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

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

DEVELOPMENT OF P-Y CRITERION FOR ANISOTROPIC ROCK AND

COHESIVE INTERMEDIATE GEOMATERIALS

A Dissertation Presented to The Graduate Faculty of the University of Akron

DEVELOPMENT OF P-Y CRITERION FOR ANISOTROPIC ROCK AND

COHESIVE INTERMEDIATE GEOMATERIALS

Ehab Salem Shatnawi

Dissertation

Dr Robert Liang Dr Wieslaw Binienda

Dr Xiaosheng Gao

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

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

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

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 Yueh- Jaw 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

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

TABLE OF CONTENTS

Page

LIST OF TABLES xiii

LIST OF FIGURES xiv

CHAPTER I INTRODUCTION 1

1.1 Statement of Problem 1

1.2 Objectives 8

1.3 Work Plan 9

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

2.5 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

4.4.2 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

6.6 Illustrative Example 146

6.7 Summary and Conclusions 149

VII HYPERBOLIC P-Y CRITERION FOR TRANSVERSELY ISOTROPIC ROCK 152

7.1 Introduction 152

7.2 General Shape of P-y Curve in Rock 153

7.3 Construction of P-y curves for transversely isotropic rock 154

7.4 Sensitivity Analysis 156

7.5 Predicting Dayton Test Results 162

7.6 Illustrative Example 164

7.7 Summary and Conclusions 167

VIII HYPERBOLIC P-Y CRITERION FOR COHESIVE INTERMEDIATE GEOMATERIAL 169

8.1 Introduction 169

8.2 Background 169

8.3 Documentation of Two Lateral Load Tests and Results 171

8.3.1 Lateral Load Test at JEF-152-1.3 171

8.3.2 Lateral Load Test at War-48-2102 (Warren County, Ohio) 179

8.4 Literature Review 186

8.4.1 Initial Tangent to p-y Curve 186

8.4.2 Ultimate Resistance, Pult 187

8.5 FE Modeling 188

8.5.1 Initial Tangent to p-y curve, Ki 188

8.5.2 Ultimate Lateral Resistance, Pult 190

8.6 Case Studies 194

8.6.2 Ohio WAR-48 Test 195

8.6.3 Ohio LOR-6 Test (Liang, 1997) 195

8.6.4 Salt Lake International Airport Test (Rollins et al, 1998) 196

8.6.5 Ohio CUY-90 Test (Liang, 2000) 197

8.6.6 Colorado I-225 Test (Nusairat, et al, 2004) 197

8.7 Summary and Conclusions 198

IX SUMMARY AND CONCLUSIONS 210

9.1 Summary 210

9.2 Conclusions 212

9.3 Recommendations for Future Studies 213

REFERENCES 215

LIST OF TABLES

Table Page

2-1 Summary of the design methods of ultimate resistance predictions 34

3-1 Input Rock Mass Parameters of I-40 Load Test 53

3-2 Parameters variation for the FEA 58

3-3 Sensitivity analysis of Ki (Stage I) 63

3-5 Effect of β on Ki 72

3-6 Effect of rock anisotropy on Ki 72

5-1 Range of model parameters for the FE parametric study 107

5-3 Input data for the proposed equation estimated using the information given in Table 5-2 122

5-4 Side shear resistance of drilled shafts, a comparison of experimental values and those predicted by empirical equations 123

6-1 Parameters variation for the FE study 134

6-2 Sensitivity analysis of CF (Stage I) 136

7-1 Effect of anisotropy on the p-y curve parameters 157

8-1 Pressuremeter Test Results 173

8-2 Laboratory Test results 173

8-3 Dilatometer Test Results 179

8-4 Maximum Bending Moment for the Six Cases 199

LIST OF FIGURES

Figure Page

1-1 Drilled shaft and soil models of p-y analysis 2

1-2 The flow chart of the works 12

2-1 Distribution of ultimate lateral force per unit length 24

2-2 Components of rock mass resistance (Zhang et al 2000) 25

2-3 Typical forces on wedge 27

2-4 Proposed wedge type failure model for the top layer of rock 28

2-5 Suggested stress distribution at failure at great depth 30

2-6 Geological map of Ohio, showing the pattern of surface rocks across the state 42

