2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis

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Copyright

by

MEHMET BARIS DARENDELI

2001


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DEVELOPMENT OF A NEW FAMILY OF NORMALIZED

MODULUS REDUCTION AND MATERIAL DAMPING

CURVES

by

MEHMET BARIS DARENDELI, B.S., M.S.

DISSERTATION

Presented to the Faculty of the Graduate School of

The University of Texas at Austin

in Partial Fulfillment

of the Requirements

for the Degree of

DOCTOR OF PHILOSOPHY

The University of Texas at Austin

August, 2001


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Dedicated

To

My Parents,

My Wife and My Daughter


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Acknowledgements

I would like to thank my supervising professor Dr. Kenneth H. Stokoe, II

for his guidance and support through the course of this study. His passion and

enthusiasm in his work has always inspired me. Our stimulating conversations

have made this study enjoyable.

Dr. Robert B. Gilberts assistance and guidance, which have made this

dissertation possible, is gratefully acknowledged. Besides his valuable input to

this work, he has influenced my perception of science and engineering with his

lectures on decision, risk and reliability.

I would also like to thank my dissertation committee members Dr. Jose M.

Roesset, Dr. Ellen M. Rathje, Dr. Alan F. Rauch and Dr. Mark F. Hamilton for

reviewing this dissertation in such a limited time frame and for their valuable

contributions to this work. Thanks are also extended to the rest of the former and

current geotechnical engineering faculty, Dr. Roy E. Olson, Dr. David E. Daniel,

and Dr. Stephen G. Wright for their lectures that broadened my knowledge.

The support from the California Department of Transportation, the

National Science Foundation, the Electric Power Research Institute, and Pacific

Gas and Electric Company is gratefully acknowledged for funding various stages

of the ROSRINE project. I would also like to acknowledge the contributions of

the National Institute of Standards and Technology, the United States Geological

Survey, the Department of Energy, the Westinghouse Savannah River

Corporation, Kajima Corporation, Geovision, Agbabian Associates, Fugro, Inc.,

Earth Mechanics, Inc., S&ME, Inc. in funding the research projects the results of


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which are utilized in this study. Encouragement and guidance from Dr. Clifford

Roblee, Dr. John Schneider, Dr. Walter Silva, Dr. Robert Pyke, Dr. Robert

Nigbor, Dr. David Boore, Prof. Mladen Vucetic and Dr. Richard Lee, who took

part in these research projects, are appreciated.

Thanks to my best friend Cem Akguner for always being there whenever I

needed him, to Dr. Brent L. Rosenblad for trying to teach me how to bat

whenever we overworked, to Dr. Ahmet Yakut for our stimulating card plays and

arguments regarding them that lasted for hours, and to Baris Binici for each and

every five minute coffee break at 100oF. You have kept me sane (although

everyone reading this paragraph will question it a little) for the past seven years.

I would also like to thank the former and current graduate students that I

have worked side by side. I enjoyed each and every day and night that I worked

together with Dr. James A. Bay, Dr. Seon-Keun Hwang, Farn-Yuh Menq, Brian

Moulin, Celestino Valle and Nicola Chiara. Thanks are also extended to other

graduate students of whom I had the pleasure of making acquaintance; Dr. Eric

Liedtke, Dr. Mike Kalinski, Jeffrey Lee, Paul Axtell, Jiun Chen, Cem Topkaya

and many others that I unfortunately omitted. I would also like to thank Teresa

Tice-Boggs and Alicia Zapata for their administrative support, and Frank Wise,

Gonzalo Zapata, Max Trevino and Paul Walters for their technical assistance over

the years.


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DEVELOPMENT OF A NEW FAMILY OF NORMALIZED

MODULUS REDUCTION AND MATERIAL DAMPING

CURVES

Publication No._____________

Mehmet Baris Darendeli, Ph.D.

The University of Texas at Austin, 2001

Supervisor: Kenneth H. Stokoe, II

As part of various research projects [including the SRS (Savannah River Site)Project AA891070, EPRI (Electric Power Research Institute) Project 3302, and

ROSRINE (Resolution of Site Response Issues from the Northridge Earthquake)

Project], numerous geotechnical sites were drilled and sampled. Intact soil

samples over a depth range of several hundred meters were recovered from 20 of

these sites. These soil samples were tested in the laboratory at The University of

Texas at Austin (UTA) to characterize the materials dynamically. The presence of

a database accumulated from testing these intact specimens motivated a re-

evaluation of empirical curves employed in the state of practice. The weaknesses

of empirical curves reported in the literature were identified and the necessity of


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developing an improved set of empirical curves was recognized. This study

focused on developing the empirical framework that can be used to generate

normalized modulus reduction and material damping curves. This framework is

composed of simple equations, which incorporate the key parameters that control

nonlinear soil behavior. The data collected over the past decade at The University

of Texas at Austin are statistically analyzed using First-order, Second-moment

Bayesian Method (FSBM). The effects of various parameters (such as confining

pressure and soil plasticity) on dynamic soil properties are evaluated and

quantified within this framework. One of the most important aspects of this study

is estimating not only the mean values of the empirical curves but also estimating

the uncertainty associated with these values. This study provides the opportunity

to handle uncertainty in the empirical estimates of dynamic soil properties within

the probabilistic seismic hazard analysis framework. A refinement in site-specific

probabilistic seismic hazard assessment is expected to materialize in the near

future by incorporating the results of this study into the state of practice.


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TABLE OF CONTENTS

LIST OF TABLES ...............................................................................................xiii

LIST OF FIGURES............................................................................................xviii

CHAPTER 1 INTRODUCTION........................................................................ 1

1.1 Background ........................................................................................... 1

1.2 Dynamic Soil Properties........................................................................ 4

1.3 Ground Response Analysis ................................................................... 8

1.4 Objectives of Research........................................................................ 10

1.5 Organization of Dissertation ............................................................... 11

CHAPTER 2 LABORATORY TESTING EQUIPMENT............................... 13

2.1 Introduction ......................................................................................... 13

2.2 Combined Resonant Column and Torsional Shear Equipment........... 14

2.3 Torsional Resonant Column Test ........................................................ 16

2.4 Cyclic Torsional Shear Test ................................................................ 21

2.5 Summary ............................................................................................. 22

CHAPTER 3 PHYSICAL PROPERTIES OF TEST SPECIMENS ................ 233.1 Introduction ......................................................................................... 23

3.2 Undisturbed Soil Specimens from Northern California...................... 25

3.3 Undisturbed Soil Specimens from Southern California...................... 29

3.4 Undisturbed Soil Specimens from South Carolina ............................. 35

3.5 Undisturbed Soil Specimens from Lotung, Taiwan ............................ 38

3.6 Overview of The Database .................................................................. 39

3.7 Summary ............................................................................................. 53

CHAPTER 4 OBSERVED TRENDS IN DYNAMIC SOIL PROPERTIES .. 54

4.1 Introduction ......................................................................................... 54

4.2 Background ......................................................................................... 54

4.3 Nonlinear Dynamic Soil Properties..................................................... 56


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4.4 Effect of Duration of Confinement on Small-Strain Dynamic SoilProperties............................................................................................. 59

