development of an energy-based liquefaction evaluation procedure kristin jane … · 2020. 9....

Development of an Energy-based Liquefaction Evaluation Procedure

Kristin Jane Ulmer

Dissertation submitted to the faculty of the Virginia Polytechnic Institute and State University in

partial fulfillment of the requirements for the degree of

Doctor of Philosophy

In

Civil Engineering

Russell A. Green, Co-Chair

Adrian Rodriguez-Marek, Co-Chair

Joseph E. Dove

Matthew R. Eatherton

December 6, 2019

Blacksburg, Virginia

Keywords: earthquakes, liquefaction, dissipated energy, cyclic direct simple shear

Copyright © 2019 by Kristin J. Ulmer


Kristin Jane Ulmer

ABSTRACT (Academic)

Soil liquefaction during earthquakes is a phenomenon that can cause tremendous damage to

structures such as bridges, roads, buildings, and pipelines. The objective of this research is to

develop an energy-based approach for evaluating the potential for liquefaction triggering. The

current state-of-practice for the evaluation of liquefaction triggering is the “simplified” stress-

based framework where resistance to liquefaction is correlated to an in situ test metric (e.g.,

normalized standard penetration test N-value, N1,60cs, normalized cone penetration tip resistance,

qc1Ncs, or normalized small strain shear wave velocity, Vs1). Although rarely used in practice, the

strain-based procedure is commonly cited as an attractive alternative to the stress-based framework

because excess pore pressure generation (and, in turn, liquefaction triggering) is more directly

related to strains than stresses. However, the method has some inherent and potentially fatal

limitations in not being able to appropriately define both the amplitude and duration of the induced

loading in a total stress framework. The energy-based method proposed herein builds on the merits

of both the stress- and strain-based procedures, while circumventing their inherent limitations.

The basis of the proposed energy-based approach is a macro-level, low cycle fatigue theory in

which dissipated energy (or work) per unit volume is used as the damage metric. Because

dissipated energy is defined by both stress and strain, this energy-based method brings together

stress- and strain-based concepts. To develop this approach, a database of liquefaction and non-

liquefaction case histories was assembled for multiple in situ test metrics. Dissipated energy per

unit volume associated with each case history was estimated and a family of limit-state curves

were developed using maximum likelihood regression for different in situ test metrics defining the

amount of dissipated energy required to trigger liquefaction. To ensure consistency between these

limit-state curves and laboratory data, a series of cyclic tests were performed on samples of sand.

These laboratory-based limit-state curves were reconciled with the field-based limit-state curves

using a consistent definition of liquefaction.


Kristin Jane Ulmer

ABSTRACT (General Audience)


structures such as bridges, roads, buildings, and pipelines. The objective of this research is to

develop an energy-based approach for evaluating the potential for liquefaction triggering. Current

procedures to evaluate liquefaction triggering include stress-based and strain-based procedures.

However, these procedures have some inherent and potentially fatal limitations. The energy-based

method proposed herein builds on the merits of both the stress- and strain-based procedures, while

circumventing their inherent limitations.

The proposed energy-based approach uses dissipated energy (or work) per unit volume to evaluate

the potential for liquefaction. Because dissipated energy is defined by both stress and strain, this

energy-based method brings together stress- and strain-based concepts. To develop this approach,

a database of case histories in which liquefaction was either observed or not observed was

assembled. Dissipated energy per unit volume associated with each case history was estimated and

a family of relationships was regressed to define the amount of dissipated energy required to trigger

liquefaction. Results from a series of cyclic laboratory tests performed on samples of sand were

reconciled with the field-based relationships using a consistent definition of liquefaction.

This research proposes a method that is based on a robust mechanistic framework that will make

it easier to evaluate liquefaction for circumstances that are not well represented in current

liquefaction evaluation procedures. The components of the proposed energy-based procedure are

developed consistently and are presented in such a way that this procedure can be readily adopted

by practitioners who are already familiar with existing liquefaction evaluation procedures. The

broader impacts of this work will help to minimize losses from earthquakes by improving the way

engineers evaluate liquefaction.

iv

ACKNOWLEDGEMENTS

It is humbling to reflect on the time I spent in my PhD program and recognize the many individuals

who have made this journey possible. My advisors, Drs. Russell Green and Adrian Rodriguez-

Marek, have trained me and spent countless hours guiding me through this process. I am deeply

grateful for their examples and their confidence in me. Many thanks to my committee members

and the faculty in the geotechnical engineering program who have taught me, provided valuable

feedback, and supported me in various ways.

There are several individuals who helped me during my years spent in the lab running tests.

Thanks to Drs. Bernardo Castellanos and Thomas Brandon for their help in navigating the

complexities of lab work. I am also grateful to Eduardo Rodriguez-Arriaga for his help in training

me to run the tests and in trouble-shooting when things went wrong, and to Alex Osuchowski and

Prakash Ghimire for their help running cyclic direct simple shear tests.

Thank you to the many PhD students who have enriched my life and made this journey an

enjoyable one: Mahdi Bahrampouri, Grace Huang, Reem Jaber, Hwanik Ju, Dennis Kiptoo, Julie

Paprocki, Tyler Quick, Sneha Upadhyaya, Kaleigh Yost, Luis Zambrano Cruzatty, Ali Albatal,

Ashly Cabas Mijares, Cagdas Bilici, Brett Maurer, and Craig Shillaber. You truly were the village

that kept me going. I am also thankful for the graduate students in the Geotechnical Student

Organization who created a tight-knit community of fantastic people. I will always be grateful for

the memories.

Finally, thank you to my family. To my parents and siblings who believed in me and supported

my dreams; to my husband, Austin, who lovingly reminded me that I can rise to the challenge; and

to my precious daughters, Claire and Renee, who brought joy to my life, even on the toughest days.

You are capable and strong, and through Christ you can do all things.

v

Table of Contents

List of Figures ................................................................................................................................ ix

List of Tables ................................................................................................................................ xv

1. Introduction ............................................................................................................................. 1

1.1. Soil Liquefaction .............................................................................................................. 1

1.2. Objectives ........................................................................................................................ 1

1.3. Organization ..................................................................................................................... 2

1.4. Significance...................................................................................................................... 4

2. Background .............................................................................................................................. 5

2.1. Stress-based Liquefaction Evaluation .............................................................................. 5

2.2. Strain-based Liquefaction Evaluation .............................................................................. 7

2.3. Energy-based Liquefaction Evaluation ............................................................................ 9

2.4. Site Response Analyses ................................................................................................. 11

References ................................................................................................................................. 11

3. Manuscript #1: b-values for Computing Magnitude Scaling Factors in Liquefaction

Triggering Evaluation of Clean Sands .................................................................................. 15

3.1. Introduction .................................................................................................................... 17

3.2. Background .................................................................................................................... 17

3.2.1. Effect of Liquefaction Triggering Criteria on b-values .......................................... 18

3.2.2. Effect of Test Acceptance Criterion on b-values .................................................... 19

3.3. Cyclic Direct Simple Shear Tests .................................................................................. 22

3.3.1. Test Setup................................................................................................................ 22

3.3.2. Dissipated Energy as Liquefaction Triggering Criterion in Laboratory Tests ....... 23

3.4. Results ............................................................................................................................ 25

3.4.1. b-values from Cyclic Tests using Different Liquefaction Triggering Criteria ....... 25

