Springer Natural Hazards
Yu Huang
Miao Yu
Hazard
Analysis of
Seismic Soil
Liquefaction
Springer Natural Hazards
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Yu Huang Miao Yu
•
Hazard Analysis of Seismic
Soil Liquefaction
123
Yu Huang
Department of Geotechnical Engineering,
College of Civil Engineering
Tongji University
Shanghai
China
Miao Yu
Department of Geotechnical Engineering,
College of Civil Engineering
Tongji University
Shanghai
China
and
Faculty of Engineering
China University of Geosciences
Wuhan, Hubei
China
ISSN 2365-0656
Springer Natural Hazards
ISBN 978-981-10-4378-9
DOI 10.1007/978-981-10-4379-6
ISSN 2365-0664
(electronic)
ISBN 978-981-10-4379-6
(eBook)
Library of Congress Control Number: 2017935832
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Preface
Liquefaction is one of the major causes of damage to soils and foundations during
earthquakes and is one of the most important aspects in seismic research and the
design of foundations. Recent seismic liquefaction-related damage to soils and
foundations demonstrates the need for comprehensive hazard analysis of seismic
soil liquefaction, in order to reduce related damages and to protect lives. The aim of
this book is to examine the disaster mechanisms and deformation evolution of
seismic liquefaction and provide references for risk assessment.
This book summarizes and generalizes the authors’ research into seismic liquefaction, including mechanisms, deformation characteristics, and comprehensive
evaluations. First, macroscopic liquefaction phenomena observed since the beginning of this century are reviewed, and then the liquefaction potential evaluations
based on in situ testing are discussed. Then, the studies of the dynamic mechanisms
of liquefaction via laboratory and model tests are presented. In addition, numerical
simulations for deformation analysis of liquefiable soils are described. Finally, a
comprehensive evaluation of liquefaction damage during earthquakes is proposed.
This book has seven chapters. Chapter 1, the introduction, gives a preliminary
presentation of seismic hazards in the world, and liquefaction hazards are detailed
using typical earthquake damage examples. After introducing these natural hazards,
current major components of liquefaction hazard analysis are reviewed.
In Chap. 2, major earthquakes and related liquefaction damage since the
beginning of this century worldwide are reviewed in detail. Conventional liquefaction phenomena and macroscopic characteristics (e.g., sand boiling or sand
blows, ground cracking or fissures, and lateral spread) are summarized by analyzing
observations from various earthquakes. In addition, several new phenomena related
to earthquakes in the twenty-first century are introduced.
Chapter 3 presents liquefaction potential evaluations based on in situ testing,
including the standard penetration, cone penetration, dynamic cone penetration or
Becker penetration, and wave velocity tests.
The next three chapters focus on dynamic behavior and deformation characteristic analyses of seismic liquefaction by laboratory experiment (Chap. 4), centrifugal shaking table testing (Chap. 5), and numerical simulation (Chap. 6). In the
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Preface
above, accelerations, excess porewater pressures, and deformations are captured.
These are all useful for the prevention and control of geo-disasters.
Chapter 7 presents a comprehensive evaluation of liquefaction damage during
earthquakes in light of performance-based seismic design criteria and reliability
analyses.
The mechanisms and deformation characteristics of liquefaction described in this
book can provide a reference for safe construction and seismic assessment. This
will benefit graduate students, engineers, and researchers in the field of geological,
geotechnical, and civil engineering.
Our work in liquefaction analysis has been profoundly influenced by the contributions of Prof. Atsushi Yashima and Prof. Kazuhide Sawada (Gifu University,
Japan), Prof. Feng Zhang (Nagoya Institute of Technology, Japan), and many others
working in this field. We express our deep gratitude to these illustrious scholars.
A number of former students in our research group at Tongji University are
gratefully acknowledged for compiling the manuscripts, especially Mr. Liang Hao,
Mr. Zhijing Zhuang, Dr. Ximiao Jiang, Mr. Chen Jin, Mr. Guanghui Li, Dr. Hu
Zheng, Dr. Wuwei Mao, and Dr. Weijie Zhang, who contributed to the comprehensive research work. Writing and editing were supported by Ph.D. students
Mr. Liuyuan Zhao, Ms. Lin Wang, Mr. Chongqiang Zhu, Ms. Yangjuan Bao, and
Mr. Min Xiong, and master’s students Mr. Wenbin Deng, Mr. Zhuoqiang Wen,
and Mr. Junjia Liu, and other group members.
