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Hydraulic gradient similitude method for geotechnical modelling tests with emphasis on laterally loaded… Yan, Li 1990

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H Y D R A U L I C G R A D I E N T SIMILITUDE M E T H O D FOR G E O T E C H N I C A L M O D E L L I N G TESTS W I T H EMPHASIS ON L A T E R A L L Y L O A D E D PILES by ' L i Yan B. Eng. Sc. Dalian Institute of Technology, China M . A . Sc. The University of British Columbia A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S C I V I L E N G I N E E R I N G We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A September 1990 © L i Yan, 1990 In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make ityfreely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Civil Engineering The University of British Columbia 2324 Main MaU Vancouver, Canada V 6 T 1W5 Date: Abstract A study has been undertaken to evaluate and apply the hydraulic gradient simili-tude method to geotechnical model testings. This method employs a high hydraulic gradient across granular soils to effectively increase self-weight stresses in the model. Testing principle and procedures are presented, and the factors affecting test results discussed. A n apparatus ( U B C - H G S T ) using this testing principle has been devel-oped. Three applications are presented in which the hydraulic gradient similitude method is evaluated, and the existing concepts and methods of analysis for the prob-lems studied are examined. In the footing tests, it is found that the scaling laws implied in the hydraulic gra-dient modelling test are satisfied, and are similar to those of the centrifuge modelling technique. Load-settlement curves are found to be similar to those in centrifuge tests. The test results illustrate the importance of the stress level in the load-settlement re-sponses. Terzaghi's bearing capacity formula is compared with the observed bearing capacities under different stress levels. It is found that due to the stress level ef-fects, the bearing capacity coefficient, Ny, decreases linearly with footing width on the log-log scale which is in accordance with other model study and analytical results. In the downhole and crosshole seismic tests, results are used to evaluate the empir-ical equations that relate shear wave velocity and soil stresses in terms of field stress condition. It is found that although the various equations can predict the insitu shear wave velocity profile reasonably well, only the equation which is based on the signifi-cant stresses in the wave propagation and particle motion directions can predict the variation of velocity ratio between the downhole and SH crosshole tests. It is also found that the stress ratio has some effects on the downhole (or S V crosshole) tests, but not on the SH crosshole tests. This indicates that only the stress ratio in the plane of wave propagation is important to the shear wave velocity. Comparison be-tween the downhole and SH crosshole tests shows that the structure anisotropy was about 10% in terms of shear wave velocity. Prediction of KD values using shear wave measurement is evaluated, and its practical difficulties are addressed. In the laterally loaded pile tests, the pile response to static and cyclic loadings at various stress levels controlled by the hydraulic gradients is examined in terms of pile head response, pile bending moment and soil-pile interaction P-y curves. For the static loading, pile head response and bending moment are found to be significantly affected by the soil-pile relative stiffness, pile diameter, loading condition and pile head fixity. However, little effects of loading eccentricity and pile head fixity are found on the P-y curves. While pile diameter is found to have effects on the P-y curves at large pile deflection, its effects are negligible at small deflecton range. The effects of relative soil-pile stiffness on the P-y curves due to stress levels can be normalized by the soil modulus and pile diameter for the curves below 1 pile diameter, as computed by the plane strain finite element analysis. Two methods of generating P-y curves are suggested, and found to give satisfactory results as compared with the test data and the prediction given by A P I code (1987). For cyclic loading, different pile responses are observed in "one-way" as compared to "two-way" cyclic loading. The cyclic P-y curves are derived, and found to be highly nonlinear and hysteretic, and change with number of loading cycles. From these studies, it is shown that the hydraulic gradient similitude method provides a simple and inexpensive means of model testing for many geotechnical engineering problems and adds to the data base from which methods of analysis can be evaluated. n i Table of Contents A b s t r a c t i i Lis t of Tables ix L i s t of F i g u r e s x ix A c k n o w l e d g e m e n t s x x 1 I n t r o d u c t i o n 1 1.1 Introduction 1 1.2 Objectives and Scope of Thesis 3 1.3 Organization of Thesis 4 2 H y d r a u l i c G r a d i e n t S i m i l i t u d e M e t h o d 6 2.1 Introduction 6 2.2 Testing Principle and Scaling Laws 6 2.3 Comparison with Centrifuge Testing 10 2.4 Factors affecting Hydraulic Gradient Similitude Tests in Sands . . . . 13 3 P r e l i m i n a r y A p p l i c a t i o n - F o o t i n g Test 17 3.1 Introduction 17 3.2 Testing Program 18 3.2.1 Test Equipment 18 3.2.2 Model Soils 20 3.2.3 Soil Preparation and Testing Procedures 24 iv 3.2.4 Sample Uniformity and Test Repeatability 25 3.2.5 Experimental Program 26 3.3 Results and Discussion 32 3.3.1 Load-Settlement Curves 32 3.3.2 Ultimate Bearing Pressure 35 3.3.3 Evaluation of Scaling Law - Modelling of Models 44 3.4 Summary and Conclusion 45 4 H y d r a u l i c G r a d i e n t S i m i l i t u d e T e s t i n g D e v i c e 49 4.1 Introduction 49 4.2 General Description 50 4.3 Sand Container and Air Pressure Chamber 53 4.4 Water Supply and Circulation System 57 4.5 Pile Head Loading and Measuring System 57 4.6 Instrumentation and Data Acquisition . 64 5 A S i m u l a t i o n of D o w n h o l e a n d C r o s s h o l e Seismic Tests i n H G S T D e v i c e 70 5.1 Introduction 70 5.2 Review of Existing Empirical Equations 72 5.2.1 Stress Level Effects 72 5.2.2 Stress Ratio Effects 74 5.3 Testing Equipment and Procedure 76 5.3.1 Bender Elements 76 5.3.2 Simulation of Downhole and Crosshole Tests 79 5.3.3 Sand Tested and Sample Preparation 81 5.3.4 Testing Series and Procedure 85 5.4 Results and Discussion 87 v 5.4.1 Horizontal Stresses or Ka values 87 5.4.2 Typical Results of Shear Wave Velocity Measurement 91 5.4.3 Downhole and SH-Crosshole Shear Waves along K0 Paths . . . 97 5.4.4 Application of Shear Wave measurement to Estimate Insitu Ka Values 110 5.5 Summary and Conclusion 114 6 R e v i e w of P i l e R e s p o n s e to L a t e r a l L o a d s at P i l e H e a d 117 6.1 Introduction 117 6.2 Theoretical Studies 118 6.2.1 Static Response 118 6.2.2 Cyclic Response 138 6.3 Experimental Studies - Static and Cyclic Loading 139 6.3.1 Field Testing 139 6.3.2 Model Testing 142 6.4 Summary 148 7 A M o d e l S t u d y of P i l e R e s p o n s e to L a t e r a l L o a d s at P i l e H e a d 149 7.1 Introduction 149 7.2 Test Procedure and Experimental Program 150 .7.2.1 Procedure 150 7.2.2 Test Repeatability 153 7.2.3 Data Reduction 154 7.2.4 Experimental Program 158 7.3 Test Results and Discussion 166 7.3.1 Scaling Law Evaluation 166 7.3.2 Pile Response to Static Loading 170 7.3.2.1 Effects of Relative Soil-pile Stiffness 170 vi 7.3.2.2 Effects of Applied Load to Moment Ratio 189 7.3.2.3 Effects of Pile Head Fixity 195 7.3.3 Pile Response to Cyclic Loading 202 7.3.3.1 Two-way Cyclic Loading 204 7.3.3.2 One-way Cyclic Loading 219 7.3.3.3 Effects of Cyclic Loading History 234 7.4 Summary and Conclusion 234 8 P r e d i c t i o n of P i l e R e s p o n s e to L a t e r a l L o a d s at P i l e H e a d 239 8.1 Introduction 239 8.2 Generation of P-y curves 239 8.2.1 A P I Code (1987) 240 8.2.2 A Modified version of A P I Code 241 8.2.3 P-y Curves from Plane Strain F E M Analysis 241 8.3 Evaluation of P-y Curves 245 8.4 Prediction of Pile Response 248 8.5 Summary and Conclusion 258 9 S u m m a r y a n d C o n c l u s i o n s 261 A p p e n d i c e s 269 A Effects of C o m p r e s s i b l e F l u i d F l o w - A i r Seepage C a s e 269 B Effects of P o r o u s Stone o n F o o t i n g Pressure a n d Soil Stress C o n d i -t ion 271 B . l Seepage Force Correction to Footing Pressure 271 B.2 Soil Stress Condition Underneath the Footing 280 C Stress A n a l y s i s a n d C a l i b r a t i o n of T o t a l Stress M e a s u r e m e n t 283 vii C l Stress Analysis 283 C. 2 Stress Transducer Calibration 286 D T h e o r e t i c a l C o n s i d e r a t i o n of E l i m i n a t i n g the N e a r F i e l d W a v e E f -fects a n d O b t a i n i n g P u r e Shear W a v e R e c o r d 290 D . l Near Field Wave Effects 290 D.2 Obtaining Pure Shear Wave Motion 293 E A i r Pressure C o n t r o l l e d S y s t e m for L a t e r a l l y L o a d e d P i l e Tests 296 F P r e d i c t i o n of P i l e R e s p o n s e u n d e r O t h e r T e s t i n g Cases 299 B i b l i o g r a p h y 313 vui List of Tables 2.1 Scaling Relations for Centrifuge and Hydraulic Gradient Tests . . . . 9 2.2 Comparison between Centrifuge and Hydraulic Gradient Modelling Tests 12 3.1 Hyperbolic Soil Parameters From Drained Compression Triaxial Tests 23 3.2 Sample Uniformity after Sedimentation, Void Ratio V at Different Locations 26 3.3 Sample Uniformity after Densification, Void Ratio 'e' at Different Lo-cations 26 3.4 A Summary of Model Footing Tests 32 3.5 Bearing Capacity for Dense Sand from H . G . Tests 38 3.6 Comparison of Bearing Capacity at the Same Prototype Scale, Dense Sand 45 4.1 A Comparison of Box Size with Some Centrifuge Boxes 54 4.2 Physical Properties of Model Piles 66 5.1 Suggested Values and Equations for A and F(e) 73 6.1 E„ for Cohesionless Soils in Elastic continuum Approach 120 6.2 rihi values for submerged soil suggested by Reese et al 127 6.4 A Summary of Field Pile Load Tests on Sand 143 6.5 Summary of Some Model Tests of Lateral Pile Load Test on Sand . . 144 7.1 Summary of Main Testing Program on Laterally loaded Pile 164 7.2 Scaling Relations for H G S T test on Laterally Loaded Piles 166 ix List of Figures 2.1 A Soil Element in The Hydraulic Gradient Similitude Tests 9 2.2 Schematic of Centrifuge Testing Set-up, after Schofield and Steedman (1988) 11 2.3 Example of Compressible Flow in Soil Sample - Air Seepage Case . . 15 3.1 Schematic of Hydraulic Gradient Footing Test Device 19 3.2 Grain Size Distribution of Fine Ottawa Sand 21 3.3 Variation of Permeabihty vs. Void Ratio 22 3.4 Comparison of Consolidation behaviour from Two Sample Preparation Methods 27 3.5 Comparison of Stress-strain behaviour at Loose Sand from Two Sample Preparation Methods, DT = 33% 28 3.6 Comparison of Volumetric behaviour at Loose Sand from Two Sample Preparation Methods, DT - 33% 28 3.7 Comparison of Stress-strain behaviour at Dense Sand from Two Sample Preparation Methods, DT = 75% 29 3.8 Comparison of Volumetric behaviour at Dense Sand from Two Sample Preparation Methods, DT - 75% 29 3.9 Typical Example of Repeatability for Loose Sand at N=40, Bm = 1.5cm 30 3.10 Typical Example of Repeatability for Dense Sand at N=60, Bm = 1.5cm 31 3.11 Observed Settlement Curves for Loose Sand Under Different N (Bm=1.5cm, A. =33%) 33 x 3.12 Observed Settlement Curves for Dense Sand Under Different N (5 m =1.5cm, A.=75%) 34 3.13 Settlement Curves observed from Centrifuge Tests (after Ovesen, 1975) 36 3.14 Illustration for Determination of Ultimate Pressure for Dense Sand . 37 3.15 Observed Ultimate Pressure vs. Scale Factor - N 39 3.16 Bearing Capacity vs. Acceleration Field in Centrifuge Tests (after Ovesen, 1975) 40 3.17 Variation of Friction Angles with Confining Stress Levels 42 3.18 Prototype Footing Size Effect on iV 7 Coefficient , . 43 3.19 Evaluation of Scaling Law for Hydraulic Gradient Footing Tests on Dense Sand at Bp = 150cm 46 3.20 Evaluation of Scaling Law for Hydraulic Gradient Footing Tests on Dense Sand at Bp = 120cm 46 4.1 Schematic of U B C - H G S T Device 51 4.2 Photograph of U B C - H G S T Device 52 4.3 Side and Plan Views of Soil Container Lid 56 4.4 Water Flow System in U B C - H G S T Device 58 4.5 A Low Friction Bushing System for Lateral Loading Ram 60 4.6 Pile Head Loading Connections 62 4.7 Pile Head Deflection Measurement 63 4.8 Layout of Strain Gauges in Model Pile 65 5.1 Stress Condition For Downhole and Crosshole Tests 75 5.3 Cantilever Deformation Mode of Bender Element 78 5.4 Simulation of Downhole and Crosshole Tests in the H G S T Device . . 80 5.5 Distribution of Gmax in Dense Sand During Hydraulic Gradient Tests measured from Downhole Tests 83 xi 5.6 Crosshole Shear Wave Velocities measured under Different Crosshole Orientations 84 5.7 Setup for Measurement of Shear Wave Velocity 86 5.8 Variation of Water Pressure and Lateral Total Stress During 1-D Load-ing and Unloading Paths in H G Test 88 5.9 KQ Values during the Loading and Unloading Phases 90 5.10 Shear Wave Records at Different Depths (Loose Sand DT — 33%) . . 92 5.11 Typical Example of Shear Waves Received under Different Hydraulic Gradients 93 5.12 Polarization of the received Shear Wave Signals 95 5.13 Prediction of Shear Modulus Profile from Various Empirical Equations 96 5.14 Measured Shear Wave vs. Hydraulic Gradient Scale Factor, (at given depth, DT = 75%) 98 5.15 Loading and Unloading Effects on Downhole and Crosshole Shear Wave Velocity 99 5.16 prediction of Velocity Ratio between Downhole and Crosshole . . . . 103 5.18 Variation of Stress Ratio in Vertical Plane with Hydraulic Gradient during Loading and Unloading phases ; 107 5.19 Stress Ratio Effects on Shear Wave Velocity During KD Unloading Phasel09 5.20 Prediction of K0 from Shear Wave Velocity Ratio 112 5.21 Sensitivity Analyses of K0 vs. Parameters 'n' and ' C d / C c ' 113 6.1 Winkler Spring Approach (after Fleming et al, 1985) 123 6.2 Reese et al (1974) P-y curves 126 6.3 rthi vs. relative density, after Murchison and O'Neill (1984) 129 6.4 Factors for Pu, after Murchison and O'Neill (1984) 129 6.5 P-y curve proposed by Scott (1981) 130 6.6 P-y curves from Nonlinear Finite Element Plane Strain Model . . . . 134 xii 6.7 Normalization of P-y curves from Finite Element Analysis 134 6.8 Anisotropic Soil Stress Effects on the P-y curves, F E M studies . . . . 136 6.9 Normalization of Anisotropic Soil Stress Effects on the P-y curves, F E M studies 136 6.10 Soil Density Effects on the P-y curves, F E M studies 137 6.11 Normalization of Soil Density Effects on the P-y curves, F E M studies 137 6.12 Variation of Coefficient, a, with Relative Density 138 6.13 Prediction of the lateral load deflection behaviour of the Mustang Is-land Test using a Centrifuge, after Scott (1977) 147 7.1 Repeatability of Test Result for Free Head Loading 155 7.2 Repeatability of Test Result for Fixed Head Loading 156 7.3 Typical Example of Representing Test Data by Cubic spline - Free Head Pile (Note: Ground Surface at Elev. 315.2 mm) 159 7.4 Typical Example of Representing Test Data by Cubic spline - Fixed Head Pile (Note: Ground Surface at Elev. 315.2 mm) 160 7.5 Example of P-y curves from the cubic spline fitting technique 161 7.6 Back Prediction of Pile Response by the L A T P I L E program using the Experimental P-y curves 162 7.7 Evaluation of Scaling Law for Pile Testing - Prototype Dimension-I: 30.48 mm diam. pile, load eccen.=1.68m 167 7.8 Evaluation of Scaling Law for Pile Testing - Prototype Dimension-II: 30.48 mm diam. pile, load eccen.=2.17m . 168 7.9 Evaluation of Scaling Law for Pile Testing - Prototype Dimension-Ill: 60.96 mm diam. pile, load eccen.=3.36m 169 7.10 Responses of Projected Prototype Piles under Different Prototype Ec-centricities 171 xin 7.11 Typical Example of Pile Head Response under Different Hydraulic Gra-dients 173 7.12 Typical Example of Pile Bending Moment Distribution, (a), under different hydraulic gradient; (b). under different loading magnitude . . 175 7.13 The P-y Curves at Different Depths for a Free-head Model Pile of 6.35 mm O . D 177 7.14 The P-y Curves at Different Hydraulic Gradients, Free head Model Pile of 6.35 mm O . D . 179 7.15 Experimental P-y curves in a Logarithmic Scale 180 7.16 Normalization of the Experimental P-y Curves over the Hydraulic Gra-dient Stresses at Different Depths 182 7.17 Comparison of Plane Stress and Plane Strain F E M analyses with the Experimental P-y Curves at Shallow and Deep Locations 183 7.18 Compilation of All the Normalized P-y curves at Different Depths . . 184 7.19 Normalization of Experimental P-y Curves by Emax 185 7.20 Compilation of Experimental P-y Curves normalized by Emax at dif-ferent Depths 186 7.21 Normalized Experimental P-y Curves for Loose Sand by Emax . . . . 188 7.22 Pile Diameter Effect on P-y curves at a Prototype Depth of 190.5mm, Prototype Pile Diameters of 63.5mm, 190.5mm, respectively 190 7.23 Pile Diameter Effect on P-y curves at a Prototype Depth of 254.0mm, Prototype Pile Diameters of 63.5mm, 127.0mm, respectively 191 7.24 Pile Diameter Effect on P-y curves at a Prototype Depth of 508.0mm, Prototype Pile Diameters of 127.0mm, 254.0mm, respectively 191 7.25 Loading Eccentricity Effects on Pile Head Response 193 7.26 Applied Lateral Load vs. Maximum Pile Bending Moment under Dif-ferent Loading Eccentricities 194 xiv 7.27 Loading Eccentricity Effects on Bending Moment Distribution . . . . 194 7.28 Loading Eccentricity Effects on the P-y Curves at 1 to 2 Pile Diameter Depths 196 7.28 Loading Eccentricity Effects on the P-y Curves at 3 to 4 Pile Diameter Depths 197 7.28 Loading Eccentricity Effects on the P-y Curves at 5 Pile Diameter Depth 198 7.29 Pile Head Fixity Effects on Pile Head Deflections 199 7.30 Pile Bending Moment Distribution under Fixed Head Loading . . . . 199 7.31 A Comparison of Normalized Pile Bending Moment Distribution from Free and Fixed Head Conditions 201 7.32 Pile Head Fixity Effects on the Applied Load to the Maximum Bending Moment Relation 201 7.33 Comparison of P-y curves from Free and Fixed Pile Head Conditions 203 7.34 Time Histories of Applied Lateral Two-way Cyclic Load and Pile Head Deflection at L V D T 1 205 7.35 Normalized Pile Head Peak Deflection with Number of Loading Cycles, 48M1 Test: AT=48, £ = 6 8 m m , Load Ampl.=23(Newton) 206 7.36 Example of Drained Sand Response under Two-way Simple Shear Load-ing Condition, after Oh-Oka, 1976 206 7.37 Pile Head Load-deflection Behavior Under Two-way Cyclic Loading Condition, AT=48, £ = 6 8 m m , Load Ampl.=23(Newton) 208 7.38 Time History of Bending Moment along the Pile, 48M1 Test: N=48, £ = 6 8 m m , Loading Ampl.=23(Newton) 209 7.38 Time History of Bending Moment along the Pile, 48M1 Test: N=48, £ = 6 8 m m , Loading A m p l =23(Newton) 210 7.39 Two-way Cyclic Loading Effects on Pile Bending Moment at Low Level of Lateral Load, Load=23(Newton) 212 xv 7.40 Two-way Cyclic Loading Effects on Pile Bending Moment at High Level of Lateral Load, Load=40(Newton) 212 7.41 Pile Residual Bending Moments under Two-way Cyclic Loadings . . . 214 7.42 Cyclic P-y Curves for different Loading Cycles at 1 to 2 Pile Diameter Depths 215 7.42 Cyclic P-y Curves for different Loading Cycles at 3 to 4 Pile Diameter Depths 216 7.42 Cyclic P-y Curves for different Loading Cycles at 5 Pile Diameter Depth217 7.43 Variation of Pile Head Deflection with Time under Constant Amplitude One-way Loading 220 7.44 Variation of Pile Slope at Ground with Time under Constant Applied Bending Moment at Ground Level 221 7.45 Pile Head Response at Loading Point under Constant Amplitude One-way Lateral Load 222 7.46 Example of Soil Element Response from Drained Cyclic Triaxial Test, after Lambe and Whitman, 1975 222 7.47 Cyclic Effect on Different Pile Head Deflection Components under One-way Cyclic Loadings 223 7.48 Pile Head Peak Deflection with Number of Loading Cycles; Free Head vs. Fixed Head Piles 223 7.49 Comparison of Pile Head Deflections with Number of Cycles; the Same applied Moment but Different Loading Magnitude 226 7.50 Comparison of Pile Head Deflections with Number of Cycles; the Same Lateral Load but Different Moment at Pile Head 226 7.51 Pile Bending Moment Distribution at the Peak Lateral Load, Free head Pile, One-way Cyclic Loading 228 xvi 7.52 Pile Residual Bending Moment after Removal of Lateral Load, Free head Pile, One-way Cyclic Loading 228 7.53 Pile Bending Moment Distribution at the Peak Lateral Load, Fixed head Pile, One-way Cyclic Loading 229 7.54 Pile Residual Bending Moment after Removal of Lateral Load, Fixed head Pile, One-way Cyclic Loading 229 7.55 P-y Curves under One-way Pile Head Loading at depths of 1 to 2 pile diameters, Fixed Head Pile, N=48 E=45 Load=40(Newton) 231 7.55 P-y Curves under One-way Pile Head Loading at depths of 3 to 4 pile diameters, Fixed Head Pile, N=48 E=45 Load=40(Newton) 232 7.55 P-y Curves under One-way Pile Head Loading at depth of 5 pile diam-eters, Fixed Head Pile, N=48 E=45 Load=40(Newton) 233 7.56 Pile Head Response under a Sequence of Two-way and One-way Cyclic Loadings 235 8.1 Comparison of Subgrade Reaction Modulus, Kh, from A P I code with the maximum soil Young's modulus, Emax 242 8.2 Plane Strain Finite Element Mesh for Obtaining P-y curves 244 8.3 P-y curves obtained from 2 — D Plane Strain Finite Element Analysis using Triaxial Test Data 246 8.4 A Comparison of Normalized P-y curves from F E M and A P I code with the Test Data, Dense Sand DT = 75% 247 8.5 A Comparison of Original and Modified A P I codes 249 8.6 Prediction of Free head Pile Response at Loading Point at Different Loading Eccentricity, N=64, DT = 75% 250 8.7 Prediction of Bending Moment Distributions at different Loading Ec-centricities, Free head Pile 252 xvii 8.8 Comparison of Pile Deflection Profile Prediction using Various Meth-ods - Different Loading Eccentricities . 253 8.9 Comparison of Soil Reaction Profile Prediction using Various Methods - Different Loading Eccentricities 254 8.10 Comparison of Pile Shear Force Prediction using Various Methods -Different Loading Eccentricities 256 8.11 Comparison of the Equivalent Subgrade Reaction Modulus used in Var-ious Method - Different Loading Eccentricities 257 B . l Forces on Footing Loading System 272 B.2 Finite ELement Mesh used for Seepage Analyses 274 B.3 Flow Nets for Hydraulic Gradient Footing Tests (Loose Sand N=60) . 275 B.4 Seepage Force Correction for the Porous Footing Plate 277 B.5 Comparison of Test Data before and after Seepage Force Correction for Loose Sand 278 B.6 Comparison of Test Data before and after Seepage Force Correction for Dense Sand 279 B. 7 Footing Permeability Effect on the Vertical Strain Profile underneath the Footing 281 C l Stress Analysis on the Water Pressure Transducer 284 C. 2 Schematic of Calibration Chamber for Lateral Total Stress Transducer 288 C. 3 Calibration of Lateral Pressure Transducer 289 D. l General 3-D Waves from a Point Source 291 D . 2 F F T Analyses of Shear Wave Traces 294 E . l Air Pressure Control System for Laterally Loaded Pile Tests 297 xvm F . l Predictions of Pile Head Response and Bending Moment Distribution for a Free Head Pile at N=48 E=45mm 300 F.2 Computed Soil Reaction and Pile Deflection Profiles for a Free Head Pile at N=48, E=45mm and a load of 22.06(N) 301 F.3 Computed Shear Force on the Pile and Equivalent Subgrade Moduli used in Various Methods for a Free Head Pile at N=48, E=45mm and a load of 22.06(N) 303 F.4 Predictions of Pile Head Response and Bending Moment Distribution for a Fixed Head Pile at N=48 E=45mm 305 F.5 Computed Pile Deflection and Shear Force Profiles for a Fixed Head Pile at N=48, E=45mm and a load of 24.44(N) 306 F.6 Computed Soil Reaction and Soil Reaction Moduli for a Fixed Head Pile at N=48, E=45mm and a load of 24.44(N) 308 F.7 Predictions of Pile Head Response and Bending Moment Distribution for a Free Head Pile embedded in Loose Sand, N=48 E=48mm . . . . 309 F.8 Computed Pile Deflection and Soil Reaction Profiles for a Free Head Pile embedded in Loose Sand, N=48 E=48mm 311 F.9 Computed Shear Force and Soil Moduli used for a Free Head Pile embedded in Loose Sand, N=48 E=48mm 312 xix Acknowledgements I wish to express my great gratitude to my research supervisor, Professor Peter M . Byrne for his support, patient and invaluable guidance during all the stages of this research work. I am also deeply indebted to Professor W . D . Liam Finn for his friend-ship and encouragement, and to Professors R . G . Campanella and Y . P . Vaid for their help with the equipment and testing procedures. Technical support from the Civil Engineering Workshop is gratefully acknowledged. Thanks are also extended to my colleagues who share common interests in Soil Mechanics and Foundation Engineering, especially to Alex Sy, Pat Stewart, Ralph Kuerbis for their helps and useful discussions. Special thanks go to my wife, Chunyan, and our lovely son, Jimmy, for their sup-port and understanding which helped me endure the pressure in the H G S T research. Research and Teaching Assistantships awarded by The Department of Civil Engi-neering, and The University Graduate Fellowship awarded by The Faculty of Gradu-ate Studies are gratefully acknowledged. xx Chapter 1 Introduction 1 . 1 Introduction Model tests are used in almost all disciplines of engineering science research. In geotechnical engineering, small scale model tests are often used to study the complex nature of soil response and soil-structure interaction under a controlled condition. In the past, model tests were mostly performed under normal lg gravity stress condition. However, it is known that soil response depends upon the level of effective stress within the soil mass, especially for granular material. At different stress levels, granular material at a given density can behave in either a contractive or dilative manner. Therefore, small scale model tests in a conventional gravity field of lg often fail to reveal some important phenomena which may exist at the prototype stress level. In order to overcome this situation, it is desirable to perform a small scale test at field stress level conditions. Although the stress level in a model soil mass can be increased in conventional manner, such as surcharge, the stress gradient within the soil mass, which is important to the soil structure response, can not be correctly simulated as in the field condition. At present, one method of correctly simulating both field stress magnitude and distribution is the centrifuge technique, in which a small model scaled 1/n from the assumed prototype is tested under an 'n ' times gravity field created by centripetal acceleration. With this escalated gravity field, the soil elements at homologous points of model and prototype have the same self-weight stresses, and a simulation of prototype behaviour is then assumed from a set of scaling relations (Roscoe, 1968; Scott, 1978; Schofield, 1981). Although the principle is simple, the 1 Chapter 1. Introduction 2 use of the centrifuge testing technique to simulate the prototype behaviour involves certain difficulties in practice. Very often, a complete similitude relation and various prototype soil conditions can not be fully satisfied and simulated by the centripetal acceleration alone (Whitman and Arulanandan, 1985; Cheney, 1985; Tan and Scott, 1985). However, the main constraint to the use of centrifugal testing so far has been the high cost of equipment and testing, and the need for specially trained personnel to operate the system. For these reasons, the centrifuge technique is presently used only for some important structures, and is not generally available in conventional soil mechanics laboratories. Many model tests reported in geotechnical engineering literature are still performed under the lg gravity condition. This is not because of a lack of understanding of stress level dependency of soil behaviour, but lack of an easily accessible testing approach with which the field stress condition can be closely represented in the model. Zelikson (1969) presented a hydraulic gradient similitude method to increase the soil self-weight stresses in model tests. This method employs a high hydraulic gra-dient which causes a seepage force within the granular soil and creates a high body force, and hence high stress level and distribution approaching field conditions. As compared to the centrifuge testing technique, this method offers an easy and inexpen-sive approach to simulate the field stress condition in some model tests, and provides some technical advantages over the centrifuge in model preparation, testing monitor-ing and data acquisition. However, this method since its development has only been used in France, and has not yet been extensively tested over different geotechnical problems. Thus, it is desirable to further develop this testing method and evaluate its potential in geotechnical model testings. The primary objective of this thesis is to evaluate the hydraulic gradient similitude method and apply it to some geotechnical engineering problems. By doing so, it is hoped to spark an interest in the use of the hydraulic gradient similitude method in Chapter 1. Introduction 3 some geotechnical modelling tests. This necessitates first of all the development of testing devices and procedures based on the hydraulic gradient similitude principle. Applications to three cases of geotechnical problems are then presented which include footing foundation, downhole and crosshole seismic tests and vertical piles under lateral pile head loading. Useful results have been obtained to further the existing knowledge and analytical methods for these problems. 1.2 Objectives and Scope of Thesis The main objectives of this thesis are as follows: 1. to present and evaluate modelling tests using the hydraulic gradient simili-tude method so as to demonstrate the usefulness of this technique for different geotechnical engineering problems; 2. to develop a general testing apparatus for geotechnical modelling tests with an emphasis on pile foundations; 3. to examine the application of this method to a footing foundation on sand and to compare the results with the existing knowledge and design methods; 4. to examine the application of this method to the downhole and crosshole seismic tests so as to evaluate the dynamic shear modulus of the model soil under field stress condition, and to evaluate stress state and stress ratio effects on the dynamic shear modulus of soils, and finally 5. to examine the application of this method to pile foundations subjected to static and cyclic lateral loads at the pile head. Chapter 1. Introduction 4 Thus, the thesis mainly consists of three parts: footing tests, downhole and cross-hole seismic tests, and lateral pile load tests. Testing procedures and devices with appropriate instrumentation have been developed for these purposes. 1.3 Organization of Thesis The thesis is comprised of 9 chapters presenting the hydraulic gradient similitude principle, the hydraulic gradient similitude testing ( H G S T ) device, and three appli-cations with emphasis on pile foundation. Chapter 1 introduces the background information and scope of this research work. Chapter 2 presents the hydraulic gradient similitude method with some discussions about factors which may have effects on the modelling tests. Comparisons with the centrifuge technique are also made in some perspectives so that the usages of the hydraulic gradient similitude testing are defined. The first application of this technique is presented in Chapter 3 on the footing test as well as the new sample preparation technique developed for the hydraulic gradient similitude test. Soil parameters obtained from soil characterization tests and triaxial tests are also presented. The scaling laws for the footing tests are evaluated experimentally using the "modelling of models" technique which has been often used in the centrifuge testing. With the experience gained from the footing tests, a hydraulic gradient similitude testing device ( U B C - H G S T ) was developed at the University of British Columbia with an emphasis on simulating pile response to static and dynamic loadings, and is described in detail in Chapter 4. Chapter 5 presents the simulation of downhole and crosshole seismic tests in the newly developed hydraulic gradient similitude testing device and the evaluation of stress state and stress ratio effects on the soil shear modulus at very small strain levels. Different empirical equations from laboratory soil element tests which relate Chapter 1. Introduction 5 the maximum shear modulus of soils, Gmax and the stress state are examined against the test results at the field stress condition. The possibility of obtaining soil lateral stress or KD values from the shear wave measurement is also discussed. Chapter 6 reviews pile response to lateral loads at the pile head. Both theoretical and experimental studies are critically reviewed. From this review, it is shown that more experimental studies are needed to substantiate the current analytical methods. Chapter 7 presents a model study of pile responses to static and cyclic lateral loads at pile head using the hydraulic gradient similitude method. The scaling laws for the pile testing are evaluated experimentally using the "modelling of models" technique. The emphasis of this study is focused on examining the effects of various governing factors on soil-pile interaction P-y curves. These factors include soil stress levels, pile head loading eccentricity, pile head fixity, pile diameter, and types of cyclic loading. Results are presented in terms of pile head response, pile bending moment, and soil-pile interaction P-y curves. Chapter 8 presents numerical predictions of the observed pile response. P-y curves obtained from the experiments are compared with those specified from some empirical and theoretical methods. Based on these comparisons, two methods of constructing P-y curves in the analysis are proposed. Nonlinear numerical analyses with P-y curves specified by various methods are performed, and the results evaluated against the test data. Finally, in Chapter 9, a summary of present research and conclusions are made. Some recommendations on future research using this model testing technique are also presented. Chapter 2 Hydraulic Gradient Similitude Method 2.1 Introduction In this chapter, the testing principle and scaling laws of hydraulic gradient similitude method are described. This testing principle was first introduced by Zelikson in 1969. Since then, it has been used in model tests of anchor and some pile problems (Zelikson, 1978 and 1988a). Zelikson et al (1982), and Zelikson and Leguay (1986) have compared hydraulic gradient tests with centrifuge tests, and similar results have been observed in the cases where comparison was possible. Recently, some researchers have combined the hydraulic gradient technique in the centrifuge testing in which large hydraulic gradient was used to consolidate large clay samples before the centrifuge model testing (Nunez and Randolph, 1984; Zelikson et al, 1987). However, possible factors affecting the hydraulic gradient test results have not yet been clearly identified. In this chapter, attempts are also made to examine theoretically some affecting factors in the hydraulic gradient similitude tests in sandy materials. 2.2 Testing Principle and Scaling Laws Similar to the centrifuge modelling technique, the hydraulic gradient similitude method is just another way of increasing the self-weight stresses of granular soils in the model. The only difference is that the body force of model soils in the hydraulic gradient simil-itude testing is increased by the seepage force through the porous material rather than by the centripetal acceleration. 6 Chapter 2. Hydraulic Gradient Similitude Method 7 As shown in Figure 2.1, for a model test in which a geometrical 1/n scale of the assumed prototype is subjected to a controlled downward hydraulic gradient across the model soil, the body force on a unit volume of the soil will be increased by seepage force by an amount of i-yw. This is equivalent to increasing the unit weight of the material by ifw and the effective unit weight, 7m, of the soil is given as: 7 m = * 7 » + 7 ' (2-1) where i is the applied downward hydraulic gradient, ~fw is the unit weight of water if water is used in the test, and 7' is the submerged unit weight of soil. As compared to the assumed prototype condition, the model unit weight has been increased by a factor of N, as follows: N — ~ 7P ilw + 7' (2.2) 7P where N is defined as the hydraulic gradient scale factor. 7p is the effective unit weight of the soil in the prototype, which could either be total or submerged unit weight depending upon the ground water conditions in the prototype soil. Therefore, when the 1/n scaled model test is performed under a hydraulic gradient scale factor N=n, the stresses due to the self-weight of soils at the homologous points of model and prototype scale will be the same. This is shown as follows: (<Tv)m = 7m 2m = = M, (2.3) where zm and zp are the model and prototype depths, and (<rv)m and (o~v)p are the effective vertical self-weight stresses at the homologous points of model and prototype soil elements respectively. This indicates that the stresses in the model and prototype Chapter 2. HydrauHc Gradient Similitude Method 8 will be identical, i.e., the scale factor for stress is unity. If the same soil is tested in the model as in the prototype and the same stress path is followed in the model and the prototype condition, the strains in the model and prototype will be expected to be the same (Roscoe, 1968), i.e., the scale factor for the strain is unity, while the displacements of the prototype will be larger than the model by the factor n=N. Therefore, the hydraulic gradient similitude tests are expected to follow the same scaling laws as in the centrifuge tests. Scaling laws for the centrifuged models have been reported for granular material by many researchers (Roscoe, 1968 and Scott, 1978). A summary (Scott 1978) is given in Table 2.1. In the actual testing, the scaling laws related to the problems studied have to be examined by the experimental evidence, as many factors due to technical limitations may not be scaled by the scaling laws. Ultimate verification of scaling relation for a modelling test is to examine the model test results against the specific prototype be-haviour. However, due to the difficulties in simulating the specific geological settings of the prototype soil conditions and the exact stress path of the prototype loading sequences, direct comparisons between the prototype and scaled modelling tests are not always successful. Therefore, another experimental technique is often used in-stead to examine the scaling laws. This technique is called the "modelling of models" with which an assumed prototype behaviour is simulated under different scaled model tests with different stress fields. In this thesis, this technique of verifying scaling laws will be used to evaluate the hydraulic gradient scaling laws associated with each of particular problems studied. A hypothetical case is provided herein as an example to show the order of insitu stress level that can be simulated in the hydraulic gradient similitude tests. In this case, a model with soil sample height, Lm, of 30 cm is assumed to be subjected to a Chapter 2. Hydraulic Gradient SimUitude Method Pt (water pressure) seef lage t Pb (water pressure) Figure 2.1: A Soil Element in The Hydraulic Gradient Similitude Tests Table 2.1: Scaling Relations for Centrifuge and Hydraulic Gradient Tests Quantity Full Scale Model at N g's Linear Dimension 1 1/N Area 1 1/N2 Volume 1 1/N3 Stress 1 1 Strain 1 1 Force 1 1/N2 Acceleration 1 N Velocity 1 1 Time - In Dynamic Terms 1 1/N Time - In Diffusion Cases 1 1/N2 Frequency in Dynamic Problems 1 N Chapter 2. Hydraulic Gradient Similitude Method 10 water pressure difference, A p , of 300 kpa across the soil sample, then, A p i = 1 + 300 1 + 10-0.3 = 101 If 7UJ = 10 k N / m 3 and 7 P = 7* = 20 k N / m 3 representing a dry soil condition in prototype, based on Eq. (2.2), 101 x 10 + 10 N 20 50 then, as LP — N LM, a depth of 30 cm in the model will simulate a 15 m deep soil in the prototype. If 7 P = 7 ' = 10 k N / m 3 representing a saturated soil condition in prototype, N % 100 (2.4) then, a depth of 30 cm in the model will simulate a 30 m deep soil in the prototype. In practice, a water pressure difference of 300 kpa across a sample height of 30 cm is not difficult to accomplish. 2.3 Comparison with Centrifuge Testing In the centrifuge testing, a model is mounted in a swinging bucket attached to the centrifuge rotating arm, as shown in Figure 2.2. Loading frame and other testing equipment have to be mounted in the bucket as well. Usually, the large centrifuges are installed underground in an enclosed basement for the purpose of safety. Tests are controlled and monitored in a remote control room. A special data acquisition system has to be designed to avoid signal noise and transmit sensing signals from a rotating test platform to a stationary data acquisition station (Shen et al, 1984). Chapter 2. Hydraulic Gradient Similitude Method 11 Figure 2.2: Schematic of Centrifuge Testing Set-up, after Schofield and Steedman (1988) In addition, the gravity field created by centripetal acceleration in the centrifuge is not homogeneous in all three directions. The extent of this stress nonhomogeneity depends upon the relative dimension between the testing model and the centrifuge arm. In contrast, the hydraulic gradient similitude method provides some advantages in modelling construction, test monitoring, and data acquisition. As compared with centrifuge testing technique, the following comparison can be made between these two stress conservation modelling techniques, as shown in Table 2.2. It can be seen that the centrifuge method is a much more expensive testing technique. However, it does have a more general application. It may be better suited for larger research projects, while the hydraulic gradient similitude method is a much cheaper approach but with some limitations in its application. Even so, it will be shown in this thesis that many important geotechnical problems can still be examined by using the hydraulic Chapter 2. Hydrauhc Gradient Similitude Method 12 Table 2.2: Comparison between Centrifuge and Hydraulic Gradient Modelling Tests Centrifuge Tests Hydrauhc Gradient Tests Principle Centripetal Forces Seepage Forces Porous Material Self-weight Stress Self-weight Stress Soil Increased Increased Solid Structure Self-weight Stress Self-weight Stress Member Increased Not Affected Applications More General Problems Problems with Level Ground and Self-weight of Structure Member is not Important gradient similitude method. Generally, the objectives of applying modelling tests in geotechnical engineering problems can fall into one of the following categories: 1. to investigate prototype behaviour directly - which is very difficult, if not im-possible, as all the similitude laws can not be simultaneously satisfied even by centrifuge technique. In addition, the exact stress path and geological condition in prototype is not easy to replicate in the model tests (Scott, 1977); 2. to investigate failure mechanism, in which case, a specific prototype condition is not directly modelled in detail; 3. to provide a data base on response of soil structure systems at field or prototype levels of stresses, so that methods of analysis can be evaluated. Model testing for the purposes of (2) and (3) are the least controversial and the most meaningful. Thus, in this thesis, the objectives of using the hydrauhc gradient similitude method are of (2) and (3) in the above list. Chapter 2. Hydraulic Gradient Similitude Method 13 2.4 Factors affecting Hydraulic Gradient Similitude Tests in Sands In the hydraulic gradient similitude tests, a downward 1-D steady state flow occurs across the soil deposit. With this downward seepage flow, it is hoped that the fluid pressure decreases linearly with depth, giving linearly distributed soil stress. This process can be described mathematically by the following equations based on the mass conservation principle: VV, = C, (2.5) where V 2 is the seepage velocity of the flow in z - direction, -jj is the unit weight of the fluid, and C\ is the integration constant. In the tests, due to the large hydraulic gradient, large seepage velocity may lead to a Non-Darcian flow in which the linear Darcy's law no longer exists. Criteria for which the Darcy's law becomes invalid have been suggested with large discrepancy by many researchers based on theoretical and experimental results (e.g. Singh, 1976 and Jocob, 1950). Various empirical expressions were also proposed to fit the experimental data when the Darcian flow is invalid (Scheidegger, 1974). One of such equation for sandy materials may be of : ki = V™ m = 1 to 2 (2.6) where i is the hydraulic gradient, k represents some measure of permeability of the soil system, and when m = 1 E q . (2.6) reduces to Darcy's law for the Darcian flow. The hydraulic gradient, i, in the tests is given by: dh i = — with h = he + hp (2.7) oz ' = ! + (2-8) Chapter 2. Hydraulic Gradient Similitude Method 14 where h is the total hydrauhc head, he is the elevation head and hp is the pressure head due to the pressure p. From Eqs. (2.5), (2.6) and (2.8), it follows: dp d z = l f rim 6 1 1 (2.9) From Eq. (2.9), it can be seen that if 7/ is independent of the pressure, p, such as in-compressible fluid flow, then the non-Darcian flow will also give a linearly distributed fluid pressure as in the case of Darcian flow. Provided the fluid pressure decreases linearly with the depth, the soil effective stress will increase linearly with the depth. However, if the fluid is compressible due to either a compressible fluid or an unsaturated soil-fluid system, the values of 7^  will be a function of fluid pressure, p (Eckart, 1958 and Fredlund, 1976). In that case, the fluid pressure will not linearly decrease with the depth, resulting in a nonuniform soil stress distribution. A n extreme condition can be considered as an air flow through the soil sample in model tests. A n example of the air pressure distribution across the soil sample is shown in Figure 2.3. The theory for air seepage through a homogeneous soil sample is presented in Appendix A . It is shown in Figure 2.3 that the air pressure distribution along the soil depth is of parabolic curve, giving a lower rate of pressure reduction along the depth. As compared to the ideal condition, this would lead to a lower soil stress distribution. Therefore, in the hydrauhc gradient simihtude tests, only incompressible fluid such as water should be used and the soil-fluid system should be saturated. In addition, k in the E q . (2.9) represents some measure of the soil permeability and is a function of soil void ratio. Thus, it is seen theoretically that if the void ratio changes during the tests, the artificial stress field created by the hydrauhc gradient will be distorted. This effect will depend on the particular problem studied and is difficult to evaluate in a general context. In the past, corrections for permeability have been made by the addition of fines, and the scale effects caused by the permeability distortion were generally found to be small in the cases studied (Zelikson, 1988b). It is Chapter 2. Hydrauhc Gradient Similitude Method 15 Example Condition: P1 = 300 kpa L = 0.3m soil sample P2 = 0 kpa 0 SO 100 150 200 2S0 Air Pressure In Soli Sample - p (kPa) Figure 2.3: Example of Compressible Flow in Soil Sample - Air Seepage Case Chapter 2. Hydraulic Gradient Similitude Method 16 recommended that this permeability effect be evaluated in each test by experimental evidence such as using the "modelling of models" technique. Chapter 3 Preliminary Application - Footing Test 3.1 Introduction In this chapter, a preliminary application of modelling tests using the hydrauhc gra-dient similitude method is conducted on the footing tests. The primary purpose of this testing series is to evaluate this modelling technique by using a relatively simple problem - footing problem, from which some experience may be gained with regard to this new type of modelling test, and be used later for constructing a more general testing device described in Chapter 4. Thus, the main objectives of present study are as follows: • To illustrate the application of modelling test using the hydrauhc gradient simil-itude method, and • To evaluate the scaling principle for footing problems and compare some results with those from centrifuge tests and triaxial tests. In the process of this study, a new method of sample preparation is developed and evaluated for the hydrauhc gradient modelling tests. A series of laboratory soil testings including sieve analysis, permeability tests and triaxial tests are also performed to characterize and estimate the soil parameters of the sand used in the tests which will be used later in the analyses of test data. 17 Chapter 3. Preliminary Application - Footing Test 18 3.2 Testing Program 3.2.1 Test Equipment A simple testing device was constructed of a conventional triaxial cell, as shown in Figure 3.1. The sand deposit was formed within a plexiglass cylinder which is 127 mm in diameter and 230 mm in length. A high water pressure was applied at the top of the sand in order to obtain a high hydraulic gradient across the soil sample. The base of the sand deposit drained to a low pressure environment. Tap water was supplied through an entry valve at the top cap of the cell. A water regulator was used to eliminate water pressure fluctuation in the water supply line. A controlled hydrauhc gradient was obtained by monitoring water pressures at both the top and bottom surfaces of the sand using water pressure transducers, and adjusting the water supply valve accordingly. A large porous stone filter was placed at the bottom of the soil deposit. The permeability of the stone was high enough relative to that of the sand so that no significant head loss occurred in the stone itself. A circulation chamber allowing free flow of water was provided beneath the stone and was connected to a drainage Une. The filter stone was supported on two plexiglass rings of different diameters within the circulation chamber. Holes were drilled in the support rings to allow water to flow through. A strain controlled loading machine was used to load the model footing. A loading rate of 0.34 m m / m i n was used. This rate allowed a completely drained condition to prevail. The load was applied to the footing through a conventional triaxial loading bushing, as shown in Figure 3.1. A n L V D T was attached to loading ram to measure the vertical displacement of the model footing. A l l instrumentation was recorded on a 4-channel strip chart recorder with analogue signals. The footing adaptor was a circular hollow cylinder with its upper end connected Chapter 3. Preliminary Application - Footing Test 19 t m o t o r d r i v e n j d i s p l a c e m e n t r o d 11 LVDT T F i x e d F r a m e (1) - pressured water Line (2) (3) - pore pressure transducer lines Figure 3.1: Schematic of Hydrauhc Gradient Footing Test Device Chapter 3. Preliminary Application - Footing Test 20 to the loading ram. A circular porous footing plate was attached to the lower end of the adaptor. Holes at the top end as well as on the cylindrical walls of the adaptor were drilled, which allowed water to flow into the head. Different size adaptors were used to simulate footings of various sizes. The footing plate was made of a ceramic porous stone which was easily machined to different sizes. The stone is rough and rigid and simulates a rigid footing with a rough surface. A thin rigid stone having a high permeability would be most desirable to eliminate significant change to the flow patten (i.e., hydrauhc gradient) within the soil deposit due to the placement of the footing plate on the soil surface. However, the permeability of the porous footing plate used in the testing series described herein was much lower than that of the sand tested. This effect will be examined later. 