3.4.2. b-values from Modulus Reduction and Damping Curves....................................... 25

3.5. Discussion ...................................................................................................................... 27

3.6. Conclusions .................................................................................................................... 29

vi

3.7. Acknowledgements ........................................................................................................ 29

References ................................................................................................................................. 30

Tables ......................................................................................................................................35

Figures....................................................................................................................................... 37

4. Manuscript #2: Energy-based Evaluation of Liquefaction Triggering (CPT-based) ............ 45

4.1. Introduction .................................................................................................................... 46

4.2. Computation of Normalized Dissipated Energy ............................................................ 48

4.3. Liquefaction Case History Database .............................................................................. 50

4.3.1. Adjustment of z, σv, σ’vo, and qc1Ncs in the Updated Database ............................... 51

4.3.2. Adjustment of amax and Mw in the Updated Database ............................................. 52

4.3.3. Computation of Input Parameters ........................................................................... 53

4.3.3.1. Stress Reduction Factor, rd .............................................................................. 53

4.3.3.2. Number of Equivalent Cycles, Neq,M ............................................................... 54

4.3.3.3. Dynamic Soil Properties, (G/Gmax)γc and Dγc .................................................. 54

4.3.3.4. Small-strain Shear Modulus, Gmax ................................................................... 55

4.3.4. Input Parameter Uncertainties................................................................................. 55

4.4. Regression of the Limit-state Function .......................................................................... 58

4.5. Discussion ...................................................................................................................... 61

4.6. Conclusions .................................................................................................................... 63


4.8. Supplemental Data ......................................................................................................... 64

References ................................................................................................................................. 64

Tables ........................................................................................................................................ 71

Figures....................................................................................................................................... 74

5. Manuscript #3: Reconciliation of Laboratory and Field Estimates of Dissipated Energy

Required to Initiate Liquefaction .......................................................................................... 80

5.1. Introduction .................................................................................................................... 81

5.2. Background .................................................................................................................... 82

5.2.1. Stress-based Methods.............................................................................................. 82

5.2.2. Strain-based Method ............................................................................................... 84

5.2.3. Energy-based Methods............................................................................................ 85

vii

5.2.3.1. Computation of Normalized Dissipated Energy .............................................. 86

5.3. Cyclic Laboratory Testing ............................................................................................. 87

5.3.1. Computing Effective and Total Dissipated Energy using Laboratory Tests .......... 89

5.3.2. Definitions of Liquefaction Used in Laboratory Tests ........................................... 90

5.4. Results ............................................................................................................................ 91

5.5. Discussion and Conclusions .......................................................................................... 92


References ................................................................................................................................. 93

Tables ....................................................................................................................................... 99

Figures..................................................................................................................................... 104

6. Manuscript #4: Epistemic Uncertainty in Site Response Analysis as Part of a PSHA ....... 111

6.1. Introduction .................................................................................................................. 112

6.1.1. Existing Methodologies for Incorporating Epistemic Uncertainty in Site Response

.............................................................................................................................. 114

6.1.2. Uncertainty in the Vs Profile ................................................................................. 115

6.1.3. Uncertainty in Non-Linear Dynamic Soil Properties............................................ 115

6.1.4. Weighted Average Amplification Curves using the Logic Tree .......................... 116

6.1.5. Probabilistic Site-Specific Soil Hazard Curves for Sa,Soil ..................................... 118

6.1.6. Issues with Current SPID Method for Quantifying Epistemic Uncertainty ......... 119

6.2. Proposed Adjustments to the SPID Method ................................................................ 120

6.2.1. First Solution: Normalization of T using Predominant Period, Tp ....................... 121

6.2.2. Second Solution: Envelope Approach .................................................................. 121

6.2.3. Development of a Relationship for α(T) ............................................................... 122

6.2.4. Development of an Envelope for the AF(T) and σlnAF(T) Curves .......................... 122

6.2.5. Modified Site-Specific Soil Hazard Curves for Sa,Soil ........................................... 123

6.3. Comparisons between SPID Method and Modified Method: Case History ................ 124

6.3.1. PSHA for Rock Motions and Input Ground Motion Selection ............................. 124

6.3.2. Vs Profiles, MRD Curves ...................................................................................... 124

6.3.3. Comparisons of Smoothed AF(T) and σlnAF(T) Curves ......................................... 125

6.3.4. Comparisons of Probabilistic Site-Specific Hazard Curves: SPID and Proposed

Method .................................................................................................................. 126

viii

6.4. Conclusions .................................................................................................................. 127

6.5. Acknowledgements ...................................................................................................... 128

References ............................................................................................................................... 128

Tables ...................................................................................................................................... 131

Figures..................................................................................................................................... 133

7. Conclusions ......................................................................................................................... 148

Appendix A. Contents of Appendices .................................................................................... 150

Appendix B. Cyclic Direct Simple Shear Testing Manual ..................................................... 151

Appendix C. Summary of Laboratory Testing Results .......................................................... 176

Appendix D. Liquefaction Case History Database (CPT-based)............................................ 196

Appendix E. Conference Paper: A Critique of b-values used for Computing Magnitude

Scaling Factors .................................................................................................................... 229

Appendix F. Conference Paper: Quality Assurance for Cyclic Direct Simple Shear Tests for

Evaluating Triggering Characteristics of Cohesionless Soils ............................................. 244

Appendix G. Conference Paper: A Consistent Correlation between Vs, SPT, and CPT Metrics

for Use in Liquefaction Evaluation Procedures .................................................................. 259

ix

List of Figures

Figure 2.1 Shear stress-strain hysteresis loops for a cyclic simple shear (CSS) test on clean sand.

................................................................................................................................................. 9

Figure 3.1 A graphical representation of the b-value and its use in an MSF equation (Ulmer et al.

2018). ..................................................................................................................................... 37

Figure 3.2 Effects of liquefaction triggering criteria on b-values from CDSS tests on clean sands

from two studies: Viana Da Fonseca et al. (2015) and Tatsuoka and Silver (1981). Error bars

represent +/- standard error, 𝜖b. Note: ru is assumed to represent ru,Residual in these studies. . 37

Figure 3.3 Effects of liquefaction triggering criteria on b-values from CTRX tests on clean sands

(data from Tatsuoka et al. 1986). Error bars represent +/- standard error, 𝜖b. ...................... 38

Figure 3.4 Range of b-values from multiple laboratories attempting to perform the same test on

the same sand (Toki et al. 1986). Dots represent b-values from individual laboratories, while

larger symbols and error bars represent the b-value and +/- standard error, 𝜖b resulting from

the data combined from all laboratories. ............................................................................... 38

Figure 3.5 Grain-size distribution of Monterey 0/30 sand. ........................................................... 39

Figure 3.6 Shear stress-strain hysteresis loops of a CDSS test on Monterey 0/30 sand (Dr = 62%,

CSR = 0.156, σ’v0 = 100 kPa). .............................................................................................. 39

Figure 3.7 Illustration of effective and total normalized dissipated energy (ΔWeff/σ’v0 and

ΔWtotal/σ’v0, respectively) during the same CDSS test on Monterey 0/30 sand represented in

Fig. 6. ..................................................................................................................................... 40

Figure 3.8 Relationship between b-values and Dr for four separate liquefaction triggering criteria

in AC CV-CDSS tests on Monterey 0/30 sand. Error bars represent +/- standard error, 𝜖𝑏. 41

