DEVELOPMENT OF P-Y CRITERION FOR ANISOTROPIC ROCK AND COHESIVE INTERMEDIATE GEOMATERIALS A Dissertation Presented to The Graduate Faculty of the University of Akron In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Ehab Salem Shatnawi August, 2008 DEVELOPMENT OF P-Y CRITERION FOR ANISOTROPIC ROCK AND COHESIVE INTERMEDIATE GEOMATERIALS Ehab Salem Shatnawi Dissertation Approved: Accepted: Advisor Dr Robert Liang Department Chair Dr Wieslaw Binienda Committee Member Dr Craig Menzemer Dean of the College Dr George K Haritos Committee Member Dr Daren Zywicki Dean of the Graduate School Dr George R Newkome Committee Member Dr Xiaosheng Gao Date Committee Member Dr Kevin Kreider ii ABSTRACT Rock-socketed drilled shaft foundations are commonly used to resist large axial and lateral loads applied to structures or as a means to stabilize an unstable slope with either marginal factor of safety or experiencing continuing slope movements One of the widely used approaches for analyzing the response of drilled shafts under lateral loads is the p-y approach Although there are past and ongoing research efforts to develop pertinent p-y criterion for the laterally loaded rock-socketed drilled shafts, most of these p-y curves were derived from basic assumptions that the rock mass behaves as an isotropic continuum The assumption of isotropy may not be applicable to the rock mass with intrinsic anisotropy or the rock formation with distinguishing joints and bedding planes Therefore, there is a need to develop a p-y curve criterion that can take into account the effects of rock anisotropy on the p-y curve of laterally loaded drilled shafts A hyperbolic non-linear p-y criterion for rock mass that exhibit distinguished transverse isotropy is developed in this study based on both theoretical derivations and numerical (finite element) parametric analysis results Evaluations based on parametric study on full-scale lateral load test on fully instrumented drilled shaft have shown the insights on the influences of rock anisotropy on the predicted response of the rock socketed drilled shaft under the lateral load Both, the orientation of the plane of transversely isotropy, and the degree of anisotropy (E/E’) has influences on the main two iii parameters required to characterize the p-y curve, the subgrade modulus (Ki) and the ultimate lateral resistance (pu) In addition to the development of a hyperbolic p-y criterion of transversely isotropic rock, another p-y criterion for cohesive intermediate geomaterials (IGM) using hyperbolic mathematical formulation is developed herein by employing the results of a series of finite element (FE) simulations and the results of two full scale lateral load test for drilled shaft socketed into IGM iv DEDICATION To my mother, my father, my wife, my sisters and brothers, my friends, and to anyone who would read this dissertation Also, I would like to dedicate this work to my expected baby v ACKNOWLEDGEMENTS All praise is due to Allah (S.W.T) without whom nothing good of this work can be ever accomplished Though only my name appears on the cover of this dissertation, a great many people have contributed to its production I owe my gratitude to all those people who have made this dissertation possible and because of whom my graduate experience has been one that I will cherish forever My deepest gratitude is to my advisor, Dr Robert Liang I have been amazingly fortunate to have an advisor who gave me the freedom to explore on my own and at the same time the guidance to recover when my steps faltered I hope that one day I would become as good an advisor to my students as Prof Robert Liang has been to me Also of a great importance are the help and constructive comments and contributions I received from my committee members, Dr Craig Menzemer, Dr Daren Zywicki, Dr YuehJaw Lin, Dr Xiaosheng Gao and Dr Kevin Kreider