4.5 Effect of Effective Confining Pressure ............................................... 61

4.6 Effect of Overconsolidation Ratio....................................................... 70

4.7 Effect of Number of Cycles ................................................................ 74

4.8 Effect of Loading Frequency............................................................... 76

4.9 Effect of Soil Type .............................................................................. 81

4.10 Effect of Sample Disturbance ............................................................. 90

4.11 Summary ........................................................................................... 104

CHAPTER 5 EMPIRICAL RELATIONSHIPS ............................................ 107

5.1 Introduction ....................................................................................... 107

5.2 Hardin and Drnevich (1972) Design Equations ................................ 107

5.3 Empirical Relationships .................................................................... 113

5.4 Summary ........................................................................................... 129

CHAPTER 6 PROPOSED SOIL MODEL .................................................... 131

6.1 Introduction ....................................................................................... 131

6.2 Normalized Modulus Reduction Curve............................................. 132

6.3 Nonlinear Material Damping Curve.................................................. 134

6.4 Parametric Study of The Soil Model................................................. 147

6.5 Summary ........................................................................................... 152

CHAPTER 7 STATISTICAL ANALYSIS OF COLLECTED DATAUSING FIRST-ORDER, SECOND-MOMENT BAYESIAN METHOD 154

7.1 Introduction ....................................................................................... 154

7.2 Bayesian Approach ........................................................................... 155

7.3 First-Order, Second-Moment Bayesian Method ............................... 164

7.4 Form of Proposed Equations ............................................................. 172

7.5 Summary ........................................................................................... 179


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CHAPTER 8 STATISTICAL ANALYSIS OF THE RCTS DATA.............. 180

8.1 Introduction ....................................................................................... 180

8.2 Analysis of Subsets of The Data ....................................................... 184

8.3 Analysis of All Credible Data ........................................................... 212

8.4 Summary ........................................................................................... 217

CHAPTER 9 PREDICTING NONLINEAR SOIL BEHAVIOR USINGTHE CALIBRATED MODEL................................................................... 220

9.1 Introduction ....................................................................................... 220

9.2 Calculation of Reference Strain, Curvature Coefficient, Small-Strain Material Damping Ratio and the Scaling Coefficient............. 221

9.3 Estimation of Normalized Modulus Reduction and MaterialDamping Curves................................................................................ 224

9.4 Effect of Overconsolidation Ratio, Loading Frequency andNumber of Loading Cycles on Nonlinear Soil Behavior .................. 228

9.5 Effect of Confining Pressure on Nonlinear Soil Behavior................ 234

9.6 Effect of Soil Type on Nonlinear Soil Behavior ............................... 238

9.7 Effects of Confining Pressure and Soil Type on Stress-StrainCurves................................................................................................ 242

9.8 Summary ........................................................................................... 248

CHAPTER 10 RECOMMENDED NORMALIZED MODULUSREDUCTION AND MATERIAL DAMPING CURVES ......................... 249

10.1 Introduction ....................................................................................... 249

10.2 Effect of PI at a Given Mean Effective Stress .................................. 250

10.3 Effect of Mean Effective Stress on a Soil with Given Plasticity ...... 250

10.4 Impact of Utilizing the Recommended Curves on EarthquakeResponse Predictions of Deep Sites .................................................. 250

10.5 Summary ........................................................................................... 272

CHAPTER 11 UNCERTAINTY ASSOCIATED WITH THE MODELPREDICTIONS.......................................................................................... 273

11.1 Introduction ....................................................................................... 273

11.2 Uncertainty in Nonlinear Soil Behavior............................................ 273


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11.3 Uncertainty in Predicted Ground Motions Due to the Uncertaintyin Nonlinear Soil Behavior................................................................ 284

11.4 Summary ........................................................................................... 295

CHAPTER 12 SUMMARY AND CONCLUSIONS....................................... 296

12.1 Summary ........................................................................................... 296

12.2 Conclusions ....................................................................................... 301

APPENDIX A ..................................................................................................... 303

APPENDIX B ..................................................................................................... 306

APPENDIX C ..................................................................................................... 311

APPENDIX D ..................................................................................................... 338

REFERENCES.................................................................................................... 357

VITA ................................................................................................................... 363


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LIST OF TABLES

Table 3.1 Physical properties of soils recovered from Oakland OuterHarbor and test pressures (Hwang, 1997) ..................................... 24

Table 3.2 Physical properties of soils recovered from Treasure Islandand test pressures (Hwang and Stokoe, 1993b; and Hwang,1997).............................................................................................. 25

Table 3.3 Physical properties of soils recovered from San FranciscoAirport and test pressures (Hwang, 1997)..................................... 27

Table 3.4 Physical properties of soils recovered from Gilroy and test

pressures (Hwang and Stokoe, 1993c; Hwang, 1997; andStokoe et al., 2001)........................................................................ 27

Table 3.5 Physical properties of soils recovered from Garner Valleyand test pressures (Stokoe and Darendeli, 1998) .......................... 28

Table 3.6 Physical properties of soils recovered from San Francisco-Oakland Bay Bridge Site and test pressures (Stokoe et al.,1998d)............................................................................................ 28

Table 3.7 Physical properties of soils recovered from Corralitos andtest pressures (Stokoe et al., 2001)................................................ 28

Table 3.8 Physical properties of soils recovered from Borrego and testpressures (Hwang, 1997)............................................................... 32

Table 3.9 Physical properties of soils recovered from Arleta and testpressures (Darendeli and Stokoe, 1997; and Darendeli, 1997) ..... 32

Table 3.10 Physical properties of soils recovered from Kagel and testpressures (Darendeli and Stokoe, 1997; and Darendeli, 1997) ..... 32

Table 3.11 Physical properties of soils recovered from La Cienega and

test pressures (Darendeli and Stokoe, 1997; Darendeli, 1997;and Stokoe et al., 1998e) ............................................................... 33

Table 3.12 Physical properties of soils recovered from Newhall and testpressures (Darendeli and Stokoe, 1997; and Darendeli, 1997) ..... 33


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Table 3.13 Physical properties of soils recovered from Sepulveda V.A.Hospital and test pressures (Darendeli and Stokoe, 1997; and

Darendeli, 1997)............................................................................ 34

Table 3.14 Physical properties of soils recovered from Potrero Canyonand test pressures (Stokoe et al., 1998e) ....................................... 34

Table 3.15 Physical properties of soils recovered from Rinaldi ReceivingStation and test pressures (Stokoe et al., 1998e). .......................... 34

Table 3.16 Physical properties of soils recovered from North PalmSprings and test pressures (Stokoe et al., 2001) ............................ 35

Table 3.17 Physical properties of soils recovered from Imperial Valley

College and test pressures (Stokoe et al., 2001)............................ 35

Table 3.18 Physical properties of soils recovered from Savannah RiverSite and test pressures (Hwang, 1997; and Stokoe et al.,1998a)............................................................................................ 37

Table 3.19 Physical properties of soils recovered from Daniel Island andtest pressures (Stokoe et al., 1998b).............................................. 37

Table 3.20 Physical properties of soils recovered from Lotung site andtest pressures (Hwang and Stokoe, 1993a; and Hwang, 1997) ..... 39

Table 3.21 Distribution of soil samples according to the sample depth ineach geographic region.................................................................. 41

Table 3.22 Distribution of collected according to the isotropic confiningpressure in each geographic region ............................................... 42

Table 3.23 Distribution of soil samples according to the Unified SoilClassification System (USCS) designation and sample depth...... 44

Table 4.1 Parameters that control nonlinear soil behavior and theirrelative importance in terms of affecting normalized modulusreduction and material damping curves based on generaltrends observed during the course of this study .......................... 105

Table 5.1 Parameters that control nonlinear soil behavior and theirrelative importance in terms of affecting shear modulus andmaterial damping (Hardin and Drnevich, 1972b) ....................... 108


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Table 7.1 Prior information provided in the discrete example.................... 160

Table 7.2 Prior information regarding the model parameters in theFSBM example............................................................................ 165

Table 7.3 Prior covariance structure of the model parameters in theFSBM example............................................................................ 165

Table 7.4 Data used to calibrate the model parameters in the FSBMexample ....................................................................................... 166

Table 7.5 Comparison of the prior and posterior information regardingthe model parameters in the FSBM example .............................. 169

Table 7.6 Posterior covariance structure of the model parameters in theFSBM example............................................................................ 170

Table 7.7 Posterior covariance structure of the model parameters in theFSBM example............................................................................ 171