We express our deep appreciation for financial support from the National Natural
Science Foundation of China (Grant Nos. 41625011, 41372355, 40841014 and
40802070), National Basic Research Program of China (973 Program) through
Grant No. 2012CB719803, National Key Technologies R&D Program of China
(Grant No. 2012BAJ11B04), and the Program of Shanghai Academic/Technology
Research Leader (Grant No.17XD1403700).
Finally, the authors would also like to thank the relevant publishers, including
Springer, Elsevier, American Society of Civil Engineers (ASCE), John Wiley and
Sons, and NRC Research Press, for their kind permission to reuse the content in this
book. The permissions include our previously published articles and other scholars’
works in this field, which would support the completeness of this book and better
understanding for readers.
Because of our limited knowledge as well as time, there are some inevitable
omissions and errors in this book. Therefore, we welcome all constructive criticism
and corrections toward continually improving the hazard analysis of seismic soil
liquefaction.
Shanghai, China
January 2017
Prof. Yu Huang
Contents
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2 Macroscopic Characteristics of Seismic Liquefaction . . . . . . . . . . . . .
2.1 Characteristics of Seismic Liquefaction . . . . . . . . . . . . . . . . . . . . .
2.1.1 Earthquakes Induced Widespread Liquefaction since
the Beginning of this Century . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Characteristics of Liquefaction Distribution. . . . . . . . . . . . .
2.1.3 Classification of Liquefaction Phenomena . . . . . . . . . . . . . .
2.1.4 Related Liquefaction Damage . . . . . . . . . . . . . . . . . . . . . . .
2.2 Case Study: Field Investigation of Liquefaction from the 2008
Wenchuan Earthquake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Introduction to Wenchuan Earthquake. . . . . . . . . . . . . . . . .
2.2.2 Survey Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Liquefaction Distribution and Characteristics . . . . . . . . . . .
2.2.4 Foundation Damage Related to Liquefaction
in the Dujiangyan Area . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 New Liquefaction Phenomena During Recent Earthquakes . . . . . .
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Seismic Hazards and Related Liquefaction Damage
Worldwide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Multi-approaches for Hazard Analysis of Seismic Soil
Liquefaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 In Situ Test Analysis . . . . . . . . . . . . . . . . . . . . .
1.2.2 Experimental Analysis. . . . . . . . . . . . . . . . . . . .
1.2.3 Numerical Simulation . . . . . . . . . . . . . . . . . . . .
1.3 Book Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3 Liquefaction Potential Evaluation Based on In Situ Testing . . .
3.1 Introduction to Liquefaction Evaluation Based
on In Situ Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Liquefaction Evaluation Procedure Based on In Situ
Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Assessment of “Triggering” (Initiation) of Soil
Liquefaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 Assessment of Liquefaction Resistance . . . . . . . . . . . .
3.2 In Situ Testing for Liquefaction Potential Evaluation . . . . . . .
3.2.1 Standard Penetration Test . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Cone Penetration Test . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Wave Velocity Test. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Becker Penetration and Dynamic Penetration Tests . . .
3.3 Assessment of Site Liquefaction Potential and Seismic
Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Assessment of Site Liquefaction Potential . . . . . . . . . .
3.3.2 Assessment of Seismic Deformation . . . . . . . . . . . . . .
3.3.3 Case Study of Liquefaction Evaluation Based on SPT
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Contents
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4 Laboratory Experimental Study on Dynamic Characteristics
of Liquefiable Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Dynamic Triaxial Tests of Soil Dynamic Properties for Large
Strain Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Introduction of Dynamic Triaxial Tests . . . . . . . . . . . . . . . .
4.2.2 Laboratory Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Test Analysis of Test Results . . . . . . . . . . . . . . . . . . . . . . .
4.3 Resonant Column Tests of Soil Dynamic Properties for Small
Strain Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Introduction of Resonant Column Tests . . . . . . . . . . . . . . .