2-7 Cross section through the rocks of central Ohio from the Indiana-Ohio border to the Ohio River (taken from Feldmann et al., 1996) 42

2-8 Definition of elastic constants for the case of transversely isotropy 43

2-9 Dilatometer test in a transversely isotropic rock (taken from Wittke, 1990) 45

2-10 (a) dilatometer test in a borehole oriented parallel to the schistosity, (b) directions of measurement 47

2-11(a)correlation of the measurement of U0 and V0, 48

2-12 Coefficient k1 and k2 determined from dilatometer test 48

3-2 Effect of GSI on Yang (2006) p-y criterion 53

3-3 Deflection and moment profile 54

3-4 FE meshes of a drilled shaft-rock system 56

3-6 Effects of transversely isotropic parameters on Ki 61

3-7 Effects of drilled shaft properties and rock density on Ki 62

3-8 Sensitivity analysis of Ki (Stage I) 63

3-9 Comparison of FEM predictions and empirical predictions for Ki 65

3-10 Design charts for estimating Ki 64

3-11 Predicted vs measured shear modulus (G’) 67

3-12 Effects of β on the shaft head deflections 73

3-13 Effects of β on the maximum moment 73

3-14 Effects of E/E’ on the shaft head deflections 74

3-15 Effects of E/E’ on the maximum moment 74

3-16 Comparison of load-deflection of test shaft at Dayton load test 75

3-17 Comparison of the maximum moment of test shaft at Dayton load test 75

4-1 Rock block with three discontinuities 84

4-2 Jointed rock block under different types of loading; 88

4-3 Effect of discontinuities properties on the axial strain 88

4-4 FE model for cubic rock block with three different spacing 89

4-5 Uniaxial strain for a rock block under uniaxial stress 89

4-6 Effect of νfilling and β on the uniaxial strain 90

4-7 Lateral strain in cubic rock block with β=0.09 90

4-8 Effect of νfiling and β on the lateral strain 91

4-9 Rock block with three discontinuities 92

4-10 Behaviour of jointed rock block under lateral stress 93

4-11 Rock block behaviour under shear stress 94

4-12 Equivalent transversely isotropic model 97

5-1 The mobilized normal force and shear resistance at peak lateral load 100

5-2 3D Model for drilled shaft socketed into rock under torque application 105

5-3 FE meshes of a drilled shaft-rock system 106

5-4 Torque vs rotation 108

5-5 Effect of coefficient of friction on τult 111

5-6 Effect of the interface adhesion on τult 111

5-7 Effect of the σv’ on τult 112

5-8 Relationship between the ultimate side shear resistance and Equation (5-2) 112