Table 8.1 Distribution of specimens with soil type and geographiclocation ........................................................................................ 181

Table 8.2 Distribution of specimens by soil group and geographiclocation ........................................................................................ 181

Table 8.3 Distribution of specimens with soil type and geographiclocation for the updated database ................................................ 182

Table 8.4 Distribution of specimens by soil group and geographiclocation for the updated database ................................................ 183

Table 8.5 Prior mean values and variances of the model parameters ......... 185

Table 8.6 Updated mean values and variances of the model parametersfor the soils from Northern California......................................... 186

Table 8.7 Updated mean values and variances of the model parameters

for the soils from Southern California......................................... 191

Table 8.8 Updated mean values and variances of the model parametersfor the soils from South Carolina ................................................ 194


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Table 8.9 Updated mean values and variances of the model parametersfor the South Carolina soil groups affected by change in the

contents of the database............................................................... 198

Table 8.10 Updated mean values and variances of the model parametersfor the soils from Lotung, Taiwan............................................... 200

Table 8.11 Updated mean values and variances of the model parametersfor the four soil groups ................................................................ 207

Table 8.12 Comparison of the prior and updated mean values andvariances of the model parameters for all the credible data........ 214

Table 8.13 Covariance structure of the updated model parameters for all

the credible data .......................................................................... 218

Table 10.1 Effect of PI on normalized modulus reduction curve: o =0.25 atm....................................................................................... 252

Table 10.2 Effect of PI on material damping curve: o = 0.25 atm.............252

Table 10.3 Effect of PI on normalized modulus reduction curve: o =1.0 atm......................................................................................... 254

Table 10.4 Effect of PI on material damping curve: o = 1.0 atm...............254

Table 10.5 Effect of PI on normalized modulus reduction curve: o =4.0 atm......................................................................................... 256

Table 10.6 Effect of PI on material damping curve: o = 4.0 atm...............256

Table 10.7 Effect of PI on normalized modulus reduction curve: o = 16atm............................................................................................... 258

Table 10.8 Effect of PI on material damping curve: o = 16 atm................ 258

Table 10.9 Effect of o on normalized modulus reduction curve: PI = 0%.................................................................................................. 260

Table 10.10 Effect of o on material damping curve: PI = 0 % ...................260


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Table 10.11 Effect of o on normalized modulus reduction curve: PI =15 %............................................................................................. 262

Table 10.12 Effect of o on material damping curve: PI = 15 % ................. 262


Table 10.14 Effect of o on material damping curve: PI = 30 % ................. 264


Table 10.16 Effect of o on material damping curve: PI = 50 % ................. 266Table 10.17 Effect of o on normalized modulus reduction curve: PI =

100 %........................................................................................... 268

Table 10.18 Effect of o on material damping curve: PI = 100 % ............... 268

Table 11.1 Predicted mean values and standard deviations accounting foruncertainty in the values of model parameters and variabilitydue to modeled uncertainty ......................................................... 275

Table 11.2 Predicted covariance structure accounting for uncertainty in

the values of model parameters and variability due tomodeled uncertainty .................................................................... 276

Table 11.3 Predicted mean values and standard deviations accountingonly for variability due to modeled uncertainty .......................... 277

Table 11.4 Predicted covariance structure accounting only for variabilitydue to modeled uncertainty ......................................................... 278

Table 12.1 Parameters that control nonlinear soil behavior and theirrelative importance in terms of affecting normalized modulusreduction and material damping curves based on general

trends observed during the course of this study .......................... 297


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LIST OF FIGURES

Figure 1.1 Evaluation of ground motion at a geotechnical site based onvertically propagating shear waves between the bedrock andground surface ................................................................................. 2

Figure 1.2 Fourier amplitude of (a) the ground motion as a result of (b)the bedrock motion at the geotechnical site shown in Figure1.1.................................................................................................... 3

Figure 1.3 Representation of a soil deposit in terms of dynamic soilproperties in geotechnical earthquake engineering ......................... 4

Figure 1.4 Nonlinear stress-strain curve of soils and variation of secantshear modulus with shearing strain amplitude ................................ 5

Figure 1.5 Estimation of shear modulus and material damping ratioduring cyclic loading....................................................................... 6

Figure 1.6 (a) Nonlinear shear modulus and (b) normalized modulusreduction curves .............................................................................. 7

Figure 1.7 Nonlinear material damping ratio curve.......................................... 7

Figure 1.8 Field curves representing nonlinear soil behavior........................... 9

Figure 2.1 Simplified diagram of the RCTS device (from Stokoe et al.,1999).............................................................................................. 14

Figure 2.2 Simplified cross-sectional view of the confining system(from Hwang, 1997) ...................................................................... 15

Figure 2.3 General Configuration of RCTS Equipment (after Hwang,1997).............................................................................................. 17

Figure 2.4 Frequency response curve measured in the RC test (fromStokoe et al., 1999)........................................................................ 18

Figure 2.5 Material damping measurement in the RC test using the half-power bandwidth (from Stokoe et al., 1999)................................. 18


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Figure 2.6 Material damping measurement in the RC test using the free-vibration decay curve (from Stokoe et al., 1999) .......................... 19

Figure 2.7 Calculation of shear modulus and material damping ratio inthe TS test...................................................................................... 21

Figure 3.1 Map of Northern California showing the locations of thegeotechnical sites in this area ........................................................ 26

Figure 3.2 Map of Southern California showing the locations of thethree geotechnical sites outside the Los Angeles area ..................30

Figure 3.3 Map of Los Angeles showing the locations of the sevengeotechnical sites in this area ........................................................ 31

Figure 3.4 Map of South Carolina showing the locations of thegeotechnical sites in this area ........................................................ 36

Figure 3.5 Map of Taiwan showing the location of Lotung site ....................38

Figure 3.6 Distribution of soil samples with geographic region .................... 40

Figure 3.7 Distribution of the number of geotechnical sites withgeographic region.......................................................................... 40

Figure 3.8 Distribution of soil samples according to the sample depth.......... 41

Figure 3.9 Distribution of confining pressures at which nonlinearmeasurements were performed...................................................... 42

Figure 3.10 Distribution of soil samples according to soil type asclassified by the Unified Soil Classification System (USCS)....... 43

Figure 3.11 Distribution of soil samples according to soil plasticity interms of the plasticity index, PI..................................................... 44

Figure 3.12 Distribution of soil samples according to total unit weight .......... 46

Figure 3.13 Distribution of soil samples according to dry unit weight ............ 46

Figure 3.14 Distribution of soil samples according to water content ............... 47

Figure 3.15 Distribution of soil samples according to void ratio ..................... 47


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Figure 3.16 Variation of dry unit weight with depth of (a) fine grainedand (b) coarse grained soils included in this study........................ 48

Figure 3.17 Variation of water content with depth of (a) fine grained and(b) coarse grained soils included in this study .............................. 49

Figure 3.18 Variation of void ratio with depth of (a) fine grained and (b)coarse grained soils included in this study .................................... 50

Figure 3.19 Distribution of soil samples according to estimatedoverconsolidation ratio.................................................................. 51

Figure 3.20 Variation of estimated overconsolidation ratio with depth of(a) fine grained and (b) coarse grained soils included in this

study .............................................................................................. 52

Figure 4.1 Linear elastic, nonlinear elastic and plastic strain ranges on(a) normalized modulus reduction and (b) material dampingcurves ............................................................................................ 57

Figure 4.2 Variation of (a) low-amplitude shear modulus, (b) low-amplitude material damping ratio, and (c) void ratio withmagnitude and duration of isotropic confining pressure............... 60

Figure 4.3 Variation of (a) low-amplitude shear modulus, (b) low-amplitude material damping ratio, and (c) void ratio with

effective isotropic confining pressure ........................................... 62