Figure 3.9 Relationship between a) ΔWtotal/σ’v0 to reach ru,Residual = 1.0 (or its maximum value),

or b) ΔWeff/σ’v0 to reach ru,Residual = 1.0 (or its maximum value), and Dr for CV-CDSS tests

performed in this study. ......................................................................................................... 42

Figure 3.10 CSR vs NL trends developed from IZ MRD curves (σ’v0 = 100 kPa). ...................... 43

Figure 3.11 Relationship between b-values and Dr using MRD curves (filled-in markers) or AC

CV-CDSS laboratory tests using ΔWtotal/σ’v0 = 0.001 as the liquefaction triggering criterion

(white markers) under a range of initial vertical effective stresses. Error bars represent +/-

standard error, 𝜖𝑏. .................................................................................................................. 44

Figure 3.12 Summary of b-values computed from published laboratory test results representing a

range of soil types, confining pressures, liquefaction triggering criteria, etc. ...................... 44

Figure 4.1 Case histories from the updated database plotted as normalized dissipated energy vs.

qc1Ncs. Also shown are median (PL = 50%) energy-based limit-state curves for two scenarios:

1) uncertainties in input parameters are ignored, and 2) uncertainties are included. Bold line

represents deterministic curve. .............................................................................................. 74

x


qc1Ncs for various intervals of FC. Blue line represents median (PL = 50%) energy-based

limit-state curve when uncertainties in input parameters are ignored. .................................. 75


qc1Ncs for various intervals of σ’vo. Blue line represents median (PL = 50%) energy-based



qc1Ncs for various intervals of Mw. Blue line represents median (PL = 50%) energy-based



qc1Ncs for various intervals of amax. Blue line represents median (PL = 50%) energy-based


Figure 4.6 Case histories common to the BI14 database and the updated database plotted as

CSR* vs. qc1Ncs for stress-based procedures and as normalized dissipated energy vs. qc1Ncs

for the proposed energy-based method. Blue lines represent median (PL = 50%) limit-state

curves when uncertainties in input parameters are ignored. Red coloring and blue stars

indicate case histories with potential issues that affect their accuracy. ................................. 79

Figure 5.1 Schematic outlining the stress-based method to estimate FSL for in situ conditions

using results of stress-controlled cyclic laboratory tests. .................................................... 104

Figure 5.2 Schematic outlining the strain-based method to predict liquefaction for in situ

conditions using results of strain-controlled cyclic laboratory tests. .................................. 104

Figure 5.3 Grain-size distribution plot for Monterey 0/30 sand. ................................................ 105

Figure 5.4 Results from a cyclic direct simple shear test: a) sample hysteresis loops and b)

relationship between both effective and total normalized dissipated energy and number of

loading cycles. ..................................................................................................................... 106

Figure 5.5 Hysteresis loops for a strain-controlled CDSS test on Monterey 0/30 sand. ............ 107

Figure 5.6 Normalized dissipated energy (effective) vs. Dr for stress- and strain-controlled

laboratory tests with σ’vo = 60 to 250 kPa where a) ru,Residual = 0.85, and b) ru,Transient = 0.95

defines liquefaction. ............................................................................................................ 107

Figure 5.7 Normalized dissipated energy (effective) vs. ru,Residual for stress- and strain-controlled

tests. ..................................................................................................................................... 108

Figure 5.8 Normalized dissipated energy (effective and total) vs. Dr for stress-controlled tests at

different initial vertical effective stresses (ru,Residual = 0.85). ............................................... 109

Figure 5.9 Normalized dissipated energy (total) vs. qc1Ncs for field case histories and stress-

controlled CDSS tests where ru,Residual = 0.85 defines liquefaction. .................................... 110

Figure 6.1. Example best estimate, lower- and upper-range Vs profiles (i.e., median, 10th and 90th

percentiles) for a hypothetical scenario: (a) low epistemic uncertainty; and (b) high

epistemic uncertainty. .......................................................................................................... 133

Figure 6.2. Example MRD curves for a hypothetical scenario (where plasticity index is zero and

mean effective stress is 100 kPa). ....................................................................................... 134

xi

Figure 6.3. Example logic tree based on SPID recommendations for a hypothetical scenario. . 134

Figure 6.4. Example of a non-linear relationship between AF(T) and Sa,Rock(T) representing a

series of branches terminating in a leaf on the logic tree for a hypothetical scenario. ........ 135

Figure 6.5. Example plots of AF vs. T, μi, μTotal, σTotal, and smoothed σTotal vs. T for a hypothetical

scenario. Gray: best estimate Vs profile, lighter colors: lower Vs profile, darker colors: upper

Vs profile, solid line: Ishibashi and Zhang (1993) MRD curve, dotted line: Darendeli and

Stokoe (Darendeli 2001) MRD curve. ................................................................................ 136

Figure 6.6. Example probabilistic site-specific soil hazard curve for a hypothetical scenario (Tj =

0.4 sec). ................................................................................................................................ 137

Figure 6.7. Example μTotal vs. T for two levels of epistemic uncertainty: low epistemic

uncertainty (σlnVs = 0.35) and high epistemic uncertainty (σlnVs = 0.5) for a hypothetical

scenario. Gray: best estimate Vs profile, lighter colors: lower Vs profile, darker colors: upper

Vs profile, solid line: Ishibashi and Zhang (1993) MRD curve, dotted line: Darendeli and

Stokoe (2001) MRD curve. ................................................................................................. 138

Figure 6.8. Example λSa,Soil vs. Sa,Soil for two levels of epistemic uncertainty: low epistemic

uncertainty (σlnVs = 0.35) and high epistemic uncertainty (σlnVs = 0.5) using the SPID

method for a hypothetical scenario (Tj = 0.4 sec). .............................................................. 139

Figure 6.9. AF(T) curves from individual site response analyses using a suite of ground motions

and all six branches of the SPID logic tree plotted against a) T, or b) T/Tp. ...................... 139

Figure 6.10. Comparison of λSa,Soil for two levels of epistemic uncertainty: low epistemic


scenario using the SPID method and the proposed normalization method. ........................ 140

Figure 6.11. Proposed modified logic tree. ................................................................................. 140

Figure 6.12. Example of fTp and α(T) for proposed method for the hypothetical scenario. ....... 141

Figure 6.13. Examples of enveloped AF(T) and σlnAF(T) curves for the hypothetical scenario.