5-9 Effect of rock mass modulus on k 113

5-10 Effect of rock cohesion, Cr on k 113

5-11 Friction angle Φ vs k 114

5-12 Effect of drilled shaft geometry on τult 114

5-13 Effect of drilled shaft shear modulus, Gs on τult 115

5-14 Comparison of FEM predictions and empirical predictions for k value 117

5-15 Idealized surface roughness model (After Brady, 2004) 119

6-1 3D Model for drilled shaft socketed into rock 128

6-2 FE meshes of a drilled shaft-rock system 128

6-3 The forward movement of rock mass along the joint 129

6-4 Locus of maximum shear at failure load 129

6-5 Proposed curved wedge model 132

6-6 Straight wedge model 133

6-7 Sensitivity analysis of CF (Stage I) 137

6-8 Design charts to estimate CF for the effects of β and Ф 137

6-9 Design charts to estimate CF for the effects of Cr, Cjoint, and H/D 138

6-11 Comparison of the predicted CF with CF obtained from the FEM 139

6-12 FE meshes of a drilled shaft-rock system 141

6-13 Normal stress distribution at the load direction 141

6-14 Shear distribution on the shaft-rock interface 142

6-15 Suggested stress distribution at failure at great depth 142

6-16 Major and minor stresses on the sample 145

6-17 Stress state at great depth 146

6-18 Comparison of the proposed method and Yang’s method for estimating Pu 148

6-19 Ultimate lateral resistance calculated for two different β 148

6-20 Ultimate lateral resistance calculated for two different E/E’ ratio 149

7-1 p-y curves for case No 1 158

7-2 Effect of β on p-y curves at shallow depths 158

7-3 Effect of β on p-y curves at great depths 159

7-4 Effect of E/E’ on p-y curves at shallow depths 159

7-5 Effect of E/E’ on p-y curves at great depths 160

7-6 Load deflection curve for different β 160

7-7 Load deflection curve for different E/E’ ratios 161

7-8 Predicted moment profile for different β 161

7-9 Predicted moment profile for different E/E’ ratios 162

7-10 Comparison between the predicted and measured load deflection curve 163

7-11 Comparison between the predicted and measured a moment profile 163

7-12 Illustrative Example profile 165

7-13 p-y curves for the hypothetical case 166

7-14 Load deflection curve for the jointed rock sockted drilled shaft 166

8-1 Test Site in JEF-152 172

8-2 Pressuremeter Test at JEF-152 172

8-3 Lateral Load Test at JEF 152 174

8-4 Test set-up of JEF-152 lateral load test 175

8-5 Measured load-deflection curves of JEF-152 test for shaft #1 177

8-6 Measured load-deflection curves of JEF-152 test for shaft #2 177

8-7 Deflection-depth profiles of drilled shaft #1 and shaft #2 at JEF-152 test 178

8-8 Tension and Compression strain profiles of test shaft #1 of JEF-152 test 178

8-9 Test Drilled shaft at Warren-48 181

8-10 Lateral Load Test at Warren-48 182

8-11 Test set-up of War 48 lateral load test 182

8-12 Measured load-deflection curves of War 48 test for shaft #29 183

8-13 Measured load-deflection curves of War 48 test for shaft #31 184

8-14 Deflection-depth profiles of drilled shaft #29 and 31 at War 48 test 184

8-15 Tension and compression strain profile of test shaft #29 of War 48 test 185

8-16 Tension and compression strain profile of test shaft #31of War 48 test 185

8-17 3-D FEM model 188

8-18 Effects of Shaft and Soils Parameters on Ki 192

8-19 Ultimate resistances vs depth 193

8-20 Predicted and Measured Load Deflection Curves of Ohio JEF-152 Test 200

8-21 Predicted and measured deflection vs depth curves of Ohio JEF-152 Test 200

8-22 Predicted and measured load deflection of Ohio WAR-48 Test 201

8-23 Predicted and measured deflection vs depth curves of Ohio WAR-48 Test 201

8-24 Soil Profile and Shaft Dimension at Ohio LOR-6 Test Site 202

8-25 Comparison of Predicted and Measured Load-Deflections of Ohio LOR-6 203

8-26 Comparison of Predicted and Measured Deflections profile of LOR-6 203

8-27 Soil Profile and pile detail at Salt Lake International Airport Test 204

8-28 Predicted and Measured Load-Deflection Curves of Salt Lake site 205

8-29 Soil Profile and Shaft Dimension at CUY-90 Test Site 206

8-30 Predicted and Measured Load-Deflection Curve of Ohio CUY-90 Test 207

8-31 Predicted and Measured Deflections vs Depth of Ohio CUY-90 Test 207

8-32 Soil Profile and Shaft Dimension at Colorado I-225 clay site 208

8-33 Predicted and Measured Load-Deflection Curves of CDOT Clay Site 209

Structures for which the rock socketed shafts are attractive foundation systems include high rise buildings, retaining walls, and bridges Foundations supporting such structures may be subjected to significant lateral loads resulting from wind and seismic forces, flowing water, ice, waves, earth pressures, groundwater pressures, and traffic The understanding of the response of these laterally loaded drilled shafts has therefore become a major concern facing the designers

One of the most widely accepted methods for analyzing the response of laterally

loaded drilled shafts is the Winkler spring method, widely known as p-y curves method

