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Mahadevan Ilankatharan

December 2008

Civil and Environmental Engineering

Centrifuge Modeling for Soil-Pile-Bridge Systems with Numerical Simulations

Accounting for Soil-Container-Shaker Interaction

Abstract

Centrifuge testing of soil-pile-bridge systems was conducted using the NEES

(Network of Earthquake Engineering Simulation) geotechnical centrifuge at UC Davis.

This testing was a part of a multi-university and multi-disciplinary collaborative research

utilizing NEES with goal of investigating the effects of Soil-Foundation-Structure-

Interaction (SFSI) while demonstrating NEES research collaboration. The centrifuge

experiments complement the 1-g shake table and field experiments conducted at other

universities. The data from the centrifuge experiments was compared and combined with

the data from other universities to provide integrated analytical models for SFSI problems

of soil-pile-bridge systems. This dissertation presents results of these experiments,

including collaborations, comparisons with other experiments and numerical simulations,

and end-to-end usage of data. Although many aspects of the collaboration exercise were

successful, one conclusion of this part of the work was that significant discrepancies

between simulations and experiments may be caused by soil-container-shaker interaction

in the experiments.

Some aspects of the interaction between the shaker and the specimen were

accounted for by implementing in the OpenSees finite element simulations a novel

method for simulating the excitation of the shaking table as a dynamic force in the

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actuator (flexible-actuator-prescribed force approach) instead of the conventional

approach of specifying the excitation as a prescribed- displacement of the shaking table.

Other aspects of the interaction were accounted for by including a more accurate model

of the model container, bearing, and reaction mass of the system. Initial attempts to

include the servo-hydraulic control system in the simulations were attempted.

Based on a systematic series of simulations of the site response of the centrifuge

model that included different approximations of the centrifuge-shaker system, it was

concluded that the sensitivity of simulation results to uncertainties in modeling

parameters depends on how the aspects of soil-container-shaker interaction are accounted

for. This raises a fundamental and very general question: How can we assess the

significance of a discrepancy between a simulation and an experimental result? Although

this dissertation does not provide a general answer to this fundamental question, it does

show that for centrifuge-shaking table experiments, the significance of errors in the

simulations cannot be rigorously assessed without accounting for test specimen-actuation

system interaction. The archives of centrifuge test data and metadata and OpenSees

numerical models of soil-container-shaker system are available for others to use at the

NEEScentral website (http://central.nees.org).

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Dedication

To my mom

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Acknowledgements

This dissertation research was supported by NSF awards CMS-0324343 and

CMS-0402490 through the George E. Brown, Jr. Network for Earthquake Engineering

Simulations (NEES). Without the support of NEES and the NSF, this research would not

have been possible. Any opinions, findings and conclusions or recommendations

expressed in this dissertation are those of the author and do not necessarily reflect those

of the NSF. The centrifuge shaker was designed and constructed with support from the

NSF, Obayashi Corp., Caltrans and the University of California. Recent upgrades have

been funded by NSF award CMS-0086566 through NEES.

Through my education, a great number of people have helped me to get where I

am today. Without all of your support and guidance, none of this would have been

possible.

First and foremost, I would like to express my gratitude to my supervisor, Prof.

Bruce Kutter. Prof. Kutter has guided me in several aspects of my development as a

graduate student, not only by giving me the opportunity to pursue exciting and relevant

research but also by teaching me how to present my work in a precise and elegant

manner. His dedication and love for research and academic excellence have rubbed off on

me. I am really glad and proud that I have had an opportunity to work closely with such a

wonderful person.

I would like to acknowledge my dissertation committee members Professor Ross

Boulanger and Professor Boris Jeremić for their valuable comments and suggestions.

Their inputs have helped to improve the research and the quality of this dissertation.

I would like to thank Center for Geotechnical Modeling (CGM) facility manger

Dr. Dan Wilson for his guidance and support on this research, and CGM staff Lars

Pedersen, Chard Justice, Tom Kohnke, Tom Coker, and Cypress Winters, for their help in

different ways for my research work.

I would like to thank my research collaborators from the University of Washington,

Dr. Hysung-Suk Shin and Professors Pedro Arduino and Steve Kramer and the collaborators

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from other universities for sharing their valuable simulation and experimental data and ideas

in the course of this research.

I have had so many wonderful teachers throughout my education who directly or

indirectly contributed to my doctoral degree. I am very grateful to all my teachers at St.

Henry’s college, Ilavalai, Sri Lanka; the University of Peradeniya, Sri Lanka; and the

University of California, Davis.

I am very obliged to the help and support provided by my uncle Santhanasamy and

family, and many relatives and friends during my college and high school years in Sri Lanka.

I would like to thank my friend Sathishbalamurugan for his help and motivation and

helping me to “stay positive” during my university years in Sri Lanka and Davis.

I wish to express my sincere gratitude to my parents for always giving top priority

to my education. My aunt, Lilly, always helped and encouraged me to achieve my

educational goals, I am very thankful to her. Without my mother’s patience and

determination and my Aunt’s guidance and support, I would not have been in a position

to write this dissertation.

Last, but not least, I would like to thank my wife, Jocy, for patiently helping me in

many ways to complete my research and dissertation.

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Table of Contents

Page

Abstract ii

Acknowledgements v

List of Figures xv

List of Tables xxx

Chapter 1: Introduction 1

1.1 Background 1

1.1.1 Centrifuge testing of soil-foundation-bridge systems 1

1.1.2 Soil – container – centrifuge shaker interaction 4

1.2 Scope of the dissertation 5

1.3 Organization of dissertation 7

Chapter 2: Collaborative research: Centrifuge testing of soil-pile-bridge

systems 14

2.1 NEES collaborative research project to study SFSI 15

2.1.1 Field tests 16

2.1.2 Structural component tests 16

2.1.3 1-g shake table experiment 16

2.1.4 Centrifuge experiments 17

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2.2 Centrifuge test program 17

2.2.1 Concept of the geotechnical centrifuge modeling 17

2.2.2 Model configurations 18

2.2.2.1 Centrifuge test series MIL01 18



2.2.3 Design of structural models 20

2.2.4 Model preparation and instrumentation 21

2.2.5 Ground motion protocols 23

2.3 Representative results from centrifuge experiments 23

2.3.1 Soil site response 23

2.3.2 Horizontal accelerations 24

2.3.3 Vertical accelerations 24

2.3.4 Bending moment, shear force and sub-grade reaction 25

2.3.5 Superstructure accelerations of MIL02 bridge bents 25

2.4 Comparisons with UT Austin field tests 26

2.5 Simulations of centrifuge models 27

2.5.1 Outline of simulation models 27

2.5.2 Predicted site response 28

2.5.3 Predicted response of individual bents and single pile 29

2.5.4 Predicted response of two-span bridge model 30

2.5.5 Sensitivity analyses 31

2.5.6 Simulations of MIL02 and MIL03 test series 32

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2.6 Simulation of the prototype bridge structure 32

2.7 Centrifuge test data archives 33

2.8 Summary 34

2.8.1 Research collaboration 34

2.8.2 Centrifuge experiments 35

2.8.3 Simulations of centrifuge experiments 36

2.8.4 Effect of modeling boundary conditions on the sensitivity of

predicted site response 37

Chapter 3: Comparison of centrifuge and 1g shake table models of a

pile supported bridge structure 79

3.1 Introduction 81

3.2 Centrifuge and Shake table bridge models 83

3.2.1 General test setup 83

3.2.2 Scale factors for 1/52 scale centrifuge model and ¼ scale 1-g

shake table model 84

3.2.3 Pile properties 84

3.2.4 Design for above ground clear heights 85

3.2.5 Deck properties and spacing between bents 86

3.2.6 Selection of input motion and testing sequence 87

3.3 Comparison of centrifuge and 1g shake table experimental results 88

x

3.3.1 During a medium level shaking event (peak base acc = 0.25 g in

centrifuge test) 88

3.3.2 During a large level shaking event (peak base acc = 0.78 g in

centrifuge test) 89

3.4 Comparison of the system (three-bent) response to the individual bent

response in the centrifuge experiment 90

3.5 Conclusions 92

3.6 References 94

Chapter 4: Modeling input motion boundary conditions for simulations of

geotechnical shaking table tests 118

4.1 Introduction 120

4.2 Modeling of a soil column mounted on a centrifuge shaking table 122

4.2.1 Representing input motion boundary conditions 123

4.2.1.1 Prescribed-force simulation 123

4.2.1.2 Prescribed-displacement simulation 124

4.2.2 Soil model 125

4.2.3 Shaker and reaction mass 125

4.2.4 Selection of damping parameters and input variables 127

4.3 Simulation results 128

4.3.1 Linear elastic soil material model simulations 128

4.3.2 Elasto- plastic PDMY soil material model simulations 132

xi

4.4 Parametric studies 134

4.4.1 Effect of ξact 134

4.4.2 Effect of ξsoil 135

4.4.3 Effect of kact & MRM 136

4.5 Ground motion analogy: Rigid and Compliant base 137

4.6 Discussion 139

4.6.1 Importance of proper treatment of boundary conditions on the

sensitivity analysis 139

4.6.2 Need for realistic numerical models of servo-hydraulic actuation

system 140

4.7 Conclusions 141

4.8 Acknowledgements 143

4.9 References 143

Chapter 5: Numerical modeling of a soil-model container-centrifuge

shaking table system 160

5.1 Introduction 162

5.2 Modeling system components 163

5.2.1 Soil Model 164

5.2.2 Model container 165

5.2.3 Shaker and Reaction mass 166

5.3 Boundary conditions in simulation models 168

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5.3.1 1-D shear beam simulations of soil 168

5.3.2 2-D simulations of soil and container 168

5.3.3 2-D simulations of soil, container, and shaker 168

5.4 Simulation results 169

5.4.1 Soil horizontal accelerations from 1-D shear beam simulations of

soil and 2-D simulations of soil and container 169

5.4.2 Soil Vertical accelerations from 2-D simulations of soil and

container 170

5.4.3 Results from the 2-D simulations of soil, container, and shaker 171

5.5 Sensitivity analysis 173

5.6 Archives of numerical models of a soil-container-shaker system 175

5.7 Summary 176

5.8 References 178

Chapter 6: Towards developing a numerical model of a servo-hydraulic

centrifuge actuation system to predict shake table response 203

6.1 Factors affecting the reproduction of a dynamic signal in a

servo-hydraulic actuation system 204

6.2 Analytical models for various components of servo-hydraulic actuation

system 205

6.3 Outline of servo-hydraulic actuation system of the UC Davis centrifuge

facility 208

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6.4 Current base motion tuning procedures 209

6.5 Modifications to the shaker model presented in chapter 5 212

6.5.1 To account for the effects of feed-back controller 212

6.5.2 To account for the oil pressure limit and the limit on oil flow

velocity 213

6.5.3 To account for servo-valve nonlinearity 214

6.6 Simulated base response 214

6.7 Discussion on the simulation results and the need for additional work 217

Chapter 7: Summary and Conclusions, and Future work 233

7.1 Summary and Conclusions 233

7.1.1 Collaborative research: Centrifuge testing of soil-pile-bridge

systems 233

7.1.1.1 Research collaborations 234

7.1.1.2 Centrifuge experiments 235

7.1.1.3 Centrifuge test data archives 238

7.1.1.4 Numerical simulations of the centrifuge experiments 238

7.1.2 Modeling input motion boundary conditions for simulations of

geotechnical shaking table experiments 240

7.1.3 Numerical simulations of the soil model accounting for

soil-container-shaker interaction 242

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7.1.4 Numerical model of a servo-hydraulic centrifuge actuation system

to predict shaking table response 244

7.2 Areas for future research 246

References 249

Appendix A: Centrifuge test and simulation data archives 258

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List of Figures

Page

Chapter 1

1.1: Collapse of San Francisco/Oakland Bay bridge section, 1989 Loma Prieta

earthquake 10

1.2: Unseating of bridge span, Nishinomiya ki bridge, 1995 Kobe earthquake 10

1.3: Schematic of a bridge supported on pile foundations shows wide variations in

structural types/configurations and soil conditions (after Martin et al. 2002) 11

1.4: Schematic of Soil-Foundation-Structure-Interaction (SFSI) phenomena for

a pile supported structure (modified from Gazetas et al. 1998) 11

1.5: Overview of the NEES collaborative project to study

soil-foundation-structure-interaction 12

1.6: 3D rendering of a soil model-model container-centrifuge shaking table

system 13

1.7: Representation of soil-container-shaker interaction (after Kutter, 1994) 13

Chapter 2

2.1: Overview of the earthquake engineering components of the NEES

collaborative project to study soil-foundation-structure-interaction 42

2.2: Example of prototype location in a multi-span bridge 42

2.3: Seismic excitation of the field test specimen using T-Rex (after Black 2005) 43

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2.4: Seismic excitation of the field test specimen using Thumper

(after Black 2005) 43

2.5: (a) 3-D rendering of test set-up and (b) photograph of a test specimen of the

structural component tests at the Purdue University (after Makido 2007) 44

2.6: (a) 3-D rendering of test set-up and (b) photograph of a test specimen of the

1-g shaking table experiment (after Johnson 2006) 45

2.7: Photograph of the 1/52 scale models of the test specimens used in the first

series of centrifuge experiments 46

2.8: 3-D rendering of model layout of the centrifuge test series MIL01 46

2.9: Details of structural models in MIL01 test series 47

2.10: (a) Schematic and (b) Rendering of model layout of MIL02 test series 48

2.11: (a) Schematic and (b) Rendering of model layout of MIL03 test series 49

2.12: Configurations and embedment lengths of structural models used in MIL03

test series 50

2.13: Shear Wave Velocity Profile of Capitol Aggregate Test Site, Austin and

Nevada Sand (Dr = 80%) 51

2.14: Instrumentation layout in one of the centrifuge test series 52

2.15: Photograph from one of the centrifuge test series showing the

instrumentation using the high-speed video cameras and high-speed

wireless data acquisition system 53

2.16: Comparison of data recorded by traditional wired data acquisition system

and the new wireless data acquisition system at UC Davis

(after Wilson et al. 2007) 54

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2.17: Time histories and response spectra of Northridge and frequency sweep

motions used in the centrifuge test series 55

2.18: Measured soil accelerations from a vertical array of horizontal accelerometers

in test MIL03 (Northridge input motion, peak base acceleration = 0.26 g) 56

2.19: Measured horizontal motions at different locations of model in MIL01 test

series (Northridge input motion, peak base acceleration = 0.23 g) 57

2.20: Measured vertical motions at the container base & 2.6m from ground surface

in MIL03 test series (Northridge input motion, peak base acceleration

= 0.26 g) 58

2.21: Bending moment, shear force, and sub-grade reaction of bridge bents

@ time of maximum bent-cap displacement (Northridge input motion,

peak base acceleration = 0.57 g) 59

2.22: Normalized depth to maximum bending moment for different

above-ground clear height bridge bents in MIL01 test series 60

2.23: Response of bridge bents oriented different directions to base shaking in

MIL02 test series (frequency sweep input motion 7-333Hz) 61

2.24: Response of bridge bents in the centrifuge and field tests to the base

excitation in the transverse direction of the bent (frequency sweep input) 62

2.25: Seismic excitation directions for (a) centrifuge test specimen, and (b) field

test specimen 63

2.26: Modeling of soil-pile-structure interaction in a single pile using p-y, t-z,

and Q-z springs in OpenSees (after Shin 2007) 64

xviii

2.27: Numerical modeling of the two-span bridge model in MIL01 test series

using OpenSees (after Shin 2007) 64

2.28: Response spectra of measured (CFG) and simulated (Open) horizontal

free-field soil accelerations in MIL02 test series (after Shin et al. 2006) 65

2.29: Time histories of measured and simulated horizontal free-field soil

accelerations in MIL03 test series; Northridge input motion, peak base

acceleration = 0.26 g (after Shin 2007) 66

2.30: Ratios of Fourier amplitudes between the horizontal soil motion @ 2.6m

and the horizontal base motion in MIL03 test series and OpenSees 1-D

shear beam simulations; frequency sweep input motion, peak base

acceleration = 0.25 g (after Shin 2007) 67

2.31: Time histories and Fourier amplitude of measured and calculated horizontal

motions at the bent-cap of a two-pile individual bent (Bent 5) in MIL01 test

series; Northridge input motion, peak base acc = 0.25 g (after Shin 2007) 68

2.32: Measured and calculated maximum pile bending moment of Bent 5

in MIL01 test series; Northridge input motion, peak base acceleration =

0.25 g (after Shin 2007) 68

2.33: Measured and calculated peak accelerations of superstructure and at 2.5m

below ground surface in MIL01 test series during different intensity base

motions (after Shin 2007) 69

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2.34: Time histories of measured and calculated horizontal motions at the

bent-caps of the two-span bridge model in MIL01 test series; Northridge

input motion, peak base acc=0.25g (after Shin et al. 2006) 70

2.35: Measured and predicted response of the two-span bridge model in MIL01

test series; Northridge input motion, peak base acceleration = 0.25 g (after

Shin et al. 2006) 71

2.36: Back calculated ultimate soil resistance from pile bending moment data in

the centrifuge test and the ultimate soil resistance obtained from p-y spring

forces in the OpenSees simulations, @ time of maximum bent-cap displace

ment (after Shin et al. 2006) 72

2.37: Regions of p-y spring parameters considered in the sensitivity analyses (after

Shin 2007) 73

2.38: Sensitivity analysis: Effect of soil motion on bent response, Northridge

motion peak base acceleration = 0.25g (after Shin 2007) 74

2.39: Sensitivity analysis: Effect of ultimate soil resistance (pult) on bent response,

Northridge motion peak base acc = 0.25 g (after Shin 2007) 75

2.40: 3-D finite element model of the prototype soil-pile-bridge system (after Jie

2007) 76

2.41: End-to-end data usage scenario (after Van Den Einde et al. 2007) 77

2.42: End-to-end usage of centrifuge test data (screen shot from UCDavis-N3DV

data viewer, after Kutter 2007) 78

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Chapter 3

3.1: Hypothetical prototype multi-span bridge 98

3.2: Layout of the bridge model in the centrifuge test series 99

3.3: Photograph of bridge model set-up on centrifuge model container 100

3.4: Layout of the bridge model in the 1g shake table experiment (Wood et al.

2004) 101

3.5: Photograph of bridge model set-up on shake tables at the University of

Nevada, Reno (after Johnson et al. 2006) 102

3.6: Typical pile cross section in the centrifuge experiment 103

3.7: Calculation of clear heights of piles based on equivalent cantilever model 104

3.8: Load, shear and bending moment diagrams for pile in the ground and column

on the shake table at ultimate state 105

3.9: Time histories and response spectra of base motions before and after

tuning and amplitude of tuning transfer function for base motion (peak

base acc = 0.23 g) 106

3.10: Time histories & acceleration response spectra of target & achieved free

field motion @ 50 mm below ground surface (before and after tuning, peak

base acc = 0.23 g) 107

3.11: Deck motions during a medium level shaking event (peak base acc= 0.25 g

in centrifuge test) 108

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3.12: Response spectra of (5% damping) of free field motions @ 2.5 m depth in

the centrifuge test & shake table base motions, and deck motions during

medium level shaking event (peak base acc = 0.25 g in centrifuge test) 109

3.13: Deck displacements during a medium level shaking event (peak base acc =

0.25g) 110

3.14: Ratio of spectral accelerations (5% damping): deck motions to free field soil

motions @ 2.5 m in the centrifuge test and deck motions to table motions in

the 1g shake table test (peak base acc = 0.25 g in centrifuge test) 111

3.15: Column strains (bending) at 1.3m below deck level during a medium level

shaking event (peak base acc = 0.25 g) 112

3.16: Response spectra of (5% damping) of free field motions @ 2.5 m depth in

centrifuge test & shake table motions, and deck motions in both experiments

during a large amplitude shaking event (peak base acc = 0.78 g in centrifuge

test) 113

3.17: Ratio of spectral accelerations (5% damping): deck motions to free field soil

motions @ 2.5 m in the centrifuge experiment and deck motions to shake table

motions in the 1g shake table experiment (peak base acc = 0.78 g in centrifuge

test) 114

3.18: Response spectra of the base input motions for two centrifuge shaking events,

one applied before attaching the bridge deck, and one after connecting the

bridge deck to the bridge bents 115

3.19: Response spectra of the bridge bent accelerations before and after attaching

the bridge deck 116

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3.20: Comparison of bending moment distributions in the columns/piles before

(single bents) and after (bridge bents) attaching the bridge deck 117

Chapter 4

4.1: 3D rendering of a soil model-container-centrifuge shaking table system 147

4.2: Reflection and refraction of seismic waves at the container base 147

4.3: Different input motion boundary conditions in the simulations 148

4.4: Configuration of the actuator elements 148

4.5: Time histories of (a) command acceleration, and (b) command displacement

of the input motion 149

4.6: Calculated frequency dependent soil damping ratio (ξsoil) by combining

stiffness proportional and mass proportional damping: an example case for

ξsoil = 2.5% at the first and the third modal frequencies (50 Hz and 250 Hz) 149

4.7: Time histories and response spectra (5% damping) of surface and base motions

in the prescribed-force and prescribed-displacement simulations employing a

linear elastic soil material 150

4.8: Time histories and response spectra (5% damping) of surface and base motions

in the prescribed-force and prescribed-displacement simulations employing a

linear elastic soil material (Gassumed/Gactual = 0.64) 150

4.9: Ratios of Fourier amplitudes between the surface motion and the base motion,

and base motion and command acceleration, in the prescribed-force and prescribed-

displacement simulations employing linear elastic soil material 151

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4.10: Sensitivity of peak & peak spectral accelerations of surface and base motions

to error in Gassumed of elastic soil material in the prescribed-force and prescribed-

displacement simulations 152

4.11: Time histories of motions at ground surface and at base of the soil column in

the prescribed-force and prescribed-displacement simulations employing the

elasto-plastic PDMY soil material 153

4.12: Time histories of motions at ground surface and at base of the soil column in

the prescribed-force and prescribed-displacement simulations employing the

elasto-plastic PDMY soil material (amplitude of the input motion 10 times

larger than that shown in Fig. 4.5) 153

4.13: Ratios of Fourier amplitudes between the surface motion and the base motion,

and the base motion and the command acceleration, in the prescribed-force and

prescribed-displacement simulations employing the elasto-plastic PDMY soil

material (simulations using the larger input motion) 154

4.14: Sensitivity of calculated peak acceleration of (a) surface motion, and (b) base

motion to error in Gr_assumed of the PDMY soil material in the prescribed-force &

prescribed-displacement simulations (simulations using the larger input

motion) 154

xxiv

4.15: Sensitivity of calculated peak acceleration of surface and base motions to

error in Gassumed of elastic soil material in the prescribed-force and prescribed-

displacement simulations, for different ξact values (ξsoil = 2.5%, ,1/

=HGA

kact

)5.0=RM

soil

MM

and

155

4.16: Sensitivity of calculated peak acceleration of surface and base motions to


displacement simulations, for different ξsoil values (ξact = 20%, ,1/

=HGA

kact

)5.0=RM

soil

MM

and

156

4.17: ARS (5% damping) of calculated surface and base motions in the prescribed-force

and prescribed-displacement simulations, involving relatively stiff actuator and

heavy reaction mass ( ,20/

=HGA

kact 1.0=RM

soil

MM

and ), for different Gassumed values of

linear elastic soil material (ξact = 20%, and ξsoil = 2.5%) 157

4.18: Procedures for deconvolution of input motion for FLAC model described in

Mejia et al. 2006 158

4.19: (a) Time histories and (b) response spectrum of computed acceleration at top

of soil column for rigid base, and compliant base with 5% velocity mismatch

(Mejia et al. 2006) 159

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Chapter 5

5.1: Photograph of the NEES geotechnical centrifuge at UC Davis 181

5.2: 3D rendering of a soil model-model container-centrifuge shaking table system181

5.3: Estimated damping ratios based on employed stiffness-proportional damping 182

5.4: Photographs of the FSB2 centrifuge model container 183

5.5: Dimensions and weights of different rings of the FSB2 container 184

5.6: Plan view of the horizontal shake table system at the UC Davis centrifuge

facility 185

5.7: 2D finite element mesh of the soil-model container-centrifuge shaker system 186

5.8: Configuration of actuator elements 186

5.9: Different boundary conditions in simulation models 187

5.10: Time histories of (a) measured acceleration at the base of the container

and (b) calculated displacement by double integration of acceleration of

the frequency sweep input (measured peak base acc = 1.3 g) 188

5.11: Measured and computed acceleration time histories and response spectra

(5% damping) from 1-D shear beam simulations of soil (frequency sweep

input, peak base acc = 1.3 g) 189


(5% damping) from 1-D shear beam simulations of soil (Northridge input,

peak base acc = 1.3 g) 190


(5% damping) from 2-D simulations of soil and container (frequency sweep


xxvi


(5% damping) from 2-D simulations of soil and container (Northridge input,


5.15: Measured and computed vertical acceleration histories and response spectra

(5% damping) from 2-D simulations of soil and container (frequency sweep


5.16: Computed vertical acceleration histories and response spectra (5% damping)

in the 2-D simulations of soil and container, with & without shear rod 194


(5% damping) from 2-D simulations of soil, container, and shaker (frequency

sweep input, peak base acc = 1.3 g) 195

5.18: Measured and computed base acceleration time histories and response spectra

(5% damping) from 2-D simulations of soil, container, and shaker (frequency

sweep input, peak base acc = 1.3 g) 196

5.19: Measured and computed base acceleration time histories and response spectra

(5% damping) from 2-D simulations of soil, container, and shaker (with

modified command displacement) 196


(5% damping) from 2-D simulations of soil, container, and shaker (with

modified command displacement) 197

5.21: Ratio of Fourier amplitudes between the calculated and measured base

accelerations from 2-D simulations of soil, container, and shaker 198

xxvii

5.22: Ratio of Fourier amplitudes between the calculated surface and base

accelerations from 2-D simulations of soil, container, and shaker 198

5.23: Ratio of Fourier amplitudes between the calculated and measured base

accelerations in the 2-D simulations of soil, container, and shaker using

different earthquake characteristics 199

5.24: Effect of varying shear modulus on calculated ground surface response

spectrum for different boundary conditions (frequency sweep input, peak

base acc = 1.3 g) 200

5.25: Effect of varying shear modulus on calculated base response spectrum

for different boundary conditions (frequency sweep input, peak base acc

= 1.3 g) 200

5.26: Sensitivity of peak and peak spectral accelerations of surface motion

to reference shear modulus of PDMY material (frequency sweep input,


5.27: Sensitivity of peak and peak spectral accelerations of base motion to

reference shear modulus of PDMY material (frequency sweep input,


5.28: Sensitivity of peak and peak spectral accelerations of surface motion to

reference shear modulus of PDMY material (frequency sweep input, peak

base acc = 13 g) 202

5.29: Sensitivity of peak and peak spectral accelerations of base motion to

reference shear modulus of PDMY material (frequency sweep input, peak

base acc = 13g) 202

xxviii

Chapter 6

6.1: Analytical model (derived based on transfer function approach) of a

servo-hydraulic actuation system of a structural shaking table system

(after Conte et al. 2000) 219

6.2: Schematic of analytical model of the servo-valve transfer function depicted

in Fig. 6.1 (after Conte et al. 2000) 220

6.3: Plan (top) and elevation (bottom) views of the horizontal shaking table

system at the UC Davis centrifuge facility 221

6.4: Servo-hydraulic actuation mechanism of the horizontal shaking table system

of the UC Davis centrifuge facility (after Kutter et al. 1994) 222

6.5: Fourier amplitudes of the command motion to the servo controller and the

achieved motions at the base of the container for different frequency sweep

inputs 223

6.6: Transfer function used to correct acceleration command in the base motion

tuning exercise 224

6.7: Time histories of the target and achieved base motions for an input from

the 1994 Northridge earthquake 224

6.8: Magnitudes of FFT of the target and achieved base motions during the base

motion tuning exercise, for an input from the 1994 Northridge earthquake 225

6.9: Configuration of shaker model used in the analyses 226

6.10: Modifications to the shaker model, using a mechanical-lever system to

incorporate the effects of feed-back controller in the analyses 226

xxix

6.11: Configuration and characteristics of different components of modified

shaker model 227

6.12: Comparison of the measured and the simulated base displacements during

a frequency sweep (50 to 125 Hz) input 228

6.13: Comparison of the measured and the simulated base displacements during

the frequency sweep input motion (sweep 50 to 125 Hz) for different ‘g’

levels and shaking intensities 229

6.14: Ratio of Fourier amplitudes between the command motion and the base

motion in (a) experiment and (b) simulation for frequency sweep input –

50 to 125 Hz 230

6.15: Ratios of Fourier amplitudes between the command motions and the

measured base motions for different ‘g’ levels and shaking intensities

(frequency sweep input – 50 to 125 Hz) 231

6.16: Ratios of Fourier amplitudes between the command motions and the

simulated base motions for different ‘g’ levels and shaking intensities

(frequency sweep input – 50 to 125 Hz) 232

xxx

List of Tables

Page

Chapter 2

2.1: Scaling factors used in this research 39

2.2: Aluminum types used for the model piles in the centrifuge experiments 39

2.3: Suite of centrifuge shaking events 40

2.4: Input parameters of the base-line model of the sensitivity analyses

(Shin 2007) 41

2.5: Selection of input variables in the sensitivity analyses (Shin 2007) 41

Chapter 3

3.1: Scale factors used to convert model data to prototype scale in the

centrifuge and 1g shake table experiments 96

3.2: Comparison of sectional properties of piles in centrifuge tests and

columns in 1g shake table tests 96

3.3: Above ground clear heights of shake table columns and calculated

clear heights of centrifuge piles 97

Chapter 4

4.1: Centrifuge scaling factors at the centrifuge acceleration (g) level of 50 145

4.2: Main modeling parameters for soil material models 145

4.3: Selection of input variables for shaker system 146

xxxi

Chapter 5

5.1: Main modeling parameters for dry dense Nevada sand (Dr=80%) 180

5.2: Some design details of FSB2 model container 180

Chapter 1

Introduction

1.1 Background

1.1.1 Centrifuge testing of soil-foundation-bridge systems

Past earthquakes, particularly the 1989 Loma Prieta and 1994 Northridge

earthquakes in California, and the 1995 Kobe earthquake in Japan, have caused collapse

of, or severe damage to, a considerable number of major bridges that were designed for

seismic forces (Priestly et al. 1998, Fig. 1.1 and Fig. 1.2)). One major reason for the poor

performance relates to the complexities of the bridge structural and sub structural systems

as compared to other structures. Some of these complexities are wide variations in

structural types and configurations (bridge decks, columns/foundations, abutments, etc.),

variations in soil conditions along the length of a highway bridge (for example, presence

of potentially liquefied layers), and variations in ground motions (magnitude and phase

shift) along the length of the bridge (Fig. 1.3). In addition, soil-foundation-superstructure

interaction (SFSI) by which the soil interacts with the below ground and the above

ground portion of the bridge has an impact on the performance of the bridge during

earthquakes (Fig. 1.4). The impact of SFSI effects on the bridge system depend on the

ground motion and the nonlinear characteristics of the soil, foundation, and

superstructure. Accurate evaluations of SFSI effects are important to understand the

performance of a bridge under the seismic loading conditions.

1

In conjunction with lessons learnt from the case histories, researchers use

laboratory experiments to understand the performance of the key components of the

bridge system under the seismic loading conditions. In this context, dynamic centrifuge

modeling has been established as a powerful tool (Armstrong et al. 2008, Deng et al,

2008, etc.). Dynamic centrifuge modeling of bridge components designed with varying

soil profile characteristics, substructure/superstructure characteristics, loading protocols,

and detailed instrumentation is used to obtain physical data, gain insight into the

mechanisms involved, and perform parametric studies to calibrate numerical models. A

vast amount of research has been focused on the components of bridge systems to

understand the SFSI effects and to calibrate and validate computational models for SFSI

problems of bridge components (Wilson 1998, Abdoun et al. 2003, Chang et al, 2005,

Brandenberg 2005, Ugalde et al. 2007, etc). While a great amount of knowledge has been

gained about the component behavior of bridge components from these experiments, it is

important to perform experiments on soil-foundation-bridge systems to understand the

SFSI aspects of bridge systems and to validate the numerical model to predict bridge

system response. Kutter and Wilson (2006) describe the basic reasons for testing soil-

foundation-superstructure systems on the centrifuge as follows:

1) mechanisms of behavior that seem important for isolated foundations may not

come into play for soil-foundation-structure systems,

2) mechanisms of foundation behavior that are critical to the performance of the

structure may become apparent if the foundations and structures are tested as a

system, and

2

3) integrated numerical models that account for behavior of the soil, foundation and

structure need to be verified, especially for dynamic problems.

Cross-disciplinary interaction and collaboration between the geotechnical and the

structural engineers are essential for proper design of system experiments with the

realistic characteristics of substructure/superstructure, interpretation of these

experimental results, calibration of numerical models, and proper implementation of

gained knowledge into practice. In the past, limitations in experimental capabilities to

perform system experiments and lack of tools for effective means of collaborations pose

difficulties in conducting a collaborative research on the soil-foundations-bridge systems.

When the National Science Foundation’s George E. Brown, Jr. Network for

Earthquake Engineering Simulation (NEES) became operational in 2004, it provided

effective means for collaboration and facilitated a major improvement in research by

integrating experimental and computational simulations (http://nees.org). A larger scale

collaborative research project had been conducted to demonstrate the capabilities of

NEES for studying the effects SFSI on bridges and to conduct a comprehensive study of

SFSI effects by integrating analytical and experimental tools at multiple universities

(Wood et al. 2004, Fig. 1.5). One of the experimental components of this project

involved centrifuge modeling of soil-pile-bridge systems using the 9 m radius NEES

geotechnical centrifuge at the University of California, Davis. The collaborative research

on the centrifuge testing of soil-pile-bridge system is presented in this dissertation.

3

1.1.2 Soil – container – centrifuge shaker interaction

A typical centrifuge experiment involves different dynamic components (a

dynamic system) such as the test specimen, the soil model, the model container, the

shaking table, and its reaction mass (Fig. 1.6). All of the different components of

dynamic system, with their own resonant frequencies, interact with the soil model during

dynamic excitation, some absorbing energy and others allowing undesired modes to

affect the response observed in the experiment. This interaction between the soil model

and other components of the dynamic system (Fig. 1.7) might attenuate or exaggerate the

discrepancies in response of the experiment and the numerical simulation (Kutter 1994).

A fundamental question then arises: ‘How should we assess the quality of a comparison

between an experiment and a simulation results?’ To answer this fundamental question, it

would be essential to understand the sensitivity of simulation results (outputs) to

uncertainties in modeling parameters (inputs). In this context, it was hypothesized that the

“sensitivity of simulation results to uncertainties in modeling parameters depends on how

the boundary conditions are incorporated in the simulations”.

Qualitative assessment of the issues of dynamic interaction among soil model,

container, and shaker were addressed by many researchers in the past (Fiegel et al. 1994

and Narayanan 1999). However, a detailed numerical model to mathematically represent

the dynamics of the soil-model container-shaker system is necessary for comprehensive

understanding of this interaction and quantifying the effect of this interaction on the test

results.

4

1.2 Scope of the dissertation

This dissertation consists of the following four components: (1) A collaborative

research project involving centrifuge testing and numerical simulation of a soil-pile-

bridge system (2) A critical study to advance understanding the effects of using different

input motion boundary conditions on the sensitivity of numerical simulation results to

errors in material properties of a specimen tested on a shaking table (3) Numerical

simulations of a soil model tested on the centrifuge experiment accounting for soil-

container-shaker interaction, and (4) A first attempt to develop a numerical model of the

UC Davis servo-hydraulic centrifuge actuation system with a goal of predicting shaking

table response.

As mentioned earlier, the centrifuge experiments were part of a larger

collaborative project with the primary objectives of demonstrating the capabilities of the

network for earthquake engineering simulation (NEES) for studying the effects of soil-

foundation-structure interaction (SFSI) on bridges and conducting a comprehensive study

of SFSI effects by integrating analytical and experimental tools at multiple universities.