3.2.2 Model Soils The sand used in the tests is a uniform rounded Ottawa sand whose mineral composi-tion is primarily quartz with a specific gravity of 2.67 and a constant volume friction angle, </>c„ of 31° . Its grain size distribution curve is shown in Figure 3.2. However, only sand retained on the #140 sieve was used in the tests. Reference maximum and minimum void ratios of 0.88 and 0.58 were determined according to A S T M standard (1972). The variation of permeability k(cm/s) vs. void ratio, e, of the tested sand was determined by the variable head method (Lambe, 1951) and is shown in Figure 3.3. The hyperbolic soil parameters of the soil tested were determined from conven-tional drained triaxial compression tests, using the procedure suggested by Duncan et al (1980). Confining stresses used in the triaxial tests ranged from 20 kPa to 200 kPa. At low stress levels, stress corrections for membrane forces were made using the methods proposed by Fukushima and Tatsuoka (1984) and Kuerbis (1988). Table 3.1 shows the soil parameters estimated from the triaxial tests for loose and dense sands. Chapter 3. Preliminary Application - Footing Test 21 Figure 3.2: Grain Size Distribution of Fine Ottawa Sand to to Chapter 3. Preliminary Application - Footing Test 23 Table 3.1: Hyperbolic Soil Parameters From Drained Compression Triaxial Tests Sands Ke n Kb m Rf A<j> 4>cv K0 Dr = 30% 600 0.88 470 0.25 0.95 32 0.0 31 0.5 Dr = 75% 1600 0.67 600 0.05 0.70 39 4.0 31 0.4 in which Ke = the Young's modulus number n = the Young's modulus exponent Kb = the bulk modulus number m = the bulk modulus exponent Rf — the failure stress ratio 4>\ = the mobihzed friction angle at a confining stress of 1 atmosphere A(/> = the decrease in mobihzed friction angle for a tenfold increase in confining stress <j)cv = the constant volume friction angle K0 — the at-rest pressure coefficient = 1 — sin <f> for our testing condition. Chapter 3. Preliminary Application - Footing Test 24 3.2.3 Soil Preparation and Testing Procedures The initial stress distribution within the model depends largely on the seepage gradi-ents. In order to keep these gradients uniform throughout the domain and thus apply a constant equivalent body force, it is necessary to keep the permeability constant in the soil domain. To achieve this, the sand should be placed as uniformly as possible. It was found that the water pluviation technique (e.g., Vaid and Negussey, 1986) used in the preparation of triaxial samples was not efficient here because large amounts of sand were required, and the procedure was time consuming. Therefore, a new sample preparation technique was developed for the present tests. This technique employs upward seepage forces, together with sedimentation and densification processes, to form and then reform soil deposits for and after each test and is described below. During sample preparation, the top cap of the cell was removed and the drainage lines from the circulation chamber were closed. De-aired water was used to fill the cell and all the measurement fines. A fixed amount of oven dried sand, about 3 kg, was weighed in flasks. Water was added to each flask and the sand water mixture was then boiled. The base porous stone was also boiled before being installed. After cooling to room temperature, the boiled sand was transferred to the cell using a water pluviation technique flask by flask. It was found that layers tended to form with each flask of sand deposited. To remove this layering effect, a controlled upward seepage gradient was applied to the sample causing it to form a loose slurry which was then stirred to obtain a homogeneous state. The upward gradient was then turned off and the sand allowed to sediment under its self-weight. Since the sand used was very uniform, no segregation was observed. When the sedimentation process was completed, the top cell cap, the lubricated loading ram, and the footing adaptor were all carefully installed. The sample was then densified to the specified density by tapping the side and base of the cell. The model testing cell was moved into the loading frame and the water supply Chapter 3. Preliminary Application - Footing Test 25 lines connected. The "gravitational" process began by applying a controlled hydrauhc gradient. The model footing was lowered onto the sand surface, and the displacement controlled footing test commenced. Continuous readings of vertical load and dis-placement were taken throughout the test. After each test was completed, the sand was loosened by an upward gradient and reformed as discussed above. In this way, a number of tests under different gradients and densities could be quickly carried out. 3.2.4 Sample Uniformity and Test Repeatability The soil sample preparation technique described above involves an upward seepage force to disturb the sample, which is then reformed by sedimentation and densifi-cation. This technique has the advantage that it is very fast to prepare a new soil deposit after each and every test. Great effort has been made to evaluate this technique, and ensure initial sample uniformity and repeatability of test results. Gelatin, as suggested by Emery et al (1973), was used to solidify samples prepared by this technique in order to examine the sample uniformity conditions at the end of sedimentation and densification processes. The horizontal as well as vertical distribution of the void ratio determined from slices of the gelatin sample are shown in Tables 3.2 and 3.3 for conditions- after sedimentation and densification, respectively. It may be seen that prior to densification, the top layer is significantly looser than the rest of the sample. After densification, the soil sample is uniform in both horizontal and vertical directions. Through several trials, it was found that the most uniform densification was achieved by tapping the side and base of the triaxial cell. The foregoing sample preparation procedure has also been evaluated by comparing the results of drained compression triaxial tests on samples prepared by the conven-tional water pluviation technique and by the present method, called the 'quick sand' technique. Results are shown in Figure 3.4 to 3.8, where it may be seen that both Chapter 3. Preliminary Application - Footing Test 26 Table 3.2: Sample Uniformity after Sedimentation, Void Ratio 'e' at Different Loca-tions Top Layer Middle Layer Bottom Layer Depth Profile T l 0.9313 M l 1.7161 B l 0.8954 D l 0.9339 T 2 0.9252 M2 0.8971 B2 0.8884 D2 0.9014 T3 0.9306 M3 0.8853 B3 0.8944 D3 0.8900 T4 0.9397 M4 0.8932 B4 0.8892 D4 0.8935 T5 0.9320 M5 0.8966 B5 0.8957 D5 0.8924 Table 3.3: Sample Uniformity after Densification, Void Ratio 'e' at Different Locations Top Layer Middle Layer Bottom Layer Depth Profile T l 0.6472 M l 0.6250 B l 0.6123 D l 0.6073 T2 0.5931 M2 0.6148 B2 0.6091 D2 0.6199 T3 0.6076 M3 0.6350 B3 0.6186 D3 0.6213 T4 0.5978 M4 0.6312 B4 0.6123 D4 0.6220 T5 0.5879 M5 0.6226 B5 0.6172 D5 0.6111 consolidation behaviour and stress-strain response produced by these two different sample preparation methods are very similar. The 'quick sand' model soil preparation technique produced test results which were highly repeatable. In the testing program, each test was performed 2 to 3 times under the same condition to assess the repeatability of the test results. As shown in Figures 3.9 and 3.10, good repeatability for each test condition was obtained for both loose and dense sands. 3.2.5 Experimental Program Tests were performed on both loose and dense sands with different footing dimensions. The experimental program is summarized in Table 3.4. Chapter 3. Prehminary Application - Footing Test 27 1 \ i - J in o ft 1 | n meth' • \ I c o cn l a \ • \ 1 c a. <u T J T J • \ O S •a si • C O C O c r H N c II Q -fc -|_> w 4) a \ I i i i i i i i I i 1 i i I i , o o o o o o o o o o o c o o o c o o o o (VdH) SS3H1S NOIlVmiOSNOD DldOHlOSI °D Figure 3.4: Comparison of Consolidation behaviour from Two Sample Preparation Methods Chapter 3. Preliminary Application - Footing Test 28 Figure 3.5: Comparison of Stress-strain behaviour at Loose Sand from Two Sample Preparation Methods, DT = 33% 0 - ! 1 1 1 1 1 1 1 1 1 1 1 1 1 0 2 4 6 0 10 12 14 AXIAL STRAIN (%) Figure 3.6: Comparison of Volumetric behaviour at Loose Sand from Two Sample Preparation Methods, DT = 33% Chapter 3. Preliminary Application - Footing Test 29 Figure 3.7: Comparison of Stress-strain behaviour at Dense Sand from Two Sample Preparation Methods, DT — 75% Figure 3.8: Comparison of Volumetric behaviour at Dense Sand from Two Sample Preparation Methods, D , = 75% Chapter 3. Preliminary Application - Footing Test 30 Figure 3.9: Typical Example of Repeatability for Loose Sand at N=40, Bm = 1.5cm Chapter 3. Preliminary Application - Footing Test 31 Figure 3.10: Typical Example of Repeatability for Dense Sand at N=60, Bm = 1.5cm Chapter 3. Preliminary Application - Footing Test 32 Table 3.4: A Summary of Model Footing Tests H . G . S . F - N 1 10 20 30 40 50 60 80 100 Z?m=1.5cm loose dense loose dense loose dense loose dense loose dense loose dense loose dense loose dense loose dense 5 m =2 .0cm dense B m =2 .5cm dense Note: Loose Sand - DT = 33%; Dense Sand - DT = 75%. 3.3 Results and Discussion 3.3.1 Load-Settlement Curves The observed load-settlement curves for loose and dense sands under a range of hy-drauhc gradient scale factors are shown in Figures 3.11 and 3.12, respectively. A small correction to the measured applied footing pressure was made to account for the hy-drauhc head loss in the porous plate at the base of the footing. This correction is discussed in Appendix B. The footing diameter, BM was 1.5 cm for all the tests shown on these figures. It may be seen that the response is greatly affected by the hydrauhc gradient applied, N , becoming much stiffer as N increases with seepage gradient. For the loose sand condition, DR = 33%, the load-settlement response for any one scale factor is essentially linear except in the early stage when it curves gently downward, but there is no break in the curve corresponding to a limit bearing pressure. For the dense sand condition, the initial portion of the curve is essentially linear, followed by a sharp break corresponding to a hmit pressure, and followed by a gradual increase in pressure with settlement. The increase in pressure beyond the hmit pressure is thought to be due to penetration of the footing into the soil resulting in a surcharge or embedment effect. Chapter 3. Preliminary Application - Footing Test 33 3 . 0 o o o o o N = 1 • • • • • N = 1 0 0 0 0 0 0 N = 4 0 » i i i i N = 6 0 • • • • • N = 8 0 N = 1 0 0 - 1 . 0 — 1 c a> E CD (V CO CT1 C 8 " 5 0 - 9 . 0 i—i—i—i—i—i—i—i—r ~i i i i i i i— i—r " i — i — i — r 0 . 0 4 0 . 0 8 0 . 0 F o o t i n g P r e s s u r e ( k p a ) "i—i—i—i—i 1 2 0 . 0 Figure 3.11: Observed Settlement Curves for Loose Sand Under Different N (5 m =1.5cm, IL=33%) Chapter 3. Preliminary Application - Footing Test 34 3 . 0 - 1 ~ O O O O O N= 1 | - ••••• N=10 - a & A f l A N = 2 0 ' _ i i i i i N = 4 0 I N = 60 I " »»••• N=80 | " N= 100, I — 9.0 | i i i i i i i i i I i i i i i i i i i I i i i i i i i i i I i i i i i i i i i | 0.0 100.0 200.0 300.0 400.0 Footing Pressure (kpa) Figure 3.12: Observed Settlement Curves for Dense Sand Under Different N (B m =1.5cm, DT=75%) Chapter 3. Preliminary Application - Footing Test 35 The test results of Figures 3.11 and 3.12 are similar to those observed by Ovesen (1975), in centrifuge tests as shown in Figure 3.13. 3.3.2 Ultimate Bearing Pressure The ultimate bearing pressure, Puit, for dense sands can be estimated from the ob-served load-settlement curves and compared with the Terzaghi bearing capacity equa-tion. Such a comparison allows the trend of the data to be checked against a well-established bearing capacity equation. The Puit values can also be checked against centrifuge test results and triaxial test data. The ultimate pressure from the footing tests on dense sand were determined by the tangent method proposed by Vesic (1975) and illustrated in Figure 3.14. The values obtained for a relative density of 75%, a footing diameter of 1.5 cm and for a range of hydrauhc gradient scale factor, N, are shown in the first row of Table 3.5. The ultimate bearing pressure from the Terzaghi theory is as follows: Puit = ^ 7 7 m B m / Y , or (3.1) Puit = ^N-y'BmNy or (3.2) log(P u < ( ) = \og(^7' BmN^ + \og(N) (3.3) in which £ 7 = a shape factor = 0.60 for a circular footing; jm = the effective unit weight of the model soil = N7'; 7' = the submerged unit weight of the soil; N = the hydrauhc gradient scale factor = ^ ; Bm = the diameter of the model footing; Chapter 3. Prehminary Application - Footing Test 36 Figure 3.13: Settlement Curves observed from Centrifuge Tests (after Ovesen, 1975) Chapter 3. Preliminary Application - Footing Test 37 10.Qj — 1 0.0 200.0 Footing Pressure (kpa) Figure 3.14: Illustration for Determination of Ultimate Pressure for Dense Sand Chapter 3. Preliminary Application - Footing Test 38 Table 3.5: Bearing Capacity for Dense Sand from H . G . Tests N 1 10 20 30 40 50 60 80 100 Puh 3.8 34.6 41.8 64.2 72.4 99.2 105.3 140.3 165.2 TV 83.4 76.8 46.5 47.6 40.2 44.1 39.0 39.0 36.7 4>' (deg.) 40.5 39.8 37.0 37.0 36.0 36.5 36.0 36.0 35.5 PuH in kPa iV 7 = the bearing capacity factor associated with the unit weight of the soil and is a function of the friction angle only. For a given footing diameter and soil density, Eq . (3.3) indicates that Putt should increase linearly with the scale factor, N , at a 45° slope on a log-log scale. The observed trend is shown in Figure 3.15 and indicates essentially a linear relationship with a 45° slope for N larger than 20. For N values in the range of 1 to 20, the observed values he above the line. Centrifuge data reported by Ovesen (1975) was found to follow a similar trend and is shown in Figure 3.16. The reason for the nonlinearity at low hydraulic gradient or low stress levels is likely due to the increased tendency for dilation at low stress levels leading to a higher mobihzed friction angle. The friction angle mobihzed in the model tests can be computed as follows: 1. iV 7 values from the model tests can be computed from E q . (3.1) and are listed in Table 3.5. 2. The mobihzed <p values were determined from the iV 7 values based upon the Brinch-Hanson (1970) relationship between <j> and N1 and are hsted in row 3 of Table 3.5. This relationship is recommended by the Canadian Foundation Engineering Manual (1985). It may be seen that the mobihzed (f> values computed from the model tests are essentially constant and equal to 36° to 37° for scale factor, N , of 20 or greater. Below Chapter 3. Preliminary Application - Footing Test 39 HYDRAULIC GRADIENT SCALE FACTOR - N Figure 3.15: Observed Ultimate Pressure vs. Scale Factor - N Chapter 3. Preliminary Application - Footing Test 40 Figure 3.16: Bearing Capacity vs. Acceleration Field in Centrifuge Tests (after Ovesen, 1975) Chapter 3. Preliminary Application - Footing Test 41 N = 20, higher (j) values are mobilized. For N = 1 which corresponds to a zero seepage force condition, or a conventional modelling condition, the mobilized friction angle is 4 0 . 5 ° . The computed friction angles shown in Table 3.5 are compared with the peak friction angles obtained from triaxial tests in Figure 3.17. It should be noted that the friction angles computed from model tests represent some "average" values mobilized along the whole failure surfaces in the model tests. It may be seen that while the computed mobilized friction angle is about 3° lower than the peak value obtained from the triaxial test, the trend of decreasing friction angle with stress level for the same relative density is in agreement with the triaxial test results. The effects of hydrauhc gradient or stress level on the bearing capacity can also be examined by considering the model footing to have a prototype dimension which increases with the scale factor, N . The calculated bearing capacity coefficient, i V 7 , in Table 3.5 can be related to the corresponding prototype footing width, Bp, using the scaling relation, Bp = N • Bm. The results are shown in Figure 3.18. It may be seen in the figure that iV 7 decreases linearly with footing size on the log-log scale. This reduction with footing size is expected because larger footings have higher stress levels in their failure zone, and this results in a lower mobilized friction angle, <j>, and hence a lower Ny value. This observation is in accordance with other model test results by De Beer (1970) and centrifuge test results by Kimura et al (1985). In addition, the experimental observation from hydrauhc gradient tests shown in Figure 3.18 tends to support the theoretical studies by Graham and Hovan (1986) in which a log-hnear decrement of N7 value against footing size is predicted using a critical state model for sand. From this study, it is demonstrated that the hydrauhc gradient modelling test has a very attractive feature that it provides a simple and inexpensive method of loading soil or foundation at stress conditions corresponding to field conditions. This allows Chapter 3. Prehminary Application - Footing Test 42 -1 t QQQQO P e a k F r i c t i o n A n g l p f r o m T r i a x i a l T e s t s •J3QDX3 A v e r a g e F r i c t i o n A n g l e f r o m M o d e l T e s t s ~i 1 1 1 1 — i — i — r n 1 1 1 1—i—i—r 10 Stress Levels ( s i g 3 / P a ) 10 Figure 3.17: Variation of Friction Angles with Confining Stress Levels Chapter 3. Preliminary Apphcation - Footing Test 43 Figure 3.18: Prototype Footing Size Effect on iV 7 Coefficient Chapter 3. Preliminary Application - Footing Test 44 characteristic behaviour to be examined at these stress levels as well as providing a data base from which method of analysis can be compared. 3.3.3 Evaluation of Scaling Law - Modelling of Models Model footing tests were carried out on dense sand using a range of model footing diameters as well as hydrauhc gradients. This allowed a given prototype condition to be modelled in more than one way and hence allowed a check on the scaling laws implied by the hydrauhc gradient tests. Ovesen (1975) has referred to this experimental method of checking the scaling laws as the method of "modelling of models". This method has been frequently used in centrifuge tests to evaluate the centrifugal scaling laws. By using this technique, some technical limitation on the modelling tests can also be identified, such as boundary effects of model container. Two sets of model tests with each set representing the same prototype are shown in Table 3.6. Set 1 involves model footings having Bm — 1.5 and 2.5 cm and subjected to hydrauhc gradient scale factor, N=100 and 60 respectively. Each test represents a prototype footing with Bp = 150 cm. The prototype responses from these two tests are shown in Figure 3.19 where it may be seen that they are very similar. The corresponding bearing capacities are shown in Table 3.6 and are in good agreement. Set 2 involves model footings having Bm = 1.5 and 2.0 cm subjected to scale factor, N = 80 and 60 respectively. Each test represents a prototype footing with Bp = 120 cm as shown on Table 3.6. The prototype responses from these tests are shown in Figure 3.20 and are again very similar. The ultimate bearing capacities are shown in Table 3.6 and the values are again in good agreement. These results verify that the experimental data follow the expected scaling laws as discussed in Chapter 2, and also show that the possible scale effects caused by the distortion of soil permeability during the loading process are very small. It is noted that in Figure 3.19 the load-settlement curve for Bm = 2.5 cm becomes Chapter 3. Preliminary Application - Footing Test 45 Table 3.6: Comparison of Bearing Capacity at the Same Prototype Scale, Dense Sand Set Model Footing Bm Prototype Bearing at Different N Dimension Capacity (kPa) 1 Bm = 1.5 cm, N = 100 150 165.2 Bm = 2.5 cm, N = 60 150 157.2 2 Bm = 1.5 cm, N = 80 120 140.3 Bm = 2.0 cm, N = 60 120 135.2 stiffer than the curve for Bm = 1.5 cm at footing pressure of about 250 kPa. This may be due to the boundary effect of the model container for this large footing diameter. The model container used in these tests is 127 mm in diameter. By comparing results in Figures 3.19 and 3.20, it may be seen that the soil container boundary only comes into effect when the diameter ratio between the soil container and the footing becomes less than 6. This is in agreement with the centrifuge result reported by Cheney (1985), who indicated that boundary effect becomes important when the diameter ratio between the soil container and the footing is less than 5. 3.4 Summary and Conclusion The response of a soil-structure system to load is highly dependent on the stress level involved. This is so because the stress-strain response of soil depends on stress level. Consequently, tests on small scale conventional models are unlikely to capture the response of large prototype structures. It is possible to overcome this problem with centrifuge tests in which the prototype stress level can be duplicated in a small model by applying very high centripetal accelerations, thus inducing large body forces. However, this is a very expensive testing procedure. High stress can also be induced in small models by using very high hydrauhc gradients to increase the body force. In this chapter, this technique was applied to a series of model footing tests. The testing apparatus and procedure were discussed, and Chapter 3. Preliminary Application - Footing Test 46 200.0 - i B„= 1.5cm N=100 o o a e o B m = 2.5cm N=60 Both producing a prototype footing width of B.= 150cm -800.0 0.0 i i i | i i i i i i i 100.0 00.0 I I I I I I I I I I I I I I I 300.0 400.0 Footing P ressu ie (kpa) Figure 3.19: Evaluation of Scaling Law for Hydraulic Gradient Footing Tests on Dense Sand at Bp = 150cm —700.0 I i i i i i i i i i | i i i i i i i i i | i i i i i i i i i | i i i i i i i i i | 0.0 100.0 200.0 300.0 400.0 Footing Pressure (kpa) Evaluation of Scaling Law for Hydraulic Gradient Footing Tests on Dense = 120cm Figure 3.20: Sand at Bp Chapter 3. Preliminary Apphcation - Footing Test 47 a new method of soil sample preparation technique was developed and evaluated for the hydraulic gradient modelling tests which enabled a fast preparation of soil sample after each and every test. The model testing results were presented and compared with centrifuge and triaxial test results. The observed load-settlement curves were found to have very similar characteristics to those observed in centrifuge tests. The footing tests on dense sands displayed a marked limit pressure effect while those on the loose sand did not. The limit pressure showed the influence of stress level in reducing the mobihzed friction angle at high stress levels. This is in agreement with both centrifuge and triaxial testing. The consistency of the model tests data was checked by comparing the results of two different model tests which simulated the same prototype. The results were found to be in very good agreement and verified that the hydraulic gradient tests followed the expected scaling laws as in the centrifuge tests. This also confirms that the distortion of soil permeability during the loading process has little effect on the test results. In addition, the "modelling of model" tests shows that the soil container boundary may only come into effect when the diameter ratio between the container and the footing becomes less than 6. It is demonstrated from this study that the hydrauhc gradient similitude method can be used to examine characteristic response of soil structure systems and existing knowledge under prototype stress levels, so as to obtain a better understanding of the importance of stress level. It is also shown that the hydrauhc gradient modelling test has the following ad-vantages as compared to the centrifuge tests: 1. The model test equipment involved is much cheaper. 2. The skills required by the experimenter are less demanding. 3. Tests can be performed much more quickly. Chapter 3. Preliminary Application - Footing Test 48 4. The tests could be readily carried out in most conventional soil laboratory. Based upon this experience, a more general testing device of larger size was built for the hydraulic gradient modelling tests with emphasis on foundation testing, which will be described in Chapter 4. Further applications of this modelling technique using the new testing device will be discussed in Chapters 5 and 7. Chapter 4 Hydraulic Gradient Similitude Testing Device 4.1 Introduction In this chapter, the newly developed hydrauhc gradient similitude test device at the University of British Columbia ( U B C - H G S T ) is described in detail. Its supplemen-tary equipment and associated techniques developed for different applications will be described in later chapters along with each application. The preliminary design and fabrication of this device started in December, 1987 and the first calibration test was operated in about one year later. Since then, the device is under continuous modification and improvement to incorporate different applications. The design of the U B C - H G S T apparatus was directed towards achieving an optimum combination of the following considerations: 1. simplicity in design, construction and operation; 2. versatility in application, and 3. reliabihty in measurements. Since the testing device of this kind is the first one in North America, full use was made in the design of the experience gained at U B C through the development of laboratory soil element testing devices and insitu testing devices, along with the experience gained from the previous preliminary application - footing tests described in Chapter 3. 49 Chapter 4. Hydraulic Gradient Similitude Testing Device 50 4.2 General Description In its present configuration, the U B C - H G S T device is mainly designed to perform the force controlled lateral loading tests on vertical piles. However, provision has been made to allow for performing displacement controlled test, and axial loading tests on piles or other types of foundations resting on level ground. The device can also be used to perform dynamic or seismic studies of piles or other foundations with due consideration of boundary effect. A schematic layout of the U B C - H G S T device is shown in Figure 4.1, and the photograph of the device is shown in Figure 4.2. The main body of the U B C - H G S T device consists of five major components, namely; 1. sand container and air pressure chamber; 2. water supply and circulation system; 3. air pressure supply system; 4. pile loading system, and 5. data acquisition and control system. During a test, the water is continuously supplied by a high power centrifugal water pump. The hydrauhc gradient across the soil deposit is obtained by applying an air pressure in the air chamber with water pressure venting to a low pressure at the base of soil container. The water level is maintained about 1 in. above the sand surface by balancing the air pressure and water flow for a given hydrauhc gradient. Three pore pressure transducers are used to measure the pore pressure distribution within the sand deposit. The average hydrauhc gradient within the sand deposit is obtained from the pore pressure measurements and sample height as followed: Chapter 4. Hydraulic Gradient Similitude Testing Device 51 bending strains air regulator pile loading system load deflection two way cyclic HZ] air pressure supply system air pressure chamber data acquisition system V 1 : i sand sample 12 3 water regulator ;• water supply system \ model! pile ! 9. 9.-1 water disperser soil container / filter Shaking Table Note: 1,2,3 - pore water pressure transducer #PWP1 ,#PWP2,#PWP3 4 - lateral soil stress transducer LATP Soil Container Dimension: 445x230x420mm Figure 4.1: Schematic of U B C - H G S T Device Chapter 4. Hydraulic Gradient Similitude Testing Device 52 Figure 4.2: Photograph of U B C - H G S T Device Chapter 4. Hydraulic Gradient Similitude Testing Device 53 • when the bottom drainage valve is closed, and there is no water flow; i = 0 (4.1) • when the bottom drainage valve is open, and water flows under its own gravity; i = JJT * 1 (4-2) • when the bottom drainage valve is open, and the controlled air pressure is applied in the air chamber; 8 \W±X 8 where Pi and P3 are the water pressures measured at the top and base, respec-tively, of the soil sample. Hs is the sample height, and Hw is the water table elevation relative to the sample base. A stress transducer latp is flush mounted on a side wall of soil container to measure the total lateral stress in the soil during a test. This transducer is installed at the same height as the pore pressure transducer pwp#2, so that the lateral effective stress in the soil at this point can be obtained by subtracting the measurements from these two transducers, as K ) i a t p = Mlatp ~ (u)p«»P#2 (4.4) where a'h is the horizontal effective stress at latp, ah is the lateral total stress measured by latp transducer, and (T i ) p T O p #2 is the water pressure measured by the water pressure transducer pwp#2. Calibration of the lateral stress transducer and discussion of stress gradient effect on the measurement are given in Appendix C . 4.3 Sand Container and Air Pressure Chamber The sand container is a rectangular box with inside cross section dimension of 405 x 190mm 2 and a depth of 350 mm. The box is comprised of 19.05 mm thick welded Chapter 4. Hydraulic Gradient Similitude Testing Device 54 aluminum plates. The whole box and aluminum platform are all anodized with hard coatings to prevent water corrosion. The size of the sand box is chosen based on consideration of minimum boundary effect and flexible pile condition under lateral pile load tests. Nonlinear finite element studies (Yan, 1986) have shown that under plane strain condition and hyperbohc soil stress-strain relation the outside boundary larger than 25 pile diameter have httle effect on pile response under lateral loading. In the real situation, this constraint may be more relaxed due to three dimensional displacement effect. In addition, the boundary condition in the direction perpendic-ular to the loading direction has much less effect. Thus, a rectangular cross section is designed to reduce the box cross section area, and the flow quantity. This reduces the requirement for water pump capacity and hydrauhc piping size for a given hydrauhc gradient. A comparison of the soil container size with some centrifuge boxes is given in Table 4.1. The maximum hydrauhc gradient is designed to increase the soil body force by 100 times. The maximum pressure expected for the maximum designed hydrauhc gradient will be about 350 kPa within the enclosed system. At the bottom of sand container, a filter is designed to retain the sand deposit. The filter is supported on a grid of perforated aluminum strips about 50 mm high, and cellular chambers are provided to allow water to freely flow before draining out of the soil tank. Table 4.1: A Comparison of Box Size with Some Centrifuge Boxes Test Reference long x wide x deep R D L D Scott; 1977 529 x 172 x 254 65D 50D Centrifuge Prevost, 1981 335.6 x 335.6 x 241.3 33D 40D Barton, 1982 860 x 860 x 380 27D 20D H . G . S . T . Zehkson, 1978 300 x 300 x 450 10D U B C 404 x 190 x 375 20 - 32D 34 - 50D Note: R - Outer Boundary of Container; D - Pile Diameter; Unit in mm. Chapter 4. Hydraulic Gradient Similitude Testing Device 55 The filter consists of a 6.35 mm thick perforated aluminum plate overlain by a series of stainless steel sieves including #10, #140, and #200 mesh sieves. As the sand used has been re-sieved and only the portion retained in sieve #140 is to be used in the test, the soil will be retained in this filter with little water pressure head loss across it. The filter and its support strips are designed as a grid system under a uniform distributed load (Timoshenko and Woinowsky-Krieger, 1959). The spacing of the cellular support is chosen so that the vertical deflection of the filter at each cell center would be less than 0.1mm. The soil container lid is made of a 19.05 mm thick aluminum plate which is bolted down on the container wall by 14 Hex Head cap stainless steel screws. A rubber gasket is used to seal the water pressure between the hd and container wall. The side view and plan view of the container hd are shown in Figure 4.3. The hd has a 127 mm open hole at its center to allow for sticking out of the model pile in the pile tests as well as the instrumentation wires. A n annular aluminum block of 63.5 mm high is bolted on the hd permanently to provide a vertical space for mounting pile loading and deflection measurement units for lateral pile head loading tests. A '0 ' ring is used between the annular block and the hd to seal the air pressure. A plexiglass cylinder rests on the annular block and is sealed by ' O ' rings at its two ends. The air pressure is supphed from an entry at the cap on the plexiglass cylinder. Several special pressure tight electrical plugs are installed on the cap to collect the instrumentation wires leading to the data acquisition unit. The plexiglass cylinder forms an air pressure chamber, and also allows for a visual observation of the test. This gives an additional advantage over the centrifuge test where remote monitoring on the test is necessary (video camera is often used for this purpose). The water is constantly supphed by the pump through a 25.4 mm I.D. entry hole at one side of the hd. Beneath the entry hole, a 25.4 mm thick dispersive material er 4. Hydraulic Gradient Similitude Testing Device (a). Plan View of Soil Container Lid double acting air piston eye link air chamber dispersive material model pile (b). Side View of Soil Container Lid Figure 4.3: Side and Plan Views of Soil Container Lid Chapter 4. Hydraulic Gradient Similitude Testing Device 57 is attached to disperse the water flow and prevent sand surface erosion. During the tests, the water table is kept about 25.4 mm above the sand surface but below the lid level so that the pile head loading and deflection measuring units are all above the water level. 4.4 Water Supply and Circulation System Figure 4.4 shows the water flow chart in U B C - H G S T device. The water pump is a centrifugal type with a capacity of 24 US G P M at a total pressure head of 30.48 m, manufactured by Monarch industries Ldt.. It has a 1.5 horse power built-in motor and requires 31.75 mm and 25.4 mm I.D. suction and discharge pipes, respectively. Plastic hoses are used to connect the pump with H G S T device. Before raining the sand into the container, the box and all the hoses connected to the pump and circulation tank are all saturated with the water. As shown in Figure 4.4, during the test, a downward water flow is created by opening valve #1 and #3. Then, after each test, an upward water flow is created by opening valve #2 while closing valve #1 and #3. De-air water is used in the whole system to ensure full saturation in the sand sample and alleviate possible nonuniform stress distribution due to nonsaturation of soil sample as discussed in Chapter 2. Although there is an air-water interface above the sand surface, considering the short duration and dynamic nature of the test, the possible effect of air diffusion can be neglected. 4.5 Pile Head Loading and Measuring System Pile Loading System For lateral pile head loading tests, a double acting air piston is mounted on the soil container hd with which a one-way or two-way force controlled cyclic load can be applied through a loading bushing to the pile head inside the air chamber. The Chapter 4. Hydraulic Gradient Similitude Testing Device 58 Figure 4.4: Water Flow System in U B C - H G S T Device Chapter 4. Hydraulic Gradient Similitude Testing Device 59 applied load is measured by a low capacity load cell mounted between the piston rod and the loading ram. Since in a model test, the load applied to the model pile for a given deflection would be expected to be small, the friction in a loading system becomes important if the pile response is to be measured accurately. Mostly the friction in a loading system comes from the bushing through which the loading ram apphes the force to the loaded object. In the conventional triaxial cell, relatively large friction exists in the loading bushing mostly due to the ' 0 ' ring seals. Correction for the friction has been used, however, the procedure is complex and is function of loading rate and cell pressure, especially for stress control tests. To avoid friction problem due to the loading bushing, load measurement inside the pressure cell have been suggested by some people. However, this option would greatly complicate the experimental set-up and sample preparation with no sure guarantee of better result (Chan, 1975). Based on these considerations, a decision was made to use a low friction system with no ' 0 ' ring seal. Chan (1975) and Mustapha (1982) have used a very low friction bushing system in the triaxial cell for testing soft soil at low stress confinement. A modified version of that system is used in current H G S T device, and is shown in Figure 4.5. In such a system, the axial guidance of the loading ram is provided by two stainless steel Thompson linear ball bearings. In the test, the water table is maintained below the hd of soil container. Thus a certain amount of air leaks out constantly around the loading ram. There are three components to seal. One is the fixed ring of brass which is press fitted against the housing with large clearance for the rod. The second is the closer-fitting Teflon floating seal that is spring loaded against the brass ring. The diametric clearance between the rod and Teflon seal is 0.0254 mm. The third is the spring that keeps the flat surfaces together and yet allows lateral movement of the floating seal. With this system, very small friction force (approximate 10 grm Chapter 4. Hydraulic Gradient Similitude Testing Device reaction bar Thompson linear bearing \ brass seal plexiglass cyliner annular aluminum block — T l o / n n ^ o l / V V .. . "O" ring -^y fibre washer "O" ring w A>l oi'niiVnn/T-) fibre washer Teflon seal V loading ram .www / ^ " s p ' r i n g " ^ " " " " " ^ * ^ ^ s P r i n 9 Teflon seal *>J!0" ring rubber gasket container wall soil container lid Figure 4.5: A Low Friction Bushing System for Lateral Loading Ram Chapter 4. Hydraulic Gradient Similitude Testing Device 61 force) may develop only at the contact between the loading ram and the linear bearing balls. Since the volume of the air leaking out is very small, there is no problem in maintaining the pressure inside the pressure chamber. Pile Head Connection Different pile head connections are made to study their effects on pile response. Free head connection is made by connecting the loading ram and model piles with rod end connector, as shown in Figure 4.6. A spherical bearing in the rod end connector allows for free rotation of piles in any direction. Fixed head connection is made by threading the loading ram into a rigid aluminum block which is capped on the pile head by two thread screws. Different loading adaptors are also made to load model piles at different eccen-tricities above the sand surface. Thus, for given lateral load and pile, the effect of moment to load ratio at ground surface can be studied, as discussed in Chapter 7. Pile Head Deflection Measurement As shown in Figure 4.7, a frictionless air leaking bearing system similar to the loading system is used for L V D T (a hnear variable displacement transformer) cores. This system is used to provide axial guidance to the L V D T cores approaching the model pile. The clearance between the Teflon bearing and the core is 0.0254 mm. Two L V D T s are used to measure pile head deflection at and above the loading points from outside the air chamber. Then, the pile head rotation at the loading point can be calculated from these two deflection measurements and the corresponding distance. The L V D T s are mounted on the soil container hd. They are in alignment with the loading ram but on the opposite side of the model pile. The pile deflection and rotation at the ground surface are then estimated from the following equations Chapter 4. Hydraulic Gradient Similitude Testing Device 62 loading ram ~7|T d • rod end connector spherical bearing loading adapter for different loading eccentricity loading ram rod end connector free head connection V c model pile loading ram fixed head connection rigid pile cap model pile Figure 4.6: Pile Head Loading Connections Chapter 4. Hydrauhc Gradient SimiHtude Testing Device 63 annular aluminum block \ I I model pile side view Figure 4.7: Pile Head Deflection Measurement Chapter 4. Hydraulic Gradient Similitude Testing Device 64 based on the elastic beam theory: 09 = 0o- (4.5) yg = yo-Og-e-F-e3 SEPIP (4.6) where F is the applied load; e is the loading eccentricity; EPIP is the pile rigidity; 6D and 6g are the pile rotation at loading point and ground level respectively; and y0 4.6 Instrumentation and Data Acquisition Model Piles Model piles are made of 6061-T6 Aluminum tubing. Three pile diameters 6.35 mm, 12.7 mm, and 9.525 mm O . D . are used in the lateral load testing program to study the pile diameter effect. Of the three piles, only one pile with 6.35 mm O . D . is instrumented with strain gauges to measure the bending moment along the pile. A three point loading test on the model pile has been performed. The yielding and plastic bending moments so determined are 5772 N.mm and 7696 N.mm, respectively. A summary of the physical properties of these three piles is hsted in Table 4.2. Pile Instrumentation The 6.35 mm O . D . model pile was instrumented by eight pair of 120fi foil strain gauges at eight positions along the pile length, as illustrated in Figure 4.8. The strain gauges are glued to the outside surface of the model pile on an axis coincident with the direction of loading. Small holes are drilled on the tubing so that all the connection wires come out from inside the tubing. A l l the strain gauges are covered by layers of M-coat which provide moisture protection and smooth the pile surface over the strain gauge areas. and yg are the pile deflection at loading point and ground level respectively. Chapter 4. Hydrauhc Gradient Sirmlitude Testing Device 65 90.8 / F T model pile (O.D. 1/4") 20.0 15.0 20.0 20.0 30.0 40.0 S.G. #1 S.G. #2 S.G. #3 S.G. #4 S.G. #5 S.G. #6 S.G. #7 sand surface ///// ////// 60.0 S.G. #8 129.2 unit: mm "~7\ bottom of sand deposit / / / / / / / / / / / / Figure 4.8: Layout of Strain Gauges in Model Pile Chapter 4. Hydrauhc Gradient Similitude Testing Device 66 Table 4.2: Physical Properties of Model Piles Diam. O . D . (in) I (inst'ed) 3 8 I 2 Wall Thick.