This method is based on the numerical solution of a beam-on-elastic foundation, where the structural behaviour of a drilled shaft is modelled as a beam and the soil-shaft interaction is represented by discrete, non-linear springs characterized by p-y curves as shown in Figure 1-1 It is essential that accurate representation of p-y curves be carried out in order to ensure the accuracy of the predicted shaft deflections and shaft internal stresses

Figure 1-1 Drilled shaft and soil models of p-y analysis

In previous attempts to formulate p-y curves for rock (e.g Reese 1997; Gabr 1993; and Yang 2006), the rock mass in generally was treated as an isotropic medium However, most rocks exhibit direction-dependent stress-strain and strength properties due to the presence of bedding planes and the preferred orientation of mineral grains Therefore, it

is very important to identify the lateral load direction in relation to the dominant planes of anisotropy in rock mass For example, the lateral capacity of a foundation loaded

y p

y p

y p

y y

z

obliquely to the bedding of a rock mass may be less than one half of the lateral capacity when the load is applied perpendicular to or parallel to the bedding plane direction (Goodman, 1989) Thus, it is reasonable to state that the method that takes into account the effect of the bedding orientation on the p-y curves for the laterally loaded drilled shafts would give more reliable analysis results than those p-y curves that ignore the influence of the bedding plane directions

Anisotropy is very common in many rocks even when there are no distinctive discontinuous structures (e.g., joints and beddings) This is because of the preferred orientation of mineral grains or the directional stress history Foliation and schistosity make schists, slates, and many other metamorphic rocks highly directional in their deformability, strength, and other properties Bedding makes shales, thin-bedded sandstone and limestone and other common sedimentary rocks highly anisotropic (Goodman, 1989)

It should be noted that in a recent review by Turner, et al (2006), they stated that characterizing the nature of the rock mass and determining its properties becomes one of the main challenges faced by foundation designers because of the rock anisotropy, especially when considering the laterally loaded rock-socketed drilled shafts Weathered rock, weak rock, soft rock, and fractured rock are some terminology used by many researchers to describe the anisotropic rock However, all these rocks could be characterized as anisotropic rock To characterize the rock properties, including the effects of joints, there are different rock mass classifications in use: Rock Mass Quality

(RMR) system of the Council for Scientific and Industrial Research, South Africa (Bieniawski, 1976 and 1989), and Geological Strength Index (GSI) system (Hoek, 1994) All these classification systems were developed initially for tunnel or dam applications and later adopted for other engineering applications, such as slope and foundation However, using these classification systems for the foundation engineering is still not well established In particular, one needs to be cognizant about the fact that solely relying

on these rock classification systems and the related empirical correlation equations can lead to erroneous designs which in term usually results in excessive socket length requirements

Another source of difficulties in making predictions of the engineering responses of rocks and rock mass comes largely from their discontinuous and variable nature In fact, rock is distinguished from other engineering materials by the presence of inherent discontinuities, which may control its mechanical behavior Discontinuities may influence the engineering response of rock masses in a variety of ways For example, the provision of planes of low shear strength along which slip might occur, reducing the overall shear and tensile strengths of the rock masses also, the presence of joints or discontinuities can introduce a wide range of potential failure mechanisms (such as unraveling, toppling, slip or the gravity fall of blocks or wedges)

In an effort to study the behavior of rock anisotropy, Hawk and Ko (1980) examined the orthotropic nature of two shales and concluded that the properties of both shales can

be represented well by a transversely isotropic model Sargand and Hazen (1987)

isotropy is an appropriate model to simulate the stress-strain relations of these shales Since most of the bedding and layering are parallel to each other in shales, and for the reason of adopting the simplest form of anisotropy, this research dissertation work will also adopt the transverse isotropy as a general framework to describe the deformability and strength of rock mass in developing pertinent p-y curves for rock