The centrifuge experiments complement the 1-g shake table and field shaker experiments

conducted at other universities. The design of test elements to facilitate direct

comparisons of experimental results between different experiments, to accounting for

different test boundary conditions and scaling laws for structural and geotechnical

modeling, was challenging and required cross-disciplinary interaction between

geotechnical and structural engineers.

The first part of this dissertation reports the lessons learnt from this collaborative

research both with respect to means for effective research collaboration and investigating

5

the SFSI effects by integrating experimental and analytical tools. It describes the

collaborative test design process, presents comparisons of experimental results in

different experiments, and reports the findings from the centrifuge testing of soil-pile-

bridge systems which involve realistic superstructure characteristics. In addition, the first

part of the dissertation describes the numerical simulations of the centrifuge experiments

performed by the collaborators from the University of Washington and compares the

simulation results with the experimental results. Understanding the discrepancies between

the results, in particular, the soil site response, in the centrifuge experiments and the

numerical simulations motivate the analyses presented in the second part of this

dissertation.

The second part of this dissertation is devoted to understand the importance of

more accurate treatment of the effects of soil-container-shaker interaction on the

numerical simulations of the centrifuge experiments. In this context, this dissertation

reports the findings from a series of numerical simulations of a hypothetical centrifuge

shaking table experiment that prove the hypothesis that “the sensitivity of simulation

results to uncertainties in modeling parameters depends on how the boundary conditions

are incorporated in the simulations”, the model development of a soil-container-

centrifuge shaker system including the modeling details of a servo-hydraulic centrifuge

actuation system , and the effects of dynamic interaction between the different

components of the centrifuge experimental system on the simulated site response results.

The centrifuge experiments produced unique data sets that span the disciplines of

geotechnical and structural engineering. This centrifuge test data and metadata and the

numerical model of the soil-container-shaker system are archived and curated in

6

NEEScentral data repository. These data archives are publically available at the

NEEScentral website (http://central.nees.org). The experimental data and the OpenSees

numerical models are available for others to use.

1.3 Organization of dissertation

The body of this dissertation is organized into seven chapters and an appendix. A

brief organizational summary of these chapters is given below.

Chapter 1 – Introduction

This chapter provides an overview of research and the scope and organizational

summary of the dissertation.

Chapter 2 – Collaborative research: Centrifuge testing of soil-pile-bridge systems

This chapter provides the summary of three dynamic centrifuge experiments on

soil-pile-bridge systems conducted at the UC Davis centrifuge facility. Details of these

experiments, including collaboration, experimental setup, representative test results,

comparisons with the complementary field shaker experiments, and a brief summary of

test data archives are presented. Numerical simulations of the centrifuge experiments,

performed by the collaborators from the University of Washington, are described and

compared with the experimental results.

Chapter 3 – Comparisons of centrifuge and 1-g shake table models of a pile supported

bridge structure

Comparisons of experimental results and the resolution of issues associated with

comparing physical models of a, two-span pile supported bridge structure tested at

different experimental facilities, at different scale, using different test boundary

conditions, and scaling laws are presented. A comparison between the system response of

7

the bridge model and the component response of individual bents during a series of

shaking events also presented in this chapter.

Chapter 4 – Modeling input motion boundary conditions for simulations of

geotechnical shaking table experiments

The effects of using different input motion boundary conditions on the sensitivity

of numerical simulation results to errors in material properties of a soil model tested on a

centrifuge shaking table are discussed using the numerical simulations of a hypothetical

centrifuge shaking table experiment involving a 1D soil column. The observation that the

sensitivity of simulation results to errors in input data depends on how the boundary

conditions are incorporated in the simulations, which increases the significance of proper

treatment of soil-container-shaker interaction on the simulations.

Chapter 5 – Numerical modeling of a soil - model container - centrifuge shaking table

system

Modeling of dynamics interaction of a soil-model container-centrifuge shaker

system is presented. Results from these simulations are compared with the experimental

results. Sensitivity studies are performed to propagate the uncertainties in modeling

parameters on the simulation results. The effects of soil-container-shaker interaction on

the sensitivities of the predicted site response results are discussed.

Chapter 6 – Towards developing a numerical model of a servo-hydraulic centrifuge

actuation system to predict shaking table response

The functioning of different components and the factors affecting the performance

of a servo-hydraulic actuation system are addressed in general. The actuation mechanism

of the UC Davis centrifuge horizontal shaking table system and the current procedures

8

used for input motion tuning in the experiments are outlined. An OpenSees numerical

model of this actuation system and the typical results from the numerical simulations are

presented. The predicted shaking table response results and the necessity for additional

work on this area are discussed.

Chapter 7 – Conclusions

This chapter provides a summary of the dissertation and its findings, and

recommendations for future work.

Appendix A – Centrifuge test and simulation data archives

This appendix provides details on the data archives of the centrifuge experiments

and the numerical simulations described in this dissertation, including the details of

collaborations with NEESit in the development of the NEEScentral data model and a

brief discussion about the current NEEScentral data model.

9

Fig. 1.1 Collapse of San Francisco/Oakland Bay bridge section, 1989 Loma Prieta earthquake

Fig. 1.2 Unseating of bridge span, Nishinomiya ki bridge, 1995 Kobe earthquake

10

Fig. 1.3 Schematic of a bridge supported on pile foundations shows wide variations in structural types/configurations and soil conditions (after Martin et al. 2002)

Fig. 1.4 Schematic of Soil-Foundation-Structure-Interaction (SFSI) phenomena for a pile supported structure (modified from Gazetas et al. 1998)

11

Fig. 1.5 Overview of the NEES collaborative project to study soil-foundation-structure-interaction

12

Fig. 1.6 3D rendering of a soil model-model container-centrifuge shaking table system

Vertical bearings

FSB container

Soil model

Structural model

Centrifugal force

Actuator

Shaking table

Reaction mass

Fig. 1.7 Representation of soil-container-shaker interaction (after Kutter, 1994)

13

Chapter 2

Collaborative research: Centrifuge testing of soil-pile-bridge systems

This chapter presents three dynamic centrifuge tests on soil-pile-bridge systems

conducted using the 9-m radius NEES geotechnical centrifuge at UC Davis. Details of the

experiments, including collaboration, experimental setup, testing, and representative test

results are presented. This centrifuge testing was part of a larger collaborative project

with the primary objectives of demonstrating the capabilities of the network for

earthquake engineering simulation (NEES) for studying the effects of soil-foundation-

structure interaction (SFSI) on bridges and conducting a comprehensive study of SFSI

effects by integrating analytical and experimental tools at multiple universities.

Numerical simulations of the centrifuge experiments, performed by the collaborators

from the University of Washington, are described and compared with the experimental

results. The centrifuge experiments complement the shaking table and field experiments

conducted at other universities; comparisons between the centrifuge, shake table, and

field shaker experiments are presented here and in Chapter 3.

14

2.1 NEES collaborative research project to study SFSI

The primary objectives of the collaborative research were: (a) to demonstrate the

Network for earthquake Engineering Simulation (NEES) for studying soil-foundation-

structure-interaction (SFSI) (Wood et al. 2004), (b) to conduct a comprehensive study of

SFSI by integrating analytical and experimental tools at multiple universities.

Experimental studies were conducted at four sites across the United States (Fig. 2.1): (a)

1-g shake table experiments at the University of Nevada, Reno (b) centrifuge tests at UC

Davis (c) field tests using the large shakers at the University of Texas, Austin, and (d)

Quasi-static structural component testing at Purdue University. The team of researchers

also included numerical analysts from the University of Washington, the University of

California, Berkeley, and the University of California, Davis, as well as a team of

researchers from Kansas University to coordinate archiving and sharing of data, and an

education and outreach component at San Jose State University. The prototype for the

experimental studies (shown in Fig. 2.2) was a two-span frame of a cast-in-place post-

tensioned reinforced concrete box girder bridge. The span lengths were 120 ft (37 m), and

the substructure was composed of 4 ft (1.2 m) diameter 2-column piers on extended pile

foundations. Due to the size and the complexity of the prototype system, it was

impossible to test a single physical model and reproduce all key aspects of the system

performance. Therefore, the tests at various facilities were intended to provide a means

for comprehensive validation of numerical procedures for analyzing the behavior of a

bridge supported on piles. Details of these different experiments are briefly described

below.

15

2.1.1 Field tests

The field test specimens consisted of two, quarter scale, two column bridge bents

which were constructed at the Capitol Aggregates test site (Kurtuluş et al. 2005). Three

different types of dynamic tests were conducted on these test specimens. Initially, the

specimens were stuck with a modal hammer to induce low-amplitude, free vibration

response. Then the large NEES mobile shaker, T-Rex, was used to induce harmonic

vibrations in the test specimens by exciting the surface of the ground (see Fig. 2.3).

Finally, the hydraulic shaker from the small NEES mobile shaker, Thumper, was attached

to the bent cap and used to excite the specimens harmonically (shown in Fig. 2.4). These

field tests were designed to provide a means of understanding the linear response of the

complete soil-foundation-super structure system during dynamic loading in insitu test

conditions. Further details on these experiments can be found in Black (2005) and

Agarwal et al 2006.

2.1.2 Structural component tests

The structural component test consisted of fixed-base, quarter-scale and half-scale

single shafts and two-column bridge bents (shown in Fig. 2.5). The purposes of these

experiments were to determine the effects of reinforcement detailing, size, and shear span

to depth ratio on the cyclic response of bridge columns. The complete details on these

experiments can be found in Makido (2007).

2.1.3 1-g shake table experiment

The shaking table experiment consisted of a quarter scale model of the two-span

prototype bridge section (shown in Fig. 2.6). The testing was performed in two phases.

16

During low amplitude tests, incoherent, bidirectional ground motion was used to excite

the specimen. Coherent ground motion in the transverse direction of the bridge was used

during the larger amplitude tests. Some additional details of this experiment including the

test set up and comparisons with the complementary centrifuge test model are presented

in Chapter 3 of this dissertation. The comprehensive details of this test program are

provided in Johnson et al. 2006.

2.1.4 Centrifuge experiments

The centrifuge test program included 1/52 scale models of single-pile bents, two-

pile bents and a two-span section of the prototype bridge. Aluminum tubes were used to

model the column and the aluminum blocks were used to represent superstructures (see

Fig. 2.7). Dry Nevada sand, placed at a relative density of 80% in a flexible shear beam

model container, was used to model soil in the experiments. Details of these centrifuge

experiments are given in the following sections.

2.2 Centrifuge test program

2.2.1 Concept of the geotechnical centrifuge modeling

Geotechnical centrifuge modeling has been established as a powerful tool to

investigate the seismic behavior of soil-structure systems. The concept of the

geotechnical centrifuge modeling is described at the web site of the Center for

Geotechnical Modeling, UC Davis as follows: “Geotechnical materials such as soil and

rock have nonlinear mechanical properties that depend on the effective confining stress

and stress history. The centrifuge applies an increased "gravitational" acceleration to

physical models in order to produce identical self-weight stresses in the model and

17

prototype. The one to one scaling of stress enhances the similarity of geotechnical models

and makes it possible to obtain accurate data to help solve complex problems such as

earthquake-induced liquefaction, soil-structure interaction and underground transport of

pollutants. Centrifuge model testing provides data to improve our understanding of basic

mechanisms of deformation and failure and provides benchmarks useful for verification

of numerical models” (http://cgm.engineering.ucdavis.edu/). A set of scaling laws are

used to convert model-scale data to appropriate prototype-scale data. The details on these

scaling laws can be found in (Schofield, 1981 and Kutter, 1992). All the centrifuge

experiments were performed at 52g centrifuge acceleration. All the results presented in

this chapter are in prototype scale unless otherwise specified. Table 2.1 lists the scale

factors which were used to convert model quantities to prototype scales.

2.2.2 Model configurations

A series of three centrifuge test series was constructed and tested. The objectives

of these experiments were to complement the field and laboratory test conducted

elsewhere and to provide insight into geotechnical-oriented aspects of the soil-pile-bridge

systems. A brief summary of these three experiments is presented below.

2.2.2.1 Centrifuge test series MIL01

This test series included a scale model of a two-bay prototype bridge structure

with the sloping ground conditions that were assumed to exist at the site of the prototype

bridge structure. Due to the sloping ground, the two bays were supported by three bents,

but the clear height between the soil and bridge deck was different for each bent. The

centrifuge test package also included an independent two-pile bent corresponding to

18

medium-height bent in the prototype structure, another independent medium height bent

which is fixed at the bridge deck and a pile cap at the ground surface level, and a single

pile corresponding to pile in the tallest bent. The model layout of the MIL01 test series,

including the details of the structural models are shown in Fig. 2.8 and in Fig. 2.9. The

1/52 scale model of the two-bay prototype bridge structure in this centrifuge test series

complements the ¼ scale model of the prototype bridge structure tested in the 1-g shake

table facility at the University of Nevada, Reno.


This test series included pile structures that allow investigation of the response of

two-pile bents. The model included four identical two-pile bents oriented at angles of 0,

30, 60, and 90 degrees to the direction of shaking, and a single pile supporting a weight

equal to the weights supported by the individual piles in the two-pile bents (depicted in

Fig. 2.10). As shown in Fig. 2.10, the above ground clear height was 75 mm (in model

scale) for all the bents and the single pile. This test series experiments provided

experimental data on the response of a two-pile bent to motions coming from different

angles in which the pile bent would have different relative flexural and axial response.

This data complements data obtained from quarter scale field tests performed at

University of Texas at Austin, in which the vibration source (T-Rex) was moved to

different locations relative to the two-pile bent.


This test series included pile structures that allow investigation of the dynamic

response of two-pile bents and single piles (4 two-pile bents and 3 single piles). The

model layout of the MIL03 test series and the 3-D rendering of the model set-up are

19

shown in Fig. 2.11. The configurations of structural models used in the experiment are

depicted in Fig. 2.12. As shown in above figures, the longer axes of the two-pile bents 2-

LL-Hy and 2-SS-Hy were oriented in the direction of shaking and those of bents 2-LS-Lt

and 2-LS-Hy were oriented 90 degrees to the direction of shaking. The bents 2-LL-Hy

and 2-SS-Hy were identical above the ground surface; however, their pile embedment

lengths were different. The bent 2-LL-Hy had an embedment length of 12.1D and the

bent 2-SS-Hy had an embedment length of 5D, where D is outer diameter of piles (22.71

mm in model scale). The bents 2-LS-Lt and 2-LS-Hy were identical below the ground

surface. Each of the above bents was supported by a longer pile (12.1D embedment) and

a shorter pile (5D embedment). In this case, it was expected to induce torsional response

in the bent by supporting one side on shorter pile and the other on a longer pile. An extra

mass attached to the bent 2-LS-Hy to support 1.5 times “heavier” mass than” lighter”

bent 2-LS-Lt. The three single piles (1-S, 1-M, and 1-L) were designed to have different

embedment lengths, the embedment lengths of these piles were 5D, 7.5D, and 12.1D,

respectively. The primary purpose of this experiment was to provide experimental data to

the collaborators in the University of Washington to validate their OpenSees

computational models of soil-pile-superstructure systems.

2.2.3 Design of structural models

The design of the centrifuge model structures was based on the dimensions and

properties of the columns, bents, and deck from the 1-g shaking table experiment. All

model piles were made of 6061-T4 (E=68.5 GPa; yield strength=130 MPa) and 6061-T6

(E=68.5 GPa; yield strength=255 MPa) aluminum tubes of 19.05 mm diameter (0.991 m

prototype) and a wall thickness of 0.889 mm (0.046 m prototype). Table 2.2 lists the

20

aluminum type used for the model piles in all three centrifuge experiments. Strain gages

were affixed to piles and piles were covered with plastic shrink-wrap. The outer diameter

of composite pile was 22.71 mm (1.181 m in prototype scale). The model pile used in the

MIL01 test series were reused in other two centrifuge experiments. All the bent blocks

were made of 6061-T6 aluminum (E=68.5 GPa; yield strength=255 MPa). Further details

of the design of structures and the dimensions and properties of the model structures can

be found in the centrifuge test series data report Ilankatharan et al. 2005.

2.2.4 Model preparation and instrumentation

The soil chosen for the centrifuge test was dry Nevada sand (80% relative

density). The relative density of Nevada sand was picked to reasonably match the low-

strain shear wave velocity profile of the Capitol Aggregates test site, Austin. Fig. 2.13

shows the shear wave velocity profile of the test site and the 80% relative density Nevada

sand calculated based on the data available in the literature (Arulnathan et al. 2000). The

field experiments are conducted under 1-g condition; while the centrifuge experiments

are conducted under increased gravity condition. Therefore the scaling is complicated

between two experiments, since we have different soils and different confining pressures

in the field and the centrifuge experiments. The field test model-bent has an embedment

length of 3.6 m (12 times the diameter of the column) and the centrifuge model bent has

embedment length of 14 m (approximately 12 times the diameter of the pile). It was

considered that the discrepancies between the shear-wave velocity profiles shown in Fig.

2.13 might counterbalance the differences in strength of soil due to the differences in

vertical stress fields in the field and the centrifuge experiments (i.e., vertical stress fields

21

are off by a factor of 4 approximately). Based on this assumption, it was considered that

the mismatch of shear wave velocity profiles in Fig. 2.13 is acceptable.

The dense sand was placed by dry pluviation. When the soil was 50 mm below

the final soil profile, accelerometers were attached on the piles and the piles were

attached to the bent caps and pushed in pairs into the soil by hand about half way. A

hammer was then used to drive the bents to the desired depth. A bubble level was used to

ensure that piles are driven in vertically. Then bent caps were removed and the barrel

pluviator was used to place top soil layer to produce soil around and above the

accelerometers to produce the final soil profile.

The model was heavily instrumented with accelerometers, linear potentiometers,

and strain gage bridges to measure the translation, rotation and bending response of the

foundations, columns, and bent cap (see Fig. 2.14). Additional accelerometers were

embedded in the soil to measure soil response during dynamic loading. Vertical linear

potentiometers were used to measure ground surface settlement during shaking. In

addition to the above conventional instrumentation, models were instrumented with high

speed video cameras and MEMS accelerometers using the UC Davis high-speed wireless

data acquisition system (shown in Fig. 2.15). Performance of the newly developed UC

Davis high-speed wireless data acquisition system was evaluated in these centrifuge test

series as it was first introduced for centrifuge test applications at the UC Davis centrifuge

facility. Fig. 2.16 presents a comparison of data recorded with traditional wired data

acquisition system and the wireless data acquisition (transducers were placed at nearly

identical locations for direct comparison).

22

2.2.5 Ground motion protocols

Each centrifuge models was subjected to a series of shaking events, beginning

with very low-level shaking events to characterize the low-strain response of the soil and

soil-pile-superstructure systems and progressive to very strong motions with peak base

accelerations of up to 0.75g. Input base motions included step displacement waves,

frequency sweeps and scaled versions of recorded earthquake motion during the 1994

Northridge Earthquake at the CDMG station 24389, Century City LACC North, 090. Fig.

2.17 shows the time histories and response spectra (5% damping) of some of the input

motions used in the experiments. The entire shaking schedule is shown in Table 2.3.

2.3 Representative results from centrifuge experiments

Representative results from some selected centrifuge shaking events are presented

in this section. The complete set of centrifuge test data and metadata is presented in the

test series data report Ilankatharan et al. (2005), which is archived in NEEScentral data

repository (http://central.nees.org).

2.3.1 Soil site response

Fig. 2.18 presents typical site response results characterized by a vertical array of

horizontal accelerometers placed in the middle of the model container. These measured

soil site response results were used to verify the numerical simulations of centrifuge

experiments. Comparisons between the measured and predicted (using 1-D shear beam

simulation model) site response results are presented later in this chapter.

23

2.3.2 Horizontal accelerations

Time histories and response spectra (5% damping) of recorded horizontal

accelerations at different locations of model during a centrifuge shaking event is shown

in Fig. 2.19. As shown in Fig. 2.19, the measured free-field soil motion at 2.5m below the

ground surface shows greater amplification (with respect to the measured base motion) in

the intermediate frequency range compare to the higher frequency (short period) range.

Measured pile motion (from an accelerometer directly attached to pile) at 2.5 m below

ground surface is nearly the same as the measured free-field soil motion at that depth.

This observation indicates that the kinematic soil-pile interaction effects (Gazetas et al.

1998) are not very significant for this problem. As expected, the superstructure is not

excited by the higher frequency content of the base motion and shows a high response

peak in the lower frequency (long period) range.

2.3.3 Vertical accelerations

Fig. 2.20 presents the measured vertical motions at the container base and at 2.6

m (in prototype scale) below the ground surface at both ends of the container. It is clear

from Fig. 2.20 that the time histories of measured vertical accelerations are 180 degrees

out of phase, show rocking response of the container. In addition, for this medium-level

shaking event, the measured peak vertical base motion is 42% of the peak base

(horizontal) motion and the measured peak vertical soil motion is 75% of the peak base

motion.

24

2.3.4 Bending moment, shear force and sub-grade reaction

Fig. 2.21 presents representative results for measured bending moment and

calculated shear force and sub-grade reaction distributions of bridge bents tested in test

MIL01. The distribution of sub-grade reaction was obtained by double differentiating the

bending moment distribution with respect to depth at each time step of the event. The

weighted-residual technique, developed by Wilson (1998), was used to double

differentiate bending moment distribution to obtain sub-grade reaction. As shown in Fig.

2.21, the magnitude of shear forces in the pile and soil reactions are smaller for piles with

large clear heights; thus depth to maximum bending moment decreases as clear height

increases. Variation of normalized depths (with respect to diameter) to maximum bending

moment with normalized clear heights for increasing shaking levels is shown in Fig. 2.22.

Fig. 2.22 indicates that maximum moment develops at a greater depth for large

accelerations and that the depths are dependent on clear heights.

2.3.5 Superstructure accelerations of MIL02 bridge bents

Representative results for superstructure responses (in terms of spectral

accelerations) of bridge bents oriented different directions to base shaking, during a

frequency sweep input motion, are presented in Fig. 2.23. As shown in Fig. 2.23,

superstructure response of Bent A (transverse axis of the bent oriented in the direction of

shaking) dominates by the transverse response and it shows negligible longitudinal

response. As the angle between the transverse axis and the direction of shaking increases,

transverse response of bridge bent decreases and the longitudinal response increases.

Compared to the natural period of longitudinal response of bent, that of the transverse

response is closer to the predominant period of the input motion (approximately 0.3 sec).

25

The large difference between the peaks of transverse response of Bent A and the

longitudinal response of Bent D may be attributable to the close proximity of natural

period of bridge bent (for transverse response) to the predominant period of the input

motion.

2.4 Comparisons with UT Austin field tests

The MIL02 test series, in which the bridge bents were oriented to the different

direction of base shaking, was designed to facilitate comparison with field tests

performed at the University of Texas at Austin, in which the vibration source (T-Rex)

was moved to different locations relative to the model bridge bent. Fig. 2.24 compares

the responses of the bridge bents in the above two experiments during a frequency sweep

input motion. For this case, excitation was applied in the transverse directions of the

bridge bents in both experiments (as indicted in Fig. 2.25). As shown in Fig 2.24, test

specimen tested in the centrifuge experiment exhibits a significant transverse response

and a negligible longitudinal response and the specimen tested in the field test shows a

significant transverse response and a noticeable longitudinal response. It is important to

note that the axis scales of Fig. 2.24(a) and Fig. 2.24(b) are different; in particular, the

period scales differ by a factor of 15. As the field shakers which have maximum force

outputs in a higher frequency range (http://nees.utexas.edu), the natural frequencies of

the field test specimens were altered (by reducing the bent-cap masses) to increase the

response to the excitation. This explains why the range of frequencies of response of field

test specimen is significantly larger than that of centrifuge test specimen. Therefore, it is

difficult to make direct comparisons between both experiments. However, both

experiments provide unique data about the response of prototype bridge structure. These

26

unique data sets were used to calibrate the simulation methods for seismic soil-

foundation-structure interaction problems (Shin 2007 and Jie 2007).

2.5 Simulations of centrifuge models

Numerical simulations of the centrifuge experiments were performed, using

OpenSees (Open System for Earthquake Engineering Simulation,

http://opensees.berkeley.edu/index.php), by the collaborators from the University of

Washington (Shin et al, 2006 and Shin 2007). A brief outline of these simulation models

and some of the comparisons of simulation results with the experimental results are

presented in the following sections.

2.5.1 Outline of simulation models

Dynamic Beam-on-Nonlinear-Winkler Foundation (BNWF) model, using p-y, t-z,

and q-z interface springs (Boulanger et al. 1999), coupled with a 1-D shear beam soil

column was used model seismic soil-pile-structure interaction in OpenSees (depicted in

Fig. 2.26 and Fig. 2.27). In OpenSees, soil was modeled using the

PressureDependMultiYield (PDMY) elasto-plastic material model proposed by Yang et

al. (2003) and the pile was modeled using the non-linear fiber beam column elements.

Details of modeling parameters of PDMY material model, interface springs, and beam

column elements which were used in the simulations can be found in Shin (2007). In

these simulations, the measured motion at the base of the container in the experiment was

used as prescribed motion at the bottom nodes of soil column to impart seismic

excitation.

27

2.5.2 Predicted site response

Representative simulation results for predicted site responses (horizontal free-

field soil motions) during two different intensity motions (in test series MIL02) are

shown in Fig. 2.28, in terms of acceleration response spectra. Depths to the accelerometer

locations from the ground surface and the intensities of (peak base accelerations) of input

motions are shown. It is clear from above figure that the predicted and the measured

motions are in good agreement at deeper depths (closer to the input specification nodes).

However, the simulated response significantly differs from the measured response closer

to the ground surface (Fig. 2.28(a) and Fig. 2.28(e)). For example, peaks in the spectral

accelerations of measured motions near to 0.25 sec (4 Hz) are not well captured in the

simulations. Fig. 2.29 compares the time histories of the predicted soil accelerations with

the experimental results in the MIL03 test series. It is again apparent that the results are

in good agreement at deeper depths and they show significant discrepancies closer to

ground surface. Fig. 2.30 compares measured and the predicted soil response at 2.6 m (in

prototype scale) below the ground surface due to a frequency sweep input motion. As

shown in above figure, Fourier amplitudes of predicted soil motion are in good agreement

with the experimental results in the frequency ranges of (0-1Hz) and (2.4-3.2Hz);

however, discrepancies between the Fourier amplitudes are significant in the frequency

range of (1-2.4Hz) which encompasses the natural frequency of the soil model. Further,

the ratios of Fourier amplitudes (transfer function) between the soil motion and the base

motion show the predominant peaks at 1.5 Hz in the experiment and at 1.8 Hz in the

simulation (i.e., the predominant frequency of soil column is 20% over predicted by the

simulation).

28

2.5.3 Predicted response of individual bents and single pile

Fig. 2.31 compares the time histories and Fourier amplitudes of horizontal

motions at the bent-cap of a two-pile individual bent (Bent 5) in the experiment (MIL01)

and in the simulation, during a medium-level Northridge event. For the same event, Fig.

2.32 compares the measured and the calculated maximum bending moment at one of two

piles of Bent 5. The above Figures suggest that the OpenSees model of the two-pile bent

reasonably predicts the bent-cap motions and the maximum bending moments during this

medium-level shaking event.

Fig. 2.33 compares the measured and the calculated peak accelerations of

superstructure (bent-cap) in a single bent and a single pile and the peak accelerations of

soil motions at 2.5 m below the ground surface in MIL01 test series, during different

intensity base motions. As the intensity of base motion increases, experimental results of

the superstructure responses in both structures exhibit non-linear behavior of soil-pile-

superstructure systems (i.e., rate of change in peak accelerations of the superstructure

with respect to the rate of change in peak base accelerations decreases in Fig 2.33(a) and

Fig 2.33(c)). This non-linear behavior is reasonably captured in the OpenSees

simulations. In addition, peak superstructure accelerations calculated from the

simulations are in reasonable agreement with the experimental measurements. From Fig.

2.33(b) and Fig. 2.33(d), it is evident that as the intensity of base motion increases, soil

model in the experiment exhibits non-linear response (which is captured in the

simulations). However, the peak accelerations of soil motions (at 2.6 m below ground

surface) calculated from the simulations are significantly different from experimental

29

results (except for low-intensity events, 30% to 40% different in some of the other

events).

2.5.4 Predicted response of two-span bridge model

Representative results from simulations of the two-span bridge model tested in the

MIL01 test series are shown in Fig. 2.34 and Fig. 2.35. At different bents, Fig. 2.34

compares the time histories of bent-caps motions predicted in the simulation with the

experiment, during a medium-level (peak base acc=0.25g) Northridge event. Fig. 2.35

compares the spectral accelerations of above motions and the maximum pile bending

moment distribution in one of the two piles of each bent. As shown in above figures, the

OpenSees bridge model (depicted in Fig. 2.27) reasonably predicted the bent-cap motions

and the maximum pile bending moments measured in the experiment.

Fig. 2.36 presents distributions of soil resistance along the depth of piles at the

time of maximum bent-cap displacement, during three different intensity Northridge

shaking events. As described earlier (in Fig. 2.21), experimental soil resistance

distributions were calculated by double differentiating measured pile bending moment

data and those of simulations were obtained by p-y spring forces. It is clear from above

figures that the back-calculated soil resistances from the experiment are greater than the

OpenSees and the Reese’s (1974) ultimate soil resistance values at shallow depths. In

addition, at deeper depths back-calculated soil resistance values are significantly different

from OpenSees values. For instance, for short bent (Bent 1) during the medium-level

shaking event (peak base acc=0.25g), the maximum soil resistance obtained from the

simulation is nearly two times greater than that of back-calculated value from the

experiment (see Fig. 2.36 (a)).

30

2.5.5 Sensitivity analyses

Shin (2007) also performed sensitivity analyses to study the sensitivity of

simulation results to uncertainties in modeling parameters. Outline of these sensitivity

studies are shown in Tables 2.4 and 2.5 and in Fig. 2.37. Representative results from two

runs of these sensitivity analyses are presented in Figs. 2.38 and 2.39. The complete

details of these analyses can be found in Shin (2007).

Fig. 2.38 shows the effect of change in soil motion on the calculated response of a

two-pile bent. As shown in Fig. 2.38(a), reference shear modulus and the soil density of

the PDMY materials were varied from the base line parameters (given in Table 2.4) to

vary soil motion. Shin (2007) showed that the changes in soil stiffness and the soil mass

density significantly affect the frequency contents of the soil motion (at 2.6 m below

ground surface) at higher frequencies (above 2 Hz). These changes in frequency content

of the soil motion are not reflected on the superstructures response, because the transfer

function between the superstructure motion and the soil motion is less than unity (de-

amplification in response) at higher frequencies (nearly above 1.5 Hz). Based on the

above observation, it was concluded that the predicted superstructure motions and

bending moments are not very sensitive to change in soil motion for this case, which was

the reason for good comparisons of superstructure response and pile bending moments

obtained in Fig. 2.31, Fig. 2.32, and Fig. 2.33 (a) for a relatively poor prediction of soil

motion obtained in Fig. 2.33 (b). Sensitivities of simulation results to changes in ultimate

soil resistance (+/- 20% change in pult) are shown in Fig. 2.39. From the above figure, it

was concluded that the predicted peak acceleration of superstructure motion was not

31

affected by the changes in pult and the predicted pile bending moment distribution was

slightly affected by the changes in pult.

2.5.6 Simulations of MIL02 and MIL03 test series

Numerical modeling of bridge bents tested in MIL02 and MIL03 test series also

performed by the collaborators from the University of Washington. As described earlier,

MIL02 test series involved individual two-pile bents oriented different directions to the

base shaking and the MIL03 test series involved individual two-pile bents and single-pile

bents with different embedment lengths, bent-cap masses, and structural configurations.

Details of these simulations including the modeling strategies, modeling parameters, and

the comparisons of simulation results with experimental results are presented in Shin et

al. (2006) and Shin (2007).

2.6 Simulation of the prototype bridge structure

Computational simulations of the prototype bridge structure (depicted in Fig. 2.2)

were performed by the collaborators from the UC Davis, UC Berkeley, and the

University of Washington. The unique data sets obtained from all four experiments (in

Fig. 2.1) were used in the model developments, verifications and validations of these

simulations. 3-D finite element model of one of the simulations of the prototype soil-pile-

bridge system is depicted in Fig. 2.40. Comprehensive details of these simulations can be

found in Jie (2007), Ranf (2007), and Dryden (2008).

32

2.7 Centrifuge test data archives

One of the goals of this collaborative research was to develop curated data

repositories of the experimental and simulation data of SFSI problems of the prototype

bridge structure. NEEScentral (http://central.nees.org), the centralized data repository of

the NEES which was developed by NEESit (http://it.nees.org), was used to archive

centrifuge test data along with the associated metadata (data, which describes the data).

On the development of the current model of the NEEScental, NEESit was collaborated

with the researchers from the University of California, Davis. One of the driving forces of

the development of current version of the NEESit data model was to reproduce one of the

centrifuge test data report (Ilankatharan et al. 2005). The ultimate goal of the

development of NEEScentral is to facilitate the end-to-end work flow of the earthquake

engineering data. An example of end-to-end usage of NEEScentral application is depicted

in Fig. 2.41. As described in Van Den Einde at al. 2007, the primary objectives of end-to-

end usage of data are to allow easy upload of data/metadata by the researchers, novel

search of the data sets within the repository, the ability of download curated data sets in

formats that allow for easy ingestion of the data/metadata into community developed

visualization or data processing programs. In this context, the centrifuge data archives

were used to demonstrate the usage of end-to-end workflow using a data viewer (N3DV)

developed by the researchers at UC Davis (http://neesforge.nees.org). Fig. 2.42 shows an

example screen shot of N3DV application for the data from the MIL01 centrifuge test

series. Further details on the centrifuge test data archives and the archives of the

simulations which are presented in Chapter 5 of this dissertation can be found in

Appendix A of this dissertation.

33

2.8 Summary

The dynamic centrifuge experiments on soil-pile-bridge systems presented in this

chapter were part of a multi-university collaborative research project utilizing NEES with

the goal of investigating the effects of soil-foundation-structure interaction (SFSI) while

demonstrating NEES research collaboration. Much had been learned from this

collaborative research both with respect to means for effective research collaboration and

investigating SFSI effects by integrating experimental and analytical tools.

2.8.1 Research collaboration

Unlike most scientific research that has been led by only one to few collaborators

working on the same project and at the same test facility, multi-institution, multi-

investigator collaborative research requires particular attention to issues related to the

involvement, coordination, and cooperation of a large number of led researchers and their

support staff. Therefore, effective communication tools to facilitate information exchange

and decision making are essential to effectively conduct a large-scale collaborative

research. Sixteen principal and co-principal investigators from ten universities were

involved in the collaborative research project described in this chapter. As indicated

earlier, in addition to the tasks with experimental components and simulation

components, several other tasks related to data tools and repository, education and

outreach, and information technology were addressed in this research. Periodic video and

audio conference calls in addition to several face-to-face meetings were held to facilitate

information exchange and decision making. These were in addition to extensive use of

group emails and one-on-one interactions through emails and phone calls. Arguably,

34

most valuable research experience was obtained from working on this collaborative

research environment.

Further, the design of test elements to account for different test boundary

conditions and test scaling laws for structural modeling and geotechnical modeling was

challenging. The design process required cross-disciplinary interaction between

geotechnical and structural engineers. The design of test elements to the satisfaction of

the cross-disciplinary research team was an extremely valuable collaborative learning

experience.

2.8.2 Centrifuge experiments

The centrifuge experiments presented in this chapter involved 1/52 scale models

of two-pile bents, single piles and a two-span segment of bridge with 20 different

superstructure configurations tested under varying earthquake characteristics (level of

shaking, frequency content, and wave from). These experiments produced unique data

sets that span the disciplines of geotechnical and structural engineering. Some of these

data complement the data obtained from other experiments. The data from the centrifuge

experiments was compared and combined with the data obtained from other experiments

to provide integrated analytical models for SFSI problems of soil-pile-bridge systems.


comparing physical models of the two-span segment of the bridge model tested at the

geotechnical centrifuge and the 1-g shaking table facilities are presented in the next

chapter of this dissertation. In addition, data from one of the centrifuge test (MIL01) was

used to compare the system (three-bent response) of the bridge model to the individual

bent response. Details of these comparisons also presented in the next chapter.

