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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
Development of an Energy-based Liquefaction Evaluation Procedure
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.
Development of an Energy-based Liquefaction Evaluation Procedure
Kristin Jane Ulmer
ABSTRACT (General Audience)
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. 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
4.7. Acknowledgements ........................................................................................................ 64
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
5.6. Acknowledgements ........................................................................................................ 93
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
Figure 4.2 Case histories from the updated database plotted as normalized dissipated energy vs.
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
Figure 4.3 Case histories from the updated database plotted as normalized dissipated energy vs.
qc1Ncs for various intervals of σ’vo. Blue line represents median (PL = 50%) energy-based
limit-state curve when uncertainties in input parameters are ignored. .................................. 76
Figure 4.4 Case histories from the updated database plotted as normalized dissipated energy vs.
qc1Ncs for various intervals of Mw. Blue line represents median (PL = 50%) energy-based
limit-state curve when uncertainties in input parameters are ignored. .................................. 77
Figure 4.5 Case histories from the updated database plotted as normalized dissipated energy vs.
qc1Ncs for various intervals of amax. Blue line represents median (PL = 50%) energy-based
limit-state curve when uncertainties in input parameters are ignored. .................................. 78
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
uncertainty (σlnVs = 0.35) and high epistemic uncertainty (σlnVs = 0.5) for a hypothetical
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
uncertainty (σlnVs = 0.35) and high epistemic uncertainty (σlnVs = 0.5) for a hypothetical
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
uncertainty, and b) high epistemic uncertainty. .................................................................. 146
Figure 6.21. α(T) curves for the new proposed method for two scenarios: a) low epistemic
uncertainty, and b) high epistemic uncertainty. .................................................................. 146
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
Table C.2 Results from Cyclic Direct Simple Shear Tests (AC, Stress-controlled) on Monterey
0/30 Sand using ru,Trans Criteria .......................................................................................... 180
Table C.3 Results from Cyclic Direct Simple Shear Tests (AC, Stress-controlled) on Monterey
0/30 Sand using γSA Criteria .............................................................................................. 183
Table C.4 Results from Cyclic Direct Simple Shear Tests (AC, Stress-controlled) on Monterey
0/30 Sand using γDA Criteria .............................................................................................. 186
Table C.5 Results from Cyclic Direct Simple Shear Tests (AC, Stress-controlled) on Monterey
0/30 Sand using ΔWEff/σ'vo Criteria ................................................................................... 189
Table C.6 Results from Cyclic Direct Simple Shear Tests (AC, Stress-controlled) on Monterey
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
Soil liquefaction during earthquakes is a phenomenon that can cause tremendous damage to
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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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.
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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.
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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