Figure 4.4 The effect of confining pressure on the variation of (a) shearmodulus, (b) normalized shear modulus, and (c) materialdamping ratio with shearing strain amplitude as measured inthe torsional resonant column ....................................................... 65

Figure 4.5 The effect of confining pressure on normalized modulusreduction curve (a) for soils with moderate plasticity, and (b)for non-plastic soils evaluated as part of the ROSRINE study(after Stokoe et al., 1999) .............................................................. 67

Figure 4.6 The effect of confining pressure on (a) normalized modulusreduction and (b) material damping curves of silty sandsevaluated as part of the ROSRINE study (after Darendeli etal., 2001)........................................................................................ 68


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Figure 4.7 Impact on nonlinear site response of accounting for the effectof confining pressure on dynamic soil properties (after

Darendeli et al., 2001) ................................................................... 70

Figure 4.8 The effect of overconsolidation ratio on the variation of (a)shear modulus, (b) material damping ratio, and (c) void ratiowith effective isotropic confining pressure as measured in thetorsional resonant column ............................................................. 71

Figure 4.9 The effect of overconsolidation ratio on the variation of (a)shear modulus, (b) normalized shear modulus, and (c)material damping ratio with shearing strain amplitude asmeasured in the torsional resonant column ................................... 72

Figure 4.10 The effect of number of loading cycles on the variation of (a)shear modulus, (b) normalized shear modulus, and (c)material damping ratio with shearing strain amplitude asdetermined in the combined RCTS testing ...................................75

Figure 4.11 The effect of loading frequency on (a) low-amplitude shearmodulus, and (b) low-amplitude material damping ratio asdetermined in the combined RCTS testing ...................................77

Figure 4.12 Comparison of the effect of loading frequency on low-amplitude shear modulus and low-amplitude materialdamping ratio (from Stokoe and Santamarina, 2000) ................... 78

Figure 4.13 The effect of loading frequency on the variation of (a) shearmodulus, (b) normalized shear modulus, and (c) materialdamping ratio with shearing strain amplitude as determinedin the combined RCTS testing ......................................................80

Figure 4.14 The effect of soil type on the variation of (a) low-amplitudeshear modulus, and (b) low-amplitude material damping ratiowith effective isotropic confining pressure as determined inthe combined RCTS testing........................................................... 82

Figure 4.15 The effect of soil type on the variation of low-amplitudeshear modulus with loading frequency as determined in thecombined RCTS testing ................................................................ 84


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Figure 4.16 The effect of soil type on the variation of low-amplitudematerial damping ratio with loading frequency as determined

in the combined RCTS testing ......................................................85

Figure 4.17 The effect of soil type on the normalized modulus reductioncurve as measured in the torsional resonant column..................... 86

Figure 4.18 The effect of soil type on the material damping curvedetermined at (a) N ~ 1000 cycles, (b) N = 1 cycle, and (c) N= 10 cycles from combined RCTS testing .................................... 87

Figure 4.19 The effect of soil type on normalized modulus reduction andmaterial damping curves (after Stokoe et al., 1999) .....................88

Figure 4.20 Comparison of field and laboratory measurements of shearwave velocity at the La Cienega site in the ROSRINE project..... 91

Figure 4.21 Variation of sampling disturbance expressed in terms of Vs,lab/Vs, field and Gmax, lab/Gmax, field with the in-situ shear wavevelocity .......................................................................................... 93

Figure 4.22 Comparison of laboratory and field measurements of smallstrain material damping ratio (from Stokoe et al., 1999) .............. 95

Figure 4.23 Comparison of nonlinear soil properties back-calculated fromthe free-field downhole accelerations with the laboratory

measurements (from Zeghal et al., 1995)...................................... 96

Figure 4.24 Comparison of the variation of (a) low-amplitude shearmodulus, (b) low-amplitude material damping ratio, and (c)void ratio with effective isotropic confining pressure of intact(undisturbed) and reconstituted (remolded) specimens ................ 99

Figure 4.25 Comparison of the variation of (a) shear modulus, (b)normalized shear modulus, and (c) material damping ratiowith shearing strain of intact (undisturbed) and reconstituted(remolded) specimens ................................................................. 100

Figure 4.26 Comparison of the variation of (a) shear modulus, (b)normalized shear modulus, and (c) material damping ratiowith shearing strain measured using various equipment oncompanion soil samples (from Stokoe et al., 1999) .................... 102


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Figure 5.1 Hyperbolic soil model proposed by Hardin and Drnevich(1972b) ........................................................................................ 110

Figure 5.2 The normalized modulus reduction and material dampingcurves estimated based on the hyperbolic model........................ 112

Figure 5.3 The effect of confining pressure on normalized modulusreduction curve for Toyoura Sand (Iwasaki et al., 1978)............ 114

Figure 5.4 The effect of confining pressure on (a) normalized modulusreduction, and (b) material damping curves for Toyoura Sand(Kokusho, 1980).......................................................................... 115

Figure 5.5 The effect of confining pressure on (a) normalized modulus

reduction, and (b) material damping curves for non-plasticsoils (Ni, 1987) ............................................................................ 116

Figure 5.6 Empirical (a) normalized modulus reduction, and (b) materialdamping curves proposed by Seed et al. (1986).......................... 118

Figure 5.7 Empirical (a) normalized modulus reduction, and (b) materialdamping curves proposed by Sun et al. (1988) for soils withplasticity ...................................................................................... 119

Figure 5.8 Empirical (a) normalized modulus reduction, and (b) materialdamping curves proposed by Idriss (1990) ................................. 121

Figure 5.9 Empirical (a) normalized modulus reduction, and (b) materialdamping curves proposed by Vucetic and Dobry (1991)............ 122

Figure 5.10 The effect of confining pressure on (a) normalized modulusreduction, and (b) material damping curves for non-plasticsoils (Ishibashi and Zhang, 1993) ............................................... 124

Figure 5.11 Empirical (a) normalized modulus reduction, and (b) materialdamping curves proposed by Ishibashi and Zhang (1993).......... 125

Figure 5.12 Variation in empirical (a) normalized modulus reduction, and(b) material damping curves with depth (EPRI, 1993c).............. 127

Figure 5.13 Variation in empirical (a) normalized modulus reduction, and(b) material damping curves with soil type (EPRI, 1993c)......... 128


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Figure 6.1 Normalized modulus reduction curve (of a silty sand at 1 atmeffective confining pressure) represented using a modified

hyperbolic model......................................................................... 133

Figure 6.2 Stress-strain curve (of a silty sand at 1 atm effectiveconfining pressure) estimated based on a modified referencestrain model ................................................................................. 135

Figure 6.3 Hysteresis loop estimated by modeling stress-strain reversalsfor two-way cyclic loading according to Masing behavior......... 137

Figure 6.4 Calculation of damping ratio utilizing a hysteresis loop............. 138

Figure 6.5 Variations of c1, c2and c3with curvature coefficient, a.............. 141

Figure 6.6 Damping curve estimated based on Masing behavior................. 143

Figure 6.7 Effect of high-amplitude cycling on low-amplitude shearmodulus and material damping ratio (from Stokoe andLodde, 1978) ............................................................................... 144

Figure 6.8 Comparison of the variation in F with shearing strain fordifferent values of p..................................................................... 145

Figure 6.9 (a) Damping curve estimated based on Masing behavior, (b)adjusted curve using the scaling coefficient, and (c) shifted

curve using the small-strain material damping ratio ................... 146

Figure 6.10 Effect of reference strain on (a) normalized modulusreduction, (b) stress-strain, and (c) material damping curves ..... 148

Figure 6.11 Effect of the curvature coefficient on the normalized modulusreduction curve............................................................................ 149

Figure 6.12 Effect of the curvature coefficient on the stress-strain curve(a) at small and intermediate strains, and (b) at high strains....... 149

