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Response of pile foundations to simulated earthquake loading : experimental and analytical results volume… Gohl, W. Blair 1991

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R E S P O N S E O F P I L E F O U N D A T I O N S T O S I M U L A T E D E A R T H Q U A K E L O A D I N G : E X P E R I M E N T A L A N D A N A L Y T I C A L R E S U L T S V O L U M E II B y W . B L A I R G O H L B . Eng. (Civi l ) M c G i l l University 1976 M . Eng. (Civi l ) M c G i l l University 1980 A THESIS S U B M I T T E D IN 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 STUDIES CIVIL 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 BRITISH C O L U M B I A July 1991 © W . B L A I R . G O H L , 1991 R E S P O N S E O F P I L E F O U N D A T I O N S T O S I M U L A T E D E A R T H Q U A K E L O A D I N G : E X P E R I M E N T A L A N D A N A L Y T I C A L R E S U L T S V O L U M E I B y W . B L A I R G O H L B . Eng. (Civil) M c G i l l University 1976 M . Eng. (Civi l) M c G i l l University 1980 A THESIS S U B M I T T E D IN 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 STUDIES CIVIL 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 BRITISH C O L U M B I A July 1991 © W . B L A I R G O H L , 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely 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. Department of Civil Engineering The University of British Columbia Vancouver, Canada Date ,luly ??, 1991 DE-6 (2/88) Abstract The analysis of the dynamic response of pile foundations to earthquake shaking is a complex problem and has been treated using concepts developed from the theory of elasticity, applicable to low level shaking, and to models incorporating non-linear soil response appropriate for stronger shaking intensities. A review of available field reports indicates that due to the lack of complete instrumental recordings describing the response of full scale pile foundations to earthquake loading, the above analysis techniques are in large measure unchecked. To provide a reliable data base suitable for checking various models of dynamic pile foundation response, a series of small scale model tests on single piles and pile groups embedded in dry sand foundations were carried out on shaking tables at the University of British Columbia. A similar series of tests were carried out using a geotechnical centrifuge equipped with a base motion actuator located at the California Institute of Technology. Under the centrifugal forces acting on the model, full scale stress conditions are simulated in the sand foundation. Since soil behaviour is stress level dependent, the centrifuge tests are considered to provide a more realistic simulation of full scale pile foundation behaviour. Both the shake table and centrifuge single pile tests were carried out using both sinusoidal and random earthquake input motions over a range of shaking intensities. From the data, details of soil-pile interaction were elucidated. This provided a basis for improvement in methods of estimating required input parameters used in the dynamic analysis of pile foundations. Prior to each test, shear wave velocity measurements were made throughout the pre-pared sand foundations using piezoceramic bender elements. This technique has proved ii particularly useful in the centrifuge environment since the bender element source and receivers could be triggered remotely from off the centrifuge arm while the model was in flight. The shear wave velocity data were used to compute small strain, elastic shear moduli in the soil which have been found to be in close agreement with predictions made using an equation proposed by Hardin and Black (1968). Elastic compression wave ve-locities were also identified from the bender element responses recorded during the shake table tests. The single pile tests demonstrated that significant non-linearity and strain softening occurs in near field soil response, which is responsible for reductions in fundamental vibration frequency and pile head stiffness parameters with increasing amplitudes of lateral pile vibration. An analysis technique developed to estimate average effective strains around a single pile leads to predictions of large modulus reduction around the pile, depending on the amplitude of pile vibration. Soil reaction pressures (p) due to relative horizontal movement between the soil and the pile (y) were deduced from the test data for various cycles of shaking, or so-called p-y curves. The cyclic p-y curves developed show clearly the non-linear, hysteretic near field response near the pile head. Approximately linear elastic p-y response occurs at greater depth. Backbone p-y curves computed using procedures recommended by the American Petroleum Institute (API) are in poor agreement with the experimental shake table and centrifuge measurements. Material damping inferred from the area within the p-y hysteresis loops increases, in general, with increasing pile deflection level. The exper-imental p-y hysteresis loops were reliably simulated using a Ramberg-Osgood backbone curve and the Masing criterion to model unload-reload response. Comparing the flexural response observed on single piles during the shake table and centrifuge tests, the depth of maximum bending moment relative to the pile diameter has been observed to be greater in the shake table tests. This can be anticipated from iii the laws of model similitude. Cyclic p-y curves developed from the shake table and centrifuge tests also show substantial differences, with the shake table p-y curves being stiffer than predicted using the A P I procedures, while the opposite behaviour was found in the high stress, centrifuge environment. Damping in the low stress level environment of the shake table has been found to be greater than under full scale stress conditions in the centrifuge. Two-pile tests, where the piles have been oriented inline, offline or at 45 degrees to the direction of shaking, indicate that pile to pile interaction is very strong for inline and 45 degree shaking, and is relatively minor for offline shaking. Interaction effects observed under low and high intensities of shaking die off with increasing pile separation distance at a quicker rate than predicted using elastic interaction theory. Interaction effects for inline and