35

Only a fraction of centrifuge test data is presented in this chapter. All centrifuge

test data and metadata is archived and curated in NEEScentral data repository. The data

archives are available at the NEEScentral website (http://central.nees.org).

2.8.3 Simulations of centrifuge experiments

As indicated earlier, numerical simulations of all the centrifuge experiments were

performed by the collaborators from the University of Washington. These simulations

employ Dynamic Beam-on-Nonlinear-Winkler Foundation (BNWF) models, using p-y, t-

z, and q-z interface springs coupled with a 1-D shear beam soil column, to model seismic

soil-pile-structure interaction. Some of these simulations were performed prior to the

experiments and during the experiments. Results from these pre-test and real-time

simulations were valuable in designing test specimens and loading protocols (i.e.

selection of earthquake characteristics). Some of the comparisons between the results

from the post-test simulations and experiments are presented in this chapter. These

comparisons suggest that overall the simulations reasonably predicted the superstructure

motions and the maximum pile bending moments. However, significant discrepancies

(especially close to ground surface) between the predicted and measured soil motions

were observed from these comparisons. Also, back-calculated soil resistances in the

experiments from the bending moment data were significantly different from the soil

resistances obtained from the simulations (from p-y spring forces).

Shin (2007) also performed sensitivity analyses to study the sensitivity of

simulation results to uncertainties in modeling parameters. As shown in Table 2.4, these

sensitivity analyses considered simulations of a single pile and a two-pile bent.

Representative results from two runs of these sensitivity analyses (for the two-pile bent)

36

were presented in this chapter. For the structural models and ground motion

characteristics considered in these sensitivity studies, it was concluded that the simulated

superstructure motions and maximum pile bending moments are not very sensitive to

change in predicted soil motions. The predicted peak acceleration of superstructure

motion was not sensitive and the predicted pile bending moment distribution was only

slightly affected by 20% changes in ultimate soil resistance, pult.

2.8.4 Effect of modeling boundary conditions on the sensitivity of predicted site

response

As mentioned earlier, the numerical simulations presented above employed a 1-D

shear beam shear-beam type finite element model to simulate soil site response. Effects

of model container on the soil site response were not explicitly modeled in these

simulations. The effect of mass of the container on the inertia forces was accounted (by

increasing unit weight of soil by 30%); however, flexibility of the container and the

stiffness of the vertical bearing supports at the base of the container were not modeled in

these simulations. In addition, these simulations adapted the measured motion at the base

of the container as a prescribed input motion for dynamic excitation. It is evident from

the presented comparisons in this chapter that, in some cases, the predicted soil motions

(especially close to ground surface) from above simulations are significantly different

from experimental results. Understanding the discrepancies of these predicted site

response results motivated the analyses presented in the second part of this dissertation.

The centrifuge experiments involve different dynamic components (a dynamic

system), such as the test specimens, the soil model, the model container, the shaking

table, and its reaction mass. All of the different components of dynamic system, with

37

their own resonant frequencies, interact with the soil model during dynamic excitation,

some absorbing energy and others allowing undesired modes to affect the response

observed in the experiment. This interaction between the soil model and other

components of the dynamic system might attenuate or exaggerate the discrepancies in

response of the experiment and the numerical simulation. A fundamental question then

arises: ‘How should we assess the quality of a comparison between an experiment and a

simulation results?’ To answer this fundamental question, it would be essential to

understand the sensitivity of simulation results (outputs) to uncertainties in modeling

parameters (inputs). In this context, it was hypothesized that the “sensitivity of simulation

results to uncertainties in modeling parameters depends on how the boundary conditions

are incorporated in the simulations”.

The second part of this dissertation is devoted to investigate the above aspects of

the problem. Chapter 4 of this dissertation presents simulations of a hypothetical

centrifuge shaking table experiment to prove above hypothesis. Site response simulations

of one of the centrifuge experiment (MIL03 test series) which involve detailed modeling

of different components of the experimental system are presented in chapter 5 of this

dissertation. Chapter 6 describes the modeling aspects of a servo-hydraulic centrifuge

actuation system.

38

Table 2.1 Scaling factors used in this research

Quantity Prototype Scale/Model Scale

Stress 1

Acceleration 1/52

Length 52

Mass 523

Time 52

Force 522

Table 2.2 Aluminum types used for the model piles in the centrifuge experiments

Test series Name of bent/pile Aluminum type

MIL01

Bent 1

Bent 2

Bent 3

Bent 4

Bent 5

Single Pile 1

6061-T4

6061-T4

6061-T4

6061-T6

6061-T6

6061-T6

MIL02

Bent A

Bent B

Bent C

Bent D

Single Pile 2

6061-T6

6061-T4

6061-T4

6061-T6

6061-T6

MIL03

2-LL-Hy

2-SS-Hy

2-LS-Hy

2-LS-Lt

1-L

1-M

1-S

6061-T4

6061-T4

6061-T6

6061-T6

6061-T4

6061-T6

6061-T4

39

Tabl

e 2.

3 Su

ite o

f cen

trifu

ge sh

akin

g ev

ents

Even

t ID

In

put

mot

ion

Peak

ba

se

acc

(g)

Even

t ID

In

put m

otio

n Pe

ak

base

ac

c (g

) Ev

ent I

D

Inpu

t mot

ion

Peak

ba

se

acc

(g)

MIL

01_0

1

MIL

01_0

2

MIL

01_0

3

MIL

01_0

4

MIL

01_0

5

MIL

01_0

6

MIL

01_0

7

MIL

01_0

8

MIL

01_0

9

MIL

01_1

0

MIL

01_1

1

MIL

01_1

2

MIL

01_1

3

MIL

01_1

4

MIL

01_1

5

MIL

01_1

6

Step

wav

e

Step

wav

e

Nor

thrid

ge

Nor

thrid

ge

Nor

thrid

ge

Nor

thrid

ge

Nor

thrid

ge

Step

wav

e

Nor

thrid

ge

Nor

thrid

ge

Step

wav

e

Nor

thrid

ge

Nor

thrid

ge

Nor

thrid

ge

Nor

thrid

ge

Nor

thrid

ge

0.01

0.02

0.02

0.05

0.18

0.22

0.07

0.04

0.03

0.07

0.04

0.03

0.07

0.23

0.57

0.74

MIL

02_0

1

MIL

02_0

2

MIL

02_0

3

MIL

02_0

4

MIL

02_0

5

MIL

02_0

6

MIL

02_0

7

MIL

02_0

8

MIL

02_0

9

MIL

02_1

0

MIL

02_1

1

MIL

02_1

2

MIL

02_1

3

MIL

02_1

4

MIL

02_1

5

MIL

02_1

6

Step

wav

e

Nor

thrid

ge

Ste

p w

ave

Swee

p (5

0-12

5Hz)

Swee

p (8

0-20

0Hz)

Swee

p (1

60-4

00H

z)

Nor

thrid

ge

Swee

p (5

0-12

5Hz)

Sine

wav

e (2

0Hz)

Nor

thrid

ge

Nor

thrid

ge

Step

wav

e

Nor

thrid

ge

Swee

p (7

-333

Hz)

Swee

p (7

-333

Hz)

Swee

p (7

-333

Hz)

0.04

0.02

0.04

0.02

0.02

0.02

0.03

0.08

0.01

0.08

0.26

0.60

0.78

0.04

0.06

0.40

MIL

03_0

1

MIL

03_0

2

MIL

03_0

3

MIL

03_0

4

MIL

03_0

5

MIL

03_0

6

MIL

03_0

7

MIL

03_0

8

MIL

03_0

9

MIL

03_1

0

MIL

03_1

1

MIL

03_1

2

MIL

03_1

3

MIL

03_1

4

MIL

03_1

5

Step

wav

e

Step

wav

e

Nor

thrid

ge

Swee

p (7

-333

Hz)

Swee

p (5

-190

Hz)

Swee

p (1

90-5

Hz)

Step

wav

e

Nor

thrid

ge

Nor

thrid

ge

Swee

p (1

90-5

Hz)

Swee

p (1

90-5

Hz)

Swee

p (1

90-5

Hz)

Swee

p (1

90-5

Hz)

Swee

p (5

-190

Hz)

Nor

thrid

ge

0.04

0.04

0.03

0.03

0.02

0.03

0.03

0.07

0.26

0.08

0.25

0.03

0.25

0.25

0.75

40

Table 2.4 Input parameters of the base-line model of the sensitivity analyses (Shin 2007)

Table 2.5 Selection of input variables in the sensitivity analyses (Shin 2007)

41

Fig. 2.2 Example of prototype location in a multi-span bridge

Fig. 2.1 Overview of the earthquake engineering components of the NEES collaborative project to study soil-foundation-structure-interaction

42

Fig. 2.3 Seismic excitation of the field test specimen using T-Rex (after Black 2005)

Fig. 2.4 Seismic excitation of the field test specimen using Thumper (after Black 2005)

43

(a)

(a)

(b)

Fig. 2.5 (a) 3-D rendering of test set-up and (b) photograph of a test specimen of the structural component tests at the Purdue University (after Makido 2007)

44

(a)

(b)

Fig. 2.6 (a) 3-D rendering of test set-up and (b) photograph of a test specimen of the 1-g shaking table experiment (after Johnson 2006)

45

Fig. 2.7 Photograph of the 1/52 scale models of the test specimens used in the first series of centrifuge experiments

Bent 1 (short)

Bent 2 (tall) Bent 3 (medium)

Bent 5

Bent 4

Single pile 1

Fig. 2.8 3-D rendering of model layout of the centrifuge test series MIL01

46

70

0.0

220.

011

0.0

120.

0

50.0

124.

075

.0

20°

23°

140.

5

20°

40.0

23°

75.0

230.

023

0.0

290.

029

0.0

146.

5

300.

0

65.0

TO

P V

IEW

TO

P V

IEW

FRO

NT

VIE

WFR

ON

T V

IEW

Ben

t 1B

ent 2

Ben

t 3B

ent 4

Sing

le

Pile

Ben

t 5

All

dim

ensi

ons a

re in

mm

226.

027

5.0

275.

022

6.0

534.

255

9.0

(a) T

wo-

span

brid

ge m

odel

(b

) Tw

o-pi

le b

ents

and

sing

le p

ile

Fig.

2.9

Det

ails

of s

truct

ural

mod

els i

n M

IL01

test

serie

s

47

75.0

0

534.

01

75.0

0

All

Dim

ensi

ons a

re in

mm

BE

NT

D

BE

NT

BB

EN

T C

SIN

GL

EPI

LE

2

BE

NT

A

PLA

N V

IEW

XX

30¡Æ

60¡Æ

90¡Æ

ELEV

ATI

ON

AT

X-X

503.

75

1800

.00

790.

00

1650

.00

(a)

Ben

t B

Ben

t C

Ben

t A

Sing

le p

ile 2

Ben

t D

(b)

Fig.

2.1

0 (a

) Sch

emat

ic a

nd (b

) Ren

derin

g of

mod

el la

yout

of M

IL02

test

serie

s

48

ELEV

ATI

ON

AT

X-X

PLA

N V

IEW

1-L

2-L

S-L

t

2-L

S-H

y

All

dim

ensi

ons a

re in

mm

1-S

2-SS

-Hy

534.

0

75.0

XX

2-L

L-H

y

1-M

75.0

1650

.0

790.

0

1800

.0

(a)

2-L

S-H

y

1-L

2-L

L-H

y

2-L

S-L

t

2-SS

-Hy

1-M

1-S (b)

Fig.

2.1

1 (a

) Sch

emat

ic a

nd (b

) Ren

derin

g of

mod

el la

yout

of M

IL03

test

serie

s

49

(a)

(b)

Shaking direction

Shaking direction

2-LL-Hy 2-SS-Hy 1-L 1-M 1-S

2-LS-Hy 2-LS-Lt

Fig. 2.12 Configurations and embedment lengths of structural models used in MIL03 test series

50

0

2

4

6

8

10

12

14

16

18

20

0 50 100 150 200 250 300 350 400 450 500

Shear wave velocity (m/s)

Dep

th (m

)Test siteNevada sand Dr=80%

Vs=65.8(σm') 0̂.25Arulnathan et al.(2000)( ) 25.0'

m8.65Vs σ=

Arulnathan et al. 2000

Fig. 2.13 Shear Wave Velocity Profile of Capitol Aggregate Test Site, Austin and Nevada Sand (Dr = 80%)

51

124

50

40

140

Horizontal Accelerometer

Vertical Accelerometer Vertical Linear Potentiometer

All Dimensions are in mm

TOP VIEW

Horizontal Linear Potentiometer

SECTION AT B - B

486

560

A A

SECTION AT A - A

1

A1

A20

A19

A21

A5,A6

A7-A10

A11,A12

A22

A24

A23

A26 A25

A28 A27

A30 A29 A34 A33

A35

A32 A31

A3A1,A2,A41

A2

A6

A5A13

A19A26 A25

A22A32 A31

A16

A36

A37 A38

L1 L7

L2 L9

L3 L8

A3

A4

A10

A9

A14A8A7

A18

L2A24 A35

L9

L6A20

A28 A27

L4

L5

L6

A3

A4

L7

L1L4 A36

A41 A39 A40

A1,A2,A41

BB

C C

L6

A1,A2,A41

A3

SECTION AT C - C

L3

A15 A11

A12

A29

76A37

A30A21

A17

A38L8

A23A34

76

A33

534

Fig. 2.14 Instrumentation layout in one of the centrifuge test series

52

Fig. 2.15 Photograph from one of the centrifuge test series showing the instrumentation using the high-speed video cameras and high-speed wireless data acquisition system

53

0 0.1 0.2 0.3 0.4 0.5Time (seconds)

-20

-10

0

10

20

Acc

eler

atio

n (g

)

-10

0

10

20

Acc

eler

atio

n (g

)-1

0

1

Mom

ent (

kN-m

)wired DAQwireless DAQ

Fig. 2.16 Comparison of data recorded by traditional wired data acquisition system and the new wireless data acquisition system at UC Davis. Transducers were placed at nearly identical locations for direct comparison. Data collected at 2048 Samples / second on each channel (after Wilson et al. 2007)

54

20 25 30 35 40 45 50-1

0

1

0 10 20 30 40 50-0.025

0.000

0.025

0 10 20 30 40 50-0.25

0.00

0.25

10 20 30 40 50 60 Spec

tral

acc

eler

atio

n (g

)

-0.5

0.0

0.5

10 20 30 40 50 60-0.05

0.00

0.05

0 20 40 60 80 100 120-0.05

0.00

0.05

Time (s)0 30 60 90 120 150 180

-0.05

0.00

0.05

0 1 2 30

3

0 1 2 30.0

0.2

0 1 2 30

2

0 1 2 30

4

0 1 2 30.0

0.2

0 1 2 30.0

0.2

0 1 2 30.0

0.2

Ave

rage

bas

e ac

cele

ratio

n (g

)

Period (s)

Northridge motionNorthridge motion

Sweep motion (5-190 Hz) Sweep motion (5-190 Hz)

Sweep motion (190-5 Hz) Sweep motion (190-5 Hz)

Sweep motion (7-333Hz) Sweep motion (7-333Hz)




Fig. 2.17 Time histories and response spectra of Northridge and frequency sweep motions used in the centrifuge test series (The axes are labeled in prototype scale, the frequencies noted in parentheses refer to frequency content in model scale)

55

0.8m

from

gro

und

surf

ace

02

17.4

m fr

om g

roun

d su

rfac

e

Horizontal acceleration (g)

-0.50.0

0.5

22.6

m fr

om g

roun

d su

rfac

e

Tim

e (s

econ

d)10

2030

-0.50.0

0.5

12.2

m fr

om g

roun

d su

rfac

e

-0.50.0

0.5

12.2

m fr

om g

roun

d su

rfac

e

02

22.6

m fr

om g

roun

d su

rfac

e

Perio

d (s

econ

d)0.

11

02

17.4

m fr

om g

roun

d su

rfac

e

Spectral acceleration (g)

02

7.0m

from

gro

und

surf

ace

-0.50.0

0.5

7.0m

from

gro

und

surf

ace

02

2.6m

from

gro

und

surf

ace

-0.50.0

0.5

0.8m

from

gro

und

surf

ace

-0.50.0

0.5

022.

6m fr

om g

roun

d su

rfac

e

Fig.

2.1

8 M

easu

red

soil

acce

lera

tions

from

a v

ertic

al a

rray

of h

oriz

onta

l acc

eler

omet

ers

in te

st M

IL03

(N

orth

ridge

inpu

t mot

ion,

pea

k ba

se a

ccel

erat

ion

= 0.

26 g

)

56

Fig.

2.1

9 M

easu

red

horiz

onta

l mot

ions

at d

iffer

ent l

ocat

ions

of m

odel

in M

IL01

test

ser

ies

(Nor

thrid

ge in

put m

otio

n, p

eak

base

acc

eler

atio

n =

0.23

g)

free

fiel

d so

il m

otio

n @

2.5

m fr

om g

roun

d su

rfac

e (A

11)


-0.50.0

0.5

Bas

e m

otio

n (a

vera

ge o

f A1&

A2)

Tim

e (s

econ

d)10

2030

-0.50.0

0.5

pile

mot

ion

@ 2

.5m

from

gro

und

surf

ace

(A15

)

-0.50.0

0.5

pile

mot

ion

@ 2

.5m

fr

om g

roun

d su

rfac

e (A

15)

012

Bas

e m

otio

n (a

vera

ge o

f A1&

A2)

Perio

d (s

econ

d)0.

11

012

free

fiel

d so

il m

otio

n @

2.5

m fr

om g

roun

d su

rfac

e (A

11)


012

Supe

r stru

ctur

e m

otio

n (A

21)

-0.50.0

0.5

Supe

r stru

ctur

e m

otio

n (A

21)

012

57

Ver

tical

bas

e m

otio

n

acceleration (g) -0.2

5

0.00

0.25

Nor

th e

ndSo

uth

end

Hor

izon

tal b

ase

mot

ion

Tim

e (s

econ

d)10

20

-0.2

5

0.00

0.25

Perio

d (s

econ

d)0.

11

01

Ver

tical

bas

e m

otio

n

Spectral acceleration (g) 01

free

fiel

d ve

rtica

l soi

l mot

ion

@ 2

.6m

from

gro

und

surf

ace

-0.2

5

0.00

0.25

01

Hor

izon

tal b

ase

mot

ion

Nor

th e

ndSo

uth

end

Nor

th e

ndSo

uth

end

Nor

th e

ndSo

uth

end

Fig.

2.2

0 M

easu

red

verti

cal m

otio

ns a

t the

con

tain

er b

ase

& 2

.6m

from

gro

und

surf

ace

in M

IL03

test

ser

ies

(Nor

thrid

ge in

put

mot

ion,

pea

k ba

se a

ccel

erat

ion

= 0.

26 g

)

58

(a) M

easu

red

bend

ing

mom

ent

Ben

ding

Mom

ent (

kNm

)-2

000

020

0040

00

Depth/Diameter

0 2 4 6 8

Depth from ground surface (m)-2 0 2 4 6 8 10

(b) C

alcu

late

d sh

ear

forc

e

Shea

r For

ce (k

N)

-100

00

1000

2000

Depth/Diameter

0 2 4 6 8


(c) C

alcu

late

d su

b gr

ade

reac

tion

(kN

/m)

Sub

grad

e R

eact

ion

(kN

/m)

040

080

0

Depth/Diameter

0 2 4 6 8


Ben

t 1 (H

c/D

=2.2

)B

ent 3

(Hc/

D=3

.3)

Ben

t 2 (H

c/D

=5.5

)U

ltim

ate

soil

resi

stan

ce (A

PI)

Ben

t 1 (H

c/D

=2.2

)B

ent 3

(Hc/

D=3

.3)

Ben

t 2 (H

c/D

=5.5

)

Fig.

2.2

1 B

endi

ng m

omen

t, sh

ear f

orce

, and

sub

-gra

de re

actio

n of

brid

ge b

ents

@ ti

me

of m

axim

um b

ent-c

ap d

ispl

acem

ent

(Nor

thrid

ge in

put m

otio

n, p

eak

base

acc

eler

atio

n =

0.57

g)

59

Peak base acc (g)0.0 0.2 0.4 0.6 0.8

Nor

mal

ized

dep

th to

max

imum

mom

ent (

L m/D

)

0

1

2

3

4

Bent 1 (Hc/D=2.2)Bent 3 (Hc/D=3.3)Bent 2 (Hc/D=5.5)

Fig. 2.22 Normalized depth to maximum bending moment for different above-ground clear height bridge bents in MIL01 test series

60

a) B

ent A

(θ=0

deg

)

01

23

Spectral acceleration (g) 0.0

0.5

1.0

1.5

2.0

Tran

sver

se re

spon

seLo

ngitu

dina

l res

pons

e

Perio

d (s

)

01

23

0.0

0.5

1.0

1.5

2.0

01

23

0.0

0.5

1.0

1.5

2.0

01

23

0.0

0.5

1.0

1.5

2.0

Perio

d (s

)

b) B

ent B

(θ=3

0 de

g)

c) B

ent B

(θ=6

0 de

g)d)

Ben

t D (θ

=90

deg)

Perio

d (s

)Pe

riod

(s)


Long

itudi

nal

resp

onse

Shak

ing

dire

ctio

n Tr

ansv

erse

re

spon

se

θ

Fig.

2.2

3 R

espo

nse

of b

ridge

ben

ts o

rient

ed d

iffer

ent d

irect

ions

to b

ase

shak

ing

in M

IL02

test

ser

ies

(fre

quen

cy s

wee

p in

put

mot

ion

7-33

3Hz)

61

Fig. 2.24 Response of bridge bents in the centrifuge and field tests to the base excitation in the transverse direction of the bent (frequency sweep input)

0.00 0.05 0.10 0.15 0.20

Spec

tral a

ccel

erat

ion

(g)

0

2

4

6

8

Longitudinal responseTransverse response

Period (s)

(b) Bent in the field test

Period (s)0 1 2 3

Spec

tral a

ccel

erat

ion

(g)

0.0

0.5

1.0

1.5

2.0

Transverse responseLongitudinal response

(a) Bent in the centrifuge test (Bent A)

62

Fig. 2.25 Seismic excitation directions for (a) centrifuge test specimen, and (b) field test specimen

(a) For centrifuge test specimen

Bent A

Transverse response

Longitudinal response

Input

(b) For field test specimen

Transverse excitation Longitudinal excitation

63

Fig. 2.26 Modeling of soil-pile-structure interaction in a single pile using p-y, t-z, and Q-z springs in OpenSees (after Shin 2007)

Fig. 2.27 Numerical modeling of the two-span bridge model in MIL01 test series using OpenSees (after Shin 2007)

64

Fig.

2.2

8 R

espo

nse

spec

tra o

f mea

sure

d (C

FG) a

nd s

imul

ated

(Ope

n) h

oriz

onta

l fre

e-fie

ld s

oil a

ccel

erat

ions

in M

IL02

test

ser

ies;

de

pths

to th

e ac

cele

rom

eter

s fro

m g

roun

d su

rfac

e an

d th

e pe

ak b

ase

acce

lera

tions

are

labe

led

(afte

r Shi

n et

al.

2006

)

65

Fig. 2.29 Time histories of measured (CFG) and simulated (Open) horizontal free-field soil accelerations in MIL03 test series (depths to the accelerometers from ground surface are labeled); Northridge input motion, peak base acceleration = 0.26 g (after Shin 2007)

66

Fig. 2.30 Ratios of Fourier amplitudes between the horizontal soil motion @ 2.6m and the horizontal base motion in MIL03 test series and OpenSees 1-D shear beam simulations; frequency sweep input motion, peak base acceleration = 0.25 g (after Shin 2007)

67

Fig. 2.31 Time histories and Fourier amplitude of measured and calculated horizontal motions at the bent-cap of a two-pile individual bent (Bent 5) in MIL01 test series; Northridge input motion, peak base acc = 0.25 g (after Shin 2007)

Fig. 2.32 Measured and calculated maximum pile bending moment of Bent 5 in MIL01 test series; Northridge input motion, peak base acceleration = 0.25 g (after Shin 2007)

68

(a) Bent 5 @ bent-cap (b) Soil (2.5m) near Bent 5

(c) Single pile 1 @ pile-head (d) Soil (2.5m) near Single pile 1

Fig. 2.33 Measured and calculated peak accelerations of superstructure and at 2.5m below ground surface in MIL01 test series during different intensity base motions (after Shin 2007)

69

Bent 1

Bent 2

Bent 3

Fig. 2.34 Time histories of measured and calculated horizontal motions at the bent-caps of the two-span bridge model in MIL01 test series; Northridge input motion, peak base acc=0.25g (after Shin et al. 2006)

70

Bent 1

Bent 2

Bent 3

Fig. 2.35 Measured and predicted response of the two-span bridge model in MIL01 test series; Northridge input motion, peak base acceleration = 0.25 g (after Shin et al. 2006)

71

Fig.

2.3

6 B

ack

calc

ulat

ed u

ltim

ate

soil

resi

stan

ce fr

om p

ile b

endi

ng m

omen

t dat

a in

the

cent

rifug

e te

st a

nd th

e ul

timat

e so

il re

sist

ance

obt

aine

d fr

om p

-y sp

ring

forc

es in

the

Ope

nSee

s sim

ulat

ions

, @ ti

me

of m

axim

um b

ent-c

ap d

ispl

acem

ent

(afte

r Shi

n et

al.

2006

)

72

Fig. 2.37 Regions of p-y spring parameters considered in the sensitivity analyses (after Shin 2007)

73

Fig. 2.38 Sensitivity analysis: Effect of soil motion on bent response, Northridge motion peak base acceleration = 0.25g (after Shin 2007)

74

Fig. 2.39 Sensitivity analysis: Effect of ultimate soil resistance (pult) on bent

response, Northridge motion peak base acc = 0.25 g (after Shin 2007)

75

Fig. 2.40 3-D finite element model of the prototype soil-pile-bridge system (after Jie 2007)

76

Fig.

2.4

1 En

d-to

-end

dat

a us

age

scen

ario

(afte

r Van

Den

Ein

de e

t al.

2007

)

77

Fig.

2.4

2 En

d-to

-end

usa

ge o

f cen

trifu

ge te

st d

ata

(scr

een

shot

from

UC

Dav

is-N

3DV

dat

a vi

ewer

, afte

r Kut

ter 2

007)

78

Chapter 3

Comparison of centrifuge and 1g shake table models of a pile supported

bridge structure

This chapter presents the comparison of experimental results and the resolution of

issues associated with comparing physical models of a, two-span, pile supported bridge

structure tested at different experimental facilities, at different scale, using different test

boundary conditions, and scaling laws. A comparison between the system response of

bridge model and component response of individual bents during a series of shaking

events also presented in this chapter. The contents of this chapter are adapted from two

published papers. The complete references of these papers and the contribution of

different authors are given below

1. Ilankatharan, M., Kutter, B.L., H. Shin, P. Arduino, S.L. Kramer, N. Johnson, and T.

Sasaki. (2006). “Comparison of Centrifuge and 1g Shaking Table Models of a Pile

Supported Bridge Structure,” Proceedings of the 6th International Conference on

Physical Modeling in Geotechnics, Hong Kong, Vol. 2: 1313-1318, August, 2006.

2. Kutter, B.L., and Wilson, D.W. (2006). "Physical Modeling of Dynamic Behavior of

Soil-Foundation-Superstructure Systems," Invited paper, International Journal of

Physical Modelling in Geotechnics. Vol. 6 No. 1, pp. 1-12.

H. Shin assisted with the centrifuge experiment and performed numerical

simulations of the experiments, T. Sasaki assisted with the centrifuge experiment, N.

Johnson provided 1-g shake table experiment data, and P. Ardunio and S. L. Kramer

79

provided valuable advice in the course of the study. The centrifuge testing of the two-

span section of the bridge model described in Chapter 2 of this dissertation, including the

collaborative test design process and some representative results were presented in the

second paper. The figures in the paper corresponding to above study were created by the

author of this dissertation.

Abstract: In small-scale centrifuge tests, it is difficult to accurately model reinforced

concrete structures; in large-scale 1-g shake table tests it is difficult to accurately model

geotechnical aspects of soil-pile-structure interaction. To provide a comprehensive

validation of a numerical procedure for analyzing the behavior of a bridge supported on

piles, a series of experiments has been conducted using centrifuge and shake tables. Two

seemingly basic questions that were difficult for the interdisciplinary research team to

resolve were: What clear height (between ground surface and bridge deck) should be

used in the centrifuge model to correspond to the fixed-fixed boundary conditions for the

pile extensions in the shake table tests, and what input motions should be used in the

shake table test to most closely correspond to the centrifuge tests? To resolve these

questions, an equivalent depth to fixity of the piles in the centrifuge were calculated, and

the free-field ground motion close to anticipated fixity point was used as a command

input motion for the 1-g shake table test. These assumptions enabled observation of

reasonable comparisons between bridge deck responses in both experiments. This

chapter presents these comparisons and discusses the above questions and other aspects

of the design of the centrifuge models. Further, this chapter compares the system

response of the centrifuge bridge model with that of component response during a series

of earthquake simulations.

80

3.1 Introduction

Past earthquakes, particularly the 1989 Loma Prieta and 1994 Northridge

earthquakes in California, and the 1995 Kobe earthquake in Japan, have caused collapse

of, or severe damage to, a considerable number of major bridges that were designed for

seismic forces (Priestly et al. 1998). One major reason for the poor performance relates to

the complexities of the bridge structural and sub structural systems as compared to other

structures. The ground motion and the nonlinear characteristics of the soil, foundation,

and structure influence the dynamic response of a bridge structure. For most bridges, the

foundation system may be designed to remain elastic while the pier portion of the

substructure is detailed for inelastic deformations and energy dissipation. This approach

is intended to avoid the difficulty of post earthquake inspection and the high cost

associated with repair of damaged foundation (Chai, 2002). This approach often leads to

very expensive design for new construction or seismic retrofits of bridges. Dissipation of

energy by the yielding of soil and foundations they support can influence the structural

performance (Gazetas et al, 1998). The degree and nature of these effects, however, are

not well defined by documented field evidence or by experimental testing. The accurate

evaluation of the seismic response of a bridge is limited by the ability to model the

behavior and interaction between a structure, its foundation and the supporting soil. It is,

however, impractical to test a single physical model of the prototype SFSI system at

reasonable scale and reproduce all key aspects of the system performance. Therefore, a

series of four complementary experimental programs had been conducted using the

NEES field shakers at the University of Texas, Austin, the large scale structural testing

facility at the Purdue University, the large scale shake tables at the University of Nevada,

81

Reno NEES equipment site, and on the 9 m radius NEES geotechnical centrifuge at the

University of California, Davis. The scale models of individual pile/columns, individual

bents, and two-span bridge models from the above experimental programs provide data to

understand the linear and nonlinear response of soil foundation system under seismic

loads, to evaluate the nonlinear response of a structure subjected to bi-directional,

incoherent support motion, and to evaluate size effects and strength degradation in shear

under cyclic loads. Computational simulations played a central role in the study by

providing a mechanism for integrating the response of each of the specimens and

evaluating the behavior of the prototype structure (Wood et al, 2004). The prototype

structure selected for the experimental studies (Fig. 3.1) is a two-span frame of a cast in

place post-tensioned reinforced concrete box girder bridge. The span lengths are 120 ft

(37 m), and the substructure is composed of 4 ft (1.2 m) diameter 2-column piers on

extended pile foundations. The UNR shake table tests involved quarter scale accurately

modeled reinforced concrete columns with fixed supports on three independent shake

tables spaced at ¼*(37 m) (Johnson et al, 2006). The 1/52 scale UCD centrifuge tests

involved aluminum tubing to represent the columns as pile extensions, but the piles were

supported in soil so that soil-structure interaction effects were more accurately simulated.

A significant collaborative effort was required to decide what free height there should be

between the bridge deck and the soil surface in the centrifuge model to correspond to the

free height between the bridge deck and the fixtures on the shake table. The primary

focuses of this chapter are on providing general information on design, and testing of the

bridge model tested on the centrifuge tests and the comparison of centrifuge bridge model

response with that of shake table tests.

82

3.2 Centrifuge and Shake table bridge models

3.2.1 General test setup

The centrifuge test series includes a scale model of a two-span bridge structure

with the sloping ground conditions that are assumed to exist at the site of the prototype

bridge structure (Fig. 3.2). Due to the sloping ground, the two spans are supported by

three bents, but the clear height between soil and bridge deck is different for each bent.

The soil profile was prepared with a 56 cm soil layer made with dry Nevada Sand having

a uniform relative density of roughly 80% throughout the flexible shear beam container.

The Flexible shear beam container has a series of stacked aluminum rings that separated

by soft rubber that enables the container to shear with the soil. A photograph of bridge

model set-up on model container is shown in Fig. 3.3.

The above-grade portion of the prototype bridge was most closely modeled by the

specimen that was tested on the shake table experiment. The prototype cast-in-place

prestressed box girder super structure was modeled using solid panels in the ¼ scale

shake table bridge model. Figs. 3.4 and 3.5 present the general layout of the bridge model

and a photograph of the bridge model set-up on the UNR shake tables. As shown in the

above Figs., each bent of the bridge model was supported on two reinforced concrete

columns, and the clear heights (height between the lower surface of the bridge deck and

the base of the column) of the columns were varied along the length of the specimen. In

Fig. 3.5, it is visible that the base of the each column was rigidly fixed to the concrete

spacer blocks that were used to produce variable heights above the shaking tables. Hence,

the effects of foundation and soil flexibility were not accounted for using this specimen.

83

The complete details about the design, construction, instrumentation, and testing of the

shake table bridge specimen can be found at Johnson et al. 2006.

3.2.2 Scale factors for 1/52 scale centrifuge model and ¼ scale 1-g shake table model

In the centrifuge experiment, increased gravity field due to centrifugal

acceleration produces identical prototype confining pressures in soil and, stresses in the

bridge model. Whereas, in 1g shaking table experiment, addition of extra masses to the

model produces identical stresses due to dead loads. These extra masses can be seen in

Fig. 3.5 (see the concrete blocks mounted on top of the model bridge deck). In this

chapter, test results from both experiments are presented in prototype scales unless

otherwise specified. Table 3.1 lists the scale factors that were used to convert model

quantities to prototype scales in the centrifuge and 1-g shake table experiments.

3.2.3 Pile properties

The design of the centrifuge model piles was based on the dimensions and

properties of the columns, bents, and deck from the shake table tests. All piles were made

of 6061-T4 (E = 68.5 GPa; yield strength = 130 MPa) aluminum tubing of 19.05 mm

diameter (0.991 m prototype) and a wall thickness of 0.889 mm (0.046 m prototype).

Strain gages were affixed to piles and piles were covered with plastic shrink-wrap. Fig

3.6 shows the typical pile cross section. Plastic shrink-wrap was used to increase the

outer diameter of piles with minimal effects on the bending stiffness. The outer diameter

of composite pile was 22.71 mm (1.181 m in prototype scale). The bent blocks were

made of 6061-T6 aluminum (E = 68.5 GPa; yield strength = 255 MPa). Special attention

was made to provide acceptable correspondence between the prototype values for axial

84

load per pile, pile diameter, EI and moment capacity in both experiments. The prototype

values of sectional properties of centrifuge piles and shake table columns are tabulated in

Table 3. 2.

3.2.4 Design for above ground clear heights

When designing above ground clear heights of centrifuge piles two different

objectives were considered. The first objective was to simulate natural frequencies of

bridge models in the 1g shake table and in the centrifuge experiments. The following

hypotheses were used in the design to get same natural frequency;

i) The height of the columns in shake table tests should be equal to the

distance from the bridge deck to the point of equivalent fixity on the pile

extensions.

ii) The columns in the shake table should be fixed to the surface of the shake

table (to the top of the spacer blocks on the shake tables) at the equivalent

fixity point.