Figure 6.13 Effect of the curvature coefficient on the material damping

curve ............................................................................................ 150

Figure 6.14 Effect of Dminon the material damping curve............................. 151

Figure 6.15 The effect of scaling coefficient on material damping curve...... 152


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Figure 7.1 Prior probability mass function for the discrete example ........... 159

Figure 7.2 Posterior probability mass function for the discrete example ..... 161

Figure 7.3 Imaginary correlation between model parameters uponupdating prior information based on limited number ofobservations................................................................................. 170

Figure 7.4 Variation of standard deviation with normalized shearmodulus ....................................................................................... 176

Figure 7.5 Standard deviation modeled for normalized modulusreduction curve............................................................................ 177

Figure 7.6 Variation of standard deviation with material damping ratio ..... 178

Figure 7.7 Standard deviation modeled for material damping curve ........... 178

Figure 8.1 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio forclean sands from Northern California...................................... 188

Figure 8.2 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for sandswith high fines content from Northern California....................... 188

Figure 8.3 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for siltsfrom Northern California ............................................................ 189

Figure 8.4 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for claysfrom Northern California ............................................................ 189

Figure 8.5 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio forclean sands from Southern California...................................... 192

Figure 8.6 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for sandswith high fines content from Southern California....................... 192


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Figure 8.7 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for silts

from Southern California ............................................................ 193

Figure 8.8 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for claysfrom Southern California ............................................................ 193

Figure 8.9 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio forclean sands from South Carolina ............................................. 195

Figure 8.10 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for sands

with high fines content from South Carolina .............................. 195

Figure 8.11 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for siltsfrom South Carolina .................................................................... 196

Figure 8.12 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for claysfrom South Carolina .................................................................... 196

Figure 8.13 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for sandswith high fines content from South Carolina (AfterDiscarding Specimens UT-39-G and UT-39-M) ........................ 199

Figure 8.14 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for claysfrom South Carolina (After Discarding Specimens UT-39-Oand UT-39-S)............................................................................... 199

Figure 8.15 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for sandswith high fines content from Lotung, Taiwan............................. 201

Figure 8.16 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for siltsfrom Lotung, Taiwan................................................................... 201


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Figure 8.17 (a) Normalized modulus reduction and (b) material dampingcurves estimated for a nonplastic silty sand using updated

mean values of model parameters calibrated at differentgeographic locations.................................................................... 203

Figure 8.18 (a) Normalized modulus reduction and (b) material dampingcurves estimated for a moderate plasticity silt using updatedmean values of model parameters calibrated at differentgeographic locations.................................................................... 204

Figure 8.19 (a) Normalized modulus reduction and (b) material dampingcurves estimated for a moderate plasticity clay using updatedmean values of model parameters calibrated at differentgeographic locations.................................................................... 205

Figure 8.20 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio forclean sands ............................................................................... 208

Figure 8.21 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for sandswith high fines content ................................................................ 208

Figure 8.22 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for silts ..... 209

Figure 8.23 Comparisons of the measured and predicted values of (a)normalized modulus and (b) material damping ratio for clays ... 209

Figure 8.24 (a) Normalized modulus reduction and (b) material dampingcurves estimated using updated mean values of modelparameters calibrated for different soil groups ........................... 211

Figure 8.25 All credible (a) normalized modulus data from the resonantcolumn tests, and (b) material damping data from theresonant column and torsional shear tests utilized to calibratethe model parameters. ................................................................. 213

Figure 8.26 Comparisons of the measured and predicted values ofnormalized modulus for all credible data.................................... 215

Figure 8.27 Comparisons of the measured and predicted values ofmaterial damping for all credible data......................................... 216


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Figure 9.1 Estimation of reference strain for given values of PI, OCRand in-situ mean effective stress ................................................. 223

Figure 9.2 Estimation of scaling coefficient for a given value of numberof loading cycles.......................................................................... 223

Figure 9.3 Estimation of small-strain material damping ratio for givenvalues of PI, OCR, in-situ mean effective stress and loadingfrequency..................................................................................... 225

Figure 9.4 Estimated (a) normalized modulus reduction and (b) materialdamping curves for the soil type and loading conditionsdiscussed in Section 9.2 .............................................................. 227

Figure 9.5 Effect of overconsolidation ratio on (a) normalized modulusreduction and (b) material damping curves predicted by thecalibrated model .......................................................................... 229

Figure 9.6 Effect of loading frequency on (a) normalized modulusreduction and (b) material damping curves predicted by thecalibrated model .......................................................................... 231

Figure 9.7 Effect of number of loading cycles on (a) normalizedmodulus reduction and (b) material damping curves predictedby the calibrated model ............................................................... 232

Figure 9.8 Comparison of (a) normalized modulus reduction and (b)material damping curves predicted for resonant column andtorsional shear tests ..................................................................... 233

Figure 9.9 Effect of confining pressure on (a) normalized modulusreduction and (b) material damping curves predicted by thecalibrated model .......................................................................... 235

Figure 9.10 Empirical (a) normalized modulus reduction, and (b) materialdamping curves proposed for sands by Seed et al. (1986) .......... 236

Figure 9.11 Comparison of the effect of confining pressure on nonlinearsoil behavior of sand (PI = 0 %) predicted by the calibratedmodel and empirical curves proposed for sands by Seed et al.(1986) .......................................................................................... 237


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Figure 9.12 Effect of soil plasticity on (a) normalized modulus reductionand (b) material damping curves predicted by the calibrated

model ........................................................................................... 239

Figure 9.13 Empirical (a) normalized modulus reduction, and (b) materialdamping curves proposed by Vucetic and Dobry (1991)............ 240

Figure 9.14 Comparison of the effect of soil plasticity on nonlinear soilbehavior predicted by the calibrated model and empiricalcurves proposed by Vucetic and Dobry (1991)........................... 241

Figure 9.15 Comparison of the measured in-situ shear wave velocitiesand values predicted using Equation 9.4..................................... 244

Figure 9.16 Effect of confining pressure on stress-strain curve predictedby the calibrated model for shearing strains ranging (a) from

= 0 to 1 % and (b) from = 0 to 0.01 %................................... 245

Figure 9.17 Effect of soil plasticity on stress-strain curve predicted by the

calibrated model for shearing strains ranging (a) from = 0 to1 % and (b) from = 0 to 0.01 %................................................ 246

Figure 9.18 Comparison of the stress-strain curves of a sand and amoderate plasticity clay based on the calibrated model for

shearing strains ranging (a) from = 0 to 1 % and (b) from

= 0 to 0.01 % ............................................................................... 247

Figure 10.1 Effect of PI on (a) normalized modulus reduction and (b)material damping curves at 0.25 atm confining pressure............ 251

Figure 10.2 Effect of PI on (a) normalized modulus reduction and (b)material damping curves at 1.0 atm confining pressure.............. 253

Figure 10.3 Effect of PI on (a) normalized modulus reduction and (b)material damping curves at 4.0 atm confining pressure.............. 255

Figure 10.4 Effect of PI on (a) normalized modulus reduction and (b)

material damping curves at 16 atm confining pressure............... 257

Figure 10.5 Effect of mean effective stress on (a) normalized modulusreduction and (b) material damping curves of a nonplasticsoil ............................................................................................... 259


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Figure 10.6 Effect of mean effective stress on (a) normalized modulusreduction and (b) material damping curves of a soil with PI =

15 %............................................................................................. 261

Figure 10.7 Effect of mean effective stress on (a) normalized modulusreduction and (b) material damping curves of a soil with PI =30 %............................................................................................. 263

Figure 10.8 Effect of mean effective stress on (a) normalized modulusreduction and (b) material damping curves of a soil with PI =50 %............................................................................................. 265

Figure 10.9 Effect of mean effective stress on (a) normalized modulusreduction and (b) material damping curves of a soil with PI =