I would also like to acknowledge the support I received from personnel in our department, particularly Mrs Kimberly Stone and Mrs Christina I must acknowledge as well the many friends, and colleagues, who assisted, advised, and supported me during these three and a vi half year Especially, I need to express my gratitude and deep appreciation to my former roommate, Dr Mohammad Yamin, whose friendship, knowledge, and wisdom have supported, enlightened, and entertained me over the ten years of our friendship I must also acknowledge my former advisor, Dr Abdulla Malkawi, I have learned so much from his keen insight, his research and problem solving abilities, and his amazing energy Special thanks also to Dr Jamal Nusairat, Dr Diya Azzam, Dr Inmar Badwan, Dr Firas Hasan, Dr Sami Khorbatli, Dr Samer Rababa’a, Dr Khalid Alakhras, Dr Wael Khasawneh, Dr Mohammad Khasawneh, Dr Qais Khasawneh, Saleh Khasawneh, Abdallah Sharo, Wassel Bdour, Madhar Tamneh, Mohannad Aljarrah, Khalid Elhindi, Jamal Tahat, Khalid Mustafa, and my friends in Jordan, Eng Kifah Ewisat, Eng Mamoun Shatnawi, Eng Mohammad Al-sakran, and Eng Sameer Mousa They have consistently helped me keep perspective on what is important in life and shown me how to deal with reality Most importantly, none of this would have been possible without the love and patience of my family My parents (Salem and Salmeh), my darling and lovely wife SAHAR, my sisters (Heba, Ruba, Waed, and the little and lovely one Lina) and brothers (Dr Mohammad, Abdulla, Hussain, Dr Murad, and Moad) to whom this dissertation is dedicated to, has been a constant source of love, concern, support and strength all these years I would like to express my heart-felt gratitude to them vii TABLE OF CONTENTS Page LIST OF TABLES xiii LIST OF FIGURES xiv CHAPTER I INTRODUCTION 1.1 Statement of Problem 1.2 Objectives 1.3 Work Plan 1.4 Dissertation Outlines 13 II LITERATURE REVIEW 15 2.1 Analysis Methods of Laterally Loaded Rock-Socketed Drilled Shafts .15 2.1.1 Elastic continuum methods 16 2.1.2 Winkler Method (Subgrade reaction approach) and P-Y method .17 2.2 Analysis Methods for Estimating Ultimate Lateral Rock Reaction 22 2.2.1 Carter and Kulhawy (1992) .24 2.2.2 Zhang et al (2000) 25 2.2.3 To, Ernst, and Einstein (2003) 26 2.2.4 Yang (2006) .27 2.3 Initial Modulus of Subgrade Reaction .30 2.4 Ultimate Side Shear Resistance 32 viii 2.5 Discussion of Analytical Models for Laterally Loaded Sockets 35 2.6 Bedrocks 38 2.6.1 Rocks in Ohio 38 2.6.2 Rock Characterization .39 2.6.3 Rock Categories .40 2.7 Laboratory and In-situ testing for Transversely Isotropic Rock 44 III TRANSVERSE ISOTROPY EFFECTS ON THE INITIAL TANGENT TO P-Y CURVE .49 3.1 Abstract 49 3.2 Introduction 50 3.3 Sensitivity Analysis .51 3.4 FE Analysis 54 3.4.1 Description of FE Model 54 3.4.2 Constitutive Models 55 3.4.3 FE Analysis .56 3.4.4 FE Parametric Study Results .57 3.5 Estimating the Transversely Isotropic Parameters 65 3.6 Sensitivity of the Transversely Isotropic Parameters 70 3.7 Summary and Conclusions 76 IV TRANSVERSELY ISOTROPIC EQUIVALENT MODEL FOR JOINTED ROCK .78 4.1 Abstract 78 4.2 Introduction 78 4.3 Literature Review 80 4.4 Equivalent Homogeneous Model 82 4.4.1 Summary 94 ix 4.4.2 Model Verification 96 4.5 Summary and Conclusions 97 V ULTIMATE SIDE SHEAR RESISTANCE OF ROCK-SOCKETED DRILLED SHAFT 99 5.1 Abstract 99 5.2 Introduction 100 5.3 Theoretical model, fundamental interface behavior 103 5.4 FE Study 104 5.4.1 3-D FE Modelling 104 5.4.2 Constitutive Models .105 5.4.3 FE Analysis Simulation 106 5.5 Factors affecting the ultimate side shear resistance 108 5.5.1 Effect of Rock Mass Properties (Em, Cr, Фr) 109 5.5.2 Effect of Drilled Shaft Geometry and Shear Modulus 110 5.6 Suggested Empirical Relationships 115 5.7 Validation of the Empirical Equation 117 5.8 Summary and Conclusions 119 VI ULTIMATE LATERAL RESISTANCE