Notation. For rotation and ultimate lateral resistance, V=F=1.2m 5. Calculate the required length. a. Initially assume caisson entirely in soil. Make an initial guess of L=4D = 4x1.37 = 5.48m Calculate the required length based on rotation: 3 35 . 0 8 . 0 2400 | . | \ | + + = L V L E n P L h sls Eq. 5.2-L* m x x x L 57 . 9 48 . 5 35 . 0 2 . 1 48 . 5 8 . 0 4 . 18 700 0 . 35 2400 3 = | . | \ | + + = m x x x L 82 . 8 57 . 9 35 . 0 2 . 1 57 . 9 8 . 0 4 . 18 700 0 . 35 2400 3 = | . | \ | + + = April 2003 39 m x x x L 93 . 8 82 . 8 35 . 0 2 . 1 82 . 8 8 . 0 4 . 18 700 0 . 35 2400 3 = | . | \ | + + = The equation has converged to L=8.9m. Thus, L+V=8.9+1.2 = 10.1m However, this length of caisson can not be provided in sand only since the rock is located 7.7m below grade during the construction and 10.1m is required. To avoid having to go 2.4m into rock, the caisson can be looked at as a pile socketed in rock. b. Check caisson socketed in rock. Since the rock is 7.7m below grade, L becomes 7.7m minus the frost depth. L=7.7-1.2=6.5m. Check the rotation of the caisson at SLS: ( ( ( ( ¸ ( ¸ | . | \ | + | . | \ | + | . | \ | + = L V L V L E L n P h sls 4 1 1 12 3 θ , must be <0.005 Eq. 7.2.1 0050 . 0 5 . 6 2 . 1 4 1 5 . 6 2 . 1 5 . 6 4 . 18 1 5 . 6 700 0 . 35 12 3 = ( ( ( ( ¸ ( ¸ | . | \ | + | . | \ | + | . | \ | + = x x θ . Satisfies rotation limit. Check the ultimate lateral capacity of the caisson at ULS: ( ( ( ( ¸ ( ¸ + | . | \ | + + | . | \ | = L V L E L V L DK P p ult 1 1 3 3 2 γ Eq. 7.2.2 kN x x x ult P 108 5 . 6 2 . 1 5 . 6 4 . 18 1 1 5 . 6 2 . 1 3 3 2 5 . 6 77 . 2 37 . 1 2 . 5 = + + + = ( ( ( ( ¸ ( ¸ | . | \ | | . | \ | >P uls (65.0kN). (o.k.) Since both equations were obeyed, the pile can be checked if it is “short”. It is not required to ensure that L>4D for the socket in rock case. The required socket depth can also be calculated. Ensure that the caisson is “short” using equation 4.1. m n D L h 5 . 11 700 37 . 1 33 33 5 1 4 5 1 4 = | | . | \ | = | | . | \ | < which is greater than L=6.5m. The pile is “short” April 2003 40 Note: There are alternative methods to solve this problem. If the equations (Eq. 7.2.1 and 7.2.2) were not met then they may be met by choosing a larger diameter, this, however does not have a great effect. The pole could also be analysed as a pile in rock and the resistance of the soil neglected. In this case V would become (0.2+7.7=) 7.9 m, and the required pile Length in the rock could be calculated using Eq. 6.1-L (for this example it would give 1.7m, but the minimum of L=2.5m in the rock would have to be used). If the problem were looked at as a layered soil condition then LREQ would be calculated for the soil as the larger of equation 5.2-L* (shown above in 5a) or equation 5.3-L* (not shown). This would give a length of 8.9m. The required length in rock would be calculated as in the previous paragraph and would give a length of 2.5m. Thus, in soil: 73 . 0 9 . 8 5 . 6 1 = = REQ L T . The rock requires: 47 . 0 73 . 0 2 . 1 2 = − = REQ L T . Thus, m x REQ L 2 . 1 5 . 2 47 . 0 = = , plus the 0.2m for weathered rock. Now, calculate the required socket length W L V f L K S horiz p + | . | \ | + = 5 . 9 . 1 2 γ and S must be 2 D ≥ . Eq. 7.2.3* m x x S 46 . 0 2 . 0 5 . 5 . 6 2 . 1 3000 5 . 6 77 . 2 2 . 5 9 . 