Gray: best estimate Vs profile, lighter green: lower Vs profile, darker green: upper Vs

profile, solid line: Ishibashi and Zhang (1993) MRD curve, dotted line: Darendeli and

Stokoe (2001) MRD curve. ................................................................................................. 141

Figure 6.14. Comparison of λSa,Soil for two levels of epistemic uncertainty: low epistemic


scenario using the SPID method and the proposed modified method. ................................ 142

Figure 6.15. Seismic hazard curves for rock motions at the case history site (USGS Unified

Hazard Tool, Site Class A). ................................................................................................. 142

Figure 6.16. Uniform hazard spectra (UHS) values compared with response spectra from the

suite of eleven scaled rock motions (5% damping). ............................................................ 143

Figure 6.17. Best estimate Vs profile and lower/upper range Vs profiles (10th and 90th percentiles)

for case history site. a) low epistemic uncertainty: σlnVs ≤ 0.35, b) high epistemic

uncertainty: σlnVs = 0.50. ..................................................................................................... 144

Figure 6.18. AF(T) curves for the SPID method (“Wtd. Avg.”) and the additional branch of the

new proposed method (“Envelope”) for two scenarios: a) low epistemic uncertainty, and b)

xii

high epistemic uncertainty. Gray lines represent mean AF(T) curves for individual branches

of the SPID-recommended logic tree, red stars represent peaks used to smooth the

“Envelope” curve. ............................................................................................................... 145

Figure 6.19. σlnAF(T) curves for the SPID method (“Smooth Wtd. Avg.”) and the additional

branch of the new proposed method (“Envelope”) for two scenarios: a) low epistemic

uncertainty, and b) high epistemic uncertainty. .................................................................. 145

Figure 6.20. fTp curves for the new proposed method for two scenarios: a) low epistemic


Figure 6.21. α(T) curves for the new proposed method for two scenarios: a) low epistemic


Figure 6.22. Comparisons of SPID method and proposed method for the Case History site in a)

hazard curves, b) direct comparisons of annual rates of exceedance (Target period is 0.4 sec,

maximum α for new method is 1.0). ................................................................................... 147

Figure B.1 The physical layout of some of the GCTS equipment. ............................................. 152

Figure B.2. The base of the cell with the shear carriage installed and two posts removed. Notice

the back pressure sensor mounted at the front. .................................................................. 153

Figure B.3. The pressure panel. ................................................................................................. 154

Figure B.4. Numbered parts from the GCTS apparatus used during test assembly. ................. 156

Figure B.5. Normal actuator connector (25). Only used for actively controlled (AC) tests. .... 156

Figure B.6. Mounting the bottom platen onto the shear carriage. ............................................. 158

Figure B.7. Membrane attached to the bottom platen. ............................................................... 159

Figure B.8. Bottom platen with membrane and confining rings................................................ 159

Figure B.9. Bottom bender-element platen with rings and fence. ............................................. 160

Figure B.10. Sample after dry pluviation sand placement. Notice the heaped sand. ................ 161

Figure B.11. Scraping the excess sand off of the top of the confining rings. ............................ 161

Figure B.12. The top platen with the top-platen-to-normal-piston block on top of the specimen-

in-preparation. .................................................................................................................... 162

Figure B.13. Using the metal beam to straighten the orientation of the top platen. .................. 163

Figure B.14. Location of the shear piston locking collar. .......................................................... 163

Figure B.15. Location of specimen height measurement. ......................................................... 164

Figure B.16. Location of valves (in front of the cell). Note bottom valve is open in this image.

............................................................................................................................................ 165

Figure B.17. Bolting the normal track assembly onto the top platen. ....................................... 166

Figure B.18. Location of set screws on black normal-movement guides (in the front and back).

............................................................................................................................................ 167

Figure B.19. The hysteresis loops of a stress versus strain plot (stress-controlled test). ........... 174

Figure B.20. An example of an output plot. .............................................................................. 175

Figure D.1. Uncertainty in ln(amax) (as a ratio of the σGMPE) from the USGS ShakeMap for

the 1989 Loma Prieta earthquake. ..................................................................................... 200

xiii

Figure D.2. An example CPT sounding showing qc1Ncs and Ic with depth. FS calculated using

BI14 equations of CRR and CSR. Red lines represent smoothed trends using a Savitzky-

Golay filter. Gray horizontal lines represent layer boundaries. Light blue layers represent

layers with > 1 m thickness, and blue squares represent mean qc1Ncs. ............................ 203

Figure D.3. Mean qc1Ncs, standard deviation, and coefficient of variation for each soil layer of

at least 1 m thickness. White stars represent moving averages and red lines represent

average values. ................................................................................................................... 204

Figure E.1. A graphical representation of the b-value and its use in an MSF equation. ........... 231

Figure E.2. Comparison of b-values estimated from Yoshimi et al. (1989) (CTRX, frozen

samples of sand). Error bars represent +/- one standard error (b) of the regressed b-value.

Data labels represent σ’c in kPa. ........................................................................................ 233

Figure E.3. Comparison of b-values estimated from Okamura et al. 2003 (CTRX, frozen

samples, εDA = 5%). N, I, and Y represent Niigata, Izumo, and Yasugi sites, respectively.

............................................................................................................................................ 234

Figure E.4. Comparison of b-values estimated from Toki et al. (1986). Each point represents

results from a single laboratory (CTRX, air pluviated samples, Toyoura Sand, σ’c = 98

kPa). ................................................................................................................................... 235

Figure E.5. Comparison of b-values estimated from Tatsuoka et al. (1986) (CTRX: εDA = 10%,

CTS: γDA = 15%)................................................................................................................ 237

Figure E.6. CTS-I tests on air-pluviated samples of Toyoura Sand with b-values calculated using

a) all data points or b) points on the linear portion of the curve (γDA = 15%). Solid lines

represent a spline fit and dotted lines represent a power law fit. ....................................... 237

Figure E.7. CTS-A tests on air-pluviated samples of Sengenyama Sand with b-values calculated

using a) all data points or b) points on the linear portion of the curve (γDA = 15%). Solid

lines represent a spline fit and dotted lines represent a power law fit. .............................. 238

Figure E.8. Studies showing b-values decreasing with increasing Dr. ...................................... 239

Figure F.1. Shear strain during the ramp-up and consolidation phases of a PC CV-CDSS test (Dr

= 58%, σ’v0 = 100 kPa). ..................................................................................................... 247

Figure F.2. Shear stress during the ramp-up and consolidation phases of a PC CV-CDSS test (Dr

= 23%, σ’v0 = 100 kPa). ..................................................................................................... 248

Figure F.3. Comparison of axial strain at two locations in the testing apparatus during the cyclic

phase of a PC CV-CDSS (Dr = 19%, σ’v0 = 250 kPa). ...................................................... 250

Figure F.4. Stress path converging at a non-zero value of vertical effective stress (PC CV-CDSS

test, Dr = 70%). .................................................................................................................. 251

Figure F.5. Stress path with vertical lines at low vertical effective stress (PC CV-CDSS test, Dr

= 85%). ............................................................................................................................... 251

Figure F.6. Stress path (in blue) with irregular spacing and normal displacement of the vertical

actuator (in red) during a PC CV-CDSS test (Dr = 20%). ................................................. 252

Figure F.7. Comparison of axial strain at two locations in the testing apparatus during the cyclic

phase of an AC CV-CDSS test (Dr = 67%, σ’v0 = 250 kPa). ............................................. 253

xiv

Figure F.8. Biased stress path (AC CV-CDSS test, Dr = 67%). ................................................ 254

Figure F.9. Liquefaction resistance curves (liquefaction defined as single-amplitude γ = 3.5%,

σ’v0 = 100 kPa) for a) all PC CV-CDSS tests, and b) PC CV-CDSS tests that passed the

acceptance criteria. ............................................................................................................. 256

Figure G.1 Computed Vs vs N1,60cs and qc1Ncs using published correlations for two different

liquefaction case history databases. ................................................................................... 262

Figure G.2. Comparison of CRRM7.5 curves (Andrus et al. 2003; Boulanger and Idriss 2012;

Green et al. 2018) when Andrus et al. (2004) is used to convert N1,60cs and qc1Ncs to Vs1. 263