The above hypotheses are schematically shown in Fig. 3.7. The equivalent depth

to fixity Lf could be determined by equating the lateral stiffness of the equivalent

cantilever to the lateral stiffness of the soil-pile system. An analytical model proposed by

Chai (2002) for elastic soil was used to calculate equivalent depth of fixity (Lf).

The second objective was to simulate the response of bridge model at ultimate

state. Fig. 3.8 shows the load, shear and moment distribution of both specimens at the

ultimate limit state. Under lateral loading at deck level, the maximum moment occurs in

the pile at some distance (Lm) below the ground level where the shear is zero. For a

column fixed to a shake table, the shear and moment are maximum at the point of fixity.

85

The approach used in this study was to reasonably simulate shear distribution while

paying more attention to simulate the moment distribution in the 1 g and centrifuge shake

tables. The depth of maximum moment of pile was calculated for linear distribution (Ll)

(see Fig. 3.8). Then the columns on the shake table should be fixed to the surface of the

shake table at a distance Ll below the ground level. According to this logic, Hcol, shake table

= Hclear, pile + Ll. The summary of clear height design at above two scenarios for different

height specimens is shown in Table 3.3. The calculated clear heights based on elastic

response (first objective) are higher than the values for inelastic system response (second

objective). The calculated clear height to match natural frequencies of both models (from

the first objective) was used in the centrifuge tests. Because the research team reasoned

that we would have a better chance of matching the elastic response in the centrifuge and

the 1 g experiments, it was decided to design the models to match the elastic stiffness.

3.2.5 Deck properties and spacing between bents

The superstructure for the shake table specimen was a solid post tensioned,

precast slab. In the centrifuge test, pile head masses (bent caps-made from 6061-T6

aluminum) were connected with light weight aluminum (5052-T6 aluminum) plates. Both

deck models were relatively stiff in the transverse direction so that the interior bent

motion was forced to be essentially equal to the average of the two exterior bents. For the

1 g bridge model, the longitudinal spacing between bents was 37 m in prototype scale.

The longitudinal spacing between bents in the centrifuge test was approximately 15.1 m

in prototype scale to fit the bridge in the container and on the assumption that the spacing

was not critical. This difference in spacing, however, resulted in a different torsional

stiffness of the system for the centrifuge and the 1 g tests.

86

3.2.6 Selection of input motion and testing sequence

The input motions used in the centrifuge and 1 g tests were based on the

Northridge 01/17/94 1231, Century City LACC North, 090 (CMG Station 24389)

earthquake recording. To account for site response effects, estimated free field motion

from site response analysis at the equivalent point of fixity (assumed to be 2.5 m below

the ground surface) was used as the input motion in the 1 g tests. To obtain comparable

results in centrifuge experiments, an exercise was performed prior to the centrifuge tests

to tune the servo hydraulic shakers to produce the same motion at a depth of 2.5 m

(prototype scale) below the ground surface. Time histories and spectral accelerations of

base motions before and after this tuning exercise and the magnitude of the transfer

function used to modify the original base motion are shown in Fig. 3.9. Time histories

and spectral accelerations of the target and achieved free field motions at the equivalent

fixity point (at 50 mm below ground surface in the centrifuge model scale) before and

after the tuning exercise are presented in Fig. 3.10. As shown in Fig. 3.10, the free field

motions were determined to agree reasonably well with the target over a range of periods

between 0.6 s and 1.0 s, which encompasses the natural period of the bridge bents. The

instrumentation details, ground motion sequence and other aspects of centrifuge

experiment are described in test series data report (Ilankatharan et al. 2005).

87

3.3 Comparison of centrifuge and 1g shake table experimental results

3.3.1 During a medium level shaking event (peak base acc=0.25 g in centrifuge test)

Fig. 3.11 compares the acceleration time histories of deck motions in both

experiments. The elastic response spectra of free field soil motions at the equivalent

depth of fixity, shake table from 1g shake table experiments and deck motions from

centrifuge and 1 g experiments are presented in Fig 3.12. The locations of sensors

(accelerometers recorded above data) in the centrifuge and shake table experiments are

shown in Fig. 3.2 and Fig. 3.4. Deck displacements from both experiments are shown in

Fig. 3.13. As shown in the above figures the results are in reasonable agreement for tall

and medium bents. Some differences are apparent in deck motions for short bent. For the

short bent, the shake table deck response shows response peaks of 0.6 and 0.8 s while the

centrifuge shows response peaks at 0.6 and 0.9 s. The observed predominant period of

centrifuge bridge model was approximately 0.9 s while that of shake table model was

approximately 0.7 s. The first two modes of bridge models involved a significant amount

of torsion about a vertical axis. The torsional natural periods will vary with longitudinal

spacing of bents, which, as described earlier, was not scaled accurately in the centrifuge

test (due to limited size of the model container). This explains why the natural periods

were different in the centrifuge and the 1 g shake table experiments (Ranf et al. 2006).

Fig. 3.14 presents the spectral ratio of deck motions to free field soil motions at 2.5 m (or

shake table base motions). To produce the above figure, for the case with the centrifuge

bridge model, spectral accelerations of deck motions are divided by the spectral

accelerations of free field soil motions at 2.5 m and for the case with the shake table

88

model, spectral accelerations of deck motions are divided by the spectral accelerations of

table motions. The magnitude of spectral ratios varies with frequencies for different bents

in two experiments. This may be explained by the different amount of energy dissipation

by various sources in centrifuge and shake table experiments: such as soil particle-

particle friction and sliding, particle crushing, friction at soil-pile interface, radiation

damping provided by the piles in the soil, pile/column yielding, and radiation damping in

shake table system. In the period range between 0.5 to 1.0 s, the magnitude of spectral

ratios in shake table test is higher than that of centrifuge test. This suggests that the

significant amount of energy dissipation that occurred in centrifuge experiment was not

present in shake table experiment. Fig. 3.15 compares the time histories of bending

strains measured in both experiments in different clear height columns, at 1.3 m below

the deck level. As shown in Fig. 3.15, the frequency contents and time histories of strains

are in reasonable agreement for the tall and the medium bents. However, the

unsymmetrical strain pattern, with spikes in the negative direction, for the reinforced

concrete model columns in the shake table experiment were not observed in centrifuge

experiment.

3.3.2 During a Large level shaking event (peak base acc = 0.78g in centrifuge test)

The elastic response spectra of free field soil motions at the equivalent fixity

point, shake table motions in the 1g tests, and deck motions from 1 g and centrifuge tests

are shown in Fig. 3.16. The peak accelerations of measured free field motions at the

equivalent depth of fixity are almost the same for the short bent and medium bent. A

small difference for the tall bent is likely due to a difference in the depth of the

accelerometers. Peak base accelerations for all three-shake table base motions have

89

noticeable differences; the table motion for the short bent is significantly different from

others. This may be due to the interaction between the short stiff bent and the shake table.

The impact of test specimen-shake table interaction on the measured table motions and

on the bridge system response was discussed by Johnson et al. (2006). It was shown in

their study that the measured shake table motion for short bent was larger than the target

table motion. This discrepancy in the table motion resulted first bent collapse in the short

bent during the experiment. However, the pre-test analyses concluded the first bent

collapse would occur in the medium bent. Fig. 3.17 compares the spectral ratios of deck

motions which were estimated as described earlier for the medium level shaking event.

During this large shaking event, compared to the centrifuge bridge model, the shake table

bridge model shows noticeable reduction (from the case with the medium level shaking)

peak amplitudes of spectral ratios. This may be attributable to the energy dissipation

occurred in the shake table bridge model due to yielding of reinforced concrete columns

during strong shaking.

3.4 Comparison of the system (three-bent) response to the individual bent

response in the centrifuge experiment

As described earlier, the bridge deck in the centrifuge model consisted of a light-

weight aluminum plate bolted to the bridge bents. This afforded the opportunity to first

test each the three bents simultaneously while they were unconnected and then to test

them as a three-bent system.

Fig. 3.18 compares the response spectra of two shaking events. One of these is

the measured base motion for an event with unconnected bents and the other is the input

motion for the case when the bents were connected by the bridge deck. It may be seen

90

that these motions were relatively weak (0.08 g in prototype scale) and nearly identical.

This weak motion produced negligible permanent deformation and limited nonlinearity in

soil and foundation. In later events (as shown earlier) the amplitude of input acceleration

was about ten times stronger and involved both structural and geotechnical yielding.

Fig. 3.19 compares the response spectra for horizontal acceleration of each bent

when they were unconnected (single bents) and when they were connected to the

neighboring bents. When unconnected, the single bents had two primary modes of

vibration, namely translation of the bent in the stiff and in the flexible directions. The

torsional mode (about a vertical axis) and vertical vibration modes did not participate

much in the observed response. For this case, the short bent had T1 ≈ 0.6 s, the medium

bent had T1 ≈ 0.9 s, and the tall bent had T1 ≈ 1.2 s. When connected, the system has two

primary modes that involved a combination of translation in the direction of shaking and

torsion about a vertical axis (due to the asymmetric stiffness of the three-bent system).

From Figure 3.19, it may be seen that one end of the deck oscillates at a different period

than the other and the middle (tall) bent shows two peaks in the response spectrum. For

this particular shaking event, the peak spectral response of the short bent ((clear height of

pile)/(pile diameter) = Hc/D = 2.2) decreased when it was connected to the bridge deck

because the natural period of the unconnected short bent is smaller than the natural period

of the connected system and the natural period of the unconnected short bent is closer to

the predominant period of the input motion (Fig. 3.18). Conversely, the relatively

flexible tall bent acted almost like an isolator when it was unconnected to the deck, hence

bent cap accelerations increased when it was connected to the bridge deck.

91

Fig. 3.20 compares the bending moment distributions at the time of maximum

bent cap displacement for the short, medium, and tall bents, comparing behavior when

the bents are connected to the deck to those for unconnected (single) bents. Although the

peak spectral acceleration of the short bent decreased by about 50% when it was

connected to the deck, the reduction in spectral acceleration did not result in a significant

reduction in the bending moment distribution. The bending moment distribution for the

medium bent increased by about 70% when it was connected, despite the small effect on

the amplitude of the peak spectral acceleration. Bending moments in the tall bent

columns also increased significantly when the deck was connected.

The above results clearly illustrate that system response is quite different from

individual bent response. If the columns or the soil around the piles were to yield

significantly this could result in additional complex interactions. Theoretically, these

interactions could be predicted using numerical methods such as finite elements; however

the methods for analyzing soil-foundation-bridge systems have not been subject to

verification exercises. It is considered important to verify the methods used to analyze

the system response, and hence it is valuable to perform model tests of system response

to provide data for this verification (Kutter and Wilson, 2006).

3.5 Conclusions

Complementary experimental programs using multiple experimental sites and

comprehensive numerical simulations were performed to develop better understanding of

bridge system seismic behavior and to demonstrate new NEES infrastructure for

conducting large-scale collaborative research. The design of test elements, especially the

above ground clear heights for the columns/pile extensions and loading protocols, to

92

account for different boundary conditions at the base of the columns in the 1g and

centrifuge tests and the different scaling laws for structural modeling and geotechnical

centrifuge modeling required significant collaborative effort between structural and

geotechnical engineers.

For intermediate levels of shaking, the agreement between deck response in

centrifuge and 1 g shake table experiments suggests that the bridge deck response can be

reasonably modeled using fixed base columns attached to a 1 g shake table if the 1 g

shake table motion corresponds to the free field soil motion at the equivalent depth of

fixity. Difference in bent spacing and interaction of shake table bridge model with the

actuation system cause some discrepancies between responses. The differences in

spectral ratios may be attributable to different amount of energy dissipation by various

sources in centrifuge and 1 g shake table experiments; soil particle-particle friction and

sliding, particle crushing, friction at soil-pile interface, radiation damping provided by the

piles in the soil, pile/column yielding and radiation damping in shake table system. A

significant amount of energy dissipation that occurred in the centrifuge test during the

medium-level shaking event was not present in shake table test. However, shake table

bridge model dissipated more energy during large-level of shaking due to concrete

column yielding. Hence, the direct comparison of results from different types of

experiments is valuable because it can clearly expose the flaws that we might otherwise

ignore.

While experiments on bridge components will continue to be valuable, tests of

soil-foundation-bridge systems lead to more complete understanding of system

performance, provide unique data sets to validate numerical methods to predict bridge

93

system response, and promote cross-disciplinary education of researchers. Continued

multi-institution, multi-disciplinary research on systems could lead to a new paradigm for

design in which foundations and superstructures are designed to have stiffness, capacity,

and energy dissipation characteristics that are compatible and complementary with the

goal of optimizing system performance.

3.6 References

Chai, Y. H. (2002). “Flexural strength and ductility of extended pile-shafts. I: Analytical

model,” Journal of Struct. Eng., 128(5), 586-594

Gazetas, G., and Mylonakis, G. (1998). “Seismic soil-structure interaction: New evidence

and emerging issues,” Proceedings, Geotechnical Earthquake Engineering and Soil

Dynamics III, Editors: P. Dakoulas, M. Yegian and R. D. Holtz, ASCE Geotechnical

Special Publication No.75, pp 1119-1174.

Ilankatharan, M., Sasaki, T., Shin, H., Kutter, B. L., Arduino, P., and Kramer, S. L.,

(2005). “A demonstration of NEES system for studying soil-foundation-structure

interaction,” Centrifuge data report for MIL01, Rep. No. UCD/CGMDR-05/05, Ctr.

for Geotech. Modeling , Dept. of Civ. and Envir. Engrg., University of California,

Davis, Calif.

Priestly, M. J. N., Seible, F., and Calvi, G. M. (1998). “Seismic design and retrofit of

bridge,” Wiley-Interscience, New York

Johnson, N., Ranf, R., Saiidi, M., Sanders, D., and Eberhard, M. (2006). “Shake-Table

Studies of a Two-Span, Reinforced Concrete Bridge,” Proceedings, Eighth National

Conference on Earthquake Engineering, April 2006.

94

Johnson, N., Saiidi, M., and Sanders, D. (2006). “Large-scale Experimental and

Analytical Seismic Studies of a Two-span Reinforced Concrete Bridge System,” Rep.

No. CCEER-06-02, Ctr. for Civil Engineering and Earthquake Research, Dept. of Civ.

and Envir. Engrg. University of Nevada, Reno, Nevada.

Wood, S.L., Anagnos, T., Arduino, A., Eberhard, M.O., Fenves, G.L., Finholt, T.A.,

Futrelle, J.M., Jeremic, B., Kramer, S.L., Kutter, B.L., Matamoros, A.B., McMullin,

K.M., Ramirez, J.A., Rathje, E.M., Saiidi, M., Sanders, D.H., Stokoe, K.H. and

Wilson, D.W. (2004) "Using NEES to Investigate Soil-Foundation-Structure

Interaction," Proceedings, 13th World Conference on Earthquake Engineering, Paper

2344, Vancouver, Canada, August 1-6.

95

Table 3.1: Scale factors used to convert model data to prototype scale in the centrifuge and 1g shake table experiments

Property Prototype/Model

(1/52 scale Centrifuge test)

Prototype/Model

(1/4 scale 1-g shake table

test)

Length, displacement 52/1 4/1

Stress, pressure 1/1 1/1

Acceleration 1/52 1/1

Force 522/1 42/1

Time 52/1 41/2/1

Table 3.2: Comparison of sectional properties of piles in centrifuge tests and columns in 1g shake table tests (values are in prototype scale)

Property Centrifuge test 1-g Shake table test

Outer diameter (m) 1.181 1.219

EI * (MNm2) 1056 1065

Axial load per pile (kN) 3310 3310

Yield moment (kNm) 4023 3811

Plastic moment (kNm) 5364 4772

* Effective stiffness for reinforced concrete column

96

Table 3.3: Above ground clear heights of shake table columns and calculated clear heights of centrifuge piles (in “prototype meters”)

Bent

Tall

Medium

Short

H col, shake table

9.75 7.32 6.10

To simulate natural frequency: Lf H clear, pile

3.31 6.44

3.41 3.91

3.50 2.60

To simulate ultimate state (Ultimate moment distribution): Ll H clear, pile

2.54 7.21

2.46 4.86

2.67 3.43

.

97

Fig. 3.1 Hypothetical prototype multi-span bridge. Models of circled portion of the bridge were tested in the 1-g shake table tests and on the centrifuge

98

-Locations of deck & free field soil accelerometers

36.4

2.6 6.4

20°

23°

12.0 12.0

15.1 15.1

7.6

15.6

TOP VIEW

FRONT VIEW

Shortbent

All dimensions are in "prototype m"

11.814.3

27.8

11.4

6.7

Tallbent

Mediumbent

3.9

Fig. 3.2 Layout of bridge model in centrifuge test series

Fig. 3.2 Layout of the bridge model in the centrifuge test series

99

Fig. 3.3 Photograph of bridge model set-up on centrifuge model container

100

Fig. 3.4 Layout of the bridge model in the 1g shake table experiment (Wood et al. 2004)

6′-0″ 12″8′-0″

5′-0″

30′-0″ 30′-0″

18″

(a) Longitudinal Elevation

10'-4"

8′-0″

18"

6'-3"

12" 12"

(b) Elevation of Tall Bent

16 - #3 Bars

12″

¾ in. CoverW2.9 Spiral1¼ in. pitch

(c) Column Cross Section

6′-0″ 12″8′-0″

5′-0″

30′-0″ 30′-0″

18″

(a) Longitudinal Elevation

10'-4"

8′-0″

18"

6'-3"

12" 12"

(b) Elevation of Tall Bent

16 - #3 Bars

12″

¾ in. CoverW2.9 Spiral1¼ in. pitch

(c) Column Cross Section

- Location of deck & table accelerometers

All dimensions are in shake table experiment model scale

101

Fig. 3.5 Photograph of bridge model set-up on shake tables at the University of Nevada, Reno (Johnson et al. 2006)

102

Fig. 3.6 Typical pile cross section in the centrifuge experiment (all dimensions are in model scale)

450

Pile tip

φ 22.71

φ 19.05

Plan View

φ 22.71

φ 15.41

φ 19.05

Shrink -wrap

Shrink -wrap

All dimensions are in mm

103

Fig. 3.7 Calculation of clear heights of piles based on equivalent cantilever model

Shake table column

Centrifuge pile

H col, shake table

H clear, pile

L f Equivalent cantilever model for

pile

H clear, pile +Lf = H col, shake table

H clear, pile +Lf

104

H clear, pile

H col, shake table

Lm

Ll

Fig. 3.8 Load, shear and bending moment diagrams for pile in the ground and column on the shake table at ultimate state

105

(a) Time histories of base motionTime (s)

0 10 20 30 40

Acc

eler

atio

n (g

)

-0.4

-0.2

0.0

0.2

0.4

Before tuningAfter tuning

(b) ARS of base motion (5% damping)

Period (s)0.01 0.1 1 10

Spec

tral a

ccel

erat

ion

(g)

0.0

0.5

1.0

1.5

2.0

(c) Tuning transfer function for base motionPeriod (s)0.01 0.1 1 10

Mag

nitu

de o

f tra

nsfe

r fun

ctio

n

0

1

2

3

Before tuningAfter tuning

Fig. 3.9 Time histories and response spectra of base motions before and after tuning and amplitude of tuning transfer function for base motion (peak base acc =0.23 g)

106

a) T

ime

hist

orie

s bef

ore

tunn

ing

010

2030

40

Acceleration (g) -0.4

-0.20.0

0.2

0.4

Tim

e (s

)

Targ

et m

otio

nA

chie

ved

mot

ion

b) T

ime

hist

orie

s afte

r tun

ning

Tim

e (s

)0

1020

3040

Acceleration (g) -0.4

-0.20.0

0.2

0.4

Targ

et m

otio

nA

chie

ved

mot

ion

c) A

RS

befo

re tu

nnin

gPe

riod

(s)

0.01

0.1

110

Acceleration response spectra (g)

0.0

0.5

1.0

1.5

2.0

Targ

et m

otio

nA

chie

ved

mot

ion

d) A

RS

afte

r tun

ning

Perio

d (s

)0.

010.

11

10Acceleration response spectra (g)

0.0

0.5

1.0

1.5

2.0

Targ

et m

otio

nA

chie

ved

mot

ion

Fig.

3.1

0 Ti

me

hist

orie

s & a

ccel

erat

ion

resp

onse

spec

tra o

f tar

get &

ach

ieve

d fr

ee fi

eld

mot

ion

@50

mm

bel

ow g

roun

d su

rfac

e (b

efor

e an

d af

ter t

unin

g, p

eak

base

acc

= 0

.23

g)

107

0 5 10 15 20 25

-0.4

-0.2

0.0

0.2

0.4

-0.4

-0.2

0.0

0.2

0.4

-0.4

-0.2

0.0

0.2

0.4

Deck motion @ Centrifuge testDeck motion @ Shaking table test

(i) Short bent

(ii) Tall bent

(iii) Medium bent

Time (prototype seconds)

Fig. 3.11 Deck motions during a medium level shaking event (peak base acc= 0.25 g in centrifuge test)

108

01

23

Perio

d (s

)0

12

3

ARS (g) 012Fr

ee fi

eld

mot

ion

@ 2

.5 m

dep

th @

Cen

trifu

ge te

stSh

akin

g ta

ble

base

mot

ion

01

23

012D

eck

mot

ion

@ C

entri

fuge

test

Dec

k m

otio

n @

Sha

king

tabl

e te

st

(i) S

hort

bent

(ii)

Tall

bent

(vi)

Med

ium

ben

t (i

v) S

hort

bent

(v) T

all b

ent

(iii)

Med

ium

ben

t

Fig.

3.1

2 R

espo

nse

spec

tra o

f (5%

dam

ping

) of f

ree

field

mot

ions

@ 2

.5 m

dep

th in

the

cent

rifug

e te

st &

shak

e ta

ble

base

m

otio

ns, a

nd d

eck

mot

ions

dur

ing

med

ium

leve

l sha

king

eve

nt (p

eak

base

acc

= 0

.25

g in

cen

trifu

ge te

st)

109

-0.1

0.0

0.1Deck displacement @ Centrifuge testDeck displacement @ Shaking table test

Dec

k di

spla

cem

ent (

m)

-0.1

0.0

0.1

(i) Short bent

Time (Prototype seconds)0 10 20 30 40

-0.1

0.0

0.1(ii) Tall bent

(iii) Medium bent

Fig. 3.13 Deck displacements during a medium level shaking event (peak base acc= 0.25g)

110

Period (s)

Rat

io o

f spe

ctra

l acc

eler

atio

ns

0

2

4

6

8 Centrifuge testShake table test

0

2

4

6

8

0.0 0.5 1.0 1.5 2.0 2.5 3.00

2

4

6

8

(i) Short Bent

(ii) Tall Bent

(iii) Medium Bent

Centrifuge testShake table test


Fig. 3.14 Ratio of spectral accelerations (5% damping): deck motions to free field soil motions @ 2.5 m in the centrifuge test and deck motions to table motions in the 1g shake table test (peak base acc = 0.25 g in centrifuge test)

111

-0.2

-0.1

0.0

0.1

0.2 column strain @ Centrifuge testcolumn strain @ Shaking table test

Ben

ding

stra

ins (

%)

-0.2

-0.1

0.0

0.1

0.2

(i) Short bent

Time (Prototype seconds)0 5 10 15 20 25 30

-0.2

-0.1

0.0

0.1

0.2

(ii) Tall bent

(iii) Medium bent

Fig. 3.15 Column strains (bending) at 1.3m below deck level during a medium level shaking event (peak base acc= 0.25 g)

112

01

23

Perio

d (s

)0

12

3

ARS (g) 0246Fr

ee fi

eld

mot

ion

@ 2

.5 m

dep

th @

Cen

trifu

ge te

stSh

akin

g ta

ble

base

mot

ion

01

23

0246D

eck

mot

ion

@ C

entri

fuge

test

Dec

k m

otio

n @

Sha

king

tabl

e te

st

(i) S

hort

bent

(ii)

Tall

bent

(vi)

Med

ium

ben

t (i

v) S

hort

ben

t (v

) Tal

l ben

t

(iii)

Med

ium

ben

t

Fig.

3.1

6 R

espo

nse

spec

tra o

f (5%

dam

ping

) of f

ree

field

mot

ions

@ 2

.5 m

dep

th in

cen

trifu

ge te

st &

sha

ke ta

ble

mot

ions

, an

d de

ck m

otio

ns in

bot

h ex

perim

ents

dur

ing

a la

rge

ampl

itude

shak

ing

even

t (pe

ak b

ase

acc

= 0.

78 g

in c

entri

fuge

test

)

113

Period (s)

Rat

io o

f spe

ctra

l acc

eler

atio

ns

0

2

4

6

8Centrifuge testShake table test

0

2

4

6

8

0.0 0.5 1.0 1.5 2.0 2.5 3.00

2

4

6

8

(i) Short Bent

(ii) Tall Bent

(iii) Medium Bent



Fig. 3.17 Ratio of spectral accelerations (5% damping): deck motions to free field soil motions @ 2.5 m in the centrifuge experiment and deck motions to shake table motions in the 1g shake table experiment (peak base acc = 0.78 g in centrifuge test)

114

Fig. 3.18 Response spectra of the base input motions for two centrifuge shaking events, one applied before attaching the bridge deck, and one after connecting the bridge deck to the bridge bents

Period (s)0.0 0.5 1.0 1.5 2.0 2.5 3.0

Spec

tral a

ccel

erat

ion

(g)

0.0

0.1

0.2Event with single bentsEvent with bridge model

(i) Short Bent (Hc/D=2.2)

115

Period (s)

Spec

tral a

ccel

erat

ion

(g)

0.0

0.5

1.0

1.5Single bentBridge bent

0.0

0.5

1.0

1.5

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.5

1.0

1.5

Single bentBridge bent


(i) Short Bent (Hc/D=2.2)

(ii) Tall Bent (Hc/D=5.5)

(iii) Medium Bent (Hc/D=3.3)

Fig. 3.19 Response spectra of the bridge bent accelerations before and after attaching the bridge deck. Hc/D represents the ratio of clear height between the soil and the bent to the column (pile extension) diameter

116

Bending Moment (kNm)-2000 -1000 0 1000

Dep

th fr

om g

roun

d su

rfac

e (m

)

-8

-4

0

4

8

12-2000 -1000 0 1000 -2000 -1000 0 1000

(i) Short Bent (Hc/D=2.2) (ii) Tall Bent (Hc/D=5.5) (iii) Medium Bent (Hc/D=3.3)




Fig. 3.20 Comparison of bending moment distributions in the columns/piles before (single bents) and after (bridge bents) attaching the bridge deck

117

Chapter 4

Modeling input motion boundary conditions for simulations of

geotechnical shaking table tests

The chapter discusses effects of using different input motion boundary conditions

on the sensitivity of numerical simulations results to errors in material properties of a soil

model tested on a centrifuge shaking table. This chapter is a journal paper which has been

submitted for publication in the Professional journal of the Earthquake Engineering

Research Institute (EERI). The complete reference of the paper is given below.

Ilankatharan, M., and Kutter, B. L. (2008). “Modeling Input Motion Boundary

Conditions for Simulations of Geotechnical Shaking Table Tests.” Earthquake Spectra,

Earthquake Engineering Research Institute (under review).

118

Abstract: This paper discusses effects of using different input motion boundary

conditions on the sensitivity of numerical simulations results to errors in material

properties of a specimen tested on a shaking table. In the flexible-actuator-prescribed-

force boundary condition, seismic input is specified by a force across an actuator element

that drives the shaking table; hence, the boundary between the test specimen and the

shaking table is an absorbing-base boundary across which energy may be transferred. In

the prescribed-displacement boundary condition, the measured shaking table motion in

the experiment is used as a prescribed displacement in the simulation. Numerical

simulations of a hypothetical centrifuge shaking table experiment involving a 1D soil

column are performed to illustrate effects of the above two input motion boundary

conditions. The flexible-actuator-prescribed-force approach generally yielded smaller,

almost constant sensitivities. The prescribed-displacement approach yielded larger and

more variable sensitivities. The observation that the sensitivity of results to errors in

input data depends on the input motion boundary conditions, raises a fundamental

question: How can we assess the significance of a discrepancy between a numerical

simulation and an experimental result? This paper shows that, for shaking table tests, the

significance of errors in the numerical simulations cannot be rigorously assessed without

accounting for dynamic interaction between the test specimen and the actuation system.

119

4.1 Introduction

One of the greatest challenges that earthquake engineers face is the paucity of

data available to calibrate the performance of numerical models for varying earthquake

characteristics (level of shaking, frequency content, and waveform), soil profile

characteristics, and superstructure/substructure characteristics. Dynamic centrifuge

modeling with detailed instrumentation is often used to obtain physical data, gain insight

into the mechanisms involved, and perform parametric studies to calibrate numerical

models. VELACS (VErification of Liquefaction Analyses by Centrifuge Studies) is just

one example of a project where the data from several series of dynamic centrifuge model

tests were used to verify various numerical procedures (Arulanandan et al, 1993).

A geotechnical centrifuge-shaker system includes a soil model, a model container,

a shaking table and its reaction mass as depicted in Fig. 4.1. All of the different

components of dynamic system, with their own resonant frequencies, interact with the

soil model during dynamic excitation, some absorbing energy and others allowing

undesired modes to affect the response observed in the experiment. This interaction of the

soil model and the centrifuge/actuation system might attenuate or exaggerate the

discrepancies in responses of the experiment and the numerical simulation. A

fundamental question then arises: ‘How should we assess the quality of a comparison

between an experiment and a numerical simulation?’ Up to now, comparisons between

theory and experiment have only been qualitative. To answer the fundamental question, it

would be essential to accomplish the following:

i. Identify the model parameters that are being investigated in the experiment and

the simulation,

120

ii. Confirm that the experiment and the numerical simulation are reasonably

sensitive to uncertainties in these model parameters, and

iii. Understand how uncertainties in the model parameters (input) are propagated

through the numerical simulation and through the experiment to the result (output); i.e.,

understand the sensitivity of output to errors in input.

Without understanding the sensitivity of output to input in the experiment and the

simulation, it is not possible to make a rigorous evaluation of the significance of

agreement or disagreement between simulation and experiment. The goal of present study

revolves around one aspect of the fundamental question raised above: To investigate how

the sensitivity of output to changes in input parameters depends on the input motion

boundary conditions assumed in a numerical simulation of a centrifuge shake table

experiment.

In a typical shake table experiment, an actuator command displacement is

specified to a servo controller and the response of the container base is measured as an

output. There is energy transfer (analogous to radiation damping through compliant

boundaries in the field) out of test specimen through the shake table and the reaction

mass (Kutter, 1995). Analogous to 1-D wave propagation in soil layers, the measured

motion at the base of the container, which is a combination of both reflected and

transmitted seismic waves at the base of the container (Fig. 4.2), depends on dynamic

properties of different components of model-shaker system. If the shaking table and

reaction mass were infinitely stiff, all the wave energy generated by the shaker would be

trapped in the soil model and the measured container base motion could be used as “true

input” to a numerical simulation. However, real shaking table tests, especially those in

121

the highly constrained payload of a geotechnical centrifuge involve flexible and finite

masses of shaking table and reaction mass, and the impedance contrast at the base of the

test specimen is not very large, which increases the significance of proper treatment of

the boundary condition.

This paper discusses two different approaches for inputting excitation to a

numerical simulation of a dynamic centrifuge shake table experiment. The first approach

involves more realistic representation of experimental boundary conditions and requires

detailed modeling of different components of model-shaker system. In this approach,

seismic input to simulation model is specified as a force input time history across the

actuator; the motion at the container as well as the response of the soil deposit is

calculated as outputs of the simulation. The boundary between the test specimen and the

shaking table is treated as an absorbing boundary so that the energy transfer out of the

test specimen through the actuator and reaction mass can be accounted for. In the second

approach, the measured shaking table motion is used as a prescribed displacement in the

numerical simulation. This paper presents numerical examples illustrating above two

approaches and results from a series of sensitivity studies using above two approaches.

Further, relative merits of these approaches and the effects of the test specimen-actuation

system interaction on the simulation results are discussed.

4.2 Modeling of a soil column mounted on a centrifuge shaking table

We consider a hypothetical experiment where a soil column, with a height of 1 m

and a cross sectional area of 1 m2, is tested on a centrifuge shaking table. The important

components of the experiment would be similar to the features of a centrifuge shaker

system shown in Fig. 4.1; except for this hypothetical example we assume that the base

122

of the container does not rock, and that the container is mass less and frictionless. An

increased gravitational field of 50 g is considered for the centrifuge experiment and the

corresponding numerical simulations. The dimensions of the finite element domain, all

modeling parameters, and the simulation results are presented in centrifuge model scale

unless otherwise specified. The centrifuge scaling factors for some physical properties are

given in Table 4.1; further details on the centrifuge scaling laws can be found in Kutter

(1992).

4.2.1 Representing input motion boundary conditions

2D finite element models are developed using OpenSees (Open System for

Earthquake Engineering Simulation, Mazzoni et al. 2006) to represent the dynamics of

soil model-shaker system. To improve understanding of interactions among different

components of the dynamic system and to evaluate how the sensitivity of simulation

results depends on the input motion boundary conditions in the simulations, the

boundary conditions are treated with two different levels of detail as described below,

and depicted in Fig. 4.3.

4.2.1.1 Prescribed-force simulation

This simulation model involves realistic representation of experimental boundary

conditions as shown in Fig. 4.3(a). In this approach, the effect of shaker and reaction

mass is included and the flexibility of the actuator is modeled. Excitation to the system is

applied by equal and opposite forces, Fcom(t), across a spring representing the stiffness of

the hydraulic actuator of the centrifuge shake table (as shown in Fig. 4.4). This paper

reserves the phrase “flexible-actuator-prescribed-force boundary condition” to denote the

123

input motion boundary condition corresponding to this approach. In this input motion

boundary condition, the boundary between the soil model and the shaking table is treated

as an “absorbing-boundary” so that the energy transfer out of the soil model through the

shaking table and the reaction mass can be taken into account. The two main outputs

corresponding to the prescribed-force simulation are the motions, which are calculated as

a function of soil shear modulus, G, at the base of the soil column ab_pf(G) and at the

ground surface as_pf(G), as schematically shown in Fig. 4.3(a).

4.2.1.2 Prescribed-displacement simulation

In this suite of analysis, the effect of shaker and reaction mass is excluded. The

calculated motion at the base of the soil column from the prescribed-force simulation

(ab_pf(G)) is used as a prescribed displacement at the base of the soil column (Fig. 4.3(b)).

The purpose of this suite of analysis is to mimic a simulation model which adapts

measured motion at the base of the soil column from the experiment as an input motion

for dynamic excitation (ab_pd). The main output corresponding to the prescribed-

displacement is the motion, which is calculated as a function of soil shear modulus at the

ground surface as_pd(G), as schematically shown in Fig. 4. 3(b).

4.2.2 Soil model

A 1D shear-beam type FE model is employed to simulate soil site response, where

soil is modeled with 4-node quad elements using two different material models. A linear

elastic nDmaterial (Mazzoni et al. 2006), with a constant shear modulus along the depth

of soil profile, is used in the first series of analysis. The second series of analysis employs

an elasto-plastic plastic constitutive model, PressureDependMultiYield (PDMY). Within

124

the PDMY material, plasticity is formulated based on the multi-surface concept. The

following equation defines the low-strain shear modulus of soil (G) as a function of

instantaneous effective confinement (p′).

5.0

''⎟⎟⎠

⎞⎜⎜⎝

⎛=

rr p

pGG (4.1)

A complete description of the PDMY material model is described in Yang et al.

2003, and a list of recommended modeling parameters is given at the UCSD website

⟨http//cyclic.ucsd.edu/opensees/⟩. The main modeling parameters of both linear elastic

and PDMY soil materials used in this current study are listed in Table 4.2.