1 2 = + | . | \ | + = But must use S m D 7 . 0 2 37 . 1 2 = = ≥ 6. Since the socket depth was based on an approximate equation (the equation number contained an asterisk), the limits on E, L, and V are to be checked. 8 . 2 5 . 6 4 . 18 = | . | \ | = | . | \ | L E . This satisfies: 7 75 . 1 < | . | \ | < L E . 18 . 0 5 . 6 2 . 1 = | . | \ | = | . | \ | L V . This satisfies 4 . 0 05 . 0 < | . | \ | < L V Thus, the total length of the caisson is: + 0.7m (S) + 7.7m (to construction ground level) + 1.0m (future fill) + 0.2m (for drainage) = 9.6m April 2003 41 7. Determine the longitudinal reinforcing. M f = 1.1 P uls (E + V) Eq. 9.1.2 = 1.1 (65.0) (18.4 + 1.2) = 1401 kN.m from Table 9.2, for D = 1.37m, required A s = 14 – 25M Thus, M r = 1440 kN.m > 1401 kN.m O.K. Thus, use 14 – 25M for longitudinal reinforcing. April 2003 42 11.4 EXAMPLE 4: CAISSON EMBEDDED IN ROCK Given: Grade to 0.9m = Clay; unconfined compressive strength (q u ) = 100 kPa 0.9m to 1.2m = Weathered rock; 1.2m & deeper = Competent rock; allow horizontal Bearing strength @ ULS (f horiz ) = 4000 kPa Frost depth = 1.5m 40m pole Location ~ q 50 = 550 Pa 1. Calculate P sls and P uls using equations 3.1 and 3.2. From Table 3.1, P unf =48kN for a 40m pole. 1 . 31 595 550 48 7 . 0 595 7 . 0 50 = | . | \ | = | . | \ | = x x q P P unf sls kN 7 . 57 595 550 48 3 . 1 595 3 . 1 50 = | . | \ | = | . | \ | = x x q P P unf uls kN 2. Calculate E. From Table 3.1, e=19.6m for a 40m pole. Add 0.1m for levelling and 0.2m for drainage. (no construction staging) Thus: E=19.6+0.1+0.2 =19.9m. 3. Select a caisson diameter from Table 11.1. For a 40m pole, use D=1.52m 4. Determine the required soil parameters. F horiz = 4000 kPa (as given) For rock, V is larger of F = 1.5m or (W + T w ) = 0.3 + 0.9 = 1.2m Thus, V = 1.5m 5. Calculate the required length. m f D V E P L horiz uls 5 . 2 , ) ( 7 ≥ + = Eq. 6.1-L m m L 5 . 2 19 . 1 ) 4000 ( 52 . 1 ) 5 . 1 9 . 19 )( 7 . 57 ( 7 < = + = minimum Thus, use L = 2.5m For piles embedded in rock, the limits on E, L, and V, and the “short” and “too short” pile limits are not required. April 2003 43 Thus, Total caisson length = L + V + distance above ground = 2.5 + 1.5 + 0.2 = 4.2m 6. Since exact equation was used, there are no limits to check. 7. Determine the longitudinal reinforcing: M f = P uls (E + V) Eq. 9.1.3* = 57.7 (19.9 + 1.5) = 1235 kN.m from Table 9.2, for D = 1.52m, required A s = 12 – 25M Thus, M r = 1410 kN.m > 1235 kN.m O.K. Thus, use 12 – 25M for longitudinal reinforcing. April 2003 44 11.5 EXAMPLE 5: FOUNDATION ANCHORED TO ROCK Given: Grade to 0.9m = Clay; (q u ) = 100 kPa (firm to stiff) 0.9m to 1.2m = Weathered rock; 1.2m & deeper = Competent rock; f vert = 4500 kPa (@ULS) Bedrock = red shale for Rock Anchors, Ultimate Bond Strength = 80 psi Frost depth = 1.5m 40m pole Location ~ q 50 = 550 Pa 1. Calculate P sls and P uls using equations 3.1 and 3.2. From Table 3.1, P unf =48kN for a 40m pole. 1 . 31 595 550 48 7 . 0 595 7 . 0 50 = | . | \ | = | . | \ | = x x q P P unf sls kN 7 . 57 595 550 48 3 . 1 595 3 . 