Figure G.3. CSR* vs. in-situ metrics for three liquefaction case history databases and selected

CRRM7.5 curves. CSR* are updated values as computed in this study. Liq.: liquefaction was

observed; No Liq.: no liquefaction was observed. ............................................................. 265

Figure G.4. Comparison of CRRM7.5 curves when correlations from Andrus et al. (2004) and this

study are used to convert N1,60cs and qc1Ncs to Vs1. ............................................................. 266

Figure G.5. Direct comparisons of qc1Ncs values (or N1,60cs values) converted from N1,60cs values

(or qc1Ncs values) using Vs-based correlations and those converted using Dr-based

correlations. ........................................................................................................................ 266

Figure G.6. Computed Vs vs N1,60cs and qc1Ncs using published correlations and correlations

given in this study for two different liquefaction case history databases. ......................... 267

Figure G.7. Pairs of N1,60cs and qc1Ncs from the same sites given in Andrus et al. (2004) compared

to the correlations developed in this study and those developed by Andrus et al. ............ 268

xv

List of Tables

Table 3.1 Acceptance Criteria for PC CV-CDSS Tests (after Ulmer et al. 2019) ........................ 35

Table 3.2 Index Properties of Monterey 0/30 Sand ...................................................................... 35

Table 3.3 Summary of b-values for different combinations of qc1Ncs, σ'v0, and MRD curves (IZ =

Ishibashi and Zhang 1999, DS = Darendeli 2001) ............................................................... 36

Table 4.1 Required Parameters to Compute ln(ΔW/σ’vo) ............................................................. 71

Table 4.2 Standard Deviations and Correlation Coefficients Required to Compute σln(ΔW/σ’vo). .. 72

Table 4.3 Regression coefficients for energy-based limit-state curves for two scenarios: 1)

uncertainties in input parameters excluded and 2) uncertainties included. ......................... 73

Table 4.4 Number of correct, false positive, and false negative predictions for the proposed

energy-based procedure and two stress-based procedures ................................................... 73

Table 5.1 Index Properties of Monterey 0/30 Sand ...................................................................... 99

Table 5.2 Acceptance Criteria for AC CV-CDSS Tests (after Ulmer et al. 2019b) ................... 100

Table 5.3 Results of Stress-controlled CDSS Tests on Monterey 0/30 Sand ............................. 101

Table 5.4 Results of Strain-controlled CDSS Tests on Monterey 0/30 Sand ............................. 103

Table 6.1. Scaling Factors used for the suite of eleven rock motions ........................................ 131

Table 6.2. Assumed layering, best estimate Vs profile, and site-specific estimates of σlnVs for each

soil layer at the case history site. ....................................................................................... 131

Table 6.3. Sa,Soil for return periods of 100 or 2000 years using the SPID method and proposed

New method (with maximum α of 1.0) for low and high epistemic uncertainties. ........... 132

Table C.1 Results from Cyclic Direct Simple Shear Tests (AC, Stress-controlled) on Monterey

0/30 Sand using ru,Resid Criteria .......................................................................................... 177


0/30 Sand using ru,Trans Criteria .......................................................................................... 180


0/30 Sand using γSA Criteria .............................................................................................. 183


0/30 Sand using γDA Criteria .............................................................................................. 186


0/30 Sand using ΔWEff/σ'vo Criteria ................................................................................... 189


0/30 Sand using ΔWTot/σ'vo Criteria ................................................................................... 192

Table C.7 Results from Cyclic Direct Simple Shear Tests (AC, Strain-controlled) on Monterey

0/30 Sand using ru Criteria ................................................................................................. 195

xvi

Table D.1 Uncertainty of ln(amax) and GMPEs for Earthquakes in BI14 CPT Database. CY:

Chiou and Youngs, Z: Zhao et al., MMU: Mean Map Uncertainty (or Mean Sigma). ..... 201

Table D.2. Liquefaction Case History Database (CPT-based) .................................................. 206

Table F.1 Grading Criteria for PC CV-CDSS Tests .................................................................. 255

Table G.1 Examples of Published Vs Correlations. Note: Vs and (Vs,1)cs in m/s. ...................... 262

1

1. Introduction

1.1. Soil Liquefaction


structures such as bridges, roads, buildings, and pipelines. Such damage can result in substantial

reconstruction time and large, unanticipated costs to homeowners, businesses, and municipalities.

One way to mitigate damage from liquefaction in future earthquake events is to improve current

methods of predicting liquefaction initiation or triggering.

1.2. Objectives

The main objective of this research is to develop an energy-based approach for evaluating the

potential for liquefaction triggering. To accomplish this objective, several sub-tasks were required,

including:

Task 1: Review currently available liquefaction case history databases for quality, identify

discrepancies between databases, modify parameters as needed, and add case histories

from recent earthquakes.

Task 2: Estimate dissipated energy for each case history in the database.

Task 3: Develop field-based limit-state curves for the energy-based approach.

Task 4: Perform constant-volume direct cyclic simple shear (CDSS) testing and develop a

laboratory-based liquefaction resistance curve.

Task 5: Reconcile limit-state curves from field-based and laboratory-based data.

Task 6: Finalize the energy-based liquefaction evaluation procedure and compare its

effectiveness to that of common stress-based procedures.

2

A secondary objective addresses a related research topic, which is to develop an approach to

incorporate epistemic uncertainty into site effects in a probabilistic seismic hazard analysis

(PSHA) with the guiding principle that higher epistemic uncertainty should lead to seismic hazards

that are equal to or greater than the hazards associated with lower epistemic uncertainty.

1.3. Organization

This dissertation is organized as a series of manuscripts with two introductory chapters, one

concluding chapter, and appendices containing supplementary data, manuals, and related

conference papers. Chapter 2 contains background information on liquefaction evaluation and

other related topics that are highlighted in this dissertation.

Chapter 3 contains the first manuscript. The focus of this manuscript is to recommend a b-value

for use in computing magnitude scaling factors (MSF) as part of liquefaction triggering evaluation

of clean sands. The b-value defines the slope of the linear relationship between the cyclic stress

ratio (CSR) and the number of uniform stress cycles to reach liquefaction (NL) on a log-log scale.

Using an analysis of cyclic direct simple shear (CDSS) tests on samples of sand, the results

presented in this manuscript shows that two significant factors can affect b-values: liquefaction

initiation criterion and quality of the cyclic laboratory testing performed. A liquefaction criterion

based on the cumulative dissipated energy in a unit volume of soil is shown to yield b-values that

are relatively insensitive to changes in relative density compared to b-values from other more

traditional criteria based on strain or excess pore pressure ratio. It is also shown that published

modulus reduction and damping (MRD) curves can be used to compute b-values using a similar

energy-based framework. These MRD-based b-values are used to recommend a single b-value for

use in computing MSF for clean sands.

Chapter 4 contains the second manuscript. The objective of the research contained in this

manuscript is to develop an energy-based approach for evaluating the potential for liquefaction

triggering as a function of cone tip resistance from the cone penetration test (CPT). Toward this

end, the framework to estimate dissipated energy in a unit volume of soil (ΔW) is presented. This

framework unites concepts from existing stress-based and strain-based liquefaction evaluation

3

frameworks. A modified database of case histories with observations of liquefaction or no

liquefaction in the field is used to develop probabilistic limit-state curves. These limit-state curves

identify the relationship between normalized dissipated energy (ΔW/σ’vo) and corrected cone tip

resistance (qc1Ncs) for contours of different values of probability of liquefaction (PL). The energy-

based procedure is shown to perform as well as existing stress-based procedures. Due to its basis

in robust mechanistic theory, it may be applicable to liquefaction evaluations for non-traditional

sources of ground shaking (e.g., induced seismicity, deep dynamic compaction).