Transverse isotropy refers to the materials that exhibit isotropic properties in a plane of transversely isotropy, and different properties in the direction normal to this plane For a rock that is transversely isotropic, only five independent elastic constants are needed to describe its elastic behavior Throughout this dissertation, these elastic constants are denoted as E, E’, ν, ν’, and G’, with the following definitions: E and ν are Young’s modulus and Poisson’s ratio in the plane of transversely isotropy, and E’, G’, and ν’ are Young’s, shear modulus, and Poisson’s ratio in the perpendicular plane to the plane of transverse isotropy

It is shown from the literature that estimating the strength and deformation properties

of the transversely isotropic rock is well established; many failure criteria together with the laboratory testing equipment are available Based on this, characterizing the elastic deformability of rock mass using the five transversely isotopic elastic constants (E, E’, ν,

ν, G’) would be more accurate and reliable than using the single parameter (deformation modulus of rock mass, Em) estimated using one of the aforementioned rock mass classification systems

Another type of geomaterial that is not investigated thoroughly as a media where the

wide array of properties with characteristics ranging from stiff or hard soil to soft weathered rock, including shale, siltstone, claystone, and some sandstones

In the last 10 years, many interim p-y criteria for weathered rock were proposed (e.g Carter and Kulhawy 1992; Reese 1997; Gabr 2002; and Yang 2006) Reese et al (1997) proposed a p-y curve composed of a linear line for the elastic response, a parabolic curve

as a transition, and a horizontal line with p equal to the ultimate resistance of rock Gabr

et al (2002) proposed a hyperbolic p-y criterion for weak rock based on field tests on small diameter drilled shafts socketed in soft to medium hard siltstone and sandstone More recently, Yang (2006) proposed a hyperbolic p-y criterion for weak rock based on two full-scale lateral load tests together with theoretical derivations and FE analysis

A source of uncertainty in all of the proposed p-y criteria derives from the choice of method for selecting rock mass modulus when more than one options is available For example, using the pressuremeter and GSI data reported by Gabr et al (2002), significantly different values of modulus can be obtained for the same rock formation In some cases, the measured shaft load-displacement response (from load testing) shows better agreement with p-y curves developed from PMT modulus, whereas in other cases the load test results show better agreement with p-y curves developed from GSI-derived modulus Proper selection of rock mass modulus for generating the p-y curves that were based on single rock mass modulus is one of the challenges for design of rock-socketed shafts Both the Reese (1997) criterion and the hyperbolic criteria require rock mass

modulus to determine the slope of p-y curves

Although, it has been shown by Vu (2006) that the interim p-y criterion proposed by Yang (2006) tends to be the most accurate p-y crterion in predicting the behaviour of the laterally loaded drilled shaft socketed into weak rock, non of the aforementioned p-y criteria could predict the behavior of laterally loaded drilled shaft socketed into IGM Also, the effect of discontinuities was not taken into account thoroughly in these existing p-y criteria, which were derived either semi-empirically or based on the assumption that the rock was an elastic isotropic continuum

Based on a study conducted by Yang (2006) who investigated different mathematical representation techniques for field load test derived p-y curves, it was concluded that hyperbolic mathematical modeling can provide the best fit to the data set Therefore, a hyperbolic equation will be adopted in this study to formulate pertinent p-y curve criterion for rock with transversely isotropic behavior Two parameters are required to characterize a hyperbola: the initial tangent slope and the asymptote For the proposed hyperbolic p-y model, these two parameters correspond to the subgrade modulus (Ki) and the ultimate resistance (pu) The hyperbolic p-y relationship is then given as

The review stated in this section has provided the necessary impetus to conduct this research; namely, to develop a more rational design approach for laterally loaded drilled shafts in rock A new p-y criterion will be developed to take into account the effects of rock anisotropy on the response of laterally loaded drilled shafts

1.2 Objectives

The objectives of this research are as follows

ƒ Develop a p-y criterion for cohesive intermediate geomaterials using hyperbolic mathematical formulation

ƒ Develop an equivalent transversely isotropic homogeneous model to characterize the stiffness of jointed rock masses with parallel discontinuities

ƒ Develop a method for determination of initial modulus of subgrade reaction of a laterally loaded drilled shaft socketed into transversely isotropic rock