4.2.3 Shaker and reaction mass

The shaking table and reaction mass are modeled as lumped masses, allowing

only horizontal movements. A relatively soft spring, kh, is used to model the suspension

system of the reaction mass (kh=kact/100). The effects of the mass and stiffness of the

model container and the compliance of the vertical bearing supports at the base of the

container are considered by Ilankatharan et al. (2008) but these effects are not considered

in this study. A simplified model of an actuator system, illustrated in Fig. 4.4, is used in

the analysis. The main components of this actuator model are briefly described below.

1k - A stiff spring across which the input excitation is applied – this represents the

stiffness of the servo-control system. In this study, it is assumed that the k1 = 10 k2.

2k - A spring to represent the stiffness of the actuator due to compressibility of oil and

mechanical connections between the actuator and the payload. Assuming that the

125

compressibility of the oil is the most flexible component, 2k can be calculated using the

following equation for an actuator with single piston.

LAk β=2 (4.2)

where, β is the bulk modulus of oil; A is the cross sectional area of piston ( 2

4DA π

= , D

is the diameter of the piston); L is the stroke of piston.

actk - A parameter is to represent the effective stiffness of the actuator; actk is defined

as follows,

21

111kkkact

+= (4.3)

The above equation implies, k1 = 11 kact and k1 = 1.1 kact. A wide range of values are used

for kact in order to vary the effective stiffness of the actuator with respect the stiffness of

the soil.

−2c A dashpot representing the damping associated with the actuator spring k2. 2c is

calculated as follows,

critactcc ξ=2 (4.4)

mkc actcrit 2= (4.5)

where, actξ is the damping ratio associated with the actuator element; a wide range of

values was used in the suite of analysis to systematically vary actξ , critc is the critical

damping, and m is the payload mass (i.e., mass of the shaking table and soil).

126

)(tFcom - Excitation force command to the system. )(tFcom is calculated as follows,

)()( 1 tdktF comcom = (4.6)

where, )(tdcom is the command displacement. Fig. 4.5 shows the time histories of

command acceleration and command displacement used in this study.

4.2.4 Selection of damping parameters and input variables

A wide range of values are chosen for main input parameters of the shaker system

and the damping parameters to characterize the dynamics of the centrifuge-shaker system

for various scenarios. The following non-dimensional groups are formulated with

important input variables of the different components of the shaker system.

HGAkact

/- Ratio between the stiffness of the actuator and the stiffness of soil

RM

soil

MM - Ratio between the mass of soil and mass of reaction mass

ST

soil

MM - Ratio between the mass of soil and mass of shaking table

Both in the simulations involving the linear elastic soil material, and the elasto-

plastic soil material in addition to the hysteric damping generated by the stress-strain

loops of PDMY material, a very small amount of frequency dependent viscous

damping, soilξ , was assigned to the soil column. For the soil damping, a combination of

mass and stiffness proportional damping was employed for the purpose of numerical

stability. The coefficients of stiffness dependent and mass dependent damping matrices

are chosen such that the resultant damping ratio soilξ is roughly constant in the frequency

127

range of interest. Specifically, the damping was set to soilξ =2.5% at the first and third

modal frequencies. An example calculation procedure is illustrated in Fig. 4.6. Table 4.3

lists the range of non-dimensional and damping parameters used in the course of the

numerical simulations.

4.3 Simulation results

A base line case is defined by using a set of damping parameters and input

variables to model a representative centrifuge-shaker system

( ,1/

=HGA

kact ,5.0=RM

soil

MM

,5=ST

soil

MM

ξact=20%, and ξsoil=2.5%). The results of the series

of simulations of the above representative centrifuge-shaker system is presented in this

section.

4.3.1 Linear elastic soil material model simulations

Representative simulation results using the linear elastic soil material model are

presented in Fig. 4.7, in terms of acceleration time histories and response spectra (5%

damping) at the base of the soil column and ground surface, for the prescribed-force and

prescribed-displacement simulations. As shown in Fig. 4.7, if the shear modulus of soil

material is perfectly modeled in the simulation (i.e. assumed shear modulus in simulation

is equal to the actual value listed in Table 4.2, Gassumed/Gactual=1), then the calculated

surface response in the prescribed-displacement simulation is identical to that of the

prescribed-force simulation; the soil properties are perfectly modeled in the simulation,

then the results are independent of the input motion boundary conditions.

128

Next we consider a hypothetical simulation of a soil model for which the shear

modulus assumed in the simulation, Gassumed, is not perfect. For example, assume that

(Gassumed/Gactual=0.64), where Gactual is the actual value of shear modulus of the soil

column. This 36% error in shear modulus corresponds to a 20% error in shear wave

velocity. For this case, prescribed-force simulation assumes the reduced G; but the

original input excitation Fcom(Gactual) is used. Since the base motion for the prescribed-

force simulation depends on the soil properties, the resulting calculated container base

motion has an error caused by the error in assumed shear modulus. For the prescribed-

displacement simulation the same reduced value of G is assumed; and the input is taken

as the base motion at the base of the actual soil column abase(Gactual) calculated by the

prescribed-force simulation, which simulation assumes accurate G (i.e. Gactual), as an

input. Fig. 4.8 shows the simulation results for this scenario, in terms of time histories

and acceleration response spectra (5% damping) of calculated motions at the base of the

soil column and at ground surface. From Fig. 4.8, it is apparent that the results are

different for different boundary conditions. The base motion calculated in the prescribed-

force simulation is quite different from that of the prescribed-displacement simulation.

Calculated surface motions from different simulation models are also significantly

different. Time history of surface motion in the prescribed-displacement simulation

shows the presence of gradually decaying periodic vibration cycles and requires a larger

number of cycles before it stabilizes to zero; but, the surface motion calculated from the

prescribed-force simulation does not show these vibration cycles. Discrepancies in the

spectral accelerations of base motion and surface motion in two boundary conditions are

significant at the vicinity of fundamental periods of soil column. For instance, the

129

response spectrum of calculated base motion in the prescribed-force simulation shows

reductions around 0.025 sec and 0.008 sec which are natural periods of first and second

vibration modes of soil column. But these reductions in spectral acceleration of base

motion are not possible in the prescribed-force simulation; since the input motion

employed in the prescribed-displacement simulation is not compatible with the shear

modulus of soil assumed in the simulation. Applying this mismatched base motion in the

prescribed-displacement simulation results in significant discrepancies in the surface

response around the fundamental vibration modes of the soil column.

Fig. 4.9 compares the ratios of Fourier amplitudes estimated, between the surface

motion and the base motion, and between the base motion and the command motion, for

different simulation models, and for different Gassumed/Gactual ratios. Fig. 4.5 shows the

command motion (acom(t)) which is used to estimate command displacement (dcom(t)), and

then the command force (Fcom(t)) in the actuator model. As expected, if the shear

modulus of soil is perfectly modeled (i.e. Gassuumed/Gactual=1) then the results are

independent of input motion boundary conditions. For this case, the plot of ratio of

Fourier amplitude between the surface motion and base motion shows peaks at 50Hz,

150Hz, and 250Hz which are corresponding to the natural frequencies of first three

vibration modes of the soil column, respectively; while the plot of ratio of Fourier

amplitude between the base motion and the command motion shows valleys at these

frequencies. A significant loss of frequency content in the base motion near the natural

frequency of the soil model is clearly observed from this plot. The soil model acts as a

vibration “absorber” near its natural frequency, which causes a significant amount of

dynamic interaction between the soil model and the actuation system. As a result, the

130

peaks in the ratio of Fourier amplitudes between the surface motion and the base motion

in Fig. 4.9(a) correspond to valleys in the ratio of Fourier amplitudes between the base

motion and the command motion in Fig. 4.9(c). Although the calculated surface motions

and base motions are quite different for the prescribed-force and prescribed-displacement

simulations, which assume a lower G (i.e. Gassuumed/Gactual=0.64), the ratio of Fourier

amplitudes between the surface motion and base motion is identical for both boundary

conditions; which is consistent with a behavior of the linear elastic soil material. In this

case, the ratio of Fourier amplitudes between the base motion and the command motion

for prescribed-displacement simulation is identical to that of the base line case

(Gassumed/Gactual=1). However, it is different for prescribed-force simulation. The

discrepancy arises because the dips in base response associated the energy absorption of

the overlying soil deposit occur at the actual natural periods of the soil, but the calculated

amplification in surface response in the simulation depends on the assumed natural

periods which depend on Gassumed. If prescribed-force input motion boundary conditions

is assumed, then the changes in frequency of the dips correspond to the changes in

frequency of amplification. These changes in base response cannot be evaluated using the

prescribed-displacement input motion boundary condition in the simulation (see Fig.

4.9(b) and Fig. 4.9(d)).

The shear modulus of the linear elastic soil material is systematically varied from

the baseline case, Gactual (the value shown in Table 4.2), to determine the sensitivity of

results for different boundary conditions. The percentage error in simulation results (in

terms of peak and peak spectral accelerations) with respect to the base line case is plotted

against the percentage error in assumed shear modulus (Gassumed) from base line case

131

(Gactual), in Fig. 4.10. If the ratio of Gassumed/Gactual=1, then the error in Gassumed is 0%; for

Gassumed/Gactual=0.64, error in Gassumed is -36%. From Fig. 4.10, it is evident that the

sensitivity of simulated surface and base response to uncertainties in modeling shear

modulus is dependent on how the input boundary conditions are incorporated in the

simulation models. Interestingly, the prescribed-force simulation yields well defined

sensitivities for both surface and base responses; whereas, the prescribed-displacement

simulation does not show a clear trend for sensitivity of surface response, in some cases it

results unreasonably large error in calculated surface response. As mentioned earlier, the

base motion cannot be predicted from the prescribed-displacement simulation, since it

uses a prescribed base displacement estimated from the base line case as an input.

Therefore the sensitivity of base response to error in shear modulus is not applicable to

the prescribed-displacement simulation.

4.3.2 Elasto- plastic PDMY soil material model simulations

Representative simulation results using the elasto-plastic PDMY soil material

model are presented in Fig. 4.11, in terms of acceleration time histories at the base of the

soil column and at ground surface, for the prescribed-force and prescribed-displacement

simulations. As seen from Fig. 4.11(a) and Fig. 4.11(c), if the material properties of the

soil column are perfectly modeled in the simulation (e.g. Gr_assumed=Gr_actual), then the

simulated surface response is independent of input motion boundary conditions. When

the assumed value of Gr is 36% lower than actual value, similar to the results shown for

the simulations using elastic soil material, error in Gr causes significant discrepancies in

simulation results in the prescribed-force and prescribed-displacement simulations (see

Fig. 4.11(b) and Fig. 4.11(d)).

132

To examine the simulated response for a significantly larger input excitation for

which soil nonlinearity becomes significant, a suite of analysis was then repeated using a

larger input command (10 times larger than the acom(t), and dcom(t) shown in Fig. 4.5).

The simulation results are shown in Fig. 4.12. As shown in Fig. 4.12, results are not

dependent on the input motion boundary conditions when the shear modulus of the soil

column is perfectly modeled in the simulations; but, the results are dependent on the

boundary conditions for the simulation with an imperfect reference shear modulus. Fig.

4.13 compares the ratios of Fourier amplitudes between the surface motion and the base

motion, and between the base motion and the command motion estimated using this

larger input, in different simulation models, for different assumed Gr values. As observed

earlier, for the simulation with the elastic soil material, a significant loss of frequency

content in the base motion near the frequencies of peaks at ratios of Fourier amplitudes

between the surface motion and base motion can be seen in Fig. 4.13. This significant

loss of frequency content in the base motion may be attributable to the dynamic

interaction between the soil model and the actuation system. It is observed in Fig. 4.13,

when Gr is perfectly modeled, there are no discrepancies in results between the

prescribed-force and prescribed-displacement simulations. However, when Gr is

imperfectly modeled, the ratios of Fourier amplitudes are very sensitive to the input

motion boundary conditions. For example, when Gr_assumed/Gr_actual=0.64, the locations

and the magnitudes of peaks of ratio of Fourier amplitudes between the surface motion

and base motion, especially at high frequencies, are significantly different in different

simulation models.

133

In the suite of analysis using the larger input motion, the reference shear modulus

of the PDMY material (Gr) is systematically varied from baseline case (the value shown

in Table 4.2) to determine the sensitivity of results for different boundary conditions.

Fig. 4.14 presents representative results from this sensitivity analysis; the percentage

error in calculated peak acceleration with respect to the base line case is plotted against

the percentage error in Gr from base line case (Gr_actual). From Fig. 4.14, it is clear that

the sensitivities of peak surface and base accelerations to uncertainties in Gr depend on

how the input motion boundary conditions are incorporated in the simulations.

Furthermore, the prescribed-force simulation yields well behaved sensitivities for peaks

of both base and surface accelerations; while the prescribed-displacement simulation

results do not show a clear trend for sensitivities of surface acceleration; also the

sensitivity of the base response to uncertainties in the modeling parameters cannot be

rigorously assessed using the prescribed-displacement idealization.

4.4 Parametric studies

A series of parametric studies is then performed by varying the damping

parameters and input variables as shown in Table 4.3. Some of the results from these

parametric studies are presented in this section.

4.4.1 Effect of ξact

Fig. 4.15 compares the sensitivity of calculated peak acceleration of the surface

and base motions to error in Gassumed of elastic soil material in the prescribed-force and

prescribed-displacement simulations, for different ξact values considered in the

simulations. As can be seen from Fig. 4.15, sensitivities of calculated peak accelerations

134

to errors in G depend on how the input motion boundary conditions are incorporated in

the simulations. For the range of ξact values considered in this study, the prescribed-force

simulation yields well behaved sensitivities for peak surface acceleration; whereas, the

sensitivities of peak surface accelerations in the prescribed-displacement simulations

show no consistent behavior. The errors are always positive due to the mismatch between

the resonance of the soil column and the frequency of the dips in the base motion; and

significantly large, in some cases. Simulation results from the prescribed-force simulation

also show that base response is sensitive to the errors in G. As presented in Fig. 4.15, the

sensitivities of peak base acceleration to errors in G generally show a consistent trend in

prescribed-force simulations. Hence, in sensitivity studies utilizing the flexible-actuator-

prescribed-force input boundary condition, in addition to surface motion, base motion can

also be used to evaluate the effect of G on the simulation results.

4.4.2 Effect of ξsoil

Fig. 4.16 compares the sensitivities of peaks of calculated surface and base

accelerations to error in Gassumed of elastic soil material in the prescribed-force and

prescribed-displacement simulations, for different ξsoil values employed in the analyses.

From Fig. 4.16, it is again clear that the both base and surface responses to error in G

depend on how the input motion boundary conditions are incorporated in the analyses.

For different ξsoil values employed in the analyses, the prescribed-force simulations

generally yield smoother variations for sensitivities of peak base and peak surface

accelerations. As shown in Fig. 4.16, in the prescribed-force simulations, the errors in

peak surface accelerations are smaller for the higher ξsoil values chosen in the analyses

135

and the errors in peak base accelerations are similar for both ξsoil=10% and ξsoil=25%;

however, they are different from the results shown for ξsoil=2.5%. For small soil damping

and the prescribed-displacement assumption, errors in G tend to result in greater peak

acceleration (due to energy being trapped in the soil specimen). In the prescribed-

displacement simulations, as soil damping increases, the sensitivity of peak surface

acceleration to errors in G decreases and shows consistent trends (see the prescribed-

displacement simulation results in Fig. 4.16 (b) and Fig. 4.16(c)). A higher soil damping

ratio may be deduced from the experiment if there are inconsistencies between the

resonant frequency (peaks in transfer function, see Fig. 4.9) and the dips in the base

motion (Elgamal et al. 2005). In some cases the sensitivity of peak surface acceleration to

errors in shear modulus was of opposite sign for the prescribed-force and prescribed-

displacement simulations.

4.4.3 Effect of actk & RMM

Representative results from a simulation of a linear soil model, with a relatively

stiff actuator ( 20/

=HGA

kact ) and a relatively heavy reaction mass ( 1.0=RM

soil

MM

), are

presented in Fig. 4.17; which may be compared to Fig. 4.7 and Fig. 4.8 for a more

flexible actuator and lighter reaction mass ( 1/

=HGA

kact , 5.0=RM

soil

MM ). Again we show

that if soil properties are perfectly modeled, the results are independent of the input

motion boundary conditions. If there is a 36% error in G, then the results do depend on

the input motion boundary condition. However if the actuator is relatively stiff and the

reaction mass is relatively heavy, the dependence on the input motion boundary condition

136

is relatively small. Hence, if a rigid actuator and heavy reaction mass are used in an

experiment, then it is reasonable to assume a prescribed-displacement input boundary

condition.

4.5 Ground motion analogy: Rigid and Compliant base

An example site response problem, illustrating how the sensitivities of predicted

surface response to uncertainties in modeling shear wave velocity of soil vary for

different input motion boundary conditions, was presented in Mejia et al. (2006). In their

study, a ‘deconvolution’ analysis using a 1-D wave propagation code, in this case a linear

analysis SHAKE, was performed to obtain an appropriate input at the base of a nonlinear

FLAC model. Seismic excitation to FLAC model was input using either a ‘rigid base’ or

a ‘compliant base’ options in FLAC. Details of these deconvolution procedures, and

different input motion boundary conditions are depicted in Fig. 4.18. As shown in Fig.

4.18, in both cases, the target earthquake, a modified recording from Kobe Earthquake,

was input at the top of the SHAKE column as an outcrop motion. Then, for the case

involving a ‘rigid base’ FLAC model, the motion at the top of the half space was

extracted as a ‘within’ motion and was applied as an acceleration time history to the base

of the FLAC model (shown in Fig. 4.18(a)). This excitation procedure is the same as the

prescribed-displacement input motion boundary condition described in this paper.

Whereas, for the case involving a ‘compliant base’ FLAC model, the upward propagating

wave motion (1/2 the outcrop motion) was extracted from SHAKE analysis at the top of

the half space and then used to convert the corresponding stress time history. Then the

estimated stress time history was applied to the base of the FLAC model (shown in Fig.

4.18(b)). This excitation procedure is analogous to the flexible-actuator-prescribed-force

137

input motion boundary condition described in this paper. When the soil properties are

perfectly modeled in the simulations, similar to the results shown in this paper, it was

shown in their study that the computed ground surface motions from FLAC models were

same for both ‘rigid base’ and ‘compliant base’ cases; and virtually identical to the target

motion, applied at ground surface as outcrop motion, used in SHAKE analysis.

Their study also addresses an interesting scenario to illustrate the relative

advantage of using the ‘compliant base’ idealization over the ‘rigid base’ idealization. In

this case, for simplicity, all layers were assigned a uniform shear wave velocity of 250

m/sec and uniform density. A SHAKE analysis was then performed to compute the

appropriate input for FLAC model. As explained earlier, the appropriate input for FLAC

model would be an acceleration time history of extracted ‘within’ motion for the ‘rigid

base’ case; and a stress time history, converted using the estimated upward propagating

wave motion for the ‘compliant base’ case. Then, the estimated inputs were adapted to

FLAC model that has a shear wave velocity 5% lower than the 250m/sec used in the

SHAKE analysis. Fig. 4.19 compares the calculated surface response from FLAC model

for both ‘rigid base’ and ‘compliant base’ cases. From Fig. 4.19, it is clear that the

sensitivity of ground surface response to a small error in shear wave velocity is very

sensitive to the input motion boundary conditions. Applying this mismatched input to

rigid-base as a prescribed displacement develops large amplitude periodic vibrations due

to the excitation of standing waves within the model (i.e. no energy transfer across the

“rigid-base” boundary). The mode shapes and the periods of vibration of these standing

waves can be seen, from the response spectrum, in Fig. 4.19(b). In contrast to the ‘rigid-

base’ case, the calculated ground surface motion in the ‘compliant-base’ case only

138

slightly differs from the target motion, and shows no presence of these standing waves

due to energy transfer across the “absorbing-base” boundary. Furthermore, it was argued

in their study that the presence of these reflections off the ‘rigid base’ is not always

readily apparent in complex non-linear FLAC analyses, as they can be masked by the

high damping at larger strains in non-linear soil models; and they can have a major

impact on analysis results, especially when cyclic degradation or liquefaction soil models

are employed. Hence a ‘compliant base’ is preferable to a ‘rigid base’, since it models

energy transfer out of the soil model through the base and accounts for the changes in the

motion at the base of the soil model caused by the errors in the frequencies of energy

absorption associated with the errors in input soil properties.

4.6 Discussion

4.6.1 Importance of proper treatment of boundary conditions on the sensitivity

analysis

In a validation phase of a computational simulation, it is common to perform in-

depth sensitivity studies to understand the sensitivity of simulation results to uncertainties

in modeling parameters. Arguably, sometimes, in these sensitivity studies less attention is

given to uncertainties in modeling boundary conditions. For example, in some cases,

numerical modelers make simplified assumptions in their simulations regarding the

complex boundary conditions involved in the actual problem (it could be an experiment

or a real physical problem) and use those simulations to perform sensitivity studies to

propagate the uncertainties in modeling parameters on the results. Results from these

sensitivity studies are then used validate the numerical simulations. But as we have

139

shown, the calculated sensitivities of the results are affected by the boundary conditions

used in the simulations. The conclusions drawn from sensitivity studies are not general if

sensitivities depend on the approximation of the boundary conditions.

4.6.2 Need for realistic numerical models of servo-hydraulic actuation system

Modeling the input motion boundary condition using the flexible-actuator-

prescribed-force approach requires a realistic representation of experimental boundary

conditions and the detailed modeling of various components of the centrifuge-shaker

system to include the effects of dynamic interaction between the test specimen and the

servo-hydraulic actuation system on the simulation results. In general, dynamic

interaction between a test specimen and the servo-hydraulic actuation system depends on

many factors such as characteristics of the test specimen, compliance of reaction mass,

compressibility of oil column in the actuator chamber, non-linear flow characteristics in

the actuator, servo valve time delay, configuration and characteristics of control loops,

etc. Therefore to fully incorporate the effects of the test specimen-actuation system

interaction on the simulation models, realistic models of actuator, servovalve, and

controller are required. Various analytical models to capture the salient features of

actuator, servovalve, and controller are available in the literature for structural shaking

table experiments and real-time pseudo dynamic testing in the context of structural

engineering (Conte et al. 2000, Williams et al. 2001, and Jung et al. 2006). It would be

ideal for a shaking table to have a heavy reaction mass and a stiff actuator so that the

effect of dynamic interaction between the soil model and actuation system on the test

results is minimal. Unfortunately, especially for most shaking tables on geotechnical

centrifuges, the real shaking tables are far from this ideal. Geotechnical centrifuge

140

experiments often involve relatively heavy and highly nonlinear test specimens (e.g., a

massive volume of liquefying sand). Additional work is required to understand the

interaction of highly nonlinear massive test specimens with non-ideal servo-hydraulic

actuation systems that are driven at their performance limits (in their nonlinear range).

4.7 Conclusions

Example simulations of a hypothetical centrifuge experiment have been presented

to illustrate the effects of using two different input motion boundary conditions on the

simulation results in various scenarios. In both the simulations using the linear elastic and

the elasto-plastic PDMY soil material models, if the shear modulus of the soil material is

perfectly modeled then the results are independent of the input motion boundary

conditions. Conversely, the predicted surface response is dependent on the input motion

boundary conditions when the shear modulus is imperfectly modeled in the simulations.

As expected, it is shown that the ratio of Fourier amplitudes between the surface motion

and the base motion (i.e surface transfer function) is also independent of the input motion

boundary conditions when a linear elastic soil material with an imperfect shear modulus

is employed in the analysis. However, the ratio of Fourier amplitude between the surface

motion and the base motion is dependent on the input motion boundary conditions when

a nonlinear soil material with an imperfect shear modulus is used in the analysis. In this

case, higher discrepancies are observed near frequencies at which peaks of ratio of

Fourier amplitudes occur. The ratio of Fourier amplitudes between the base motion and

the command motion (i.e. base transfer function) is dependent on the input motion

boundary conditions when the shear modulus of the soil material (both in linear elastic

and PDMY material) is imperfectly modeled in the simulations. This is because the dips

141

(valleys) in the base transfer function associated the energy absorption of the overlying

soil deposit occur at the natural periods of the soil, but the calculated amplification

(peaks) in the surface transfer function depends on the assumed natural periods which

depend on the assumed shear modulus in the simulations. If a prescribed-force input

motion boundary condition is assumed then the changes in frequency of dips correspond

to the changes in frequency of amplification. These changes in base response cannot be

evaluated using the prescribed-displacement input motion boundary condition.

Further, the flexible-actuator-prescribed-force approach which employs an

absorbing-base boundary generally yields well behaved sensitivities for results in a wide

range of simulation conditions. The prescribed-displacement approach, however, may

produce chaotic results. Therefore, when performing the numerical simulations on a

geotechnical centrifuge experiment, modeling input excitation using the first approach

may be preferable to the second approach.

The most general conclusion of this study is that the sensitivity of numerical

simulation results to uncertainties in modeling parameters depends on how the input

motion boundary conditions are accounted for and the dynamic interactions among the

various components of the dynamic system. This raises a fundamental question: How can

we assess the significance of a discrepancy between a numerical simulation and an

experimental result? A large error in response may be caused by a small error in input

parameter if, for example, a rigid boundary condition is assumed. . This paper shows that,

for shaking table tests, the significance of errors in the numerical simulations cannot be

rigorously assessed without accounting for dynamic interaction between the test

specimen and the actuation system.

142

4.8 Acknowledgements

The authors would like to acknowledge Prof. Ross Boulanger, Dr. Dan Wilson,

Lars Pedersen, and the staff of the UC Davis Center for Geotechnical Modeling for their

support in the course of this study. The operation and maintenance of the centrifuge

including development of a numerical model of the centrifuge shaker is made possible by

funding from NSF award # CMS-0402490 through a sub award from NEESinc.

4.9 References

Arulanandan, K,, and Scott, R. F., 1993. Project VELACS; control test results, Journal of

geotechnical engineering, 119(8), 1276-1292.

Conte, J. P., and Trombetti, T. L., 2000. Linear Dynamic Modeling of a Uni-Axial Servo-

Hydraulic Shaking Table System, Earthquake Engineering and Structural Dynamics,

Vol. 29, No. 9, pp. 1375-1404.

Elgamal, A., Yang, Z., Lai, T., Kutter, B.L., and Wilson, D.W., 2005. Dynamic Response

of Saturated Dense Sand in Laminated Centrifuge Container, J. Geotech. Geoenviron.

Eng., ASCE, 131(5) pp. 598-609.

Ilankatharan, M., and Kutter, B. L., 2008. Numerical Simulation of a Soil Model-Model

Container-Centrifuge Shaking Table System, Geotechnical Earthquake Engineering

and Soil Dynamics IV, D. Zeng, M. Manzari, and D. Hiltunen, eds., Geotechnical

Special Publication No. 181, ASCE, NY.

Jung, R. Y., and Shing, P. B., 2006. Performance evaluation of a real-time

pseudodynamic test system, Earthquake Engineering and Structural Dynamics, Vol.

35, No. 7, pp. 789-810.

143

Kutter, B.L., 1992. Dynamic centrifuge modeling of geotechnical structures,

Transportation Research Record 1336, TRB, National Research Council, National

Academy Press, Washington, D.C., pp. 24-30.

Kutter, B.L., 1995. Recent Advances in Centrifuge Modeling of Seismic Shaking, State-

of-the-Art Paper, Proceedings, Third International Conference on Recent Advances

in Geotechnical Earthquake Engineering and Soil Dynamics, St. Louis, MO, Vol.2,

pp. 927-942.

Mazzoni, S., McKenna, F., Scott, M.H., and Fenves, G., 2006. The OpenSees Command

Language Manual: version 1.7.3, Pacific Earthquake Engineering Center, Univ. of

Calif., Berkeley. ⟨http://opensees.berkeley.edu⟩.

Mejia, L.H., and Dawson, E.M., 2006. Earthquake Deconvolution for FLAC,

Proceedings, Fourth International FLAC Symposium on Numerical Modeling in

Geomechanics, Madrid, Spain.

Williams, D. M., Williams, M. S., and Blakeborough, A., 2001. Numerical Modeling of a

Servohydraulic Testing System for Structures, Journal of engineering mechanics,

127(8), 816-827.

Yang, Z., Elgamal, A., & Parra, E., 2003. Computational model for cyclic mobility and

associated shear deformation, Journal of geotechnical and geoenvironmental

engineering, 129(12), 1119-1127.

144

Table 4.1 Centrifuge scaling factors at the centrifuge acceleration (g) level of 50

Quantity Prototype Scale/Model Scale

Stress 1

Acceleration 1/50

Length 50

Mass 503

Time 50

Force 502

Table 4.2 Main modeling parameters for soil material models

Linear elastic nDmaterial

Elasto-plastic PDMY material

Modeling parameter Parameter

value Modeling parameter

Parameter

value

Soil mass density (Mg/m3) 2.0 Soil mass density (Mg/m3) 2.0

Shear modulus, G (kPa) 80000 Reference mean effective

confining pressure, p′r (kPa) 80

Poison’s ratio 0.35 Reference low-strain shear

modulus at p′r=80kPa, Gr (kPa) 36000

Reference Bulk Modulus at

p′r=80kPa, 108000

Friction angle, φ (deg) 29

Peak shear strain 0.1

Phase transformation angle (deg) 27

145

Table 4.3 Selection of input variables for shaker system

Variable Values used in the analysis

HGAkact

/ 1 and 20

RM

soil

MM

0.1 and 0.5

ST

soil

MM

5

actξ (%) 5, 20 and 40

soilξ (%) 2.5, 10 and 25

146

Fig. 4.1 3D rendering of a soil model-container-centrifuge shaking table system

Vertical bearings

FSB container

Soil model

Structural model

Centrifugal force

Actuator

Shaking table

Reaction mass

Fig. 4.2 Reflection and refraction of seismic waves at the container base

Reflected wave

Transmitted energy

Reflected wave

Soil

Container base Excitation

Ground surface

147

Fig. 4.4 Configuration of the actuator elements

Connected to reaction mass

k2

c2

Fcom(t)

Connected to shaking table

k1

Fcom(t)

Fig. 4.3 Different input motion boundary conditions in the simulations

(a) Flexible-Actuator-Prescribed-Force boundary condition

H=1m

Actuator

Soil G

aba(G)

as_pf(G)

Fcom(t)

Soil G

ab_pf(G)

Shaking table Actuator

kh Reaction mass

(b) Prescribed-Displacement boundary condition

Soil G

ab_pd=ab_pf(G)

as_pd(G)

148

Fig. 4.5 Time histories of (a) command acceleration, and (b) command displacement of the input motion

(a) command acceleration

a com

(t) (g

)

-0.05

0.00

0.05

(b) command displacement

time (sec)0.00 0.25 0.50 0.75 1.00

d com

(t) (m

m)

-0.2

0.0

0.2

Fig. 4.6 Calculated frequency dependent soil damping ratio (ξsoil) by combining stiffness proportional and mass proportional damping: an example case for ξsoil = 2.5% at the first and the third modal frequencies (50 Hz and 250 Hz)

frequency (Hz)0 50 100 150 200 250 300 350 400

dam

ping

ratio

(%)

0

1

2

3

4

5

stiffness proportional dampingmass proportional dampingresultant damping ratio (ξsoil)

149

(c) base motion

time (second)

0.2 0.3 0.4 0.5 0.6

-2

0

2

(a) surface motion

horiz

onta

l acc

eler

atio

n (g

)

-2

0

2

prescribed-forceprescribed-displacement

(d) ARS of base motion

period (second)

0.00 0.02 0.04 0.06 0.080

5

(b) ARS of surface motion

0.00 0.02 0.04 0.06 0.08

spec

tral a

ccel

erat

ion

(g)

0

5

Fig. 4.8 Time histories and response spectra (5% damping) of surface and base motions in

the prescribed-force and prescribed-displacement simulations employing a linear elastic soil

material (Gassumed/Gactual=0.64)

Fig. 4.7 Time histories and response spectra (5% damping) of surface and base motions in

the prescribed-force and prescribed-displacement simulations employing a linear elastic soil

material

(c) base motion

time (second)

0.2 0.3 0.4 0.5 0.6

-2

0

2

(a) surface motion

horiz

onta

l acc

eler

atio

n (g

)

-2

0

2


(b) ARS of surface motion

0.00 0.02 0.04 0.06 0.08

spec

tral a

ccel

erat

ion

(g)

0

5

(d) ARS of base motion

period (second)

0.00 0.02 0.04 0.06 0.080

5

150

Gassumed/Gactual=1

|FFT

of s

urfa

ce a

cc| /|

FFT

of b

ase

acc|

0

10

20

30


Gassumed/Gactual=1

frequency (Hz)50 100 150 200 250 300 350

|FFT

of b

ase

acc| /

|FFT

of c

omm

and

acc|

0.0

0.5

1.0

1.5

Gassumed/Gactual=0.64

|FFT

of s

urfa

ce a

cc| /|

FFT

of b

ase

acc|

0

10

20

30

Gassumed/Gactual=0.64

frequency (Hz)50 100 150 200 250 300 350

|FFT

of b

ase

acc| /

|FFT

of c

omm

and

acc|

0.0

0.5

1.0

1.5

(a) (b)

(c) (d)


Fig. 4.9 Ratios of Fourier amplitudes between the surface motion and the base motion, and

the base motion and the command acceleration, in the prescribed-force and prescribed-

displacement simulations employing a linear elastic soil material

151

(a)

erro

r in

peak

surf

ace

acc

(%)

0

50

100prescribed-forceprescribed-displacement

(c)

error in Gassumed (%)

-40 -20 0 20 40

erro

r in

peak

bas

e ac

c (%

)

0

50

100

(b)

erro

r in

peak

surf

ace

AR

S (%

)

0

50

100

(d)


-40 -20 0 20 40

erro

r in

peak

bas

e A

RS

(%)

0

50

100




Fig. 4.10 Sensitivity of peak & peak spectral accelerations of surface and base motions to


displacement simulations

152

time (second)0.2 0.3 0.4 0.5

base

mot

ion

(g)

-2

0

2

Gr_assumed/Gr_actual=1

surf

ace

mot

ion

(g)

-2

0

2

-2

0

2

absorbing-baserigid-base

time (second)0.2 0.3 0.4 0.5


Gr_assumed/Gr_actual=0.64


(a) (b)

(c) (d)




Fig. 4.11 Time histories of motions at ground surface and at base of the soil column in the prescribed-force and prescribed-displacement simulations employing the elasto-plastic PDMY soil material

Fig. 4.12 Time histories of motions at ground surface and at base of the soil column in the prescribed-force and prescribed-displacement simulations employing the elasto-plastic PDMY soil material (amplitude of the input motion 10 times larger than that shown in Fig. 4.5)

time (second)0.2 0.3 0.4 0.5

base

mot

ion

(g)

-20

0

20


surf

ace

mot

ion

(g)

-20

0

20

-20

0

20


time (second)0.2 0.3 0.4 0.5




(a) (b)

(c) (d)




153


frequency (Hz)50 100 150 200 250 300 350

|FFT

of b

ase

acc| /

|FFT

of c

omm

and

acc|

0

1

2

3


|FFT

of s

urfa

ce a

cc| /|

FFT

of b

ase

acc|

0

10

20

30



|FFT

of s

urfa

ce a

cc| /|

FFT

of b

ase

acc|

0

10

20

30


frequency (Hz)50 100 150 200 250 300 350

|FFT

of b

ase

acc| /

|FFT

of c

omm

and

acc|

0

1

2

3

(a)

(c)

(b)

(d)

Fig.4.13 Ratios of Fourier amplitudes between the surface motion and the base motion, and

the base motion and the command acceleration, in the prescribed-force and prescribed-

displacement simulations employing the elasto-plastic PDMY soil material (using the larger

input motion)

Fig. 4.14. Sensitivity of calculated peak acceleration of (a) surface motion, and (b) base motion to error in Gr_assumed of the PDMY soil material in the prescribed-force and prescribed-displacement simulations (simulations using the larger input motion)

(b) base motion

error in Gr_assumed (%)

-40 -20 0 20 40

(a) surface motion

error in Gr_assumed (%)

-40 -20 0 20 40

erro

r in

peak

acc

eler

atio

n (%

)

-20

-10

0

10

20





154

-40 -20 0 20 40

erro

r in

peak

bas

e ac

c (%

)

-25

0

25

50

erro

r in

peak

surf

ace

acc

(%)

-25

0

25

50


-40 -20 0 20 40 -40 -20 0 20 40


ξact=20% ξact=40%ξact=5%

ξact=5% ξact=20% ξact=40%

(a) (b) (c)(d) (e) (f)

Fig. 4.15 Sensitivity of calculated peak acceleration of surface and base motions to error in

Gassumed of elastic soil material in the prescribed-force and prescribed-displacement

simulations, for different ξact values (ξsoil=2.5%, ,1/

=HGA

kact

)5.0=

RM

soil

MM

and

155

-40 -20 0 20 40

erro

r in

peak

bas

e ac

c (%

)

-25

0

25

50

erro

r in

peak

surf

ace

acc

(%)

-25

0

25

50


-40 -20 0 20 40 -40 -20 0 20 40


ξsoil=10% ξsoil=25%ξsoil=2.5%

ξsoil=2.5% ξsoil=10% ξsoil=25%

(a) (b) (c)(d) (e) (f)

Fig. 4.16 Sensitivity of calculated peak acceleration of surface and base motions to error in

Gassumed of elastic soil material in the prescribed-force and prescribed-displacement

simulations, for different ξsoil values (ξact =20%, ,1/

=HGA

kact

)5.0=

RM

soil

MM

and

156

period (second)

0.000 0.025 0.050 0.075

period (second)

0.000 0.025 0.050 0.075

AR

S of

bas

e ac

c (g

)

0

5

10

15

AR

S of

surf

ace

acc

(g)

0

5

10

15


Gassumed/Gactual=1 Gassumed/Gactual=0.64

Gassumed/Gactual=1 Gassumed/Gactual=0.64

(a) (b)

(c) (d)


Fig. 4.17 ARS (5% damping) of calculated surface and base motions in the prescribed-force and

prescribed-displacement simulations, involving relatively stiff actuator and heavy reaction mass

( ,20/

=HGA

kact 1.0=RM

soil

MM

and ), for different Gassumed values of linear elastic soil material

(ξact=20%, and ξsoil=2.5%)

157

Fig. 4.18 Procedures for deconvolution of input motion for FLAC model described in Mejia et al. 2006

(a) Deconvolution procedure for rigid base

(b) Deconvolution procedure for compliant base

158

Fig. 4.19 (a) Time histories and (b) response spectrum of computed acceleration at top of soil column for rigid base, and compliant base with 5% velocity mismatch (Mejia et al. 2006)

(a)

Rigid Compliant base

Target motion (b)

159

Chapter 5

Numerical modeling of a soil-model container-centrifuge shaking table

system

This chapter presents a numerical model that was developed using OpenSees to

represent the dynamics of a soil-model container-centrifuge shaking table system. In the

numerical model, the soil, container, and shaking table were modeled using 2-D solid finite

elements. The mass and stiffness of the container as well as shear rods used to provide

complementary shear stress at the ends of the container were taken into account. The

actuator flexibility was included, and the excitation to the system was applied through the

actuator elements. Stiffness of the vertical bearing supports on the base of the container

and mass of the reaction mass were included in the analysis. The contents of this chapter

are extracted from a published paper and some additional details also included here for

completeness. The complete reference of the paper is given below.