offline cyclic loading may be neglected for centre to centre pile spacings of about six and three pile diameters, respectively. For close pile separations during inline shaking, elastic theory underpredicts the extent of interaction. Similar conclusions were reached from the shake table and centrifuge tests conducted. Based on the experimental data and data available from the literature, modifications to elastic pile interaction coefficients have been suggested. Predictions of single pile response to earthquake shaking have been made using an uncoupled, sub- structure approach incorporating non-linear pile head springs and equiv-alent viscous dashpots (foundation compliances) derived from the test data. The founda-tion compliances account for the deflection level dependent stiffness and damping char-acteristics of the below ground soil-pile system. The measured free field surface motions have been used as the input excitation. Agreement between computed and measured pile responses was found to be excellent. A fully coupled analysis using the commercially available program SPASM8, where the below ground portions of the pile are directly iv considered in the numerical discretization of the problem has also been used. Interac-tion between the soil and vibrating ground is accounted for using a Kelvin-Voight model which includes non-linear Winkler springs and equivalent viscous dashpots to simulate radiation damping. Free field ground motions deduced from an independent free field response analysis using the computer program S H A K E are applied to the free field end of the soil-pile interaction elements. Using this full coupled model, the possible effects of kinematic interaction are accounted for. Results from the analysis show that SPASM8 underpredicts pile flexural response. A key difficulty in using an analysis of this k ind is the accurate determination of free field input motions to be used along the embedded length of the pile. A computer program, P G D Y N A , has been developed to analyse the uncoupled re-sponse of a superstructure supported by a group of foundation piles, taking into account non-linearity of the pile head compliances and the effects of pile group interaction. In-teraction factors developed from the experimental test program were used to calculate deflection level dependent pile head stiffnesses. Preliminary testing of the program indi-cates that use of the free field surface motions as input, neglecting the effects of kinematic interaction, leads to an overestimate of pile group response. v Table of Contents Abstract i i List of Tables x i i List of Figures x v Acknowledgement x x x v i 1 Statement of Research 1 1.1 Behavioural Aspects of Single Pile Response to Cycl ic Lateral Loading . 1 ] .2 Observations of Full Scale Pile Response Dur ing Earthquake Loading . . 7 1.3 Experimental Observations of Pile Group Interaction 9 1.4 Numerical Modell ing of Single Pi le Response to Earthquake Loading . . . 15 1.5 Numerical Modell ing of Pile Group Behaviour to Static and Dynamic Loading 25 1.5.1 Low Frequency, Quasi-Static Loading 25 1.5.2 Higher Frequency Dynamic Loading 28 1.6 Scope of Study 30 2 Shake Table Test Procedures 35 2.1 U B C Shaking Table Characteristics 35 2.2 Foundation Sand Characteristics 40 2.3 Sand Foundation Preparation 46 2.4 Single Pile Characteristics and Model Layout 49 vi 2.5 Pile Group Characteristics and Model Layout 54 2.6 Instrumentation and Measurement Resolution 58 2.7 Elastic Wave Velocity Measurements on the Shake Table 60 2.8 Accuracy of Elastic Wave Velocity Measurements 68 3 Centrifuge Test. Procedures 75 3.1 The Principles of Centrifuge Modelling 75 3.2 Description of Caltech Centrifuge and Base Motion Actuator 80 3.3 Pile Characteristics and Model Layout 83 3.4 Pile Group Characteristics and Model Layout 86 3.5 Instrumentation and Measurement Resolution 89 3.6 Foundation Sand Characteristics 91 3.7 Sand Foundation Preparation and Test Procedures 93 3.8 Elastic Wave Velocity Measurements on the Centrifuge 95 3.9 Accuracy of Shear Wave Velocity Measurements 97 4 Centrifuge Test Results 103 4.1 Introduction 103 4.2 Shear Wave Velocities 104 4.2.1 Measured Wave Arrivals 104 4.2.2 Theoretical Bender Response 106 4.2.3 Wave Velocity Distributions 108 4.3 Base Motion Excitation of Single Piles 110 4.3.1 Low-level Sinusoidal Shaking 113 4.3.2 Random Earthquake Excitation 115 4.4 Soil-Pile Interaction 129 4.4.1 Introduction 129 vi i 4.4.2 Earthquake Excitation 144 4.4.3 Low Level Sinusoidal Shaking 157 4.4.4 Near Field Hysteretic Damping 169 4.5 Equivalent Visco-Elastic Soil Resistance 172 4.5.1 Computed Lateral Winkler Stiffness and Material Damping . . . . 176 4.6 Non-Linear Modelling of P -Y Hysteresis Loops 190 4.7 Base Motion Excitation of Pile Groups 201 4.7.1 Introduction 201 4.7.2 Low Level Shaking - Two Pile Groups 203 4.7.3 Pile Group Interaction Analysis 220 4.7.4 Base Motion Excitation of a 2 x 2 Pile Group 230 4.7.5 Summary 240 5 Shake Table Test Results 244 5.1 Introduction 244 5.2 Elastic Wave Velocities 245 5.3 Natural Frequency Tests 255 5.3.1 Introduction 255 5.3.2 Test Procedures 257 5.3.3 Single Pile Tests in Loose Sand 260 5.3.4 Single Pile Tests in Dense Sand 286 5.3.5 Natural Frequency Tests - 2 Pile Groups in Dense Sand 306 5.4 Base Motion Excitation of Single Piles 323 5.4.1 Free Field Response 323 5.4.2 Single Pile Flexural Response - Shake Table vs. Centrifuge Results 324 5.4.3 Shake Table Test Results 333 v i i i 5.5 Soil-Pile Interaction 348 5.5.1 Hysteretic Damping 356 5.5.2 Non-Linear Modelling of P -Y Hysteresis Loops 358 5.6 Base Motion Excitation of Pile Groups 366 5.6.1 Introduction 366 5.6.2 High Level Shaking - Two Pile Groups 368 5.6.3 Pile Group Interaction Analysis 380 5.6.4 Base Motion Excitation of 2 x 2 Pile Group 384 5.6.5 Summary 390 5.7 Cyclic Axial Load Behaviour of Model Piles 393 6 Single Pile Response to Earthquake Excitation 396 6.1 Introduction 396 6.2 Uncoupled Non-Linear Analysis 398 6.2.1 Pile Head Stiffnesses 398 6.2.2 Pile Head Damping 400 6.2.3 Coupled Versus Uncoupled Analytical Solution 404 6.2.4 Uncoupled Equations of Motion - Single Pile 410 6.2.5 Prediction of Ringdown Test Results 412 6.2.6 Prediction of Pile Response to Free Field Ground Motions . . . . 