100 %........................................................................................... 267

Figure 10.10 Shear wave velocity profile assumed for the 100-m thick siltysand deposit ................................................................................. 269

Figure 10.11 An example of utilizing the recommended normalizedmodulus reduction and material damping curves and itsimpact on estimated nonlinear site response ............................... 271

Figure 11.1 Mean values and standard deviations associated with thepoint estimates of (a) normalized modulus reduction and (b)material damping curves ............................................................. 280

Figure 11.2 Comparison of the correlated random realization of (a)normalized modulus reduction and (b) material dampingcurves relative to the mean curves and one standard deviationranges shown in Figure 11.1 ....................................................... 283

Figure 11.3 Comparison of spectral accelerations calculated using

perfectly correlated soil layers with , + and normalized modulus reduction and material damping curves..... 286

Figure 11.4 Comparison of spectral accelerations calculated using

perfectly correlated soil layers with 1) curves, 2)+normalized modulus reduction and material dampingcurves, and 3) normalized modulus reduction and+ material damping curves........................................................ 288


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Figure 11.5 Fifty realizations of spectral acceleration computed usingcompletely uncorrelated soil layers with randomly generated

normalized modulus reduction and material damping curves..... 290

Figure 11.6 Histograms of spectral accelerations from fifty realizationspresented in Figure 11.5 (a) at 0.1 sec and (b) at 0.3 sec ............ 291

Figure 11.7 Histograms of spectral accelerations from fifty realizationspresented in Figure 11.5 (a) at 1 sec and (b) at 3 sec .................. 292

Figure 11.8 Distribution of fifty realizations of spectral accelerationpresented in Figure 11.5 .............................................................. 293

Figure 11.9 Comparison of the spectral accelerations from the fifty

realizations with the results computed utilizing meannormalized modulus reduction and material damping curves..... 294

Figure 12.1 Comparison of the effect of confining pressure on nonlinearsoil behavior of sand (PI = 0 %) predicted by the calibratedmodel and empirical curves proposed for sands by Seed et al.(1986) .......................................................................................... 299

Figure 12.2 Comparison of the effect of soil plasticity on nonlinear soilbehavior predicted by the calibrated model and empiricalcurves proposed by Vucetic and Dobry (1991)........................... 300

Figure 12.3 Mean values and standard deviations associated with thepoint estimates of (a) normalized modulus reduction and (b)material damping curves ............................................................. 302


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CHAPTER 1

INTRODUCTION

1.1 BACKGROUND

In earthquake engineering, the energy released during an earthquake is

represented by stress waves propagating through the bedrock and surfacing at the

site of interest. In terms of the geotechnical characteristics of the site, the site is

typically modeled as a series of horizontal layers with varying properties. In most

cases, the site is represented by softer soils close to the surface and stiffer soils at

depth. The increase in stiffness with depth is due to the older age of deeper

material and the confining effect of the overburden. Because of the progressive

increase in stiffness with depth, stress waves coming from depth often surface in a

propagation direction that is almost vertical.

Often times, an earthquake analysis includes predicting the dynamic

response of a structure at the geotechnical site. Since structures are always

designed with a factor of safety to support a static load (its self weight and the live

load) as a result of 1g vertical acceleration, the vertical component of the ground

motion does not generally have as much an impact on earthquake resistant design

as the horizontal component for which less precaution is often taken in the static

design.

With vertically propagating shear waves and a higher susceptibility of

structures to horizontal motions, the ground motion in many earthquake problems

is simply modeled as horizontal shaking due to vertically propagating shear


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waves. In such a model, the soil deposit acts like a filter that amplifies energy at

some frequencies while attenuating it at others. Therefore, the estimated ground

motion is a function of the earthquake event and the local soil conditions as

shown in Figure 1.1. Two acceleration-time records are presented in this figure.

One of these is the bedrock motion and the second is the ground motion estimated

based on the bedrock motion and characteristics of the soil deposit.

BEDROCK

SOIL LAYER 1

SOIL LAYER 2

SOIL LAYER ..

SOIL LAYER n

bedrock

ground

Time, sec

BedrockAcceleration,

g

GroundAcceleration,

g

Time, sec

-0.5

0.0

0.5

6050403020100

-0.5

0.0

0.5

6050403020100BEDROCK

SOIL LAYER 1

SOIL LAYER 2

SOIL LAYER ..

SOIL LAYER n

bedrock

ground

BEDROCK

SOIL LAYER 1

SOIL LAYER 2

SOIL LAYER ..

SOIL LAYER n

bedrock

ground

Time, sec


g

GroundAcceleration,

g

Time, sec

-0.5

0.0

0.5

6050403020100

-0.5

0.0

0.5

6050403020100

Time, sec


g

GroundAcceleration,

g

Time, sec

-0.5

0.0

0.5

6050403020100

-0.5

0.0

0.5

6050403020100

Figure 1.1 Evaluation of ground motion at a geotechnical site based onvertically propagating shear waves between the bedrock and groundsurface

The filtering effect of the soil deposit is demonstrated in Figure 1.2 by

looking at the Fourier amplitude spectra of the two acceleration records. In this

figure, the acceleration components at different frequencies are shown for the

motions at the bedrock and ground surface. In this case, the low-frequency

motions (below 3 Hz) are amplified significantly. On the other hand, the high-


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frequency motions are slightly attenuated. This effect can also be observed from

the comparison of the time records presented in Figure 1.1. Different cycles can

more easily be identified in the ground motion time record than in the bedrock

record.

0.010

0.008

0.006

0.004

0.002

0.000

Fourier

Amplitude,g * sec

(a)

0.010

0.008

0.006

0.004

0.002

0.000

Fourier

1086420

Frequency, Hz

Amplitude,g * sec

(b)

Figure 1.2 Fourier amplitude of (a) the ground motion as a result of (b) thebedrock motion at the geotechnical site shown in Figure 1.1


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1.2 DYNAMIC SOIL PROPERTIES

As discussed above, to analyze the response of structures during an

earthquake, it is necessary to characterize the ground motion underneath the

structure caused by the earthquake. Some of the most important ground motion

parameters are amplitude of motion (e.g., peak acceleration, peak velocity and

peak displacement), frequency content (e.g., Fourier spectra, response spectra,

predominant period, bandwidth) and duration. These parameters are primarily

affected by three factors: 1. source effects or the characteristics of the earthquake

(such as amount of energy released and type of faulting), 2. path effects (the

distance from the point of energy release to the site), and 3. site effects (such as

characteristics of the soil deposit, topography and other near-surface features).

This study focuses on characterization of the soil deposit. The properties that

typically need to be characterized are shear modulus, G, and material damping

ratio, D, as presented in Figure 1.3.

Shear

Modulus, G Material

Damping

Ratio, D

SOIL DEPOSIT

BEDROCK

Shear

Modulus, G Material

Damping

Ratio, D

SOIL DEPOSIT

BEDROCK

SOIL DEPOSIT

BEDROCK

Figure 1.3 Representation of a soil deposit in terms of dynamic soil propertiesin geotechnical earthquake engineering


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Shear modulus, G, represents the shear stiffness of the soil. It is essentially

the slope of the relationship between shear stress () and shearing strain ().Because of the nonlinear nature of the stress-strain curve of soils, shear modulus

of soils change with strain amplitude as shown in Figure 1.4. The secant shear

modulus can also be approximated for the case of dynamic loading over a cycle of

loading at a given strain amplitude as shown in Figure 1.5. The stress-strain path

illustrated in this figure is called a hysteresis loop. The slope of the line that

connects the end points of the hysteresis loop represents the average shear

stiffness of the soil, hence the secant shear modulus.