ƒ Investigate through FE simulation techniques the mechanisms of the mobilization of side shear resistance of a rock socketed drilled shaft to develop an empirical solution

so that it can be used to estimate the ultimate side shear resistance

ƒ Develop a method to estimate the ultimate lateral resistance of transversely isotropic rock and jointed rock due to the lateral deflection of a drilled shaft

ƒ Develop a p-y criterion that can be used to analyze the response of drilled shaft socketed into transversely isotropic rock or jointed rock

ƒ Identify the appropriate field or laboratory test methods for determining the transversely isotropic rock properties used in the developed p-y criterion Necessary correlation relations between these properties will also be investigated

ƒ Perform sensitivity and parametric analysis to shed insight on the effects of the rock anisotropy on the predicted drilled shaft behaviour under the lateral loads

ƒ Perform full-scale field lateral load tests on fully instrumented drilled shafts socketed into cohesive IGM to obtain reliable and comprehensive field test data for validating the p-y criterion

1.3 Work Plan

The work involved in this study mainly consists of two parts: one is the theoretical work to develop p-y criteria for cohesive intermediate geomaterial and for the rock mass that can be characterized as transversely isotropic; the other one is to evaluate the developed p-y criteria for rock based on one full-scale field lateral load test results Design examples of the developed p-y criterion will be presented to demonstrate the application of the p-y criterion for the laterally loaded drilled shafts in rock Specifically, the tasks to be carried out in this research are outlined below and depicted in Figure 1-2

Two parameters are needed to construct a hyperbolic p-y curve; the initial slope, Ki

and the ultimate rock resistance, Pu The 3-D FE parametric study results of a laterally loaded drilled shaft socketed in a transversely isotropic continuum are employed to develop a series of design charts for estimating Ki as a function of the transversely

isotropic elastic constants The same methodology is used to develop an empirical solution for Ki for the intermediate geomaterial

A simple practical method to characterize the stiffness of jointed rock masses with parallel discontinuities is proposed by developing a homogeneous transversely isotropic model to replace the jointed rock The equivalent elastic parameters for this model as a function of the properties of intact rock and joint are derived based on 3D FE parametric study on a rock block, where the effects of the joint spacing, joint thickness, and the Poisson’s effect of the joints filling are considered in the derivations

The determination of ultimate rock resistance involves performing a parametric study

on 3-D FE models of a laterally drilled shaft socketed into jointed rock to identify the possible failure modes of rocks The results of this study in conjunction with the companion theoretical derivations and the relevant rock strength criteria are utilized to derive the semi-analytical equations to estimate the ultimate rock resistance per unit shaft length, pu for the transversely isotropic rock

The ultimate side shear resistance between rock and shaft is an important parameter in determining the ultimate lateral rock resistance Therefore, a comprehensive FE simulation study is undertaken to study the factors affecting this related mobilization mechanisms and to develop a theoretical solution for predicting the ultimate shaft resistance

An extensive literature review to identify the most appropriate field and laboratory test methods for determining the transversely isotropic rock properties and to enhance and

simplify characterization procedures for the transversely isotropic rock mass is conducted from which useful empirical correlations are developed for the interrelationship between the transversely isotropic elastic constants

Finally, based on the ultimate rock reaction and initial slope of p-y curve, a hyperbolic p-y criterion for cohesive IGM and the transversely isotropic rock are proposed Two field lateral load test results are used to facilitate the development and validation of the p-

y criterion for cohesive IGM

Figure 1-2 The flow chart of the works

Anisotropic Rock

Transversely

Isotropic Rock

Jointed Rock

Cohesive IGM

Laboratory and

In-situ Tests EquivalentModel

Transversely Isotropic Elastic

Constants (E, E’, ν, ν’, G’)

Strength,

PL

Side Resistance, τult

Failure Mode

Ultimate Resistance, pu

Laboratory and In-situ Tests, Em

Load Test Data

Pu by Matlock (1970) Validation

Comparison

Verification

1.4 Dissertation Outlines

Chapter II provides review of the work done by previous researchers on the subject relevant to p-y method of analysis for the laterally loaded drilled shafts in both cohesive IGM and rock mass Both the practical and theoretical implications of this review have provided the necessary impetus to the current research work in the development of pertinent p-y criterion for cohesive IGM and for the rock mass exhibiting transversely isotropic behavior

