2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
-
Upload
ederenzotapiabanez -
Category
Documents
-
view
221 -
download
3
Transcript of 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
1/394
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
2/394
Copyright
by
MEHMET BARIS DARENDELI
2001
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
3/394
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
4/394
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
5/394
Dedicated
To
My Parents,
My Wife and My Daughter
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
6/394
v
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
7/394
vi
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.
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
8/394
vii
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
9/394
viii
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.
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
10/394
ix
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
11/394
x
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
12/394
xi
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
13/394
xii
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
14/394
xiii
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
15/394
xiv
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
16/394
xv
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
17/394
xvi
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
18/394
xvii
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 10.13 Effect of o on normalized modulus reduction curve: PI =30 %............................................................................................. 264
Table 10.14 Effect of o on material damping curve: PI = 30 % ................. 264
Table 10.15 Effect of o on normalized modulus reduction curve: PI =50 %............................................................................................. 266
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
19/394
xviii
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
20/394
xix
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
21/394
xx
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
22/394
xxi
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
23/394
xxii
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
24/394
xxiii
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
25/394
xxiv
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
26/394
xxv
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
27/394
xxvi
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
28/394
xxvii
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
29/394
xxviii
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
30/394
xxix
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
31/394
xxx
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
32/394
xxxi
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
33/394
1
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
34/394
2
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
BedrockAcceleration,
g
GroundAcceleration,
g
Time, sec
-0.5
0.0
0.5
6050403020100
-0.5
0.0
0.5
6050403020100
Time, sec
BedrockAcceleration,
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-
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
35/394
3
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
36/394
4
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
37/394
5
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
38/394
6
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
39/394
7
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
Shearing Strain, , %
Figure 1.7 Nonlinear material damping ratio curve
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
40/394
8
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.
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
41/394
9
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
Shearing Strain, , %
150
100
50
0
0.001 0.01 0.1 1
Shearing Strain, , %
G,
MPa
Gfield = Gmax, field *
empirical
( )GGmax
Gmax, field
Dfield = Dempirical
D,
%
16
8
00.001 0.01 0.1 1
Shearing Strain, , %
Dfield = Dempirical
D,
%
16
8
00.001 0.01 0.1 1
Shearing Strain, , %
150
100
50
0
0.001 0.01 0.1 1
Shearing Strain, , %
G,
MPa
Gfield = Gmax, field *
empirical
( )GGmax
Gmax, field150
100
50
0
0.001 0.01 0.1 1
Shearing Strain, , %
G,
MPa
Gfield = Gmax, field *
empirical
( )GGmax
Gmax, field
Figure 1.8 Field curves representing nonlinear soil behavior
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
42/394
10
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
43/394
11
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
44/394
12
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.
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
45/394
13
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.
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
46/394
14
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
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
47/394
15
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)
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
48/394
16
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.
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping PhD Thesis
49/394
17
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)
-
7/25/2019 2001 Darendeli - Normalized Shear Modulus and Damping P