OF TRANSVERSELY ISOTROPIC ROCK .124 6.1 Abstract 124 6.2 Introduction 125 6.3 Rock Failure at Shallow Depth 127 6.3.1 Derivation of pu at shallow depth 130 6.3.2 FE Parametric Study Results 133 6.4 Rock Failure at the Great Depth 139 6.5 Strength of Transversely Isotropic Rock 143 x Figure 8-32 Soil Profile and Shaft Dimension at Colorado I-225 clay site 208 100 90 80 Lateral Load (ki ps) 70 60 50 40 M easured 30 Proposed p-y R eese & W el p-y ch 20 10 0 0.4 0.6 1.2 D efl on at Shaft Top (i ecti n) Figure 8-33 Predicted and Measured Load-Deflection Curves of CDOT Clay Site 209 CHAPTER IX SUMMARY AND CONCLUSIONS 9.1 Summary Towards the objective of developing a new p-y criterion of anisotropic rock, extensive theoretical and numerical simulation works have been carried out A detailed literature review was performed to study the existing design and analysis methods of the laterally loaded drilled shafts and piles in rock A new hyperbolic p-y criterion of transversely isotropic rock and cohesive IGM was proposed based on the field test data and extensive theoretical work For a rock with transversely isotropic properties, an empirical formula for estimating the shear modulus (G’) is proposed to simplify the characterization procedures of the elastic properties for this type of rock For jointed rock, an equivalent transversely isotropic homogeneous model to describe the jointed rock’s stress-strain behaviour was developed to obtain the equivalent five transversely isotropic elastic constants 3D FE models simulating the response of the laterally loaded drilled shafts in rock using ANSYS was established to develop the pertinent methods that can be used to estimate the main two parameters required to characterize a hyperbolic p-y curve, the subgrade modulus (Ki) and the ultimate resistance (pu) The first FE parametric study 210 was performed for a drilled shaft socketed into transversely isotropic media to develop a series of design charts for estimating the initial tangent to the p-y curve Another series of FE simulations was undertaken to investigate the effect of various influencing factors on the maximum side shear resistance, including the interface strength parameters, the moduli of the drilled shaft and rock mass, and the drilled shaft geometry Based on the results of the FE parametric study, an empirical equation is proposed that can be used to estimate the ultimate side shear resistance of the drilled shafts embedded in rock Additionally, theoretical equations for determining the ultimate lateral resistance of transversely isotropic rock was derived based on the identified failure modes of jointed rock, and transversely isotropic rock strength criterion The failure modes of rock mass were identified through a series of 3D FE study The evaluation of the proposed p-y criterion for rock has been done by performing a parametric study on hypothetical cases of a rock socketed drilled shaft under lateral load In these cases, a range of parameters differentiating the isotropic vs transversely isotropic p-y curves was selected in a systematic numerical study using the LPILE computer program with the specific p-y curves By employing the results of FE simulations of a drilled shaft socketed into cohesive soil, and in conjunction with the empirical equation recommended by Matlock (1970) for estimate the ultimate lateral resistance of cohesive material, a hyperbolic p-y criterion was developed for the cohesive intermediate geomaterial 211 9.2 Conclusions Based on the research work performed, the following conclusions can be drawn The 3D FE simulations have provided basic understanding of the mobilization mechanisms of the lateral resistance of rock mass to the drilled shafts, from which analytical equations are derived for computing the ultimate lateral resistance of transversely isotropic rock pu Based on the sensitivity