Chapter III presents the 3D FE modeling techniques and results using the ANSYS computer program Based on the FE simulation results and comprehensive statistical regression analyses, a methodology for estimating the initial modulus of subgrade reaction of a laterally loaded drilled shaft socketed into transversely isotropic rock is derived

Chapter IV presents the 3D FE modeling performed to develop an equivalent transversely isotropic homogeneous model to describe the stress-strain behavior of a rock mass with parallel joints

Chapter V presents a method for estimating the ultimate side shear resistance based on the results of a series of FE simulations The FE simulations have included a systematic parametric study of the effects of various influencing factors on the ultimate side shear resistance between the rock and drilled shaft, including the interface strength parameters, the modulus of the drilled shaft and rock mass, and the drilled shaft geometry

Chapter VI presents the equations for estimating the ultimate lateral resistance in rock The formulation for the predictive equations for the ultimate lateral resistance in rock was based on the theoretical mechanics using the limit equilibrium method and the results of a series of 3-D FE model simulations of a drilled shaft socketed into jointed rock The predictive equations are applied to both shallow and at-depth conditions

Chapter VII presents a hyperbolic p-y criterion for transversely isotropic rock The evaluation of this criterion is also presented in this chapter

Chapter VIII presents a unified p-y criterion for cohesive soils and cohesive IGM using the hyperbolic mathematical formulation Validation of the proposed p-y curve is also presented in this chapter by comparing the predictions with the two full scale lateral load test results

Chapter IX presents summary of the work done, conclusions, and recommendations for future research

CHAPTER II

LITERATURE REVIEW

The problem of the laterally loaded drilled shaft was originally of particular interest in the offshore industry Lateral loads from wind and waves are frequently the most critical factor in the design of such structures Solutions of the general problem also apply to a variety of onshore cases including drilled shaft supported earthquake resistance structures, power poles, and drilled shaft-supported structures which may be subjected to lateral blast forces or wind forces

To date, there are few published analysis methods for the lateral response of socketed drilled shafts It has been a customary practice to adopt the p-y analysis with p-y criterion developed for soils to solve the problem of rock-socketed drilled shafts (Gabr, 1993) Currently, two categories of analysis methods for laterally loaded rock-socketed drilled shafts have been developed One category treats rock as a continuum mass (Carter and Kulhawy 1992; and Zhang et al 2000), the other one discretizes the rock mass into a set of non-linear springs (Reese 1997; Gabr et al 2002; and Yang 2006)

rock-2.1 Analysis Methods of Laterally Loaded Rock-Socketed Drilled Shafts

Several analytical methods have been proposed that attempt to model laterally loaded

that influence lateral soil drilled shaft interaction These approaches fall into two general categories: (1) continuum methods (Carter and Kulhawy 1992; and Zhang et al 2000) and (2) subgrade reaction approach (Reese 1997; and Gabr et al 2002; Yang et al 2006) The latter approach is the one adopted in this study, thus, a detailed literature review is performed on this method

2.1.1 Elastic continuum methods

Continuum approaches treat the soil or rock as a semi-infinite elastic continuum and the deep foundation as an elastic inclusion This approach has been extended to rock socketed shafts and to incorporate elasto-plastic response of the soil or rock mass

The elastic continuum approach for laterally loaded deep foundations was developed

by Poulos (1971), initially for analysis of a single pile under lateral and moment loading

at the pile head The numerical solution is based on the boundary element method, with the pile modeled as a thin elastic strip and the soil modeled as a homogeneous, isotropic elastic material