414 6.3 Coupled Dynamic Pile Analysis 440 6.3.1 Introduction 440 6.3.2 Methodology 441 6.3.3 Results of Analysis 446 6.3.4 Summary 457 ix 7 Uncoupled Dynamic Solution for a Pile Group 470 7.1 Introduction 470 7.2 Preliminary Testing of P G D Y N A 472 7.3 Dynamic Analysis Results 476 7.3.1 Shake Table Test - Four Pile Group Subjected to Strong Sinusoidal Shaking 476 7.3.2 Centrifuge Test - Four Pile Group Subjected to Earthquake Exci-tation 483 7.4 Summary 486 8 Summary and Suggestions for Future Work 490 8.1 Introduction 490 8.2 Single Pile Test Results 492 8.3 Pile Group Test Results 499 8.4 Suggestions for Future Work 502 Bibliography 503 A Shake Table Tests - Instrumentation and Data Acquisition 533 A . l Strain Gauges 533 A.2 Displacement. Transducers (LVDT's) 536 A.3 Accelerometers 538 A.4 Data Acquisition 540 A.5 Spectral Analysis and Waveform Aliassing 541 A. 6 Digital Filtering 543 B Centrifuge Tests - Instrumentation and Data Acquisition 547 B. l Strain Gauges 547 X B.2 Displacement Transducers 549 B.3 Accelerometers 550 B.4 Data Acquisition 551 B. 5 Data Processing 552 C Strain Fields Around Laterally Loaded Piles 554 C. l Introduction 554 C.2 Navier's Equations of Motion in Three Dimensions 555 C.3 Simplifications to the Three Dimensional Equations of Motion 555 C.4 Solution to Navier's Equations of Motion - Plane Displacement Case . . . 557 C.5 Solution to Navier's Equations of Motion - Plane Strain Case 560 C.6 Comparison of Plane Strain Analytic Solution With Non- Linear Finite Element Solution 563 C. 7 Comparison of Strain Fields - Plane Displacement versus Plane Strain Solutions 567 D Static Laterally Loaded Pile Solutions 570 D. l Introduction 570 D.2 Winkler Modulus Proportional to the Square Root of Depth 573 D. 3 Winkler Modulus Linearly Proportional to Depth 579 E Calculation of Soil Resistance - Lateral Pile Displacement Curves 580 E. l Methodology 580 E. 2 Comparison of Method With Cubic Spline Differentiation 583 F Single Pile Response in a Winkler Medium to Base Motion Excitation588 F. l Equations of Motion 588 F.2 Free Vibration Response 590 X i F. 3 Forced Vibration Response 592 G Uncoupled Solution for a Pile - Structural Mass System 596 G. l Equations of Motion 596 G.2 Free Vibration Response 596 G.3 Forced Vibration Response 599 G. 4 Pile Head Stiffnesses 601 H Finite Element. Solution for a Pile - Structural Mass System 604 H. l Equations of Motion 604 H. 2 Solution of Equations of Motion 609 I Shake Table Tests - Low Level Shaking of 2-Pile Groups 612 I. 1 Test Data 612 1.2 Effects of Group Interaction on Lateral Soil Stiffness 621 J Uncoupled Dynamic Analysis of a Pile Group 627 J . l Finite Element Discretization 628 J.2 Dynamic Solution Methodology 633 x i i List of Tables 2.1 Summary of Pile Cap Structural Properties - Shake Table Tests for Two and Four Pile Groups 57 2.2 Instrument Noise Levels After Digital Filtering (Shake Table Tests) . . . 59 3.1 Centrifuge Scaling Relations 79 3.2 Summary of Model Pile and Pile Cap Structural Properties Used in Cen-trifuge Tests) 85 3.3 Summary of Pile and Pile Cap Structural Properties - Centrifuge Tests on Two Pile Group 87 3.4 Summary of Pile and Pile Cap Structural Properties - Four Pile Group (Centrifuge Tests) 89 3.5 Centrifuge Instrument Noise Levels 91 4.1 Parameters used in dynamic analysis of bender response to a travelling shear wave 108 4.2 Single Pile Test Characteristics - Centrifuge 112 4.3 Fundamental Frequencies of the Pile and Free Field 115 4.4 Winkler Model Predictions of Single Pile Deflections - Centrifuge Tests . 150 4.5 Computed Relative Soil-Pile Stiffnesses, KT, for Low Level Shaking . . . 179 4.6 Hyperbolic Stress-Strain Parameters Used in Finite Element Analysis . . 182 4.7 Computed vs. Measured Deflections and Bending Moments Using Equiv-alent Elastic Winkler Moduli - L A T P I L E Analysis 194 4.8 Cyclic p-y Curves - Masing Loop Parameters 201 xi i i 4.9 Pile Group Fundamental Natural Frequencies 207 4.10 Pile Group Test Data 210 4.11 Average Forces and Deflections of Centrifuged Pile Groups - Low Level Shaking .217 4.12 Pile Group Interaction Analysis - Centrifuge Tests -Low Level Shaking . 225 4.13 Measured and Computed Deflections in a 2 x2 Pile Group 236 5.1 Frequency Sweep Test Data - Free Field Response in Loose Sand 266 5.2 Frequency Sweep Test Data - Pile Response in Loose Sand 281 5.3 Frequency Sweep Test Data - Free Field Response in Dense Sand . . . . 290 5.4 Frequency Sweep Test Series III - Pile Response in Dense Sand 302 5.5 Frequency Sweep Test Series IV - Pile Response in Dense Sand 302 5.6 Ringdown Test Measurements - 2 Pile Groups in Dense Sand 315 5.7 Single Pile Test. Characteristics for Moderate Shaking - Shake Table vs. Centrifuge 327 5.8 Single Pile Test Characteristics'for Strong Shaking on the Shake Table . 334 5.9 Winkler Model Predictions of Single Pile Deflections - Shake Table Tests 351 5.10 Backbone P-y Curve Parameters for Shake Table Test 23 363 5.11 Pile Group Test Data - High Level Shaking 374 5.12 Average Forces and Deflections - High Level Shaking 378 5.13 Pile Group Interaction Analysis - Strong Shaking 383 6.1 Pile and Soil Properties Used in Test. Case 407 6.2 Superstructure Response to Harmonic Base Motion - Coupled Analysis (Test Case) 408 6.3 Superstructure Response to Harmonic Base Motion - Uncoupled Analysis (Test Case) 409 xiv 6.4 Ringdown Analysis Parameters - Tests R-L5 and R-D2 414 6.5 Uncoupled Analysis Parameters - Centrifuge Tests 431 6.6 Uncoupled Analysis Parameters - Shake Table Tests 432 6.7 Computed Versus Measured Pile Response 458 7.1 Computed Natural Frequencies - P G D Y N A vs. M A C E Solution 473 7.2 Computed Natural Frequencies With and Without Group Interaction Ef-fects - P G D Y N A 475 7.3 Computed Vs. Measured Pile Group Response for Strong Sinusoidal Shak-ing - Four Pile Group on the Shake Table 483 7.4 Computed Vs. Measured Peak Pile Group Response for Moderate Level Earthquake Shaking - Four Pile Group on the Centrifuge 486 C . l Elastic Soil Properties Used in Plane Strain Analytic Solution 564 C.2 Parameters Used in Plane Strain/Plane Displacement Analyses 568 1.1 Pile Group Test Data - Low Level Shaking 618 1.2 Average Forces and Deflections - Low Level Shaking 623 XV List of Figures 1.1 Cycl ic lateral load - displacement characteristics of soil in soft clay (a) zone of unconfined response (b) confined response (after Bea et al , 1980) 3 2.1 Shake table pump vibration recorded using a sampling rate of 1 k H z per channel (a) Shake table A - measured table accelerations, (b) Shake ta-ble A - com puted Fourier spectra, (c) Shake table B - measured table accelerations, (d) Shake table B - computed Fourier spectra 37 2.2 Typica l sinusoidal input base motions recorded using a sampling rate of 303 H z per channel - shake table A : (a) table accelerations - moderate in-tensity shaking (b) table accelerations - high int. ensity shaking (c) Fourier spectrum - moderate intensity shaking (d) Fourier spectrum - high inten-sity shaking 39 2.3 Typica l earthquake input base motions recorded using a sampling rate of 303 Hz per channel - shake table A (a) measured table accelerations (b) Fourier spectrum 40 2.4 Gradation curve for C-109 Ottawa sand used in shake table tests and comparison wi th Toyoura sand (after Tatsuoka and Fukushima, 1984) . . 