(in) 0.032 0.05 0.05 Length (mm) 424.0 423.5 425.0 Wt . (g) 20.3 38.2 53.4 m (g/mm) 0.0479 0.0902 0.1256 EI (N.mm2) 4.03 x 106 19.56 x 106 52.05 x 106 The first two pairs of strain gauges are located above the sand surface to register the linear portion of the bending moment distribution above the ground. The strain gauge pairs are at spacings of 20, 15, 20, 20, 30, 40, 60 mm down the pile with closer measurements near the soil surface. Each pair of strain gauges is arranged across the pile diameter so that one gauge registered compression and the other tension strain. This arrangement will reduce the adverse effects of temperature, and cancel any axial strain effects at that level. Each pair of strain gauges in the model pile become the two active resistors in the Wheatstone bridge circuit. Normally, the half bridge circuit formed by each pair of gauges is completed to make up a full bridge by another two dummy resistors, as shown in Figure 4.9(a). Thus, a total of 16 dummy resistors and 32 wires are required for the present pile instrumentation scheme. This will lead to a great complication in the circuitry wiring and testing set-up. Complicated wiring may also create potential problems such as noisy signals. In the present design, a simpler circuit has been adopted. As the strain gauges all have the same resistance (120Q), they can be configured to share the same pair of dummy resistors, as shown in Figure 4.9(b). In addition, all the strain gauges can be excited by the same power supply. Their signal outputs can be in common at one end while different at the other, giving single ended signals. In this configuration, only two dummy resistors are required, and only 11 wires are needed to complete the Chapter 4. Hydraulic Gradient Similitude Testing Device 67 pile instrumentation. This greatly simplifies the wiring connection and experimental set-up, and also reduces potential problems in signal noise. With this strain gauge configuration, a Wheatstone bridge completion board using only two dummy precision resistors has been installed underneath the air chamber cap to complete all the strain gauge signals in a full bridge before they go out the air chamber. The calibration of the instrumented model pile was carried out by fastening the pile at one end as a cantilever, and applying dead weights at the other end. By knowing the distance to strain gauges from the dead weight, the strain gauge output signals can be calibrated against the known bending moment. As expected, a hnear calibration was obtained. By measuring the deflection at the dead weight loading point, the equivalent rigidities, EI, of the model piles were also obtained, and were shown in Table 4.2. Data Acquisition System A micro-computer based data acquisition system was used in this research. This system consists of three components: a multi-channel signal amplifier, a multi-channel analog/digital converter DT2801A card, and a I B M - P C micro computer. A l l the transducers were excited by a common power supply which was set at 6.00 volts. In the lateral load testing on piles, a total of 15 channels were monitored, and 12 of them were recorded on each scan. The first channel carried time reference. Transducer readings were contained in the subsequent 11 channels (8 strain gauges, 2 L V D T s , and 1 load cell). The transducer signals except the 2 L V D T ' s were all amplified at a gain of 1000 by the amplifier before they reached A / D converter through a ribbon cable. The DT2801A A / D converter has 12 bits in its accuracy, which gives a = 4.88mv in accuracy for a ± 1 0 V bipolar configuration. The noise level has been mon-itored for each channel, and was found to be in the order of ± 5 m v at the prescribed Chapter 4. Hydraulic Gradient Similitude Testing Device 68 8 sets of bridges (need 16 S.G.; 16 dummy resistors; 32 wire leads) Figure 4.9(a) Normal Wheatstone Bridge Connection v 8 single ended output signals (need only 16 S.G.; 2 dummy resistors; 11 wire leads) strain gauge (S.G.) - V \ A A - dummy resistor Figure 4.9(b) Simpler Wheatstone Bridge Connection Chapter 4. Hydraulic Gradient Similitude Testing Device 69 scanning frequency in the tests. This corresponds to an accuracy of ± 0 . 2 kPa for the pore water pressure, ± 0 . 0 2 mm for the displacement, and ± 0 . 0 1 4 kg for the load. During the gravitational process, a monitoring program written in QuickBasic was used to monitor all transducer readings, especially for the three pore pressure readings, in engineering units. This permitted a control on the gravitational process. However, during the actual lateral load tests on piles, a commercial software LabtechNotebook was employed to scan and record all the readings in the disk at a prescribed rate. The data acquired were in voltage changes, and were processed at the end of each test to the desired level using other data processing programs written in F O R T R A N that will be discussed in Chapter 7. Chapter 5 A Simulation of Downhole and Crosshole Seismic Tests in HGST Device 5.1 Introduction In soil dynamics and geotechnical earthquake engineering, the shear modulus of soils at small strain level ( < 10 _ 4 % ), often called Gmax, is one of the important param-eters to be determined. It is often used to directly evaluate dynamic soil structure interaction response at small strain that occurs in machine foundation problems, or is used as an initial reference value for large strain problems that arise due to earthquake loading. In the laboratory, the dynamic shear modulus is usually obtained from a resonant column test in which a cylindrical soil sample is subjected to torsional vibration with a resonant frequency proportional to Gmax. For practical applications, the relevance of the measurement by this technique depends upon the extent to which the sample represents the actual field condition, which is usually difficult to duplicate especially for granular material such as sands. The resonant column test has been more fre-quently used to study the various factors affecting Gmax, such as the ambient stress state and soil void ratio. From these studies, various empirical formulae have now been developed to describe these effects. More recently, the interrelationships be-tween Gmax and stress state under different stress paths have been studied by Stokoe et al (1985) using a large true triaxial cell. In the field, Gmax, can be derived from measurement of shear wave velocity, Vs, 70 Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 71 using the equation: Gma*=PVl2 (5.1) where p is the bulk density of soil mass. Crosshole and downhole tests including seismic C P T (cone penetration tests) are now commonly used to determine the insitu shear wave velocity (Stokoe and Woods, 1972, Stokoe and Hoar, 1978, Woods, 1978 and Robertson et al, 1984). These methods employ procedures for generating a po-larized shear wave in one borehole, or at the surface, and measuring the time for the shear wave to travel a known distance to a sensor in another or the same borehole. However, large differences have been reported between the shear wave velocity ob-tained from laboratory resonant column tests and insitu downhole and crosshole tests (Stokoe and Richart, 1973, Anderson and Woods, 1975, Woods, 1978 and Arango, et al 1978). The shear wave velocities from insitu measurements are commonly twice the values from laboratory tests. Soil disturbance, aging and differences in bound-ary conditions have been suggested as factors to account for this large discrepancy between field and laboratory test results. Therefore, it is desirable to perform insitu downhole and crosshole shear wave tests under more controlled conditions, so that the interrelationships between the stress state and shear wave velocity developed from the conventional laboratory techniques can be compared with field conditions. In this chapter, a method of simulating downhole and crosshole tests on sand in a laboratory model scale is presented. The downhole and crosshole shear waves are generated and received by piezoceramic bender elements, while the insitu stress conditions (Ka condition) are simulated by using the Hydrauhc Gradient Similitude method. With this technique, the soil state and field stress conditions including Ka values can be controlled and measured. The primary objectives of the testing program are as follows: Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 72 • to develop a technique of using piezoceramic bender element to measure Gmax in the model soils that will be used later in the pile tests presented in Chapter 8; • to examine the validity of existing empirical equations for Gmax in terms of field stress condition; • to compare the downhole and crosshole shear wave velocities to evaluate the soil structure anisotropy; • to examine the possibility of using shear wave velocity to determine horizontal stress (or K0 values) in the field. In addition, an application of this kind itself, although in its infancy, will illustrate the usefulness of the hydrauhc gradient similitude method in studying certain soil dynamics problems. 5.2 Review of Existing Empirical Equations 5.2.1 Stress Level Effects Various forms of empirical relationships for Gmax of sand based on the results of laboratory tests have been proposed by a number of researchers. These equations generally include factors to account for grain shape, void ratio or density, and stress state or level. Based upon early resonant column test data, Hardin (1978) proposed the following equation: Gmax=A.F(e).Pa-(^)m (5.2) where A is a factor related to particle size and shape, F(e) is a function of void ratio, Pa is the atmospheric pressure, m is the stress exponent, and crm is the mean effective normal stress, i.e. crm — c r ' + c ^ + 0 ' 3 . Values of A , F(e), and exponent m as proposed Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 73 by various researchers are presented in Table 5.1. As Eq.(5.2) suggests that Gmax is a function of mean normal stress level, this formula is called the mean normal stress method. A modified version of Hardin's equation proposed by Yu and Richart (1984) called the average stress method suggests that the shear modulus is dependent upon the average stress within the plane of wave travel, i.e. Gmax = A • F(e) • Pa • (5-3) where aav = A A + ° T ; rra is the stress component in the wave propagation direction, and crp is the stress component in the particle motion direction. In Eq.(5.3), A and F(e) have the same values as in Eq.(5.2). A n alternative equation called the individual stress method was first proposed by Roesler (1979) based on his tests on a cubic sample upon which three principal stresses were applied independently. His results also suggested that it is not the mean normal stress, but the individual stress components in the plane of wave travel, which have the major influence on the shear modulus. His relation is expressed as follows: Gmax = A • F(e) • p^-ma-mP) . ama . ^  (54) From a dimensional analysis, it can be shown that ma + mp = m, which is also Table 5.1: Suggested Values and Equations for A and F(e) Sands A F(e) m References Clean Rounded 700 (2.17-e)2 0.5 Yu and Richart (1984) Clean Angular 326 (2.97-e)2 ° r (0.3+0.7e2) 0.5 Yu and Richart (1984) Clean Sand 320 (2.97-e)2 (1+e) 0.5 Hardin and Drnevich (1972) Clean Sand 625 1 (0.3+0.7e2) 0.5 Hardin (1978) Clean Sand 900 (2.17-e)2 (1+e) 0.38 Iwasaki and Tatsuoka (1977) Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 74 supported by test results (Roesler, 1979). Shear wave velocity measurement by Stokoe et al (1985) in large triaxial device supports Roesler's equation, but with ma — mp = m/2 . Interpretation of some resonant column test results in terms of Roesler's equation (Yu and Richart, 1984, and Stokoe et al, 1985) also suggests that ma = mp = m/2 . In fact, as the shear wave propagates through a soil element, it imposes a set of complementary dynamic shear stress both on a a and a p planes in the directions as shown in Figure 5.1. Since the same amount of shear stress is applied on both a a and <rp planes, it is reasonably to expect that the stress components o~a and a p have the same degree of influence on the shear wave velocity. This leads to the conclusion that mo = mp = m/2 . Based on this consideration, Eq.(5.4) is modified as: G m a x = A . F ( e ) . P 0 p ^ J (5.5) The predictions from these three empirical equations will be compared with test data in the sections that follow. 5.2.2 Stress Ratio Effects In the actual field condition, soil is generally subjected to anisotropic stress state, i.e., a a and a p are not generally the same. The stress ratio defined here as C \ j a 3 in the plane of wave travel may affect the shear wave velocity. In the laboratory, stress ratio effects have been studied by some researchers using different testing devices. Tatsuoka et al (1979) measured the shear modulus of sand under various triaxial stress conditions with a torsional shear device. Their result, as shown in Figure 5.2(a), indicates that stress ratio does affect the shear modulus. The effect is more significant in triaxial extension as compared to triaxial compression state. More recently, Yu and Richart (1984) presented a comprehensive study using the resonant column test, and showed that at high stress ratios, Gmax is reduced by 20% ~ 30%. No significant Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests Figure 5.1: Stress Condition For Downhole and Crosshole Tests Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 76 reduction occurs for stress ratio less than two. They also suggested that there is little difference in stress ratio effect between the compression and extension stress states. Their data as shown in Figure 5.2(b) were fitted by the following equations, i.e: Gmax = A.F(e)-P™*°J ( l - 0 . 3 i C 5 ) (5.6) Gmax = A • F(e) • P ° ' 5 a°26 cr°- 2 5 (1 - 0.18-K^) (5.7) where H - i K - = ( i f ^ ( 5 - 8 ) \az)max In this chapter, the possible stress ratio effects on the downhole and crosshole tests will be examined by performing shear wave velocity tests along Ka loading and unloading paths in which Ka ranges between 0.45 and 2.5. 5.3 Testing Equipment and Procedure 5.3.1 Bender Elements The piezoceramic bender element was first introduced by Shirley (1978) for generating and receiving shear waves in laboratory testing. The bender element consists of a sandwich of two thin piezoceramic plates rigidly bonded together. The polarization of the ceramic material in each plate and the electrical connections are such that when a driving voltage is applied to the element, one plate elongates and the other shortens. If one edge of the element is securely mounted into a fixed reference, the element protruding into the specimen as a cantilever will deform in the shape as shown in Figure 5.3. The surrounding soil particles will move in the same direction as the tip of the element, thus generating a shear wave in soil which propagates in a direction parallel to the length of the elements. The element can also be used as a receiver, i.e. when a mechanical vibration acts on the element, one layer of the element will be in tension, while the other is in compression, thus resulting in Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 77 o CD 1.2 1.0 0.8 0.6 T0Y0URA SAND -(Saturated) - x O"0= l.Okgf/cm / = 5 x i o " 3 ay / cra G ' - Shear Modulus at Stress Ratio larger than one G o - S h e a r Modulus at Stress Ratio equals one Figure 5.2(a). Stress Ratio Effects from Tatsuoka et al (1979) (a) : 1 .. • o o 0) d CD d d to o"0 0.2 0.4 0.6 0.8 I Normalized stress ratio K, .0 0.2 0.4 0.6 0.8 1.0 Normalized stress ratio K„ SAND OTTAWA BRAZIL TOYOURA COMPRESSION • • A EXTENSION X x SAND OTTAWA BRAZIL TOYOURA COMPRESSION • • A EXTENSION x x (a) Data reduced by Average S t ress Method (b) Data reduced by Individual Stress Method Figure 5.2(b). Stress Ratio Effects from Yu and Richart (1984) Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 78 wave propagation direction soil particle vibration direction soil specimen piezoceramic bender bearing plate + : Figure 5.3: Cantilever Deformation Mode of Bender Element Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 79 an electrical signal which can be measured through the wire leads connected to the bender. One of the difficulties in using bender elements is that the bender element is a high impedance device and can not be exposed to moisture as this will electrically short the transducer. Thus, in the tests an epoxy coating was used on the bender element, and a sihcon rubber coating on the wire lead connection to prevent intrusion of water. Piezoceramic bender elements have been used by Shirley and Hampton (1978) for shear wave measurements in laboratory sediments, and by Schulthesis (1981), (1983), Hamdi and Taylor Smith (1982) in oedometer and triaxial apparatus to measure the shear wave velocity in soil specimens. Evaluation of bender element and comparison of Gmax so obtained with those from resonant column tests has been presented by Dyvik and Madshus (1985). Finn and Gohl (1987) used bender elements in centrifuge test to obtain Gmax profile of soil in flight. Herein, the use of bender elements is extended to hydraulic gradient simihtude tests to simulate downhole and crosshole seismic tests under different stress levels. 5.3.2 Simulation of Downhole and Crosshole Tests Bender elements were assembled along the length of two aluminum rods (diameter of 3/8") to simulate downhole and crosshole tests. For downhole shear wave measure-ment, an array of six bender elements rigidly mounted on small bearing plates was connected to a rod simulating the downhole condition, as shown in Figure 5.4. The position of these bender elements can be changed by thread screws. The position and alignment of the receiver elements relative to the source element are designed based on a theoretical consideration of eliminating the near field wave effects (Aid and Richards, 1980) and obtaining a pure shear wave motion in the measurement (See Appendix D). The top bender element is installed near the sand surface with its tip down, and is used as a shear wave source during the tests, while the rest of the Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 81 elements are installed within the soil specimen with their tips facing up toward the source element. To simulate crosshole tests, two elements are assembled at the same elevation but on different rods with the source element at the D H rod and the receiver element at the C H rod as shown in Figure 5.4. In order to prevent blockage of water flow, these two elements are aligned vertically, thus they generate and receive an SH wave within the horizontal plane. This is similar to the crosshole test by a torsional shear wave source in the field (Hoar and Stokoe, 1978). According to the hydrauhc gradient similitude principle, a prototype will be simu-lated by a 1/n scaled model with n = N, i.e. the stresses (including dynamic stresses) at homologous points of model and prototype are equal, and the scaling factors for linear dimension and time are the same. This leads to the result that the scahng fac-tors for shear modulus and shear wave velocity are both unitj'. Thus, the shear wave velocity measured under different hydrauhc gradients at a given depth in a model can be considered to directly give the shear wave velocity at the homologous depths in the prototype. However, in this study, the model test will be used to develop a data base from which some current empirical equations and understandings of stress effects on shear modulus can be evaluated. Thus, the model test itself will be examined directly without referring to any prototype scale. 5.3.3 Sand Tested and Sample Preparation The sand used in the tests is a uniform rounded Ottawa sand as described in Chap-ter 3. The soil preparation method employed in this study is the 'quick sand' technique developed by Yan and Byrne (1989) and has been described in Chapter 3. Thus, for each test, fresh sample was prepared using the same sand. During sample preparation, the top cap platform and air chamber cylinder are Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests ... 82 all removed, and replaced by an open-ended plexiglass extension box. The drainage lines from the bottom water circulation chamber are closed and water is filled up to the top of extension box. A given weight of dry sand is then rained through • the water uniformly. After the water table is lowered down to the sand surface, a controlled upward seepage gradient was applied by pumping water into the sample from the bottom, causing the sand sample to expand and to form a loose slurry state. Typically, the sand sample during the slurry state would expand up to 60% of its original volume. When the sample is in the slurry state, the D H and C H simulating rods with ben-der elements are lowered down into the sample vertically, and then fastened against the extension box with a plastic brace. The upward gradient is then turned off and the sand particles are allowed to settle under their self-weight. The sand used is uniform, and no segregation was observed. After the sedimentation process is complete, the water table is lowered again and the sample is then densified by tapping the base and sides of soil container with a soft hammer. The soil density is controlled by measuring the average sand surface height against a reference height. After a given sample density is reached, the top extension box and extension rods are removed, and the top cap platform and air chamber cylinder are carefully installed. After this stage, the hydrauhc gradient test can commence. It has been shown by Yan and Byrne (1989) that soil samples prepared by the above 'quick sand' technique are uniform with stress-strain response similar to samples formed by the water pluviation method (Vaid and Negussey, 1986). Shear wave measurements in this study also support these findings. As shown in Figure 5.5, the shear wave velocity profile measurements from down-hole tests in two dense sand samples prepared using the above technique are repeat-able. Figure 5.6 shows shear wave velocities measured from crosshole tests in loose Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 83 Gmax (MPa) 0.0 50.0 100.0 150.0 O.o <k' ' ' 1 ' 1 1 ' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ' 1 1 1 1 1 o o o D CO C L CD 20.0 Ct) D\ 5.0 H io.o H 15.0 H 25.0 J o o o o o Test #1 D O D D D Test #2 o • to N = 1 'I cb N = 60 \ \ a \ \ \ 6 Figure 5.5: Distribution of Gmax in Dense Sand During Hydraulic Gradient Tests measured from Downhole Tests Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 85 soil specimens with different crosshole orientation. It is seen that the shear wave velocities travelling within horizontal plane but in different directions are generally in good agreement. This indicates that the soil samples prepared are quite uniform in density and the results are repeatable. 5 .3.4 Testing Series and Procedure In the testing series, the hydrauhc gradient was incrementally increased from 0 to 70, then decreased from 70 to 0. During this loading and unloading sequence, the lateral stress was measured and K0 value calculated for the soil deposit. Under a given hydrauhc gradient, D H and C H tests were performed independently in order to prevent any wave interference between the D H and C H tests. The source elements were excited continuously with a ± 1 5 volts, 10 Hz square wave which was generated from a function generator. The small amplitude bending of the source element under the continuous impulses generated the downward or horizontal SH shear waves as required. The shear waves were picked up by each of the receiver elements. The shear wave signals were amplified and then sent to an oscilloscope. The digital oscilloscope, model NIC-310 from the Nicolet Instrumentation Co. at Madison, Wisconsin, was employed to monitor and record the outputs from the bender elements. To determine the shear wave velocity, the time lag between the source element and each receiver element, i.e. the first arrival time for each receiver, was monitored and recorded in the oscilloscope as illustrated in Figure 5.7. The interval shear wave velocity was then calculated from the element separation distance and the interval travel time between the elements. The interval shear wave velocity so obtained is assumed to represent the shear wave velocity at the mid point between the elements considered. Most of the test data presented below were obtained from the tests on loose sand Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 86 Figure 5.7: Setup for Measurement of Shear Wave Velocity Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 87 (DT = 30%) with a limited number of data on dense sand (DT = 75%). 5.4 Results and Discussion 5.4.1 Horizontal Stresses or KQ values The variations of lateral total stress measured by the L A T P and pore water pressures measured at the top and mid height of the soil specimen during the K0 loading and unloading cycle are shown in Figure 5.8. As shown in the figure, the pore water pres-sure at mid height of the soil specimen (pwp#2) varies linearly with the apphed water pressure at the sand surface (pwp#l) during both loading and unloading phases, i.e. P2 = aPi (5.9) where Pi and P2 are water pressures at top and mid height of sample, and a is the proportional factor as defined in Figure 5.8. From Eq.(4.3) and (5.9), the hydrauhc gradient within the sample becomes: i = ^ + ^ = > f t (5.10) where 7^ is unit weight of water, H12 is the distance between transducer p w p # l and pwp#2. ' From Eq.(5.10), the hydrauhc gradient is hnearly increased or decreased with the water pressure apphed at the sand surface. The effective vertical stress a'v at any depth is given as : c'v = (*7u> + l')z (5-n) The total lateral stress measurements during a loading and unloading cycle, as shown in Figure 5.8, are higher than the corresponding water pressures measured at the same point. The difference between them is the effective horizontal stress at the mid height of the sample. During the loading phase, the lateral total stress varies Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 89 linearly with the applied water pressure. This indicates that the horizontal effective stress increases linearly with hydrauhc gradient, thus giving a constant KQ during ID loading. However, during the unloading phase, the response of the lateral stress is nonlinear, giving a nonlinear variation of KD during ID unloading. The variations of KD values with the hydrauhc gradient similitude scale factor, N, during loading and unloading phases are shown in Figure 5.9. As shown in Figure 5.9, the K0 value remains essentially constant in the loading phase. However, during the unloading phase, K0 increases as the scale factor, N, decreases. When the scale factor is reduced from the peak value of 70 to about 20, K0 increases from 0.45 to unity and the stress state becomes isotropic. Further reducing the hydrauhc gradient in the test to zero (i.e. corresponding to N — 1) brings KD close to a passive extension failure condition. During the loading phase, the soil deposit is in a normally consolidated state. At this stage, the (K0)NC values measured can be compared with Jaky's empirical formula (Jaky, 1944): (KD)NC = 1 - sin(j>' (5.12) where (/>' is the peak friction angle. While in the unloading phase, the soil deposit is in an over-consohdated condition. The over-consolidation ratio, OCR, is defined as: OCR = (5.13) + 7' ilw + 7' where (o-'v)max and imax are the maximum effective vertical stress and applied hy-drauhc gradient, a'v and i are the correspondent current values. For the over-consolidation stage, the measured K0 values can be compared with Schmidt's empirical equation esn|EA-o>i Figure 5.9: Ka Values during the Loading and Unloading Phases Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 91 (Schmidt, 1966), i.e. (K0)ocR = (K0)NC-(OCR)m (5.14) where m = sincf)1. The comparison of measured K0 values with those calculated from Eqs.(5.12) and (5.14) is shown in Figure 5.9. It can be seen that the predictions from the empirical equations are generally in good agreement with the measurements. The friction angle used in the predictions was obtained from conventional triaxial test results on the same sand as described in Table 3.1 of Chapter 3 or Yan and Byrne (1989). The K0 values were measured at the mid height of sample and are assumed to be constant with soil depth. This is considered a reasonable assumption since the O C R is always constant with depth in the tests (Eq. 5.13) and is used later to calculate the effective horizontal stress at different elevation for the shear wave bender element tests. 5.4.2 Typical Results of Shear Wave Velocity Measurement Typical shear wave records received by downhole bender elements at different depths in loose sand at a given hydrauhc gradient are shown in Figure 5.10. The shear waves and their arrival time at each receiver bender element are clearly identified. It is also seen from the figure that the amphtude of the shear wave attenuates with depth in the soil deposit as depicted by the decreasing vibration output signal with increasing depth. If these bender elements are properly calibrated, it may be possible to obtain damping values from these shear wave measurements (Sanchez-Salinero et al, 1986). Shear waves propagating through the soil deposit at different levels of hydrauhc gradient in a crosshole test are shown in Figure 5.11. As shown in the figure, the arrival time of the shear wave from the source element decreases as the hydrauhc gradient increases, clearly indicating the dependency of the shear wave velocity upon the stress levels in the soil deposit. Again, for the crosshole tests, the arrival times of the shear waves are also clearly identified from the traces. Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests ... 92 -1 H -1.5 0.5 0 3 O -1 --1.5 0.5 0 3 D. 3 o -1.5 0.4 0.8 1.2 1.6 0.4 0.8 1.2 1.6 Ta R2 i=70 0.4 0.8 1.2 1.6 0.4 0.8 1.2 1.6 2 Time after Triggering (ms) 2.4 2.8 2.4 2.8 2.4 2.8 Ta R3 i=70 2.4 2.8 Figure 5.10: Shear Wave Records at Different Depths (Loose Sand Dr = 33%) Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 93 20 15 H ^ 1 0 - 1 -co c ja to 3 a. "3 O 5 H 0 -5 --10 --15 -20 1.1 0.9 -c co 0.3 a 0.1 O -0.1 -0.3 -0.5 0.6 Triggering Signal at R3 Loose Sand Dr=33% 0.2 0.4 0.6 0.8 Rec Ta eived Signal at R4 \ A Hydraulic Gradient i=13 0.2 0.4 0.6 0.8 Received Signal at R4 Hydraulic Gradient i=60 0.2 0.4 0.6 Time after Triggering (ms) 0.8 Figure 5.11: Typical Example of Shear Waves Received under Different Hydrauhc Gradients Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 94 In order to confirm that the waves generated from the impulsive bending of the source element and the waves received by the receivers are mainly shear waves, a voltage of positive polarity was applied to the source element to bend first in one direction. The voltage polarity was then reversed causing the element to bend in the opposite direction. As shown in Figure 5.12, the receiver gave positive or negative voltage changes in response to different direction of impulsive bending in the source element. This confirms that the waves generated and received by bender elements in the current configuration are mostly shear wave, which is in agreement with Dyvik and Madshus (1985). Dyvik and Madshus (1985) also showed that the effective travel distance between the source and receiver elements is their tip distance. Thus in the present studies, the tip distance between the bender elements is used to calculate the shear wave velocity. Typical profile of Gmax versus depth in dense sand determined by the downhole method under a hydrauhc gradient of 80 is shown in Figure 5.13. The measurements are compared with empirical equations based on the mean normal stress method, the average stress method and the individual stress methods, using Hardin and Drnevich recommended A and F(e) values for clean sand, as given in Table 5.1. As shown in Figure 5.13, the above three types of empirical equations gave different predictions with the individual stress method yielding the stiffest profile, the average stress method giving the softest prediction and the mean normal stress method in between. The individual stress method is in best agreement with the test data. The differences, however, are not that large. This indicates that the Gmax derived from resonant column tests in the laboratory and reflected in the empirical equations are in reasonably good agreement with those measured from the model seismic downhole tests. The large difference reported between Gmax values from resonant column tests on 'undisturbed' samples and insitu shear wave velocity tests is likely due to both disturbance and aging effects. ) Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 95 at R 4 t r o m S2 O N - 1 to«tf2 Dr—BC.*: 0 5 C 0 > Times (ms) at R4 from S2 O N - 6 0 D r - B O X Ttmas (ms) Figure 5.12: Polarization of the received Shear Wave Signals Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 96 Gmax (MPa) 0 0 4^ 20 40 i i i i 60 80 i i i 4 -_ 8 o u i 12 w o QJ m £ 16-5T Q 20 24 1 T E S T DATA INDIVIDUAL S T R E S S M E A N N O R M A L S T R E S S A V E R A G E S T R E S S 100 120 i i Figure 5.13: Prediction of Shear Modulus Profile from Various Empirical Equations Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 97 5.4.3 Downhole and SH-Crosshole Shear Waves along KD Paths a). Stress Level Effects The variation of shear moduli, Gmax, with stress levels in downhole and crosshole conditions can be examined by plotting the shear wave velocities measured at a given depth under the different hydrauhc gradients. Figure 5.14 shows the shear wave velocity from the downhole test in dense sand plotted against the hydrauhc gradient scale factor, JV. It can be seen from the figure that during the loading phase, the variation of shear wave velocity follows a straight line in the log-log plot with a slope of 0.22. This indicates that the stress level effects on the shear wave velocity in the loading phase can be fitted well by a power function. Figure 5.15 shows the measured shear wave velocity versus JV for both downhole and SH-crosshole tests in loose sand at one depth. Again, the loading paths follow straight lines, both with slopes of approximately 0.27. By comparing Figure 5.14 and 5.15, it can be seen that the slopes of the linear variations for the loose sand are slightly higher than that for the dense sand. This may be due to a larger volume change in the loose sample as compared to that in dense sample during the loading phase as the measured Vs values have not been corrected for void ratio changes. The slopes obtained, which represent the stress level effects, generally agree with the values determined by previous testing methods such as resonant column tests. It should be noted that a slope of 0.22 would correspond to an exponent of 0.44 for Gmax relationship. As shown in Figure 5.14, 5.15, the shear wave velocities in the unloading phase are higher than those during the loading phase. Furthermore, the variation of shear wave velocity in unloading is not linear with the scale factor, JV, in the log-log plot. The variation in KD upon unloading significantly affects the measured shear wave velocity. Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 98 Figure 5.14: Measured Shear Wave vs. Hydrauhc Gradient Scale Factor, (at given depth, Dr = 75%) Figure 5.15: Loading and Unloading Effects on Downhole and Crosshole Shear Wave Velocity Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 100 Figure 5.15 also gives a comparison of the downhole and SH-crosshole shear wave velocities measured at the same elevation. It is seen that during the loading phase, the variations of downhole and crosshole shear wave velocities parallel each other. The downhole tests give a higher shear wave velocity as compared with the SH-crosshole tests under the same hydraulic gradient. The difference shown is about 16%. This difference may be partly due to the difference in the stress state effect on the waves propagating in vertical and horizontal planes, and partly due to the inherent anisotropy effect associated with the sample. The stress state effects on the shear wave propagation can be more clearly iden-tified by examining the downhole and SH-crosshole shear wave velocities during the unloading phase. As shown in Figure 5.15, the downhole shear wave velocity decreases at a faster rate with applied hydrauhc gradient as compared to that in SH-crosshole test, although in both tests the mean normal stresses are the same. At the initial unloading stage, the downhole shear wave velocity is higher than the crosshole. As the hydrauhc gradient reduces, the two curves approach each other, and start to cross over at about N = 4. At the end of unloading, the crosshole test gives a higher shear wave velocity than does the downhole test. These observations tend to support the concept that the shear wave velocity depends upon the stress components within the plane of wave travel rather than the mean normal stress level as suggested by the early studies (Hardin and Richart, 1963, and Hardin and Drnevich, 1972). Examination of the velocity ratios from the downhole and SH-crosshole tests dur-ing loading and unloading reveals that the shear wave velocity is more directly related to the individual stress components in the wave propagation and the particle motion directions, i.e. the individual stress method suggested in Eq.(5.5) rather than the average stress method as in Eq.(5.3). By applying Eq.(5.2), (5.3), (5.5) to the downhole and crosshole tests, and assum-ing the downhole velocity measured represents the measurement at the mid-height Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 101 point of the interval, which is at the same depth as the crosshole test, the following relationships between shear wave velocity and stress state are obtained: (1). Mean Normal St ress Method: {V.)D = C D M (K)c = CcW for downhole for SH-crosshole where: On = 1 + 2KC (2). Average Stress Method: (V.)D C D <rv + crh\n {V.)c = C c ( '(Th+CJhV = CC^.K: for downhole for SH-crosshole (3). Individual Stress Method: = CD(crv)n {K0)NL2 for downhole (Ve)c = C c W 2 W = Cc(o-v)n (K0)N for SH-crosshole (5.15) (5.16) (5.17) (5.18) (5.19) (5.20) By assuming that the exponents in the downhole and crosshole tests are the same, the shear wave velocity ratio between the downhole and SH-crosshole tests becomes: (1). Mean Normal Stress Method: (Va)D CD (V.)c Cr (5.21) Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 102 (2). Average Stress Method: (VS)D C D ( l + K0\n (V.)c Cc V 2K, (3). Individual Stress Method: (5.22) TVyc = c^{K°) (5-23) where ^ represents the cross anisotropy of the soil sample, and is equal to the downhole and crosshole velocity ratio when soil element is in an isotropic stress state, i.e. K0 = 1. The variations of shear wave velocity ratio with K0 during loading and unloading as derived from Eq.(5.21), (5.22) and (5.23) are shown in Figure 5.16. Based on a trial-and-error method, it was found that ^ = 1.08 and n = 0.24 give the best fit of the test data. This may indicate the average structure anisotropic effect is in the range of 10% between the downhole and crosshole, which is in agreement with the structure anisotropic effect reported by Lee and Stokoe (1986). Thus, based on Eq.(5.1) the shear moduli, G m a i , will differ by about 20% between vertical and horizontal planes while remaining basically constant in all horizontal directions (see Figure 5.6). It can be seen from Figure 5.16 that neither Eq.(5.21) nor Eq.(5.22) can predict the trend of decreasing velocity ratio with increasing K0 values during the unloading path. In fact, Eq.(5.21) shows an independency of the K0 values, whereas Eq.(5.22) gives an opposite trend of velocity ratio variation with K0. The trend of shear wave velocity ratio variation with K„, can only be correctly predicted by Eq.(5.23), i.e. the individual stress method. This indicates that the interrelationship between the shear wave velocity and the stress state is better represented by the individual stress method. However, as will be discussed below, the existing equation based on the individual stress method may need to be modified to take account of stress ratio effects for the downhole tests. Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 104 b). Stress Ratio Effects If the shear wave velocities from downhole and SH-crosshole tests are fully de-pendent upon the individual stress components as discussed before, the test data in loading and unloading paths will be similar when they are plotted according to Eqs.(5.19) and (5.20). In Figure 5.17, the shear wave velocities shown in Figure 5.15 from SH-crosshole and downhole tests are replotted against the combined stresses, <ra • o-p, in the plane of wave travel based on the individual stress method. As shown in Figure 5.17(a), the shear wave velocity data in loading and unloading paths from SH-crosshole tests basically merge together, as expected, with a single line. This indicates that for SH-crosshole tests the shear wave velocity paths during loading and unloading phases are the same, and are fully represented by the individual stress components alone. However, as shown in Figure 5.17(b), for the downhole tests the shear wave velocity data in the unloading path does not collapse to the corresponding loading path as suggested by Eq . (5.19). Instead, they rise initially, and then curve back to the loading path. These different observations between the downhole and SH-crosshole shear wave velocity during loading and unloading paths can be explained as below by considering the effects of stress ratio in the plane of wave travel. In the SH-crosshole test, the wave travels in a horizontal plane. Both stress com-ponents in wave propagation and particle motion directions are horizontal stresses, i.e.: Oa = °~h Op = Oh Therefore, the stress ratio, ( ^ ) h , defined in this horizontal plane remains constant during the loading and unloading cycle, and equals unity, i.e.: Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 105 Figure 5.17(a) SH-Crosshole Shear Wave Velocity vs. the Combined Stress in the Wave Travelling Plane u _o s> > o > o 3 c" 100 • o Qfifisp Downhole Test — loading path MOH Downhole Test — unloading poth y (Vs)„ «. 56.40 (CvOO 1 - ) 1 1—I I I I I l| 1 1—I I l l l l j 1 1—I I I I I 11 1 1—1 M i l l 1 10 100 1000 10000 Combined Stress in Wave Travelling Plane - 0 Y » 6h(kPa»kPa) Figure 5.17(b) Downhole Shear Wave Velocity vs. the Combined Stress in the Wave Travelling Plane Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 106 There is therefore no stress ratio effect on the shear wave measurement at any stage of loading and unloading cycle. Shear wave velocity is fully represented by Eq.(5.20) and depicted by a single line in Figure 5.17(a). The observations in Figure 5.17(a) are in good accord with this concept. However, for the downhole tests, the shear wave travels in a vertical plane, and the significant stresses associated with wave propagation direction and particle motion direction are the vertical and horizontal stresses, respectively. In this case, the stress ratio, (f^)i>) defined in the vertical plane changes from a constant value during the • loading phase to varying values while in the unloading phase. As shown in Figure 5.18, during the loading phase, soil elements are in a normally consolidated state, the stress ratio in the vertical plane is independent of hydrauhc gradient i.e.: ^). = a- = a- = {±-W. (5.25) However, during the unloading phase, the stress ratio first reduces from the value of (•£-)N.C. f ° unity when hydrauhc gradient reduces from the peak value of 70 to 20. In this stage, the Ka value rises from 0.45 to unity, and the vertical effective stress is still the major principal stress, i.e. o~v > o v When the hydrauhc gradient is further reduced to zero, the major principal stress direction suddenly rotates 90° , the horizontal effective stress becomes the major prin-cipal stress, i.e. > av. In this stage, the stress ratio rises again and is given by: (-)» = - = {K0)o, (5.26) with (K0)oc larger than unity. It has been observed by Tatsuoka et al (1979) and Yu and Richart (1984) that an increase of stress ratio in the plane of wave travel will reduce the measured shear modulus (or shear wave velocity). Therefore, during the unloading test, the variation of stress ratio in the vertical plane as described in Figure 5.18 will result in the Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 107 Figure 5.18: Variation of Stress Ratio in Vertical Plane with Hydrauhc Gradient during Loading and Unloading phases Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 108 nonlinear loop in the downhole shear wave velocity path as shown in Fig. 5.17(b). This indicates that for downhole tests, the interrelationship between shear wave velocity and stress state can not be satisfactorily represented by Eq . (5.19). Stress ratio effects need to be considered. The amount of stress ratio effects on the downhole shear wave velocity measure-ments may be evaluated by comparing the measurement data with those predicted by Eq.(5.2), (5.3) and (5.5) which represent no stress ratio effects. The ratio of the measured and predicted shear wave velocity, ^/J" , are shown in Figure 5.19. It can be seen from the figure that the differences among Eq.