4.3.2 Laboratory Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Comprehensive Liquefaction Potential and Dynamic
Characteristic Analysis of a Reservoir Dam Foundation . . . . . . . . .
4.4.1 Site Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Analysis of Standard Penetration Test Results . . . . . . . . . .
4.4.3 Analysis of Dynamic Triaxial Test Results . . . . . . . . . . . . .
4.4.4 Analysis of Resonant Column Test Result . . . . . . . . . . . . .
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Contents
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5 Physical Model Testing for Dynamic Characteristics of Seismic
Soil Liquefaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Principles and Scaling Relationships in Geotechnical Centrifuge
Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Principles of Geotechnical Centrifuge Modeling . . . . . . . . .
5.2.2 Scaling Relationships in Geotechnical Centrifuge
Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Physical Model Testing for Dynamic Characteristics
of a Reservoir Dam Foundation . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Dynamic Centrifuge Modeling Tests . . . . . . . . . . . . . . . . . .
5.3.3 Model Test Result Analysis . . . . . . . . . . . . . . . . . . . . . . . .
5.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Numerical Simulation for Deformation of Liquefiable Soils . . . .
6.1 Numerical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Constitutive Models for Liquefiable Soils . . . . . . . . . . . . . . . .
6.2.1 Nonlinear Constitutive Model . . . . . . . . . . . . . . . . . . .
6.2.2 Cycle Elastoplastic Constitutive Model . . . . . . . . . . . .
6.3 Simulation and Analysis of Various Engineering Problems . .
6.3.1 Earth Embankment Foundation on Liquefiable Soils . .
6.3.2 Mitigation of Liquefaction-Induced Soil Deformation
of Sandy Ground Improved by Cement Grouting . . . .
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 Comprehensive Evaluation of Liquefaction Damage During
Earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Comprehensive Evaluation Methods of Seismic Liquefaction
Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.1 Field Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.2 Laboratory Dynamic Test . . . . . . . . . . . . . . . . . . . . . .
7.2.3 Dynamic Centrifuge Model Test . . . . . . . . . . . . . . . . .
7.2.4 Security Evaluation of Seismic Liquefaction Based
on the PBSD Criteria . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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About the Authors
Prof. Yu Huang first author of this book, born 1973, received his Ph.D. in
geotechnical engineering from Tongji University, Shanghai, China in 1999.
Professor Huang’s primary area of research includes earthquake engineering
geology, geological disasters, computational geomechanics, foundation engineering, and environmental geology. He has authored more than 170 technical publications, including more than 50 papers in international refereed journals such as the
Engineering Geology, Landslides, Journal of Geotechnical and Geoenvironmental
Engineering (ASCE), Bulletin of Engineering Geology and the Environment,
Natural Hazards, Environmental Earth Sciences, Earthquake Engineering and
Structural Dynamics, Soil Dynamics and Earthquake Engineering, and Journal of
Performance of Constructed Facilities (ASCE). As the first author, he has written a
monograph entitled “Geo-disaster modeling and analysis: An SPH-based approach”
published by Springer-Verlag in 2014. He now serves on the editorial board for the
Engineering Geology (Elsevier), Bulletin of Engineering Geology and the
Environment (Springer), Geotechnical Research (ICE), and Geoenvironmental
Disasters (Springer).
Dr. Miao Yu Co-author of this book, born 1989, received her Ph.D. in geological
engineering from Tongji University under the guidance of Prof. Yu Huang in 2016.
She is currently working as assistant professor at the China University of
Geosciences, Wuhan.
xi
List of Figures
Figure 1.1
Figure 1.2
Figure 1.3
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Figure 2.7
Figure 2.8
Figure 2.9
Distribution of seismicity worldwide, 1900–2013 (United
States Geological Survey 2016) . . . . . . . . . . . . . . . . . . . . . .
Widespread liquefaction in Disneyland parking area
(reprinted from Bhattacharya et al. (2011) with permission of
Elsevier) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Main logical structure of the book . . . . . . . . . . . . . . . . . . . .
Sand boiling by eruption on the surface through existing
cracks (reprinted from Bhattacharya et al. (2011) with
permission of Elsevier) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cracks observed with ejected sand (Pacific Earthquake
Engineering Research Center 2001a) . . . . . . . . . . . . . . . . . .