41 2.5 Peak friction angles versus void ratio for C-109 Ottawa sand 42 2.6 Normalized secant, shear modulus versus cyclic shear strain for C-109 Ot-tawa sand (a) medium dense sand (Dr = 50 percent) (b) loose sand (DT = 30 percent) (c) dense sand (DT = 90 p ercent) 45 2.7 Single pile used in shake table tests showing instrumentation layout . . . 53 xvi 2.8 Two pile group used in shake table tests showing instrumentation layout 55 2.9 Four pile group used in shake table tests showing instrumentation layout 56 2.10 Body wave propagation from a bender source, showing the dependance of receiver location on measured body waves 64 2.11 Piezoceramic bender elements (a) single element (b) general layout of source and receivers 66 2.12 Electrical layout of bender elements (a) source (b) receiver 67 3.1 Side view of Caltech centrifuge (after Allard, 1983) 76 3.2 Vertical effective stress distribution in the sand taking into account g-gradients in the centrifuged soil model 77 3.3 Schematic drawing of centrifuge arm (after Scott, 1979) 81 3.4 Single pile used in centrifuge tests showing instrumentation layout . . . . 84 3.5 Two pile group showing instrumentation layout 86 3.6 Four pile group showing instrumentation layout 88 3.7 Gradation curve for Nevada 120 sand used in centrifuge tests 92 3.8 Peak friction angles versus void ratio after consolidation from drained tri-axial tests on Nevada 120 sand 93 4.1 Source and receiver bender element voltage outputs 105 4.2 Lumped mass mechanical model used to describe bender element response to a travelling wave pulse 107 4.3 Theoretical bender element response to a travelling shear wave 109 4.4 Shear wave velocities during centrifuge flight at 60 g (a) loose sand (b) dense sand I l l 4.5 Measured accelerations - centrifuge test 17 (a) input base accelerations (b) free field surface accelerations (c) pile cap accelerations 116 xvii 4.6 Measured accelerations - centrifuge test 41 (a) input base accelerations (b) free field surface accelerations (c) pile cap accelerations 117 4.7 Measured displacements parallel to shaking direction - centrifuge test 17 118 4.8 Measured displacements parallel to shaking direction - centrifuge test 41 119 4.9 Computed Fourier amplitude ratios ( A P H / A F F ) - test 17 120 4.10 Computed Fourier amplitude ratios ( A P H / A F F ) - test 41 121 4.11 Measured bending moment time histories - centrifuge test 17 (a) strain gauge 1 (b) strain gauge 3 (c) strain gauge 6 122 4.12 Measured bending moment distribution during steady state excitation (t = 16.5 sec.) - centrifuge test 17 123 4.13 Measured bending moment distribution during steady state excitation (t. = 17.0 sec) - centrifuge test 41 124 4.14 Measured accelerations - centrifuge test 12 (a) input base accelerations (b) free field surface accelerations (c) pile cap accelerations 127 4.15 Computed Fourier amplitude ratios - test 12 (a) pile amplitude ratio ( A P H / A F F ) (b) free field amplitude ratio ( A F F / A B ) 128 4.16 Measured displacements parallel to shaking direction - centrifuge test 12 129 4.17 Measured bending moment time histories - centrifuge test 12 (a) strain gauge 1 (b) strain gauge 4 (c) strain gauge 7 130 4.18 Measured bending moment distribution during peak pile displacement (t = 12.0 sec) - centrifuge test 12 131 4.19 Measured accelerations - centrifuge test 14 (a) input, base accelerations (b) free field surface accelerations (c) pile cap accelerations 132 4.20 Computed Fourier amplitude ratios - test 14 (a) pile amplitude ratio ( A P H / A F F ) (b) free field amplitude ratio ( A F F / A B ) 133 4.21 Measured displacements parallel to shaking direction - centrifuge test 14 134 xvi i i 4.22 Measured bending moment time histories - centrifuge test 14 (a) strain gauge 1 (b) strain gauge 3 (c) strain gauge 6 135 4.23 Measured bending moment distribution during peak pile displacement, (t = 11.0 sec) - centrifuge test 14 136 4.24 Measured accelerations - centrifuge test 15 (a) input base accelerations (b) free field surface accelerations (c) pile cap accelerations 137 4.25 Computed Fourier spectra - test 15 (a) pile amplitude ratio ( A P H / A F F ) (b) free field amplitude ratio ( A F F / A B ) 138 4.26 Measured displacements parallel to shaking direction - centrifuge test 15 139 4.27 Measured bending moment time histories - centrifuge test 15 (a) strain gauge 1 (b) strain gauge 3 (c) strain gauge 6 140 4.28 Measured bending moment distribution during peak pile displacement, (t = 10.9 sec) - centrifuge test 15 141 4.29 Lateral soil reaction distribution at peak pile deflection (t = 12.0 sec) -centrifuge test 12 145 4.30 Cyclic p-y curves at three different times during shaking at the 3 pile diameter depth - centrifuge test 12 146 4.31 Cyclic p-y curves at various depths during the shaking cycle when peak pile deflection occurred (t = 11.72 - 12.78 sec) and comparison with API curves - centrifuge test. 12 148 4.32 Equivalent lateral stiffnesses versus depth derived from experimental and A P I p-y curves - centrifuge test 12 149 4.33 Computed bending moment distribution during peak pile deflection (t = 12.0 sec) using lateral stiffnesses from experimental and A P I p-y curves -centri fuge test 12 151 xix 4.34 Cyclic p-y curves at various depths and times, and comparison with A P I p-y curves - centrifuge test 14 153 4.35 Equivalent lateral stiffnesses versus depth derived from experimental and A P I p-y curves - centrifuge test 14 154 4.36 Computed bending moment