Ilankatharan, M., and Kutter, B. L. (2008). “Numerical Simulation of a Soil Model-Model

Container-Centrifuge Shaking Table System.” Geotechnical Earthquake Engineering and

Soil Dynamics IV, D. Zeng, M. Manzari, and D. Hiltunen, eds., Geotechnical Special

Publication No. 181, ASCE, NY.

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Abstract: A numerical model is developed using OpenSees to represent the dynamics of a

soil model-model container-centrifuge shaking table system. The centrifuge shaker-system

includes soil model, the flexible shear beam model container, shaking table and its reaction

mass. All of these different components interact with the soil model during dynamic

excitation, with some absorbing energy and others allowing undesired modes to affect the

response observed in the experiment. This interaction of soil model and

centrifuge/actuation system might attenuate or amplify the discrepancies in the responses

of the numerical and physical models. The relative error between a numerical simulation

and a physical simulation depends on how the boundary conditions and interaction among

different components in the physical model are included in the numerical model.

Assessment of the quality of a comparison between a numerical and physical simulation

should account for the effects of the boundary conditions and dynamic interaction among

different components in the dynamic system. This chapter outlines the details of the

simulation model, presents some representative results from simulations, discusses the

effect of interaction among different components on the responses, and presents how the

sensitivity of simulation outputs to uncertainties in the material properties depends on

boundary conditions in the physical and numerical simulations.

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5.1 Introduction

One of the greatest challenges that earthquake engineers face is the paucity of data

available to evaluate the performance of geotechnical/structural systems during strong

earthquake motions. Earthquake engineers use laboratory experiments to understand the

performance of key components of foundation and structural systems under control

loading conditions. In this context, the use of dynamic centrifuge modeling has been

recognized by the researchers over the past 30 years. Dynamic centrifuge modeling of

geotechnical systems designed with varying soil profile characteristics,

substructure/superstructure characteristics, loading protocols, and detailed instrumentation

is used to obtain physical data, gain insight into the mechanisms involved, and perform

parametric studies to calibrate numerical models.

The Center for Geotechnical Modeling at University of California, Davis operates a

9.1m radius geotechnical centrifuge (a photograph shown in Fig 5.1) equipped with a 2 m x

1 m servo hydraulic shaking table to perform realistic earthquake simulations on the soil

models at prototype stress field conditions. Recent upgrades, funded by National Science

Foundation of United States through NEES (Network for Earthquake Engineering

Simulation), has increased the capacity of centrifuge and involved implementation of

advanced instrumentation (wireless data acquisition system, high speed video cameras,

etc), robotics, geophysical testing tools, and bi-axial shaking capability. These upgrades

increased the quantity as well as the quality of physical simulations (Wilson et al. 2007).

A 3D rendering of the UC Davis centrifuge-shaker system is shown in Fig. 5.2. The

centrifuge-shaker system includes a soil model, a flexible shear beam model container, a

shaking table and its reaction mass. All of these different components, with their own

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resonant frequencies of vibration, interact with the soil model during dynamic excitation,

some absorbing energy, some allowing undesired modes to affect the response observed in

the experiment. This interaction of the soil model and the centrifuge/actuation system

might attenuate or amplify the discrepancies in responses of the numerical and physical

models. Qualitative assessment of issues of this interaction among soil model, container,

and shaker were addressed by many researchers in the past (Fiegel et al. 1994, Narayanan,

1999). However, a detailed numerical model to mathematically represent the dynamics of

the soil-model container-shaker system is necessary for comprehensive understanding of

this interaction and quantifying the effect of this interaction on the test results.

A 2D finite element model is developed using OpenSees (Open System for

Earthquake Engineering Simulation, http://opensees.berkeley.edu/index.php) to represent

the dynamics of centrifuge-shaking table-model container-soil model system. Data from

series of highly instrumented centrifuge tests that were performed as a part of NEES

collaboration project (Ilankatharan et al. 2005) and presented in the Chapter 2 of this

dissertation are used to validate the numerical procedure. The dimensions of the finite

element domain, all modeling parameters, and the results are presented in centrifuge model

scale (52g-increased gravity field) unless otherwise specified. The centrifuge scaling

factors for some physical properties was given in Table 4.1, further details on the

centrifuge scaling laws can be found in Kutter (1992).

5.2 Modeling system components

In the numerical model, the soil, container, and shaking table are modeled using

2-D solid finite elements. The following sections describe the details of numerical models

of these various system components.

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5.2.1 Soil Model

Dry Nevada sand of a target relative density of 80% (with a thickness of 534mm) is

considered to represent the soil profile. The key soil properties of Nevada sand can be

found in centrifuge test series data report Ilankatharan et al. 2005. In OpenSees, soil is

modeled with four-node quad elements using PressureDependentMultiYield (PDMY),

elasto-plastic constitutive model (Yang et al, 2003). A complete description of material

model and recommended modeling parameters can be found at

http//cyclic.ucsd.edu/opensees/. Table 5.1 lists the main modeling parameters for this

dry-dense Nevada sand stratum. Within the PDMY material, the following equation

defines the low-strain shear modulus of soil (G) as a function of instantaneous effective

confinement (p’).

5.0

''⎟⎟⎠

⎞⎜⎜⎝

⎛=

rr p

pGG

The reference low-strain shear modulus (Gr) of Nevada sand is defined based on the

shear wave velocity data available in the literature for 80% relative density dry Nevada

sand (Arulnathan et al. 2000). In addition to the hysteric damping generated by the

stress-strain loops of PDMY material, very small amount of stiffness-proportional

damping is employed for the purpose of numerical stability with an average of 3% over the

frequency range of interest (1-500Hz). The estimated damping ratios at different

frequencies based on this employed stiffness-proportional damping are shown in Fig. 5.3.

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5.2.2 Model container

A flexible shear beam container (FSB2) was considered in this study. Fig. 5.4

presents the photographs showing the key components of the FSB2 model container. The

FSB2 container consists of an aluminum base plate and five metal rings, with overall

dimensions of 1.651×0.788×0.584 m in length, width, and height, respectively. The

container rings are sandwiched with 12 mm thick soft neoprene rubber rings providing

lateral flexibility. The dimensions and design details of various components of the

container are presented in Fig. 5.5 and Table 5.2. In OpenSees, the container metal rings,

neoprene rubber rings, and the base plate are modeled using 2D plane strain finite elements

using elastic nD material. The shear stiffness of the FSB container was determined by

matching data from static lateral loading of the empty container (Stevens, 2001). Some 3-D

behavior was approximately accounted by including the mass and stiffness contributions of

the side walls and end walls. Based on this approximation, the mass and stiffness properties

of 2D finite element container were calculated to match the mass and stiffness of the real

container when the thickness of the plane strain finite element domain set to the width of

the container (0.788m). Further, one truss element connected the centroid of each ring

section, which forced the one end of the container to follow the other end along the

longitudinal direction and allowed free twisting of the rings about an axis normal to the

plane of the problem. Stiffness of this truss element was calculated to match the axial

stiffness of the side wall tubing. As shown in Fig. 5.4, series of steel rods (shear rods) are

attached to the both end of the container. The purpose of these shear rods is to transfer the

complementary shear stresses, which would develop during a seismic shaking event, to the

base of the model container (Madabhushi et al. 1998). These shear rods are modeled using

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elastic beam column elements in the OpenSees numerical model. At the both ends of the

container, soil nodes are slaved with shear rod nodes in both horizontal and vertical

directions. The vertical bearing supports at the base of the container (shown in Fig. 5.6) are

included to incorporate the possibility of rocking of the container; the stiffness of these

bearings is modeled using elastic zero-length elements. Torsional stiffness and bending of

the rings and friction on the sides of the container were not accounted for; these were

considered to have a secondary effect on the conclusions of this study.

5.2.3 Shaker and Reaction mass

The horizontal shaking table system of the UC Davis centrifuge facility is

considered for this present study. The plan view of this shaking table system is shown in

Fig. 5.6. The horizontal shaker is driven by two servo-hydraulic actuators, which are

visible in above Figure. The design detail and actuator mechanism of the horizontal

actuation system is described in Kutter et al. (1994). The 2D finite element mesh of the

soil-model container-shaker system is depicted in Fig. 5.7. Zero-length elements, to

represent stiffness of the vertical bearing supports, connect the container base and the

reaction mass. The reaction mass is modeled using an elastic nD material, the mass of the

reaction mass is assumed to be two times the payload mass (mass of container and soil).

Excitation to the system is applied through the actuator elements. A simplified model of

actuator system, illustrated in Fig 5.8, was used for the analysis. The main components of

this actuator model are briefly described below.

1k - A stiff spring across which the input excitation is applied – this represents the stiffness

of the servo-control system; for the data presented here, it was chosen k1 = 10 k2. ( 1k =

8764640 kN/m)

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2k - A spring to represent stiffness of the actuator due to compressibility of oil and

mechanical connections between the actuator and the payload. Assuming that the

compressibility of the oil is the most flexible component. 2k can be calculated using

following equation.

LAk β42 =

where, β is the bulk modulus of oil (105 psi); A is the cross sectional area of piston

( 2

4DA π

= , D=4inches); L is the stroke of piston (L=0.5 inches for average piston

position); and the multiplier four is to account for four pistons-two pistons per actuator

(the calculated 2k is then reduced by 50% to account for the reduction in stiffness due

to the volume of trapped oil and mechanical connections).

−2c A dashpot representing the damping associated with the actuator spring, k2. 2c is

calculated as follows.

critcc ξ=2

mkccrit 22=

where, ξ is the damping ratio (ξ =40%, assumed), critc is the critical damping, and

m is the payload mass (i.e., mass of the container and soil).

inputF - Excitation force command to the system. inputF is calculated as follows.

dkFinput 1=

where, d is the command displacement.

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5.3 Boundary conditions in simulation models

To improve understanding of interactions among soil model, container, and shaker

system and to evaluate how the sensitivity of simulation results depends on boundary

conditions in experiment and simulation, the boundary conditions were treated with three

different levels of detail as described below (and depicted in Fig. 5.9).

5.3.1 1-D shear beam simulations of soil

In this suite of analyses, the container and actuator were excluded; a 1D shear-beam

type FE model is employed to simulate soil site response (Fig. 5.9(a)). The unit weight of

soil is increased by 30% to account for the effect of container mass (which is 30% of the

soil mass) on the inertia forces. Dynamic excitation, equal to the measured acceleration

time history at the base of the container, is applied to the bottom soil nodes as prescribed

displacements.

5.3.2 2-D simulations of soil and container

The FSB2 container is included in this simulation model. The mass and stiffness of

the container, and the vertical bearing supports at the base of the container are taken into

account. Dynamic excitation is imparted to the bottom container nodes along horizontal

direction (Fig. 5.9(b)). Measured acceleration time history at the base of the container is

used as prescribed displacements.

5.3.3 2-D simulations of soil, container, and shaker

The effect of the shaker is included, the flexibility of actuator and the mass of the

reaction mass are modeled as indicated in detail in Fig. 5.7 and schematically in Fig. 5.9(c).

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In this series of simulations, the base of the container is treated as an absorbing boundary

so that the energy transfer out of the soil model through the shaking table and reaction mass

can be accounted; excitation to the system is applied as a force time history through the

actuator elements (Fig. 5.8) so that the motion at the container base can be calculated.

To begin the analysis, the command displacement (d) is calculated by double

integration of the acceleration time history measured at the base of the container in the

experiment. Fig 5.10 shows the time histories of, the measured acceleration at the base of

the container and the calculated command displacement for a frequency sweep input. The

base acceleration predicted from the simulation is then compared with measured base

acceleration in the experiment. A transfer function is calculated between the measured and

the predicted responses. This transfer function is then used to modify the initial command

displacement, to obtain a reasonable (but still not identical) agreement between the base

motion calculated and the input base motions for other two cases (1-D shear beam

simulations of soil and 2-D simulations of soil and container). Further details on this

process of modifying command displacement is described later in this chapter.

5.4 Simulation results

5.4.1 Soil horizontal accelerations from 1-D shear beam simulations of soil and 2-D

simulations of soil and container

Representative simulation results of a frequency sweep excitation from the 1-D soil

shear beam simulations and 2-D simulations of soil and container are shown in Fig. 5.11

and Fig. 5.12, in terms of acceleration time histories and the corresponding response

spectra (5% damping) along the soil profile. The computed accelerations close to base of

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the container (100mm from bottom of the container) in both simulations are in reasonable

agreement with experiment. However, there are significant differences in simulation

results at other two locations. For instance, the peak in the response spectra at a period of

0.009 sec in the 1-D shear beam simulations of soil disappears when the container is

included. Also, the gradually decaying periodic vibration cycles present in the time

histories of acceleration (after 0.6 sec) predicted in the shear beam simulations are not

visible in the 2-D simulations of soil and container.

Fig. 5.13 and Fig. 5.14 compare the soil horizontal accelerations calculated in

above two simulation models for an input motion obtained from an earthquake recording

from the 1994 Northridge earthquake. Details of this Northridge input motion can be found

in Ilankatharan et al. 2005. As shown in the above figures soil accelerations predicted in

two simulation models show significant discrepancies (except near the base of the

container). Peaks shown in the response spectra at a period of 0.0095 sec in the 1-D shear

beam simulations of soil diminish when the container is included. Further, peak shown in

the response spectra, at a period of 0.0045 sec in the experiment, is better captured in the

2-D simulations of soil and container. The above results show the effects of dynamic

interaction between the soil model and model container on the soil site response. It can be

seen from above figures that, the inclusion of the model container in the simulation

improves the quality of the comparison between the simulation and the experiment.

5.4.2 Soil Vertical accelerations from 2-D simulations of soil and container

Fig. 5.15 compares the time histories and response spectra (5% damping) of soil

vertical accelerations computed in the 2-D simulations of soil and container at 50mm

below the ground surface at both ends of the container. The time histories of accelerations

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in the experiment are 180 out of phase, show rocking response of the container. It can be

seen in the time histories of the computed accelerations, the rocking behavior of the

container is well captured when the compliance of the vertical bearing supports at the base

of the container is included in the analysis.

To understand the effect of shear rods on the vertical accelerations, the above

analysis was repeated without shear rods. In this case, the elastic beam column elements

which were used to model shear rods were excluded and at both ends of the container, soil

nodes were slaved with container nodes in both horizontal and vertical directions. Fig. 5.16

compares the vertical accelerations computed with and without shear rods. As expected,

the computed vertical accelerations without shear rods are larger than that of calculated

with shear rods. The shear rods in the simulations transfer the complementary shear

stresses, which would developed during dynamic shaking, to the base of the model

container and decrease the vertical accelerations which would caused by the unequal

vertical stress distribution.

5.4.3 Results from the 2-D simulations of soil, container, and shaker

Representative simulation results from the 2-D simulations of soil, container, and

shaker are presented in Fig. 5.17, in terms of acceleration time histories and response

spectra (5% damping) along the soil profile. As mentioned earlier, in this series of

simulations excitation to the system is applied as a force time history through the actuator

elements so that the motion at the base of the container can be calculated. Fig. 5.18

compares the calculated base motion with the measured base motion from the experiment.

From Fig. 5.18, the low frequency (higher period) components of the base motions are in

reasonable agreement; however, the base response shows discrepancies in other frequency

171

ranges. These discrepancies in calculated base response propagate along the soil profile;

hence, the computed soil accelerations significantly deviate from the measured

accelerations (see Fig. 5.17).

To provide an acceptable correspondence between the computed base motion and

the measured base motion, the initial command displacement is then modified using a

transfer function calculated between the measured and the computed base motion. Fig.

5.19 presents the computed base response using the modified command displacement. As

shown in Fig. 5.19, results are in reasonable (but not identical) agreement with the

experiment. Fig. 5.20 compares the computed site response using the modified command

displacement with the experimental results. The presented simplified shaker model (Fig.

5.8), with the modified command displacement, allows a reasonable prediction of the soil

site response.

Fig. 5.21 presents the transfer function which was used to modify the original

command displacement. As described before, the original command displacement was

obtained by double integration of measured acceleration time history at the base of the

container in the experiment (shown in Fig. 5.10). Therefore, when creating Fig. 5.21, the

command acceleration was same as the measured base acceleration. Transfer function

between the surface and base motions calculated in the simulations using the original

command displacement is shown in Fig. 5.22. It can be seen from the above figures, the

valleys in the transfer function between the calculated base motion and command motion

occur at the frequencies of the peaks in the transfer function between the calculated surface

and base motions, especially around 90Hz and 224Hz which are the natural frequencies of

the soil model. The soil model acts as a vibration absorber near its natural frequency, which

172

causes a significant amount of dynamic interaction between the soil model and the

actuation system.

Fig. 5.23 compares the transfer function the between the calculated and measured

base motions for different characteristics of input. As shown in Fig. 5.23, the transfer

functions for different inputs are identical in the low frequency range (up to 60Hz) and

nearly same in the frequency range of 80Hz to 200Hz; however, they are different in the

frequency range of 60Hz to 80Hz and in the high frequency range (after 200Hz).

Therefore, when using different seismic excitations in the simulations, it would require

different transfer functions to modify the original command displacements to get

reasonable prediction of the base motions.

The shaker model presented in this chapter (Fig. 5. 10) was extended to employ the

actuator command displacement, which was specified to the servo controller during the

experiment, to calculate the force input in the simulations. Details of these simulations and

the implications of results on the base motion prediction are presented in chapter 6 of this

dissertation.

5.5 Sensitivity Analysis

The reference shear modulus of the PDMY material is systematically varied from

baseline case (the value shown in Table 1) to determine the sensitivity of simulation results

for different boundary conditions. Fig 5.24 and Fig 5.25 compare the effect of varying

shear modulus on the calculated ground surface and base response spectrum for different

boundary conditions. Fig 5.26 presents the percentage change in ground surface response

(in terms of peak and peak spectral accelerations), with respect to the base line case, against

the percentage change in reference shear modulus (Gr) from base line case (Grbaseline). A

173

similar plot for base response is presented in Fig 5.27. From figures 5.24 and 5.26, it is

evident that the sensitivity of ground surface response depends on how the experimental

boundary conditions are incorporated in the simulation models. Interestingly, for this

example, the calculated ground surface response is almost insensitive to the shear modulus

when the boundary conditions are more realistically modeled in the simulation (see Fig.

5.24 (c)). However, in some cases, calculated ground surface responses from the 1-D shear

beam simulations of soil and the 2-D simulations of soil and container are very much

sensitive to the shear modulus used in the analysis. For instance, a 25% negative change in

Gr yields, a 95% increase in peak acceleration in the 1-D shear beam simulation of soil, a

73% increase in 2-D simulation of soil and container, and a 8% increase in the 2-D

simulation of soil, container and shaker (see Fig. 5.26 (a)). As shown in Fig 5.23 and Fig

5.25, base response is sensitive to the shear modulus used in the 2-D simulations of soil,

container, and shaker simulations. The other two simulation models use prescribed base

displacement (measured motion at the base of the container in the experiment) as an input;

therefore, the sensitivities of base responses to changes in shear modulus are not applicable

to these simulation models.

Fig. 5.28 and Fig. 5.29 present the sensitivity analysis results using different

earthquake motion. The earthquake motion used here is a frequency sweep, composed of

sinusoidal cycles with gradually decreasing frequencies (the frequency sweep used in the

previous simulations composed of sinusoidal cycles of gradually increasing frequencies

(see Fig. 5.10) ), with a peak base acceleration of 13g (measured at the container base). The

percentage changes in surface and base responses are shown against the percentage

changes shear modulus, in Fig. 5.28 and Fig. 5.29. It is again clear that the results are

174

dependent on how the boundary conditions are incorporated in the simulations. Further,

sensitivities of results predicted from the 2-D simulations of soil, container, and shaker

show consistent behaviors; whereas, the results from other two simulations do not show

consistent trends.

Similar to the findings presented in chapter 4, it is again observed that, the 2-D

simulations of soil, container, and shaker, which employ the

flexible-actuator-prescribed-force boundary condition to specify the seismic input,

generally yield well behaved sensitivities for results in different simulation conditions;

however, the other two simulation models, which use the prescribed-displacement

boundary condition to adapt the seismic input, may produce chaotic results for

sensitivities.

5.6 Archives of numerical models of a soil-container-shaker system

The OpenSees numerical models of the soil-container-shaker system are archived

in NEEScentral (http://central.nees.org). These simulation archives are categorized into 3

different simulation folders as follows (based on complexities in the boundary conditions):

Simulation of MIL 03_ 2D Soil Shear beam (described in section 5.3.1)

Simulation of MIL 03_2D Soil and FSB2 container (described in section 5.3.2)

Simulation of MIL 03_2D Soil, FSB2 container, and Shaker (described in section

5.3.3)

The simulation archives are publically available in NEEScentral for others to use.

As described earlier, the simulations of the soil-container-shaker system consider a

uniform dry-dense sand soil model, a flexible shear beam, and the horizontal shaker of the

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UC Davis centrifuge facility. These numerical models could be modified to accommodate

different soil models. To do this, a user may follow the following guidelines;

a) Modify the geometry of the FE mesh and the definition of constitutive

models and input parameters of the soil model according to the soil model

used in a new experiment.

b) Update the FE mesh (i.e., node and element numbers) of the model

container and the shaker based on the new soil mesh (OpenSees

post-processor available on the OpenSees website may be used to visualize

the nodes).

c) Follow the modeling details of different components of the container

(container rings, shear rods, etc) and the shaker described in sections 5.2.2

and 5.2.3 of this chapter (some of these details are provided on the input

files of the archived simulations)

d) Define the input motion boundary condition (i.e., location and time history

of input excitation) as the procedures described in sections 5.3.3 and 5.4.3

of this chapter.

5.7 Summary

Modeling of complex dynamics interaction of a soil-model

container-centrifuge-shaker system is presented in this chapter. This modeling

incorporates mass and flexibility of the container, the effect of shear rods at both ends of

the container, stiffness of the vertical bearing supports at the base of the container,

flexibility of the actuator, and the effect of reaction mass. A simplistic approximation of

the actuator and control system using springs and dashpots is used to include first-order

176

effects of actuator flexibility on the interaction between the specimen and the shaking

table. As opposed to the 1-D shear beam simulations of soil, inclusion of the container in

the simulations results in more accurate simulation of the experiment. In addition, the

rocking behavior of the container is well captured when the compliance of the vertical

bearing supports at the base of the container is included in the analysis.

Results from sensitivity studies show that the sensitivity of computational

simulation output to changes in input parameters depends on how boundary conditions are

modeled in the simulation; to provide an unbiased validation of a numerical model, it is

important evaluate the effects of boundary conditions on the sensitivity of simulation

results. Similar to the results presented in chapter 4 for the simulations with the

hypothetical centrifuge experiment, it is again clear that the sensitivity results of the

simulations heavily depend on the input motion boundary conditions. In the simulations,

converse to specifying input using the prescribed-displacement boundary condition, using

the flexible-actuator-prescribed-force boundary condition generally yield well behaved

sensitivities for simulation results.

A spin-off benefit of accurate modeling the centrifuge shaker system is the

prediction of base motions in the simulations. Further, this numerical model could be used

to predict base motions during input motion tuning exercises prior to the actual experiment.

However, the dynamic interaction between the soil model and the servo-hydraulic

actuation system significantly affect the accuracy of predicted base motion. In general,

dynamic interaction between the soil model and the servo-hydraulic actuation system

depends on numerous factors such as the characteristics of the soil model, compressibility

of oil column in the actuator, non-linear flow characteristics in the actuator, servo valve

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time delay, configuration and characteristics of control loops etc. The simplified shaker

model presented in this chapter incorporates some of the above features and uses measured

motion in the container base (in the experiment) to develop input command displacement.

Application of this model was extended to accommodate the actual command

displacement specified to the servo controller (during the experiment) as the command

displacement in the shaker model so that the motion at the container base could be

calculated. Details of these extensions and the results from these analyses are presented in

chapter 6 of this dissertation.

5.8 References

Arulnathan, R., Boulanger, R. W., Kutter, B. L., and Sluis, W. K. (2000). “New tool for

shear wave velocity measurements in model tests.” Geotechnical testing journal,

23(4): 444-453.

Fiegel, G.L., M.Hudson, I.M. Idriss, B.L. Kutter, and X. Zeng, (1994) "Effect of Model

Containers on Dynamic Soil Response", Centrifuge 94, Leung, Lee and Tan (eds.),

Balkema, Rotterdam, pp. 145-150.

Ilankatharan, M., Sasaki, T., Shin, H., Kutter, B. L., Arduino, P., and Kramer, S. L., 2005.

“A demonstration of NEES system for studying soil-foundation-structure interaction”

Centrifuge data report for MIL01. Rep. No. UCD/CGMDR-05/05, Ctr. for Geotech.

Modeling , Dept. of Civ. and Envir. Engrg., UC Davis.

Kutter, B.L. (1992). "Dynamic centrifuge modeling of geotechnical structures."



Kutter, B.L., Idriss, I.M., Kohnke, T., Lakeland, J., Li, X.S., Sluis, W., Zeng, X.,

178

Tauscher, R., Goto, Y., and Kubodera, I. (1994). "Design of a large earthquake

simulator at UC Davis." Proceedings, Centrifuge 94, Leung, Lee, and Tan, Eds.,


Madabhushi, S.P.G., Bulter, G., and Schofield, A.N. (1998) "Design of an equivalent shear

beam (ESB) container for use on the US Army Centrifuge", Centrifuge 98, Kimura,

Kusakabe and Takemura (eds.), Balkema, Rotterdam, pp. 117-122.

Narayanan, K.R. (1999). "Modeling the seismic response of stratified soil," Masters of

Science Thesis, University of California, Davis.

Stevens, D.K. (2001). "Comprehensive investigation of nonlinear site response:

Collaborative Research with UC San Diego and UC Davis," Masters of Science Thesis,

University of California, Davis.

Wilson, D., Kutter, B.L., Ilankatharan, M., Robidart, C. (2007) “The UC Davis high- speed

wireless data acquisition system”, Proceedings 7th International Symposium on Field

Measurements in Geomechanics, Boston, MA, September, 2007.

Yang, Z., Elgamal, A., & Parra, E. (2003). “Computational model for cyclic mobility and

associated shear deformation.” Journal of geotechnical and geoenvironmental

engineering, 129(12), 1119-1127.

179

Table 5.1 Main modeling parameters for dry dense Nevada sand (Dr=80%)

Modeling parameter Parameter value

Soil mass density (Mg/m3) 1.66

Reference mean effective confining pressure, p’r (kPa) 80

Reference low-strain shear modulus at p’r=80kPa, Gr (kPa) 64284

Reference Bulk Modulus at p’r=80kPa, 192852

Friction angle, φ (deg) 37

Peak shear strain 0.1

Phase transformation angle (deg) 27

Table 5.2 Some design details of FSB2 model container

Ring location

Section size Area of rubber on lower face (m2)

1 (bottom) 4" x 4" and 6" x 4" tubing, ¼ " wall

0.597

2 6" x 4" tubing, ½ " wall 0.538

3 6" x 4" tubing, ¼ " wall 0.538

4 6" x 4" tubing, ¼ " wall 0.439

5 (top) 2" x 4" channel 0.258

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Fig. 5.1 Photograph of the NEES geotechnical centrifuge at UC Davis

Fig. 5.2 3D rendering of a soil model-model container-centrifuge shaking table system

Vertical bearings

FSB container

Soil model

Structural model

Centrifugal force

Actuator

Shaking table

Reaction mass

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0 100 200 300 400 5000

1

2

3

4

5

6

7

8

Frequency (Hz)

Dam

ping

rat

io (%

)

Fig. 5.3 Estimated damping ratios based on employed stiffness-proportional damping

182

Aluminum rings

Neoprene rings Base plate

(a)

(b)

Steel shear rods

Fig. 5.4 Photographs of the FSB2 centrifuge model container (key components are labeled)

183

Fig.

5.5

Dim

ensi

ons (

in in

ches

) and

wei

ghts

of d

iffer

ent r

ings

of t

he F

SB2

cont

aine

r

184

Fig

5.6

Plan

vie

w o

f the

hor

izon

tal s

hake

tabl

e sy

stem

at t

he U

C D

avis

cen

trifu

ge fa

cilit

y, lo

catio

ns o

f ver

tical

bea

ring

supp

orts

are

labe

led

in in

ches

Hor

izon

tal

actu

ator

s

Ver

tical

be

arin

g su

ppor

ts

Rea

ctio

n m

ass

185

Fig 5.8 Configuration of actuator elements


k2

c2

Fcom

Connected to container base

k1

Fcom

Fig. 5.7 2D finite element mesh of the soil-model container-centrifuge shaker system

Container base

Reaction mass

Actuator elements Zero length elements (vertical bearing supports)

186

Fig.

5.9

Diff

eren

t bou

ndar

y co

nditi

ons i

n si

mul

atio

n m

odel

s

Act

uato

r el

emen

t

Inpu

t mot

ion

Inpu

t mot

ion

Rea

ctio

n m

ass

Inpu

t for

ce

Shea

r ro

ds

Alu

min

um

ring

s R

ubbe

r ri

ngs

Soil

Ver

tical

bea

ring

supp

orts

(to

tal 1

2 sp

rings

alo

ng th

e le

ngth

of t

he b

ase

plat

e)

(a)

1-D

shea

r-be

am

sim

ulat

ions

of

soil

(b) 2

-D si

mul

atio

ns o

f

soil

and

cont

aine

r (c

) 2-

D si

mul

atio

ns o

f soi

l, co

ntai

ner,

and

shak

er

187

(a) measured acceleration at the base of the container

acc

(g)

-2

-1

0

1

2

(b) calculated command displacement

time (sec)0.00 0.25 0.50 0.75 1.00

dis (

mm

)

-0.2-0.10.00.10.2

Fig. 5.10 Time histories of (a) measured acceleration at the base of the container and (b) calculated displacement by double integration of acceleration of the frequency sweep input (measured peak base acc=1.3g)

188

300m

m fr

om b

otto

m o

f the

con

tain

er


-505

100m

m fr

om b

otto

m o

f the

con

tain

er

Tim

e (s

econ

d)

0.25

0.50

0.75

1.00

-505

Gro

und

surf

ace

-505

Sim

ulat

ion

Expe

rimen

t

Gro

und

surf

ace

025

100m

m fr

om b

otto

m o

f the

con

tain

er

Perio

d (s

econ

d)

0.00

10.

010.

1025

300m

m fr

om b

otto

m o

f the

con

tain

er


025

Sim

ulat

ion

Expe

rimen

tIn

put

Fig.

5.1

1 M

easu

red

and

com

pute

d ac

cele

ratio

n tim

e hi

stor

ies a

nd re

spon

se sp

ectra

(5%

dam

ping

) fro

m 1

-D sh

ear b

eam

si

mul

atio

ns o

f soi

l (fr

eque

ncy

swee

p in

put,

peak

bas

e ac

c=1.

3g)

189

300m

m fr

om b

otto

m o

f the

con

tain

er


-505

100m

m fr

om b

otto

m o

f the

con

tain

er

Tim

e (s

econ

d)

0.00

0.25

0.50

0.75

-505

Gro

und

surf

ace

-505

Sim

ulat

ion

Expe

rimen

t

Gro

und

surfa

ce

025

100m

m fr

om b

otto

m o

f the

con

tain

er

Perio

d (s

econ

d)

0.00

10.

010.

1025

300m

m fr

om b

otto

m o

f the

con

tain

er


025

Sim

ulat

ion

Expe

rimen

tIn

put

Fig.

5.1

2 M

easu

red

and

com

pute

d ac

cele

ratio

n tim

e hi

stor

ies

and

resp

onse

spe

ctra

(5%

dam

ping

) fr

om 1

-D s

hear

bea

m

sim

ulat

ions

of s

oil (

Nor

thrid

ge in

put,

peak

bas

e ac

c=1.

3g)

190

300m

m fr

om b

otto

m o

f the

con

tain

er


-505

100m

m fr

om b

otto

m o

f the

con

tain

er

Tim

e (s

econ

d)

0.25

0.50

0.75

1.00

-505

Gro

und

surf

ace

-505

Sim

ulat

ion

Expe

rimen

t

Gro

und

surf

ace

025

100m

m fr

om b

otto

m o

f the

con

tain

er

Perio

d (s

econ

d)

0.00

10.

010.

1025

300m

m fr

om b

otto

m o

f the

con

tain

er


025

Sim

ulat

ion

Expe

rimen

tIn

put

Fig.