study, the influences of rock anisotropy on the predicted response of the rock socketed drilled shaft under the lateral load are clearly observed Both the orientation of the plane of transversely isotropy and the degree of anisotropy (E/E’) have exerted great influences on the main two parameters required to characterize the hyperbolic p-y curve: the subgrade modulus (Ki) and the ultimate lateral resistance (pu) Moreover, it was shown that if there was no anisotropy, the proposed p-y curve will be reduced to Yang (2006) p-y curve Finally, it was shown that the proposed p-y criterion can provide reasonable predictions of the behavior of the drilled shaft socketed in rock under the applied lateral loads The positive evaluation of the proposed p-y criterion for cohesive IGM based on comparisons between the predicted and measured responses of full-scale lateral load tests on fully instrumented drilled shafts has shown the practical uses of the proposed p-y criterion The average prediction of the maximum moment error was around 18% which is acceptable for practice 212 The evaluation of the empirical equation for estimating the ultimate side shear resistance against the available load test data has shown that the prediction by the proposed method is conservative but with improved accuracy compared with other existing empirical equations From the statistical analysis, the proposed empirical equation can improve our prediction capability for the ultimate side shear resistance of a rock socket The hyperbolic p-y criteria for rock developed in this study can be used in conjunction with computer analysis program, such as COM624P, LIPLE, or FBPIER, to predict the deflection, moment, and shear responses of a drilled shaft embedded in rock under the applied lateral loads Considerations of the effects of joints and discontinuities on the rock mass modulus and strength were included in the proposed p-y criterion 9.3 Recommendations for Future Studies More lateral load tests on the full-scale drilled shafts socketed in various types of rock, with the accompanying dilatometer tests at the load test sites to characterize rock properties, should be performed in order to further validate the developed p-y criteria It is believed that the group effect of drilled shaft socketed into rock is negligible However, due to the presence of the inclined bedding and joints, the group effects would be significant in the transversely isotropic rock Therefore, a future study to investigate the relevant p-multipliers for a drilled shaft group in transversely 213 isotropic rock can be highly desirable This research objective can be accomplished through a well-planned field test program of drilled shafts groups Additionally, 3D FE study could also be employed to determine the p-multiplier for a drilled shaft group socketed in the transversely isotropic rock Since the required input for the proposed p-y criterion includes the five elastic constants of the transversely isotropic rock mass, and since the indirect pressuremeter and dilatometer tests are the most frequently used in-situ tests for estimating the rock mass modulus, a future study on the use of pressuremeter test to estimate these five elastic constants would be highly desirable 214 REFERENCES 1) ABAQUS (1998) ABAQUS Standard User’s Manual, Version 5.8, Hibbitt, Karlsson & Sorensen, Inc 2) AMADEI B, and GOODMAN R E (1981) “A 3D Constitutive Relation for Fractured Rock Mass” International Symptom on Mechanical Behaviour of Structured Media”pp 249-268, 1981 3) AMADEI B (1996) “Importance of anisotropy when estimating and measuring in situ stresses in rock” International Journal of Rock Mechanics and Mining Science; Vol 33 No 3, pp.293-325 1996 4) AMADEI B., SAVAGE W., and SWOLFS H (1987) “ Gravitational Stresses in Anisotropic Rock Masses” Int J Rock Mech Min Sci & Geomechanics Vol 24, No 1, pp 