distribution during peak pile deflection (t = 11.0 sec) using secant lateral stiffnesses from experimental and API p-y curves - centrifuge test 14 155 4.37 Cyclic p-y curves at different times during shaking at the 3 pile diameter depth - centrifuge test 15 156 4.38 Cyclic p-y curves at various depths during shaking cycle when peak pile deflection occurred (t = 10.82 - 11.58 sec) and comparison with API p-y curves - centrifuge test 15 158 4.39 Equivalent lateral stiffnesses versus depth derived from experimental and A P I p-y curves - centrifuge test 15 159 4.40 Computed bending moment distribution during peak pile deflection (t = 10.9 sec) using secant lateral stiffnesses from experimental and A P I p-y curves - centrifuge test 15 160 4.41 Cyclic p-y curves in loose sand during sinusoidal shaking at various depths and comparison with A P I p-y curves - centrifuge test 17 162 4.42 Cyclic, p-y curves in very dense sand during sinusoidal excitation at various depths and comparison with A P I p-y curves - centrifuge test 41 163 4.43 Secant lateral stiffnesses versus depth derived from experimental and A P I p-y curves - centrifuge test 17 165 4.44 Computed bending moment distribution during steady state shaking using secant lateral stiffnesses derived from experimental and A P I p-y curves -centri fuge test 17 166 XX 4.45 Equivalent lateral stiffnesses versus depth derived from cyclic p-y curves -centrifuge test 41 167 4.46 Computed bending moment distribution during steady state shaking using secant lateral stiffnesses derived from experimental and A P I p-y curves -centri fuge test 41 168 4.47 Frictional damping ratios, D, versus dimensionless pile deflection y /d (a) test no. 17 (b) test no. 12 (c) test no. 15 173 4.48 Proposed relationship between 8 and Kr for various values of H/2r0 at zero frequency and comparison with other researcher 's relationships, (after Kagawa and Kraft, 1980a) 178 4.49 Plane strain finite element model of a rigid translating disc 181 4.50 Computed lateral load - deflection relationships for plane strain translation of a rigid disc in a no-tension soil (a) loose sand (b) dense sand 183 4.51 Computed lateral Winkler stiffnesses, k^, for plane strain translation of a rigid disc in a no-tension soil (a) loose sand (b) dense sand 185 4.52 Computed variation of proportionality constant 8 versus dimensionless pile deflection y/d in a no-tension soil 186 4.53 Computed relationship between zone of influence factor Ie and lateral pile deflection 188 4.54 Results of elastic analysis - test 17 (a) effective shear strains (b) effective shear moduli (c) Winkler moduli . 1 9 1 4.55 Results of elastic analysis - test 14 (a) effective shear strains (b) effective shear moduli (c) Winkler moduli 192 4.56 Results of elastic analysis - test 41 (a) effective shear strains (b) effective shear moduli (c) Winkler moduli 193 4.57 Construction of unloading and reloading curves based on the Masing rule 195 xxi 4.58 Computed Masing loops versus measured p-y hysteresis loops - test 12 (a) z/d = 1 (b) z/d = 2 (c) z/d = 3 (d) z/d = 5 (e) z/d = 7 199 4.59 Computed Masing loops versus measured p-y hysteresis loops - test 15 (a) z/d = 1 (b) z/d = 2 (c) z/d = 3 (d) z/d = 5 (e) z/d = 7 200 4.60 Typical input base and free field surface motions - centrifuge test 39 (a) base accelerations (b) free field accelerations 203 4.61 Pile cap response - inline shaking test 39 (s/d = 4) (a) pile cap accelerations (b) pile cap displacements in direction of shaking 205 4.62 Comparison of Fourier spectra - inline test 39 (s/d = 4) (a) pile cap ac-celerations (b) free field accelerations 206 4.63 Bending moment, vs. depth in a two pile group for s/d = 2 (a) offline shaking (b) inline shaking 208 4.64 Bending moment vs. depth in a two pile group - inline shaking - s/d = 6 209 4.65 Pile cap displacements (a) parallel and (b) perpendicular to the direction of shaking - s/d = 2 (8 = 45°) 212 4.66 Steady state pile cap displacements versus pile spacing ratio 213 4.67 Comparison of predicted and measured bending moments using a Winkler model for offline shaking (a) s/d = 2 (b) s/d = 4 (c) s/d = 6 216 4.68 Comparison of predicted and measured bending moments using a Winkler model for inline shaking (a) s/d = 2 (b) s/d = 4 (c) s/d = 6 218 4.69 Comparison of predicted and measured bending moments using a Winkler model - 8 ~ 45° (a) s/d = 2 (b) s/d = 4 (c) s/d = 6 219 4.70 Experimental versus Randolph and Poulos' interaction factor -quv (a) 3 = 0 degrees (b) 3 = 45 degrees (c) 3 = 90 degrees 22 9 xx i i 4.71 2 x 2 pile group response to low level sinusoidal shaking - test 43 (a) input base accelerations (b) free field accelerations (c) pile cap acceleration s (d) displacements at top of mass 233 4.72 2 x 2 group response for low level sinusoidal shaking - test 43 (a) strain gauge 1 (b) strain gauge 3 (c) strain gauge 7 (d) dynamic axial load . . . 234 4.73 Bending moment vs. depth for both directions of shaking in a four pile group - low level sinusoidal shaking 235 4.74 2 x 2 group response during earthquake shaking - test 46 (a) base acceler-ations (b) free field accelerations (c) pile cap accelerations (d) top of mass displacements 238 4.75 Computed Fourier spectra during earthquake shaking of a four pile group (a) base accelerations (b) free field accelerations (c.) pile cap accelerations 239 4.76 2 x 2 group response to earthquake base motion - test 46 (a) strain gauge 1 (b) strain gauge 3 (c) strain gauge 7 (d) dynamic axial load 241 4.77 Bending moment vs. depth at peak pile cap deflection during earthquake shaking of a four pile group 242 5.1 Bender element voltage outputs recorded on the shake table (a) receiver R - l (b) receiver R-2 (c) receiver R-3 247 5.2 Bender element voltage outputs - confirmatory test in dense vibrated sand (a) source (b) receiver 248 5.3 Receiver response during P-wave velocity measurements in dense sand using a hammer plate source and an accelerometer receiver 249 5.4 Shear wave velocities in loose sand foundations with no cyclic pre-strain on the shake table 251 5.5 Shear wave velocities in vibrated dense sand foundations on the shake table.252 xxi i i 5.6 Compression wave velocities in loose sand foundations with no cyclic pre-strain on the shake table 253 5.7 Compression wave velocities in vibrated dense sand foundations on the shake table 254 5.8 Typical