5.1

3 M

easu

red

and

com

pute

d ac

cele

ratio

n tim

e hi

stor

ies

and

resp

onse

spe

ctra

(5%

dam

ping

) fro

m 2

-D s

imul

atio

ns

of so

il an

d co

ntai

ner (

freq

uenc

y sw

eep

inpu

t, pe

ak b

ase

acc=

1.3g

)

191

300m

m fr

om b

otto

m o

f the

con

tain

er


-505

100m

m fr

om b

otto

m o

f the

con

tain

er

Tim

e (s

econ

d)

0.00

0.25

0.50

0.75

-505

Gro

und

surf

ace

-505

Sim

ulat

ion

Expe

rimen

t

Gro

und

surf

ace

025

100m

m fr

om b

otto

m o

f the

con

tain

er

Perio

d (s

econ

d)

0.00

10.

010.

1025

300m

m fr

om b

otto

m o

f the

con

tain

er


025

Sim

ulat

ion

Expe

rimen

tIn

put

Fig.

5.1

4 M

easu

red

and

com

pute

d ac

cele

ratio

n tim

e hi

stor

ies

and

resp

onse

spe

ctra

(5%

dam

ping

) fro

m 2

-D s

imul

atio

ns

of so

il an

d co

ntai

ner (

Nor

thrid

ge in

put,

peak

bas

e ac

c=1.

3g)

192

Nor

th e

nd (5

0mm

bel

ow th

e gr

ound

surf

ace)


05

Tim

e (s

econ

d)

0.5

0.6

0.7

-101

Nor

th e

nd (5

0mm

bel

ow th

e gr

ound

surf

ace)

Vertical acceleration (g) -101

Sim

ulat

ion

Expe

rimen

t

Sout

h en

d (5

0mm

bel

ow th

e gr

ound

surf

ace)

Perio

d (s

econ

d)

0.00

10.

010.

105

Sout

h en

d (5

0mm

bel

ow th

e gr

ound

surf

ace)

Fig.

5.1

5 M

easu

red

and

com

pute

d ve

rtica

l acc

eler

atio

n hi

stor

ies

and

resp

onse

spe

ctra

(5%

dam

ping

) fro

m 2

-D s

imul

atio

ns

of so

il an

d co

ntai

ner (

freq

uenc

y sw

eep

inpu

t, pe

ak b

ase

acc=

1.3g

)

193

Nor

th e

nd (5

0mm

bel

ow th

e gr

ound

surf

ace)


05

Tim

e (s

econ

d)

0.5

0.6

0.7

-101

Nor

th e

nd (5

0mm

bel

ow th

e gr

ound

surf

ace)

Vertical acceleration (g) -101

Sim

ulat

ion

(with

shea

r rod

)Si

mul

atio

n (w

ith o

ut sh

ear r

od)

Sout

h en

d (5

0mm

bel

ow th

e gr

ound

surf

ace)

Perio

d (s

econ

d)

0.00

10.

010.

105

Sout

h en

d (5

0mm

bel

ow th

e gr

ound

surf

ace)

Fig.

5.1

6 C

ompu

ted

verti

cal a

ccel

erat

ion

hist

orie

s an

d re

spon

se s

pect

ra (

5% d

ampi

ng)

in th

e 2-

D s

imul

atio

ns o

f so

il an

d co

ntai

ner,

with

& w

ithou

t she

ar ro

d

194

300m

m fr

om b

otto

m o

f the

con

tain

er


-505

100m

m fr

om b

otto

m o

f the

con

tain

er

Tim

e (s

econ

d)

0.25

0.50

0.75

1.00

-505

Gro

und

surf

ace

-505

Sim

ulat

ion

Expe

rimen

t

Gro

und

surf

ace

025

100m

m fr

om b

otto

m o

f the

con

tain

er

Perio

d (s

econ

d)

0.00

10.

010.

1025

300m

m fr

om b

otto

m o

f the

con

tain

er


025

Sim

ulat

ion

Expe

rimen

t

Fig.

5.1

7 M

easu

red

and

com

pute

d ac

cele

ratio

n tim

e hi

stor

ies

and

resp

onse

spe

ctra

(5%

dam

ping

) fr

om 2

-D s

imul

atio

ns o

f so

il, c

onta

iner

, and

shak

er (f

requ

ency

swee

p in

put,

peak

bas

e ac

c=1.

3g)

195

Bas

e m

otio

n

Tim

e (s

econ

d)

0.25

0.50

0.75

1.00


-505

Sim

ulat

ion

Expe

rimen

t

Bas

e m

otio

n

Perio

d (s

econ

d)

0.00

10.

010.

1


05101520

Fig.

5.1

8 M

easu

red

and

com

pute

d ba

se a

ccel

erat

ion

time

hist

orie

s an

d re

spon

se s

pect

ra (5

% d

ampi

ng) f

rom

2-D

sim

ulat

ions

of

soil,

con

tain

er, a

nd sh

aker

(fre

quen

cy sw

eep

inpu

t, pe

ak b

ase

acc=

1.3g

)

Bas

e m

otio

n

Tim

e (s

econ

d)

0.25

0.50

0.75

1.00


-505

Sim

ulat

ion

Expe

rimen

t

Bas

e m

otio

n

Perio

d (s

econ

d)

0.00

10.

010.

1Spectral acceleration (g)

05101520

Fig.

5.1

9 M

easu

red

and

com

pute

d ba

se a

ccel

erat

ion

time

hist

orie

s an

d re

spon

se s

pect

ra (5

% d

ampi

ng) f

rom

2-D

sim

ulat

ions

of

soil,

con

tain

er, a

nd sh

aker

(with

mod

ified

com

man

d di

spla

cem

ent)

196

300m

m fr

om b

otto

m o

f the

con

tain

er


-505

100m

m fr

om b

otto

m o

f the

con

tain

er

Tim

e (s

econ

d)

0.25

0.50

0.75

1.00

-505

Gro

und

surf

ace

-505

Sim

ulat

ion

Expe

rimen

t

Gro

und

surf

ace

025

100m

m fr

om b

otto

m o

f the

con

tain

er

Perio

d (s

econ

d)

0.00

10.

010.

1025

300m

m fr

om b

otto

m o

f the

con

tain

er


025

Sim

ulat

ion

Expe

rimen

t

Fig.

5.2

0 M

easu

red

and

com

pute

d ac

cele

ratio

n tim

e hi

stor

ies

and

resp

onse

spe

ctra

(5%

dam

ping

) fr

om 2

-D s

imul

atio

ns o

f so

il, c

onta

iner

, and

shak

er (w

ith m

odifi

ed c

omm

and

disp

lace

men

t)

197

frequency (Hz)50 100 150 200 250 300m

ag_F

FT o

f bas

e ac

c/m

ag_F

FT o

f com

man

d ac

c

0

1

2

3

4

Fig. 5.21 Ratio of Fourier amplitudes between the calculated and measured base accelerations from 2-D simulations of soil, container, and shaker

frequency (Hz)50 100 150 200 250 300

mag

_FFT

of s

urfa

ce a

cc/m

ag_F

FT o

f bas

e ac

c

0

5

10

15

20

Fig. 5.22 Ratio of Fourier amplitudes between the calculated surface and base accelerations from 2-D simulations of soil, container, and shaker

198

freq

uenc

y (H

z)50

100

150

200

250

300

mag_FFT of base acc/mag_FFT of command acc

01234

freq

uenc

y sw

eep

(pea

k ba

se a

cc=1

.3g)

Nor

thrid

ge (p

eak

base

acc

=1.3

g)fr

eque

ncy

swee

p (p

eak

base

acc

=13g

)N

orth

ridge

(pea

k ba

se a

cc=1

4g)

Fig.

5.2

3 R

atio

of

Four

ier

ampl

itude

s be

twee

n th

e ca

lcul

ated

and

mea

sure

d ba

se a

ccel

erat

ions

in th

e 2-

D

sim

ulat

ions

of s

oil,

cont

aine

r, an

d sh

aker

usi

ng d

iffer

ent e

arth

quak

e ch

arac

teris

tics

199

(c) 2

-D s

imul

atio

ns o

f soi

l,

con

tain

er, a

nd s

hake

r

0.00

10.

01

(a) 1

-D s

hear

bea

m

s

imul

atio

ns o

f soi

l

0.00

10.

01025

(b) 2

-D s

imul

atio

ns o

f

soi

l and

con

tain

er

Perio

d (s

econ

d)0.

001

0.01


base

line

cas

ere

duce

ref G

max

by

10%

incr

ease

ref G

max

by

10%

Fig

5.24

Eff

ect o

f var

ying

she

ar m

odul

us o

n ca

lcul

ated

gro

und

surf

ace

resp

onse

spe

ctru

m fo

r diff

eren

t bou

ndar

y co

nditi

ons

(fre

quen

cy sw

eep

inpu

t, pe

ak b

ase

acc=

1.3g

)

(c) 2

-D s

imul

atio

ns o

f soi

l,

con

tain

er, a

nd s

hake

r

0.00

10.

01

(a) 1

-D s

hear

bea

m

s

imul

atio

ns o

f soi

l

0.00

10.

01025

(b) 2

-D s

imul

atio

ns o

f

soi

l and

con

tain

er

Perio

d (s

econ

d)0.

001

0.01


base

line

cas

ere

duce

ref G

max

by

10%

incr

ease

ref G

max

by

10%

Fig

5.25

Eff

ect o

f var

ying

shea

r mod

ulus

on

calc

ulat

ed b

ase

resp

onse

spec

trum

for d

iffer

ent b

ound

ary

cond

ition

s (fr

eque

ncy

swee

p in

put,

peak

bas

e ac

c=1.

3g)

200

chan

ge in

Gr w

ith re

spec

t to

Gr ba

se li

ne (%

)

-25

025

change in peak spectral acceleration (%)

050100

chan

ge in

Gr w

ith re

spec

t to

Gr ba

se li

ne (%

)

-25

025

change in peak acceleration (%)

050100

1-D

she

ar b

eam

sim

ulat

ions

of s

oil

2-D

sim

ulat

ions

of

soi

l and

con

tain

er2-

D s

imul

atio

ns o

f s

oil,

cont

aine

r, an

d sh

aker

Fig.

5.2

6 Se

nsiti

vity

of p

eak

and

peak

spe

ctra

l acc

eler

atio

ns o

f sur

face

mot

ion

to re

fere

nce

shea

r mod

ulus

of

PD

MY

mat

eria

l (fr

eque

ncy

swee

p in

put,

peak

bas

e ac

c=1.

3g)

chan

ge in

Gr w

ith re

spec

t to

Gr ba

se li

ne (%

)

-25

025


050100

chan

ge in

Gr w

ith re

spec

t to

Gr ba

se li

ne (%

)

-25

025


050100

1-D

she

ar b

eam

sim

ulat

ions

of s

oil

2-D

sim

ulat

ions

of s

oil

and

con

tain

er2-

D s

imul

atio

ns o

f s

oil,

cont

aine

r, an

d sh

aker

Fig.

5.2

7 Se

nsiti

vity

of p

eak

and

peak

spe

ctra

l acc

eler

atio

ns o

f bas

e m

otio

n to

refe

renc

e sh

ear m

odul

us o

f PD

MY

mat

eria

l (fr

eque

ncy

swee

p in

put,

peak

bas

e ac

c=1.

3g)

201

chan

ge in

Gr w

ith re

spec

t to

Gr ba

se li

ne (%

)-2

50

25


-25025

chan

ge in

Gr w

ith re

spec

t to

Gr ba

se li

ne (%

)-2

50

25


-25025

1-D

shea

r bea

m si

mul

atio

ns o

f soi

l2-

D si

mul

atio

ns o

f soi

l and

con

tain

er2-

D si

mul

atio

ns o

f soi

l, co

ntai

ner,

and

shak

er

Fig.

5.2

8 Se

nsiti

vity

of

peak

and

pea

k sp

ectra

l acc

eler

atio

ns o

f su

rfac

e m

otio

n to

ref

eren

ce s

hear

mod

ulus

of

PDM

Y m

ater

ial (

freq

uenc

y sw

eep

inpu

t, pe

ak b

ase

acc=

13g)

chan

ge in

Gr w

ith re

spec

t to

Gr ba

se li

ne (%

)

-25

025


-25025

chan

ge in

Gr w

ith re

spec

t to

Gr ba

se li

ne (%

)

-25

025


-25025

1-D

shea

r bea

m si

mul

atio

ns o

f soi

l2-

D si

mul

atio

ns o

f soi

l and

con

tain

er2-

D si

mul

atio

ns o

f soi

l, c

onta

iner

, and

shak

er

Fig.

5.2

9 Se

nsiti

vity

of

peak

and

pea

k sp

ectra

l ac

cele

ratio

ns o

f ba

se m

otio

n to

ref

eren

ce s

hear

mod

ulus

of

PDM

Y m

ater

ial (

freq

uenc

y sw

eep

inpu

t, pe

ak b

ase

acc=

13g)

202

Chapter 6

Towards developing a numerical model of a servo-hydraulic

centrifuge actuation system to predict shaking table response

This chapter presents a study on the modeling of a servo-hydraulic centrifuge

actuation system with a goal of predicting shaking table response prior to the experiment

for a target earthquake motion. First, the functioning of different components and the

factors affecting the performance of a servo-hydraulic actuation are addressed using an

example analytical model of the servo-hydraulic actuation system available in the

literature. Second, the actuation mechanism of the UC Davis centrifuge horizontal

shaking table system and the details of base motion tuning procedures are briefly

described. Third, an OpenSees numerical model of this actuation system and typical

results from the numerical simulations are presented. Finally, the simulation results and

the need for additional work on this numerical modeling are discussed.

203

6.1 Factors affecting the reproduction of a dynamic signal in a servo-hydraulic

actuation system

In a typical shaking table experiment, an actuator command displacement (could

be a dynamic signal obtained from a real earthquake recording or created by combining

sinusoidal wave forms) is specified to a servo controller and the response of the shaking

table is measured as an output. The degree of distortion between the input command and

the measured output depends on many factors such as characteristics of the test specimen,

physical system parameters (e.g. compliance of reaction mass, compressibility of oil

column in the actuator chamber, oil leakage through the actuator seals, non-linear flow

characteristics in the actuator, servo valve time delay, etc), and configuration and

characteristics of control loops (e.g. type of control algorithm, feedback signals,

dynamics of sensors measuring the feedback response, signal conditioning,

characteristics of the digital data acquisition and control system, anti-aliasing filters,

control gain setting, etc) (Conte et al. 2000). Therefore to evaluate the capability of the

actuation system in reproducing base motions (measured motions at shaking table), it is

important to understand the effects of above factors on the performance of the actuation

system under wide range of test configurations and operation conditions. Furthermore, a

thorough understanding of the performance of the actuation system is essential for the

proper design of loading protocols (ground motion characteristics) in the experiment,

proper interpretation of experimental results, and for the safety of the equipment.

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6.2 Analytical models for various components of servo-hydraulic actuation

system

Various analytical models to capture the salient features different components of

the servo-hydraulic actuation system (such as actuator, servo valve, controller, etc.) are

available in the literature for structural shaking table experiments and real-time pseudo

dynamic testing in the context of structural engineering (Conte et al. 2000, Williams et al.

2001, and Jung et al. 2006). To improve our understanding of functions and modeling

issues of diffent components of the servo-hydraulic actuation system, it is worth looking

at one of the examples from above literature.

A linear analytical model of a uni-axial, displacement controlled shaking table

system, presented by Conte et al. (2000), is depicted in Fig. 6.1 and briefly described

below. As indicated in Fig. 6.1, the analytical model is developed following the modular

approach in the form of ‘Shaking Table Transfer Function’ (T(s) in Laplace domain)

between desired (or commanded) and actual absolute shaking table motions. This

modular approach breaks down the shaking table system into several subsystems.

i) Three-stage servo valve transfer function, Ht(s)

Functioning (characterized by an ‘inner feedback control loop) and the analytical

model of the three-stage servo valve transfer function are schematically shown in Fig.

6.2. As shown in Fig. 6.2, the servo valve command signal, xc(s), before being sent to the

first stage of the servo valve, is processed by the inner control loop in order to yield the

inner loop conditioned servo valve command signal, xci(s). The electric signal, xci(s),

controls the rotation of the pilot flapper which generates a differential pressure in the

pilot stage (or second stage), ΔPp(s). The differential pressure ΔPp(s) thus created controls

205

the position of the pilot spool which in turns controls the oil flow rate into the third-stage

and the position of the third-stage spool, x3s(s). Finally the position of the third-stage

spool, x3s(s), controls the oil flow rate into the actuator chamber, qs(s). Ht(s), is defined as

the ratio between the oil flow rate, qs(s), provided by the third-stage of the servo valve to

the actuator chamber and the electrical command signal to the servo valve, xc(s):

Ht(s) = qs(s)/xc(s) (6.1)

For the model presented here, linear relationships are assumed in the functioning of

different stages of the servo valve assembly.

ii) Servo valve-actuator transfer function, S(s)

The three-stage servo valve transfer function presented in equation (6.1) is then

used in conjunction with the flow continuity equation in the actuator to yield the ‘Servo

valve-Actuator Transfer Function’, S(s). The flow continuity equation in the actuator

incorporates (a) the change in volume (per unit time) of the actuator pressure chamber

due to the actuator piston motion, (b) the flow rate of oil leaking through the actuator

seals, and (c) the compressibility of the oil in the actuator pressure chamber. A linear

relationship is assumed between the oil leakage through the actuator seals and the oil

pressure in the actuator chamber. S(s) is defined as,

S(s) = xt(s)/xc(s) (6.2)

where, xt(s) is actual displacement (relative to the body of the actuator or the top of the

reaction mass) of the actuator arm.

iii) Servo – hydraulic system transfer function, H(s)

The servo valve-actuator model is incorporated into the analytical model for the

controller (outer table control loop) to derive ‘Servo-Hydraulic System Transfer

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Function’, H(s). The controller determine the servo valve command signal, xc(t) as a sum

of (a) a component proportional to the table error (i.e. difference between the table

desired displacement, xd(t), and the actual displacement, xt(t), of the actuator arm)

conditioned through the PID control scheme (b) a feed-forward component proportional

to the derivative of the desired displacement, and (c) a component proportional to the

differential pressure across the actuator position (delta pressure component). H(s) is

defined as,

H(s) = xt(s)/xd(s) (6.3)

where, xd(s) is desired table displacement.

iv) Base Transfer function, B(s)

The effects of the flexibility (or compliance) of the actuator reaction mass are

accounted for through the ‘Base Transfer Function’, B(s). B(s) is defined as,

B(s) = xb(s)/xt(s) (6.4)

where, xb(s) is displacement of the reaction mass relative to an inertial reference system.

v) Total shaking table transfer function, T(s)

The total shaking table transfer function is defined as the transfer function

between the desired absolute table displacement, xd(s), and the actual absolute table

displacement response, xta(s):

T(s) = xta(s)/xd(s) (6.5)

where, xta(s) is sum of xb(s) and xt(s).

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vi) Payload transfer function, Hp(s)

Lastly, the effects of the payload dynamic characteristics, modeled through

‘Payload Transfer Function’, Hp(s). The payload is modeled as a linear elastic structure

for the analytical model presented here.

Similar to the model present above, for the structural engineering applications,

most of the analytical models of different components of servo-hydraulic actuation

system are developed by linearising the inherently non-linear servo-hydraulic actuation

system and assuming a payload with linear response characteristics. Application of these

models may be extended for geotechnical centrifuge applications to simulate linear soil

models under small amplitude earthquake simulations (i.e. linear flow characteristics in

the actuator). However, geotechnical centrifuge experiments often involve relatively

heavy and highly nonlinear test specimens (e.g., a massive volume of liquefying sand),

and large amplitude earthquake simulations when the test operating conditions are near

the performance capacity of servo-hydraulic actuation system. These nonlinearities in the

actuation system and the payload characteristics pose difficulties in analytical modeling

of different components of the servo-hydraulic centrifuge actuation system. Following

sections of this chapter present a study about the servo-hydraulic centrifuge actuation

system of the UC Davis centrifuge facility.

6.3 Outline of servo-hydraulic actuation system of the UC Davis centrifuge

facility

The horizontal shaking table system of the UC Davis centrifuge facility is

considered in the study presented in this dissertation. As shown in Fig. 6.3, the horizontal

shaking table system is driven by two-servo hydraulic actuators. The design detail and the

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actuator mechanism of the horizontal actuation system is described in detail by Kutter et

al. (1994), and some of these details are briefly described here. A schematic of the

actuator mechanism (adapted from Kutter et al. (1994)) is shown in Fig. 6.4. Each

actuator consists of a two stage servo-valve block sandwiched by single acting actuators.

When a shaking event is triggered, excitation to the voice coil moves a pilot valve which

provides hydraulic pressure to actuate the slave valve. The slave valve supplies the

pressure to the single acting actuators which in turn move the shaking table. At each end

of the pistons, sliding and spherical hydrostatic bearings are provided to eliminate the

undesirable shear and bending deflections caused by centrifuging the bucket and stressing

the surrounding structure. The single acting actuators are externally tied together by the

stiff load frames on the sides of the model container. The shaking table is supported by a

combination of 24 elastomeric bearing pads (shown in Fig. 5.6) and 4 hydrostatic

bearings. These bearings are attached to the base of the centrifuge bucket which is made

of I beams (see Fig. 6.3). Accumulators, mounted on each corners of the centrifuge

bucket, serve as oil reservoirs and supply oil to the actuators. These accumulators are

backed up by a separate nitrogen pressure vessel. This pressure vessel acts as power

supply and provides power to the servo-valve assembly when an earthquake simulation is

triggered. The pressure vessel can be recharged on-board so that multiple earthquake

simulation events can be triggered.

6.4 Current base motion tuning procedures

In a geotechnical centrifuge shaking table experiment, when the actuators are

driven to their capacity and above their resonant frequency and when the nonlinear

payload mass is a significant fraction of the system mass, it is extremely challenging to

209

accurately reproduce the desired earthquake signal at the base of the container. Fig 6.5

compares the Fourier amplitudes of the command (desired) motions and the achieved

motions at the base of the container during a series of centrifuge shaking events which

included frequency sweep input motions. As shown in the above figure, at frequencies

below 200 Hz, Fourier amplitudes of achieved motions at the base of the container

reasonably retain the frequency contents of the command motion (see Fig. 6.5 (a) and

Fig. 6.5 (b)); however, there are significant discrepancies between the magnitudes of

Fourier amplitudes. For example, valleys shown in the Fourier amplitudes of the achieved

motions at 90 Hz are not shown in the Fourier amplitudes of the command motions in Fig

6.5 (a) and Fig. 6.5 (b), and the achieved motion in Fig. 6.5 (c) shows significant loss of

frequency content in the higher frequency range (above 200 Hz). For these shaking

events, the observed fundamental frequencies of the soil model were in the vicinity of 90

Hz (Stevens et al. 2001). The soil model acts as a vibration “absorber” near its natural

frequency, which causes a significant loss of frequency content in the base motion near

the natural frequency of the soil model. The above examples clearly illustrate that the

dynamic interactions among different components of the centrifuge actuation system and

the specimen significantly affect the frequency content of the achieved base motions at

the base of the container.

One base motion tuning exercise used at the UC Davis centrifuge facility involves

a initial pre-conditioning of the desired earthquake signal using a trial transfer function

shown in Fig. 6.6 and a trial shaking event (using the pre-conditioned command signal)

on a similar dummy test model. The trial transfer function shown in Fig. 6.6 was obtained

based on previous experience (i.e., measured base response with different payload

210

characteristics and earthquake characteristics) to approximate (linear approximation) the

non-linear behavior of the centrifuge actuation system. The shape of this transfer function

in the lower frequency range (frequencies less than 20 Hz) is derived to minimize the

excitation of the centrifuge arm at its resonant frequencies (i.e., 5 Hz and 20 Hz are 1st

and 2nd bending resonant frequencies of the centrifuge arm, desired earthquake signal at

these frequencies are filtered to a significant amount in Fig. 6.6). Representative base

motion tuning results using this initial preconditioning scheme are presented in Fig. 6.7

and Fig. 6.8, in terms of time histories and the magnitude of the Fourier amplitude

spectrums, respectively. As shown in above figures, for this particular case, peak

accelerations of the target (desired) and the achieved base motions are nearly equal, the

pre-conditioning scheme reasonably capture the locations of peaks and the valleys of FFT

of base motions except in the lower frequency range (frequencies less than 20 Hz were

filtered in the pre-conditioning scheme) and in the higher frequency range (frequencies

higher than 200 Hz). Also, discrepancies between the magnitudes of FFT of base motions

are apparent in Fig. 6.8. If matching target motion at the ground surface or any other

location of the model is important, in addition to the pre-conditioning scheme described

above, further corrections on the achieved base motion are necessary. An example of the

base motion tuning exercise, which included some additional correction procedures to get

a good match with target motion specified at 50 mm below the ground surface within the

test specimen, was presented in section 3.2.6 of this dissertation.

211

6.5 Modifications to the shaker model presented in chapter 5 (depicted in Fig.

5.8)

The shaker model presented in chapter 5 (see Fig. 5.8) employs a simplistic

approximation of the actuator and control system, using the springs and dashpots, to

include the first-order effects of actuator flexibility on the interaction between the test

specimen and the shaking table and it uses the measured container base motion (from

experiment) to develop input command displacement and then the input command force.

Application of this shaker model is extended to accommodate the actual command

displacement, specified to the servo controller (during the experiment), as a command

displacement in the shaker model; so that the base response could be obtained as an

output in the numerical model. Details of these modifications and the results from these

analyses and are presented in the following sections.

6.5.1 To account for the effects of feed-back controller

A simplistic approximation using a mechanical-lever system (BCD in Fig. 6.10) is

added to the original shaker model, with a goal of incorporating the first order effects of

feed-back controller on the command displacement (or command force in the numerical

model). In the OpenSees model, node A (node A is connected to shaking table) is

connected using a rigid link to the node B. BCD is a mechanical-lever system (BC =

CD), it has the pivot point at node C (node C is connected to reaction mass) such that

nodes B and D will have equal but opposite displacement relative to node C. Two

additional stiff springs k3 and k4 are used to account for the effect of controller, which is

proportional to the relative displacement of the shaking table with respect to reaction

212

mass (i.e., x1-x2), on the command displacement. Let’s consider the equation of motions

of the shaker system to further understand the functioning of this mechanical feed-back

system. For this purpose, the payload and reaction mass are represented as lumped

masses (i.e., only to write equation of motion, not in the actual numerical model) in Fig.

6.9 and in Fig. 6.10 and the degrees of freedoms of these lumped masses are indicated in

the above figures. Based on these representations, the equations of motion of the dynamic

system in Fig 6.10 could be written as follows:

0)}()({)]()([ 321421313213211 =+−+−+−−−− xxxkxxkxxkxxcxm &&&& (6.6)

0)}(2)({)]()([ 321421332122 =+−−−−+−+ xxxkxxktFxxkxm com&& (6.7)

0)}({)]()()()([ 321432113213233 =+−+−−−−+−+ xxxktFxxkxxkxxcxm com&&&& (6.8)

In the above equations, the terms inside [ ] are the components from the equation

of motion of the dynamic system shown in Fig. 6.9 and the terms inside { } are the

additional components in the equation of motion due to the addition of mechanical feed-

back system in Fig. 6.10. In the model calibration process, both k3 and k4 are represented

in terms of k1 (k3=k1/10 and k4=k1).

6.5.2 To account for the oil pressure limit and the limit on oil flow velocity

As indicated in Fig. 6.11 (a), a stiff spring, kL (kL = 100k1), and a dashpot, cL, are

added to the shaker model to account for the limit oil pressure and the limit oil flow

velocity. Fig. 6.11 (b) and Fig. 6.11 (c) present the characteristics of kL and cL,

respectively.

213

6.5.3 To account for servo-valve nonlinearity

In Fig. 6.11 (a), a bi-linear spring k1* (across which the input command is

specified) is used to accommodate the effects of non-linearity of the servo-valve on the

simulated shaking table response. The configuration of k1* is depicted in Fig. 6.11 (d).

The purpose of this element is to account for the different behavior of the actuators

during low and high amplitude excitations; the actuators have been observed to perform

better under larger amplitude excitation.

In addition to the above modifications, as mentioned earlier, numerical

simulations are performed by adapting the input force command calculated using the

actual command displacement specified to the servo controller during the experiment.

Typical results from some of these simulations are presented below.

6.6 Simulated base response

A series of shaking event from the centrifuge test series dks02 are considered in

these simulations. These shaking events included a series of frequency sweep input

motions. Dry Nevada sand, placed at a relative density of 100% in a flexible shear beam

model container, was used to model soil in the dks02 test series. Further details of this

experiment can be found in the test series data report Stevens et al. (1999).

Fig. 6.12 compares simulated displacements at the base of container with the

experimental result. Base displacements in the experiment were obtained by double

integrating the accelerations measured at the base of the container. As shown in Fig 6.12,

for this particular input motion, the simulation reasonably captures the steady state

response observed in the experiment (i.e., good match in the displacements in the time

214

range of 0.75 to 1 seconds); however, higher frequency cycles of the displacements (after

1.8 seconds) are poorly predicted by the simulations and the spikes shown at the

beginning and end of the time histories of base displacements in the experiment are not

shown in the simulation results. Fig. 6.13 compares the simulated and the measured base

displacements for the same the frequency sweep input motion (50 to 125 Hz), for

different ‘g’ levels and shaking intensities. In Fig. 6.13 (a) and Fig. 6.13 (c), at 20g level

for two different levels of shaking intensities, simulations reasonably predicted the steady

state displacements obtained from the experiment. Whereas, in Fig. 6.13 (b), at 40g level

for a relatively larger shaking intensity (i.e., Amplification factor for base motion is 2.2),

there are significant discrepancies between the simulated and the measured base

displacements. This suggests that the non-linear response exhibits by the servo-hydraulic

actuation system at a relatively larger shaking intensity is not perfectly modeled in the

shaker model depicted in Fig. 6.11 (a).

Ratios of Fourier amplitudes between the command motion and the achieved base

motions in the experiment and the simulations are shown in Fig. 6.14 for the same event

considered in Fig. 6.12. As indicated in Fig. 6.14, the ratios of Fourier amplitudes

between the command motion and the achieved base motion in the experiment and the

simulation both show peaks around 105 Hz which is close to the experimentally observed

natural frequency (102 Hz) of the soil column (Stevens, 2002). This may be attributable

to the presence of the strong dynamic interaction between the soil model and the

actuation system close to the natural frequency of the soil model. However, the

magnitudes of ratios of Fourier amplitudes are significantly different in the experiment

and the simulation (i.e., scales of y axes off by a factor of 10).

215

For the same frequency sweep input motion, Fig. 6.15 presents the ratios of the

Fourier amplitudes between the command motions and the measured base motions, for

different ‘g’ levels and shaking intensities. As indicated in Fig. 6.15, for different levels

of shaking intensities, ratios of Fourier amplitudes exhibit predominant peaks around 105

Hz and 90 Hz at 40 g and 20 g levels, respectively. These frequencies are close to the

natural frequencies of the soil column at 40 g and 20 g levels, respectively (i.e. for the

linear elastic soil model, frequency is proportional to the confining pressure). At a same

‘g’ level, ratios of Fourier amplitudes show a bigger predominant peak for the lower

intensity motion and a lower predominant peak for the higher intensity motion. In

addition, at a same ‘g’ level, the ratios of Fourier amplitudes are off by a factor of two in

the lower frequency range (50 to 125 Hz) for different levels of shaking intensities

considered. These differences may be attributable to the non-linear behavior of the servo-

hydraulic actuation system (i.e. shaker requires relatively larger input for a smaller

shaking event than a larger shaking event).

Fig. 6.16 presents the ratios of Fourier amplitudes between the command motions

and the simulated base motions for the same events presented in Fig. 6.15. As shown in

Fig. 6.16, at 40 g level, ratios of Fourier amplitudes exhibit peaks close to 105 Hz for

different intensity motions (dks02_w and dks02_bw). In addition, at 20 g level, the

smaller intensity event (dks02_ca) shows a smaller peak at the vicinity of 90 Hz;

whereas, the larger intensity event (dks02_bz), does not show a peak close to this

frequency. At the lower frequency range of the input motion (50 to 75 Hz), the ratios of

Fourier amplitudes are almost identical for different levels of shaking intensities; which is

different from the behavior observed in the experimental results in Fig. 6.15. Further, the

216

magnitudes of ratios of Fourier amplitudes are significantly different in the experiment

and the simulation.

6.7 Discussion on the simulation results and the need for additional work

In the absence OpensSees material models and elements to model various

components of the servo-hydraulic actuation system, a simplistic approximation using

springs and dashpots was used to model the actuator, servo-valve and the control system

in the numerical model of the centrifuge actuation system depicted in Fig. 6.11.

Generally, for the soil model and the frequency sweep input (50 to 125 Hz) considered in

the simulations, the above shaker model reasonably reproduce some features of the base

response observed in the experiment. For example, steady state components of base

displacements were reasonably predicted up to a certain extent in Fig. 6.12 and Fig. 6.13

and, in some cases, the frequencies of the peaks of ratios of Fourier amplitudes (base

transfer functions) between the command and the measured or simulated base motions in

Fig. 6.16 and in Fig. 6.17 were located at the proximity of the experimentally observed

natural frequencies of the soil model. However, the higher frequency components of the

base displacements and the magnitudes of the base transfer functions were poorly

predicted in the simulations. Also, while the results were not presented here, the

simulations using the command motions with significantly higher frequency contents (see

Fig. 6.5 (b) and Fig. 6.5 (c)) resulted in poor predictions of the base displacements and

the base transfer functions.

As described earlier, the degree of distortion between the input command motion

and the measured motion at the shaking table depends on numerous factors such as the

characteristics of the soil model, compressibility of oil column in the actuator, non-linear

217

flow characteristics in the actuator, servo-valve time delay, configuration of control loops

etc. Geotechnical centrifuge experiments often involve highly non-linear test specimens

where the payload mass is a significant fraction of the system mass and the larger

amplitude earthquake simulations where the actuator characteristics are themselves non-

linear. In addition, in the centrifuge experiments frequencies are scaled by the factor of

‘g’ level. The resonant frequencies of higher vibration modes of different components of

the actuation system and the higher frequency responses of the actuator, the servo-valve

and the control system would affect the characteristics (magnitude, frequency content,

and wave form) of the dynamic signal measured at the shaking table. Therefore, to

capture the salient features of the non-linear actuator and servo-valve and to compensate

for the effects of poles and zeros that develop in the feed-back control system on the

shaking table response, it is concluded that more sophisticated analytical models of the

actuator, servo-valve, and controller are required. Development of these advanced

analytical models, especially for the geotechnical centrifuge applications, is a topic for

future research. These analytical models could then be used to model the servo-hydraulic

actuation system to predict the shaking table response in the centrifuge experiments,

involving different characteristics of payload and earthquake motions, and wide range of

test operating conditions.

218

Fig. 6.1 Analytical model (derived based on transfer function approach) of a servo-hydraulic actuation system of a structural shaking table system (after Conte et al. 2000)

219

Fig. 6.2 Schematic of analytical model of the servo-valve transfer function depicted in Fig. 6.1 (after Conte et al. 2000)

220

Fig. 6.3 Plan (top) and elevation (bottom) views of the horizontal shaking table system at the UC Davis centrifuge facility (after Kutter at al. 1994)

221

Fig. 6.4 Servo-hydraulic actuation mechanism of the horizontal shaking table system of the UC Davis centrifuge facility (after Kutter et al. 1994)

222

Fig. 6.5 Fourier amplitudes of the command motion to the servo controller and the achieved motions at the base of the container for different frequency sweep inputs

(a) frequency sweep input (50 to 125 Hz)

0 100 200 300 4000.1

1.0

10.0

100.0

1000.0FFT of command motion to servo controllerFFT of achieved motion at the base of the container

(b) frequency sweep input (80 to 200 Hz)

0 100 200 300 400

mag

nitu

de o

f FFT

(m/s

2 )

0.1

1.0

10.0

100.0

1000.0

(c) frequency sweep input (160 to 400 Hz)

frequency (Hz)0 100 200 300 400

0.1

1.0

10.0

100.0

1000.0

223

frequency (Hz)10 100

mag

nitu

de o

f tra

nsfe

r fun

ctio

n

0

5

10

15

20

25

Fig. 6.6 Transfer function used to correct acceleration command in the base motion tuning exercise

(a) time history of the target base motion

Time (second)

0.0 0.1 0.2 0.3 0.4

Acc

eler

atio

n (g

)

-10

0

10

(b) time history of the achieved base motion

Time (second)

0.0 0.1 0.2 0.3 0.4

Acc

eler

atio

n (g

)

-10

0

10

Fig. 6.7 Time histories of the target and achieved base motions for an input from the 1994 Northridge earthquake (data is presented in centrifuge model scale-52g & time scales are not exactly synchronized)

224

Freq

uenc

y (H

z)10

100

Magnitude of FFT of base motion

0510

FFT

of ta

rget

bas

e m

otio

nFF

T of

ach

ieve

d ba

se m

otio

n

Fig.