5-14, 1987 5) ANSYS 11.0 (2007) User manual volume IV, theory Swanson Analysis Systems Inc 6) BARTON, N., LIEN, R., and LUNDE, J (1974) “Engineering classification of rock masses for the design of tunnel support.” Rock Mechanics, Vol 6, No 4, Vienna, Austria, p 189-236 7) BENMOKRANE B., MOUCHAORAB K S., BALLIVY G (1994) “Laboratory investigation of shaft resistance of rock-socketed pier using the constant normal stiffness direct shear test” Can Geotech J 31, 407-419 (1994) 8) BIENIAWSKI, Z T (1976) “Rock mass classifications in rock engineering.” Proceedings of the Symposium on Exploration for Rock Engineering, Z T Bieniawski, ed., Vol 1, A A Balkema, Rotterdam, Holland, p 97-106 9) BIENIAWSKI, Z.T., (1978) “Determining rock mass deformability: experience from case histories.” Int J Rock Mech Min Sci & Geomech Abstr., 15, p 237248 10) BORESI, A P (1965), “Elasticity in engineering mechanics”, Prentice-Hall, Englewood Cliffs, N.J 11) BOWLES, J E (1988) Foundation analysis and design, 4th Edition, McGraw Hill, New York, 1004 215 12) BRADY B H G, and BROWN, E T (2004) “Rock Mechanics for Underground Mining”, George Allen & Unwin: London, 3rd edition, 2004, 628 pp, Kluwer Academic Publishers, Dordrecht 13) BRANSBY, M.F and SPRINGMAN, S.(1999) “Selection of load-transfer functions for passive lateral loading of pile groups.” Computers and Geotechnics, 24(3):155-184 14) BRIAUD, J L., SMITH, T D., and MEYER, B J (1983), “Using the Pressuremeter Curve to Design Laterally Loaded Piles.” Proceedings of Annual Offshore Technology Conference, Vol 8, p 495-502 15) BROWN, D and SHIE, C.(1990) “Numerical experiments into group effects on the response of piles to lateral loading.” Computers and Geotechnics, 10 (3): 211230 16) BROWN, E.T (1993) “The nature and fundamentals of rock engineering.” Comprehensive Rock Engineering – Principle, Practice and Projects Ed; J.A Hudson, Pergamon Press, p.1-23 17) CARTER, J P., and KULHAWY, F H (1992) “Analysis of laterally loaded shafts in rock.” Journal of Geotechnical Engineering, ASCE, 118(6), p 839-855 18) CARTER, J P., BOOKER, J R., and YEUNG, S K (1986) “Cavity expansion in cohesive frictional soils.” Geotechnique, 36(3), p 349-358 19) CHEN C S, PAN E., and AMADEI B.(1998) “Determination of Deformability and Tensile Strength of Anisotropic Rock Using Brazilian Tests” International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, Volume 35, Number 1, January 1998, pp 43-61(19) 20) CHO, K H., CLARK, S C., KEANEY, B D., GABR, M A., and BORDEN, R H (2001) “Laterally loaded drilled shafts embedded in soft rock.” Transportation Research Record 1772, p 3-11 21) DUNNAVANT T.W and O’NEILL M.W.(1989) “Experimental p-y model for submerged stiff clay.” J Geotechnical Engineering 115(1), 95-114 22) DYKEMAN, P., and VALSANGKAR, A.J (1996) “Model Studies of Socketed Caissons in Soft Rock,” Canadian Geotechnical Journal, Vol 33, No 5, pp 747759 23) EXADAKTYLOS G.E (2001) “On the Constraints and Relations of Elastic Constants of Transversely Isotropic Geomaterial” Int J Rock Mech Min Sci & Geomech Vol 38, pp 941-956, 2001 24) FELDMANN, R.M., and HACKATHORN, M (1996) Fossils of Ohio, Bulletin 70, 216 Ohio Division of Geological Survery 25) GABR, M A (1993) “Discussion on ‘Analysis of laterally loaded shafts in rock.’” Journal of Geotechnical Engineering, ASCE, 119(12), p 2015-2018 26) GABR, M.A., BORDEN, R.H., CHO, K.H., CLARK, S.C., and NIXON, J.B (2002) “P-y curves for laterally loaded drilled shafts embedded in weathered rock.” FHWA/NC/2002-08, North Carolina Department of Transportation 27) GAZIOGLU S.M and O’NEILL M.W.