1 50 = | . | \ | = | . | \ | = x x q P P unf uls kN 2. Calculate E. From Table 3.1, e=19.6m for a 40m pole. Add 0.1m for levelling and 0.2m for drainage. (no construction staging) Thus: E=19.6+0.1+0.2 =19.9m. 3. Select a caisson diameter from Table 6.2. For a 40m pole, use D top = 1.52m D = 1.83m 4. Determine the required soil parameters. F vert = 4500 kPa (as given) For rock, V is larger of: F = 1.5m or (W + T w ) = 0.3 + 0.9 = 1.2m or (L lim – ∆ drainage ) = 2.0 – 0.2 = 1.8m Thus, V = 1.8m 5. Calculate the socket depth. From Section 6.2, S is the larger of the following: S = W = 0.3m or S = (F – T w ) = (1.5 – 0.9) = 0.6m or S = (L lim – ∆ drainage – T w ) = (2.0 – 0.2 – 0.9) = 0.9m Thus, S = 0.9m April 2003 45 6. Calculate the factored applied moment. M f = P uls (E + V) Eq. 9.1.4* = 57.7 (19.9 + 1.8) = 1252 kN.m 7. Determine the Longitudinal reinforcing. from Table 9.2, for D = 1.83m, required A s = 12 – 25M Thus, M r = 1760 kN.m > 1252 kN.m O.K. Thus, use 12 – 25M for longitudinal reinforcing. 8. Design the Rock Anchor Reinforcing. from Table 6.2, for 40m pole, required Rock Anchor = 8 – 45M Thus, M r = 1560 kN.m > 1252 kN.m O.K. Thus, use 8 – 45M for rock anchor reinforcing. 9. Calculate embedment length of Rock Anchors. (a) Embedment into rock: From Foundation Report, Ultimate Bond Strength = 80 psi = 0.552 Mpa Ultimate force per rebar = y s s f A φ = 0.9(1500)(400) = 540 kN For 45M rebar anchor, hole Ø = 110 mm from Table 6.2 perimeter = π (110) = 346 mm L anch = embedment length required for anchorage in rock Thus, (L anch )(346)(0.552) = 540,000 L anch = 2830 mm ~ 2900mm (b) Embedment into concrete caisson (from RSIC Manual, d l = 1900(0.75)(0.8) = 1140mm ~ 1200mm) from CHBDC, b cr y d d f f k k k 3 2 1 18 . 0 = l ( ) 44 19 . 2 400 18 . 0 | . | \ | = = 1450mm k 1 1.0 k 2 1.0 k 3 1.0 f y 400 f cr 2.19MPa d b 44mm April 2003 46 Thus, the total length of the caisson is: 0.9m (through clay) + 0.9m (socket) + 0.2m (above ground) = 2.0m With 8-45M rock anchors April 2003 47 11.6 EXAMPLE 6: CAISSON DESIGN USING EXACT EQUATIONS Given: A sand with a density of 16 kN/m 3 and an internal friction angle of 28˚. The frost depth is 1.5m and the water table is located 1.0m below the surface. Use a 25m pole in an area with q 50 of 535 Pa. 1. Calculate P sls and P uls using equations 3.1 and 3.2. From Table 3.1, P unf =29kN for a 25m pole. 3 . 18 595 535 29 7 . 0 595 7 . 0 50 = | . | \ | = | . | \ | = x x q P P unf sls kN 9 . 33 595 535 29 3 . 1 595 3 . 1 50 = | . | \ | = | . | \ | = x x q P P unf uls kN 2. Calculate E. From Table 3.1, e=13.8m for a 25m pole. Add 0.1m for levelling and 0.2m for drainage. There is no construction staging to consider. Thus: E=13.8+0.1+0.2=14.1m. 3. Select a caisson diameter from Table 11.1. For a 25m pole, use D=1.22m 4. Determine the required soil parameters. Since the water table is in the frost depth, the entire resisting soil below the frost depth has the same properties. γ= 16.0-9.8=6.2 kN/m3. φ= 28˚. n h =700 kN/m 3 (from Figure 12.1.2) . Calculate 77 . 2 28 sin 1 28 sin 1 sin 1 sin 1 = − + = − + = ϕ ϕ p K Calculate V, refer to Section 2 – Notation. For rotation and ultimate lateral resistance, V=F=1.5m 5. Calculate the required length. Make an initial guess of L=4D = 4x1.22 = 4.88m Calculate the required length based on rotation from the approximate equation to obtain a starting guess for the exact equations: 3 35 . 0 8 . 0 2400 | . | \ | + + = L V L E n P L h sls Eq. 5.2-L* m x x x L 04 . 7 88 . 4 35 . 0 5 . 1 88 . 4 8 . 0 1 . 14 700 3 . 