(5.2), (5.3) and (5.5) are not significant, they all show similar trends. The shear wave velocity reduces with the increase of stress ratio (or departure from an isotropic condition). However, the stress ratio appears to have more effects when the major principal stress is the horizontal stress, i.e. — > 1. This is in accord with the observation by Tatsuoka et al (1979). The ratio of measured to predicted shear wave velocity decreases by about 8% in the region where ^ > 1. In practice, the crosshole tests usually employ a vertical impulsive source (Auld, 1977, Stokoe and Woods, 1972), which generate S V shear waves with particle motion in the vertical direction. The significant stress components with wave propagation and particle motion are the same as in the downhole test. In fact, this may be the theoretical reason why the impulsive crosshole test results have been often found to be similar to the corresponding downhole test results in the field (Wilson et al, 1978 and Robertson et al, 1984). Therefore, it is reasonably to expect that the stress ratio effect discussed above for the downhole test would also apply to the impulsive crosshole tests. However, as shown in Figure 5.19, for the normally consolidated or slightly overconsohdated soils, the effects are small, and may be easily masked by the test error. Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 109 d(SA)/w(SA) Figure 5.19: Stress Ratio Effects on Shear Wave Velocity During K0 Unloading Phase Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 110 5.4.4 Application of Shear Wave measurement to Estimate Insitu KD Values Recently, there has been an attempt to apply shear wave velocity measurement to estimating insitu K0 values (Lee and Stokoe, 1986). The procedure involves measuring shear wave velocity insitu, then employing one of the interrelations between the shear wave velocity and stress state to back calculate the K0 value. By doing so, it is hoped that the disturbance problems associated with current penetration type of insitu test methods for determining K0 can be circumvented, as the shear wave velocity measurement has been found to be less affected by local soil disturbance around boreholes (Hoar, 1982, Lee and Stokoe, 1986). A n attempt to estimate K0 values from shear wave velocity ratio obtained in the hydrauhc gradient model tests is presented and evaluated herein. In principle, once the relationship between shear wave velocity and stress state is known, back calculation of the stress state is possible from the insitu wave measure-ment. However, in actual practice, it may involve some difficulties. In view of the various types of existing relations available, the first question is which formula should be used. From the preceding discussions, it seems that the equation based on individual stress method should be used to back calculate the K0 value. If Eq.(5.5) is used directly, however, the determination of K0 from shear wave velocity would require independent measurements of insitu soil void ratio, grain shape, etc. These measurements are difficult in the field. Alternatively, if a downhole (or S V crosshole) and a SH crosshole test are performed simultaneously at a given location, K0 values may be estimated from the velocity ratio between these two tests, as suggested by Eq.(5.23), i.e.: K \CD (Vs)D ° [Cc1(Vs)c This procedure will eliminate the necessity to determine the insitu void ratio. (5.27) Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 111 As shown in Eq.(5.27), the estimation of K0 from shear wave velocity ratio involves two parameters, namely; 1. - cross anisotropy coefficient, which relates waves travelling in different planes; 2. n - exponent on the stress level. From the downhole and crosshole test data, it was found that: I = 1 0 8 n = 0.24 Based upon these values, KD values are predicted using Eq.(5.27) and the measured velocity ratio. The comparisons between predicted and measured K0 under different hydrauhc gradients are shown in Figure 5.20. As shown in the figure, the method gives a reasonably good prediction of KD in the loading phase, but not that good in the unloading phase, especially in the very low stress level. This may be related to the high sensitivity of this method. Figure 5.21 gives the results of a sensitivity study, in which ^ is varied in the range of 1.0 ~ 1.2, and n in 0.2 ~ 0.3. Although the variation of these values are relatively small, their influence on the K0 values is quite significant. It can be seen from this figure that the derived K0 value is sensitive to both ^ and n values. The effect of ^ 7 is larger than that of n. In the field application, ^ would be a difficult parameter to measure accurately. In addition, as can be expected from Eq.(5.27), K0 would also be quite sensitive to the velocity ratio • Thus, successful estimation of Kc values from shear waves will require the development of a technique to measure ^ as well as a high degree of accuracy in the measurement of {Vs)r> and (Vs)c-Reliable K0 values will be difficult to achieve. Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests ... 1 112 0.9 -0.8 -0.7 -W 0.6 H 5 0.5 -I CO CD J3 CO > o 0.4 -0.3 -0.2 -0.1 -4 H 3 H 1 H B Measured + Predicted (a) loading phase + + 20 40 60 ao + (b) s Measured unloading phase + Predicted s B + + + S + + e 20 40 60 Hydraulic Gradient Scale Factor - N Figure 5.20: Prediction of K0 from Shear Wave Velocity Ratio Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 0 -j 1 1 1 1 1 1 1 1 0.85 0.95 1.05 1.15 1.25 Velocity Ratio - (Vs)d/(Vs)c Figure 5.21: Sensitivity Analyses of K0 vs. Parameters 'n ' and ' C d / C c ' Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 114 5.5 Summary and Conclusion Shear modulus, G m a x at small strain level ( < 10~4% ) is an important parameter in soil dynamics problems. In this chapter, the results of shear wave velocity measure-ment in small model tests subjected to field stress conditions have been presented. Controlled K0 conditions including loading and unloading paths were simulated using the hydrauhc gradient similitude method, and downhole and crosshole shear waves were generated and received by piezoceramic bender elements. The lateral stress or K0 value was measured directly by a total stress transducer and pore pressure transducer. The primary purpose of this study was to carry out in-situ downhole and SH-crosshole shear wave velocity tests in a controlled stress and soil state so that existing laboratory-based empirical Gmax equations or concepts can be evaluated in terms of field stress condition. In addition, downhole and crosshole tests using bender elements provide a means to evaluate sample uniformity, cross-anisotropy, and insitu soil parameters in the model tests. Maximum shear modulus values from the shear wave velocity measurements were found to be in good agreement with those obtained from laboratory resonant column tests as reflected by the empirical equations. This suggests that the large difference reported between Gmax from laboratory tests and in situ shear wave velocity tests is likely due to both disturbance and aging effects. It was also found that although the three basic types of empirical equations all gave results that were in good agreement with those measured from shear wave velocities, the variation of velocity ratio between downhole and SH-crosshole tests with the stress level was correctly predicted only by the equation based on the individual stress method. This shows that the stress level effect on the shear modulus is best represented by consideration of the individual stresses in the wave propagation and the particle motion directions. From examination of the downhole and crosshole shear wave velocity during the Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 115 K0 loading and unloading paths, it was found that for the crosshole tests where the wave propagation and particle vibration directions were all in the horizontal plane (SH crosshole), the shear wave velocities in loading and unloading paths fell on a straight line when plotted using the individual stress method, while for the downhole tests this was not the case. This difference was found to be due to the effects of stress ratio from the stresses in the plane of wave travel. When the shear wave velocities in the unloading path were normalized with respect to a stress ratio of unity, it was found the stress ratio reduced the observed shear wave velocity, and this was in accord with the results from previous researchers. It was also found that the stress ratio effect was more significant when the horizontal stress became the major principal stress. With regards to the possible application of shear wave measurement in estimating insitu KD values, it is concluded that only the equation based on individual stress method should be applied. A n approach based upon the velocity ratio has been pre-sented and discussed. The prediction of K0 values was in a reasonably good agreement with the measurement in the loading phase, but not so good in the unloading phase, especially at low stress levels. This was thought to be due to the high sensitivity of the method to testing error. Thus, although in principle the methodology is promis-ing, reliable estimation of K0 will require high testing accuracy and either experience or measurement of the anisotropy factor. Further research is necessary before this method can be reliably utihzed in practice. From this study, it is also demonstrated that with innovative instrumentation tech-niques the hydrauhc gradient similitude method can provide an inexpensive means to calibrate in-situ testing methods, including soil dynamics problems, with which the theories for interpreting in-situ test results can be evaluated. In addition, this method can bring a bridge between laboratory soil element testing and full scale in-situ testing so that results obtained from laboratory soil element tests can be examined in terms Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 116 of field stress condition. Further studies on downhole and crosshole tests using the hydraulic gradient similitude method may consist of measuring shear modulus and damping of soils under different shear strain levels. Chapter 6 Review of Pile Response to Lateral Loads at Pile Head 6.1 Introduction Piles have been used as part of structural foundations for many decades. For many years the design of pile foundation has rehed heavily on empirical procedures and local experience. Due to the continuous need for safe and cost-effective construction of various types of massive structures at more andjnore unfavourable sites, especially in the offshore industry, much research effort is still concentrated on pile foundations despite their long time service in civil engineering. Over the last two decades, analytical methods in pile design have advanced very rapidly, which has enabled many of the traditional empirical approaches to be sub-stantiated, or in many cases replaced by more soundly based theory. However, accu-mulation of experimental data on pile foundation under different loading conditions is far behind the development of our current analytical abihty. Fundamental aspects of soil-pile interaction are still poorly understood. Soil parameters required for various analytical models have not yet been fully calibrated in a fundamental manner. Thus, engineers are still not able to design pile foundation confidently and cost-effectively. In this chapter, both the currently available methods for the analysis of vertical piles subjected to static and cyclic lateral loads and the previous experimental work are critically reviewed. Emphasis is placed on discussing the advantage and hmitation of each analytical method and its experimental base. The review is limited to the 117 Chapter 6. Review of Pile Response to Lateral Loads 118 study of laterally loaded pile response in sand. 6.2 Theoretical Studies 6.2.1 Static Response Early research on single piles was directed mainly towards estimating their static ca-pacity, implicitly assuming that the deformations will be acceptable if an appropriate factor of safety is used in determining the allowable range of loads. However, in designing pile foundations to resist lateral loads, the critical factor in the majority of cases is the maximum deflection of the piles, rather than the ultimate lateral capacity. The ultimate lateral capacity only becomes critical when a large pile deflection is allowed and developed, and the yielding bending moment of the pile is reached. For a short and rigid pile, the ultimate lateral capacity is reached when plastic failure of soil occurs along the full length of the pile, while for the. flexible pile, the ultimate condition is reached when plastic hinge forms at the maximum pile bending moment position (Broms 1964, Poulos and Davis 1980). This result is quite different from the mechanism of axially loaded pile failure, which depends entirely on soil yielding under normal circumstances. Nowadays, more attention has been focused on the lateral deflection prediction. However, a complete analysis of pile foundation under lateral loads is a very com-plicated process, requiring a 3D analysis with nonlinear stress-strain relation for the soil. For the practical application, simplifications of soil behaviour are always made in an analysis. At present, available methods of static analysis can be classified as follows accord-ing to their degrees of simplifying soil-pile interaction behaviour: • the elastic boundary element approach; • the finite element approach, and Chapter 6. Review of Pile Response to Lateral Loads 119 • the modulus of subgrade reaction approach. E las t i c B o u n d a r y E l e m e n t A p p r o a c h The elastic continuum approach developed by Poulos (1971) was the first systematic analytical study of load-displacement behaviour of piles under static lateral loading, and was summarised by Poulos and Davis (1980). This approach is based on hnear elastic theory for the soil medium, and Mindhn's solutions for the soil displacements due to a point load within an elastic isotropic homogeneous halfspace. The pile is simulated in the analysis using a vertical strip with equivalent, EI, of pile. Compat-ibility of soil and pile displacements is enforced at discrete points along the pile. The main input parameters for this method are the Young's modulus and Poisson's ratio of the soil. Results from Poulos's work have been cast in the form of design charts, and have been widely used by researchers and practising engineers. Strictly speaking, the elastic continuum solution is only applicable to small strain level with constant Young's modulus in soil which, in practice, may only occur for stiff clay deposit. For cohesionless material where the elastic modulus increases with depth, only an approximate solution can be obtained. In this analysis, soil yielding, finite depth of soil layer, soil inhomogeneity, stiffer bearing stratum, and enlarged pile base can be taken into account approximately by correction factors to the elastic solution. The correction factors depend upon the assumed magnitude and distribution of the Young's modulus, and the limiting lateral stress in soil layers. However, pile-soil slippage or separation were not addressed in these studies. The advantage of this approach is that it considers the soil as a continuum, which makes it easy to extend it to analysis of pile group problems. However, as the soil surrounding the pile exhibit a nonhnear stress-strain behaviour under the loading, an appropriate choice of Young's modulus and Poisson's ratio of soils is very difficult to select a priori. Severe soil yielding and softening at upper soil layers under the lateral Chapter 6. Review of Pile Response to Lateral Loads 120 pile loading greatly modify the equivalent Young's modulus profile for the analysis. This equivalent modulus profile depends upon the pile loading level- and soil types, so it does not resemble the initial soil modulus profile and is difficult to correlate with fundamental soil parameters. Perhaps, the best way of using this approach is to calibrate the method for each project. That is, for given project, a full scale pile load test is performed and analyzed, and the equivalent soil modulus profile is backcalculated. Then this backfigured equivalent soil modulus profile is used for analyzing other pile foundation, where piles, soils and pile loading condition are assumed to be the same. This technique has been illustrated in Poulos (1971). It has been shown that by a careful calibration, the elastic boundary element method is able to reproduce the field observations (Poulos, 1980 and 1987). From a series of analyses of full scale tests, Poulos (1974) suggests the following E„ values for cohesionless soils in the absence of full scale pile tests, as shown in Table 6.1. Table 6.1: Es for Cohesionless Soils in Elastic continuum Approach Soil Range of Values Average E„ Density of Es (kPa) (kPa) Loose 900 - 2070 1720 Medium 2070 - 4140 3450 Dense 4140 - 9650 6900 These values, however, have to be used with caution as EB used will depend upon pile deflection which is a function of soil-pile relative stiffness and pile load intensity. Finite Element Approach Chapter 6. Review of Pile Response to Lateral Loads 121 Finite element formulation are the most powerful numerical method in handling com-plex soil-pile interaction behaviour in a rigorous manner. In this approach, the sur-rounding soil media is discretized into finite elements in which sophisticated stress-strain-strength characteristics of soils and soil-pile interface may be properly simu-lated. At present, various formulations that directly simulate the whole pile founda-tion and loading sequence are available. These range from the true nonhnear 3D finite element analysis (Faruque and Desai, 1982) to elastic quasi-3D finite element model (Desai 1977, Kuhlemeyer 1979, Baguehn et al 1979 and Randolph 1981). The latter model takes advantages of the symmetry of pile problem, and expands the displace-ment field in terms of a Fourier series. Thus the solution is much more economical. Although recent developments in numerical computation and their successful applica-tion in geotechnical engineering field allow a nonhnear analysis of three dimensional problem to be carried out, current practice is still limited to using elastic finite element solution, due partly to the difficulties in selecting soil parameters for the nonhnear soil and interface models, and partly to the cost and work required for this type of analysis on a real problem. Of the elastic finite element solutions, results from Randolph (1981) are most often used in practice, as they have been expressed in a series of algebraic equations which fitted the results of a parametric study using finite element analysis. Comparisons between solutions from elastic continuum method and elastic finite element model have been made (Poulos and Randolph 1982, Poulos 1982), and were shown to be in good agreement. This is not surprising as both models treat soil as the same elastic continuum. However, the advantage of elastic quasi-3D finite element analysis versus the elastic continuum (or boundary integral) method is that the nonhomogeneous soil deposit can be rigorously handled. The input parameters required in Randolph's solution are shear modulus and Poisson's ratio of the soil deposit and their distribution along the depth. Linear distribution with depth has been assumed in the analysis. Chapter 6. Review of Pile Response to Lateral Loads 122 As was the case for the boundary element approach, the elastic parameters re-quired for the finite element method depend upon the loading intensity and pile deflec-tion level. They are difficult to determine a priori, can only be reliably obtained from a back analysis of a load test. Barton (1982) has shown that the equivalent shear modulus decreases with the increasing pile head deflection. The rate of reduction should be related to the relative stiffness of soil-pile system. T h e M o d u l u s of Soi l R e a c t i o n A p p r o a c h The modulus of soil reaction method, which may be one of the oldest methods used to analyze the soil-structure interaction problem, treats the pile as a linearly elastic beam and replaces the surrounding soil with a bed of uncoupled Winkler springs. These uncoupled Winkler springs are shown in Figure 6.1 and represent the soil-load-deflection properties under the lateral loadings. The governing equation for this type of soil-pile system is derived based on the classical Hetenyi's solution for a beam-column on an elastic foundation, where soil reaction is taken as a linearly distributed load (Hetenyi, 1946). The governing equation is in the form: d4v d2v , x E!ir<+p'jr>-p = 0 <"> where Pz — axial load on piles; y — lateral deflection of the pile at point z along the pile length; P = soil reaction per unit length; and EI is the flexural rigidity of the pile. In the above model, the Winkler's springs representing the soil reaction, P, can be either linear or, more reasonably, nonlinear springs usually termed as P-y curves specified at points along the pile length. The modulus of subgrade reaction method provides a versatile analytical tool to incorporate soil nonhomogeneity and soil non-linear response, although this approach ignores the soil continuity and is not readily apphcable to pile group analysis. Chapter 6. Review of Pile Response to Lateral Loads 123 M H pile segments independent springs •a»>-e Figure 6.1: Winkler Spring Approach (after Fleming et al, 1985) In the early apphcation of subgrade reaction approach, the soil reaction, P, in Eq . (6.1) is related linearly to the lateral deflection, y, via the horizontal subgrade reaction modulus, Kh, viz; P = Khy (6.2) where Kh is in unit FL~2. The coefficient of horizontal subgrade reaction kh, com-monly used in the soil mechanics literature partly due to Terzaghi (1955) classic paper, is defined as: p = khy (6.3) where p is the soil pressure, kh is in unit FL~3, and is related to the horizontal subgrade modulus Kh through the pile diameter, D, i.e; h = 4 r (6-4) Chapter 6. Review of Pile Response to Lateral Loads ... 124 Terzaghi (1955) defined kh as: (6.5) which implies that kh varies linearhy with depth, and rih is defined as constant of subgrade reaction modulus, and varies with soil density. In practice, kh may vary in various fashion with depth. For a constant and linear distribution, closed form solutions are available to Eq.(6.1) (Scott, 1981; Poulos, 1982). For a parabolic distribution which may be the case for cohesionless soil deposit, a numerical solution has been obtained, and is represented in form of table and chart (Franklin and Scott, 1979; Scott, 1981). Because of availability of closed form solutions, up to now, great effort has been made in using Eq.(6.1) with the above linear soil reaction theory to analyze different case histories and back figure the appropriate ra^ values for different soil conditions. As a.result, a wealth of information exists on different rih values, which has created difficulties and sometimes confusion in selecting appropriate design values (Habiba-gahi and Langer 1984; Robinson 1979). Various factors affecting ra/, value has been reported, including pile diameter, rela-tive soil-pile stiffness, soil condition, and pile head loading condition, etc. This stems partly from the fact that the uncoupled Winkler springs ignore the soil continuity, and rih will never be a fundamental soil property. It also stems from ignoring soil nonlinear response by forcing a linear spring theory. As a result, rih largely depends upon pile load intensity, soil-pile relative stiffness, and pile head loading condition. The load versus deflection and load versus rotation relationships for laterally loaded pile are highly nonlinear due to the progressive soil yielding downward from the surface, and the apphcation of a hnear theory, whether based on a subgrade re-action approach or an elastic approach, can only be expected to give an approximate prediction of deflection and rotation (Poulos, 1987). A more logical approach is to use a nonhnear spring approach, i.e the P-y curve approach which has been widely Chapter 6. Review of Pile Response to Lateral Loads 125 used in the offshore industry. The key element in applying the nonlinear subgrade reaction method to analyzing laterally loaded pile response is to construct these nonlinear soil reaction curves based on basic soil parameters. The concept of P-y curves was first proposed by McClelland and Focht (1958). Since then the rational development of P-y curves has become an intensive research area owing to the easy application of the subgrade reaction method in routine design practice. To date, P-y curves for granular materials are generally constructed based on following three methods, namely; • semi-empirical method; • insitu testing method, and • finite element method. Semi-empirical Method Of the semi-empirical methods, the procedure proposed by Reese et al (1974) has been most used, and was incorporated into the American Petroleum Institute (API) design code in 1976. This procedure was initially based on a back-analysis of one full scale instrumented pile load test on sand at Mustang island, Texas (Cox et al, 1974). P-y curves are constructed at each desired depth. Each curve consists of three straight hnes and a parabola, as shown in Figure 6.2. The initial portion is a straight hne representing the "elastic" behaviour of the sand, and the final straight portion is horizontal, representing the "ultimate" soil resistance. These two straight hnes are connected with a parabola and a sloping straight hne. The parabola and the intermediate straight hne were selected empirically to fit the shape of experimental P-y curves. Chapter 6. Review of Pile Response to Lateral Loads 126 Y Figure 6.2: Reese et al (1974) P-y curves The initial slope, Khi, of Reese's P-y curve is defined as: Khi = nhiz (6.6) where z is the depth of P-y curve, Khi is the subgrade reaction modulus [FL~2], and nhi is the coefficient of subgrade reaction modulus [FL~3]. Taking Terzaghi's (1955) approach, Reese et al (1974) suggested n^ values according to soil density that are 2.5 to 4 times larger than those recommended by Terzaghi, as shown in Table 6.2. These higher values may result because Terzaghi's values were intended to apply more at working loads whereas the Reese et al values are for initial loading. Reese et al values were further modified by Jamiolkowski and Garassino (1977), Murchison and O'Neill (1984). Jamiolkowski and Garassino expressed nhi in terms of relative density, Dr, for submerged soils as: nhi = 19 7 u, (A-) 1" 1 9 (6-7) where ^ w is the unit weight of water, and nhi has the same unit as 7 ™ . Chapter 6. Review of Pile Response to Lateral Loads ... 127 Table 6.2: n^i values for submerged soil suggested by Reese et al Relative Density Loose Medium Dense n-hi value, kef 35 (8) 104 (28) 216 (68) Dimensionless - n 560 1700 3500 n = nhi/-)w (130) (450) (1100) Notes: (1) . Terzaghi's values are shown in paren-theses for comparison; (2) . The constant of subgrade reaction modulus can be expressed in a dimension-less form by normalizing it against the wa-ter unit weight, fw, i.e. n^i = n • 7^ , and n - nhi/fw. Murchison and O'Neill extended Reese et al values to dry soil condition, and expressed them in terms of relative density and friction angle, as shown in Figure 6.3. By comparison with the model test data, Yan and Byrne (1991a) have shown that the initial slope of the P-y curve can well be represented by the maximum soil Young's modulus, Emax, obtained from downhole or crosshole seismic tests. This subject will be discussed in details in Chapter 8. The ultimate soil resistance, Pu, in the Reese et al P-y curve was determined from the lesser value of the following two equations which were derived theoretically for two cases; wedge and flow type failure conditions (Reese, 1962; Reese et al, 1974): Pu = jz[D(Kp- Ka) + zKp tan (6.8) Pu = -yDz[K* + 2KaK2 tancj> + tan<f>- Ka) (6.9) where Pu is the ultimate soil resistance per unit depth, z is the depth, 7 is the effective unit weight of soil (submerged or total), Ka, Kp are the Rankine active and passive coefficients respectively, Ka is the at rest earth press coefficient, <j> is the angle of internal friction, /3 = 45° 4- </»/2. However, it was found by Reese et al (1974) that Eqs.(6.8, 6.9) considerably underestimated field measurements, adjustment factors Chapter 6. Review of Pile Response to Lateral Loads 128 were introduced to increase Pm and Pu. Even so, the recent field test data at the University of Houston suggested that the ultimate soil resistance predictions are still lower than the observed (Reese et al, 1988). In fact, a number of studies indicate that Pu for cohesionless soil is not well defined. (Kubo, 1966; Yoshida and Yoshinaka, 1972; Scott, 1981; Ting et al, 1987). Despite these findings, the concept of Pu is still used to define the P-y curves. By reahzing that some terms in the above equations for Pu can be taken as con-stants with little error, Bogard and Matlock (1980) proposed the following equations for Pu in sand: Pu = (ClZ + C2D)lz (6.10) Pu = (6.11) The parameters C l 5 C2, and C 3 are prescribed in Figure 6.4. One concern in using Reese et al P-y curve is that three distinctly different func-tions are involved. Murchison and O'Neill (1984) proposed a single analytical function to describe the Reese et al P-y curve, i.e. (6.12) in which Pu is taken as the lesser value of Eqs.(6.10, 6.11), is given in Figure 6.3, the empirical adjustment factor- A is given as: A = 0.9 for cychc loading (6.13) ,4 = 3 - 0.8-^ > 0.9 for static loading (6.14) and rj is a factor used to describe pile shape effect. The recent version of A P I code (1987) has adopted this equation to describe P-y curves. Another semi-empirical approach is the method proposed by Scott (1980) based on centrifuge tests results on model piles. The method has two unique features which P = r]APu tanh {AnPj er 6. Review of Pile Response to Lateral Loads 300 250 200 C 150 i c 100 50 (1) / (2). 8,000 6,000 = <g co c 4,000 | c g 'co c 2,000 E Q 20 40 60 80 Relative Density - Dr (%) (1) - SAND ABOVE THE WATER TABLE (2) - SAND BELOW THE WATER TABLE 100 Figure 6.3: vs. relative density, after Murchison and O'Neill (1984) CM O T J C CO O 2 c o> 'o o O CO CD _ 3 CO > • • •** .A • C2 V " ' ••""V C3 1 20 25 30 35 Angle of Internal Friction (Deg.) 80 20 40 8 60 o 40 CD b 1 o O o CO Cl) _ 3 CO > Figure 6.4: Factors for Pu, after Murchison and O'Neill (1984) Chapter 6. Review of Pile Response to Lateral Loads 130 P Figure 6.5: P-y curve proposed by Scott (1981) distinguishes it from others. One is that the P-y curves are simply represented by bilinear curves as shown in Figure 6.5. By comparison with the model data, Scott found that such a simple bilinear P-y curve can serve just as well as the Reese et al procedure. In his method, the slope of the initial segment is denned as the Young's modulus, E„, of soil. However, he did not specify the strain level at which the soil Young's modulus, Es, is to be evaluated nor the method to obtain it. The other feature of this method is that the second segment of the P-y curve is empirically denned by a slope of -E«/4, which implies that soil resistance increases linearly with the lateral displacement with no ultimate value. The ultimate soil resistance concept is thus not applied. Insitu Testing Method Insitu testing tools, especially cone penetration tests, have long been used in pile foundation design (Davis, 1987), as it has been normally believed that they provide Chapter 6. Review of Pile Response to Lateral Loads 131 more direct assessment of pile performance in the field. For laterally loaded piles, the soil element in front of the pile may undergo similar loading patten as in the pres-suremeter test, and this tool has been used to characterize soil reaction for laterally loaded pile design in last ten years. It appears that there are two approaches to make use of pressuremeter test results: 1. obtaining the horizontal modulus of soil reaction, Kh] 2. obtaining P-y curves from scaled pressuremeter curves. In the first category, Menard and Gambin proposed a set of empirical formulae for Kh from Menard pressuremeter modulus, Em (Gambin, 1979). However, Menard pressuremeter suffers from many operational problems, its results are largely affected by soil disturbance and stress relief. In the second category, two approaches have been taken; (a) , the P-y curves are constructed by scaling the entire pressure-expansion curves with certain factors (Robertson et al, 1984; Atukorala et al, 1986); (b) . Alternatively, the mechanism of soil resistance to the lateral movement of piles is separated into two components: frontal reaction and side frictional reaction (Briaud et al, 1982; 1983 and Smith, 1987). The frontal reaction is obtained from the pressuremeter curve directly, but a theoretical assumption has to be made in order to interpret the side frictional reaction. Then, the P-y curve is constructed from the combined frontal and side frictional reaction curves. So far it has been shown that both approaches are promising and of practical interest. However, none of the above methods have properly taken account of the different installation effects on the pressuremeter curve and P-y curve. Based on a parametric finite element analysis, Yan (1986) has shown that even with the same amount of soil disturbance, the pressuremeter curve and P-y curve are affected differ-ently due to the different loading mechanisms associated with the pressuremeter and Chapter 6. Review of Pile Response to Lateral Loads 132 laterally loaded piles. Thus, the scaling factors developed from one test site should be used with caution. This method developed so far is still very much site specific. Finite Element Method In recent years, application of the finite element method to the development of P-y curve has received more and more attention due to the continuous need to develop the P-y curve more rigorously. The finite element method has proved to be a powerful tool for analyzing soil-structure interaction problems in a more detailed and fundamental level when used with proper soil constitutive laws. But high cost and tedious input data still prohibit 3D analysis from being a routine design means for pile foundation. However, with the application of its 2D formulation to P-y curves, the finite element method possesses the potential of being a direct design tool for laterally loaded pile foundations. The first attempt in this regard was done for clay by Yegian and Wright (1973). They analyzed the response of a single pile under the short term static loads in soft clay using both plane stress and plane strain models, and compared results with Matlock (1970) P-y curve. Many limitations were found in that study (Yan, 1986). First of all, the outer fixed boundary distance of 8 pile diameter was selected from a plane stress analysis and then used for the plane strain analysis. Bardet (1979) has shown that the outer boundary has a more significant effect on a plane strain solution, and a 50 pile diameter outer boundary has been suggested (Scott, 1981). In addition, Yegian and Wright in their analysis employed a quarter of 2D domain that contained a symmetrical boundary in the lateral loading direction and an antisym-metrical boundary in the perpendicular direction. This antisymmetrical condition will not exist in the soil exhibiting nonlinear response. Furthermore, the interface element they used did not allow soil-pile separation if it occurred. A similar study was carried out by Barton et al (1983) on piles embedded in sand in which a plane strain model was used and the soil was modelled as an elasto-plastic Chapter 6. Review of Pile Response to Lateral Loads ... 133 material incapable of tension. By comparing the computed P-y curves with centrifugal test data, they found that at the shallow depth, the computed P-y curves were in a close agreement with the experimental curves, however, at depths greater than about 5 pile diameters, the computed P-y curves were softer than the experimental ones, and the difference became more severe as depths increasing to 10 pile diameters. Further studies on development of P-y curve from 2D finite element procedure were carried on by Yan (1986). A plane strain model was also employed but the soil was modeled using a simple hyperbolic stress strain law. The soil-pile interface behaviour (slip and gapping) was simulated by using the thin layer interface element (Desai, 1981; Desai et al, 1984 and Yan, 1986). It was found that under plane strain condition the computed P-y curve can be normalized and fitted by a power function in the following form: (6.15) where P is the soil reaction per unit length [FL-1], y is the pile deflection [L], D is the pile diameter [L], a and /3 are curve fitting parameters that were found to be independent of depth and pile diameter for a given soil condition, and E{ is the initial Young's modulus of soil calculated from: Ei = KePa(^Y (6.16). where Ke is the Young's modulus parameter; Pa is atmospheric pressure; 07, is the effective horizontal stress; and n is the stress level exponent. The hyperbolic stress-strain soil parameters can be evaluated from laboratory tests (Duncan and Chang, 1970; Duncan et al, 1980) or from field correlation (Byrne et al, 1987). Some of the results from this study are shown in Figures 6.6 to 6.11. Figure 6.6 shows the results of nonlinear P-y curves computed for the given soil condition from the finite element analyses for various depths below the ground and pile diameters. The hyperbolic soil parameters used in the parametric finite element Chapter 6. Review of Pile Response to Lateral Loads 1,000 800 600 c o I 0) cr o co 400 200 A * A* A* I 20 A A _ A A • 0 • • Depth-2.5D Depth-5D Dpeth-2.50 Depth-2.5D D-g.6m D-g.6m D-J.2m D-1.2m Ko-1 Depth-40 Depth-10D Depth-BD Depth-4D D-1.2m • D-J^.2m D-J.Bm D-0.6m 40 60 BO 100 120 140 160 Pile Deflection - y (mm) Figure 6.6: P-y curves from Nonlinear Finite Element Plane Strain Model 1.5 5 § 1 I cr "6 w 0.5 • • _ • A • • - • A • A • A . A • Depth-2.5D Depth«5D Dpeth-2.5D Depth-2.5D D-g.oTn D-g.6m D - p n D-1.2m Ko-1 * Depth-4D Depth-10D Depth-8D Depth—4D D-1.2m D-^ .2m D-J.em D-0.6m i . i . i 5 10 15 20 Pile Deflection - y/D (%) Figure 6.7: Normalization of P-y curves from Finite Element Analysis Chapter 6. Review of Pile Response to Lateral Loads 135 analysis are those proposed by Byrne et al (1987). The depths of P-y curves and the pile diameters selected for the studies are within the range of practical interests. It can be seen that the computed individual P-y curves varied significantly with depth and pile diameter. However, after normalization with respect to initial soil Young's modulus at the given depth and the pile diameter, all these P-y curves collapse within a narrow band, as shown in Figure 6.7. For the practical interest, these normalized P-y curves may be approximately represented by a single mathematical function in form of Eq. (6.15). In the normalization process, the initial Young's modulus of soils is calculated using Eq.(6.16), where the horizontal effective stress, <r^ , of soil mass is used. It is found from the analysis that the effect of anisotropic soil stress condition on the P-y curves can be normalized if the horizontal effective soil stress is used in Eq.(6.16). This is illustrated in Figure 6.8 and 6.9. The effects of different soil density on the P-y curves have also been investigated in the finite element analyses. Figure 6.10 shows the computed P-y curves at both loose (DT — 30%) and dense (Dr =75%) sand conditions. It is seen that the P-y curve for the loose sand is much softer than that for the dense one. When these P-y curves are normalized as just described, the two curves will not collapse, as shown in Figure 6.11. The normalized P-y curve for the loose sand becomes stiffer due to the much smaller Young's modulus value in loose sand as compared to that in dense sand. Thus, it appears from the finite element studies that the P-y curves at different depths and pile diameter may be normalized with respect to the soil initial Young's modulus and the pile diameter. However, this normalization is dependent upon the soil condition. Finite element analyses show that the coefficient, /3, has a value of about 0.5 while the coefficient, a , varies with the soil density. A n order of variation of coefficient, a, with the relative density is shown in Figure 6.12. So far, Eq.(6.15) has not yet been evaluated against experimental test data. In Chapter 6. Review of Pile Response to Lateral Loads 136 600 500 400 0) 200 o CO 100 A • A o A • ' A D Depth-2.5D D-1.2m Depth-250 D-1.2m Ko-1-Sln* Ko-1 10 15 20 25 Pile Deflection - y (mm) 30 35 Figure 6.8: Anisotropic Soil Stress Effects on the P-y curves, F E M studies 0.8 O IS c o I cc o CO 0.6 0.4 0.2 Depth-250 D-1.2m Depth-25D D-1.2m Ko-1-SinO Ko-1 2 3 Pile Deflection - y/D (%) Figure 6.9: Normalization of Anisotropic Soil Stress Effects on the P-y curves, F E M studies Chapter 6. Review of Pile Response to Lateral Loads 137 600 20 30 Pile Deflection - y (mm) so Figure 6.10: Soil Density Effects on the P-y curves, F E M studies 2.5 I Figure 6.11: Normahzation of Soil Density Effects on the P-y curves, F E M studies Chapter 6. Review of Pile Response to Lateral Loads 138 1 0 I i i i i i i ' • ' 0 20 40 60 80 100 Relative Density - Dr (%) Figure 6.12: Variation of Coefficient, a , with Relative Density the chapters to follow, the studies presented by Yan (1986) are extended, and results are compared with the model test data, from which a new method of generating P-y curves from the finite element analysis using fundamental soil properties is proposed. 6.2.2 C y c l i c R e s p o n s e Research on pile response to lateral cyclic loading has mostly concentrated on piles embedded in clays. Field pile tests in stiff clay show a large increase of pile head deflection and pile bending moment with the number of loading cycles, which is more severe under the "two-way" than the "one-way" cyclic loading (Reese et al, 1988). The changing response of a pile to cyclic lateral load is due to degradation of the pile-soil system. Theoretically, this degradation may take two forms (Swane and Poulos, 1982): 1. material degradation; 2. mechanical degradation. Chapter 6. Review of Pile Response to Lateral Loads 139 Increased pore pressures, changes in soil density, and rotation of principal stress directions are evidence of material degradation. Mechanical degradation is denned as the result of residual pressures developed along the pile or separation between the soil and the pile due to the plastic deformation of the soil. During cyclic lateral loading, these two forms of degradation will interact, leading to the increase of pile deflection, rotation and hence bending stresses along the pile. If this degradation stabilizes, the pile is said to "shakedown" to a state of permanent strains and residual stresses, and will basically react elastically to any further cycles of load. If the degradation does not stabilize then the pile will collapse. Methods to model structural shakedown have been presented by a number of people (Pande et al, 1980; Aboustit and Reddy, 1980 and Swane and Poulos, 1982). A summary of currently available analytical methods for cyclic response of piles has been given by Poulos (1982, 1987) and is listed in Table 6.3. As shown in the table, only the methods based on P-y curves are versatile and applicable to piles embedded in sands. As in the case of static P-y curves, the cyclic P-y curves were backfigured from very limited field pile test data. Their usage at other site conditions is questionable. So far, only a few well instrumented pile test data is available to understand the cyclic response of piles in sands. 6.3 Experimental Studies - Static and Cycl ic Loading 6.3.1 Field Testing In most cases of field pile tests, a hydrauhc actuator and reaction piles are used to apply horizontal force to piles at or some distance above the ground level (Crowther, 1988). A free-head loading connection is usually made. Cyclic loading normally con-sists of only one-way cychc loading. Depending upon the objectives of the pile load testing, the instrumentation may consist of measurements at pile head or/and along Table 6.3 Methods of Analysing Pile Responses under Cyclic Lateral Loads Application Method Parameters Required Comments Reference Sand Empirical from l g model tests Soil Unit Weight Deflection related to No. of cycles, and loading cond. Gudehus & Hettler (1981) Clay Solution from Elast. Bound. Element Theory Es, pu, critical cyclic strain vs. No. of Cycles e.g. Idriss et al (1978) Corr. fact, for pile deflection and bending moment Poulos (1982) Clay Sand P-y curves P-y curve envelope Derived from field data; give envelope to the response Reese & Desai (1977) Clay Sand Cyclic P-y curves Cyclic, hysteretic P-y curves Cycle-by-cycle analysis. Allows for cyclic degradation and gapping, S P A S M program Matlock et el (1978) Chapter 6. Review of Pile Response to Lateral Loads 141 the pile length. Measurements at pile head consist of apphed load, pile head deflec-tion and rotation, and standard procedures can be used to obtain these measurements (Reese, 1979). Measurements along the pile length normally consist of bending mo-ment distribution in the pile, from which soil reaction and pile deflection (P-y curves) can be evaluated. A method has been proposed by Reese and Cox (1968) to obtain P-y curves from a knowledge of only the pile head deflection and rotation, along with the corresponding loading conditions and pre-assumption of the soil reaction distri-bution with depth. While the method may be useful, there is little confidence in the curves so derived. A n inchnometer can also be employed to obtain the pile rotation as a function of depth (FeUenius, 1972). Such measurements are principally useful in obtaining pile deflection. Triple differentiation of the rotation curve is necessary to obtain soil response and would lead to serious inaccuracies, which will be discussed in more detail in Chapter 7. A soil dynamometer has been reported by Kolensnikov et al (1981) to measure aU the three components of soil reaction on a pile. However, such a device has not been available for practical apphcation. In practice, most field works are project oriented, and the costs involved to conduct a parametric study would be prohibitive. Among the numerous reported case histo-ries, only a few full scale pile load tests have been performed on fully instrumented piles from which soil-pile interaction behaviour along the pile has been evaluated. In most cases, only pile response at the pile head was measured. The classic early field work on fully instrumented piles was the lateral load tests on steel-H piles in medium dense sand during the Arkansas River Project (Ahzadeh and Davisson, 1970) in which static and one-way cyclic loading was performed. Loads were apphed horizontally at the ground hne with a free-head connection. The load-deflection behaviour of the pile and the bending moments calculated from the strain-gauge data at various load levels were reported. Unfortunately, neither the unloading behaviour of the pile nor the residual moments left in the pile when the load returned Chapter 6. Review of Pile Response to Lateral Loads 142 to zero were given, which are important information under any loading condition, es-pecially for cyclic loading. It was found that when the observed pile head response was modelled elastically using Matlock and Reese (1960) method, the model parameter rih required depends heavily on the load or displacement level specified. In addition, the pile deflection was found to significantly increase with number of loading cycles under one-way cyclic loading. However, soil-pile interaction in terms of nonlinear P-y curves was not evaluated in these studies. Lateral monotonic and cyclic loading tests on single instrumented piles embedded in sand have been reported by Cox et al (1974). This was the basis for the early P-y curve construction method proposed by Reese et al (1974). More recently, single pile tests under displacement controlled two-way cyclic load-ing were conducted at the University of Houston by Brown et al (1987) for piles embedded about 10 pile diameter deep in sand overlaying a stiff clay deposit. From this study, it was found that, unlike in the case of stiff clay, piles embedded in sand were not affected significantly by the number of two-way loading cycles. In addition, Reese et al (1974) P-y curve procedure was found to underestimate the field mea-surement. Pu values were then increased by a factor of 1.55 to match the field data (Reese et al, 1988). Some full scale tests on piles in sand under cyclic loading are summarized in Table 6.4. It can be seen that these studies are not comprehensive and do not allow for a fundamental study. It is desirable to continue performing well-instrumented full scale pile load tests. However, such tests are expensive and time consuming, and involve many different organizations, and are only feasible at a few research institutes. 