1G1

1 2

1

G2

Shear

Stress,

Shearing

Strain,

1G1

1 2

1

G2

Shear

Stress,

Shearing

Strain,

Figure 1.4 Nonlinear stress-strain curve of soils and variation of secant shear

modulus with shearing strain amplitude


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1

GShear

Stress,

Shearing Strain,

G = /D = AL / (4 AT)

AL

AT

1

GShear

Stress,

Shearing Strain,

G = /D = AL / (4 AT)

AL

AT

Figure 1.5 Estimation of shear modulus and material damping ratio duringcyclic loading

Material damping ratio, D, is a measure of the proportion of dissipated

energy to the maximum retained strain energy during each cycle at a given strain

amplitude as shown in Figure 1.5. The energy dissipated over a loading cycle is

represented by the gray area within the hysteresis loop (AL), and the maximum

retained strain energy is represented by the triangular area (AT) that is calculated

using peak shear stress and peak shearing strain. Material damping ratio is a result

of friction between soil particles, strain rate effects and nonlinearity of the stress-

strain relationship in soils.

As presented in Figure 1.4, soils exhibit nonlinear behavior in shear. The

secant shear modulus decreases with increasing strain amplitude as shown in

Figure 1.6a. Shear modulus at small strains, at which soil behavior is linear, is

referred to as small-strain shear modulus, Gmax. The relationship between shear


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modulus and strain amplitude is typically characterized by a normalized modulus

reduction curve as shown in Figure 1.6b.

Gmax

120

80

40

0

0.001 0.01 0.1 1Shearing Strain, , %

G,

MPa

1.0

0.5

0

0.001 0.01 0.1 1Shearing Strain, , %

G

Gmax

(a) (b)

Gmax

120

80

40

0

0.001 0.01 0.1 1Shearing Strain, , %

G,

MPa

1.0

0.5

0

0.001 0.01 0.1 1Shearing Strain, , %

G

GmaxGmax

120

80

40

0

0.001 0.01 0.1 1Shearing Strain, , %

G,

MPa Gmax

120

80

40

0

0.001 0.01 0.1 1Shearing Strain, , %

G,

MPa

1.0

0.5

0

0.001 0.01 0.1 1Shearing Strain, , %

G

Gmax

1.0

0.5

0

0.001 0.01 0.1 1Shearing Strain, , %

G

Gmax

(a) (b)

Figure 1.6 (a) Nonlinear shear modulus and (b) normalized modulus reductioncurves

The nonlinearity in the stress-strain relationship results in an increase in

energy dissipation and, therefore, an increase in material damping ratio with

increasing strain amplitude as presented in Figure 1.7. Material damping ratio at

small strains (in the linear range) is referred to as small-strain material damping

ratio, Dmin, herein.

Dmin

D,

%

16

8

00.001 0.01 0.1 1

Shearing Strain, , %

Dmin

D,

%

16

8

00.001 0.01 0.1 1


Figure 1.7 Nonlinear material damping ratio curve


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1.3 GROUND RESPONSE ANALYSIS

In analyzing ground motions due to small vibrations, soil behavior is

assumed to be linear. Each soil layer is assigned a shear modulus and a material

damping ratio. Since a horizontally layered system is being modeled, the task of

ground response analysis is reduced to a simple 1-D wave propagation problem

that has a closed-form solution (Kramer, 1996).

On the other hand, dynamic soil properties can be extremely nonlinear

when ground motions are caused by large vibrations (such as design level

earthquakes). As a result, the change in shear modulus and material damping ratio

with shearing strain amplitude must be accounted for in ground response analysis.

The linear solution, which is applicable for small vibration levels, can be modified

to overcome this problem.

One approach to handling nonlinear soil behavior due to shaking during a

design level event is to perform linear analyses with dynamic soil properties that

are iterated in a manner consistent with an effective shearing strain induced in

the soil layer (Schnabel et al., 1972; and EduPro, 1998). This iterative approach is

called equivalent linear analysis.

The effective shearing strain is defined as a certain portion of the

maximum strain amplitude throughout the time history. The ratio of effective

shearing strain to maximum strain amplitude is typically related to the magnitude

of the earthquake event or the characteristics of the acceleration-time record

employed in the analysis. When a design level earthquake is analyzed, the ratio of

effective to maximum shearing strain is typically about 0.6.


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The state of practice in equivalent linear analysis often employs empirical

normalized modulus reduction and a material damping curves. These empirical

curves are developed based on laboratory studies performed over the past three

decades.

The empirical normalized modulus reduction curve is scaled using an

estimate of the small-strain shear modulus, Gmax. The small-strain shear modulus

can be calculated using shear wave velocity, Vs, from in-situ seismic

measurements and mass density,.

Gmax= * Vs2 (1.1)

The curve calculated by scaling the empirical normalized modulus

reduction curve is called the field shear modulus curve (Figure 1.8). Since

material damping ratio can not be estimated accurately in-situ, the field material

damping curve is assumed to be identical to the empirical material damping curve

as shown in Figure 1.8.

Dfield = Dempirical

D,

%

16

8

00.001 0.01 0.1 1


150

100

50

0

0.001 0.01 0.1 1


G,

MPa

Gfield = Gmax, field *

empirical

( )GGmax

Gmax, field

Dfield = Dempirical

D,

%

16

8

00.001 0.01 0.1 1


Dfield = Dempirical

D,

%

16

8

00.001 0.01 0.1 1


150

100

50

0

0.001 0.01 0.1 1


G,

MPa


empirical

( )GGmax

Gmax, field150

100

50

0

0.001 0.01 0.1 1


G,

MPa


empirical

( )GGmax

Gmax, field

Figure 1.8 Field curves representing nonlinear soil behavior


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1.4 OBJECTIVES OF RESEARCH

As part of various research projects [including the SRS (Savannah River

Site) Project AA891070, EPRI (Electric Power Research Institute) Project 3302,

and ROSRINE (Resolution of Site Response Issues from the Northridge

Earthquake) Project] numerous sites were drilled and sampled. Intact soil samples

over a depth range of several hundred meters were recovered from 20 of these

sites. These soil samples were tested in the soil dynamics laboratory at The

University of Texas at Austin (UTA) to characterize the materials.

The presence of a database accumulated from testing these intact

specimens motivated a re-evaluation of empirical curves often employed in

seismic site response analyses. The weaknesses of empirical curves reported in

the literature were recognized and the necessity of developing an improved set of

empirical curves was acknowledged.

This study focuses on generating an improved set of empirical curves that

can be represented in the form of a set of simple equations. The data collected

over the past decade at The University of Texas at Austin are statistically

analyzed using the First-order, Second-moment Bayesian Method (FSBM). The

effects of various parameters (such as confining pressure and soil plasticity) on

dynamic soil properties are evaluated and quantified within this framework.

One of the most important aspects of this study is estimating not only the

mean values of the empirical curves but also the uncertainty associated with these

values. The handling of uncertainty in the empirical estimates of dynamic soil


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properties is expected to result in a refinement of probabilistic seismic hazard

analysis.

1.5 ORGANIZATION OF DISSERTATION

A general overview of the dynamic laboratory test equipment used to

evaluate the nonlinear soil properties is presented in Chapter Two along with a

brief review of the theory upon which the laboratory testing is founded.

Information regarding the soil samples analyzed in this work is

summarized in Chapter Three. All testing was conducted at The University of

Texas at Austin over the past decade.

The sensitivity of dynamic soil properties to soil type and loading

conditions are described in Chapter Four. The general trends (in terms of how

these parameters affect nonlinear soil behavior) observed during the course of this

work and those reported in the literature are discussed.

The empirical relationships reported in the literature are summarized in

Chapter Five. The empirical normalized modulus reduction and material damping

curves proposed in the literature are evaluated in terms of capturing the general

trends discussed in Chapter Four.