East–West view of lateral spread of embankment at Capitol
Interpretive Center (Pacific Earthquake Engineering
Research Center, 2001b) . . . . . . . . . . . . . . . . . . . . . . . . . . .
Aerial photograph of central Kaiapoi River, indicating
former river channel (reprinted from Wotherspoon et al.
(2012) with permission of Elsevier) . . . . . . . . . . . . . . . . . . .
Map of investigation sites (modified from Jiang 2009) . . . .
Liquefaction points in the Wenchuan earthquake (modified
from Yuan et al. 2009) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Liquefaction of fine-grained yellow sand (ejection area
*1094 m2) (reprinted from Huang and Jiang (2010) with
permission of Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Liquefaction of white sand (ejection area *294 m2)
(reprinted from Huang and Jiang (2010) with permission
of Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subsidence caused by liquefaction (length of subsidence
area *12 m, mean width *3 cm) (reprinted from Huang
and Jiang (2010) with permission of Springer) . . . . . . . . . .
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List of Figures
Figure 2.10
Figure 2.11
Figure 2.12
Figure 2.13
Figure 2.14
Figure 2.15
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5
Figure 3.6
Figure 3.7
Figure 4.1
Figure 4.2
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
Cracks caused by liquefaction (cracks distributed over
8 5 m2 area) (reprinted from Huang and Jiang (2010)
with permission of Springer) . . . . . . . . . . . . . . . . . . . . . . . .
Subsidence caused by liquefaction. . . . . . . . . . . . . . . . . . . .
Bridge foundation displacement caused by liquefaction . . . .
Building cracks caused by liquefaction (reprinted from
Huang and Jiang (2010) with permission of Springer). . . . .
Partially collapsed buildings near dam (reprinted from
Huang and Jiang (2010) with permission of Springer). . . . .
Collapsed buildings near Minjiang River (reprinted from
Huang and Jiang (2010) with permission of Springer). . . . .
Analysis process of site liquefaction evaluation . . . . . . . . . .
Magnitude scaling factors derived by various investigators
(reprinted from Youd et al. (2001) with permission of
American Society of Civil Engineers) . . . . . . . . . . . . . . . . .
SPT clean sand base curve for a magnitude‐7.5 earthquake,
with data from liquefaction case histories (reprinted from
Youd et al. (2001) with permission of American Society of
Civil Engineers) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic diagram of downhole seismic test . . . . . . . . . . . .
Apparatus for the dynamic penetration test (reprinted from
Cao et al. (2012) with permission of American Society of
Civil Engineers) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Volumetric strain for saturated sand based on CSR and
(N1)60 (reprinted from Tokimatsu and Seed (1987) with
permission of American Society of Civil Engineers) . . . . . .
Stratum distribution of case study . . . . . . . . . . . . . . . . . . . .
Stress change of dynamic triaxial specimen at under isobaric
consolidation conditions (Modified on Seed
and Lee 1966) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stress changes of dynamic triaxial specimen under
anisobaric consolidation conditions (Modified on Seed and
Lee 1966) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dynamic triaxial stress path diagram under cycle loading . .
GDS dynamic triaxial apparatus . . . . . . . . . . . . . . . . . . . . .
Soil cutter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Soil-fixed knives and fretsaw . . . . . . . . . . . . . . . . . . . . . . . .
Half-open mold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rubber hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sieve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mortar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Oven . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Compaction device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Electronic scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
..
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23
24
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49
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.
.
.
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.
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.
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.
.
.
.
64
64
66
66
67
67
68
68
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68
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69
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.
.
.
.
.
.
.
.
.
.
.
List of Figures
Figure
Figure
Figure
Figure
4.14
4.15
4.16
4.17
Figure 4.18
Figure 4.19
Figure 4.20
Figure 4.21
Figure 4.22
Figure 4.23
Figure 4.24
Figure 4.25
Figure 4.26
Figure 4.27
Figure 4.28
Figure 4.29
Figure 4.30
Figure 4.31
Figure 4.32
Figure 4.33
Figure 4.34
Figure 5.1
Figure 5.2
Figure 5.3
xv
Vernier caliper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dried soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Grinded and sieved soil . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Time series data of pure silty sand sample
for varying CSR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CSR versus number of cycles to liquefaction according to
two criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
V. P. Drnevich resonant column apparatus . . . . . . . . . . . . .
Experimental procedures of resonant column test . . . . . . . .