6.3.2 Model Testing Model tests are often resorted to for parametric studies because of their convenience and lower cost as compared to field tests. In the past, most model tests were performed Chapter 6. Review of Pile Response to Lateral Loads ... 143 Table 6.4: A Summary of Field Pile Load Tests on Sand Reference Loading Cond. Soil & Pile Cond. Comments Alizadeh free head, one- natural soil, timber (1969) way cyclic uninstr'ed pile Gleser similar to above steel pipe pile (1953) fixed and free uninstr'ed Wagner static and free Uninstr'ed timber (1953) head at G . L . pile in clay, silt, till Alixadeh &; Free head, stat. Natural fine silty Matlock and Davisson (1970) & one-way cyclic at G . L . sand, instr'ed piles Reese(1956) method Cox et al Free head,two-way Backfilled Med. developed (1974) cyclic, at 1ft to dense sand Reese et al above G . L . instr'ed pile P-y curves Brown et al same as above same as above examine Reese (1987) instr'ed pile et al P-y curve Robinson free headed one- Natural soil Reese & Matlock (1979) way at G . L Timber pile uninstr'ed pile (1956), nh, kh values Davis same as above uninstr'ed pipe D M T P-y curve (1987) pile, back fill Robertson et al (1986) under a lg gravity condition. Such tests have severe limitation when extrapolated to field condition due to lack of similitude arising from stress level effects in soils. Such lack of similitude arises not from any misunderstanding of the stress dependent stress-strain behaviour of soils but a result of not having an appropriate convenient testing device which will allow for the simulation of insitu stress condition in a small model scale. Table 6.5 summarizes some of the model tests on laterally loaded piles. As can be seen, only a few of the recent tests were performed under stresses corresponding to the field stress condition. Kubo (1963) conducted 59 lg-model pile tests in sand with both fixed head and free head restraint conditions. The pile section was either rectangular or circular, Chapter 6. Review of Pile Response to Lateral Loads ... 144 Table 6.5: Summary of Some Model Tests of Lateral Pile Load Test on Sand Reference Testing Features Comments Davisson and Salley (1970) lg-model test, sand box 48x48x48in, pile diam. 0.5in O . D . Alum, tubing stat. & one-way cycl. at sand surface (S.S.) Examine Matlock &i Reese (1956) Back figure nh Bending moment measured Kubo (1963) lg-model, sand box: Pile: 1.75-30cm in diam. 60-240cm in length, Stat, load, load eccen. varies: 0 to 117cm parametric studies Bending moment measured P-y curves obtained Hughes and Goldsmith (1977) lg-model, sand box 125mm deep, free head, stat. load, uninstrumented pile quahtative observation on displacement field Singh and Prakash (1971) lg-model, sand tank dimen. 120x120x120cm, pile 12.7mm in square sec. with 1.6mm wall thickness. One-way cychc, free and fixed pile head, bending moment meas'ed P-y curves not derived Saglamer and Parry (1979) lg-model, pile O . D . 7.94mm sand box: 1015x168x407mm, radiographic observation on displacement field Static & one-way cychc, free head, bending moment meas'ed, hnear analysis, P-y curves not derived. Zehkson (1978) high stress level test, hydrauhc gradient method Rigid pile, free head pile head response bending moment not measured Scott (1976-77) high stress level test, centrifuge method, stat. & two-way cychc, free head at S.S.level, pile: 0.162x0.162x8.0in pile head response and P-y curve are measured, simulating Mustang island test Barton (1982) high stress model test, centrifuge method, static & two-way cychc, varies load eccen.& pile diam. pile head and P-y curve also simulating Mustand test Oldham (1984) similar as above, pile driving in flight the same as above Shibata et al (1989) lg's stress model, sand tank diam.x Ht.=165cm x 105 cm, static loading, Free head. Bending moment meas'ed Analysis using Randolph (1981) elastic method, P-y curves not derived. Chapter 6. Review of Pile Response to Lateral Loads 145 and diameters (or widths) ranged from 1.75 to 30 cm. From the test results, it was proposed that soil pressure, p, along the pile could be expressed as follows: p = kz-y0-5 (6.17) where k is the fitting parameter with a unit of [FL~3m5], z is the depth and y is the pile deflection. Of particular interest is the effect of pile diameter on the parameter, k. It was found that beyond a pile diameter of 20 cm, the parameter k was independent of pile diameter, D. From Eqs.(6.2), (6.4), the subgrade reaction modulus, Kh is: then, substituting for p from Eq.(6.17), which shows that the secant soil reaction modulus is a linear function of pile diameter and inversely proportional to the square root of deflection. From Eq.(6.4), kh - the coefficient of soil reaction modulus is thus independent of pile diameter. From an analysis of some lateral plate load tests on sandy and clayey soils using the subgrade reaction method, Yoshida and Yoshinaka (1972) indicated that for a circulate plate the horizontal soil reaction modulus is a function of diameter as follows: Kh oc D1-25 (6.20) These results are somewhat contradictory to those reported by Terzaghi (1955), and Reese et al (1974), etc. where the horizontal subgrade reaction modulus has been shown to be independent of pile diameter. The low stress level of Kubo's Ig model tests may cast some doubts on his results. The issue of what factors actually affect the subgrade reaction modulus has become the main debate between the elastic boundary element method and the subgrade pD kzy05D y kzD y 0.5 (6.18) (6.19) Chapter 6. Review of Pile Response to Lateral Loads 146 reaction method. Some theoretical studies comparing the linear subgrade reaction method with the elastic continuum solution have shown that the subgrade reaction modulus depends heavily upon pile diameter, soil-pile relative stiffness, pile fixity and pile head loading condition (Baquehn et al, 1977; Kagawa and Kraft, 1980a; 1980b; Fleming et al, 1985). Neglecting soil continuity in the subgrade reaction method has been suggested as the reason. Thus, it is desirable to provide more experimental evidence on this aspect. However, to date, this has not been done satisfactorily. Some model tests under lg condition were also conducted by Poulos and his co-worker for studying single pile and pile group responses in clay (Mattes and Poulos, 1971) and in sand (Selby and Poulos, 1983), and the results were used to calibrate the elastic boundary element approach. Zehkson (1978) employed the hydrauhc gradient similitude technique to increase the stress level in model soils and .tested rigid model piles under inchned loads. How-ever, the results were not evaluated in terms of any current analytical theories. Scott (1976-77) performed a series of model pile tests in the centrifuge. The testing program undertaken was designed primarily to simulate the conditions of the full scale pile tests at Mustang Island, performed by Cox et al. The full scale pile testing condition was simulated in centrifuge under the lOOg with both dry and saturated soil conditions. The comparison between the model pile response and the field recorded load deflection is shown in Figure 6.13. As can be seen in the figure, the comparison with the prototype observation is not very good. Although the dry model test gives apparent good agreement, the comparison should be made with the wet model test as the full-scale test was performed in soil saturated to ground surface. In addition, the prototype pile was loaded at a distance of 1 ft above the ground surface, but, in the centrifuge tests the load was apphed at the surface. If a moment had been apphed to the model pile to simulate the load eccentricity in the field, the resulting deflection would have been larger and a worse correlation obtained. In general, the model pile Chapter 6. Review of Pile Response to Lateral Loads 147 M O D E L DEFLECTION (cm) .01 .02 . 03 .04 0 . 0 1.0 2 .0 3 .0 4 . 0 F U L L S C A L E D E F L E C T I O N AT G R O U N D S U R F A C E (cm) Figure 6.13: Prediction of the lateral load deflection behaviour of the Mustang Island Test using a Centrifuge, after Scott (1977) tests tended to underestimate the prototype stiffness. This illustrates the difficulties in attempting to predict prototype behaviour using centrifuge technique. A more comprehensive testing of model piles in the centrifuge was carried out by Barton (1982), where the Mustang island test was also simulated. The experimen-tal P-y curves were derived from the experimental data and compared with those proposed by Reese et al (1974). Comparisons with Reese et al curves showed that test data seems to qualitatively support the general shape of Reese et al curve, but indicated that the Reese et al method underestimated the ultimate soil resistance near the pile head, and overestimated it at depth. They also indicated that the initial stiffness and its distribution with depth are overestimated by Reese et al method. Chapter 6. Review of Pile Response to Lateral Loads 148 6.4 Summary It appears from the above review that it is essential to incorporate the nonlinear soil-pile interaction and nonhomogeneity of soil deposit in any practical analysis of laterally loaded pile foundations. At present, despite its shortcomings, the nonlinear subgrade reaction method based on nonlinear P-y curve appears to be the most simple and versatile method of modelling the soil. The successful application of this method requires a rational expression for the soil-pile interaction or P-y curves that is based on fundamental soil parameters that include all the factors that significantly influence the curves. To achieve this objective, the best way is to perform a series of model pile tests under a well controlled pile loading and soil conditions. The analytical method can then be evaluated by comparison with the experimental observations. A useful model pile test can only be obtained from a model test in which the insitu soil stress condition is simulated. In the past ten years, the centrifuge test technique has become a viable way to meet this aim. However, due to expensive and complex equipment, the centrifuge testing facilities are not yet readily available. As a result, most model pile tests are still performed under normal lg stress conditions (Scott, 1988). Therefore, it is desirable to have an inexpensive and readily accessible testing device so that these fundamental studies can be easily fulfilled, and our current data base be quickly enriched. In order to accomplish this a new Hydrauhc Gradient Similitude Testing ( H G S T ) apparatus has been developed at the University of British Columbia as described in Chapter 4. A n application of this testing method to the study of laterally loaded pile response is presented in the following chapter. Chapter 7 A Model Study of Pile Response to Lateral Loads at Pile Head 7.1 Introduction In this chapter, a model study of vertical piles embedded in sand under static as well as cychc lateral pile head loading is carried out in a well controlled laboratory condition using the hydrauhc gradient similitude technique. Single piles of different diameters are studied under different loading and soil conditions. The objectives of this study are threefold, namely: • to demonstrate the usefulness of using the hydrauhc gradient similitude tech-nique to study pile foundation problems; • to study the fundamentals of pile responses under a well controlled soil condi-tion, and with such a data base • to examine our current analytical methods and evaluate appropriate soil prop-erties for the analyses. It is hoped with such a study that a better understanding of pile responses to static and cychc lateral load can be achieved, and a better data base can be established so that our design confidence and predictive ability will be enhanced. 149 Chapter 7. A Model Study of Pile Response to Lateral Loads 150 7.2 Test Procedure and Experimental Program 7.2.1 Procedure The U B C - H G S T device described in Chapter 4 was used in this research. Testing procedure in this application consists of • Reconstitution of Sand Deposit; • Pile Installation; • Soil Loading Process, and • Pile Head Loading Test. Reconstitution of Soil Deposit The "quick sand" sample reconstitution technique was also employed in this research to form and reform soil deposit for each test as described in Chapter 3. Thus, a fresh soil sample is used for each test condition. The sand used in this study is the same as in the previous apphcations and discussed in Chapter 3 and 5. In-situ measurements of the maximum shear modulus, Gmax, of model soils within the H G S T device were discussed in Chapter 5 or in Yan and Byrne (1990, 1991b), while the hyperbohc soil parameters from triaxial tests were presented in Chapter 3 or Yan and Byrne (1987). Pile Installation After the soil deposit was formed at a given soil density, the model pile was installed by pushing the pile into the sand deposit. A pile driving guide for different pile diameters was developed so that the model piles can be driven at the center of the soil container and be in alignment with the loading ram and L V D T measurement cores. A l l the model piles were close-ended at the tip, and all were driven to the Chapter 7. A Model Study of Pile Response to Lateral Loads 151 bottom of the sand deposit, resting on the filter surface with an embedment length of 315.2 mm. Thus, the model piles simulate full displacement end bearing piles. The action of driving a full-displacement pile into soil ground will disturb the soil around the pile and create a zone of soil within which the soil properties and soil stresses are different from the original soil deposit. At present, since equipment for driving model piles at high hydrauhc gradient to simulate full scale pile driving condition has not yet been built, the model piles were hand pushed into the sand at normal stress conditions. Subsequently, a given hydrauhc gradient was apphed to the model and the lateral pile load test performed. As a result, the soil and stress conditions equivalent to those developed by the full-scale pile driving was probably not achieved in the model tests. Robinsky and Morrison (1964) performed a series of model pile installation studies in sand at lg stress condition. The sand displacement and compaction around model friction piles were observed by means of radiography technique, and found to be dependent upon the pile property, soil stress level and soil density. The envelope of soil displacement due to pile installation extends 3 to 4 pile diameters to the sides of piles in loose sand, and 4.5 to 5.5 pile diameters in dense sand. The shape of this envelope resembles an elongated bulb, its diameter decreases significantly near the ground level due to the free surface boundary and low stress confinement." Thus, the stress field created by hydrauhc gradient in the tests may be affected by the disturbed soils due to the pile installation. However, for the laterally loaded pile tests, its effect may be insignificant as pile behavior is dominated by the soil reaction near the soil surface where the pile installation effect is minimum. In addition, the observation by Robinsky and Morrison also indicated that the soil compaction due to pile installation is less severe for close-ended pipe piles than for cone tip or tapered piles. The process of soil displacement and compaction below the pile tip of a close-ended pile is followed by an unloading process in soil elements Chapter 7. A Model Study of Pile Response to Lateral Loads 152 when soil elements pass the pile tip and move along the pile shaft. This unloading process in soil elements reduces the soil density in the immediate vicinity of the pile shaft and thus may nullify some of the effects on the applied hydraulic gradient due to the initial compaction at the pile tip. In the centrifugal modelling, many tests were performed on piles installed at lg stress condition (Scott, 1977 and Barton, 1982). Only Oldham (1984), Craig (1984, 1985) have reported a series of lateral pile head loading tests on sand following pile installation in flight. Their limited test data from centrifuge tests demonstrated that the effects of stress level at pile installation are important for pile response under axial loading, but are much less important for pile response due to lateral loading. This is because in lateral pile head loading condition, the behavior is controlled by soil reaction in the upper levels where stress changes induced by pile installation are the least. Furthermore, the lateral pile head loading will modify the soil stress regime around the pile to a much greater extent than due to the pile installation. Based on the above considerations, the procedure of installing pile at the normal stress condition and then performing pile loading tests at a higher stress level was employed in this study. After the model piles were installed, the lateral loading unit including the double acting air piston and load cell was mounted on the soil container lid. The appropriate loading connection was made depending on the free or fixed head conditions and loading eccentricity. Two L V D T measurement cores were also attached to the pile head to measure the corresponding deflections. The air pressure chamber was thereafter installed and all the instrumentation wires connected to the data acquisition unit. Soil Loading Process After enclosing the whole testing device, the soil loading process began by applying an air pressure in the air chamber and simultaneously pumping the water to the sand Chapter 7. A Model Study of Pile Response to Lateral Loads 153 container. During this process, the micro-computer with a monitoring program was used to monitor the hydrauhc gradient in the test until the given hydrauhc gradient was reached. Similar to that in the triaxial tests, when the pressure in the H G S T air chamber is increased so as to increase the hydrauhc gradient in the soil, a horizontal force will act on the loading ram, pushing it out of the chamber due to the unequal end area. Then, if this horizontal force is not counter balanced during the soil loading process, the pile will be subjected to an increasing lateral pulling force as the hydraulic gradient in the soil increases. It is important to counter balance this force so that the pile can be maintained at its original position before the lateral load test starts. A special air pressure control unit was designed for this purpose. Its operation during the soil loading process is discussed in Appendix E . P i l e H e a d L o a d i n g s A constant amphtude of cychc lateral load was apphed to the model piles. The load was apphed at a period of 40 seconds per cycle. Both one-way and two-way cychc loadings were apphed in this study. The scanning rate of data acquisition was 1 Hz. Parameters changed in the loading included loading amphtude, eccentricity and pile head fixity. Load controlled tests were carried out because they would more closely represent the field loading condition. 7.2.2 Test Repeatability Repeatabihty of test results is an important requirement for the consistency of con-clusions to be derived from U B C - H G S T test results. Strict adherence to identical model preparation technique and test control routines is central to achieving repeat-able test results. Good repeatabihty of test results in terms of pile head response and Chapter 7. A Model Study of Pile Response to Lateral Loads 154 bending moment distribution can be noted in Figure 7.1 and Figure 7.2 for free and fixed head pile load tests, respectively. 7.2.3 Data Reduction In the tests, the bending moment distribution along the pile is obtained from the strain gauge readings. Based on the simple beam theory, the bending moment can be integrated or differentiated to obtain the pile inclination, 6, deflection, y or shear force, Q, and soil resistance, P, as follows (ignoring the sign): 1 = ITI* (7'1) Q = f (7.3) dz where EI is the flexural rigidity of the model pile, z is the distance along the pile. Since the bending moments are only known at some discrete locations along the pile, a numerical curve fitting scheme is necessary to obtain the needed soil resistances and pile deflections along the pile length at each loading stage. The desired P-y curve at a given depth can be obtained by repeating the curve fitting scheme at various loading stages. For the deflections, simple numerical integration suffices, as any slight errors in the bending moment data become smoothed in the integration process. However, for the soil resistances, any slight errors or deviations in the bending moment data become greatly magnified during double differentiation. To alleviate this problem, various curve fitting techniques have been proposed to process the bending moment data. In contrast to most field test data, the application of curve fitting technique to model test data is possible as model tests usually are performed in a uniform soil Chapter 7. A Model Study of Pile Response to Lateral Loads 25 Pile Head Deflection at LVDT1 (mm) Figure 7.1: Repeatability of Test Result for Free Head Loading Chapter 7. A Model Study of Pile Response to Lateral Loads 50 Pile Head Deflection at LVDT1 (mm) (100) E £ o o o •g =3 CO •o c CO CO o o 100 t 2 0 0 CD D Fixed Head N=48 E=45mm Dr=75% i I i l i I 400 300 200 100 300 (1,000) (500) 0 500 1,000 1,500 Pile Bending Moment along Depth (N.mm) Figure 7.2: Repeatability of Test Result for Fixed Head Loading Chapter 7. A Model Study of Pile Response to Lateral Loads 157 condition, and the bending moment data can be represented by a smooth continuous curve. Erratic data such as those in the field due to alternating dense and loose soil layers do not present. Scott (1979) has reviewed various curve fitting functions which can be used for representing the bending moment data from centrifuge tests. Based on this study, he rejected the use of polynomial functions, as although these functions have the advantage of passing close to but not through the data points, they deviate widely from the known behavior of the pile below the level of the last moment data points. The use of rational functions as fitting functions was also rejected as their use depends upon pre-assumption of soil-pile interaction. A fifth order spline curve fitting was recommended by Scott as it gave reasonable soil resistance distribution and required no pre-acknowledge about the soil-pile interaction. Recently, Ting (1987) and Ting et al (1987) proposed a curve fitting technique consisting of fitting a seventh degree polynomial to bending data below the soil surface and a linear function above the soil surface. The origin of the seventh degree polyno-mial was selected at an arbitrary point at which the pile deflection, slope, moment, shear, and net soil pressure were all zero. The coefficients of the seventh polynomial were obtained by subjecting them to the constraint that the net soil resistance was zero at the ground surface. In this study, curve fitting techniques using both a cubic spline and the method proposed by Ting (1987) have been evaluated with present test data. The bending moment fitting by Ting's method was found to be very sensitive to the selection of the origin of the seventh order polynomial. It gave reasonable fitting at the low hydrauhc gradient condition. However, at the higher stress level, the fitting on bending moment data was much worse than that obtained from the cubic spline. Based on this experience, the cubic spline fitting is used in this study. This technique has been used by many researchers (Barton, 1982; Finn et al, 1983; 1984) Chapter 7. A Model Study of Pile Response to Lateral Loads 158 with reasonable good results. In this procedure, a collection of cubic sphne is fitted to the bending moment data, one between each two data points. Continuity of slope is assured at each point. Then the sphne is differentiated to give the distributed shear force and soil resistance along the pile, and integrated to give the pile inclination and deflection. Boundary conditions are also apphed to the fitted curves: 1. for the free-head piles, the bending moment is set to be zero at the loading point; 2. the shear force at the ground level is set equal to the apphed load; 3. the soil resistance at ground level is set to zero, and 4. the moment, shear, soil resistance, deflection and pile inclination are all set to be zero at the pile tip. Typical results using this procedure for the test data are shown in Figure 7.3 and 7.4 for free and fixed head piles, respectively. The P-y curves at specific depths can be obtained from the computed soil resistances and pile deflections at different loading stages. A n example of the P-y curves so obtained is shown in Figure 7.5. The experimental P-y curves so obtained have been employed to back predict the pile response using the computer program L A T P I L E (Reese, 1977). As shown in Figure 7.6, good agreement with the measurement is obtained. This indicates that the numerical scheme used to derive the experimental P-y curves can provide reasonably good results. 7.2.4 Experimental Program The experimental program was designed to examine the various factors which may affect the pile response to the lateral pile head loading. Then the test results are used to evaluate the current procedures for analyzing pile response under lateral pile head Chapter 7. A Model Study of Pile Response to Lateral Loads 159 E E. a F 2 CL 8 -Bending Moment (N.mm) (Thousands) 2 1 0 - 1 - 2 E E, Q. F 2 CL i Pile deflection (mm) 5 4 3 2 1 0 -1 -2 - 3 - 4 - 5 Q.S.L. Bending Moment Fit Pile Deflection Fit 60 40 Shear Force (N) 20 0 -=20 Soil Reaction (N/mm) 1 0 - 1 -2 Shear Force Fit Soil Reaction Fit Free Head Pile N=64 E=68mm Q.S.L. = ground surface line Figure 7.3: Typical Example of Representing Test Data by Cubic spline - Free Head Pile (Note: Ground Surface at Elev. 315.2 mm) Chapter 7. A Model Study of Pile Response to Lateral Loads 160 Shear Force Fit Soil Reaction Fit Fixed Head Pile N=48 E=45mm G.S.L, = ground surface line Figure 7.4: Typical Example of Representing Test Data by Cubic spline - Fixed Head Pile (Note: Ground Surface at Elev. 315.2 mm) Chapter 7. A Model Study of Pile Response to Lateral Loads ... Depth of 1D 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Pile Lateral Deflection - y (mm) Figure 7.5: Example of P-y curves from the cubic spline fitting technique Chapter 7. A Model Study of Pile Response to Lateral Loads 50-, ooooo Test Data LATPILE H i i i i i I I i | i I I i i i i i i | i i 1 i i i i i i | i i i i i i i i i | i i i i i i i i i | i i i i i i i i i 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Pile Deflection at Loadina Pile (mm) Bending Moment Profi le (N.mm) O-500 0 500 1000 1500 2000 2500 3000 i i i i i i i i i I i i i i I i i i t I i i j i | i i i i I i i i i i I -o I J P ° -t m <u o u o -D "~ V.-c n o m -T3 •-C o o - ° o m -" a . c u Q a o -o in-to o o -with Derived P—Y curves ooooo Test Data Free Head Pile N=64 Figure 7.6: Back Prediction of Pile Response by the L A T P I L E program using Experimental P-y curves Chapter 7. A Model Study of Pile Response to Lateral Loads 163 loading with attention focused on the selection of appropriate soil parameters. The results are interpreted in terms of pile head response, pile bending moment, and the nonlinear soil-pile interaction P-y curves. The experimental parameters changed in this study include: • pile diameter; • soil stress level and soil density; • loading amphtude and eccentricity; • nature of loading - static and cyclic; • nature of cychc loading - one-way or two-way; • number of loading cycles, and • pile head loading connection - free head or fixed head. Table 7.1 summaries all the testing series performed. The testing program consists of three testing series. Series-I was primarily designed to experimentally examine the hydrauhc gradient scahng laws for the laterally loaded pile testing. The "modelling of models" technique was once again employed as described in Chapter 3. Three model piles were tested under different stress levels and loading eccentricities. Series-II was the testing series aimed at studying different pile responses under different stress levels but the same loading eccentricity. By comparing the results from Series-I and II, it is demonstrated that the loading eccentricity has important influence on the pile head responses. In Series-Ill, the tests were carried out exclusively on the instrumented pile (6.35 mm O.D.) , aimed at evaluating the pile responses under various testing conditions hsted above. Chapter 7. A Model Study of Pile Response to Lateral Loads 164 Table 7.1: Summary of Main Testing Program on Laterally loaded Pile Series-I: scaling law evaluation - "modelling of models" technique; soil density = 75 %; free-head piles  Prototype N Model Pile Diam.(mm) Model Eccen.(mm) Load Ampl . Scale Dm Em (Newton) Dp = 0.31m 32 9.53 52.5 74.00 Ep = 1.68m 24 12.7 70.0 100.0 Dp - 0.31m 48 6.35 45.0 24.50 Ev = 2.17m 32 9.53 68.0 74.00 Dp = 0.61m 64 9.53 52.5 74.00 Ep = 3.36m 48 12.7 70.0 100.0 Series-II: all tests were performed at the same loading amphtude, eccentricity and soil density  Piles Dr (%) N Eccen.(mm) Load Ampl.(N) Head Fixity 1 68.0 100.0 Free Head uninstrumented 24 68.0 100.0 Free Head pile 75 % 48 68.0 100.0 Free Head (12.7mm O.D.) 64 68.0 100.0 Free Head 1 68.0 74.0 Free Head uninstrumented 24 68.0 74.0 Free Head pile 75 % 48 68.0 74.0 Free Head (9.53mm O.D.) 64 68.0 74.0 Free Head 1 68.0 24.5 Free Head instrumented 24 68.0 24.5 Free Head pile 75 % 48 68.0 24.5 Free Head (6.35mm O.D.) 64 68.0 24.5 Free Head Chapter 7. A Model Study of Pile Response to Lateral Loads 165 Series-Ill: all tests were performed on the 6.35mm instrumented pile Exp. factors Eccen.(mm) N Load Ampl.(N) Head Fixity Cyclic Load Eccen. 45.0 64 49.5 Free Head two-way studies, sand 52.5 64 49.5 Free Head two-way 7Jr=75% 70.0 64 49.5 Free Head two-way Load Ampl . 45.0 64 24.5 Free Head two-way A.=75% 45.0 64 49.5 Free Head two-way 45.0 1 24.5 Free Head two-way 45.0 10 24.5 Free Head two-way Stress Level 45.0 20 37.0 Free Head two-way D P =75% 45.0 30 37.0 Free Head two-way 45.0 40 49.5 Free Head two-way 45.0 52.7 55.8 Free Head two-way 45.0 70.7 80.1 Free Head two-way 45.0 48 32.9 Free Head one 45.0 48 32.9 Free Head two One-way vs. 47.0 48 49.5 Free Head one * L * M two-way cyclic 68.8 48 49.5 Free Head one * L D r =75% 68.8 48 34.0 Free Head one * M 68.0 48 34.3 Free Head two * M 45.0 48 49.5 Free Head two * M 45.0 48 49.5 Fixed one Fixed Head 45.0 48 49.5 Fixed two £ > P = 7 5 % 45.0 48 49.5 Fixed two — > one 48.0 48 32.9 Free two — > one Loose Sand 45.0 48 32.9 Free one — > two £> r=33% 51.0 48 32.9 Fixed two 48.0 48 32.9 Fixed one Note: * L - indicate having the same lateral load at ground level; * M - having the same applied moment at the ground level. Chapter 7. A Model Study of Pile Response to Lateral Loads 166 7.3 Test Results and Discussion 7.3.1 Scaling Law Evaluation A hydraulic gradient model tests can be regarded as an experiment on the model materials at prototype stress levels without a specific prototype, against which theo-retical and numerical predictions can be compared. However, if results from a para-metric study are valid, then the hydrauhc gradient scahng laws must be obeyed. It is important that model tests can scale correctly with each other, so as to ensure the consistency of the test data. The hydrauhc gradient scahng laws for the laterally loaded pile tests are summarized in Table 7.2 Table 7.2: Scahng Relations for H G S T test on Laterally Loaded Piles quantity Full Scale H G S T testing (Prototype) Model at Ng's Linear dimension, displacement 1 1/N Angular rotation, slope 1 1 Stress 1 1 Strain 1 1 Force 1 1/N2 Soil resistance 1 1/N 1/N3 1/N3 Bending moment 1 Mass 1 Young's modulus 1 1 Moment of inertia of pile 1 1/N4 The scahng relations can be evaluated by experimental evidence using the "mod-elling of models" technique as used in Chapter 3. For this purpose, a testing series has been devised to examine both 30.48 mm and 60.96 mm prototype piles at differ-ent loading eccentricities using the model tests shown in Series-I of Table 7.1. The results are shown in Figure 7.7, 7.8 and 7.9 for three prototype conditions in terms of pile head response. For a given model test, its prototype response is obtained by Chapter 7. A Model Study of Pile Response to Lateral Loads 167 120' o o 80-T J O CU I CP D_ 40 -D a Q < M * > e p1 n24-2 d i a . « l / 2 " e=70mm N=24 * * * * * p2n32e1 dia.~3/8" e=52.5mm N=32 0 Ti 11111 1111 11 i i 11111111111111111111111111111111111|11111 i 1111111111 i 11 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Pile Head Deflection at Load Point (mm) (at Mode! Scale) 80000 TJ 60000 o o . j ooooo p"ln243c2 * * * * * p2n32esc dia= l /2" e=70mm N=24 dia=3/8" e=52.5mm N=32 prototype dimemsion: pile dia.=1 ft eccentricity=1,680mm 0 T i i i i i i i i i | i i i i i i i 0 20 Pile Head Deflection at Load Point (mm) l i i i i i i i i i l i i i I i i i i i 40 60 80 (at Prototype Scale) Figure 7.7: Evaluation of Scaling Law for Pile Testing - Prototype Dimension-I: 30.48 mm diam. pile, load eccen.=1.68m Chapter 7. A Model Study of Pile Response to Lateral Loads 168 80-•o o o O U 40-Q) O L . CO BBOBB p3hd48e2 pile dla.=1/4" N=48 e=45mm oeoee p2hd32-2 pile dla."3/8" N=32 e-68mm n T T T r m yr\ i M 1 1 1 1 1 1 1 1 1 M 1111 i i i i i i 11 i 11 i i i i r 111111 111 11 111 111 1 1 1 1 ; 0.0 0.5 1.0 1.5 2.0 2.5 Pile Head Deflection (mm) 3.0 3.5 (at Model Scale) 80000 c 60000 D O o 40000 tt) CL. CO a 20000 -D M se pile dia.= 1/4" N»48 e~45mm s « « e e pile dia.=3/8" N=32 e=68mm Prototype Pile DIameter=12 in and Loading Eccentrlclty=2170mm TTTT I I I I | I I I I I I I I I | I I 1 I I I I I I | I I I 1 I 1 I I I | I I I I I I I I I | I 1 I I I I 0 20 40 60 80 100 Pile Head Deflection at Loading Point (mm) 1 2 U (at Prototype Scale) Figure 7.8: Evaluation of Scaling Law for Pile Testing - Prototype Dimension-II: 30.48 mm diam. pile, load eccen.=2.17m Chapter 7. A Model Study of Pile Response to Lateral Loads 169 (at Model Scale) 3E+005-1 0 20 40 60 80 100 120 Pile Head Def lect ion at Load ing Point ( m m ) (at Prototype Scale) Figure 7.9: Evaluation of Scaling Law for Pile Testing - Prototype Dimension-Ill: 60.96 mm diam. pile, load eccen.=3.36m Chapter 7. A Model Study of Pile Response to Lateral Loads 170 multiplying the load and deflection measurements by N2 and N respectively at the corresponding N - value. For the purpose of comparison, the results in the model scale are also shown. It can be seen from these results that similar prototype behav-ior is obtained from different model tests under scaled stress conditions. This verifies that the H G S T modelling technique for laterally loaded pile tests is self-consistent and obeys the scahng principle. It is interesting to note that if two model tests were not prepared according to the scahng law, different prototype behavior would have been observed. A n example of this is shown in Figure 7.10. In this example, two different model piles were tested under such hydrauhc gradient conditions that they were both projected to simulate a 30.48 mm prototype pile. However, the loading eccentricities in the two models were the same, giving different loading eccentricities in the prototype. As shown in Figure 7.10, the pile head responses in terms of prototype scale are quite different, although they have the same prototype pile diameter. The pile having the larger loading eccentricity in the prototype gives a much softer response. This also illustrates the important influence of loading eccentricity on the pile head response. 7.3.2 Pile Response to Static Loading Static loading is considered to be the first half cycle of the cychc loading. In this loading process, the soil-pile system starts from a virgin state, and then experiences nonhnear soil reaction as the load increases. Its general behavior may be greatly influenced by the relative soil-pile stiffness, the apphed load/moment ratio, and the pile head loading fixity. 7.3.2.1 Effects of Relative Soil-pile Stiffness The influence of the relative soil-pile stiffness can be easily studied in H G S T tests in two ways: Chapter 7. A Model Study of Pile Response to Lateral Loads 171 8E+004--o 6E+004-3 D O D u 4E+004-0E+000 eeee© P3N48-1 D m 1=l/4" N, = 48 E m 1 = 68mm ••••• P2N32-2 Dm3=3/8" N,=32 Em2=68mm Prototype Dimension: Dp1 = 12" Ep1=3,264mm Dp2=12" Ep2=2,176mm i i i i i i i i | i i i i i i i i i | i i i i i i i i i | i i i i i i i i i [ i i i i i i i i i | i i i i i i i !~r 0 20 40 60 80 100 ; 20 Pile Head Def lect ion at Load ing Point (mm) (at Prototype Scale) Figure 7.10: Responses of Projected Prototype Piles under Different Prototype Ec-centricities Chapter 7. A Model Study of Pile Response to Lateral Loads 172 • the same model pile is tested under different soil stress levels by gradually increasing the hydraulic gradients in each test; • the model piles of different diameters (or different stiffness) are tested under the same soil stress level (i.e. the same hydrauhc gradient). In this section, the effect of soil-pile stiffness is discussed comprehensively in terms of varying hydrauhc gradient in the tests. The effect of pile diameter is only briefly discussed as only one model pile was instrumented with the strain gauges. The test results are presented in terms of pile head response, pile bending moment distribution, and the soil-pile interaction P-y curves. Pile Head Response ' Pile head responses under different hydrauhc gradients are shown in Figure 7.11 for a 6.35mm O . D . free head pile and a loading eccentricity of 45mm. The deflections are those measured at L V D T 1 (20mm above loading point) and the slopes are those cal-culated at the ground level (see Eq.(4.5)). Due to the subtraction from the deflection measurements, the slope data at the ground level shows more scatter. Nevertheless, it is clearly shown from the figure that the pile head response is significantly influenced by the soil stiffness. As the hydrauhc gradient increases, the pile response becomes stiffer. This influence is very marked as the hydrauhc gradient scale factor N changes from zero to 10, above 10 the influence is less marked. This indicates that the pile response under the lateral loading is strongly dependent upon the soil stress levels, or the relative soil-pile stiffness. The pile head response shown in Figure 7.11 is typical of those for piles under lateral loading. The pile load-deflection response has a gentle curve all the way and has an appearance very different from that under axial loading. It is difficult to pick out any portion of the lateral behavior, to which a hnearly elastic model could be ascribed. It was observed that the soil elements in front of the pile yielded while at Chapter 7. A Model Study of Pile Response to Lateral Loads 173 N=1 N=10 A N=20 N=30 N=70 (a) Pile Diam.=1/4" Free-headed pile Load Eccen. =45mm 2 4 6 8 Pile Head Deflection (mm) at LVDT1 10 N=1 N=10 A. N=20 o N=30 N=70 (b) Pile Diam.=1/4" Free-headed pile Load Eccen. =45mm 0.5 1 1.5 2 2.5 Pile Slope (deg.) at ground level Figure 7.11: Typical Example of Pile Head Response under Different Hydraulic Gra-dients Chapter 7. A Model Study of Pile Response to Lateral Loads 174 the back a gap commenced to appear between the soil and the pile. As the load was increased, the soil yielding in the front progressed down further, and the gap behind widened and deepened. These observations explain the observed nonlinear pile head response, and are similar in characteristics with those in the centrifuge tests (Barton, 1982). Bending Moment Typical bending moment distributions along the pile length under different hydraulic gradients are given in Figure 7.12(a). The measured bending moments along the pile have been normalized to the applied lateral load at the pile head so as to eliminate the bending moment difference due to the different load magnitudes. It may be seen that the applied hydrauhc gradient greatly changes both the shape and the magnitude of pile bending moment distribution. The change is also most prominent when the hydrauhc gradient increases from one to 10. Such observations result because at low soil stress level, the pile is deflected down to almost its full length in order to mobilize enough soil resistance to the applied load. For the same applied load and moment, this deflected pile length (or the mobihzed soil layer) is greatly reduced as the soil stress or stiffness increases due to the apphed hydrauhc gradient. As a result, with increasing hydrauhc gradient, the maximum bending moment decreases, and the depth to the maximum bending moment moves toward the soil surface. At the hydrauhc gradient scale factor equals 70, some negative bending moments were developed at depth. These observations also indicate that it is important to have a field stress condition when studying soil-pile interaction using small scale model tests. Results from lg's model tests may be misleading. A comparison of pile bending moment distribution measured under different mag-nitudes of lateral loads is shown in Figure 7.12(b) for a given hydrauhc gradient scale factor N = 30. It is seen that the maximum bending moment in the pile occurs at Chapter 7. A Model Study of Pile Response to Lateral Loads 175 (100) E E, <D o CB •c 3 (0 TJ C 03 (0 o CD n SL 200 a . CD Q 100 300 contour of max. bending moment at different hydraulic gradients N=1 N=10 N=20 N=30 N=70 _i_ _L_ 400 300 200 100 (20) 0 20 40 60 80 100 Normalized Bending Moment (Moment/Applied Load - mm) (100) E E, CD O CO •c 3 V) TJ C CO V) $ o "53 n r. S. CD Q 100 200 300 at given hydraulic gradient, N=30 contour of max. bending moment (b) load=10,81 (N) k>ad=18.18(N) load=25.92(N) 400 300 200 100 (200) 200 600 1,000 1,400 0 400 800 1,200 1,600 Pile Bending Moment (N.mm) Pile diam.=1/4", free-headed pile loading eccentriclty=45mm Figure 7.12: Typical Example of Pile Bending Moment Distribution, (a), under different hydraulic gradient; (b). under different loading magnitude Chapter 7. A Model Study of Pile Response to Lateral Loads 176 a depth of from 20 to 30mm, i.e. 3 to 5 pile diameter depth, and appears to move down as the load increases. The downward movement of the location of the maximum bending moment is another indication of nonlinear soil-pile interaction. As the pile is displaced by the load, the maximum bending moment will keep increasing until it reaches the pile yielding bending moment, which is the ultimate criterion for failure of a laterally loaded pile. However, displacements also increase, and generally the allowable displacement is reached before the bending moment reaches the yielding value. Regarding the example given in Figure 7.12(b), the maximum bending mo-ment is about 1400 N.mm at a load of 25.9 Newton, which is about 1/4 of the yielding value. However, the pile head deflection at the ground has reached about 22% of the pile diameter under this loading condition. This would be a large amount for a pro-totype condition and would generally be the controlling factor. Thus, in practice, the accurate prediction of pile deflection is very important. Soil-pile Interaction P-y curves Effects of Soil Stress Levels The effects of soil stress level on the soil-pile interaction are evaluated in terms of nonlinear P-y curves of given pile at different depths and under different hydrauhc gradients. The P-y curves are derived according to the method described in Sec-tion 7.2. Figure 7.13 shows the P-y curves of different depths for the model pile of 6.35 mm O . D . under a free head loading condition. The hydrauhc gradient scale factors shown are 10 and 70. It can be seen that the soil-pile interaction is highly nonlinear. At the shallow depth, the derived curves are very soft due to the low confining stress and gapping behind the pile. They becomes stiffer and less nonlinear as the depth increases. At higher hydrauhc gradient condition, the derived curves at depths beyond Chapter 7. A Model Study of Pile Response to Lateral Loads 177 £ 0.B E U- 0.6 • 0 O c 03 "5 « CC O 0.2 (a). Scale Factor N=10 /,*-'''o /y'o Depth=1D Depth=2D Depth=3D Depth=4D Depth=5D 0.2 0.4 0.6 Pile Deflection - y (mm) 0.8 3.5 Depth=1D Depth=2D Depth =3D Depth=4D Depth=5D (b). Scale Factor N=70 Pile Deflection - y (mm) Figure 7.13: The P-y Curves at Different Depths for a Free-head Model Pile of 6.35 mm O . D . Chapter 7. A Model Study of Pile Response to Lateral Loads 178 3 to 4 pile diameters become hard to differentiate. Similar results have been reported in centrifuge tests (Finn et al, 1984; Ting et al, 1987) and full scale tests (Ting, 1987). Figure 7.14 shows the experimental P-y curves at four locations below the ground under different hydraulic gradient conditions. It is seen that at all depths the P-y curves at A^=l are very soft and reach some ultimate values at small pile deformation. However, as the soil stresses increase due to the apphed hydraulic gradient, stiffer and less nonhnear soil-pile interaction curves are obtained. If the experimental P-y curves are plotted on a logarithmic scale, as shown in Figure 7.15, they become linear. The slopes of these linear curves are in the range of 0.4 to 0.6. This indicates that the derived P-y curves may be approximated by some power functions. This finding is in accordance with the experimental P-y curves described by Kubo (1966), Yoshida and Yoshinaka (1972) and Tajimi (1977) and the results from the finite element studies using a plane strain model (Yan, 1986). It appears that the general behavior of soil-pile interaction at different depths and hydrauhc gradients is much ahke, ah being the results of soil stress level effects. It will be very useful if the soil-pile interaction P-y curves can be normahzed relative to the soil stress levels, then for the given soil condition the P-y curves at various depths below the ground can be specified by a single equation. Parametric nonhnear finite element analyses using a plane strain domain and a hyperbohc stress-strain relation for sand indicate that the computed P-y curves under different soil stress conditions and pile diameters can be normahzed by a power function using the initial soil Young's modulus and pile diameters as described in Chapter 6. In hght of the theoretical studies shown in Chapter 6, the experimental curves are also normalized in form of Eq.