Chapter 5 contains the third manuscript, which is a companion paper to the second manuscript.

The focus of this paper is reconciliation between results of laboratory tests and field estimates of

liquefaction demand. This reconciliation has been successfully achieved in stress-based

liquefaction evaluation procedures. However, without careful interpretation of the results, the

results of laboratory tests may be incompatible with estimates of in situ demand in strain- and

energy-based methods. The objective of the research contained in this third manuscript is to show

how laboratory test data can be used to evaluate liquefaction triggering potential within an energy-

based, total stress framework that is consistent with field-based limit-state curves. A series of

cyclic direct simple shear tests performed on Monterey 0/30 sand are interpreted in such a way

that the results of stress- and strain-controlled tests are aligned and these same results align with

field estimates of dissipated energy to trigger liquefaction using a database of case histories.

Chapter 6 contains the fourth manuscript. The focus of this manuscript is the incorporation of

epistemic uncertainty in site response analyses as part of a probabilistic seismic hazard analysis

(PSHA). A PSHA performed for rock conditions and modified for soil conditions using

deterministic site amplification factors does not account for uncertainty in site effects, which can

be significant. One approach to account for such uncertainty is to compute a weighted average

amplification curve using a logic tree that accounts for several possible scenarios with assigned

weights corresponding to their relative likelihood or confidence. However, this approach can lead

to statistical smoothing of the amplification curve and to increased hazard when epistemic

uncertainty is low. This study proposes a modified approach in which the epistemic uncertainty is

captured in the plot of amplification factors versus period. Using a case history, the proposed

method is shown to improve the issue with the weighted average method for at least two oscillator

4

periods and to yield similar results for two other periods where the highlighted issue is less

significant.

General conclusions and a summary of the work in this dissertation are given in Chapter 7.

1.4. Significance

The broader impacts of this work will help to minimize losses from earthquakes by improving the

way engineers evaluate liquefaction. This research proposes a method that is based on a robust

mechanistic framework that will make it easier to evaluate liquefaction potential for circumstances

that are not well represented in current liquefaction evaluation procedures. The components of the

proposed energy-based procedure are developed consistently and are presented in such a way that

this procedure can be readily adopted by practitioners who are already familiar with existing

liquefaction evaluation procedures. With improved evaluation techniques, engineers can more

accurately assess liquefaction hazard, leading to a reduction of losses due to liquefaction.

5

2. Background

Under cyclic shear loading, such as during an earthquake, soil particles tend to dilate or contract

depending on the soil’s initial effective vertical stress (σ’v0) and relative density (Dr). If the

particles tend to contract but the loading, soil permeability, and boundary conditions are such that

no pore pressures are allowed to dissipate, then pore pressures will increase. If the excess pore

pressures (Δu) increase to the point that Δu = σ’v0 or excess pore pressure ratio (ru = Δu / σ’v0)

reaches 1.0, then liquefaction initiates (or triggers) in the soil. Note that there must be some

tendency of the soil particles to move relative to each other (i.e., shear strain) or else the pore

pressures will not increase. In other words, liquefaction is a strain-related phenomenon.

Liquefaction initiation can lead to several problems including excessive settlement, loss of bearing

capacity, lateral spreading, and slope failure. To avoid these issues, practitioners assess the

probability of liquefaction triggering (i.e., ru ≈ 1.0) using one of several currently available

procedures. These liquefaction evaluation procedures can be organized into three main categories:

stress-, strain-, and energy-based methods, with the most popular method in practice being stress-

based methods.

2.1. Stress-based Liquefaction Evaluation

Seed and Idriss (1971) and Whitman (1971) first developed the “simplified” liquefaction

evaluation method, which removed the need for a numerical site-specific response analysis to be

performed to estimate the maximum induced shear stress (τmax) at a depth of interest in the soil

profile. The central focus of this method is the definition of the cyclic stress ratio, CSR, as shown

below:

𝐶𝑆𝑅 =𝜏𝑎𝑣𝑔

𝜎′𝑣0= 0.65

𝑎𝑚𝑎𝑥

𝑔

𝜎𝑣

𝜎′𝑣0𝑟𝑑 (1)

6

where τavg is the average shear stress in the time history, amax is the maximum acceleration in the

time history at the ground surface, g is the acceleration of gravity in the same units as amax, rd is

the stress reduction factor, and σv is the total vertical stress at a given depth in a soil profile. The

value 0.65 is an arbitrary value defining the ratio of τavg to τmax (i.e., τavg = 0.65∙τmax). The rd

parameter accounts for the non-rigid response of the soil column. The factor of safety against

liquefaction is defined CRR divided by CSR, where CRR represents the cyclic resistance of the

soil of interest. CRR is either determined from laboratory tests or from empirical correlations

developed from analyses of liquefaction/non-liquefaction field case histories.

For several decades, many researchers have worked to refine the simplified liquefaction evaluation

method. The original simplified method used standard penetration test (SPT) measurements from

field case histories to develop its CRR curve. Some researchers developed alternative CRR curves

using SPT data (Liao et al. 1988; Cetin et al. 2004, 2018; Boulanger and Idriss 2014), but others

chose to use cone penetration test, CPT (Robertson and Wride 1998; Moss et al. 2006; Boulanger

and Idriss 2014) or shear-wave velocity, Vs measurements (Andrus et al. 2003; Kayen et al. 2013).

For some of these stress-based procedures, correction factors were developed to account for

duration of ground motion shaking, overburden stress, and sloping ground.

The simplified stress-based liquefaction evaluation procedure is commonly used in practice and is

generally preferred for most routine projects, in part because of the following merits and perceived

benefits:

Liquefaction demand (i.e., CSR) can be estimated using a simplified, total stress

framework

o Site response analyses are not required to refine the estimate of amax at depth

(though site response analyses can be performed, if desired).

o Stress-based parameters (i.e., τavg) can be estimated from readily available

earthquake parameters (i.e., amax).

In situ testing, such as SPT, CPT, and Vs tests can be used instead of laboratory tests to

estimate a soil’s resistance to liquefaction (though laboratory tests can be used, if desired).

7

The combined efforts of many researchers and decades of practice have led to significant

accumulation of experience in stress-based procedures.

However, the utility of existing stress-based procedures is hindered by the following shortcomings:

Laboratory tests used to estimate a soil’s resistance to liquefaction require either expensive

undisturbed soil sampling or an exact match in soil fabric between the reconstituted

laboratory sample and the in situ soil (which is unlikely).

In the most commonly used procedures, the proxies for earthquake duration are based on a

high-cycle implementation of the P-M fatigue theory despite liquefaction being a low-cycle

phenomenon (though this can be overcome, as in Green et al. 2019).

The CRR curves based on liquefaction case histories are not “true” liquefaction triggering

curves because they rely on surface manifestations of liquefaction rather than observations

of liquefaction at depth in the soil profile. This implies that the absence of surface

manifestations of liquefaction means that liquefaction does not trigger at any soil layer

below the ground surface, which may not be true.