hammer impact test (a) input, base accelerations, (b) Fourier spec-trum 258 5.9 Typical frequency sweep test at a predominant input frequency of 12 Hz (a) input base accelerations, (b) Fourier spectrum 261 5.10 Measured foundation surface settlements during natural frequency tests in loose sand 263 5.11 Hammer impact test in loose sand (a) Foundation surface accelerations, (b) the Fourier spectrum 265 5.12 Frequency sweep test in loose sand: normalized Fourier spectra of free field surface accelerations and comparison with S H A K E output 267 5.13 Ringdown test R - L l in loose sand (a) pile head displacements ( L V D T 2), (b) pile head displacements (LVDT 1), (c) bending moments (strain gauge 3) 27 1 5.14 Ringdown test R-L3 in loose sand (a) pile head acceleration, (b) pile head displacement (LVDT 1), (c) pile head displacement (LVDT 2), (d) bending mome nt (strain gauge 3) 274 5.15 Ringdown test R-L4 in loose sand (a) pile head acceleration, (b) pile head displacement (LVDT 1), (c) pile head displacement (LVDT 2), (d) bending mome nt (strain gauge 3) 276 5.16 Ringdown test R-L5 in loose sand (a) pile head acceleration (b) peak bend-ing moment distribution in the first cycle of ringdown (c) pile deflections in the first cycle of ringdown 278 xxiv 5.17 Hammer impact test H - L l in loose sand (a) pile head acceleration, (b) foundation surface acceleration, (c) pile head displacement (LVDT 2), (d) bending moment (strain gauge 3) 280 5.18 Frequency sweep test in loose sand: (a) normalized Fourier spectra of pile head accelerations; (b) normalized peak bending moment at strain gauge 3 2 83 5.19 Hammer impact test. HI-Dl in dense sand (a) Foundation surface acceler-ations (b) the Fourier spectrum 288 5.20 Hammer impact test HI-D2 in dense sand (a) Foundation surface acceler-ations (b) the Fourier spectrum 289 5.21 Frequency sweep test in dense sand: normalized Fourier spectra of free field accelerations and comparison with S H A K E output 291 5.22 Effect of location in sand container on measured free field surface response 294 5.23 Hammer impact test HI-Dl (a) Pile head accelerations (b) Fourier spec-trum of pile head accelerations (c) pile head displacements - L V D T 1 . . 296 5.24 Hammer impact test HI-D2 (a) Pile head accelerations (b) pile head dis-placements - L V D T 1 (c) Bending moment distribution along the pile at the start o f free vibration 298 5.25 Ringdown test R - D l (a) pile head accelerations (b) Fourier spectrum of pile head accelerations (c) pile head displacement - L V D T 1 299 5.26 Ringdown test R-D2 (a) pile head accelerations (b) pile head displace-ments - L V D T 1 (c) peak bending moment distribution during first, cycle of ringdown 301 5.27 Fourier spectra from frequency sweep test in dense sand (a) pile accelera-tions normalized with respect to base accelerations - test series III and IV ( b) pile accelerations normalized with resp ect to free field accelerations - test series III 304 x x v 5.28 Frequency sweep test in dense sand - normalized peak bending moments 305 5.29 Ringdown test P G R l - inline shaking at s/d = 2 (a) accelerations at the centre of gravity of mass (b) bending moments at the peak of the first cycle of ringdown 309 5.30 Ringdown test PGR6 - offline shaking at s/d = 2 (a) accelerations at the centre of gravity of mass (b) bending moments at the peak of the first cycle o f ringdown 310 5.31 Free body diagram of forces acting on a two pile group for (a) inline shaking (b) offline shaking 312 5.32 Pile head accelerations measured during a ringdown test on a single pile for comparison with offline pile group tests 314 5.33 Typical input base motions at 10 Hz used in pile group frequency sweep tests (a) low level shaking (b) strong shaking 316 5.34 Frequency sweep tests for a two pile group subjected to offline shaking (a) low level shaking (b) strong shaking 318 5.35 Frequency sweep tests for a two pile group subjected to inline shaking (a) low level shaking (b) strong shaking 321 5.36 Fourier amplitudes of free field accelerations - loose sand tests (a) base (b) mid-height (c) soil surface 325 5.37 Fourier amplitudes of free field accelerations - dense sand tests (a) base (b) mid-height (c) soil surface 326 5.38 Comparison of pile flexural response observed on the centrifuge and the shake table - moderate level shaking in loose sand 329 5.39 Comparison of pile flexural response observed on the centrifuge and the shake table - moderate level shaking in dense sand 330 xxvi 5.40 Theoretical versus measured bending moment distribution - shake table test 15 332 5.41 Input base accelerations (a) test 14 (b) test 25 335 5.42 Computed Fourier spectra of input base accelerations (a) test 14 (b) test 25336 5.43 Free field surface accelerations (a) test 14 (b) test 25 (c) test 23 338 5.44 Computed Fourier spectra of free field surface accelerations (a) test 14 (b) test. 25 (c) test 23 339 5.45 Pile head mass accelerations (a) test 14 (b) test 25 (c.) test 23 340 5.46 Computed Fourier spectra of pile head mass accelerations (a) test 14 (b) test 25 (c) test 23 341 5.47 Bending moment time histories - shake table test 14 (a) strain gauge 1 (b) strain gauge 4 (c) strain gauge 6 343 5.48 Peak bending moment distribution - shake table test 14 344 5.49 Peak bending moment distribution - shake table test 23 345 5.50 Peak bending moment, distribution - shake table test 25 346 5.51 Pile head mass displacements (a) test 23 (b) test 25 (c) test 14 347 5.52 Cyclic p-y curves - shake table test 14 (a) z/d = 1 (b) z /d = 3 (c.) z /d = 5 (d) z/d = 10 (e) z /d = 15 349 5.53 Computed secant lateral stiffnesses from p-y curves during steady state shaking - shake table test 14 350 5.54 Cyclic p-y curves - shake table test 25 (a) z/d = 1 (b) z /d = 3 (c) z /d = 5 (d) z/d = 10 (e) z /d = 15 353 5.55 Computed secant lateral stiffnesses from p-y curves during low and peak amplitude shaking - shake table test 25 354 5.56 Cyclic p-y curves - shake table test 23 (a) z/d = 1 (b) z /d = 5 (c) z /d = 10 (d) z /d = 15 (e) z /d = 25 357 xxv i i 5.57 Cyclic p-y curves at the 1 pile diameter depth for constant amplitude shaking - shake table test 23 358 5.58 Computed secant lateral stiffnesses from p-y curves during low and peak amplitude shaking - shake table test 23 359 5.59 Cyclic, p-y curves - shake table test 30 (low level shaking) (a) z/d = 1 (b) z/d = 3 (c) z/d = 5 (d) z/d = 10 (e) z/d = 15 360 5.60 Frictional damping ratios, D, versus dimensionless pile deflection y /d in loose sand (shake table test 23) 361 5.61 Frictional damping ratios, D, versus dimensionless pile deflection y / d in dense sand (shake table tests 14, 25 and 30) 362 5.62 Computed versus measured p-y hysteresis loops at various dimensionless depths - shake table test 23 (a) z/d = 1 (b) z/d = 5 (c) z /d = 10 (d) z /d = 15 365 5.63 Pile group response - high level, inline shaking (s/d = 2) (a) base acceler-ation (b) free field surface acceleration (c) acceleration at the e.g. of ma ss (d) pile cap displacement (LVDT 1) 36 9 5.64 Computed Fourier spectra - high level, inline shaking (s/d=2) (a) base acceleration (b) free field acceleration (c) acceleration at the e.g. of mass 370 5.65 Bending moment, vs. depth in a two pile group - high level shaking (s/d = 2) (a) offline shaking (b) inline shaking 372 5.66 Bending moment vs. depth in a two pile group - high level, inline shaking (s/d = 8) 373 5.67 Comparison of Fourier spectra - inline shaking (a) input base accelerations (b) pile cap accelerations (s/d = 4) (c) pile cap accelerations (s/d = 6) . 375 5.68 Influence of pile spacing on pile cap displacement for high level shaking. . 376 xxviii 5.69 Single pile test 34 - bending moments vs. depth for strong shaking and comparison to Winkler model 378 5.70 Comparison of predicted and measured bending moments using a Winkler model for high level, offline shaking (a) s/d = 2 (b) s/d = 4 (c) s/d = 6 . 379 5.71 Comparison of predicted and measured bending moments using a Winkler model for inline, high level shaking (a) s/d = 2 (b) s/d = 4 (c) s/d = 6 (d) s/d 8 381 5.72 Shake table interaction factor, 77"", and comparison with other experimen-tal and theoretical (Randolph- Poulos) results (a) inline shaking (b) offline shaking 385 5.73 2 x 2 pile group response - high level shaking (s/d = 3) (a) base acceleration (b) free field surface acceleration (c) acceleration at the e.g. of mas s (d) pile cap displacement (LVDT 1) (e) pi le mass displacement (LVDT 2) . 387 5.74 Computed Fourier spectra (a) base acceleration (b) free field acceleration (c) acceleration at the e.g. of mass 388 5.75 2 x 2 pile group response - bending moment and axial load time histories (a) strain gauge 1 (b) strain gauge 3 (c) strain gauge 5 (d) dynamic axial lo ad -. 389 5.76 Average bending moment vs. depth in the four pile group and comparison with Winkler model 391 5.77 Cyclic axial loading test on a single model pile in dense sand 395 6.1 Computed bending moment distribution - coupled versus uncoupled ana-lytic solution 405 6.2 Computed pile and free field displacements relative to base motion - cou-pled analytic solution 406 x x i x 6.3 Computed versus measured ringdown time histories - test R- L5 (a) dis-placements at L V D T 2 (b) bending moments at the soil surface 415 6.4 Computed versus measured ringdown time histories - test R- D2 (a) dis-placements at L V D T 2 (b) bending moments at the soil surface 416 6.5 Experimental variation of the logarithm of pile head stiffness Kld ver-sus pile deflection y0 and comparison with A.P.I, recommendations - cent rifuge test 12 418 6.6 Normalized shear modulus-shear strain attenuation relationships used in S H A K E analysis of centrifuge tests 419 6.7 S H A K E analysis of free field test 10 (a,b) input base accelerations and computed Fourier spectra (c,d) computed versus measured Fourier spectra at found ation mid- depth and sand surface, respect ively 421 6.8 Fourier spectra of free field surface accelerations computed using S H A K E versus measured spectra - shake table test 14 423 6.9 Fourier spectra of free field surface accelerations computed using S H A K E versus measured spectra - shake table test 23 (a) measured spectra (b) computed spectra 424 6.10 Fourier spectra of free field surface accelerations computed using S H A K E versus measured spectra - centrifuge test 41 425 6.11 Fourier spectra of free field surface accelerations computed using S H A K E versus measured spectra - centrifuge test 12 (a) measured spectra (b) com-puted spectra 426 6.12 Free field surface accelerations computed using S H A K E versus measured accelerations - centrifuge test 12 (a) measured accelerations (b) computed accele rations 427 XXX 6.13 Computed pile response using exp't. pile head stiffnesses versus measured pile response - C.T. 41 (a) pile head accelerations (b) pile head displacemen ts (c) shear force at soil surface (d) ben ding moment at soil surface . . . 435 6.14 Computed pile response using exp't. pile head stiffnesses versus measured pile response - C.T. 12 (a) pile head accelerations (b) pile head displacemen ts (c) shear force at soil surface (d) ben ding moment at soil surface . . . 436 6.15 Computed pile response using A.P.I, pile head stiffnesses versus measured pile response - C.T. 12 (a) pile head accelerations (b) pile head displacemen ts (c) shear force at soil surface (d) ben ding moment at soil surface . . . 437 6.16 Computed pile response using exp't. pile head stiffnesses versus measured pile response - S.T. 14 (a) pile head accelerations (b) pile head displacemen ts (c) shear force at soil surface (d) ben ding moment at soil surface . . . 438 6.17 Computed pile response using exp't. pile head stiffnesses versus measured pile response - S.T. 23 (a) pile head accelerations (b) pile, head displacemen ts (c) shear force at soil surface (d) ben ding moment at soil surface . . . 