(6.15). The initial soil Young's modulus in the tests is calculated as in Eq.(6.16) with Ke and n values from the conventional triaxial compression tests on the same soil condition, as given in Chapter 3. Chapter 7. A Model Study of Pile Response to Lateral Loads 179 E 2 " 5 E £ 2 a. i i . 5 1 0.5 0 N=1 N=10 No20 N=30 N=70 0.5 1 1.5 Pile Deflection - y (mm) Depth=1D S c 1 a> DC 3 2.5 2 1.5 1 0.5 N=1 N=20 N=30 N=70 ...o" ..of? 0.5 1 1.5 Pile Deflection - y (mm) Depth=2D S c a 3 2.5 2 .5 1 0.5 0 N=1 N=10 m N=20 N=30 N=70 -• • • -t / J - / / ° J/ t—G—a-—— B —;— B —r~°—r*^ ' a—s-ti 0 0.5 1 1.5 * 3 2.5 2 1.5 1 0.5 0 \ l 0 & N = 1 N = 10 N=20 N=30 N=70 2 Z L Pile Deflection - y (mm) Depth=3D 0.5 1 1.5 Pile Deflection - y (mm) Depth=4D Figure 7.14: The P-y Curves at Different Hydrauhc Gradients, Free head Model Pile of 6.35 mm O . D . Chapter 7. A Model Study of Pile Response to Lateral Loads Figure 7.15: Experimental P-y curves in a Logarithmic Scale Chapter 7. A Model Study of Pile Response to Lateral Loads 181 Figure 7.16 shows the experimental P-y curves at different depths normahzed over the hydrauhc gradients. It is seen that the experimental curves collapse to a narrow band in agreement with the plane strain finite element analyses except those at 1 pile diameter depth and i V = l stress condition. This indicates that at low stress conditions, the effects of stress levels induced by the hydrauhc gradient may not be normahzed as in Eq.(6.15). This may result from the low confining stress effects. Near the sand surface (at 1 pile diameter depth) or at la's (N=l) stress condition, due to the low soil stress confinement, the mode of soil-pile interaction may be far from that in the plane strain model. As shown in Figure 7.17. a comparison of plane strain and plane stress finite element analyses with the experimental P-y curves at the shallow and deep depths suggests that the soil-pile interaction behavior near the sand surface may be closer to that in the plane stress model, while at depths below 1 pile diameter the plane strain model may become more appropriate. Figure 7.18 compiles all the normahzed P-y curves at different depths shown in Figure 7.16. It is noted that except those at 1 pile diameter depth all the normahzed P-y curves at different depths fall into a narrow band. The average curve may be expressed as: This indicates that the stress level effects on P-y curves due to different depths below the ground can be properly taken into account by Eq.(6.15). In the practical apphcation, evaluation of the initial soil Young's modulus may be difficult. Thus, it would be useful to see if the initial soil Young's modulus in Eq.(6.15) can be replaced by the maximum soil Young's modulus, Emax, as the maximum soil Young's modulus can be easily evaluated from the maximum shear modulus, Gmax, measured from insitu downhole and crosshole seismic tests. Figure 7.19 and 7.20 show the experimental P-y curves normahzed by Emax, where the Emax was evaluated from Gmax measured in the model sand as described in Chapter 5. It is seen from the figures (7.5) Chapter 7. A Model Study of Pile Response to Lateral Loads 182 _ 2.5 o Normalized Pile Deflection - y/D (%) Depth=1D N=1 N=10N=20N=30N=70 - O - ~tV- •••©•• - • -Normalized Pile Deflection - y/D (%) Depth=2D N=1 N=10N=20N=30N=70 ^ 2.5 ^2.5 0 5 10 15 20 25 30 Normalized Pile Deflection - y/D (%) Depth=3D N=1 N = 1 0 N = 2 0 N = 3 0 N = 7 0 _e- - A-- -o- -*>-- -5 10 15 20 25 Normalized Pile Deflection - y/D (%) Depth=4D 30 N=1 N=10N=20N=30N=70 Figure 7.16: Normalization of the Experimental P-y Curves over the Hydrauhc Gra-dient Stresses at Different Depths Chapter 7. A Model Study of Pile Response to Lateral Loads 183 1 Pile Deflection - y (mm) o © PLANE STRESS I ' I ' I L _ . _ L 0.0 0.02 0.04 0.08 O.OB 0.1 0.13 0.14 0.16 O.IB 0.2 LATERAL DEFLECTION (FT) A F T E R A T U K O R A L A E T A L ( 1 9 8 6) Figure 7.17: Comparison of Plane Stress and Plane Strain F E M analyses with the Experimental P-y Curves at Shallow and Deep Locations Chapter 7. A Model Study of Pile Response to Lateral Loads ... - 2 . 5 *_ UJ rT 2 • c a 0) = 1 o 0) "S 0-5 N 75 I 0 o z aSax O C A o^  * - g 5 10 15 20 25 Normalized Pile Deflection - y/D (%) 30 Depth=1D Depth=2D Depth=3D Depth=4D & a O . . - - "A average curve without those data at depth=1D 5 10 15 20 25 Normalized Pile Deflection - y/D (%) Depth=2D Depth=3D Depth=4D 30 Figure 7.18: Compilation of A l l the Normalized P-y curves at Different Depth Chapter 7. A Model Study of Pile Response to Lateral Loads 185 0.8 N=1 N=10N=20N=30N=70 5 10 15 20 25 30 Normalized Pile Deflection • y/D (%) Depth=1D o * 0.8 c o CO CD CC 0.6 0.4 0.2 E o z N=1 N=10N=20N=30N=70 0 5 10 15 20 25 30 Normalized Pile Deflection - y/D (%) Depth=2D 0.8 c o 1 a CD EC 1 0.6 0.4 0.2 a E o z N=1 N=10 N=20 N=30 N=70 /'' t*% <fi 0 5 10 15 20 25 30 Normalized Pile Deflection - y/D (%) Depth=3D 0 5 10 15 20 25 30 Normalized Pile Deflection - y/D (%) Depth=4D Figure 7.19: Normalization of Experimental P-y Curves by E, Chapter 7. A Model Study of Pile Response to Lateral Loads 186 Depth=1D Depth=2D Depth=3D Depth=4D O O A * A < & o a » « * _ A * A • D * Q A „ n CE - * 0 * * 3 D O D * 6 a * a • • D %• ° • ° • • » I , I u _ 10 15 20 25 Normalized Pile Deflection - y/D (%) 30 D s E 0.8 ui c 0.6 o ts a £ 0.4 75 CO "o 0.2 N 75 Depths 2D Depths 3D Depth=4D A-a g&xjfl* o n o a [F ,a^--~ average curve without those data at depth=1D 10 15 20 Normalized Pile Deflection - y/D (%) 25 30 Figure 7.20: Compilation of Experimental P-y Curves normalized by Emax at different Depths Chapter 7. A Model Study of Pile Response to Lateral Loads 187 that similar patten is observed in the P-y curves normahzed by Emax as compared to those in Figure 7.16 and 7.18. The best fit equation is now: However, there is more divergence at large deformation when the P-y curves normal-ized by Emax rather than Ei. This divergence may be expected as Emax occurs at much smaller strain level than Ei, and is not able to accommodate the stress level effect at intermediate and large strain range due to the nonhnear soil response. The ratio of Emax to Ei is found to be about 3 in this study. Similarly, the experimental P-y curves for loose sand, DT = 33%, is normahzed by the maximum Young's modulus, E m a i ) and shown in Figure 7.21. The curve fitting equation is as follows: loose sand is higher than that for dense sand, as indicated by the plane strain finite element analyses. Effects of Pile Diameter As only one model pile was instrumented to measure the bending moment distribution along the length, a direct study of pile diameter effect on the P-y curves is not possible. However, the pile diameter effects on the P-y curves can be indirectly studied by projecting the same model pile to different prototypes using the corresponding hydrauhc gradient scale factors, as explained in the following paragraph. According to the hydrauhc gradient scahng law listed in Table 7.2, for the given model pile, the P-y curves derived at a given depth under different hydrauhc gradients will represent the soil-pile interaction of different prototype piles at different prototype depths. (7.6) (7.7) By comparing Eqs.(7.6) and (7.7), it can be seen that the normahzed P-y curve for Figure 7.21: Normalized Experimental P-y Curves for Loose Sand by E, Chapter 7. A Model Study of Pile Response to Lateral Loads 189 If the P-y curves under different hydraulic gradients are derived at some model depths in such a way that the same prototype depth is maintained; i.e zP = N, • ( z m ) a = JV2 • (zm)2 (7.8) then, these derived P-y curves at prototype scale will represent the effect of prototype pile diameter. The different prototype pile diameter will be obtained as: (A>)l = W l - C A n ) (7-9) (Dp)2 = N2.(Dm) (7.10) where (zm)i2 are the different model depths, i V l i 2 are the corresponding hydrauhc gradient scale factors, Dm is the model pile diameter, and zp and (Dp)i.2 are the prototype depth and the prototype pile diameters, respectively. Figure 7.22 presents the pile diameter effects on the P-y curves at a prototype depth of 190.5 mm. For the purpose of comparison, the P-y curves at model scale are also included in the figure. Similar results at other prototype depths are shown in Figure 7.23 and 7.24. It is seen from the results that the pile diameter only affect the P-y curves at large pile deflection. At small deflection, the effects are negligible. 7.3.2.2 Effects of Applied Load to Moment Ratio In the above discussions, all the test data were obtained under the same loading eccentricity at the pile head. By changing the loading eccentricity relative to the ground surface, different bending moments at the ground level will be applied to the pile under the same lateral load, i.e different load to moment ratio will be obtained at pile head. As reviewed in Chapter 6, some comparisons of hnear elastic solutions from subgrade reaction method and elastic boundary integral method have suggested that the subgrade reaction modulus depends upon the loading eccentricity. Thus, it is important to check experimentally the effects of loading eccentricity on the P-y curves. Chapter 7. A Model Study of Pile Response to Lateral Loads 190 0.6 Pile Deflection in Prototype Scale (mm) Figure 7.22: Pile Diameter Effect on P-y curves at a Prototype Depth of 190.5mm, Prototype Pile Diameters of 63.5mm, 190.5mm, respectively Chapter 7. A Model Study of Pile Response to Lateral Loads 191 20 0 5 10 15 20 Pile Deflection in Prototype (mm) Figure 7.23: Pile Diameter Effect on P-y curves at a Prototype Depth of 254.0mm, Prototype Pile Diameters of 63.5mm, 127.0mm, respectively 60 E Pile Deflection in Prototype (mm) Dp = Prototype Pile Diameter Dm = Model Pile Diameter Figure 7.24: Pile Diameter Effect on P-y curves at a Prototype Depth of 508.0mm, Prototype Pile Diameters of 127.0mm, 254.0mm, respectively Chapter 7. A Model Study of Pile Response to Lateral Loads 192 The effects of loading eccentricity are studied here by evaluating the test results under three loading eccentricities, i.e. the lateral loads are applied at 45.0 mm, 52.5 mm and 68.0 mm distances that are about 7, 8.3 and 11 pile diameters above the ground levels. Loading adaptors used for this testing series were discussed in Chapter 4. Results are evaluated in terms of pile head response, bending moment and the P-y curve. Pile Head Response Figure 7.25 shows the pile head response under the three loading eccentricities. The hydrauhc gradient scale factor, TV, in all these three tests was 64. It is seen that higher loading eccentricity causes a softer pile head response. Extra pile deflection and pile rotation are induced by the additional moment resulting from the higher loading eccentricity. Bending Moment Figure 7.26 shows the relationship between the apphed lateral load and the maximum bending moment in the pile. It is seen that for the given lateral load a large loading eccentricity results in a larger maximum bending moment in the pile. It is also seen that the relation between the lateral load and the maximum bending moment appears to be linear at a low loading eccentricity, but becomes nonhnear at a high loading eccentricity. Figure 7.27 shows the bending moment distributions under the three loading ec-centricities. The bending moments were normahzed so as to compare the bending moment under the same loading magnitude. As expected, a higher loading eccen-tricity leads to a higher bending moment distribution. Consequently, the pile will be deflected to a deeper position below the ground. However, it seems that the depth to the maximum bending moment does not change significantly with the loading eccentricity. Chapter 7. A Model Study of Pile Response to Lateral Loads 193 40 0 2 4 6 8 Pile Head Deflection at LVDT1 (mm) Hydraulic Gradient Scale Factor N=64 Model Pile of 1/4" O.D. Free Headed Condition 40 0 0.01 0.02 0.03 0.04 0.0S Pile Head Rotation at Loading Point (rad.) Hydraulic Gradient Scale Factor N=64 Model Pile of 1/4" O.D. Free Headed Condition Figure 7.25: Loading Eccentricity Effects on Pile Head Response Chapter 7. A Model Study of Pile Response to Lateral Loads 194 1,000 2,000 3,000 Maximum Pile Bending Moment (N.mm) Eccen.=45.0mm Eccen.=52.5mm Eccen.=68.0mm 4,000 Figure 7.26: Applied Lateral Load vs. Maximum Pile Bending Moment under Dif-ferent Loading Eccentricities (100) E E ' ' 0 o u CO 1— 3 CO TJ C 100 CO to 5 o o .a .c 200 Q. v Q 300 • Q A . . . o .. ^J&& -O" .. O ' (b) E c c e n . = 4 5 . 0 m m E c c e n . = 5 2 . 5 m m E c c e n . = 6 8 . 0 m m I I I I t I - I , I 400 300 200 100 (20) 0 20 40 60 80 100 Normalized Bending Moment - moment/load (mm) Figure 7.27: Loading Eccentricity Effects on Bending Moment Distribution Chapter 7. A Model Study of Pile Response to Lateral Loads 195 Soil-Pile Interaction P-y Curves Figure 7.28 shows the derived P-y curves at different depths from these tests. It is seen that the loading eccentricity has some effects on the P-y curves at depth of 1 pile diameter. A higher load to moment ratio leads to a softer P-y curve. However, at deeper locations below the ground, the loading eccentricity basically has httle effect on the soil-pile interaction in terms of P-y curves. Thus, for the practical apphcation, the limited effects of load to moment ratio on the P-y curves may well be neglected, and the same set of P-y curves can be used to predict the pile response under different loading eccentricities, as will be shown in Chapter 8. This lends support to the A P I code in which the P-y curve is not a function of loading eccentricity. 7.3.2.3 Effects of Pile Head Fixity In all the above tests, the model piles were loaded in a free head condition, i.e. the free rotation of pile head under lateral loading is permitted. In practice, few piles are connected to the superstructure in this free head condition. Some constraints in pile head rotation are always present. In this section, the effects of pile head fixity on pile response are studied by performing two parallel tests under free and fixed head conditions. The loading connections for this purpose were discussed in Chapter 4. The results are also presented in terms of pile head response, pile bending moment and the P-y curves. Pile Head Response Figure 7.29 shows the pile head fixity effects on the pile head response. It can be seen that in contrast to the pile head response of a free head pile the relation between the pile head deflection and the apphed lateral load appears to be more linear at the fixed head condition. In the case of fixed head condition, the pile head deflection is about half of that in the free head condition. The smaller pile deflection in the fixed Chapter 7. A Model Study of Pile Response to Lateral Loads 196 3 Figure 7.28: Loading Eccentricity Effects on the P-y Curves at 1 to 2 Pile Diameter Depths Chapter 7. A Model Study of Pile Response to Lateral Loads 197 3 3 Figure 7.28: Loading Eccentricity Effects on the P-y Curves at 3 to 4 Pile Diameter Depths Chapter 7. A Model Study of Pile Response to Lateral Loads ... 198 2.5 Depth=5D Eccen.=45.0mm Eccen. =52.5mm Eccen.=68.0mm 0.3 Pile Deflection - y (mm) Model Pile DIam.=1/4" Free Headed Connection Hydraulic Gradient Scale Factor N=64 0.3S Figure 7.28: Loading Eccentricity Effects on the P-y Curves at 5 Pile Diameter Depth Chapter 7. A Model Study of Pile Response to Lateral Loads ... Figure 7.29: Pile Head Fixity Effects on Pile Head Deflections (100) E E, u o ra k. 3' CO TJ C «3 CO a> sz 3 o <D n a. Q 100 300 N=48; Eccentricity=45.0mm * • o .A ' ' A ""'-••o'" A ' , c " " Load = 1.2 N Load=12.7 N Load=24.44 N Load=40.50 N 400 300 200 500 1,000 1,500 (1,000) (500) 0 Pile Bending Moment (N.mm) Figure 7.30: Pile Bending Moment Distribution under Fixed Head Loading Chapter 7. A Model Study of Pile Response to Lateral Loads 200 head condition results from the negative moment applied at the pile head due to the rigid loading connection. This order of difference between the free and fixed head pile deflection is in an agreement with the predictions given by the linear elastic solutions of either subgrade reaction method or the boundary integral method (Tomlinson, 1977; Randolph, 1981 and Poulos, 1986). Pile Bending Moment Figure 7.30 shows the pile bending moment distribution along the pile length under different load magnitude. It is shown that as the pile is deflected under a lateral load, a negative bending moment is developed above the ground surface due to the restriction of pile head rotation by the rigid pile cap. A comparison of the normalized pile bending moment distributions from free and fixed head conditions is given in Figure 7.31. It is shown that owing to the negative bending moment at the pile head, the pile bending moment distribution below the ground surface is much less as compared with that at the free head loading condition. The depth to the peak positive bending moment for the fixed head condition is also found to be deeper than that for the free head condition. Figure 7.32 compares the relations between the apphed lateral load and the max-imum pile bending moment under different pile head fixity conditions. For the free head condition, the maximum positive bending moment below the ground is presented while for the fixed head condition both maximum positive and negative bending mo-ments are also included. It is seen from the figure that under the given lateral load a rigid pile head connection reduces the peak positive pile bending moment below the ground to about half of that developed in a free head condition. In the fixed head condition, it is found that the absolute value of the negative bending moment at the pile head is much larger than the peak positive bending moment below the ground. This indicates that in the case of fixed head condition the critical moment is Chapter 7. A Model Study of Pile Response to Lateral Loads 201 Figure 7.31: A Comparison of Normalized Pile Bending Moment Distribution from Free and Fixed Head Conditions 100 z 8 0 J 60 -40 Free Head (positive moment) — e — Fixed Head (positive moment) Fixed Head (negative moment) Hydraulic Gradient Scale Factor N =48 Model Pile of 1/4" O.D. Loading Eccentricity=45.0mm 500 1,000 1,500 Maximum Pile Bending Moment (N.mm) 2,000 Figure 7.32: Pile Head Fixity Effects on the Apphed Load to the Maximum Bending Moment Relation Chapter 7. A Model Study of Pile Response to Lateral Loads 202 the negative bending moment beneath the pile cap rather than the positive bending moment. The magnitude of this negative bending moment, however, is lower than the maximum positive bending moment occurred at the free head condition. Thus, in practice, more lateral resistance will be provided by the fixed head piles than that by the free head piles. Soil Pile Interaction P-y curve The P-y curves at different depths for the fixed head pile are shown in Figure 7.33(a). It is seen that these curves are similar in shape to those for free head piles. A compar-ison of P-y curves at free and fixed head pile conditions is shown in Figure 7.33(b). As shown, little effect due to the pile head fixity on the P-y curves is observed. Thus, the same set of P-y curves can be used to analyze the pile response under either free or fixed head conditions. This lends support to the P-y curves specified in A P I code which is not a function of pile head fixity. 7.3.3 Pile Response to Cyclic Loading In practice, the pile foundation may often be subjected to cyclic lateral loads at the pile head due to the wind, ocean wave, or the inertial force of earthquake loading. Thus, the response of pile to the cyclic pile head loading is an important aspect to be examined. In this section, the response of model piles in sand subjected to slow cyclic horizontal load is discussed, which may more closely simulate the action of pile to the wind, offshore wave or ice loading condition. The lateral load was applied in a period of 40 seconds per cycle. The drained condition prevailed in the sand under such a slow loading condition. The loading device and data acquisition system used were discussed in Chapter 4. The various factors on the static pile behavior discussed in the preceding section also affect the pile response to the cyclic loading. Thus, in this section, the attention will be focused on the pile responses to different types of Chapter 7. A Model Study of Pile Response to Lateral Loads 203 2.5 E 2 .E . z O, 1.5 (a). A. - A ' " A Depth=1D Depth=2D Depth=3D —o Depth=4D Depth=5D 0.2 0.3 0.4 Pile Deflection - y (mm) Hydraulic Gradient Scale Factor N=48 Model Pile of 1/4"O.D. Eccen.=45.0mm Fixed Head Condition 0.5 2.5 E E z, Q , 1.5 I C O t> a 0) CC 2 -Free-depths ID Free-depth=2D Free-depth=3D Frae-depths40 Fixed-depth=1D Fixed^iepth=2D Fixed-depth ° 3 D Fixed-depth=4D (b). (0 0.5 0.2 0.3 0.4 Pile Deflection - y (mm) Hydraulic Gradient Scale Factor N=48 Model Pile of 1/4"O.D. Eccen.=45.0mm Free Head vs. Fixed Head Conditions 0.5 0.6 0.6 Figure 7.33: Comparison of P-y curves from Free and Fixed Pile Head Conditions Chapter 7. A Model Study of Pile Response to Lateral Loads 204 cyclic loading which includes one-way unsymmetric and two-way symmetric loadings. Loads with constant amplitude are applied, and the results are presented in terms of pile head response, pile bending moment and the soil-pile interaction P-y curves. 7.3.3.1 Two-way Cyclic Loading Pile Head Response Figure 7.34 shows the time histories of applied lateral load and pile head deflection for a free head model pile under the two-way cyclic loading condition. Figure 7.35 shows the pile head peak deflections with the number of loading cycles. The pile head deflection in Figure 7.35 has been normalized to the maximum lateral load applied to the pile. Both pile deflections in compression loading and tension loading are shown in the figure. It may be seen from the figures that the pile head deflection under a constant two-way cyclic loading decreases initially then increases with the number of loading cycles in both compression and tension directions. The initial reduction of pile head deflection with loading cycles may be related to the initial soil densification due to the cyclic pile movement. It is a well known fact that in a drained condition a sand element will be densified under cyclic loading, and the two-way cyclic load in a simple shear condition is the most effective way to densify the sand element (Oh-oka, 1976; Shaw and Brown, 1986; Leshchinsky and Rawlings, 1988). The stress strain behavior of sand under constant two-way cychc simple shear loading condition is shown in Figure 7.36 to illustrate this densification process. After about 10 cycles of loading, the pile deflection starts to increase gradually with the loading cycles. This may be due to soil-pile gapping which may cause the soil loosen up under further cychc loadings. During the cychc loading tests, symmetrical cavities similar to those reported by Barton (1982) in centrifuge tests were observed at both faces of the pile in the direction of loading. It was also observed that the cavity between the pile and soil became larger and deeper as the loading cycles increased. Chapter 7. A Model Study of Pile Response to Lateral Loads 205 Applied Lateral Load Time History T 0.4 0.6 (Thousands) r 0.8 Time (s) Pile Head Deflection Time History 3 -b 1 to o c o t> . , o -1 -O cZ -3 -48M1 test: free head, N=48, E=68mm —i— 0.2 —I 1 1— 0.4 0.6 (Thousands) 0.8 Time (s) Figure 7.34: Time Histories of Applied Lateral Two-way Cyclic Load and Pile Head Deflection at L V D T 1 Chapter 7. A Model Study of Pile Response to Lateral Loads ... 206 z E E p. Q CD C o o 0) «•— CD Q •o 0) N "5 E o z 18 17 16 15 14 13 12 B Compression Load Tension Load J 3 . . . . J 3 - - E » - e ' " 24 4 8 12 16 20 Number of Loading Cycles 48M1 Test: N=48 E=68mm Load Ampl.=23(N) Figure 7.35: Normalized Pile Head Peak Deflection with Number of Loading Cycles, 48M1 Test: iV=48, £ = 6 8 m m , Load Ampl.=23(Newton) Dr-38% Dr-64 % Dr= 85% T (Kg/cm*) T (kg/cm2) T (kgAnf) 0.3 Q2 0.I; f I i I i 1 -0.5 / / / ' // / 1.0 /(%) i I -05 u W 05 1.0 0.5 1.0 0.5 __2> • 1.0 1.0 (c) ev(%) (d) ev(%j ( e ) ev (%) 02" 1.0 kg/cm2 Toyoura sand Figure 7.36: Example of Drained Sand Response under Two-way Simple Shear Load-ing Condition, after Oh-Oka, 1976 Chapter 7. A Model Study of Pile Response to Lateral Loads 207 The gapping was most severe in the two-way cyclic loading condition as compared to that in the one-way loading condition. Figure 7.37 shows the load-deflection behavior at the pile head under the two-way cychc lateral loading. As shown in the figure, the relation is nonhnear and hysteretic, and is not significantly affected by the number of loading cycles at this loading condition. Similar results were also found in the full scale pile tests reported by Reese et al (1988) where the cychc load was apphed by controlled displacement rather than load. Furthermore, it may also be observed in Figure 7.34 and 7.35 that the pile response to the symmetrical two-way lateral loading is not symmetrical. The deflection in the compression (the first loading) direction appears to be larger than that in the tension direction. Some nonrecoverable deflections have been developed during the first half loading cycle due to the inelastic deformation characteristics of soils. Thus, when the pile is unloaded and then loaded in the reverse direction, some extra load would be required to overcome the plastic deformation generated from the first half loading cycle. Consequently, smaller peak deflection results in the tension direction under the symmetrical loading amphtude. The unsymmetric pile deflection response under symmetric lateral loading is another indication of nonhnear, inelastic soil action involved in the lateral soil-pile system. Similar observation of unsymmetrical pile response to symmetrical two-way cychc load has also been reported by Scott (1979) and Barton (1982) from their centrifuge tests. Pile Bending Moment Figure 7.38 shows the time history of pile bending moments measured by the eight strain gauges along the pile length. The strain gauge #1 and #2 were located" above the ground surface. It is seen that the peak bending moments measured by these two strain gauges did not change significantly with the number of loading cycles. How-ever, the pile bending moments observed at all the strain gauges are unsymmetrical Chapter 7. A Model Study of Pile Response to Lateral Loads 208 30 -30 H 1 1 1 1 1 1 1 r -4 -2 0 2 4 Pile Head Deflection at LVDT1 (mm) 481M test: free head E=68 mm Figure 7.37: Pile Head Load-deflection Behavior Under Two-way Cychc Loading Condition, JV=48, £ = 6 8 m m , Load Ampl.=23(Newton) Chapter 7. A Model Study of Pile Response to Lateral Loads 209 Time (s) Time (s) At Strain Gauge #3 At Strain Gauge #4 Figure 7.38: Time History of Bending Moment along the Pile, 48M1 Test: iV=48, £ ' = 6 8 m m , Loading Ampl.=23(Newton) Chapter 7. A Model Study of Pile Response to Lateral Loads 210 < U *V4 Cit) «L* 1 Time (s) At Strain Gauge #5 _ -1 1 1 1 1 1 1 1 1— • *J «4 Time (s) At Strain Gauge #6 Time (s) Time (s) At strain Gauge #7 At Strain Gauge #8 Figure 7.38: Time History of Bending Moment along the Pile, 48M1 Test: 7V=48, i £ = 6 8 m m , Loading Ampl.=23(Newton) Chapter 7. A Model Study of Pile Response to Lateral Loads 211 with the tension moment less than the compression one, which is the result of the unsymmetrical pile deflection. The bending moment measured at strain gauge #3 gives the maximum value along the pile length, as compared to the bending moment measured at the rest of strain gauges. However, tit appears that the bending moment measured at strain gauge #4 tends to increase with the loading cycles. This indicates that the maximum bending moment in the pile tends to migrate downward under the two-way cychc loading. This migration of the maximum bending moment with the number of loading cycle is related to the soil gapping and weakening in the upper layer. The extent of soil-pile gapping seems to increase with the number of loading cycles and loading magnitude. The effect of two-way cychc loading on the pile bending moment can also be eval-uated from the pile bending moment distribution along the pile length at different loading cycle and loading magnitude. Figure 7.39 shows the normahzed pile bend-ing moment distribution along the pile length at TV=48, the loading eccentricity of .E=68mm, and the loading magnitude of 23 Newton. It is seen that the pile bending moment distribution at this loading level is also unsymmetrical with regard to the bending moment at the compression and tension loadings. In comparing the pile bending moment distribution at the 1st and 25th loading cycles, it is noted that the bending moments measured below the ground surface tend to increase with the load-ing cycle, especially in the upper layer due to the soil gapping around the pile. After a number of loading cycles, the bending moment measured at strain gauge #3 (the first measurement below the ground surface) has increased so that a hnear bending moment distribution occurs at the first three bending moment measurement points. This indicates that after 25 cycles of loading the soil cavity has extended to the depth of strain gauge #3, little soil reaction being exerted on the pile from the sand at this depth. Figure 7.40 gives the similar pile bending moment distribution at N=48 and loading eccentricity of 45mm but with loading magnitude of 40 Newton. It is seen Chapter 7. A Model Study of Pile Response to Lateral Loads 212 Normalized Bending Moment - moment/load (mm) E E, <t> o « ^ 3 CO TJ C ra CO CD 5 O CD m £ CL CU o o -80 -60 -40 -20 0 20 40 60 80 i i i i i i i i 1st cycle | 25th cycle - 481M test: free head E=68mm Figure 7.39: Two-way Cyclic Loading Effects on Pile Bending Moment at Low Level of Lateral Load, Load=23(Newton) (100) E E CD O CO » -3 CO TJ C CO CO CD £ 200 o v m 100 300 Q. CD D 400 48M2 lest Free Headed Pile - N = 4 » E=46mm, Loed=40(N) j -1st Cycle 25th Cycle = 'Compreeelon Compression j , i , i . i , i 1st Cycle Tension © ! 25th Cycle Tension I i I i 400 300 200 - 100 (80) (60) (40) (20) 0 20 40 60 80 Normalized Bending Moment - moment/load (mm) Figure 7.40: Two-way Cyclic Loading Effects on Pile Bending Moment at High Level of Lateral Load, Load=40(Newton) Chapter 7. A Model Study of Pile Response to Lateral Loads 213 that at this higher level of cychc loading condition, the two-way cychc loading effect on the pile bending moment discussed above is more evident. A downward migration of maximum bending moment due to the cychc loading is clearly shown in Figure 7.40. Another unique feature in pile response under cychc loading is that upon removal of lateral load, residual bending moments are induced in the pile and therefore the pile remains in a distinctly distorted shape. Changes in the residual bending moment with number of cycles are shown in Figure 7.41. It appears that under two-way cychc loading conditions the residual bending moment after compression load is larger than that which occurs under tension load, and the residual pile bending moment due to the compression load increases with the loading cycles while the residual bending moment due to the tension load decreases. This indicates that the pile will accumulate the residual bending moment in the first loading direction under the two-way cychc loading. Cyclic Soil-pile Interaction The soil-pile interaction under two-way cychc loading is evaluated in terms of cychc P-y curves. Figure 7.42 shows the experimental cychc P-y curves at different depths for the free head pile with ^=48, E=68mm and loading amphtude of 23(Newton). It is seen that the general shape of the cychc P-y curves is nonhnear and hys-teretic. The curves are very soft near the surface and become stiffer with depth as the soil confining stress increases. Due to the nonsymmetrical pile deflection under the symmetrical two-way cychc loading, the cychc P-y curves also appear nonsym-metrical about the zero pile deflection axis with the P-y curves moving toward the compression loading direction. The effects of loading cycles on the cychc P-y curves can also be seen in Figure 7.42. Initially, the cychc P-y curves becomes stiffer with the loading cycles due to the soil densification around the pile, and the hysteretic loops remain quite open, indicating Chapter 7. A Model Study of Pile Response to Lateral Loads 214 Normalized Bending Moment (M/Mt) B 1 st cycle (+) o 25th cycle (+) + 1st cycle (-) A 25th cycle (-) 48M1 Test: Free Headed N=48 E=68 Load=27.8(N) Residual Pile Bending Moment under 2-way cyclic Loading Figure 7.41: Pile Residual Bending Moments under Two-way Cyclic Loadings Chapter 7. A Model Study of Pile Response to Lateral Loads 215 E E 1 o co CD rr = (1) o (2) 1st cycle 2nd cycle 5th gycle 25th cycle At Depth of 1D (3) (1) (0.S) 0 Pile Deflection - y (mm) 0.5 E E 1 c .2 o +-> o CO CO CC = 0) o w 1st cycle 2nd cycle 5th cycle 25th cycle At Depth of 2D (2) (3) (1) (0.5) 0 Pile Deflection - y (mm) Figure 7.42: Cyclic P-y Curves for different Loading Cycles at 1 to 2 Pile Diameter Depths Chapter 7. A Model Study of Pile Response to Lateral Loads 216 Figure 7.42: Cyclic P-y Curves for different Loading Cycles at 3 to 4 Pile Diameter Depths Chapter 7. A Model Study of Pile Response to Lateral Loads 217 At Depth of 5D 0) (0.5) Pile Deflection - y (mm) 0.5 1st cycle 2nd cycle 5th cycle 25th cycle Figure 7.42: Cyclic P-y Curves for different Loading Cycles at 5 Pile Diameter Depth 9 a Chapter 7. A Model Study of Pile Response to Lateral Loads ... 218 large material damping associated in the first few cychc loadings. However, as the loading cycle further increases, the shapes of cychc P-y curves begin to change due to the soil-pile gapping and soil remoulding starting from the sand surface. As shown in Figure 7.42, at the 25th loading cycle, the soil-pile interaction curve at 1 pile diameter depth becomes very flat with neghgible soil resistance, indicating the development of soil cavity around the pile at this depth. The hysteretic loops of P-y curves at depths of 2 to 4 pile diameters are also changed, resembhng elongated "peanut" shape. The softening of P-y curves at the smaU pile deflection range may be the results of soil remoulding and stress rehef associated with the two-way cychc pile movement. At a greater depth, e.g. 5 pile diameter depth, although the hysteretic loop of the P-y curve also becomes elongated, httle softening in cychc P-y curves is observed. In fact, the cychc P-y curve at 5 pile diameter becomes stiffer and more elastic, giving less hysteretic damping with number of cycles. This is because at greater depths soil elements around the pile become densified rather than weakened due to the high soil stress confinement and low pile deflection. Therefore, under the two-way cychc loading, the cychc soil-pile interaction is constantly modified with number of cychc loading cycles. Depending upon the loading amphtude and duration, the weakening of soil-pile interaction may travel downward from the sand surface to a considerable depth, which may greatly deteriorate the whole soil-pile system. The above observed shapes of cychc P-y curves are very similar to those reported by Matlock et al (1978) and Ting et al (1987). A method has been developed by Matlock et al (1978) to analyze the response of soil-pile system under two-way cychc loading condition in which the nonhnear hysteretic cychc P-y curves of the above "peanut" shapes can be incorporated. However, the deterioration in the shape of cychc P-y curves with loading cycles has not been properly addressed. Thus, a proper selection of cychc P-y curves for the analysis is difficult. Chapter 7. A Model Study of Pile Response to Lateral Loads 219 7.3.3.2 One-way Cyclic Loading Pile Head Response Figure 7.43 shows the time history of applied one-way lateral load and the correspond-ing pile head deflections at various positions above the ground level, while Figure 7.44 shows the time history of applied moment and the corresponding pile rotation at the ground surface. In contrast to the pile head response under two-way cyclic loading condition, the pile head deflection and slope have been found to increase gradually with each number of the loading cycle under the constant amplitude one-way cychc loading. As indicated in the figures, after the applied lateral load was unloaded to zero, the pile head deflection and slope did not return to zero. Instead, some perma-nent plastic deformation has developed after each loading cycle. The corresponding relation between the applied lateral load and the pile head deflection under one-way cychc loading is shown in Figure 7.45. It is seen that the largest increment in pile deflection occurs at the first cycle, and then the increment becomes smaller as the soil-pile system tends to become progressively more elastic with the increase of num-ber of cycles. At the 6th loading cycle, the pile head deflection has increased by 12% at the loading point. This typical behavior, however, is expected to depend upon the level of lateral loads. The relation observed in Figure 7.45 is very similar to that for the drained cychc triaxial tests on a sand sample as shown in Figure 7.46, which in-dicates that the soil rather than the pile is responsible for the accumulation of plastic pile deflection under the cychc loading. The pile head deflection under one-way cychc loading can be decomposed into elastic and plastic components as shown in Figure 7.45. The cyclic effect on different pile head deflection components is given in Figure 7.47. As shown, the nonlinear elastic component of the pile head deflection is independent of the loading cycle, and the accumulation of the pile peak deflection is solely due to the plastic deformation. It is also shown that the increment of pile head deflection with loading decreases with Chapter 7. A Model Study of Pile Response to Lateral Loads 220 Figure 7.43: Variation of Pile Head Deflection with Time under Constant Amphtude One-way Loading Chapter 7. A Model Study of Pile Response to Lateral Loads 221 Figure 7.44: Variation of Pile Slope at Ground with Time under Constant Applied Bending Moment at Ground Level Chapter 7. A Model Study of Pile Response to Lateral Loads 222 Figure 7.45: Pile Head Response at Loading Point under Constant Amplitude One-way Lateral Load Axial strain (b) Figure 7.46: Example of Soil Element Response from Drained Cyclic Triaxial Test, after Lambe and Whitman, 1975 Chapter 7. A Model Study of Pile Response to Lateral Loads 223 2.5 p3hd48e5.prn test N=48 E=45mm constant load amplitude o 1.5 % Q T? 1 o I 0.5 peak permanent nonlinear elastic 2 3 4 5 6 Number of Cycles in One-way Loading Condition Figure 7.47: Cyclic Effect on Different Pile Head Deflection Components under One-way Cyclic Loadings c o l a a cu 0) a 3 T3 ta 01 I a 2 Free Headed Fixed Headed E=45mm E=45mm (1) : Yt = 4.75 + 0.186 Log(N) - free headed (2) : Yt = 1.79 + 0.080 Log(N) - fixed headed Constant Load Amplitude One-way Cyclic Loading -A 4 6 -(2) 10 20 30 Number of Cycles - N Figure 7.48: Pile Head Peak Deflection with Number of Loading Cycles; Free Head vs. Fixed Head Piles Chapter 7. A Model Study of Pile Response to Lateral Loads 224 the number of cycles. Hettler and Gudehus (1980) proposed empirical expressions for the cyclic deflec-tion of piles based on the results of published field load test data by Alizadeh and Davission (1970). For load levels low enough not to cause failure, they found that the following relationship was applicable to the piles in sand subjected to one-way cychc lateral loads: [1+ C70ln(JV)] (7.11) where y is the pile head deflection, D is pile diameter or width, Pc is the one-way cychc lateral load, L is the pile length, N is the number of loading cycles. A , a, CD are empirical constants independent of the type of piles and loading condition. However, the generality of this equation must be questioned since, as discussed before, the pile head deflection depends upon the pile head fixity, applied load and bending moment magnitude as well as the relative soil-pile flexibility. Figure 7.48 compares the pile head deflection with number of loading cycles be-tween the free head and fixed head piles in which the same lateral load magnitude and loading eccentricity are imposed. The hydrauhc gradient scale factors in both tests are 48. It may be seen from the figure that at the first loading cycle the pile head deflection in the fixed head pile is reduced by a factor of 2.6 as compared to that in the free head pile. Although the form of cycle dependence of lateral pile deflection is as suggested in Eq.(7.11), the incremental rate of the lateral pile head deflection is very much dependent upon the pile head fixity. For the free head pile, the rate of pile head deflection increment with the loading cycles is about 2.3 times that for the fixed head pile. Therefore, a restraint to the rotation of the pile cap not only reduces the deflection under the first time loading, but also appears to be significant in lowering the percentage increase in lateral deflection upon one-way cychc loading. The observed effect of pile head fixity on the percentage increase in lateral pile de-flection appears more severe than that reported by Singh and Prakash (1971) where - n - A iDL7 Chapter 7. A Model Study of Pile Response to Lateral Loads 225 the study was performed using lg model tests. The effect of lateral load magnitude on the one-way cychc behavior of pile head deflection is shown in Figure 7.49. Two tests of free head piles were performed with different lateral load magnitudes but the same bending moment apphed at the ground level. The same bending moment was applied in both tests by adjusting the loading amphtude and eccentricity relative to the ground level. The hydrauhc gradient scale factors in these two tests are also 48. It is noted that the cychc dependence of pile head deflection under different lateral loading magnitude also has the same form as suggested in Eq.(7.11). The incremental rate of pile head deflection with the loading cycles is also found to be very dependent upon the lateral loading magnitude. The incremental rate of pile head deflection is increased by a factor of 2.3 when the loading magnitude is increased by about 55%, and the difference of two pile head deflections at the first time loading is only 17%. Figure 7.50 shows the effect of apphed bending moment magnitude on the cyclic dependence of pile head deflection under one-way cychc loading. Two free head piles were tested under the same magnitude of lateral loads but different loading eccentricities to produce different bending moment magnitudes at the ground surface. The tests were performed under the hydrauhc gradient scale factor of 48. It is shown that the incremental rate in pile head deflection also depends upon the magnitude of apphed bending moment at the ground surface. For an increase of 50% in the apphed bending moment, the incremental rate of the pile head deflection with the loading cycles is increased by about 80%, while the difference in pile head deflection at the first cycle due to the bending moment difference is about 40%. In addition, the cychc dependence of pile head deflection under different bending moment magnitudes is in the form as suggested in Eq.(7.11). Thus, as compared to the effects of pile head fixity and magnitude of lateral load, the magnitude of bending moment apphed at the ground level has smaller effects on the incremental rate of lateral pile deflection Chapter 7. A Model Study of Pile Response to Lateral Loads 226 X 4 Constant Load Amplitude One-way C y c l i c Loading Free Headed Pi l e s Load Eccen.=45mm Load Eccon.-68mm Load=36.S2(N) Load=23.61(N) B A (1) (2) 0>r _e—s—B—B—u u • t l U T H j u o a n r " : 1 (1) : Yt=4.75+0.186 Log(N) - applied moment at pile head = 1648 N.mm (2) : Yt=4.06+0.077 Log(N) - applied moment at pile head = 1606 N.mm 10 20 30 Number of Cycles - N Figure 7.49: Comparison of Pile Head Deflections with Number of Cycles; the Same apphed Moment but Different Loading Magnitude o I 4 (2) c u • D u a ot a (1) : Yt=6.70+0.333 Log(N) - applied moment at pile head = 2490 N.mm (2) : Yt=4.75+0.186 Log(N) • applied moment at pile head = 1648 N.mm (2) Load Eccea=4Smm Load=36.62(N) 0) Load Eccon.