Map showing the location of the project in Tianjin (reprinted
from Huang et al. 2012 with permission from Springer) . . .
Typical dam and soil layer distribution under a dam body
(reprinted from Huang et al. 2012 with permission from
Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Location of SPT boreholes (reprinted from Huang et al.
2012 with permission from Springer) . . . . . . . . . . . . . . . . .
Time series data for dynamic stress = 90 kPa (reprinted from
Huang et al. 2012 with permission from Springer) . . . . . . .
Time series data for dynamic stress = 65 kPa (reprinted from
Huang et al. 2012 with permission from Springer) . . . . . . .
Dynamic stress change with consolidation pressure
(reprinted from Huang et al. 2012 with permission from
Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CSR versus number of cycles to liquefaction change with
consolidation pressure (reprinted from Huang et al.
2012 with permission from Springer) . . . . . . . . . . . . . . . . .
Time series data of stress, strain, and porewater pressure
(isobaric consolidation) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Time series data of stress, strain, and porewater pressure
(anisobaric consolidation) . . . . . . . . . . . . . . . . . . . . . . . . . .
Liquefaction resistance of silts with three different dry
densities (owing to the loss of clay content during sample
preparation, there is error of 15%) . . . . . . . . . . . . . . . . . . . .
Liquefaction resistance of undisturbed
and reconstituted soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Relationship between dynamic shear modulus Gd and shear
strain c (Gd-c curve) of silt in the west of Tianjin . . . . . . .
Relationship between shear modulus ratio Gd/G0 and shear
strain c (Gd/G0 − c curve) of silt in western Tianjin . . . . . .
Relationship between damping ratio D and shear strain c
(D-c curve) of silt in western Tianjin . . . . . . . . . . . . . . . . .
Stress in prototype and scale model. . . . . . . . . . . . . . . . . . .
Coordinate system in 1/N scale model. . . . . . . . . . . . . . . . .
Acceleration of point A′ in local coordinate system . . . . . .
..
..
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69
70
70
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74
..
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77
78
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79
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.
.
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90
94
95
95
.
.
.
.
xvi
List of Figures
Figure 5.4
Figure 5.5
Figure 5.6
Figure
Figure
Figure
Figure
5.7
5.8
5.9
5.10
Figure 5.11
Figure 5.12
Figure 5.13
Figure 5.14
Figure 5.15
Figure 5.16
Figure 5.17
Figure 5.18
Figure 5.19
Figure 5.20
Figure 5.21
Stress relationship between prototype and scale model . . . .
Cross-section diagram of embankment foundation (reprinted
from Huang and Zhu (2016) with permission from American
Society of Civil Engineers) . . . . . . . . . . . . . . . . . . . . . . . . .
Overview of the TJL-150 geotechnical centrifuge (reprinted
from Huang and Zhu (2016) with permission from American
Society of Civil Engineers) . . . . . . . . . . . . . . . . . . . . . . . . .
Overview of the shaking table . . . . . . . . . . . . . . . . . . . . . . .
Configuration of the laminar model box . . . . . . . . . . . . . . .
Rotational viscometer used in experiment . . . . . . . . . . . . . .
Relationship between concentration of CMC and viscosity
(at indoor temperature) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Geotextile tensile testing machine . . . . . . . . . . . . . . . . . . . .
Relationship of shear modulus ratio and damping ratio with
shear strain for Shanghai soil (reprinted from Huang and Zhu
(2016) with permission from American Society of Civil
Engineers) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of ground acceleration between official data and
SHAKE91 simulated result (reprinted from Huang and Zhu
(2016) with permission from American Society of Civil
Engineers) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Input earthquake wave of dynamic centrifuge model tests
(reprinted from Huang and Zhu (2016) with permission from
American Society of Civil Engineers) . . . . . . . . . . . . . . . . .