18 2400 3 = | . | \ | + + = m x x x L 78 . 6 04 . 7 35 . 0 5 . 1 04 . 7 8 . 0 1 . 14 700 3 . 18 2400 3 = | . | \ | + + = m x x x L 81 . 6 78 . 6 35 . 0 5 . 1 78 . 6 8 . 0 1 . 14 700 3 . 18 2400 3 = | . | \ | + + = The equation has converged to L=6.8m. Use L=6.9m and check in exact equations. April 2003 48 Use the exact equation for rotation from Section 5.1 ( ( ( ( ( ( ¸ ( ¸ ) ` ¹ ¹ ´ ¦ | . | \ | ¦ ) ¦ ` ¹ ¦ ¹ ¦ ´ ¦ | . | \ | | . | \ | | . | \ | | . | \ | | . | \ | | . | \ | | . | \ | | . | \ | | . | \ | | . | \ | + + + + + + + + + = L V L V L V L V L V L E L V L V L V L E L E L h n sls P 3 2 2 6 6 1 3 18 2 18 2 30 18 21 6 4 3 12 θ 6 004 . 0 9 . 6 5 . 1 3 2 2 9 . 6 5 . 1 6 9 . 6 5 . 1 6 1 3 9 . 6 5 . 1 18 2 9 . 6 5 . 1 9 . 6 1 . 14 18 2 9 . 6 5 . 1 30 9 . 6 5 . 1 18 9 . 6 5 . 1 9 . 6 1 . 14 21 9 . 6 1 . 14 6 4 3 9 . 6 700 3 . 18 12 = + + + + + + + + + = ( ( ( ( ( ( ¸ ( ¸ ) ` ¹ ¹ ´ ¦ | . | \ | ¦ ) ¦ ` ¹ ¦ ¹ ¦ ´ ¦ | . | \ | | . | \ | | . | \ | | . | \ | | . | \ | | . | \ | | . | \ | | . | \ | | . | \ | | . | \ | x x θ This rotation is less than the limit of 0.005. Thus, the chosen length is adequate for rotation. Check the ultimate capacity of the caisson using the exact equations from Section 5.1. ( ( ( ( ( ¸ ( ¸ + | . | \ | + | . | \ | + | . | \ | − | . | \ | | . | \ | − | . | \ | + = L V L E L u L u L u L V L V L DK P p ult 1 3 4 2 2 3 1 3 2 2 2 γ where u is the distance to the point above the caisson tip about which the caisson rotates. It is calculated from: 2 2 2 2 1 1 L DK P L V L V L V L u p ult γ + + | . | \ | + | . | \ | − | . | \ | + = Guess P ult =100kN. Calculate 315 . 0 = L u (from the second equation) Calculate P ult =107.4kN (from the first equation) Calculate 313 . 0 = L u (from the second equation) Calculate P ult =108.1kN (from the first equation) Calculate 312 . 0 = L u (from the second equation) Calculate P ult =108.2kN (from the first equation) Calculate 312 . 0 = L u (from the second equation) Calculate P ult =108.2kN (from the first equation). April 2003 49 Thus, the equation converges to P ult =108.2kN. This exceeds P uls =33.9kN. Therefore, the ultimate lateral capacity is adequate. The governing length is the one with the larger L+V. Thus, L=6.9m and V=1.5m. Ensure that the caisson is “short” using equation 5.1. m n D L h 4 . 10 700 22 . 1 33 33 5 1 4 5 1 4 = | | . | \ | = | | . | \ | < which is greater than L=6.9m. The pile is “short”. Note also that L>4D. The solution of L=6.9m is acceptable but not necessarily the optimum. The process can be iterated by choosing a smaller length, L, so that both the rotation and ultimate lateral capacity limits will be satisfied. By performing these calculations, it is found that the optimum caisson length is 6.696m. May 2004 50 12.0 APPENDICES 12.1 APPENDIX A: PROPERTIES OF SOILS This appendix describes typical soil parameters needed for the caisson design. It is essential that the soil properties for a specific site be obtained from the geotechnical engineer prior to the design process. 12.1.1 COHESIVE SOILS For typical soils, the unconfined compressive strength, q u , can be related to the standard penetration number, N, for the soil. The soil properties are required for the full depth of the proposed foundation, thus it is important that different layers are identified. The properties given in Table 12.1.1 are derived from the following sources: 1. Terzaghi, K. and Peck, R.B., “Soil Mechanics in Engineering Practice”, 2 nd Edition, John Wiley & Sons, Inc., New York, 1968, pp. 31,341 and 347. 