6.8

Mag

nitu

des

of F

FT o

f th

e ta

rget

and

ach

ieve

d ba

se m

otio

ns d

urin

g th

e ba

se m

otio

n tu

ning

exe

rcis

e, f

or a

n in

put

from

the

1994

Nor

thrid

ge e

arth

quak

e

(g)

225

k2

c2

k1 m1 m2 m3

x3

Fcom(t) x1

x2

Reference

Reaction mass

Payload

Fcom(t)

Fig. 6.9 Configuration of shaker model used in the analyses (same as Fig. 5.8, lumped masses are assumed to represent payload and reaction mass, and degrees of freedoms of the lumped masses are labeled)

k2

c2 k1 m2 m3

Fcom(t) x1

Reference

Mechanical lever system

Fcom(t)

x3

x2 (x2-x1)

x1

m1

Rigid link

k4

k3

A

B

C

D

Fig. 6.10 Modifications to the shaker model, using a mechanical-lever system to incorporate the effects of feed-back controller in the analyses (node A is rigidly connected with node B and BCD is a mechanical lever system it has a pivot point at node C; i.e., nodes B and D will have equal but opposite displacement relative to node C )

226

Fig. 6.11 Configuration and characteristics of different components of modified

shaker model

kL

k3

k2

cL

k1*

k4

c2 Fcom(t) Fcom(t)


Connected to container base

(a) Configuration of modified shaker model

Force

Velocity

1m/s

(c) Characteristics of cL (b) Characteristics of kL

FL= p x A=2500psi x 25in2Force

Displacement

FL

1 kL

Force

Displacement 1mm

slope=5k1:1

slope=k1:1

-1mm

(d) Characteristics of k1*

227

0.0 0.2 0.4 0.6 0.8 1.0

-0.0002

0.0000

0.0002

1.2 1.4 1.6 1.8 2.0 2.2

base

dis

plac

emen

t (m

)

-0.0002

0.0000

0.0002 Experiment: dks02_w ('g' level = 40 & Amp. factor for base motion = 1.2)Simulation

time (second)

2.2 2.4 2.6 2.8 3.0 3.2

-0.0002

0.0000

0.0002

Fig. 6.12 Comparison of the measured and the simulated base displacements during a frequency sweep (50 to 125 Hz) input (base displacement for the experiment was obtained by double integrating the acceleration time history measured at the base of the container)

228

(a) 'g' level = 20 & Amp. factor for base motion = 1.2 (event dks02_ca)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

-0.0002

0.0000

0.0002

(b) 'g' level = 40 & Amp. factor for base motion = 2.2 (event dks02_bw)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

base

dis

plac

emen

t (m

)

-0.0008

-0.0004

0.0000

0.0004

ExperimentSimulation

(c) 'g' level = 20 & Amp. factor for base motion = 2 (event dks02_bz)

time (second)

0.0 0.2 0.4 0.6 0.8 1.0 1.2-0.0008

-0.0004

0.0000

0.0004

Fig. 6.13 Comparison of the measured and the simulated base displacements during the frequency sweep input motion (sweep 50 to 125 Hz) for different ‘g’ levels and shaking intensities

229

frequency (Hz)25 50 75 100 125 150m

ag_F

FT o

f com

man

d ac

c/m

ag_F

FT o

f bas

e ac

c

0

50

100

150

200

250

(b) Simulation

frequency (Hz)25 50 75 100 125 150m

ag_F

FT o

f com

man

d ac

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FT o

f bas

e ac

c

0

5

10

15

20

25

(a) Experiment: dks02_w ('g' level = 40 & Amp.factor for base motion = 1.2)

Fig. 6.14 Ratio of Fourier amplitudes between the command motion and the base motion in (a) experiment and (b) simulation for frequency sweep input – 50 to 125 Hz (Note that “y” axis scales are off by a factor of 10 in (a) and (b))

230

Freq

uenc

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z)25

5075

100

125

150

mag_FFT of command acc/mag_FFT of base acc

050100

150

200

250

dks0

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0, A

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r bas

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n =

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dks0

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2)

Fig.

6.1

5 R

atio

s of

Fou

rier a

mpl

itude

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twee

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mm

and

mot

ions

and

the

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r diff

eren

t ‘g’

le

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and

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inte

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231

Freq

uenc

y (H

z)25

5075

100

125

150

mag_FFT of command acc/mag_FFT of base acc

0510152025dk

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Am

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for b

ase

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mot

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Am

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ctor

for b

ase

mot

ion

= 2)

Fig.

6.1

6 R

atio

s of

Fou

rier

ampl

itude

s be

twee

n th

e co

mm

and

mot

ions

and

the

sim

ulat

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ase

mot

ions

for

diff

eren

t ‘g’

le

vels

and

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put –

50

to 1

25 H

z)

232

Chapter 7

Summary and Conclusions, and Future work

7.1 Summary and Conclusions

This dissertation consists of the following four components: (1) A collaborative

research project involving centrifuge testing and numerical simulation of a soil-pile-

bridge system (2) A critical study to advance understanding the effects of using different

input motion boundary conditions on the sensitivity of numerical simulation results to

errors in material properties of a specimen tested on a shaking table (3) Numerical

simulations of a soil model tested on the centrifuge experiment accounting for soil-

container-shaker interaction, and (4) A first attempt to develop a numerical model of the

UC Davis servo-hydraulic centrifuge actuation system with a goal of predicting shaking

table response.

7.1.1 Collaborative research: Centrifuge testing of soil-pile-bridge systems

The centrifuge experiments on soil-pile-bridge systems presented in this

dissertation were a part of a multi-university collaborative research project utilizing

NEES with goal of investigating the effects of Soil-Foundation-Structure-Interaction

(SFSI) while demonstrating NEES research collaboration (Wood et al. 2004). Much had

been learned from this collaborative research with respect to means for effective research

collaboration and investigating SFSI effects by integrating experimental and analytical

tools.

233

7.1.1.1 Research collaborations

Sixteen principal and co-principal investigators from ten universities were

involved in this collaborative research. The experimental component of the research

involved 1-g shake table experiment at the University of Nevada at Reno (Johnson et al.

2006), field tests using the large mobile shakers at the University of Texas at Austin

(Black 2005), centrifuge tests at the University of California at Davis (Ilankatharan et al.

2005), and quasi-static structural component testing at Purdue University (Makido 2007).

The team of researchers also included numerical analysts from the University of

Washington (Shin 2007 and Ranf 2007), the University of California at Davis (Jie 2007),

and the University of California at Berkeley (Dryden 2008), as well as a team of

researchers at Kansas University to coordinate and sharing of data, and an education and

outreach team at San Jose State University.

Unlike most scientific research that has been led by only one to few collaborators

working on the same project and at the same test facility, multi-institution, multi-

investigator collaborative research requires particular attention to issues related to the

involvement, coordination, and cooperation of a large number of led researchers and their

support staff. Therefore, effective communication tools to facilitate information exchange

and decision making are essential to effectively conduct a large-scale collaborative

research. Periodic video and audio conference calls in addition to several face-to-face

meetings were held to facilitate information exchange and decision making. These were

in addition to extensive use of group emails and one-on-one interactions through emails

and phone calls. Arguably, a valuable research experience was obtained about open

234

exchange of ideas and effective dissemination of knowledge, from working on this

geographically distributed and diverse research environment.

Furthermore, the design of test elements to account for different test boundary

conditions and test scaling laws for structural modeling and geotechnical modeling was

challenging. The design process required cross-disciplinary interaction between

geotechnical and structural engineering. This cross disciplinary interaction may lead to

more holistic soil-structure system designs. The negotiation of the designs of test

elements to the satisfaction of the cross-disciplinary research team was an extremely

valuable learning experience.

7.1.1.2 Centrifuge experiments

The centrifuge experiments presented in this dissertation involved 1/52 scale

models of two-pile bents, single piles and a two-span segment of bridge with 20 different

superstructure configurations tested under varying earthquake characteristics (level of

shaking, frequency content, and wave from). These experiments produced unique data

sets that span the disciplines of geotechnical and structural engineering. Some of these

data complement the data obtained from other experiments. The data from the centrifuge

experiments was compared and combined with the data obtained from other experiments

to provide integrated analytical models for SFSI problems of soil-pile-bridge systems.

Comparisons with field tests

The MIL02 test series, in which the bridge bents were oriented to the different

directions of base shaking, was designed to facilitate comparisons with the field tests

performed at the University of Texas at Austin, in which the vibration source (T-Rex)

was moved to different locations relative to the model bridge bent. As the field shakers

235

which have maximum force outputs in a higher frequency range (http://nees.utexas.edu),

the natural frequencies of the field test specimens were altered by a factor of 18 (by

reducing the bent-cap masses) to increase the response to the excitation. These

differences in the range of frequencies of response of test specimens in both experiments

posed difficulties in making direct comparisons between experimental results. However,

both experiments provided unique data about the response of prototype bridge structure.

These unique data sets were used to calibrate the simulation methods for seismic soil-

foundation-structure interaction problems (Shin 2007 and Jie 2007).

Comparisons with 1-g shake table experiment


comparing physical models of the two-span segment of the bridge model tested at the

geotechnical centrifuge and the 1-g shake table facilities were presented in Chapter 3 of

this dissertation. For intermediate levels of shaking, the agreement between deck

response in centrifuge and 1 g shake table experiments suggests that the bridge deck

response can be reasonably modeled using fixed base columns attached to a 1 g shake

table if the 1 g shake table motion corresponds to the free field soil motion at the

equivalent depth of fixity (Chai, 2002). A difference in prototype bent spacing between

the centrifuge and 1-g shaking table models in addition to the interaction between the 1 g

shake table bridge model with the 1 g shaking table/actuation system caused some

discrepancies between centrifuge results and 1 g shaking table results. There were also

differences in spectral ratios (ratio of spectral acceleration of the deck to spectral

acceleration at the depth of fixity) that may be attributable to different energy dissipation

mechanisms in centrifuge and 1 g shake table experiments: soil particle-particle friction

236

and sliding, particle crushing, friction at soil-pile interface, radiation damping provided

by the piles in the soil, pile/column yielding and radiation damping in shake table system.

A significant amount of energy dissipation that occurred in the centrifuge test during the

medium-level shaking event was not present in shake table test. However, shake table

bridge model dissipated more energy during large-level of shaking due to yielding of the

reinforced concrete column. Hence, the direct comparison of results from different types

of experiments is valuable because it can clearly expose the flaws that we might

otherwise ignore.

Comparison of the system (three-bent) response to the individual bent response

The bridge deck in the centrifuge model of the two-span segment of the bridge

consisted of a light-weight aluminum plate bolted to the bridge bents. This afforded the

opportunity to first test each the three bents simultaneously while they were unconnected

and then to test them as a three-bent system. The comparisons of bent responses,

presented in Chapter 3 for a relatively weak input motion (measured base motion 0.08 g

in prototype scale), showed that the system response was quite different from individual

bent response. If the columns or the soil around the piles were to yield significantly this

could result in additional complex interactions. Theoretically, these interactions could be

predicted using numerical methods such as finite elements; however the methods for

analyzing soil-foundation-bridge systems have not been subject to verification exercises.

While experiments on bridge components will continue to be valuable, tests of

soil-foundation-bridge systems lead to more complete understanding of system

performance, provide unique data sets to validate numerical methods to predict bridge

system response, and promote cross-disciplinary education of researchers. Continued

237

multi-institution, multi-disciplinary research on systems could lead to a new paradigm for

design in which foundations and superstructures are designed to have stiffness, capacity,

and energy dissipation characteristics that are compatible and complementary with the

goal of optimizing system performance.

7.1.1.3 Centrifuge test data archives

One of the goals of this collaborative research was to develop curated data

repositories of the experimental and simulation data of SFSI problems of the prototype

bridge structure. In this context, all centrifuge test data and metadata was archived and

curated in NEEScentral data repository, and was used to demonstrate the usage of end-to-

end flow of data (Van Den Einde at al. 2007) using a data viewer (N3DV) developed by

the researchers at UC Davis (http://neesforge.nees.org). The data archives are publically

available at the NEEScentral website (http://central.nees.org).

7.1.1.4 Numerical simulations of the centrifuge experiments

The numerical simulations of all the centrifuge experiments were performed by

the collaborators from the University of Washington (Shin 2007). These simulations

employed Dynamic Beam-on-Nonlinear-Winkler Foundation (BNWF) models, using p-y,

t-z, and q-z interface springs (Boulanger et al. 1999) coupled with a 1-D shear beam soil

column, to model seismic soil-pile-structure interaction. Some of these simulations were

performed prior to the experiments and during the experiments. Results from these pre-

test and real-time simulations were valuable in designing test specimens and loading

protocols (i.e. selection of earthquake characteristics).

Some of the comparisons between the results from the post-test simulations and

experiments were presented in Chapter 2. These comparisons suggest that overall the

238

simulations reasonably predicted the superstructure motions and the maximum pile

bending moments. However, significant discrepancies (especially those near the ground

surface) between the predicted and measured soil motions were observed from these

comparisons. Shin (2007) also performed sensitivity analyses to study the sensitivity of

simulation results to uncertainties in modeling parameters. These sensitivity analyses

considered simulations of a single pile and a two-pile bent. For the structural models and

ground motion characteristics considered in these sensitivity studies, it was concluded

that the simulated superstructure motions and maximum pile bending moments were not

very sensitive to change in soil motions.

Effect of modeling boundary conditions on the sensitivity of predicted site

response

As mentioned earlier, the numerical simulations presented above employed a 1-D

shear beam shear-beam type finite element model to simulate soil site response. Effects

of model container on the soil site response were not explicitly modeled in these

simulations. The effect of mass of the container on the inertia forces was accounted (by

increasing unit weight of soil by 30%); however, flexibility of the container and the

stiffness of the vertical bearing supports at the base of the container were not modeled in

these simulations. In addition, these simulations adapted the measured motion at the base

of the container a prescribed motion for dynamic excitation. It is evident from the

presented comparisons in this dissertation that, in some cases, the predicted soil motions

(especially those near the ground surface) from the above simulations were significantly

different from experimental results. Understanding the discrepancies of these predicted

site response results motivated the analyses presented in the second part of this

239

dissertation. In this context, it was hypothesized that the “sensitivity of simulation results

to uncertainties in modeling parameters depends on how the boundary conditions are

incorporated in the simulations”. The second part of this dissertation is intended to prove

this hypothesis.

7.1.2 Modeling input motion boundary conditions for simulations of geotechnical

shaking table experiments

Numerical simulations of a hypothetical centrifuge shaking table experiment

involving a 1D soil column were performed in Chapter 4 to illustrate effects of using

different input motion boundary conditions on the sensitivity of numerical simulation

results to errors in material properties of a specimen. A novel method for handling the

boundary developed in this dissertation is the flexible-actuator-prescribed-force boundary

condition; by this method seismic input is specified by a force across a relatively stiff

spring in series with the actuator that drives the shaking table; hence, the boundary

between the test specimen and the shaking table is an absorbing-base boundary across

which energy may be transferred. In the prescribed-displacement boundary condition (the

more conventional method for introducing the excitation), the measured shaking table

motion in the experiment is used as a prescribed displacement in the simulation.

In both the simulations using the linear elastic and the elasto-plastic PDMY soil

material models, if the shear modulus of the soil material is perfectly modeled then the

results are independent of the input motion boundary conditions. Conversely, the

predicted surface response is dependent on the input motion boundary conditions when

the shear modulus is imperfectly modeled in the simulations. As expected, it is shown

that the ratio of Fourier amplitudes between the surface motion and the base motion (i.e

240

surface transfer function) is independent of the input motion boundary conditions when a

linear elastic soil material with an imperfect shear modulus is employed in the analysis.

However, the ratio of Fourier amplitude between the surface motion and the base motion

is dependent on the input motion boundary conditions when a nonlinear soil material with

an imperfect shear modulus is used in the analysis. In this case, greater discrepancies are

observed near frequencies at which peaks of ratio of Fourier amplitudes occur. The ratio

of Fourier amplitudes between the base motion and the command motion (i.e. base

transfer function) is dependent on the input motion boundary conditions when the shear

modulus of the soil material (both in linear elastic and PDMY material) is imperfectly

modeled in the simulations. This is because the dips (valleys) in the base transfer function

associated the energy absorption of the overlying soil deposit occur at the natural periods

of the soil, but the calculated amplification (peaks) in the surface transfer function

depends on the assumed natural periods which depend on the assumed shear modulus in

the simulations. If an absorbing-base boundary is assumed then the changes in frequency

of dips is compensated for by the changes in frequency of amplification. These changes

in base response cannot be evaluated using the prescribed-displacement input motion

boundary condition.

Furthermore, the flexible-actuator-prescribed-force approach which employs an

absorbing-base boundary generally yields well behaved sensitivities for results in a wide

range of simulation conditions. The prescribed-displacement approach, however, may

produce chaotic results in the sense that small errors in the simulation lead to large errors

in the results. Therefore, when performing the numerical simulations of a shaking table

experiment, modeling input excitation using the flexible-actuator-prescribed-force

241

boundary condition may be preferable to the prescribed-displacement boundary

condition.

The most general conclusion of this study is that the sensitivity of numerical

simulation results to uncertainties in modeling parameters depends on how the input

motion boundary conditions are accounted for and the dynamic interactions among the

various components of the dynamic system. This raises a fundamental question: How can

we assess the significance of a discrepancy between a numerical simulation and an

experimental result? A large error in response may be caused by a small error in input

parameter if, for example, a rigid boundary condition is assumed. This study shows that,

for shaking table tests, the significance of errors in the numerical simulations cannot be

rigorously assessed without accounting for dynamic interaction between the test

specimen and the actuation system.

7.1.3 Numerical simulations of the soil model accounting for soil-container-shaker

interaction

Numerical modeling of complex dynamic interaction of a soil-model container-

centrifuge-shaker system was presented in Chapter 5 of this dissertation. This modeling

incorporated mass and flexibility of the container (a flexible shear beam container), the

effect of shear rods at both ends of the container, stiffness of the vertical bearing supports

at the base of the container, flexibility of the actuator, and the effect of reaction mass. A

simplistic approximation of the actuator and control system using springs and dashpots

was used to include first-order effects of actuator flexibility on the interaction between

the specimen and the shaking table.

242

To improve understanding of interactions among soil model, container, and

shaker system and to evaluate how the sensitivity of simulation results depends on

boundary conditions in experiment and simulation, the boundary conditions were treated

with three different levels of detail: (a) 1-D shear beam simulations of soil column (b) 2-

D simulations of soil and container, and (c) 2-D simulations of soil, container, and

shaker. Site response simulations using the above numerical models were performed and

results were compared with the site response results measured in the centrifuge test series

MIL03.

As opposed to the 1-D shear beam simulations of soil, the inclusion of the

container in the simulations resulted in more accurate simulation of the experiment. In

addition, the rocking behavior of the container was well captured when the compliance of

the vertical bearing supports at the base of the container was included in the analysis.

Sensitivity studies were performed to propagate the uncertainties in modeling shear

modulus of the soil on the predicted site response results for models at the three levels of

detail. Results from sensitivity studies showed that the sensitivity of computational

simulation output (soil site response) to changes in input parameters (shear modulus of

soil) depends on how boundary conditions were modeled in the simulation; to provide an

unbiased validation of a numerical model, it is important evaluate the effects of boundary

conditions on the sensitivity of simulation results. Similar to the results presented in

chapter 4 for the simulations with the hypothetical centrifuge experiment, it was again

shown that the sensitivity of predicted site response results heavily depends on the input

motion boundary conditions. In addition, the 2-D simulations of soil, container, and

shaker, which employed the flexible-actuator-prescribed-force input motion boundary

243

condition for input excitation, generally yield well behaved sensitivities for predicted site

response results.

The numerical models of the soil-container-shaker system are archived and

publically available for other to use in NEEScentral data repository

(http://central.nees.org). These simulations of the soil-container-shaker system consider a

uniform dry-dense sand soil model, a flexible shear beam, and the horizontal shaker of

the UC Davis centrifuge facility. Others could access these numerical models, modify

the geometry of the FE mesh and the definition of constitutive models and input

parameters of the soil model, and update the FE mesh of the soil-container-shaker

system, to simulate different experiments. Additional details on the simulation archives

are given in Chapter 5 and Appendix A of this dissertation.

7.1.4 Numerical model of a servo-hydraulic centrifuge actuation system to predict

shaking table response

Modeling the input motion boundary condition using the flexible-actuator-

prescribed-force approach requires a realistic representation of experimental boundary

conditions and the detailed modeling of various components of the centrifuge-shaker

system to include the effects of dynamic interaction between the test specimen and the

servo-hydraulic actuation system on the simulation results. Another benefit of accurate

modeling of the centrifuge-shaker system is the accurate prediction of base motions in the

simulations. Further, this numerical model could be used to predict base motions during

input motion tuning exercises prior to the actual experiment.

In the absence OpensSees material models and elements to model various

components of the servo-hydraulic actuation system, a simplistic approximation using

244

springs and dashpots was used to model the actuator, servo-valve and the control system

in the numerical model of the UC Davis centrifuge actuation system. Generally, for the

soil model (dry dense Nevada sand) and the frequency sweep input (50 to 125 Hz)

considered in the simulations, the above shaker model reasonably reproduced some

features (for example, steady state components of base displacements) of the base

response observed in the experiment. However, the higher frequency components of the

base displacements and the magnitudes of the base transfer functions (i.e., ratios of

Fourier amplitude between the base motion and command motion) were poorly predicted

in the simulations. Also, while the results were not presented in this dissertation, the

simulations using the command motions with significantly higher frequency contents

resulted in poor predictions of the base displacements and the base transfer functions.

In general, the degree of distortion between the input command motion and the

measured motion at the shaking table depends on numerous factors such as the

characteristics of the soil model, compressibility of oil column in the actuator, non-linear

flow characteristics in the actuator, servo-valve time delay, configuration of control loops

etc. Geotechnical centrifuge experiments often involve highly non-linear test specimens

where the payload mass is a significant fraction of the system mass and the larger

amplitude earthquake simulations where the actuator characteristics are themselves non-

linear. In addition, in the centrifuge experiments frequencies are scaled by the factor of

‘g’ level. The resonant frequencies of higher vibration modes of different components of

the actuation system and the higher frequency responses of the actuator, the servo-valve

and the control system would affect the characteristics (magnitude, frequency content,

and wave form) of the dynamic signal measured at the shaking table. Therefore, to

245

capture the salient features of the non-linear actuator and servo-valve and to compensate

for the effects of poles and zeros that develop in the feed-back control system on the

shaking table response, it is concluded that more sophisticated analytical models of the

actuator, servo-valve, and controller are required.

7.2 Areas for future research

Recent research has begun to further understand the seismic response of soil-

foundation-bridge systems and to verify and validate computational simulations for

seismic response of bridge systems. Some ideas for future research on seismic response

of soil-foundation-bridge systems are listed below.

Experimental research on soil-foundation-bridge systems which involves poor soil

conditions need to be conducted (to investigate the effects of liquefaction and

lateral spreading for example). Data from these experiments could then be used to

calibrate the integrated numerical models of complete bridge systems (i.e., soil-

foundation systems with realistic superstructure characteristics) which involve

complex mechanisms of behavior (response to kinematic loads from liquefaction

induced lateral spreading for example).

Additional experimental data is required to evaluate the effects of inelastic

deformations and energy dissipation characteristics (formation of an in-ground

plastic hinge for example) of the foundation on the system response of the bridge.

The experiments presented in this dissertation involved bridge systems with a

larger diameter drilled shaft foundation configuration. Additional experimental

data is required to fully understand the seismic response of soil-foundation-bridge

246

systems which involve other foundation configurations (for example, pile groups,

shallow foundations, etc.)

The effect of abutment structures on the performance of bridge system needs to be

completely evaluated; which requires experimental research on soil-foundation-

deck-abutment systems. Results from these studies could then be used to calibrate

integrated numerical models of complete bridge systems and to develop improved

design guidelines for seismic applications.

The analyses presented in the second part of this dissertation provided insight into

the importance of proper treatment of experimental boundary conditions on the

sensitivity studies of numerical simulations. The effects of dynamic interaction between

the soil model and the centrifuge shaker system on the simulations of the centrifuge

experiments were incorporated up to a certain extent, yet much research need to be

performed to fully understand effects of dynamic interaction between a test specimen and

the centrifuge shaker system in various scenarios. Some ideas for future research on this

problem are listed below.

The analyses presented in the second part of the dissertation focused solely on the

site response simulations and investigated the effects of soil-container-shaker

interaction on the site response results. Numerical simulations of the complete

experimental system (i.e., includes bridge model, soil, container, and shaker),

with a realistic representation of experimental boundary conditions and the

detailed modeling of dynamic interactions between the test specimen and the

centrifuge shaker system (i.e., interactions between bridge model-soil-container-

shaker), are to be performed to fully understand the sensitivity of simulated bridge

247

model response (such as super structure response, pile bending moment, etc) to

uncertainties in modeling parameters.

Dynamic interaction between a test specimen and the servo-hydraulic actuation

system depends on many factors such as characteristics of the test specimen,

compliance of reaction mass, compressibility of oil column in the actuator

chamber, non-linear flow characteristics in the actuator, servo valve time delay,

configuration and characteristics of control loops, etc. Therefore to fully

incorporate the effects of the test specimen-actuation system interaction on the

simulation models, sophisticated models of actuator, servovalve, and controller

are required. Development of these analytical models, especially for the

geotechnical centrifuge applications, is a topic for future research.

Geotechnical centrifuge experiments often involve relatively heavy and highly

nonlinear test specimens (e.g., a massive volume of liquefying sand). Additional

work is required to understand the interaction of highly nonlinear massive test

specimens with servo-hydraulic centrifuge actuation systems that are driven at

their performance limits (in their nonlinear range).

248

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Appendix A

Centrifuge test and simulation data archives

A.1 Introduction

One of the missions of the Network for Earthquake Engineering Simulation

(NEES) is to foster the open exchange of data and information among researchers and

practicing engineers (http://nees.org). In order to organize and structure data so that the

information can be shared, accessed, and used by the broader earthquake engineering

community, the NEES Cyberinfrastructure Center (NEESit) has developed the

centralized data repository, NEEScentral (http://central.nees.org).

On the development of the current model of the NEEScental, NEESit has

collaborated with the researchers from the University of California, Davis. One of the

driving forces of the development of current version of the NEESit data model was to

reproduce one of the centrifuge test data reports (Ilankatharan et al. 2005). The ultimate

goal of the development of NEEScentral is to facilitate the end-to-end work flow of the

earthquake engineering data. An example of end-to-end usage of NEEScentral

application is depicted in Fig. A.1. As described in Van Den Einde at al. 2007, the

primary objectives of end-to-end usage of data are to allow easy upload of data/metadata

by the researchers, novel search of the data sets within the repository, the ability of

download curated data sets in formats that allow for easy ingestion of the data/metadata

into community developed visualization or data processing programs. In this context, the

centrifuge data archives (which were developed from the collaborative research project

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described in Chapter 2 of this dissertation) were used to demonstrate the usage of end-to-

end workflow using a data viewer (N3DV) developed by the researchers at UC Davis

(http://neesforge.nees.org).

This appendix provides the details on the collaboration with NEESit in the

development of NEEScentral data model and outlines the archives of the centrifuge test

data and the numerical models of the soil-container-shaker system that were described in

the Chapter 5 of this dissertation. The capabilities of the current NEEScentral data model

are discussed at the end of this Appendix.

A.2 NEESit - UC Davis collaboration in the development of NEEScentral data

model

On the development of the current model of the NEEScentral in the summer of

2006, NEESit established a data working group, which included the researchers from

different universities, members of the IT strategy committee of NEES, IT managers from

different test facilities, and developers from NEESit, to accelerate the development

process by effectively exchanging ideas between the members of the earthquake

engineering community and the IT experts at NEESit. In this context, the primary efforts

of the researchers at UC Davis were to exercise the data and metadata uploading

interfaces (Fig. A.2) of the NEEScentral by putting in real data from the centrifuge test

series described in Chapter 2 and recommend critical features and bugs that need to be

addressed. The ultimate goal of these efforts was to complete an end-to-end

demonstration of the use of the NEES data repository. A significant amount of work was

done by the researchers at UC Davis on the following tasks and goals:

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Archive data and metadata from all three centrifuge experiments in NEEScentral

and attempt to exercise all of the features of NEEScentral that are relevant to the

centrifuge experiments.

Figure out how to upload more metadata and recommend mechanisms for

automatic ingestion of metadata (sensor locations and channel lists) into

NEEScentral using excel spreadsheet templates

Recommend convenient mechanisms for data/metadata download out of the

repository

Integration of NEEScentral with the UC Davis data viewer N3DV

Recommend procedures to upload, sort, and document metadata for experiments

including better mechanisms to document metadata associated with photographs

and videos (such as efficient way to label and organize photos and videos).

Archive OpenSees numerical simulations of the centrifuge experiments and

centrifuge experiment

Test the ability of NEEScentral to search for important metadata and make

suggestions as to which data fields need to be searchable (idea of data dictionary)

Recommend capabilities to delete projects, experiments, trials and perform more

file management, including: moving, copying, and deleting

Recommend features of enhanced navigation and access of information and data

in NEEScentral through a tree browser navigation feature and mouse highlight

dropdown menus

Comment on the aspects of NEEScentral that make it burdensome and awkward

to upload information

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Work on a staging machine of NEEScentral, prior to releases to the general public

at the request of NEESit

Recommend capabilities to produce public data archives

Recommend capabilities to produce customizable experiment report

The end-to-end concept thus included entry of data and metadata, download,

viewing and visualizing data and numerical simulation of data in the repository, including

archiving of numerical models of the experiments. Data and metadata from the centrifuge

experiments and associated analysis was curated and publically available at the

NEEScentral website (http://central.nees.org). A brief outline of these data archives of the

centrifuge experiments and numerical simulations is given in the following sections.

A.3 Outline of the centrifuge test data archives in NEEScentral

The test data archives follow the NEEScentral data hierarchical classes (depicted

in Fig. A.3).

NEES Project: Collaborative Research: Demonstration of NEES for Studying Soil-

Foundation-Structure Interaction (UC Davis)

Project ID: NEES-2006-0180

Project Nickname: SFSI (UC Davis)

NEES Equipment site: NEES geotechnical centrifuge at University of California, Davis

Project experiments:

MIL01: First Centrifuge Test Series

MIL02: Second Centrifuge Test Series

MIL03: Third Centrifuge Test Series

Experiment documentation:

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This section consists of;

Pictures taken during the experiments (with proper captions)

Test data report

Data files used to create data report (such as excel tables, time history plots,

figures, etc)

Experiment setup:

This section consists of;

Details of measurement units for the experiment

Material properties used in the various part of the experiment

Coordinate spaces used in the various part of the experiment (See Fig. A.4 for an

example)

Sensor location plans used in the experiment (See Fig. A.5 for an example)

List of scale factors used in the experiment

Drawings of the models used in the experiment

Trials in the experiments:

The test series MIL01 and MIL02 consist of 16 trails (dynamic shaking events)

and the test series MIL03 consists of 15 trials. An example definition of list of trails for

one of the experiment is depicted Fig. A.6.

Trial setup:

This section consists of definition of DAQ configurations (i.e., channel lists) used

in the experiments along with the prototype data files. Prototype files (with extensions

.prt) are output files that have been converted to engineering prototype units using the

262

appropriate channel gain list and centrifuge scaling laws. An example definition of a

DAQ configuration is depicted in Fig. A.7.

Trial data:

This section consists of unprocessed, converted (i.e., .prt files), and derived data

files (calculated time histories of bent rotations for example) in separate folders. The

above folders are categorized into sub-folders (as described below) for each data

acquisition system used in the experiment.

RESDAQ_Main: Traditional wired DAQ system (samples accelerometers,

displacement transducers and strain gages).

WIDAQ: Wireless DAQ system (samples MEMS accelerometers and strain

gages)

VIDAQ: High speed video DAQ system (recorded videos from the high-speed

video cameras are uploaded here)

Data Viewer:

The data obtained from different sensors in the experiment can be visualized

using the data viewer (N3DV) developed by the researchers at UC Davis

(http://neesforge.nees.org). The data viewer section in NEEScentral has an option called

“N3DV Export” to export sensor locations, DAQ configurations, and sensor data from all

trials of the experiment in a format readable by N3DV. Example screen shots of N3DV

application for the data from the MIL01 test series are shown in Figs. A.8 to A.11

263

A.4 Outline of the archives of the numerical simulations

Archives of OpenSees numerical models of the soil-container-shaker system are

categorized into 3 different simulation folders as follows (based on complexities in the

boundary conditions):

Simulation of MIL 03_ 2D Soil Shear beam (described in section 5.3.1)

Simulation of MIL 03_2D Soil and FSB2 container (described in section 5.3.2)

Simulation of MIL 03_2D Soil, FSB2 container, and Shaker (described in section

5.3.3)

Each simulation folder consists of following data/metadata.

Simulation Setup:

This section;

defines the computer hardware and software used in the simulation

defines the material materials properties used in the various parts of the

simulation (for example, soil, aluminum, steel, neoprene rubber, etc)

defines the model types used in the various parts of the simulation (for example,

soil, container rings, shear rods, actuator, etc)

Simulation Runs:

Main and supplemental input files and output files of selected runs of numerical

simulations of the soil-container-shaker system are archived in this section (see Fig.

A.12).

264

A.5 Discussion on the current NEEScentral data model

The latest version of NEEScentral (version 1.8, released on June 16, 2008) has an

improved ability to upload, download, search, browse, view, and edit data and metadata

in NEEScentral (http://it.nees.org/library/data/neescentral-release-notes.php). It has

improved capabilities to facilitate end-to-end work flow of the earthquake engineering

data.

One of the limitations of the current NEEScentral data model is that it has

different data hierarchical classes for experimental data and simulation data. Use of

similar data structures and data formats for experimental and simulation data might allow

numerical modelers to easily input metadata from an experiment to generate meshes and

define input parameters directly from metadata from the experiment. In addition, if the

data model has similar structures and data formats for experimental and simulation data,

then simulation data could be easily compared to experimental data using the

visualization tools.

A.6 Summary and Conclusions

Data exchange is a key component of collaboration; wasting data wastes data and

knowledge. Therefore it is important to share and archive data. NEES has established

NEEScentral data repository to organize and structure data so that the information can be

shared, accessed, and used by the broader earthquake engineering community. In this

context, all centrifuge test data and metadata and numerical models were archived and

curated in NEEScentral data repository, and were used to demonstrate the usage of end-

to-end flow of data using a data viewer (N3DV) developed by the researchers at UC

265

Davis (http://neesforge.nees.org). The data archives are publically available at the

NEEScentral website (http://central.nees.org). These archives were used by NEESit in

many presentations at NEES annual meetings, NEESit workshops, NSF site visits to

demonstrate the capabilities of NEEScentral data model.

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Fig. A.1 End-to-end data usage scenario (after Van Den Einde et al. 2007)

267

Fig. A.2 NEEScentral data model (after Van Den Einde et al. 2007)

268

Fig. A.3 Experimental data hierarchical classes in NEEScentral (after Van Den Einde et al. 2007)

269

Fig. A.4 An example definition of a coordinate space

Fig. A.5 An example definition of a sensor location plan

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Fig. A.6 An example definition of a list of trials

Fig. A.7 An example definition of a DAQ configuration

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