Model dimensions and instrumental layout (unit mm)
(reprinted from Huang and Zhu (2016) with permission from
American Society of Civil Engineers) . . . . . . . . . . . . . . . . .
Time history of acceleration in embankment body model test
(reprinted from Huang and Zhu (2016) with permission from
American Society of Civil Engineers) . . . . . . . . . . . . . . . . .
Time history of acceleration in embankment toe model test
(reprinted from Huang and Zhu (2016) with permission from
American Society of Civil Engineers) . . . . . . . . . . . . . . . . .
Time history of excess pore pressure ratio in embankment
body model test (reprinted from Huang and Zhu (2016) with
permission from American Society of Civil Engineers) . . . .
Time history of excess pore pressure ratio in embankment
toe model test (reprinted from Huang and Zhu (2016) with
permission from American Society of Civil Engineers) . . . .
Time history of vertical displacement in embankment body
model test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Time history of vertical displacement in embankment toe
model test (reprinted from Huang and Zhu (2016) with
permission from American Society of Civil Engineers) . . . .
..
97
. . 100
.
.
.
.
.
.
.
.
101
102
102
103
. . 104
. . 105
. . 106
. . 107
. . 107
. . 108
. . 110
. . 111
. . 112
. . 113
. . 114
. . 114
List of Figures
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 6.5
Figure 6.6
Figure 6.7
Figure 6.8
Figure 6.9
Figure 6.10
Figure 6.11
Figure 6.12
Figure 6.13
Figure 6.14
Figure 6.15
xvii
Relationship between shear modulus ratio and shear strain of
Shanghai clay (reprinted from Huang et al. (2009b) with
permission of Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Relationship between damping ratio and shear strain of
Shanghai clay (reprinted from Huang et al. (2009b) with
permission of Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Relationship between pore-water pressure ratio and N of
Shanghai clay (reprinted from Huang et al. (2009b) with
permission of Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of theoretical and experimental results of
undrained torsional shear tests (after Matsuo et al. 2000)
a shear stress—shear strain b effective stress paths . . . . . . .
Configuration of earth embankment (unit: m) (reprinted from
Huang et al. (2009a) with permission of Springer) . . . . . . .
Simulation of liquefaction strength of liquefiable sand layers
(reprinted from Huang et al. (2009a) with permission of
Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Input earthquake wave with maximum acceleration 1.5 m/s2
(reprinted from Huang et al. (2009a) with permission of
Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Accelerations at points A through D (reprinted from Huang
et al. (2009a) with permission of Springer) . . . . . . . . . . . . .
Horizontal and vertical displacement at points A through
D (reprinted from Huang et al. (2009a) with permission of
Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Configuration of earth embankment at end of earthquake
(reprinted from Huang et al. (2009a) with permission of
Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Time histories of excess pore-water pressure ratios (ηEPWPR)
at points B and D (reprinted from Huang et al. (2009a) with
permission of Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Excess pore-water pressure ratio of earth embankment at end
of earthquake (reprinted from Huang et al. (2009a) with
permission of Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic cross-section showing ground improvement
constructed as a liquefaction countermeasure for a sluice
gate (reprinted from Huang et al. (2008b) with permission of
Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numerical simulation of undrained response of foundation
soil, As (reprinted from Huang et al. (2008b) with
permission of Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Time histories of horizontal displacements (reprinted from
Huang et al. (2008b) with permission of Springer) . . . . . . .
. . 122
. . 122
. . 123
. . 125
. . 128
. . 130
. . 130
. . 131
. . 132
. . 132
. . 133
. . 133
. . 134
. . 135
. . 136
xviii
Figure 6.16
Figure 6.17
Figure 6.18
Figure 7.1
Figure 7.2
Figure 7.3
Figure 7.4
Figure 7.5
Figure 7.6
Figure 7.7
Figure 7.8
Figure 7.9
Figure 7.10
Figure 7.11
Figure 7.12
Figure 7.13
Figure 7.14
List of Figures
Time histories of vertical displacements (reprinted from
Huang et al. (2008b) with permission of Springer) . . . . . . .
Time histories of accelerations (reprinted from Huang et al.
(2008b) with permission of Springer) . . . . . . . . . . . . . . . . .