=68mm Load=36.S2(N) Constant Load Amplitude One-way Cyclic Loading Free Headed Pllee 10 Number of Cycles Figure 7.50: Comparison of Pile Head Deflections with Number of Cycles; the Same Lateral Load but Different Moment at Pile Head Chapter 7. A Model Study of Pile Response to Lateral Loads 227 under one-way cyclic loading. Thus, it is shown from above discussions that before the deflection stabilizes, the lateral deflection of the pile increases with number of loading cycles according to a logarithmic function that has an incremental rate depending upon pile head fixity, pile flexibility and pile head loading conditions. Pile Bending Moment As a consequence of the plastic pile deflection under each one-way loading cycle dis-cussed above, the pile bending moment may also accumulate with each loading cycle. Figures 7.51 and 7.52 show the peak and residual pile bending moment distribution with depth, respectively, for a free head pile under different loading cycles. It is shown that for the present loading condition the peak pile bending moment distribution did not change significantly with number of cycles. As compared to the pile deflection in-crement at the loading point as shown in Figure 7.45, the maximum bending moment is only increased by 7% at the 6th loading cycle, and the largest increment occurs after the 1st cycle. However, it appears that the peak bending moment distribution at the lower depth is affected more by the loading cycles. The bending moment at about 14 pile diameter depth has been increased by a factor of 2.5 at the 6th loading cycle. As shown in Figure 7.52, the residual bending moment after removal of lateral load appears to be more affected by the number of cycles, as compared to the bending moment distribution at the peak load. The residual bending moment increases by about 35% at the 6th loading cycle. Figures 7.53 and 7.54 show the peak and residual bending moment distribution for a fixed head pile. As shown, similar observations can be made for the fixed head piles as for the free head piles with regard to the cychc effect on the pile bending moment. Chapter 7. A Model Study of Pile Response to Lateral Loads 228 1.4 1.3 --0.1 H i 1 1 1 i 1 1 1 1 1 i 1 r 0 40 80 120 160 200 240 280 Figure 7.51: Pile Bending Moment Distribution at the Peak Lateral Load, Free head Pile, One-way Cyclic Loading -100 H 1 1 1 1 1 i 1 1 1 1 i 1 1 r 0 40 80 120 160 200 240 280 Depth below the Sand Surface (mm) Figure 7.52: Pile Residual Bending Moment after Removal of Lateral Load, Free head Pile, One-way Cychc Loading Chapter 7. A Model Study of Pile Response to Lateral Loads 229 Figure 7.53: Pile Bending Moment Distribution at the Peak Lateral Load, Fixed head Pile, One-way Cychc Loading 900 -400 -\ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ; -20 20 60 100 140 180 220 260 300 Depth Below Surface (mm) Figure 7.54: Pile Residual Bending Moment after Removal of Lateral Load, Fixed head Pile, One-way Cychc Loading Chapter 7. A Model Study of Pile Response to Lateral Loads 230 Cyclic Soil-pile Interaction The soil-pile interaction under one-way cyclic pile head loadings is also evaluated in terms of P-y curves. Figure 7.55 shows the one-way cychc P-y curves at different depths and cycles for a fixed head pile at JV=48, j £ = 4 5 m m , and loading magnitude of 40(Newton). It is shown that as in the two-way cychc loading, the P-y curves under one-way cychc loading are also nonlinear and hysteretic. However, as compared to the curves for the two-way cyclic loading in Figure 7.42, the shapes of one-way cychc P-y curves do not deteriorate with number of cycles, even at the shallow depth. This is consistent with the observation during the pile load tests that smaller soil gapping occurred around the pile under the one-way cychc loading than that under the two-way cyclic loading. A l l the P-y curves become more linear with number of cycles. Due to the accumulated pile deflection during the cyclic loading, the cychc curves shift toward the left with the accumulated plastic deformation. In addition, the enclosed area of the hysteretic loop in the cychc curves decreases with number of loading cycles. These indicate that the soil-pile system under the one-way cychc loading progressively becomes more elastic with number of cycles. As in the cases of static and two-way cychc loading, the cychc P-y curves become stiffer with the depth. High soil stress confinement at depth also results in smaller hysteretic loops in the curves. In view of the above observation, the analysis of pile response to the one-way cychc loading using the cychc P-y curves is very difficult, as the generation of these cychc P-y curves cycle-by-cycle for the analysis a priori is difficult. At present, there is still no single analytical method which can give satisfactory solution to the pile response to the cychc loading. Chapter 7. A Model Study of Pile Response to Lateral Loads ... 231 E E 2 c o TS (0 oc o E E z c o ts CB 0> OC o CO 1.6 0.8 0.6 0.4 0.2 0 -0.2 4.4 -0.6 ~ at depth of 1D first time loading / f 1st cycle / i I I I I 25th cycle I • • T 1 1 - " 2 1.8 1 0.8 0.4 •0.6 -0.8 -1 0.2 0.4 0.6 0.8 Pile Deflection - y (mm) at depth of 2D first t i m ^ ^ a d i n g ^ ^ ^ ^ L B / 7 /BE lm / Jt_m 1 1st cycle ^ % ^ / i s H ' \ 25th cycle n r 0.2 0.4 0.6 0.8 Pile Deflection - y (mm) Figure 7.55: P-y Curves under One-way Pile Head Loading at depths of 1 to 2 pile diameters, Fixed Head Pile, N=48 E=45 Load=40(Newton) Chapter 7. A Model Study of Pile Response to Lateral Loads 232 Figure 7.55: P-y Curves under One-way Pile Head Loading at depths of 3 to 4 pile diameters, Fixed Head Pile, N=48 E=45 Load=40(Newton) Chapter 7. A Model Study of Pile Response to Lateral Loads 233 Figure 7.55: P-y Curves under One-way Pile Head Loading at depth of 5 pile diame-ters, Fixed Head Pile, N=48 E=45 Load=40(Newton) Chapter 7. A Model Study of Pile Response to Lateral Loads 234 7.3.3.3 Effects of Cyclic Loading History The effects of loading sequence of different cyclic loading have also been studied. The pile was subjected first to the two-way cyclic loading for a number of cycles, and then to the own-way cychc loading. The pile responses to such a loading sequence are presented in Figure 7.56 in terms of pile head deflection. It appears that the pile response to the different types of cychc loadings are independent of the cychc loading history. Under the two-way cychc loads, the pile head deflections are not symmetrical with larger deflection in the first loading direction, and the pile deflection tends to decrease with the loading cycles. However, after one-way cychc loads are applied, the pile deflection gradually increases with the loading cycles. These are consistent with previous discussions when only one type of cychc loading is applied. 7.4 Summary and Conclusion Pile response under lateral loads applied at pile head is an important aspect in the design of deep foundation. Although pile foundations have been used in civil engi-neering for a long time, the fundamental aspects of soil-pile interaction under different loading conditions are still poorly understood, and the soil parameters required for nonhnear analyses of soil-pile system under lateral loading have not yet been fully calibrated in a fundamental manner. Engineers are still not able to design pile foun-dation confidently and cost-effectively. In this chapter, a model study of vertical piles embedded in sand under monotonic as well as cychc lateral pile head loading has been presented. The tests were con-ducted in the newly developed Hydrauhc Gradient Similitude Testing ( H G S T ) device using the hydrauhc gradient similitude principle. Single piles of different diameters were studied under different hydrauhc gradients and loading conditions. Tests were exclusively conducted using a medium dense sand with the emphasis on examining Chapter 7. A Model Study of Pile Response to Lateral Loads ... 235 T i m e H is to ry of A p p l i e d L a t e r a l L o a d ~r~ 0.4 0.6 (Thousands) Time (8) T i m e H is to ry of P i l e H e a d D e f l e c t i o n 1.5 -1 -E E. 8 £ 0.5 H s Z -0.5 - \ "cx -1 --1.5 -V v 48f5 test Fixed Headed N-48 E=46mm -r— 02 —\ 1 r— 0.4 0.6 (Thousands) Time (s) i 0.6 Figure 7.56: Pile Head Response under a Sequence of Two-way and One-way Cychc Loadings Chapter 7. A Model Study of Pile Response to Lateral Loads 236 various factors that affect soil-pile interaction P-y curves. However, a few tests were also performed using a loose sand for the purpose of evaluating analytical procedures. The primary purpose of the study was to determine soil-pile interaction under the lateral pile head loading in a well controlled stress and soil condition so that the current understanding and analytical methods could be evaluated. In addition, a study of this type itself constitute an evaluation and demonstration of the use of the hydrauhc gradient similitude technique for pile foundation problems. The hydrauhc gradient scahng laws for the laterally pile problems have been evaluated experimen-tally using the "modelling of models" technique, and found to be the same as those in the centrifuge tests. For the piles under monotonic lateral pile head loading, it was found that the pile head response, bending moment distribution and the P-y curves were dependent upon the applied hydrauhc gradient or the soil stress levels. At the low stress level, the observed P-y curves were soft, leading to a soft pile head response and large pile bending moments along the depth. With the increasing soil stress level due to the imposed hydrauhc gradients, the soil reaction (or P-y curves) became stiffer, giving a stiffer pile head response, and the maximum pile bending moment became smaller and shallower. It was found that for the monotonic loading the stress level dependency of the P-y curves can be normahzed by the Young's moduli of the soil and the pile diameter, as indicated by the plane strain finite element analysis using nonlinear soil parameters. The normahzed P-y curve started with an initial slope of 45° and can be represented by a power function of exponent close to 0.5. The other coefficient of the fitted power function appears to be solely dependent upon the soil density. It was also found that although the pile head response and bending moment were dependent upon the loading eccentricity and pile head fixity, the soil-pile interaction in terms of P-y curves was not significantly affected by these factors. The effect of Chapter 7. A Model Study of Pile Response to Lateral Loads 237 pile diameter on the P-y curves was also evaluated in terms of prototype scale, and found to only have small effect on the P-y curves, especially at the small range of pile deflection. These results suggest that lateral pile responses under various pile head fixity and loading eccentricity conditions may be analyzed by a set of P-y curves which are solely a function of soil condition. These results lend support to the A P I code in which the P-y curves are not a function of pile head fixity and loading eccentricity. For the piles subjected to cychc lateral loading, different responses were observed depending on the nature of cychc loading. When piles were subjected to a two-way symmetrical loading, it was found that the soil-pile system became stiffer initially due to soil densification under the two-way cychc movement of the pile. The system then deteriorated after a certain number of loading cycles when significant soil gapping and remoulding had weaken the soil reaction at the upper layers. This deterioration of the soil-pile system depends upon the loading intensity and duration. Under the symmetrical two-way cyclic loading, the responses of pile deflection and bending mo-ment were not symmetric with pile deflection and bending moment being larger in the first loading direction. The residual values of bending moment after removal of the lateral load tended to accumulate in the first loading direction with number of cycles. The soil-pile interaction under the two-way lateral loading were evaluated in terms of cychc P-y curves. The cychc P-y curves were found to be highly nonhnear and hysteretic, and change in shape with number of loading cycles. For the first few loading cycles, the P-y curves became stiffer due to soil densification, and the hys-teretic loop stayed very open giving a large hysteretic damping. With the increase of loading cycles, the shapes of cychc P-y curves at shallow depths became elon-gated as a "peanut" shape indicating soil gapping and remoulding around the pile. At this stage, the loops of cychc P-y curves were quite narrow. Stiffer P-y curves were observed at deeper depths. During the cychc loading, the cychc P-y curves also experienced a drift toward the first loading direction due to the unsymmetrical pile Chapter 7. A Model Study of Pile Response to Lateral Loads 238 response to the symmetrical load. When piles were subjected to one-way unsymmetrical loading, it was found that the pile head deflection steadily increased with each number of loading cycle before the soil-pile system stablized. The increment of pile deflection was most significant in the first few cycles, and could be expressed by a logarithmic function with the number of loading cycles. However, the incremental rate of pile head deflection due to the one-way cyclic loading was found to be highly dependent upon several factors that include pile head fixity, and magnitudes of cyclic load and applied bending moment at the ground level. Although the maximum bending moment did not significantly change during the cyclic loading, the residual bending moment increased significantly with the number of loading cycle. The soil-pile interaction under one-way cychc loading was also evaluated in terms of cychc P-y curves. As in the two-way cychc loading, the P-y curves were also highly nonlinear and hysteretic. However, unlike the two-way cychc curves, the P-y curves under one-way loading condition did not deteriorate with the loading cycles. Instead, all the cychc P-y curves became stiffer and more linear with smaller hysteretic loop as the loading cycles increased. This observation reflects that the soil-pile system under the one-way cychc loading progressively becomes more elastic with number of cycles. It was also found that the above observation on pile response to either type of cyclic loading will not be changed due to different cychc loading history. Chapter 8 Prediction of Pile Response to Lateral Loads at Pile Head 8.1 Introduction In the preceding chapter, test results have been presented to reveal the soil-pile inter-action mechanism under both static and cychc loadings. It was found that soil-pile interaction is highly nonhnear and hysteretic with pile deflection, and also depends upon the loading cycles. It was found that for the monotonic loading a unique func-tion is apparent for the P-j r curves at depths below 1 pile diameter. For a given soil condition, this relation may be generated based on a nonhnear plane strain finite element analysis using fundamental soil parameters. This relation may also be used to serve as the backbone curve for the cychc P-y curves. In this chapter, the nonhnear subgrade reaction method is used to analyze the test data from the monotonic loading tests. The discussion will be focused on the generation of appropriate P-y curves for the analysis. First, different procedures for generating P-y curves are described, and compared with the experimental curves. Then, the P-y curves from these procedures are used to predict the observed pile responses under various test conditions. 8.2 Generation of P-y curves In this chapter, three methods of generating static P-y curves will be evaluated, namely: 239 Chapter 8. Prediction of Pile Response to Lateral Loads 240 1. A P I code (1987); 2. A modified version of A P I code, and 3. P-y curves from the finite element analysis. 8.2.1 API Code (1987) The constructing procedure of P-y curves using A P I code (1987) has been reviewed in Chapter 6. It consists of using a hyperbohc-tangent function, i.e. Eq.(6.12) to define the shape of P-y curve at a specific depth. The initial slope of the curve at a given depth is defined as "rihi • z", where rihi is evaluated according to the values shown in Figure 6.5. The ultimate soil resistance is obtained from the lesser value given by Eqs.(6.10) and (6.11) with the coefficients shown in Figure 6.6, and the adjustment factor, A , in Eq.(6.13). For the present test condition, the curve for saturated sand shown in Figure 6.5 was used to obtain the coefficient of subgrade reaction modulus, rihi- Both relative density and friction angle of sand can be used to enter the chart. However, the stress level at which the friction angle is to be evaluated is not specified in the design code. Herein, the peak friction angle of 30° and 39° obtained from conventional triaxial test data (see Table 3.1 of Chapter 3) are used for loose (DT — 33%) and dense (DT = 75%) sand conditions. It is noted that the A P I code was originally developed for a prototype pile condi-tion. Thus, in applying the A P I code to a model test under given hydrauhc gradient or scale factor, N, the initial slope of the P-y curve is obtained as follows: to incorporate the model soil stress level, as " n ^ " should include the soil unit weight effect, and the model soil unit weight, 7 m , is: Khi = N • nhi • z (8.1) 7m = N-lp (8.2) Chapter 8. Prediction of Pile Response to Lateral Loads 241 where ~yp is the prototype soil unit weight. For the same reason, the model soil unit weight, 7m = Njp, is used in either Eqs.(6.10) or (6.11) to determine the ultimate soil resistance in the model tests. 8.2.2 A Modified version of API Code As indicated in Figure 7.20, the initial slope of the P-y curves may start with the maximum Young's modulus of soil, Emax, at a very small strain level. A comparison of the initial slope of P-y curves of A P I code (1987) with Emax values given by Yu and Richart (1984) is shown in Figure 8.1 in a prototype scale. It is seen that the Kh value suggested in the A P I code is very close to the maximum Young's modulus of soils at the shallow depths. At the deeper depths, the Kh value actually become larger than the Emax value, as it increases linearly with depth. As discussed in Chapter 6, the soil-pile interaction at depth may be represented by a plane strain solution. It is also shown from the finite element analysis that the P-y curve at plane strain condition starts with Young's modulus of soil. Therefore, it may be inappropriate to use the Kh values at depth which are much higher than the maximum Young's modulus, Emax- I n view of this discussion, a modified version of A P I code is proposed. In this procedure, the initial slope of the P-y curves is calculated from the maximum Young's modulus, Emax, rather than from the coefficient of subgrade modulus, n/,;. In practice, this approach has the advantage that the initial slope of the P-y curve can be evaluated from the in-situ seismic test rather than the empirical correlation. This modified version of A P I code will also be evaluated against the test data and compared with the other methods of analysis in the sections followed. 8.2.3 P-y Curves from Plane Strain F E M Analysis In this approach, a 2D plane strain finite element formulation is used to obtain the P-y curves for the analysis of laterally loaded piles. The finite element mesh used is Chapter 8. Prediction of Pile Response to Lateral Loads 242 (0 0. 8 E LU co 0. 3 E 800 700 H 600 500 400 H 300 200 H 100 0 1.5 1.4 1.3 1.2 1.1 f 0.9 3 0.8 UJ o 0.7 o B 0.6 6 0.5 Dry Condition Dense Sand Dr=75% Kh values-API code (1987) Emax - Yu and Richart (1984) i 1 r n 1 r 4 6 8 10 12 14 Depth below Surface (m) Saturated Condition Dense Sand Dr=75% Kh values - API code (1987) 4 6 8 10 Depth below Surface (m) Figure 8.1: Comparison of Subgrade Reaction Modulus, Kh, from A P I code with the maximum soil Young's modulus, Emax Chapter 8. Prediction of Pile Response to Lateral Loads 243 shown in Figure 8.2. A ring of thin layer interface elements is employed around the pile surface to simulate the soil-pile interface behavior (Desai, 1981; Desai et al, 1984 and Yan, 1986). A semi-disk model of finite element mesh is used as a symmetry boundary exists along the lateral loading axis. Along the symmetrical boundary, a series of rollers are placed to ensure no displacement induced perpendicularly to the boundary. At the outer boundary, no displacement boundary condition is imposed at nodes. Details of computing P-y curves using 2D plane strain finite element method and boundary effects have been discussed by Yan (1986). The procedure involved in constructing P-y curves using finite element analysis consists of : 1. obtaining hyperbolic soil parameters for the given soil layer; % 2. predicting P-y curve at a given depth for the given soil and pile conditions using a plane strain finite element model; 3. obtaining the generalized P-y curve for the given soil layer by normalizing the computed P-y curve with respect to the corresponding soil Young's modulus, Ei, which is the input in the finite element analysis, and the pile diameter; 4. fitting the normalized P-y curve using a power function with the coefficient ct and (3 obtained, and then 5. specifying P-y curves at different depths within the given soil layer using the normalized curves. For the present test condition, uniform sand deposit of given density is present, and the hyperbohc soil parameters given in Table 3.1 of Chapter 3 from conventional triaxial tests are used to predict the P-y curves for dense and loose sand conditions. From the finite element analyses, the normalized P-y curves based on the triaxial soil parameters for the present soil conditions are shown in Figure 8.3 with the curve Figure 8.2: Plane Strain Finite Element Mesh for Obtaining P-y curves Chapter 8. Prediction of Pile Response to Lateral Loads 245 fitting equations in the following forms: P = 0 40 (i 0 .45 EiD P for dense sand (8.3) = 0 60 (£ 0.50 EiD for loose sand (8.4) As shown in Figure 8.3, the normahzed P-y curves start with a 45° slope for both loose and dense sand, and the coefficient a in the curve fitted equation for the loose sand is higher than that for the dense sand. 8.3 Evaluation of P-y Curves A comparison of normahzed P-y curves from plane strain finite element analyses using triaxial test data and original A P I code has been made with the test data, and is shown in Figure 8.4. AU the P-y curves shown are normahzed by the soil Young's modulus, Ei, and pile diameter, D. It is shown from the figure that the normahzed P-y curves from A P I code are not independent of the depth below the surface, and do not resemble the shape of experimental curve. The A P I curves are essentially bilinear while the experimental curves exhibit a parabolic shape. At the small pile deflection, the A P I P-y curves are stiffer than the observed while at pile deflection of about 1% pile diameter, the P-y curves from A P I code reach ultimate soil resistances that are lower than the experimental curve. O n the other hand, the P-y curve from the 2D plane strain finite element analysis exhibits a similar characteristic shape as the experimental P-y curve, it starts with the same initial slope but becomes about 1.5 times softer than the experimental one at large pile deflection. This may be attributed to the soil layer interaction ignored in the finite element analysis in which a plane strain disk model is used, giving a softer P-y curve under the lateral loading. Similar observation was noted by Atukorala et al (1986) when the P-y curves from plane strain finite element analyses Chapter 8. Prediction of Pile Response to Lateral Loads 246 Figure 8.3: P-y curves obtained from 2 — using Triaxial Test Data D Plane Strain Finite Element Analysis Chapter 8. Prediction of Pile Response to Lateral Loads 247 Test Data without those at depth of 1D average curve API curves at different depths FEM PLN STRN WITH TC Data 10 15 20 25 Normalized Pile Deflection - y/D (%) 30 API-1D API-4D API-2D - * - API-5D - e - API-3D FEM-PLN STRN Figure 8.4: A Comparison of Normahzed P-y curves from F E M and A P I code with the Test Data, Dense Sand Dr = 75% Chapter 8. Prediction of Pile Response to Lateral Loads 248 were compared with those by Reese et al (1974). In the following analyses of pile response, a correction factor of about 1.5 is applied to the P-y curves obtained from the finite element analysis to account for this effect approximately. A comparison of the original and the modified version of A P I code is shown in Figure 8.5. As shown, they are very similar. 8.4 Prediction of Pile Response In this section, the P-y curves constructed in the procedures discussed above are used to predict the observed response of model piles to static lateral loading. The finite difference computer program L A T P I L E (Reese, 1977) which incorporates the nonlinear subgrade reaction method is used in the analysis. Analyses are made for various testing conditions which include the cases of free head pile responses under different loading eccentricity, soil stress level and density, and the case of fixed head pile response as well. The predictions of free head pile response at different loading eccentricities are discussed in the following while the predictions for the cases of other testing conditions are presented in Appendix F . Different Loading Eccentricity Predictions were made on the free head pile response for loading eccentricities of 45 mm and 68 mm respectively. In both cases, the hydrauhc gradient scale factor is 64 and the relative density of sand is 75%. In the analysis, the soil reactions to the pile deflection are prescribed along the pile length at given depths starting from the sand surface. A hnear interpretation scheme is used by the program to estimate the soil reaction between the P-y curves specified. Figure 8.6 shows the prediction of pile head response under different loading levels at the loading point. It is shown that all three methods give remarkable predictions as compared to the test data at both loading eccentricities. Chapter 8. Prediction of Pile Response to Lateral Loads 249 O N=48 at 5D depth Orig. API Mod. API Orig. API Mod. API at 1D depth at 1D depth at SD depth at 5D depth B A- 0 — * — at 1D depth - a a a a a 3 a a s-—a & a a a——a a a a o *~ 0.08 Pile deflection (cm) Emax - from Yu and Richart (1984) Figure 8.5: A Comparison of Original and Modified A P I codes Chapter 8. Prediction of Pile Response to Lateral Loads 250 50-| p3hd64ec.prn N=64 E=68.0mm 0.0 1.0 2.0 3.0 4.0 5.0 6.0 Pile Deflection at Loading Pile ( m m ) Figure 8.6: Prediction of Free head Pile Response at Loading Point at Different Loading Eccentricity, N=64, DT = 75% Chapter 8. Prediction of Pile Response to Lateral Loads 251 Figure 8.7 shows the prediction of pile bending moment distribution along the depth at the loading level of about 35(N) for the above eccentricities. Analyses using both original and modified A P I code give similar results. For this loading level, they all predict higher values of the maximum bending moment at a deeper depth. Excellent agreement in terms of maximum bending moment value and its depth of occurrence is obtained between the prediction using plane strain finite element method and the test data. Besides the pile head deflection and pile bending moment distribution, other pa-rameters including pile deflection profile, soil reaction, shear force on the pile and the equivalent subgrade soil modulus used in the analysis can be determined from the computer program L A T P I L E . Such information can be useful in evaluating the role of the P-y curves specified in the analyses by various methods. As direct measurements of these values are not available, comparison is made against the predictions using experimental P-y curves. Figure 8.8 shows the predictions of pile deflection profiles for the loading level of 35(N). It is shown that both A P I methods give slightly larger deflections at this large loading level, which is consistent with the overprediction of maximum bending moment observed above. Figure 8.9 shows the predictions of soil reaction profiles for the loading level of 35(N). It may be seen that analysis using finite element P-y curves gives very good agreement with the experimental P-y curves. However, at this loading level, A P I codes give smaller soil reactions at shallow depths where pile deflection is large and the A P I P-y curves have reached the specified ultimate values that are much lower than the experimental data. On the other hand, A P I codes give larger soil reactions at depths below 5 pile diameter where the pile deflection is small and the A P I P-y curves are much stiffer than the experimental curves. s-' £ CD 0> cn OO H • • CD CD &-CD P- S-•i: S3 H ft cd CD S3 cw o 3 CD a o cn' • a. cr 0 <rf-o S3 & CD H CD S3 c+-f < o p S3 CW W o o CD S3 Bending Moment Profile (N.mm) O-500 0 500 1000 1500 2000 2500 3000 O I i i i i I I I I I I I I i i I i i i i I i I I I I i i i i N i i i I I o a> o o o -a — r o m-c D 0 0 O c u -° Cr _ IO-CL Q o o -o lo-rn o o -p3hd64ea.prn test N=64 E=45mm ooooo test data at lateral load = 35.04(N) with exp. p-y curves with API code (1987) WET with API code (1987) WET+Emax with FEM PLN power function Bending Moment Profile (N .mm) O-500 0 500 1000 1500 2000 2500 3000 ' ' ' • ' ' ' ' • ' ' ' ' ' I i • i i I i i i ' l i i i i I i i i i I o ID. I O -I"] CD O O O -a t co T3 C o GO CD O a. CD Q o o -ro O to-rn o o -p3hd64ec.prn: N=64 E=68.0mm ooooo test data at lateral load «= 35.80(N) with API code (1987) WET with API code (1987) WET+Emax with FEM PLN power function § g CD &> CD cn O S3 cn CD t-< o C L cn to to Chapter 8. Prediction of Pile Response to Lateral Loads 253 E E o 06 O I  o UJCO t i t " 5 5 § coco g > a " I I I I | I I I I | I I I I | I I I I | I I I I | I I I I | I I I I | I I I I | I i i i | i i I I | 00 L— 09- 0 OS 001 OS I 003 0SZ 00£? 0S£ DOt (aiuu) 90Dpns P U D S MO|sq u,}d9Q Tl V o 1 .-stjb E o Q. O-TJ «> - S < < L u E E lO r> In || C <3 D — CO "D O J : — rO-w I I I I | I I I I | I 001- OS- 0 I I I I I I I I I I I I I [ I 1 I I I I I I I I I I I I I I I I I I I I I I I OS 001 OS I 002 OSZ 00C OSS? DOt (uuuu) eoDjjns P U D S MOjeq iflderj Figure 8.8: Comparison of Pile Deflection Profile Prediction using Various Methods - Different Loading Eccentricities U TJ ro CJ Z oo t-H <? o £ O a - o B' B § 1 ss B a ° C O o CD P n o fc! TJ n o fcfc TJ H o 0 cm a. o o cx Soil Reaction P (N /mm) o - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 ° 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 o i n . o -E <D o o t CO • o c D CO s ^> CD o - C CM •*-> CL CD a o o -o i n -to a o -e x p . p—y c u r v e s API WET API WET+Emax FEM PLN—power f unc . \ 7 p 3 h d 6 4 e a . p r n t e s t N = 6 4 E = 4 5 m m o t lateral load = 3 5 . 0 4 ( N ) Soil Reaction ( N / m m ) o - 8 - 6 o i i i I I I I o i n . I c: o . a> o o t CO x> c o 0 0 ? o 0J o ^- xr>-CL CD Q o o -to o in-to o o -- 4 - 2 I I I t ' ' I ' I 0 i I i i 2 4 i I i i i i I with API c o d e — — with API c o d e with FEM P L N ( 1 9 8 7 ) WET ( 1 9 8 7 ) W E T + E m a x power f unc t i on with Exp . P - y c u r v e s p3hd64ec.pm: N=64 E=68.0mm at loading level of 35.80(N) •8 OD CL o % o Si co 01 9 5 t-1 o e> CL C o K 5 at Chapter 8. Prediction of Pile Response to Lateral Loads 255 Figure 8.10 shows that A P I codes overestimate the maximum shear force acting on the pile while a good agreement between the predictions from finite element and experimental P-y curves is obtained. A comparison of the equivalent subgrade modulus, Ee, used in the analyses by different methods is shown in Figure 8.11 at the loading level of about 35 (N). It is shown at this loading level that only the finite element P-y curve provides equivalent subgrade reaction modulus distribution along the pile which is similar to that from the experimental P-y curve. As compared to the one from experimental P-y curve, the equivalent subgrade moduh used by both A P I methods are smaller at the first 5 pile diameter depth where the pile deflection is large and A P I P-y curves have reached the ultimate pressures. Below this depth, they become much larger, as in this region the pile deflection is small and the A P I P-y curves are much stiffer than the other methods. It is seen that the pile response under lateral pile head loading is dominated by the soil-pile interaction at the first 5 pile diameter depth. The smaller values of subgrade reaction modulus within this depth have led to overpredictions of pile deflection, bending moment and shear force by both A P I methods, as have discussed before. Similar predictions have also been made for other cases of test conditions. This includes pile response under free head condition at different hydrauhc gradients and in loose sand deposit, and pile response under a fixed head condition. The results are presented in Appendix F . From all these analyses, it may be concluded that: 1. The same set of P-y curves can be used to give good predictions of pile response regardless of the pile head loading eccentricity and fixity; 2. There is no significant difference between the predictions given by the original A P I code and the modified one. In view of practical significance in obtaining the initial slope of A P I P-y curve from the in-situ seismic measurement rather than o T l s § ft tl) S3 rt- 00 I—I ^ o P p S3 o o P n CD S3 a a. cn O S3 y. o ST* CD P n o m ft o S3 S3 Orq a. o C3 S3-o fa-Shed! Force Profile (N) O - 1 0 0 - 7 5 - 5 0 - 2 5 0 2 5 5 0 ° I i i i i I i i i i I i i i i I i i i i I i i i i I i i i i I o i n . CD o o o -n cn o m -c D 0 0 O 5 8" O) jQ O _ m-5 " Q . CD Q O ea-rn o m -o o -e x p . p—y cu rves API WET API WET+Emax FEM PLN—power func. p 3 h d 6 4 e a . p r n t e s t N = 6 4 E = 4 5 m m a t l a t e r a l l o a d = 3 5 . 0 4 ( N ) Sheor Force Profile (N) © - 1 2 5 - 1 0 0 - 7 5 - 5 0 - 2 5 0 2 5 5 0 ° I ' i ' I I ' I I ' I ' i i i I ' ' ' ' I ' I ' ' I ' ' ' ' I ' ' i ' l p 3 h d 6 4 e c . p r n : N = 6 4 E = 6 8 . 0 m m a t l o a d i n g l e v e l o f 3 5 . 8 0 ( N ) with API c o d e ( 1 9 8 7 ) WET with API c o d e ( 1 9 8 7 ) W E T + E m a x with F E M P L N power f unc t i on with E x p . P - y c u r v e s Chapter 8. Prediction of Pile Response to Lateral Loads 257 o (uuuu) soDjjns puD$ MO|eq iftdeQ > 'D cr UJ O 001 I I I I 09 i I i i i i I i i i i I i i i i I i i i i | i i i i | i i i i | i i i i | os ooi os i oos osz ooe oss: oot (aiuu) eoDjjns PUDS MO|aq n^derj Figure 8.11: Comparison of the Equivalent Subgrade Reaction Modulus used in Var-ious Method - Different Loading Eccentricities Chapter 8. Prediction of Pile Response to Lateral Loads 258 the empirical correlation, the modified version of A P I code which incorporates the maximum soil Young's modulus, Emax, is thus favoured; 3. A P I methods tend to overpredict pile bending moment and shear force at large loading level, and slightly underestimate the pile head deflection, especially for the fixed head pile condition, at low loading level. 4. P-y curves from the plane strain finite element analysis using hyperbolic soil parameters overall give better prediction in all aspects of pile response. Good prediction has been obtained under different hydraulic gradients, different load-ing eccentricities and pile head fixities, and different soil densities, as they es-sentially resemble the characteristic shape of the experimental P-y curves. In this approach, the hyperbolic stress-strain parameters of soils may be obtained from triaxial tests of undisturbed soil sample or correlation from field test data as described in Byrne et al (1987). However, a correction factor of about 1.5 is needed to approximately account for the 3D effect which is neglected in the 2D finite element analysis to obtain the soil-pile interaction P-y curves. Such correction factor may be better established by comparing the P-y curves from 2D and ZD finite element analyses employing given soil stress-strain law. 8.5 Summary and Conclusion Nonlinear analyses of pile response to lateral pile loading were performed using cur-rent design practice A P I code (1987) and the methods proposed in this study. Two methods of specifying P-y curves for the analyses have been proposed and evaluated. Based on the comparison of initial subgrade reaction modulus given by A P I code (1987) with the maximum Young's soil modulus, Emax, given by Yu and Richart (1984), it was found that the initial subgrade modulus may be better represented Chapter 8. Prediction of Pile Response to Lateral Loads 259 by the maximurri Young's modulus. Thus, a modified version of A P I code was pre-sented. This approach has the advantage that the initial slope of the P-y curves can be measured from the insitu seismic testing, such as seismic cone penetration tests (Robertson et al, 1984). The another method which is based on the 2D plane strain finite element analysis was also proposed to specify P-y curves for the pile analysis. A comparison of normahzed P-y curves from the finite element analysis and the A P I code with the test data has shown that P-y curves from A P I code are stiffer at small pile deflection and quickly become softer after the ultimate soil resistance is reached. The ultimate soil resistance specified in A P I code, however, is not supported by the test data. The P-y curves from the plane strain finite element analysis using triaxial soil data resemble the characteristic shape of the experimental P-y curve although it becomes softer at large deflection. The softer finite element P-y curves at larger deformation was thought to be due to the interaction between the soil layers ignored in the plane strain finite element analysis. A correction factor of 1.5 was found to be appropriate to account for this effect. Predictions of pile response under various test conditions using P-y curves from these methods have been compared against the measurement data as well as the pre-diction from experimental P-y curves in terms of pile head response, bending moment, shear force, soil reaction and the secant soil modulus used in the analysis. The test conditions analyzed included the pile response under different hydrauhc gradient, dif-ferent loading eccentricity, different pile head fixity, and different soil density. From all these analyses, it was found that the same set of P-y curves can be used to give good prediction of pile response regardless of the pile head loading eccentricity and fixity. There is no significant difference between the predictions given by the original A P I code and the modified one. In view of practical significance in obtaining the initial slope of A P I P-y curve from the in-situ seismic measurement rather than the Chapter 8. Prediction of Pile Response to Lateral Loads 260 empirical correlation, the modified version of A P I code which incorporates the max-imum soil Young's modulus, Emax, is thus favoured. Both the original and modified versions of A P I methods tend to overpredict pile bending moment and shear force, and slightly underestimate the pile head deflection, especially for the fixed head pile condition. It was also found that the P-y curves from 2D plane strain finite element analyses using hyperbolic soil parameters overall give better predictions in all aspects of pile response when the 3D interaction effect is properly taken into account. In this approach, the hyperbolic stress-strain parameters of soils may be obtained from tri-axial tests of undisturbed soil sample or correlation from field test data as suggested in Byrne et al (1987). Chapter 9 Summary and Conclusions It is important to conserve the field stress condition in geotechnical model testing where the soil response is much dependent upon the stress level. In this thesis, a model testing technique using the hydrauhc gradient similitude method was pre-sented. This method employs a high hydrauhc gradient across the porous soil material and hence increase the body force in the model soil approaching to the field condi-tion. Its testing principle is very similar to that of the centrifuge technique where centripetal acceleration is used to increase the model stress level. As compared to the centrifuge technique, this method provides an easy and inexpensive means that can be readily available in conventional soil laboratories for some geotechnical modelling problems. Possible factors affecting the test results were theoretically examined, and the limitation of the method discussed. A new testing device ( U B C - H G S T ) has been developed for the general hydrauhc gradient similitude tests with emphasis on the study of pile response to monotonic and cychc loading. A sample preparation technique using "quick sand" condition was also developed for the hydrauhc gradient model tests. This "quick sand" sample preparation technique was found to be able to produce a uniform soil sample that has similar stress-strain response to that of water pluviation samples. Apphcation of this new model testing technique to three different geotechnical problems was presented. This included footing foundation, downhole and crosshole tests and the pile foundation under lateral loads. Testing equipment and procedures were described in detail. 261 Chapter 9. Summary and Conclusions 262 The apphcation to the footing foundation constituted a preliminary apphcation of this model testing technique. Tests were conducted in a modified triaxial cell. The results were presented and compared with centrifuge tests. The observed load-settlement curves were found to have very similar characteristics to those observed in centrifuge tests. The footing tests on dense sand displayed a marked limit pres-sure while those on the loose sands did not. The limit pressure showed the influence of stress level in reducing the mobihzed friction angle at high stress levels, which was found to be in agreement with both centrifuge and triaxial testing results. The bearing capacity coefficient, 7V7 was found to decrease with the footing width in a linear logarithmic manner which depicted a stress level effect on the bearing capacity formula. Comparisons of test results with Terzaghi bearing capacity formula at dif-ferent stress level shown that at the high stress level the test results foUowed Terzaghi formula while at the low stress level deviation with the formula was observed. This was attributed to the results of stress level effects on the mobihzed friction angles. The scahng relations implied in the hydrauhc gradient model tests have been examined by comparing the results of two different model tests which simulated the same prototype dimension. The results were found to be in very good agreement and verified that the hydrauhc gradient tests followed similar scahng relations as in centrifuge tests. The results also indicated that the possible stress distortion due to the change of soil, permeability in the test has little effect on the consistency of model tests. In the apphcation to downhole and crosshole seismic tests, the controlled K0 condition including loading and unloading paths were simulated using the hydrauhc gradient similitude method, and downhole and crosshole shear waves were generated and received by piezoceramic bender elements. Shear wave velocity was measured in the principle stress directions for a KD stress condition. With this technique, downhole and SH-crosshole shear wave tests were performed in a controlled stress and soil Chapter 9. Summary and Conclusions 263 state, and the existing laboratory-based empirical Gmax equations or concepts were evaluated in terms of field stress condition. In addition, measuring shear modulus, Gmax, distribution within a model soil sample provided the insitu soil parameter for the model analyses. It was found that the three basic types of empirical equations for predicting the maximum shear modulus all gave results that were in good agreement with the mea-sured shear wave velocities. However, the variation of velocity ratio .between downhole and SH-crosshole tests with the stress level was only correctly predicted by equation based on the 'individual stress method.' This indicated that the stress level effect on the shear modulus can be best represented by consideration of the individual stresses in the wave propagation and the particle motion directions. From examination of the downhole and crosshole shear wave velocity during the Ka loading and unloading paths, it was found that for the crosshole tests where the wave propagation and particle vibration directions were all in the horizontal plane (SH-crosshole), the shear wave velocities in loading and unloading paths fall on a straight hne when plotted using the individual stress method, while for the downhole tests this was not the case. This observation was attributed to the effects of stress ratio defined in different wave travelling planes. It was also found that the stress ratio reduces the observed shear wave velocity, and the effect is more significant in extension stress state than in compression state. The possibility of using shear wave velocity measurement to predict the Ka values was also examined. It was concluded that only the equation based on 'individual stress' method should be applied for this purpose. A n approach based upon velocity ratio was proposed and discussed to eliminate the necessity of estimating insitu soil void ratio. It was found that the prediction of K0 values was in reasonably good agreement with the measurement in the loading phase, but not that good in the un-loading phase, especially in very low stress level. This was attributed to the high Chapter 9. Summary and Conclusions 264 sensitivity of the method to testing error. Thus, although in principle the method-ology is promising, rehable estimation of K0 may depend upon the testing accuracy. Further research was suggested before this method could be used reliably in practice. In the apphcation to laterally loaded piles, the consistency of test results was also examined by using the "modelling of models" technique, and the results were found to follow the expected scahng laws. In this apphcation, emphasis was focused on evaluating various factors affecting the pile response under static and cyclic lateral pile head loads, and forming a data base to examine the existing methods of analysis. The factors examined in the study included relative soil-pile stiffness, pile diameter, loading eccentricity, and pile head fixity. For the piles subjected to static lateral loading, it was found that pile head re-sponse and bending moment are significantly affected by the relative soil-pile stiff-ness, pile diameter, pile head loading eccentricity and pile head fixity. However, it was found that the soil-pile interaction in terms of P-y curves are not significantly affected by pile diameter, pile head loading eccentricity, and pile head fixity but sig-nificantly affected by the relative soil-pile stiffness due to the soil stress levels. It was found that for the monotonic loading the stress level dependency of the P-y curves can be reasonably normahzed by the Young's moduh of soils and the pile diameter for those P-y curves at depths below 1 pile diameter, as indicated by a plane strain finite element analysis using the hyperbolic stress-strain relationship for soils. The normahzed P-y curves were found to have a 45° initial slope and may be represented by a power function of exponent close to 0.5, while the other coefficient of the power function appeared to be solely dependent upon the soil density. Thus, an approach to predict soil-pile interaction P-y curves based on the plane strain finite element analysis using the fundamental soil parameters was proposed. For the piles subjected to cychc lateral loading, it was found that different pile responses were observed depending upon the nature of the cychc loadings. In two-way Chapter 9. Summary and Conclusions 265 cyclic loadings, the pile response was found to become stiffer initiaUy with number of cycles, followed by a deterioration of soil-pile system due to the significant soil gapping and remoulding at the upper soil layers. The pile deflection and bending moment response to the two-way symmetrical loading was found to be not symmetric with larger deflection and bending moment in the first loading direction. While in one-way cychc loadings, the pile head