2. Cooling, L.F., Skempton, A.W. and Glossop, R., Discussion of – Casagrande, A., “Classification and Identification of Soils”, Transactions, ASCE, 1948. Table 12.1.1: Properties of typical cohesive soils. N Consistency q u (kPa) Field Test 0-1 Very Soft 0-25 Squeezes between fingers when fist is closed. 2-4 Soft 25-50 Easily moulded by fingers. 5-8 Firm 50-100 Moulded by strong pressure of fingers. 9-15 Stiff 100-150 Dented by strong pressure of fingers. 16-30 Very Stiff 150-200 Dented only slightly by finger pressure. >30 Hard >200 Dented only slightly by pencil point. 12.1.2 COHESIONLESS SOILS For typical cohesionless soils, the standard penetration number, N, can be related to the soil unit weight, γ, the internal friction angle, φ, and the coefficient of horizontal subgrade reaction (n h ). The information below is based on several sources including discussion with MTO’s Foundation Design Section. For cohesionless soils, the presence of soil layer boundaries and the location of the water table must be determined. Below are a list of source used to obtain Table 12.1.2 and Figure 12.1.2. 1. Sowers, G.B. and Sowers, G.F., “Introductory Soil Mechanics and Foundations”, 3 rd Edition, The MacMillan Company, 1970, p 75. 2. Terzaghi, K. and Peck, R.B., “Soil Mechanics in Engineering Practice”, 2 nd Edition, John Wiley & Sons, Inc., New York, 1968, pp. 341 and 347. 3. Foundation Design Section, Engineering Materials Office, Ministry of Transportation, Dec. 10, 1992, Internal Memorandum. May 2004 51 Table 12.1.2: Properties of typical cohesionless soils. N Relative Density Field Test φ (degrees) γ (kN/m3) 0-4 Very Loose Easily penetrated with a ½” rebar pushed by hand. <27 <14 5-10 Loose Easily penetrated with a ½” rebar pushed by hand. 27-30 13-16 11-30 Medium Dense Easily penetrated with a ½” rebar driven by a 5 lb. hammer. 30-34 15-19 31-50 Dense Penetrated a foot with a ½” rebar driven by a 5 lb. hammer. 34-38 18-21 >50 Very Dense Penetrated only a few inches with a ½” rebar driven by a 5 lb. hammer. >38 >20 n Figure 12.1.2: h η vs. Φ for typical soils 3 April 2003 52 12.2 APPENDIX B: DESIGN AIDS The design aids provided can be used to determine the foundation length for many situations. For the larger tabulated lengths, it may be desirable to compute a more accurate length by formulae given elsewhere to optimize the solution. The soil properties are taken from “12.1 Appendix A: Properties of Soils”. 12.2.1 COHESIVE SOILS The required caisson lengths (L) in homogeneous cohesive soil can be found using Table 12.2.1. The length depends on the soil type, pole height, reference wind pressure, frost depth and the additional eccentricity (∆, as defined in Section 2). The tabulated values assume the use of standard diameters of caissons as given in Table 11.1. The values denoted with an asterisk indicate lengths where the limiting value of L ≥ 4D governs. Table 12.2.1: Required caisson length (L) below frost depth for cohesive soils, in metres. q 50 ≤ 475 (Pa) 475<q 50 <595 (Pa) POLE HEIGHT SOIL STRENGTH F+ ∆ <2.0 F+ ∆ <5.0 F+ ∆ <2.0 F+ ∆ <5.0 Soft 9.6 10.2 10.6 11.2 Firm 7.1 7.6 7.8 8.3 Stiff 5.3 5.6 5.8 6.2 25 Very Stiff 4.9* 4.9* 4.9* 5.2 Soft 11.0 11.6 12.1 12.8 Firm 8.1 8.6 8.9 9.4 Stiff 6.0 6.4 6.6 7.0 30 Very Stiff 5.5* 5.5* 5.6 5.9 Soft 12.7 13.3 14.0 14.7 Firm 9.4 9.8 10.3 10.8 Stiff 7.0 7.3 7.7 8.1 35 Very Stiff 5.9 6.2 6.4 6.8 Soft 12.7 13.2 14.0 14.6 Firm 9.4 9.8 10.3 10.8 Stiff 7.0 7.3 7.7 8.1 40 Very Stiff 6.1* 6.2 6.5 6.8 Soft 14.0 14.6 15.4 16.1 Firm 10.4 10.8 11.4 11.9 Stiff 7.7 8.1 8.5 8.9 45 Very Stiff 6.5 6.8 7.2 7.5 12.2.2 COHESIONLESS SOILS The required caisson lengths (L) in homogeneous cohesionless soil can be found using Table 12.2.2. The length depends on the soil type, pole height, reference wind pressure, location of water table (whether the water table is located above or April 2003 53 below the bottom of the caisson) and the additional eccentricity (∆, as defined in Section 2). The tabulated values assume the use of standard diameters of caissons as given in Table 11.1. The values denoted with an asterisk indicate lengths where the limiting value of L ≥ 4D governs. Table 12.2.2: Required caisson length (L) below frost depth for cohesionless soils, in metres. q 50 ≤ 475 (Pa) 475 <q 50 <595 (Pa) Above Water Table Below Water Table Above Water Table Below Water Table POLE HEIGHT SOIL STRENGTH ∆ <0.5 ∆ <3.0 ∆ <0.5 ∆ <3.0 ∆ <0.5 ∆ <3.0 ∆ <0.5 ∆ <3.0 Loose 5.6 5.9 7.0 7.3 6.0 6.3 7.5 7.8 Medium 4.9* 4.9* 5.0 5.2 4.9* 4.9* 5.3 5.6 Dense 4.9* 4.9* 4.9* 4.9* 4.9* 4.9* 4.9* 4.9* 25 Very Dense 4.9* 4.9* 4.9* 4.9* 4.9* 4.9* 4.9* 4.9* Loose 6.2 6.5 7.8 8.1 6.6 6.9 8.3 8.7 Medium 5.5* 5.5* 5.5* 5.8 5.5* 5.5* 5.9 6.2 Dense 5.5* 5.5* 5.5* 5.5* 5.5* 5.5* 5.5* 5.5* 30 Very Dense 5.5* 5.5* 5.5* 5.5* 5.5* 5.5* 5.5* 5.5* Loose 6.9 7.1 8.6 8.9 7.3 7.6 9.2 9.5 Medium 5.5* 5.5* 6.1 6.4 5.7 5.9 6.5 6.8 Dense 5.5* 5.5* 5.5* 5.5* 5.5* 5.5* 5.5* 5.7 35 Very Dense 5.5* 5.5* 5.5* 5.5* 5.5* 5.5* 5.5* 5.5* Loose 7.0 7.2 8.7 9.0 7.5 7.7 9.3 9.6 Medium 6.1* 6.1* 6.2 6.4 6.1* 6.1* 6.6 6.9 Dense 6.1* 6.1* 6.1* 6.1* 6.1* 6.1* 6.1* 6.1* 40 Very Dense 6.1* 6.1* 6.1* 6.1* 6.1* 6.1* 6.1* 6.1* Loose 7.5 7.7 9.3 9.6 8.0 8.2 9.9 10.3 Medium 6.1* 6.1* 6.6 6.9 6.2 6.4 7.1 7.3 Dense 6.1* 6.1* 6.1* 6.1* 6.1* 6.1* 6.1* 6.2 45 Very Dense 6.1* 6.1* 6.1* 6.1* 6.1* 6.1* 6.1* 6.1* 12.2.3 FOUNDATIONS ANCHORED TO ROCK Refer to Section 6.2. 12.2.4 REINFORCEMENT REQUIRED FOR CAISSON FOUNDATIONS The minimum required reinforcement for caisson foundations can be found using Table 12.2.4. The reinforcing bars have a yield strength of 400 MPa while the compressive strength of the concrete is 30 MPa. The reinforcement depends on the pole height, the 50-year reference wind pressure, the frost depth and the eccentricity (∆ as defined in Section 2 – Notation). April 2003 54 Table 12.2.4 – Minimum Reinforcement for Caisson Foundations Pole Height (m) 25 30 35 40 45 Caisson Diameter (m) 1.22 1.37 1.37 1.52 1.52 ∆+V ≤ 3.0 m 12-25M 12-25M 12-25M 12-25M 12-30M 3.0 m < ∆+V ≤ 6.0 m 12-25M 12-25M 14-25M 12-25M 12-30M q 50 ≤ 475 (Pa) 6.0 m < ∆+V ≤ 10.0 m 12-25M 12-25M 12-30M 12-30M 14-30M ∆+V ≤ 3.0 m 12-25M 12-25M 12-30M 12-30M 14-30M 3.0 m < ∆+V ≤ 6.0 m 12-25M 12-25M 12-30M 12-30M 12-35M 475<q 50 <595 (Pa) 6.0 m < ∆+V ≤ 10.0 m 12-25M 14-25M 14-30M 14-30M 12-35M April 2003 55 This page is intentionally left blank.