(1984) “Evaluation of p-y relationships in cohesive soil.” Analysis and Design of Pile Foundations, Proceedings, San Francisco, California, 192-213 28) GERRARD C M (1975) “Background to mathematical modeling in geomechanic: the role of fabric and stress history” Proc Int Symp On Numerical methods, Karlsruhe, p 33-120 (1975) 29) GERRARD C M (1982) “Elastic Models of Rock Masses Having One, Two, and Three Sets of Joints” International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, Volume 19, 1982, pp 15-23 30) GOODMAN, R., and SHI, G (1985) “Block theory and its application to rock engineering”, Prentice-Hall, Englewood Cliffs, N.J 31) GUO, W D (2001) “Subgrade modulus for laterally loaded piles.” Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing, Vienna, Austria 32) HAWK, D J., and HO, H Y., (1980) “A study of the orthotropy of coal and other rock materials,” Final Report to U.S Dept of Interior and Bureau of Mines, University of Colorado 33) HOEK, E (1983) “Strenth of jointed rock massses” Geotechnique, v 33 issue 3, p 187-223 34) Hoek, E., 2002 Practical Rock Engineering, http://www.rocscience.com/roc/Hoek/Hoeknotes2000.htm 2002 Edition 35) HOEK, E., and BROWN, E.T (1988) “The Hoek-Brown criterion – a 1988 update.” 15th Canadian Rock Mechanics Symposium: rock engineering for underground excavations, University of Toronto, p 31-38 36) HOMAND, F., MOREL E., HENRY H., CUXAC P., and HAMMADE E (1993) “Characterization of the moduli of Elasticity of an Anisotropic Rock using Dynamic and Static Methods” Int J Rock Mech Min Sci & Geomech Vol 30, No 5, pp 527-535, 1993 217 37) HOOLEY P, LEFROY SR (1993), “The ultimate shaft frictional resistance mobilized by bored piles in over-consolidated clays and socketed into weak and weathered rock”, In: Cripps JC et al., editors The engineering geology of weak rock Rotterdam: Balkema; 1993 p 447–55 38) HORVATH, R G., KENNEY, T C., and KOZICKI, P (1983) “Methods of improving the performance of drilled piers in weak rock” Canadian Geotechnical Journal, 20(4), pp 758-772 39) HSIUNG Y and CHEN Y.(1997) “Simplified method for analyzing laterally loaded single piles in clays.” J Geotech Geoenviron Engrg., 123(11), 1018-1029 40) J.L Justo, E Justo, P.Durand and J.M Azón “The foundation of a 40-storey tower in jointed basalt” International Journal of Rock Mechanics and Mining Sciences,Volume 43, Issue 2, February 2006, Pages 267-281 41) JAEGER JC (1960) “Shear failure of anisotropic rocks” Geol Mag 1960;97:65–72 42) JOHNSTON J., and CHRISTENSEN N (1993) “Elastic Constants and Velocity Surfaces of Indurated Anisotropic Shales” Survey in Geophysics Vol 15 No pp 481-494, Sep 1994 43) JOHNSTON, I.W and CHOI, S.K (1986) A synthetic soft rock for laboratory model studies Geotechnique 36(2), 251–263 44) JOHNSTON, J W and LAM, T S K., (1989a), “Shear Behaviour of Regular Triangular Concrete/Rock Joints⎯Analysis,” Journal of Geotechnical Engineering, Vol 115, No 5, p 711-727 45) JYH J.L., YANG M.-T., and HSIEH H.-Y (1997) “Direct Tensile Behavior of a Transversely Isotropic Rock” International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, Volume 34, Number 5, July 1997 , pp 837849(13) 46) KONG K H , KODIKARA J., and HAQUE A ( 2006)“Numerical modelling of the side resistance development of piles in mudstone with direct use of sidewall roughness” International Journal of Rock Mechanics & Mining Sciences 43 (2006) 987–995 47) LAMBORN, R.E., AUSTIN, C R., and SCHAAF, D (1938) “Shales and surface clays of Ohio”, Geological Survey of Ohio, fourth series, bulletin 39 48) LIANG, R.Y, (2000) “Instrumentation, Monitoring, and Testing at the CUY-9015.24 Central Viaduct Project”, a research report submitted to the Ohio department of transportation and FHWA, June,2000 49) LIAO J J., HU T., and CHANG C (1997) “Determination of Dynamic Elastic 218 Constants of Transversely Isotropic Rock using a Single Cylindrical Specimen” Int J Rock Mech Min Sci & Geomech Vol 34, No 5, pp 837-849, 1997 50) LIAO J J., YANG M., and HSEIH H (1997) “Direct Tensile Behavior of a Transversely Isotropic Rock” Int J Rock Mech Min Sci & Geomech Vol 34, No 5, pp 837-849, 1997 51) LIU W., and