deflection was found to increase steadily with each number of loading cycle before the soil-pile system stabihzed due to the plastic soil deformation. In this process, the soil-pile system becomes progressively more elastic as the number of cycles increases. The increment of pile deflection in the one-way loading was most significant in the first few cycles, and was able to be expressed in a logarithmic function with number of cycles. But the incremental rate was found to be significantly affected by loading eccentricity, magnitudes of load and pile head moment, and pile head fixity. Under the two-way cyclic loading a downward migration and increment of pile maximum bending moment with number of loading cycles was observed while this was not found for the one-way cychc loading condition. This was attributed to the different observation of soil gapping around the pile under these two types of cychc loading. Larger and deeper soil cavity was found in the case of two-way loading as compared to that in the one-way cychc loading. However, in both cases of cychc loadings, the pile residual bending moment all tended to increase with number of cycles. The cychc P-y curves observed under both cases of cychc loadings were all found to be highly nonhnear and hysteretic in nature. However, for the two-way cychc loading, due to the more severe soil gapping around the pile, soil-pile interaction de-teriorated with number of cycles, exhibiting "peanut" shapes of nonhnear P-y curves after certain number of loading cycles. While for one-way cychc loading, the nonhn-ear cychc P-y curves tended to be more linear and elastic hysteretic loop after certain Chapter 9. Summary and Conclusions 266 number of loading cycles, indicating the stabilization of the soil-pile system. Nonlinear numerical analyses were also performed to predict pile response to the static lateral loads using the finite difference program L A T P I L E . Three methods of constructing soil-pile interaction P-y curves have been evaluated. This included the original A P I code (1987), a modified A P I code and the finite element method using triaxial soil parameters. A comparison of both finite element and A P I P-y curves with the test data indicated that A P I methods give stiffer P-y curves before the specified ultimate soil resistance is reached. The ultimate soil resistances specified in A P I method are too small and not supported by the test data. The predicted P-y curves from finite element analyses using triaxial soil parameters resemble the characteristic shape of the experimental curve although they are still softer at large deflections. This softer response from finite element analysis was thought to be due to neglecting the interaction between the plane layers in the plane strain finite element analysis. Thus, a correction factor was applied. Comparisons between the predictions given by the original and the modified A P I methods indicated that there is little difference between these two methods in predict-ing pile response. Thus, the modified A P I method which incorporates the maximum Young's modulus of soils, Emax as the initial subgrade soil modulus was favoured. This indicates that the initial subgrade modulus in A P I code can be evaluated from the insitu seismic tests rather than based on empirical correlations. Comparison of predictions given by all these three methods under various testing conditions shown that A P I methods tend to overpredict the maximum pile bending moment and shear force at the large loading level, but slightly underestimate the pile head deflection, especially for the fixed head pile condition, at the small loading level. It was also found that the P-y curves from plane strain finite element analyses using hyperbolic soil parameters generally give better predictions in all aspects of pile response when the correction factor is applied to account for the ZD effect. Chapter 9. Summary and Conclusions 267 Comparison of the predictions with the test data shown that good predictions of pile responses to different loading eccentricity and pile head fixity can be obtained by using the same set of P-y curves which are only a function of soil condition. From these studies, it is clearly shown that the hydrauhc gradient simihtude method provides a simple and inexpensive means of studying many geotechnical en-gineering problems under a well controlled condition. The main drawback of the hydrauhc gradient test is that the body force apphed to the model depends on both the boundary conditions and the permeability of the soil. It is basically hmited to soil-structures comprised of uniform sands where the applied flow boundaries are hor-izontal. However, there are many problems that fall into this category such as the problems examined in this thesis. The main objectives of using this technique is to perform geotechnical model tests under a controlled field stress and soil conditions so that the soil-structure behavior can be examined under a field stress level and existing concepts and methods of analysis can be evaluated. Further studies of using this model testing technique can be easily extended to include: 1. Repeated vertical loading and rocking and shding of footings on sand; 2. Examination of the insitu seismic methods to evaluate the shear modulus and damping of sands under different shear strain levels; 3. Studying vertical piles and pile group under vertical loading; and 4. Studying vertical piles and pile group responses to lateral static and cychc pile head loading as well as earthquake loadings with direct measurement of pile-soil-pile interaction factors. Research on vertical piles response to earthquake loading is currently underway using the H G S T apparatus and the shaking table facilities at U B C (Dou, 1991). Preliminary Chapter 9. Summary and Conclusions 268 results have shown that by combining the H G S T apparatus and the normal shaking table a soil-structure model can be tested on the common shake table with a field stress level (Yan and Byrne, 1991c). This technique eliminates the limitation of low stress problems commonly associated with the shake table model tests, and provides an easy way of shaking models at prototype stress condition as compared to that in the centrifuge technique. Appendix A Effects of Compressible Fluid Flow - Air Seepage Case Example of air seepage in soil sample is used to estimate the upper bound effects of compressible fluid flow on the effective stress field of soils. The basic theory for a steady-state air flow through soil is presented herein. Based on the continuity of air mass, the following equation is obtained: laVz = C1 ( A . l ) where 7 a is the density of the air at given pressure and temperature conditions, Vz is the flow velocity in z-direction, and C\ is the integration constant. For the isothermal condition, based on Boyle's law, the air state can be expressed as: 7 a = 7 a 0 ^ ^ (A.2) a where 7 a o is the air density at the atmosphere pressure, Pa, P is the air pressure above the atmosphere pressure. Assuming the air flow is induced by the internal pressure difference, then the flow velocity, Vz is of (Muskat, 1946): dP Vz = -kz — (A.3) oz where kz is the air permeabihty of soil sample. From Eqs. ( A . l ) , (A.2) and (A.3) with integration, it is shown the air pressure 269 Appendix A. Effects of Compressible Fluid Flow - Air Seepage Case 270 distribution along the soil sample will be as: P = 0.5 / P Q 2 + AA - Pa (AA) in which + P? + P 0 P a where L - the sample height, z - the depth below the sample surface, P 1 ) 2 - the controlled air pressures at the top and bottom of soil sample respectively. Thus, it is shown from Eq . (A.4) that the gradient of air pressure along the soil sample, and consequently the effective stress of soils are no longer uniform, as indicated in Figure 2.3 of Chapter 2. Appendix B Effects of Porous Stone on Footing Pressure and Soil Stress Condition A porous stone which was relatively impermeable was used to form the footing base in the tests. Its effects on the footing pressure and the soil stress condition underneath the footing are examined herein. B . l Seepage Force Correction to Footing Pressure A small correction to the measured applied footing pressure is required to account for the hydrauhc head loss in the porous plate at the base of the footing. The various forces acting on the footing adaptor and the loading ram system are shown in Figure B l . While the ram is moving down but before the footing contacts the sand, there is no load applied by the footing to the sand, and there is no seepage on the footing plate as depicted in Figure Bl(a) . The force on the load cell at this point is (FLc)i and is given by: {FLC)I = Ff — Fp — Fd — Fl ( B . l ) in which Ff = the friction on the ram the uphft force due to the cell pressure Fa — the drag force on the loading system due to water flow Fw = the weight of the ram and footing adaptor 271 Appendix B. Effects of Porous Stone on Footing Pressure and 272 Figure B . l : Forces on Footing Loading System Appendix B. Effects of Porous Stone on Footing Pressure and 273 When the footing comes in contact with the soil, the force in the load cell will increase reflecting the soil reaction force. However, because the porous plate at the base of the footing has a relatively low permeability, an additional correction force must be considered when computing the soil reaction force as follows: FR = AFLC + F8 (B.2) in which FR = the soil reaction force AFLC — the change in loading cell force from the initial condition F, — the seepage force on the porous footing. The seepage force FS depends on the gradient in the porous plate which in turn depends upon the relative permeability of the sand and the porous plate. FT was computed from a finite element seepage analysis. The coefficient of permeability used for the sand was taken from the laboratory test results shown in Figure (3.3). The permeability of the porous stone material was obtained from tests and found to be 0.5 X 10 - 3crri/sec, which was about 20 to 30 times less permeable than that of the underlying sand. The finite element analysis was first carried out on a coarse mesh using an ax-isymmetric domain identical to the physical domain tested. It was found that the gradient was essentially uniform except in the region adjacent to the footing base. Therefore, detailed analyses were performed on a finer mesh of a smaller domain as shown in Figure B2. Analyses were carried out for each hydrauhc gradient condition at the beginning of test when footing contact first occurred and at the end of the test when the maximum penetration of the footing into the sand occurred. Typical results showing flow nets force loose sand at N = 60 are shown in Figure B3. Appendix B. Effects of Porous Stone on Footing Pressure and 274 ° 1 2 J CD i—i C3 CJ X C i n e 0) _) C3 CO "3 (3 + 1 ! 1 1 11 11 11 1 1 0 5 CJ Footing (a) inilial stale Footing (a) inilial stale Footing (a) inilial stale 1 1 Footing (a) inilial stale Footing (a) inilial stale j Footing (a) inilial stale Footing (a) inilial stale Footing (a) inilial stale Footing (a) inilial stale 1 1 i i V 1 t M l fl 1 1' . i ' t 1 1 Figure B.2: Finite ELement Mesh used for Seepage Analyses Figure B.3: Flow Nets for Hydraulic Gradient Footing Tests (Loose Sand N=60) Appendix B. Effects of Porous Stone on Footing Pressure and 276 The average hydraulic gradients in the footing plate were computed from the seepage analyses and are shown in Figure B4 for the beginning and end of a test respectively. The dimensionless parameters used in the figure are: 1. The hydraulic gradient ratio iav/is m which is = the applied gradient prior to placing the footing, iav = the average gradient in the footing plate, and 2. The permeability ratio kp/ks in which kp = the permeability of the plate and ks — the permeability of the soil. It may be seen that the gradient ratio and hence the seepage forces are highest at the end of the test. It may also be seen that the gradient ratios are independent of the permeability ratio for permeability ratios less than 0.1. For our case, the permeability ratios were in the range 0.01 to 0.1 for loose to dense sand, and hence the seepage force correction is insensitive to the absolute value of the permeability. In addition, the curves shown in Figure B4 were found to be independent of the apphed gradient. The seepage force F, at the beginning and end of a test was computed as follows: F„ = Vpiavlw (B.3) where Vp = the volume of the porous plate iav = the average gradient in the plate 7„j = the unit weight of water. For intermediate conditions, a linear interpolation of the results was used to de-termine Fs. The seepage force Fs was then used in E q . (B.2) to compute a corrected soil reaction force and soil pressure. Examples of observed load-settlement curves before and after correction are shown in Figures B5 and B6 where it may be seen that the corrections do not significantly affect the measured curves. Appendix B. Effects of Porous Stone on Footing Pressure and 277 o o o o o o in o m o CN » — * - • O O Figure B.4: Seepage Force Correction for the Porous Footing Plate Appendix B. Effects of Porous Stone on Footing Pressure and 278 Figure B.5: Comparison of Test Data before and after Seepage Force Correction for Loose Sand Appendix B. Effects of Porous Stone on Footing Pressure and 279 Figure B.6: Comparison of Test Data before and after Seepage Force Correction for Dense Sand Appendix B. Effects of Porous Stone on Footing Pressure and 280 B.2 Soil Stress Condition Underneath the Footing As shown in Figure B3, due to the relatively low permeability of the porous footing base, the flow lines around the footing are distorted. Most of the water flows around the footing base and into the underlying sand, creating a "shadow" beneath the foot-ing to a depth about 1/2 the footing diameter. The hydraulic gradient immediately underneath the footing base is about 75% lower than that of the free field, while the hydrauhc gradient at the edge of footing base is 25% higher. Therefore, the soil stresses underneath the footing due to seepage force do not increase uniformly with depth. However, the distorted region is very small as shown in Figure B3. The most seriously distorted region is the zone to a depth of about 0.25B m below the footing. A finite element analysis was performed to evaluate the possible effect of such a small distorted stress zone on footing settlement. The analysis employed the same finite element mesh shown in Figure 3.21. The computed vertical soil strain profiles for two initial stress conditions are shown in Figure B7, namely, 1. Initial soil effective stress calculated from an undistorted free field hydrauhc gradient (i.e., stone has infinite permeability), and; 2. Initial soil effective stress calculated from the distorted hydrauhc gradient field computed from the seepage analysis shown in Figure B3(a). It may be seen from Figure B7 that the strain fields resulting from the two initial stress conditions are very similar. The integration of these two strain curves leads to a difference in settlement of only 5%. Therefore, the effect of local stress distortion due to the low permeability of the porous stone footing base is insignificant on the settlement. It may be seen from Figure B7 that the maximum vertical strain occurs at a depth of 0.5 Bm rather than at the base of the footing as might have been expected. However, these computed centreline vertical strain profiles are similar in shape to those reported Appendix B. Effects of Porous Stone on Footing Pressure and ... 281 5.00 - i E CO in ; I i i i i i i i i i I i i i i i r~i—i—i—|—i—i—i—i—i—i—|—|—|—1 0.00 0.04 0.08 0.12 V e r t i c a l s t ra in a l o n g the D e p t h ( 5 5 ) Figure B.7: Footing Permeability Effect on the Vertical Strain Profile underneath the Footing Appendix B. Effects of Porous Stone on Footing Pressure and ... 282 by Schmertmann (1970) and Schmertmann et al (1978). The Schmertmann profiles were obtained from both model tests and theoretical studies. * 0 Appendix C Stress Analysis and Calibration of Total Stress Measurement C . l Stress Analysis In this study, the lateral total stress was directly measured by a pressure transducer mounted on the soil container wall. The pressure transducer is a flush mounted, diaphragm-type transducer which senses the pressure by the center deflection of its diaphragm. In the normal pore water pressure measurement, a uniform pressure distributed over the diaphragm is usually expected. However, in the hydraulic gradient similitude tests, the lateral total stress on the wall is not uniform but has a linear distribution along the depth, as shown in Figure Cl(a) . When using the pressure transducer of this type in H G S T test condition, the possible effects of this nonuniform stress distribution over the diaphragm should be examined. It will be shown below that for a linear stress distribution, the pressure transducer measures the stress at the center point of its diaphragm. In the analysis, the transducer can be modelled as an elastic circular plate with fixed outer edge under a distributed pressure. Since the amount of deflection at the diaphragm center determines the stress measurement in this type of transducer, only the deflection at the center of the plate is of interest. This deflection can be obtained by using the following consideration (Timoshenko and Woinowsky-Krieger, 1959). Due to the complete symmetry of the plate and of its boundary conditions, the 283 Figure C l : Stress Analysis on the Water Pressure Transducer Appendix C. Stress Analysis and Calibration of Total Stress Measurement 285 deflection produced by an isolated load P depends upon the magnitude of the load and its radial distance from the center, i.e. the deflection remains unchanged if the load P is moved to another position provided its radial distance to the center is the same. The deflection is also the same if the isolated load is replaced by a uniformly distributed ring load whose summation equals load P with the same radial distance 'tV as the isolated load P. For the load uniformly distributed along a circle of radius 'b', the deflection at the center of a circular plate with fixed outer edge is (Timoshenko and Woinowsky-Krieger, 1959) : 8 T T £ > { \aj 2 where a is the plate radius, b is the distance of the load to plate center, P is the magnitude of the isolated load, and D is the plate flexural rigidity, i.e. Et3 1 2 ( l - i / 2 ) E = Young's modulus of the plate t = plate thickness v = Poisson's ratio of the plate (C.2) E q . C . l gives the deflection at the center of the plate produced by an isolated load P at a distance 'b' from the center of the plate. Then, the deflection at the center due to any kind of load can be obtained by superposition using E q . C . l , as discussed below. As shown in Figure Cl (b) , in the Cartesian coordinate system, the hnearly dis-tributed pressure p(x,y) is : p(X,y) = (P™*-Pmin)y+po Za P{x,y) = p(x,y)dxdy (C.3) Appendix C. Stress Analysis and Calibration of Total Stress Measurement 286 where Pmax, Pmin are maximum and minimum pressures across the plate respectively, p0 is the pressure at the plate center, and P(x,y) is the isolated load, as shown in Figure Cl (b) . When Eq.C.3 is changed to the polar coordinate system : P(T,6) = p(r,9)rdrd8 = | ^ maX ~aPmi^rsin6 + p 0 | r dr d9 (C.4) Thus, the total deflection at the plate center is : where 'a' is the plate radius. Substituting Eq.C.4 into the above equation, and after integration, we have the total deflection at the plate center : («*)-- = s£ <c-6> This solution is exactly the same as the deflection at the plate center under a uniformly distributed pressure with magnitude po (Timoshenko and Woinowsky-Kriegger, 1959). This indicates that with this type of transducer, the stresses measured correspond to the pressures at the center of the diaphragm. C.2 Stress Transducer Calibration Accurate measurement of soil stress is very difficult as the response of stress trans-ducer embedded in soil mass is a function of many factors, such as relative stiffness between the soil and transducer diaphragm, transducer gage configuration, and stress level. Therefore, a successful interpretation of test results from stress transducer re-quires proper calibration and a knowledge of the performance of the gages installed in soil in a manner similar to the actual measurement condition. Appendix C. Stress Analysis and Calibration of Total Stress Measurement 287 In order to calibrate the pore water pressure transducer for the purpose of mea-suring soil stress, a ID calibration chamber was built. A schematic drawing of the calibration chamber and transducer setup is shown in Figure C2. The ratio of soil chamber diameter to the specimen height is about 3, and the diameter ratio between the calibration chamber and the transducer is 5 to reduce the effects of friction at the chamber wall (Selig, 1980). Two types of calibration were performed : • Fluid Calibration; • Soil Calibration. In fluid calibration, water was used in the test. While in the soil calibration, both loose and dense dry sands were tested, and a thin silicon greece was also applied on the soil chamber wall to further reduce the possible wall friction effect. The calibration results are shown in Figure C3 with pressure transducer output plotted against applied pressure. As shown in the figure, the calibration curve is linear and the data from both fluid and soil calibrations follow the same calibration curve. Appendix C. Stress Analysis and Calibration of Total Stress Measurement 288 - 7 -2" Air Gauge (y Air Inlet v Air Regulator Bellofram Air Chamber Fluid or Dry Sand Lateral Stress Transducer JD' = 0.65" 1.5" 1.25" 3.5" Figure C.2: Schematic of Calibration Chamber for Lateral Total Stress Transducer Appendix C. Stress Analysis and Calibration of Total Stress Measurement o C N o C N m o •o 0) TJ CP i _ 3 CO to QJ -a xi c c c o a o coen-to cn -a Q> to co •— cn w l_ cr o co cu _ i _ ! o r r c o "a O S3 \ i i i i i i i i i | i i i i i i i i i | i i i i i i i i i ] : i i i i i i i i | i i i i i i i ?V o •o . o 00 o D CO CO CU . o . o C N i n C N m C N ( A ) 3 6 D + | O A }nd}no Figure C.3: Calibration of Lateral Pressure Transducer Appendix D Theoretical Consideration of Eliminating the Near Field Wave Effects and Obtaining Pure Shear Wave Record D . l Near Field Wave Effects When spacing the bender elements in the downhole and crosshole simulating rods, due consideration has to be given to ehmination of the near-field wave effect (Aki and Richards, 1980 and White, 1983). For the testing condition in this study, an elastic wave theory for a point force within a homogeneous, isotropic, linearly elastic medium can be used to simulate the 3D waves generated from the bender element source. The elastic solution for the waves generated from a point force Xo(t) acting in Xj-direction at the origin of the coordinate system shown in Figure D l (Aki and Richards, 1980) is: 1 1 rTlv> Ui(f,t) = ^ ^ ( 3 7 i 7 j ~~ jt TXo(t - r)cir(near field) 1 1 „ / r i H1j~ Xo\t (P-wave far field) 4Trpv£ r \ VpJ 1 I T — (7,-7,- - 8ij)-XQ(t )(S-wave far field) (D.l ) 4 7 r /w; r v, i = 1,2,3 290 Figure D.l : General 3-D Waves from a Point Source Appendix D. Theoretical Consideration of Ehminating 292 where f 1 if i = 7' [ 0 i f» ^ j li = — r r = | r | f = {a?!,332,2:3} (D.2) v„, vp are shear and compression wave velocities, respectively, and p is the bulk density of soil medium. From this equation, it can be seen that wave motion generated from a point source is composed of three terms : 1. The first term is a function of ^ 3 , and is dependent upon both shear and com-pression wave speeds. Since this term is only dominant at r —> 0, it is the so called 'near field' effect. 2. The second term is a function of ^  and propagates with the compression wave speed, and is relatively dominant at large r. It is a far field term for the compression wave. 3. The third term is also a function of but travels with the shear wave speed. Again, it also only dominates at the far field. It can also be seen from the equation that separation of the 5-wave and P-wave is only possible in the far field. In the near field, even with pure shear motion, some amount of wave energy would always be transmitted in P-wave speed (Sanchez-Sahnero et al, 1986). This near field effect will result in an 'apparent' faster shear wave velocity measurement in the tests when the shear wave velocity is determined based on the wave first arrival time. To eliminate this effect, a minimum distance between the source and the receiver has to be imposed. Based on a parametric study, Appendix D. Theoretical Consideration of Eliminating 293 Sanchez-Salinero et al (1986) suggested that for the transverse (shear wave) motion, this minimum distance, dmin, should be larger than 2A, i.e.: dmin > 2A (D.3) and A = v.lh (D.4) where A is the shear wave length, v8 is the shear wave velocity, and fi is the predomi-nant frequency of the shear wave through the soil. In the tests, the frequency, / 1 } can be estimated from FFT analysis of the wave record measured by the bender element, as shown in Figure D2. From Eqs.(D.3) and (D.4), it can be seen that the near field effects depend upon shear wave velocity and the wave propagating frequency which is a function of soil stiffness and source frequency. In the downhole test, the criti-cal condition is the first receiver below the source, while for the crosshole, it is the distance between the two simulating rods. From some trial tests, the frequency, / l 5 estimated for loose sand is : • For i = 1, / i = 0.8 ~ 1.2 kHz • For i = 60, / i = 6 ~ 11 kHz Substitution of these fi values and corresponding measured shear wave velocity into Eqs.(D.3), (D.4) suggests a minimum distance between the source and the re-ceiver, d m i n > 5cm. This criterion has been used in spacing the bender element in downhole and crosshole simulating rods in this study. D .2 Obtaining Pure Shear Wave M o t i o n In the far field, both shear and compression wave are generated with a spherical wave front for a point source and this may be the case for the bender element source. By endix D. Theoretical Consideration of Eliminating 294 (9-31 MUILI) (9-31 MUILU *H/W>A XH/WA (v -3l«wuu) (9-3l*«>iLl) Figure D.2: F F T Analyses of Shear Wave Traces Appendix D. Theoretical Consideration of Eliminating ... 295 examining Eq.(D.2), it can be seen that for those points where r • X0 = 0 : P — wave «• = 0; i ^ j S — wave UJ + 0; i.e. only shear wave motion exists at those points. Thus, in order to predominantly measure shear wave, the source and receiver bender elements were assembled in a straight hne which was perpendicular to the bending direction of the source. Test results shown in this study also suggest that under this bender element configuration, only shear waves are measured by the receivers. Appendix E Air Pressure Controlled System for Laterally Loaded Pile Tests A n air pressure control unit was designed to counter balance the lateral pushing force on the loading ram as a result of air pressure inside the H G S T system. This unit is shown in Figure E . l . The design of this pressure control unit has to satisfy the following requirements: • during the gravitational process to automatically counter balance the horizontal force acted on the loading ram so that the pile will stay in its original position before the load test begins; • after the gravitational process, the cyclic horizontal load can be easily apphed to the model pile. To satisfy the first requirement, a double acting air piston was employed whose piston rod has the exact same diameter as the loading ram connecting to the model pile. Thus, the same unequal end area is created in the double acting piston as compared to that inside the air chamber. During the gravitational stage, the air pressure supphed to the H G S T air pressure chamber was also connected to the front and back cells of the double acting piston, thus the loading ram was automatically balanced by the horizontal forces in the double acting piston and the H G S T air chamber, and the model pile remained in its original position. 296 Appendix E. Air Pressure Controlled System for Laterally Loaded Pile Tests Figure E . l : Air Pressure Control System for Laterally Loaded Pile Tests Appendix E. Air Pressure Controlled System for Laterally Loaded Pile Tests 298 When the air pressure in the H G S T air chamber has reached certain value that gives the desired hydrauhc gradient, the load cell reading indicated by the monitor-ing program was initialized. Then, the air pressure in the front cell of the double acting piston was reduced by switching the two-way valve VI to the pressure hne controlled by air regulator R2 in which the air pressure has not yet been supplied. The movements of load cell and loading ram were stopped by two adjustable rigid blocks against the annular aluminum block. At this stage, the back pressure in the double acting pressure was also switched by the two-way valve V2 to the pressure hne controlled by the function generator. This pressure hne was constantly under a pressure of 400 kPa set by the D . C . offset in the function generator. This pressure was to be larger than the maximum pressure expected in the H G S T air chamber. As a result, a compression force was applied on the load cell against the annular aluminum block. By increasing the front pressure in the double acting piston through regulator R2, a new equilibrium in the loading ram would be established again when the load cell reading indicated zero load. At this moment, the adjustable rigid block in front of the eye-link was removed, and a variable pressure was supplied by the function generator to the back pressure of the double acting piston. Thus, a one-way or two-way horizontal load was applied to the model piles, and the lateral pile head loading tests commenced. Appendix F Prediction of Pile Response under Other Testing Cases Predictions from the computer L A T P I L E using three methods of constructing P-y curves have been made on the pile response under different test conditions. For the cases of free head pile under different loading eccentricity, the results have been presented in Chapter 8. Herein, prediction on other testing conditions are presented. Different Hydraulic Gradient Predictions on the free head pile response under the hydrauhc gradient scale factor of 48 are presented. In this analysis, the simulation of pile free length above the ground and the specification of P-y curves along the depth are in the same way as when the hydrauhc gradient scale factor is equal to 64. Figure F . l shows the predictions on pile head deflection at loading point under different loading level and pile bending moment at a load of 22.06(N) along the depth. It is shown that both A P I codes give very similar prediction on pile head response, being slightly stiffer than the experimental data at deflections below 1.4 mm. In the pile bending moment distribution, the prediction from the finite element P-y curves is very close to the test data and the prediction based on the experimental P-y curves, while the predictions from both A P I codes are slightly overestimated. Figure F.2 shows the soil reaction and pile deflection profiles computed by various methods at the load level of 22.06(N). It is shown that while large difference exists between the soil reaction profiles computed by A P I codes and finite element analysis, 299 Appendix F. Prediction of Pile Response under Other Testing Cases 300 30-p3hd48e6.prn N=48 E=45.0mm ooooo test data API code (1987) WET+Emax FEM-PLN power function exp. P-Y curves API code (1987) WET 0.0 i i i i i i i i i i i i i i i i i i | i i ' ' ' ' ' ' ' I ' ' ' ' 1 ' 1 ' 1 l 0.5 1.0 1.5 2.0 Pile Deflection at Loading Pile (mm) - 1 0 0 Pile Bending Moment (N.mm) 1000 - 5 0 0 0 500 !0DD 1500 1111 n 11111111 n 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 E E o a TJ C 3 O CD > 100 200 £ 300 C L a> Q 400 - 1 p3hd48e6.prn: N-48.E-45.0mm at Load Level of 22.06N exp. p— y curves — — API code curves API code+Emax FEM-PLN power func. ooooo test data Figure F . l : Predictions of Pile Head Response and Bending Moment Distribution for a Free Head Pile at N=48 E=45mm II 3 00 T) 1 « *>• o 3 I 3 I ^ c n P 2. o CL. to to o 05 fD P o S" CL, O fD tb fD fi 5" TJ o fD fD W fD f» PL, -100-E E CO (J t to TJ C D 8 CD > CO CD o-1 0 0 -2 0 0 -3 0 0 -4 0 0 -Soil Reaction - P ( N / m m ) 6 - 4 0 2 > 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 p 3 h d 4 8 e 6 . p r n : N = 4 8 , E = 4 5 . 0 m m at L o a d Level of 2 2 . 0 6 N e x p . p—y c u r v e s A P I c o d e c u r v e s A P I c o d e + E m a x F E M - P L N p o w e r f u n c . - 1 0 0 E E o o t cn TJ c D 8 cn CD > CO 1_ CL CD Q Pile deflection (mm) - 0 . 5 1.5 3 . 5 i : I i i I i I I I I I I I 1—1—I—I—I o-1 0 0 -2 0 0 -3 0 0 -4 0 0 -p 3 h d 4 8 e 6 . p r n : N = 4 8 . E = 4 5 . 8 m m a t L o o d L e v e l o f 2 2 . 0 6 N o o o o o t e s t d a t a e x p . p—y c u r v e s — A P I c o d e • - A P I c o d e + E m a x - - - F E M - P L N p o w e r f u n c . Appendix F. Prediction of Pile Response under Other Testing Cases 302 little difference is observed in the computed pile deflection profiles. The soil reactions computed by both A P I codes are similar and have larger peak values at the deeper location. This indicates that load transfers to further depths when the P-y curves reach the ultimate values at shallow depths. The computed soil reaction profile from the finite element P-y curves is in a close agreement with that computed from the experimental P-y curves. Figure F.3 gives the computed shear force acting on the pile and the equivalent subgrade moduli used in various analyses at given loading level. It is shown that the maximum value of shear force on the pile is overestimated by both A P I codes while good agreement is obtained between the predictions from finite element and experi-mental P-y curves. Within the first 3 pile diameter depth, the equivalent subgrade reaction moduli used by all the methods are very similar with the A P I code values slightly smaller. Beyond this depth, large difference exists among different meth-ods. The original A P I code results in a stiffest distribution, finite element analysis a smallest, and the modified A P I code in between. The distribution given by the finite element method has a good correlation with that by the experimental P-y curves. F i x e d H e a d P i l e R e s p o n s e The pile load test under fixed head condition was also analyzed. The test was per-formed at a hydrauhc gradient scale factor of 48 with the loading eccentricity of 45 mm above the groundhne. In the analysis, the P-y curves representing the soil reaction were specified at given depths below the surface. The free length between the loading point to the surface was simulated by specifying P-y curves at these two points where soil reactions were nearly zero. The fixed head condition was initially simulated in the analysis with zero pile slope at the loading point. However, it was found that such an analysis severely underestimated pile deflection and bending moments. This was thought to be due to the imperfect rigid fixed head connection which was noted in Appendix F. Prediction of Pile Response under Other Testing Cases 303 o o -CN 3 s o -T> D 3 cr bJ C D q C N C N E ° ° a J in > :-••<»- o £ II _ CO 03 § .c Q . / / / / / / / I / I / o c — S n v *-D 3 £ O 0 f j U J O ->.«> tt>Z 1 -OTJ -1 CL O O 0 -O O | CL 2 X 0_ Q_ U J c f l < < U . I I I I I I I I I I I I I I I I I I I I I I I I I I I I 1 I I I I I I I I I I I I I 1 I I I I I I I O o O O O O O O O O O * - * - I N n •<}• I ( U J U J ) SDDjjns punojB o} aArj ,D|3j LndsQ Figure F.3: Computed Shear Force on the Pile and Equivalent Subgrade Moduli used in Various Methods for a Free Head Pile at N=48, E=45mm and a load of 22.06(N) Appendix F. Prediction of Pile Response under Other Testing Cases 304 the test. The imperfect fixed head connection may be induced by the bending of the loading ram or/and the loose connection between the pile and rigid cap. Thus, the fixed head connection at pile head was instead simulated by imposing the negative bending moment at the loading point. The negative bending moment at the loading point was interpreted from the bending moment measurements at two strain gauges above the ground surface. With such an analysis, predictions of pile head deflection at loading point and bending moment distribution using different P-y curves are shown in Figure F.4. It appears that the predictions from three methods are all stiffer than the test data. However, as compared to the response predicted by the experimental P-y curves, the predictions from the finite element P-y curves are in a very good agreement while the predictions from both A P I codes are much stiffer in the range of 0.2 mm to 1.2 mm at the pile head deflection. As in the prediction for free head pile response, the predictions from both A P I codes are very similar. As shown in Figure F.4, reasonably good agreement is obtained among the bending moment data and the predictions from various methods. This indicates that bending moment prediction is much less sensitive to the selection of P-y curves. The computed pile deflection and shear force profiles are shown in Figure F.5. for the loading level of 24.44(N). As shown, the deflection profile given by the finite element P-y curves are almost the same as that by the experimental P-y curves while smaller pile deflection are computed by both A P I codes to a depth of about 6 pile diameter. Below this depth, all methods essentially give the same pile deflection. In the profile of shear forces, similar results are obtained from both A P I codes that are higher than the one from experimental P-y curves at shallow depth and become smaller below the 10 pile diameter depth. The shear force computed from the finite element P-y curves has the similar shape as in the experimental curve but with less maximum value at the depth of about 9.5 pile diameter. Below the depth of 20.5 pile Appendix F. Prediction of Pile Response under Other Testing Cases 305 60 •o o o 4 0 ooooo Test data exp. p—y curves API wet (1987) API wet+Emax FEM-PLN power tunc. P i l e H e a d D e f l e c t i o n ( m m ) B e n d i n g M o m e n t P r o f i l e ( N . m m ) - 3 0 0 C - 1 0 0 0 1000 3 0 0 0 - 1 0 0 -a> > a> 0-o o D r ioo-CO x> c D CO a> £ 2 0 0 ' 3 0 0 a. a 4 0 0 - 1 at Applied Lateral Load Level of 24.4-4(N) Fixed Head N=48 E=45mm o o o o o test data API WET (1987) API WET+Emax (1987) FEM PLN Power Func. exp. p —y curves Figure F.4: Predictions of Pile Head Response and Bending Moment Distribution for a Fixed Head Pile at N=48 E=45mm 2 PS II 3 CX hcj II CJX P pa-O o X) pi CD ea-TJ P CL5 CD P D 0- a. „ P» O CD 1- *> O to o p Q-> cn ps* CD P H n CD TJ n o p TJ X CD pa-W CD P pa-T) Pile Deflection Profile (mm) - 1 1 100-E E a> o £ 100 cn c o cn a> > o a> C L CD Q 2 0 0 -3 0 0 -400 J _1 1 I I I I L . I I I I I I J I I at Applied Lateral Load Level of 24.44 (N) Fixed Head N=48 E=45mm API WET (1987) API WET+Emax (1987) FEM PLN power func. exp. p-y curves - 4 0 Shear Force Profile (N) - 2 0 0 20 40 - 1 0 0 - • ' ' ' ' ' ' • • ' • • • • • ' • ' 11 1 1 1 1 1 1 1 1 1 11 11 11 11 11 i T) cl ci-at Applied Lateral Load Lever of 24.44(N) Fixed Head N=48 E=45mm 0-t : 1 0 0 -2 0 0 -o a o CD P § CO CD C a C L PT-co cr-f~ >—. !3 Q PJ co CD co 3 0 0 -400 J API WET (1987) API WET+Emax (1987) FEM PLN power func. exp. p -y curves to o C5 Appendix F. Prediction of Pile Response under Other Testing Cases 307 diameter, little difference in the computed shear force is observed among the various methods. By comparing the shear force in free head pile, it is noted that less shear force is experienced in the fixed head pile. Figure F.6 shows the computed soil reaction force and the soil secant moduh used in the analysis at the loading level of 24.44(N). The soil reaction forces computed by both A P I codes have higher peak values at deeper location as compared to the experimental curve. The results of soil reaction by the finite element method have very similar trace as that of the experimental curve although the values are shghtly smaUer. As in the results for free head pile, the soil secant moduli used all the methods are very small at shallow depths. Below the depth of about 3 pile diameter, the moduh used by A P I codes are much higher than the experimental curve. However, reasonably good agreement is obtained between the secant moduh used by the finite element and experimental P-y curves. Free H e a d P i l e i n Loose S a n d Predictions of pile response for piles embedded in a loose sand deposit were also performed. The relative density of the loose sand deposit was 33%. The test was conducted on a free head pile with the hydrauhc gradient scale factor of 48 and the loading eccentricity of 48 mm. The free length of the pile above the ground surface and the free head condition are simulated in the same way as in the case of dense sand deposit. The P-y curves were specified in the same way as for the dense sand but with the appropriate soil parameters for the loose sand condition. Figure F.7(a) shows the predictions of pile head deflection at the loading point under different loading level. It is shown that the prediction from experimental P-y curves is shghtly softer than the test data. This may indicate some inconsistency among the test data. It should be- noted that a lateral loading test on pile under such a loose sand deposit is extremely difficult. Sample disturbance in installing the pile a. a 5! 0 0 0 o o 3 a 0 & PL, cn pj o p^ g 4i. ts rt*. j-j C O o p o o" o P L , Sri cf H P • PL, w CT) P P L . Soil Reaction Force (N /mm) - 3 - 2 - 1 0 1 . 1 Q Q | I I I I I I I ! I I I 1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I E £ a> o r ioo-CO c D CO CD £ 200-o CD > CL a> a 300-400 J at Applied Lateral Load Lever of 24.44(N) Fixed Head N=48 E=45mm -<r: API WET (1987) API WET+Emax (1987) FEM PLN power func. exp. p-y curves Soil Reaction Modulus ( N / m m 2 ) 0 200 400 600 . 1 Q Q | I I I I I I I I I I I I I I I I I I I .1 I I I I I I I I I I 100-200-300-400 at Applied Lateral Load Level of 24.44(N) Fixed Head N=48 E=45mm \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ API WET (1987) API WET+Emax (1987) FEM PLN power func. exp. p-y curves Appendix F. Prediction of Pile Response under Other Testing Cases 309 30.0- i i i i i i i i—i i i i i i i i—i i i | i i i i i i i i i | i i i i i i — i i i TJ o 2 0 . 0 ooooo test data at loose sand of Dr=33s exp. p—y curves API WET (1987) API WET (1987) + Emax 0,0, FEM PLN Power Func. P i l e H e a d D e f l e c t i o n ( m m ) B e n d i n g M o m e n t P r o f i l e ( N . m m ) - 3 0 0 0 - 1 0 0 0 1 0 0 0 . •) Q Q I I I . i I I I I I i I I I I I I I T I I I I I I 0 -O O r 1 0 0 H (A X> c o XL CD > D-O 2 0 0 -3 0 0 -4 0 0 at Applied Loterol Load n\\ Level of 22.20<N) at E-+8mm fl > Loose Sand Dr=33* N=48 ooooo test data exp. p—y curves API WET 0 987) API WET+Emax (1987) FEM PLN Power Func. 4 . 0 Figure F.7: Predictions of Pile Head Response and Bending Moment Distribution for a Free Head Pile embedded in Loose Sand, N=48 E=48mm Appendix F. Prediction of Pile Response under Other Testing Cases 310 and connecting the loading ram is almost inevitable. Thus, the prediction shown in Figure F.7(a) among the various methods can be considered to be in good agreement. Figure F.7(b) shows the bending moment predictions for piles in loose sand. As in the case of piles in dense sand, the bending moments given by both A P I codes are slightly larger at the maximum values in comparison with the test data and those from other methods. Again, good agreement in bending moment is obtained between the test data and that by the finite element P-y curves. The computed pile deflection and soil reaction profiles are shown in Figure F.8 at the loading level of 22.2(N). It is seen that the predictions in deflection profile from the A P I codes and finite element method are very close to each other that are smaller than the experimental curve. Soil reaction profile computed by the finite element P-y curves has similar trace as the experimental curve. However, the soil reaction forces from both A P I codes have larger peak values occurred at a deeper depth. Figure F.9 shows the computed shear force and secant soil moduli used in the analyses for the loading level of 22.2(N). As in the case of dense sand, the shear forces on the pile are overestimated by both A P I methods while good agreement is obtained between those from the finite element and experimental P-y curves. Similar observation is also made with regard to the secant soil moduli used in the analyses as compared to the results in dense sand. With a depth of 5 pile diameter, the secant soil moduli used by all the methods are very small, but beyond this depth the soil moduli used by both A P I codes quickly increases with depth, and are much larger than the values from other methods. Good agreement is observed between the secant moduh used by the finite element and experimental P-y curves. Thus, the finite element P-y curves generally give good prediction on the pile response when the correction factor for the 3D effect is apphed. Appendix F. Prediction of Pile Response under Other Testing Cases 311 i i I i i i i i i i i i I i i i i i i i i i I O O O O O O CN ro (lUU-l) SOD^nS PUDS 3L|; 0} 8Aj}D|9J IftdSQ IT ; E C M - i c o o _© CN : i -1 ^ o oo c O) 3 fl! - - 1 ->rv y Q> = O i c o o c n ^ + 2 CL 2 X Q - O - L U 0) < < Lu I I I I I I I T ~ T T O I I I I I I I I I i i i i i i i i i | n i i r~r o o o o T- CN -pr | n i n i i n | o o o o n •si-tD o (UJUJ ) soDpns PUDS 0} eAj}D|ej q^dsQ Figure F.8: Computed Pile Deflection and Soil Reaction Profiles for a Free Head Pile embedded in Loose Sand, N=48 E=48mm Appendix F. Prediction of Pile Response under Other Testing Cases 312 o o-CN E E \ 2 to LU CO o " _ 3 CD-IS *~ . T> O - O U J o _ 1 o O 00 > CT LU E E C C N ° - " c N T J - • C M C Q V < g> ff> > O -•-» © o O - J - J I I I I I I I I I f * I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I g O O O O O O O O O O 1- CN ro (UJUJ) soDijns puD$ 0} aAip|9j iftdarj o o o o o O O O O T- CN ro xj-(LUUJ) eoDijns P U D S su,} 0 } a A i p p j i^deo Figure F.9: Computed Shear Force and Soil Moduli used for a Free Head Pile em-bedded in Loose Sand, N=48 E=48mm \ Bibliography [1] Aboustit, B . L . and Reddy, D . V . (1980), "Finite Element Linear Programming Approach to Foundation Shakedown", International Symposium on Soils under Cychc and Transient Loading, Swansea, Vol. 2, pp727-738. [2] A k i , K . and Richards, P . G . (1980), Quantitative Seismology, Theory  and Methods, Freeman and Company, San Francisco. [3] Singh, Alan (1976), Soil Engineering in Theory and Practice, Vol. 1 of Funda-mentals and General Principles, Asia Pubhshing House, 1976. [4] Alizadeh, M . 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