Correction factors added to the original simplified stress-based method were each

developed separately and inconsistently.

This framework is not easily implemented for non-seismic sources (e.g., vibrocompaction,

induced seismicity, and deep dynamic compaction).

2.2. Strain-based Liquefaction Evaluation

Because excess pore pressure during cyclic shear loading is more directly related to shear strains

(Martin et al. 1975), Dobry et al. (1982) proposed a method to evaluate liquefaction using shear

strains as opposed to shear stresses. In this method, the amplitude of applied cyclic shear strain

(γc) can be estimated iteratively using the following expression developed using total stress

framework:

𝛾𝑐 = 0.65(𝑎𝑚𝑎𝑥

𝑔)

𝜎𝑣𝑟𝑑

𝐺𝑚𝑎𝑥(𝐺 𝐺𝑚𝑎𝑥⁄ )𝛾𝑐 (2)

8

where G is the secant shear modulus of the soil, Gmax is the small-strain (less than 10-4% shear

strain) shear modulus of the soil, and (G/Gmax)γc is the normalized secant shear modulus reduction

ratio of the soil corresponding to γc. The value of (G/Gmax)γc can be determined from established

modulus reduction curves such as those developed by Ishibashi and Zhang (1993) or Darendeli

and Stokoe (2001). Dobry et al. concluded that if γc is less than 0.01%, then no liquefaction will

occur. If γc exceeds 0.01%, then γc and Neq,M (from an established correlation with earthquake

parameters) are used with resistance curves developed from strain-controlled cyclic tests

performed on reconstituted samples of soil prepared to the same Dr as the soil in situ. If ru ≈ 1.0 at

the end of Neq,M cycles of strain with amplitude γc, then liquefaction is predicted to trigger in situ.

The major issue with this process is that the Neq,M - ru - γc relationship is inherently in an effective

stress framework (i.e., increased pore pressures soften the soil) but the value of γc in the field

(Equation 2) is calculated in a total stress framework, thus ignoring the softening effects of excess

pore pressures in the field. In other words, it is inconsistent to use an effective stress Neq,M - ru - γc

relationship to estimate ru in the field using a total stress proxy of γc.

The most significant benefits of the strain-based liquefaction evaluation method are:

Excess pore water pressure better correlates with strain than with stress.

Laboratory tests on reconstituted soil samples can be used to develop the relationship

between Neq,M and γc associated with cyclic loading and ru without concern for soil fabric

(which is a concern in the stress-based framework).

However, the utility of the strain-based framework is hindered by the following shortcomings:

Strain-controlled cyclic laboratory tests are required, making this method more difficult to

implement.

As the framework is currently written, there is an inconsistency in the way that liquefaction

is handled in the field (i.e., total stress) and in the laboratory (i.e., effective stress).

If a total stress framework is used to compute γc, then an effective stress framework is

needed to compute the duration of the cyclic loading, Neq,M. In other words, a “simplified”

strain-based method is not currently available.

9

2.3. Energy-based Liquefaction Evaluation

In general, energy-based liquefaction evaluation methods are rooted in the concept of energy as

defined by the cumulative area bound by stress-strain hysteresis loops (e.g., Figure 1). Nemat-

Nasser and Shokooh (1979) were the first to suggest that dissipated energy is directly linked to the

development of excess pore pressure in saturated sands. Since then, several methods have been

developed based on this concept. Some methods rely on case histories to develop a correlation

between in situ soil properties and dissipated energy required to liquefy a given soil (Davis and

Berrill 1982; Berrill and Davis 1985; Law et al. 1990; Trifunac 1995; Green 2001; Jafarian et al.

2014; Lasley 2015; Baziar and Rostami 2017), while other methods rely on laboratory tests to

estimate dissipated energy to liquefaction of small-scale samples (Figueroa et al. 1994; Liang et

al. 1995; Liang 1995; Davis and Berrill 1996; Desai 2000; Baziar and Jafarian 2007; Baziar et al.

2011; Alavi and Gandomi 2012; Jafarian et al. 2012; Kokusho and Mimori 2015; Lasley 2015;

Zhang et al. 2015). Though these methods generally use similar energy-based concepts, they do

not all apply these concepts consistently and there are several issues that have restricted the

implementation of energy-based liquefaction evaluation methods in common practice. These

issues can be organized into three main categories: 1) no reconciliation of effective and total stress

frameworks, 2) outdated or crude estimations of dissipated energy, and 3) difficulties in

implementation.

Figure 2.1 Shear stress-strain hysteresis loops for a cyclic simple shear (CSS) test on clean

sand.

10

The basis of the proposed energy-based approach is a macro-level, low cycle fatigue theory

described by Green and Terri (2005) and adapted from the Palmgren-Miner fatigue theory

(Palmgren 1924; Miner 1945). The details of the proposed approach are described in more detail

in Manuscript #2 (Chapter 4). Some of the benefits associated with stress- and strain-based

frameworks that will be retained in the proposed energy-based framework include:

The proposed method will be relatively simple to implement at its most basic level, but can

be refined to meet the required complexity of any project.

o In situ testing, such as SPT, CPT, and Vs tests can be used instead of laboratory

tests to estimate a soil’s resistance to liquefaction (though laboratory tests can be

used, if desired).

o Empirical correlations of rd to help estimate τmax remove the need for site response

analyses (though site response analyses can be performed to refine the estimate of

τmax). The chosen correlation to estimate rd was developed in an energy-based

framework consistent with the proposed research (Lasley et al. 2016b).

o Required parameters (i.e., τmax) can be estimated from readily available earthquake

parameters (i.e., amax).

The proposed method will be presented in such a way that it is not totally unfamiliar to

those who use the stress-based methods (i.e., similar parameters required, no need to get

additional data that would not be required for the stress-based method).

In addition to these benefits, the proposed energy-based method can also be applied to non-seismic

sources and to a variety of tectonic regimes (i.e., inter-plate and intra-plate events). One

shortcoming that the proposed research cannot overcome is the resistance curve developed from

field observations is still not a “true” liquefaction triggering curve because it is based on surface

manifestations instead of observations at depth. Though not addressed in this research, this

shortcoming can be overcome by considering the influence of the entire soil profile on liquefaction

manifestations when developing a liquefaction triggering curve. Despite this limitation, the

proposed energy-based liquefaction evaluation method can overcome many of the shortcomings

of currently available liquefaction evaluation methods, while maintaining the simplicity and

familiarity of the methods that practitioners most commonly use.

11

2.4. Site Response Analyses

One of the essential parameters required for liquefaction evaluation is the ground motion,

represented by τavg or amax in the frameworks outlined previously. There are several methods that

can be used to characterize the ground motion, including site response analysis. Using site response

analyses, rock motions applied at the location of bedrock can be modified based on information

about the overlying soil column to estimate surface motions, or a surface motion recording can be

converted to rock motions using the same principles.

Manuscript #4 (Chapter 6) provided in this dissertation may initially seem out of place because it

does not address liquefaction directly like the first three manuscripts do. However, this final

manuscript addresses issues with site response analyses which are linked to liquefaction

evaluations via the estimation of ground motions. Specifically, this manuscript outlines some of

the challenges associated with incorporating uncertainties in the site response analysis when

performing a probabilistic seismic hazard analysis (PSHA). For more background on this topic

and on site response in general, the reader is directed to the background section of Manuscript #4.