A four-parameter soil model that describes the change in normalized shear

modulus and material damping ratio with shearing strain is presented in Chapter

Six along with a parametric study of the model. Two of these parameters,

reference strain and curvature coefficient, are utilized in describing the

normalized modulus reduction curve. Masing behavior is used as a criterion in

evaluating material damping. A scaling coefficient and small-strain material


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damping ratio are utilized in describing the material damping curve relative to the

damping curve estimated from the normalized modulus reduction curve and

assuming Masing Behavior. The impact of soil type and loading conditions on the

model parameters are also described herein.

The First-order, Second-moment Bayesian method is briefly discussed in

Chapter Seven. The form of the equations that are used in relating model

parameters to soil type and loading conditions are discussed in this chapter.

Results of the statistical analysis are presented in Chapter Eight. Measured

and predicted curves are compared in order to evaluate the success of the model in

representing nonlinear soil behavior.

In Chapter Nine, the impact of soil type and loading conditions on model

parameters are quantified. Equations and graphical solutions that are utilized to

construct normalized shear modulus reduction and material damping curves for

different soil types and loading conditions are presented. These curves are

compared with other empirical curves reported in the literature.

In Chapter Ten, recommended normalized modulus reduction and material

damping curves are presented for soils with a broad range plasticity confined at

different mean effective stresses.

Uncertainty associated with the predicted normalized modulus reduction

and material damping curves is discussed in Chapter Eleven. Recommendations

for future work related with handling uncertainty in nonlinear soil behavior arepresented for probabilistic seismic hazard analysis.

A summary of the study and conclusions are presented in Chapter Twelve.


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CHAPTER 2

LABORATORY TESTING EQUIPMENT

2.1 INTRODUCTION

Combined resonant column and torsional shear (RCTS) equipment was

employed in this work to evaluate the dynamic soil properties of undisturbed soil

specimens. This equipment was developed by Professor Stokoe and his graduate

students (Isenhower, 1979; Lodde, 1982; Ni, 1987; and Hwang, 1997) following

earlier designs by Hall and Richart (1963), Hardin and Music (1965), and

Drnevich (1967). Detailed information regarding the equipment, testing method,

theory and calibration is presented in Darendeli (1997).

The RCTS equipment uses a fixed-free configuration. The soil specimen

rests on a fixed bottom pedestal (fixed at the bottom) and is free at the top. At the

free end, four magnets are attached to the top cap and fixed coils surrounding the

magnets are used to excite the top of the specimen with torsional vibrations

without constraining the top of the specimen (hence the top of the specimen is

free). A simplified diagram of the combined RCTS equipment is presented in

Figure 2.1.


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Proximitor ProbesAccelerometer

Support

Plate

Fluid Bath

Securing

Plate

Magnet

Inner

Cylinder

Specimen

PorousStone O-ring

Rubber

Membrane

Top Cap

Resonant or Slow Cyclic

Torsional Excitation

Counter Weight

Drive

Coil

Base Plate

Proximitor TargetProximitor ProbesAccelerometer

Support

Plate

Fluid Bath

Securing

Plate

Magnet

Inner

Cylinder

Specimen

PorousStone O-ring

Rubber

Membrane

Top Cap

Resonant or Slow Cyclic

Torsional Excitation

Counter Weight

Drive

Coil

Base Plate

Proximitor Target

Figure 2.1 Simplified diagram of the RCTS device (from Stokoe et al., 1999)

2.2 COMBINED RESONANT COLUMN AND TORSIONAL SHEAR EQUIPMENT

Combined RCTS equipment is capable of testing a soil specimen in two

different modes. These modes are: 1. low frequency cyclic testing, and 2. higher

frequency dynamic testing during resonance. Thus, the same specimen can be

tested using both modes and variability due to testing different specimens or

testing the same specimen after it has been subjected to a different stress history is

eliminated. The data collected from the two independent modes of testing can

effectively be compared in order to gain more insight regarding material behavior.

One of the testing modes is called the torsional resonant column (RC) test,

which is based on the theory of torsional wave propagation in a fixed-free

cylinder with a mass attached at the free end. In this mode, well-defined boundary


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conditions and specimen geometry are utilized in evaluating the shear modulus

and material damping ratio in shear from measurements at first-mode resonance.

The second testing mode is called the cyclic torsional shear (TS) test,

which involves monitoring the applied torque and displacement at the top of the

specimen. The torque is converted into shear stress and the displacement is

converted into shearing strain. Thus, hysteresis loops, which are utilized in

evaluation of shear modulus and material damping ratio, are generated.

These tests are typically carried out while the specimen is confined

isotropically. The confining chamber is designed to handle pressures up to 40

atmospheres (4.1 MPa). A cross-sectional view of the confining system is

presented in Figure 2.2.

AirPressure

Membrane

FixingRod

Top Plate

HollowCylinder

SiliconFluid Bath

O-Ring

Soil

ThinMetal Tube

Drainage

Figure 2.2 Simplified cross-sectional view of the confining system (fromHwang, 1997)


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The soil specimen is tested using both the cyclic torsional shear and

resonance modes simply by changing: 1) the amplitude and frequency of the

current in the drive coils, and 2) the motion monitoring devices (shown in Figure

2.3) used to record the specimen response. These changes are performed outside

the confining chamber; hence, they can be done without changing the state of

stress on the specimen.

2.3 TORSIONAL RESONANT COLUMN TEST

In torsional RC testing, a forcing function with fixed amplitude and

varying frequency is applied at the top of a cylindrical soil specimen. The output

from the accelerometer on the drive plate (shown in Figure 2.3) is recorded versus

the vibration frequency during a frequency sweep. The graph of accelerometer

output versus vibration frequency is called the frequency response curve. A

typical response curve is shown in Figure 2.4. The frequency at which the

accelerometer output reaches a maximum during first-mode torsional resonance is

denoted as the resonant frequency, fr, and it is used in calculating the shear wave

velocity of the specimen. The value of accelerometer output, Ar, at this frequency

is then used in calculating the peak shearing strain amplitude during the test.

The frequency response curve is also utilized in evaluating the material

damping ratio at small shearing strains, , ( < 0.005 %). The half-power points

are identified as the two points on the frequency response curve with an amplitude

of 1/2 times the peak value. The frequencies associated with the half-power

points, f1and f2, are used in evaluating the material damping ratio as presented in

Figure 2.5.


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SupportPlate

CounterWeight

Drive Plate

Accelerometer

Magnet

Drive Coil

Holder

A

A Proximitor Probe

(a) Top View

Leveling andS

LVDT

ProximitorTarget

Accelerometer

ecuringScrew

SupportPlate

Fluid Bath

SecuringPlate

Magnet

DriveCoil

InnerCylinder

Base Pedestal

ProximitorProbe

SupportPost

ProximitorHolder

PorousStone

(b) Section AA

Drainage Line

Top Cap

Specimen

SupportPlate

CounterWeight

Drive Plate

Accelerometer

Magnet

Drive Coil

Holder

A

A Proximitor Probe

(a) Top View

SupportPlate

CounterWeight

Drive Plate

Accelerometer

Magnet

Drive Coil

Holder

A

A Proximitor Probe

(a) Top View

Leveling andS

LVDT

ProximitorTarget

Accelerometer

ecuringScrew

SupportPlate

Fluid Bath

SecuringPlate

Magnet

DriveCoil

InnerCylinder

Base Pedestal

ProximitorProbe

SupportPost

ProximitorHolder

PorousStone

(b) Section AA

Drainage Line

Top Cap

Specimen

Leveling andS

LVDT

ProximitorTarget

Accelerometer

ecuringScrew

SupportPlate

Fluid Bath

SecuringPlate

Magnet

DriveCoil

InnerCylinder

Base Pedestal

ProximitorProbe

SupportPost

ProximitorHolder

PorousStone

(b) Section AA

Drainage Line

Top Cap

Specimen

Figure 2.3 General Configuration of RCTS Equipment (after Hwang, 1997)

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2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis

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