NOVAK M (1994) “Dynamic response of single pile embedded in transversely isotropic layered media” Earthquake Engineering and Structural Dynamics, Vol 23, pp 1239-1257 (1994) 52) LO, T., COYNER, K, and TOKSOZ, M (1986) “Experimental determination of Elastic anisotropy of Berea sandstone, Chicopee Shale, and Chelmsford granite) Geophysics, Vol 51, No.1, pp 164-171, (Jan, 1986) 53) MALMGREN L., NORDLUND E and ROLUND S (2004) “Adhesion strength and shrinkage of shotcrete” Tunnel and Underground Space Technology 20, 2004, pp.33-48 54) MATLOCK, H (1970) “Correlation for design of laterally loaded piles in soft clays.” 2nd Offshore Technology Conference, Houston, Texas, 577-594 55) NUSAIRAT, J., LIANG, R., and ENGEL, R., (2006).“Design of Rock Socketed Drilled shafts”, a research report submitted to the Ohio Department of Transportation and FHWA, July,2006 56) O’NEILL, M W., and REESE, L C (1999) “Drilled Shafts: Construction Procedure and Design Methods”, FHWA-IF-99-025 57) O’NEILL, M.W., TOWNSEND, F.C., HASSAN, K.M., BULLER, A., and CHAN, P.S (1995) “Load transfer for drilled shafts in intermediate geomaterials” U.S Department of Transportation, FHWA-RD-95-172, Draft report 58) PARTOS, A J., SANDER, E J., and HUNGSPRUKE, U (1989) "Performance of large diameter drilled pier” Proc International Conference on piling an deep foundations London, 309-316 59) PELLS, P J N, ROWE, R.K., and TURNER, R.M (1980), “An Experimental Investigation into the Side Shear of Socketed in Sandstone,” Proceedings, International Conference on Structural Foundations in Rock, Sydney, p 291-302 60) POULOS, H G (1971) “Behavior of laterally loaded piles I: Single piles.” J Soil Mech Found Div., ASCE, 97(5), p 711-731 61) RANDOLPH, M F (1981) “The response of flexible piles to lateral loading.” Geotechnique, 31(2), p 247-259 219 62) REESE, L C (1983) “Behavior of Piles and Pile Groups Under Lateral Load, ” Report to the U.S Department of Transportation, Federal Highway Administration, Office of Research, Development, and Technology, Washington, D.C., September, 1983 63) REESE, L C (1997) “Analysis of laterally loaded piles in weak rock.” J Geotech Envir Engrg., ASCE, 123(11), p 1010-1017 64) REESE, L C., and MATLOCK, H (1956) “Non-dimensional solutions for laterally loaded piles with soil modulus assumed proportional to depth.” Proceedings, Eight Texas Conference on Soil Mechanics and Foundation Engineering, Austin, Texas, p 1-23 65) REESE, L C., COX, W R and KOOP, F D (1974) “Analysis of laterally loaded piles in sand.” Proc Of 6th offshore Tech Conf., Houston, TX, Vol 2, p 473-483 66) REESE, L.C and WELCH, R.C.(1975) “Lateral loading of deep foundations in stiff clay.” J Geotech Engrg Div., ASCE, 101(7), 633-649 67) REESE, L.C., COX, W.R., and KOOP, F.D (1975) “Field testing and analysis of laterally loaded piles in stiff clay.” Seventh Annual Offshore Technology Conference, Dallas, Texas, 671-690 68) ROCSCIENCE (2006), RocLab, free software from www.rocscience.com, Rocscience, Inc., Toronto, Canada 69) ROSENBERG, P., and JOURNEAUX, N (1976) “Friction and end bearing tests on bedrock for high capacity socket design”, Canadian Geotechnical Journal, 13(3): 324–333 70) ROWE RK, ARMITAGE HH (1987) “A design method for drilled piers in soft rock” Can Geotech J, Ottawa, Canada 1987;24(1):126–42 71) SARGAND, S M, and HAZEN, G A (1987) “Deformation behavior of shales” Int J Rock Mech Min Sci & Geomech Abstr., Vol 24, No 6, p 365-370 72) SEOL, H., and JEONG S., (2007) “Shaft Resistance Characteristics of RockSocketed Drilled Shafts Based on Pile Load Tests” Jour of the KGS, Vol 23, No September 2007, pp 51 63 73) SHATNAWI, E S (2007) “Transverse Isotropy Effects on P-Y analysis” Proceedings of Deep Foundations Institute 32 Annual Conference on Deep Foundations, Oct 2007 74) SINGH B (1973) “Continuum characterization of jointed rock masses Part I–the