439 6.18 Structural model used in SPASM8 analysis (a) centrifuge tests (b) shake table tests 442 6.19 Free field surface accelerations computed using S H A K E versus measured accelerations - centrifuge test 41 (a) computed (b) measured 447 6.20 Free field surface accelerations computed using S H A K E versus measured accelerations - centrifuge test 15 (a) computed (b) measured 448 6.21 Free field surface accelerations computed using S H A K E versus measured accelerations - shake table test 23 (a) computed (b) measured 449 6.22 Relative free field displacements computed using S H A K E - centrifuge test 41 (a) mid-depth of sand layer (b) top of sand layer 450 xxxi 6.23 Relative free field displacements computed using S H A K E - centrifuge test 15 (a) mid-depth of sand layer (b) top of sand layer 451 6.24 Relative free held displacements computed using S H A K E - centrifuge test 12 (a) mid-depth of sand layer (b) top of sand layer 452 6.25 Relative free field displacements computed using S H A K E - shake table test 23 (a) mid-depth of sand layer (b) top of sand layer 453 6.26 Computed shear force at the soil surface (cent, test 12) using radiation damping coefficients computed using the equations of Gazetas and Dobry (1984) and Lysmer and Richart (1966) 455 6.27 Computed shear force at soil surface using A.P.I, p-y curves and compar-ison with measured response - centrifuge test 12 459 6.28 Computed bending moment at soil surface using A.P.I, p-y curves and comparison with measured response - centrifuge test 12 459 6.29 Computed shear force at soil surface using experimentally derived p-y curves and comparison with measured response - centrifuge test 12 . . . . 460 6.30 Computed bending moment at soil surface using experimentally derived p-y curves and comparison with measured response - centrifuge test 12 . 460 6.31 Computed displacement at the top of the structural mass using A.P.I, p-y curves and comparison with measured response - centrifuge test 12 . . . . 461 6.32 Computed displacement at the top of the structural mass using exper-imentally derived p-y curves and comparison with measured response -centrifuge test 12 462 6.33 Computed shear force at soil surface using A.P .L p-y curves and compar-ison with measured response - centrifuge test 41 463 6.34 Computed bending moment at soil surface using A.P.I , p-y curves and comparison with measured response - centrifuge test 41 463 xxxi i 6.35 Computed shear force at soil surface using experimentally derived p-y curves and comparison with measured response - centrifuge test 41 . . . . 464 6.36 Computed bending moment, at soil surface using experimentally derived p-y curves and comparison with measured response - centrifuge test 41 . 464 6.37 Computed shear force at soil surface using A.P.I, p-y curves and compar-ison with measured response - centrifuge test 15 465 6.38 Computed bending moment at soil surface using A.P.I, p-y curves and comparison with measured response - centrifuge test 15 . . . . 466 6.39 Computed shear force at soil surface using experimentally derived p-y curves and comparison with measured response - centrifuge test 15 . . . . 466 6.40 Computed bending moment at soil surface using experimentally derived p-y curves and comparison with measured response - centrifuge test 15 . 467 6.41 Computed shear force at soil surface using A.P.I, p-y curves and compar-ison with measured response - shake table test 23 467 6.42 Computed bending moment at soil surface using A.P.I, p-y curves and comparison with measured response - shake table test 23 468 6.43 Computed shear force at soil surface using experimentally derived p-y curves and comparison with measured response - shake table" test 23 . . . 468 6.44 Computed bending moment at soil surface using experimentally derived p-y curves and comparison with measured response - shake table test 23 . 469 7.1 Plane frame structural model for two pile group subjected to inline shaking on the shake table 474 7.2 Sample earthquake record used as input into P G D Y N A 476 7.3 Structural model for four pile group subjected to inline shaking on the shake table ' 481 xxx i i i 7.4 Pile group response computed using P G D Y N A versus measured response for a 4-pile group subjected to inline shaking on the shake table 482 7.5 Structural model for symmetrical four pile group tested on the Caltech centrifuge 487 7.6 Pile group response computed using P G D Y N A versus measured response for a symmetric 4-pile group subjected to moderate level, earthquake shak-ing on the c entrifuge 488 A . l Half bridge configuration to measure pile bending strains 534 A.2 Half bridge configuration to measure pile axial strains 535 A.3 Waveform aliassing: (a) sampling a lower frequency waveform at interval At (b) sampling a higher frequency waveform at interval At (afte r Sheriff and Geldart, 1983) 542 A. 4 Test case showing the effect of a low pass filter on a sine series (a) spectral input (b) comparison of unfiltered and filtered time series data compute d using a 50 Hz cutoff filter 546 B. l Chevron bridge circuit used in pile strain gauging 548 C. I Computed maximum shear strains around a vibrating disc - analytic versus finite element solution (a) 9 = 10 degrees (b) 6 = 40 degrees (c) 9 = 80 degrees 565 C.2 Pile displacement profiles yP(z) used in analysis of strain field around vi-brating pile 567 C.3 Computed maximum shear strains around a vibrating disc - plane dis-placement versus plane strain solution (a) 6 = 0 degrees (b) 9 = 40 degr ees (c) 9 = 90 degrees 569 xxxi v D. l Pile deflection, rotation, shear force and bending moment positive sign conventions 575 E . l Lateral loading of a cantilever beam - test case 584 E.2 Bending moment distribution along laterally loaded beam - test case . . . 586 E . 3 Distribution of lateral reaction force p(x) along a laterally loaded beam -test case 587 F. l Single pile model 589 G. l Single pile model - uncoupled analysis 597 H. l Structural layout assumed for finite element discretization of pile-structural mass system (uncoupled analysis) 605 I. 1 Pile group response - low level inline shaking (s/d = 2) (a) base accelera-tion (b) free field surface acceleration (c) acceleration at the e.g. of mas s (c) pile cap displacement (LVDT 1) 613 1.2 Computed Fourier spectra - low level inline shaking (s/d = 2) (a) base acceleration (b) free field acceleration (c) acceleration at the e.g. of mass 6 14 1.3 Bending moment vs. depth in a two pile group - low level shaking for s/d = 2 (a) offline shaking (b) inline shaking 616 1.4 Bending moment vs. depth in a two pile group - low level, inline shaking -s/d = 6 617 1.5 Influence of pile spacing on pile cap displacement for low level shaking. . 620 1.6 Pile group test PG4C - bending moments vs. depth for low level offline shaking (s/d = 6) and comparison to Winkler model 622 XXXV 1.7 Comparison of predicted and measured bending moments using a Winkler model for low level, offline shaking (a) s/d = 2 (b) s/d = 4 624 1.8 Comparison of predicted and measured bending moments using a Winkler model for inline, low level shaking (a) s/d = 2 (b) s/d — 4 (c) s/d = 6 . . 626 J . l Three dimensional beam element and local nodal num