Development of p y criterion for anisotropic rock and cohesive intermediate geomaterials

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 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