constitutive equations” Int J Rock Mech Sci & Geomech Abstr 1973;10:311–35 220 75) SITHARAM T G., SRIDEVI J., SHIMIZU N (2001), “Practical Equivalent Continuum Characterization of Jointed Rock Masses” International Journal of Rock Mechanics and Mining Sciences, Volume 38, 2001, pp 437-448 76) SMITH, T D., SLYH, R (1986), “Side Friction Mobilization Rates for Laterally Loaded Piles from the Pressuremeter,” The Pressuremeter and Its Marine Applications: Second International Symposium ASTM STP 950, J.L Briaud and J.M.E Audibert, Eds., American Society for Testing and Materials 77) SUN, K (1994) “Laterally loaded piles in elastic media.” Journal of Geotechnical Engineering, ASCE, 120(8), p 1324-1344 78) THORNE CP (1977), “The allowable loadings of foundations on shale and sandstone in the Sydney region” Part 3: Field tests results Chapter presented to the Sydney Group of Aust Geomechanics Soc., Int of Engineers of Australia 1977 79) TIEN Y M., and KUO M C (2001) “A Failure Criterion for Transversely Isotropic Rocks” International Journal of Rock Mechanics & Mining Sciences 38 (2001), pp.399–412 80) TIEN YM, KUO MC, and JUANG C., (2006) “An experimental investigation of the failure mechanism of simulated transversely isotropic rocks” International Journal of Rock Mechanics & Mining Sciences 43 (2006) 1163–1181 81) TO, A C., ERNST, H., and Einstein, H H (2003) “Lateral load capacity of drilled shafts in jointed rock.” Journal of Geotechnical and Geoenvironmental Engineering, Vol 129, No 8, p 711-726 82) TURNER, J.P (2006) NCHRP Synthesis 360, “Rock Socketed Drilled Shafts for Highway Transportation Structures”, Transportation Research Board of the National Academies, Washington, D.C., 83) U.S Army Corps of Engineers (1990) Engineering Manual (1110-1-1904) “Engineering and Design: Settlement Analysis” 84) VESIC, A S (1961) “Beam on elastic subgrade and the Winkler hypothesis.” Proc 5th Int Conf Soil Mechanics and Foundation Engineering, Paris, Vol 1, p 845-850 85) VU T T., (2006) “Laterally Loaded Rock-Socketed Drilled Shafts” Master Thesis, The University of Wyoming, May 2006, pp 106 86) WALLACE, J W et al (2002) “Cyclic large deflection testing of shaft bridges part II: analytical studies.” Report from California Dept of Transportation 87) WEI Z Q (1986), “Moduli of Jointed Rock Masses” Proceeding of the international symposium, Helsinki, Finland, 25-28 Aug 1986, pp 1073-1083 221 88) WILLIAMS, A F., and PELLS P J N (1981) “Side Resistance Rock Sockets in Sandstone, Mudstone, and Shale,” Canadian Geotechnical Journal, Vol 18, p 502523 89) WILLIAMS, A F., JOHNSTON, I W., and DONALD, I B (1980) “The Design of Socketed piles in weak rock,” Proceedings of International Conference on Structural Foundations on Rock, Sydney, p 327-347 90) WITTKE W (1990), “Rock Mechanics Theory and Applications with Case Histories” Spring-Verlag, Berlin Heidelberg, 1990 91) YANG M Z., ISLAM M Z., and DRUMM E C (2004) “Side Resistance of Drilled Shaft Socketed into Wissahickon Mica Schist” Geosupport 2004 pp 765777 92) YANG, K and LIANG, R.(2005) “Lateral response of large diameter drilled shafts in clay.” Proc 30th Annual Conference on Deep Foundations, Deep Foundation Institute, 115-126 93) YANG, K., (2006) “Analysis of Laterally Loaded Drilled Shafts in Rock,” Ph.D dissertation, University of Akron, Akron, Ohio, 2006, 291 pp 94) YANG, Z and JEREMIĆ, B (2002) “Numerical analysis of pile behaviour under lateral loads in layered elastic-plastic soils” Int J Numer Anal Meth Geomech 26:1385-1406 95) ZHANG, L (1997) “Analysis and design of axially loaded drilled shafts socketed into rock” MS thesis, Massachusetts Institute of Technology, Cambridge, MA 96) ZHANG, L., ERNST, H., and EINSTEIN, H H (2000) “Nonlinear analysis of laterally loaded rock-socketed shafts”, Journal of Geotechnical and Geoenvironmental Engineering v 126 issue 11, p 955-968 222