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Trifunac, M. D. (1995). “Empirical criteria for liquefaction in sands via standard penetration tests

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Engineering Geology, 188, 29–37.

15

3. Manuscript #1: b-values for Computing Magnitude Scaling

Factors in Liquefaction Triggering Evaluation of Clean Sands

The following manuscript will be submitted to ASTM’s Geotechnical Testing Journal.

Kristin Ulmer made the following contributions:

Summarized results of laboratory tests published in the literature and computed b-values

for these results

Conducted cyclic direct simple shear tests and supervised other students performing the

tests

Reduced laboratory testing data

Performed statistical analyses

Prepared figures and tables

Wrote the first draft of the manuscript and incorporated subsequent edits

Dr. Green made the following contributions:

Suggested the idea of looking for trends in b-values as a function of other parameters such

as relative density, vertical confining stress, type of testing apparatus, etc.

Developed the idea of computing b-values using contours of constant dissipated energy

Drs. Green and Rodriguez-Marek made the following contributions:

Provided valuable feedback throughout the study

Edited the manuscript

16

b-values for Computing Magnitude Scaling Factors in Liquefaction Triggering Evaluation

of Clean Sands

K.J. Ulmer1, R.A. Green2, A. Rodriguez-Marek2

1 PhD Candidate, Department of Civil and Environmental Engineering, Virginia Tech,

Blacksburg, Virginia, U.S.A.; [email protected]

2 Professor, Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg,

Virginia, U.S.A.; [email protected], [email protected]

Keywords: magnitude scaling factor, cyclic direct simple shear, liquefaction evaluation,

dissipated energy, Monterey 0/30 sand

Abstract

The objective of this study is to recommend a b-value for use in computing magnitude scaling

factors (MSF) as part of liquefaction triggering evaluation of clean sands. The b-value defines the

slope of the linear relationship between the cyclic stress ratio (CSR) and the number of uniform

stress cycles to reach liquefaction (NL) on a log-log scale. Many parameters can affect b-values,

including soil type, sample preparation method, relative density, confining stress, and type of

cyclic laboratory test. An analysis of constant-volume cyclic direct simple shear tests (CV-CDSS)

on a clean sand performed as part of this study shows that two other factors can affect b-values:

liquefaction initiation criterion and cyclic laboratory testing protocol and acceptance criteria. A

liquefaction criterion based on the cumulative dissipated energy in a unit volume of soil is shown

to yield b-values that are relatively insensitive to changes in relative density compared to b-values

from other, more traditional criteria based on strain or excess pore pressure ratio. It is also shown

that published modulus reduction and damping (MRD) curves can be used to compute b-values

using a similar energy-based framework. These MRD-based b-values are used to recommend a

single b-value for use in computing MSF for clean sands.

17

3.1. Introduction

Magnitude scaling factors (MSF) are used in simplified, stress-based liquefaction evaluation

procedures to account for durational effects of ground shaking during earthquakes (Boulanger and

Idriss 2014; Kishida and Tsai 2014). Inherent to these MSFs is the estimation of a b-value that

relates cyclic stress ratio (CSR) to number of uniform stress cycles to trigger liquefaction (NL).

Fig. 1 shows the relationship between MSF and the b-value, where Neq M and Neq M7.5 are the

number of equivalent cycles for earthquake motions having magnitudes M and M7.5, respectively.

Procedures for computing Neq M and Neq M7.5 also rely on b-values (e.g. Green and Terri 2005;

Hancock and Bommer 2005; Stafford and Bommer 2009; Lasley et al. 2017). The relationship

between CSR and NL is assumed to be linear, though this is not always the case for some soils,

which can result in misleading b-values (Mandokhail et al. 2017; Ulmer et al. 2018). In addition,

other factors may affect b-values for a given soil, such as soil density, effective confining pressure,

type of cyclic test, and liquefaction triggering criterion, though the effects are not always consistent

(Ulmer et al. 2018).

The objective of this study is to propose b-values for computing MSF for evaluating liquefaction

triggering in clean sands, including a discussion on the effects of assumed liquefaction triggering

criterion and laboratory testing acceptance criterion. Toward this end, this study includes a

summary of b-values computed from results of cyclic laboratory tests found in the literature and

an analysis of constant-volume cyclic direct simple shear (CV-CDSS) tests on clean sand

performed as part of this study.

3.2. Background

Several types of laboratory tests can be used to develop CSR vs NL relationships (and thus, b-

values), including cyclic direct simple shear (CDSS), cyclic triaxial (CTRX), and cyclic torsional

shear (CTS) tests. As mentioned previously and as outlined by Ulmer et al. (2018), there are several

factors that can affect the b-values computed from these tests. Two factors in particular that were

not fully addressed by Ulmer et al. (2018) will be discussed as part of this paper: the assumed

liquefaction triggering criteria and the acceptance criteria for cyclic tests.

18

3.2.1. Effect of Liquefaction Triggering Criteria on b-values

A predetermined liquefaction triggering criterion is required to estimate NL in each cyclic test,

though this criterion is somewhat ambiguous and inconsistent among published studies (Ulmer et

al. 2018; Wu et al. 2004). Liquefaction is initiated (or triggered) when the vertical effective stress

(σ’v) reduces to zero (i.e., the complete transfer of the overburden stress to the pore water). This is

often expressed in terms of excess pore water pressure ratio (ru), where ru is defined as excess pore

water pressure, Δu, divided by initial vertical effective stress, σ’v0, and ru = 1 for the state of

liquefaction. However, due to the dilative tendencies of medium-dense to dense soils, σ’v = 0 or ru

= 1 is never achieved. As a result, strain-based definitions for liquefaction triggering are commonly

used, although defining liquefaction this way is largely based on judgement. Common thresholds

for CDSS and CTS tests range from 3% to 4% single-amplitude shear strain (γSA) and 1.5% to

15% double-amplitude shear strain (γDA), and common thresholds for CTRX tests range from 2%

to 10% double-amplitude axial strain (εDA) (Tatsuoka and Silver 1981; Tatsuoka et al. 1986;

Mandokhail et al. 2017).

In addition to the ambiguity in what liquefaction triggering criterion to use to determine NL, there

are also several issues surrounding the most commonly used criteria. For example, strain-based

criteria may only be reliable for soils that show a sudden increase in strain as ru approaches 1.0

(e.g. loose, clean sands) and may not be reliable for soils that gradually accumulate strain before

ru reaches 1.0 (El Mohtar 2009). In other words, the value of NL in dense sands can be sensitive to

the assumed strain threshold while the value for loose sands is not as sensitive (Wu et al. 2004).

Additionally, ambiguity exists in how the ru-based criterion should be interpreted in determining

liquefaction triggering in cyclic tests. As stated previously, liquefaction is initiated when σ’v = 0,

which corresponds to ru = 1, but only when the applied cyclic loading is zero. In this case ru is

referred to residual ru (i.e., ru,Residual) and is the value of ru in cyclic tests at times when the applied

cyclic deviatoric stress (for CTRX tests) or cyclic shear stress (for CDSS or CTS tests) equals zero

(e.g., ru = ru,Residual. This occurs two times during a loading cycle for a specimen that does not have

an imposed static bias imposed). In lieu of using ru,Residual = 1 to def

development of an energy-based liquefaction evaluation procedure kristin jane … · 2020. 9....

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