The elastic continuum approach was further developed by Randolph (1981) through use of the FE method (FEM) Solutions presented by Randolph cover a wide range of conditions for flexible drilled shafts and the results are presented in the form of charts as well as convenient closed-form solutions for a limited range of parameters The solutions

do not adequately cover the full range of parameters applicable to rock socketed shafts used in practice Extension of this approach by Carter and Kulhawy (1992) to rigid shafts and shafts of intermediate flexibility has led to practical analytical tools based on the

continuum approach Sun (1994) applied elastic continuum theory to deep foundations using variational calculus to obtain the governing differential equations of the soil and drilled shaft system, based on the Vlasov model for a beam on elastic foundation This approach was extended to rock-socketed shafts by Zhang et al (2000)

2.1.2 Winkler Method (Subgrade reaction approach) and P-Y method

The Winkler method, or sometimes known as the subgrade reaction method, currently appears to be the most widely used in a design of laterally loaded drilled shafts It is based on modeling the shaft as a beam on elastic foundation

One of the great advantages of this method over the elastic continuum method is that the idea is easy to program in the finite difference or FE methods and that the soil nonlinearity and multiple soil layers can be easily taken into account The concept can be easily implemented in dynamic analysis In addition, the computational cost is significantly less than the FE method However, the obvious disadvantage of this method

is the lack of continuity; real soil is at least to some extent continuous

The term of subgrade reaction indicates the pressure, P, per unit area of the surface of the contact between a loaded beam or slab and the subgrade on which it rests and on to which it transfers the loads The coefficient of subgrade reaction, k, is the ratio between the soil pressure, P, at any given point of the surface of contact and the displacement, y, produced by the load application at that point:

y

P

To implement this concept for a laterally loaded drilled shaft, Equation (2-1) has been modified frequently (e.g Reese and Matlock, 1956) as:

With the subgrade reaction concept, the lateral drilled shaft response can be obtained

by solving the forth order differential equation as:

0Kydz

where Ep is the modulus of elasticity of the drilled shaft, Ip is the moment of inertia of

the drilled shaft, and z is depth Solutions of Equation (2-3) can be obtained either

analytically or numerically

The aforementioned solution based on subgrade reaction theory is valid only for a case

of linear soil properties In reality, the relationship between soil pressure per unit drilled

shaft length p and deflection y is nonlinear Taking the nonlinearity of soil into account,

the linear soil springs are replaced with a series of nonlinear soil springs, which represent the soil resistance-deflection curve so called, “p-y” curve The p-y curves of the soil have been developed based on the back analysis of the full scale lateral drilled shaft load test

Several researchers have proposed methods to construct p-y curves for various soil

extended to the analysis of single rock-socketed drilled shaft under lateral loading by Reese (1997) An interim p-y criterion for weak rock was proposed Thereafter, Gabr et

al (2002) proposed a p-y criterion for weak rock based on their field test data Recently Yang (2006) proposed a hyperbolic p-y criterion The following sections present the brief

description of each p-y curves currently available in the industry

2.1.2.1 Reese (1997)

Reese (1997), based on two load tests, proposed the most widely used method to construct p-y curves for “weak” rock The ultimate resistance Pu for weak rock was calculated as follows based on limit equilibrium as a function of depth below ground surface:

) D

z 4 1 1 (

The slope of initial portion of p-y curves was given by

where Kir = initial tangent to p-y curve; Em = deformation modulus of rock masses, which may be obtained from a pressuremeter or dilatometer test; and kir = dimensionless constant

Equation (2-7) through (2-10) describe the interim p-y criterion for the first, second, and third segment, respectively

25 0

ir 25 0 rm

u A

K)y

be used to construct a p-y curve according to Gabr et al (2002)

Step 1: Calculation of Coefficient of Subgrade Reaction

The coefficient of subgrade reaction can be calculated using Equation (2-36) proposed

by (Vesic, 1961)

Step 2: Calculation of Flexibility Factor

A flexibility factor, KR, is computed as follows (Poulos and Davis, 1972):

where, L is the embedment length of shaft

Step 3: Calculation of Point of Rotation

The following equation is used to define the turning point as a function of the embedded shaft length:

Step 6: Calculation of Ultimate Resistance of Rock Mass Pu

Equation (2-20) proposed by Zhang et al (2000) was employed to calculate the ultimate resistance of rock