Time histories of excess pore-water pressure ratios (reprinted
from Huang et al. (2008b) with permission of Springer) . . .
Typical intensity non-stationary earthquake
acceleration sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Characteristics of typical non-stationary seismic
accelerations for sample ensembles and targets . . . . . . . . . .
Performance evaluation system of earthen
and rockfill dam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Main cross section of earthen dam (reprinted from Huang
and Xiong (2016) with permission from
John Wiley and Sons) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The acceleration-time history corresponding to the OBE . . .
Vertical displacement time history of dam
crest under OBE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acceleration time history corresponding to SEE . . . . . . . . .
The vertical displacement-time history of the dam crest
under the SEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Typical sample curve of OBE seismic ground motion . . . . .
Probability density evolution surface for settlement of
earthen dam under OBE . . . . . . . . . . . . . . . . . . . . . . . . . . .
CDF for permanent settlement of earthen dam under OBE
(reprinted from Huang and Xiong (2016) with permission
from John Wiley and Sons) . . . . . . . . . . . . . . . . . . . . . . . . .
The typical sample curve of the seismic ground motion
of the SEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The probability density evolution surface of the settlement
of the earth dam under the SEE . . . . . . . . . . . . . . . . . . . . .
CDF of permanent settlement of earthen dam under SEE
(reprinted from Huang and Xiong (2016) with permission
from John Wiley and Sons) . . . . . . . . . . . . . . . . . . . . . . . . .
. . 136
. . 136
. . 137
. . 151
. . 152
. . 153
. . 154
. . 155
. . 156
. . 157
. . 158
. . 159
. . 160
. . 161
. . 162
. . 163
. . 164
List of Tables
Table 1.1
Table 2.1
Ten largest earthquakes since 1900 . . . . . . . . . . . . . . . . . . . .
General information on major earthquakes in the twenty-first
century (reprinted from Huang and Yu (2013) with permission
of Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 2.2 Earthquake damage survey list . . . . . . . . . . . . . . . . . . . . . . .
Table 3.1 Characteristic depth of liquefied soil (m) (Ministry of
Construction of China 2010) . . . . . . . . . . . . . . . . . . . . . . . . .
Table 3.2 Cases of soil liquefaction containing fine clay particles (Based
on: Bol et al. 2010; Hwang and Yang 2001; Tan et al. 2013;
Tokimatsu and Yoshimi 1983). . . . . . . . . . . . . . . . . . . . . . . .
Table 3.3 Safety factors of the three codes . . . . . . . . . . . . . . . . . . . . . .
Table 3.4 Advantages and disadvantages of field tests (reprinted from
Youd et al. (2001) with permission of American Society of
Civil Engineers) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 3.5 Value of N0 for Chinese code (Ministry of Construction of
China 2010 and Ministry of Water Resources
of China 2008) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 3.6 SPT for sandy silt and sand relative density (Ministry of
Construction of China 2009) . . . . . . . . . . . . . . . . . . . . . . . . .
Table 3.7 Boundaries of soil behavior type (reprinted from Robertson
and Wride (1998) with permission of NRC
Research Press) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 3.8 Reference values for critical shear wave velocity (m/s)
(Ministry of Construction of China 2009) . . . . . . . . . . . . . . .
Table 3.9 Assessment of site liquefaction potential (Japan Road
Association 2002; Ministry of Construction of China 2010) .
Table 3.10 Liquefaction potential evaluation based on SPT . . . . . . . . . .
Table 4.1 Laboratory soil dynamic experiments . . . . . . . . . . . . . . . . . .
Table 4.2 Determination of liquefaction index and liquefaction level
(code for Seismic Design of Buildings (DGJ08-9-2013)). . . .
Table 4.3 Cycles to liquefaction according to two criteria . . . . . . . . . . .
..
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19
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62
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74
xix
xx
Table 4.4
Table 4.5
Table 4.6
Table 5.1
Table 5.2
Table 5.3
Table 6.1
Table 6.2
Table 6.3
Table 6.4
Table 6.5
Table 6.6
Table 7.1
List of Tables
Liquefaction evaluation results for selected boreholes by SPT
(seismic intensity VII) (reprinted from Huang et al. 2012 with
permission from Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . .
Results of liquefaction evaluation by Seed’s simplified
method (seismic intensity VII) (reprinted from Huang et al.
2012 with permission from Springer) . . . . . . . . . . . . . . . . . .
Relation between grain composition
and liquefaction resistance . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scaling relationship (Based on Ko 1988) . . . . . . . . . . . . . . . .
Parameters of soil deposits of embankment foundation . . . . .
Evaluation of liquefaction potential based on dynamic triaxial
tests (seismic intensity VII) . . . . . . . . . . . . . . . . . . . . . . . . . .
Reference values of A, B, and C (reprinted from Huang et al.
(2009b) with permission of Springer) . . . . . . . . . . . . . . . . . .
Reference values of a and b (reprinted from Huang et al.
(2009b) with permission of Springer) . . . . . . . . . . . . . . . . . .
Parameters of E-P model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameters used for sands and clays (elastoplastic model)
(reprinted from Huang et al. (2009a) with
permission of Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameters used for sands (Ramberg-Osgood model)
(reprinted from Huang et al. (2009a) with
permission of Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Soil parameters used for numerical analysis of the case
(reprinted from Huang et al. (2008b) with
permission of Springer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Seismic security grade classification of SEE . . . . . . . . . . . . .
..
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..
81
..
88
..
99
. . 106
. . 116
. . 122
. . 123
. . 124
. . 129
. . 129
. . 134
. . 157
Chapter 1
Introduction
1.1
Seismic Hazards and Related Liquefaction Damage
Worldwide
An earthquake can be defined as the result of a sudden energy release of the Earth’s
crust that creates seismic waves and leads to shaking of the ground. Earthquakes
happen frequently and have a wide distribution around the world according to
statistics. Figure 1.1 shows the distribution of seismicity worldwide from 1900 to
2013; different colors indicate different earthquake depths. Powerful earthquakes
could lead to great loss of life and property owing to the shaking and secondary
destruction from seismic liquefaction or tsunamis. The 10 largest earthquakes since
1900 are listed in Table 1.1. It can be seen that three-tenths of the largest earthquakes occurred in the first 10 years of the 21st century.
During these strong earthquakes, liquefaction hazards were widely distributed
and caused serious losses. Since the 1964 Niigata Earthquake (Japan) and 1964
Great Alaskan Earthquake (United States), seismic liquefaction has been studied
extensively (Seed and Idriss 1967). However, over the past five decades, research
into seismic liquefaction is still being conducted on recent earthquakes (Huang et al.
2014). Liquefaction of gravelly soils was found in the 2008 Wenchuan Earthquake,
with mean grain sizes ranging from 1 to >30 mm (Cao et al. 2011; Huang and Jiang
2010). On March 11, 2011, the Tohoku earthquake (Mw 9.0) triggered widespread
liquefaction in the Tohoku and Kanto regions of Japan. Damage to structures was
extensive, including widespread liquefaction around the parking area of Disneyland
(Fig. 1.2) (Bhattacharya et al. 2011). Since the beginning of the 21st century,
several new liquefaction phenomena related to earthquakes have been found, which
will be introduced in detail in Chap. 2. Further seismic liquefaction data must be
collected, and comprehensive evaluation of liquefaction should be conducted to
improve safety in earthquake-prone areas.
© Springer Nature Singapore Pte Ltd. 2017
Y. Huang and M. Yu, Hazard Analysis of Seismic Soil Liquefaction,
Springer Natural Hazards, DOI 10.1007/978-981-10-4379-6_1
1
2
1
Introduction
Fig. 1.1 Distribution of seismicity worldwide, 1900–2013 (United States Geological Survey
2016)
Table 1.1 Ten largest earthquakes since 1900
Earthquake
Country
Date (local time)
Magnitude
1
2
3
Valdivia
Alaska
Andreanof Islands
May 22, 1960
March 28, 1964
March 9, 1957
9.5
9.2
9.1
4
5
6
7
8
9
10
Tohoku
Kamchatka
Colombia–Ecuador
Offshore Maule
Rat Islands
Assam–Tibet
Andreanof Islands
Chile
USA
Andreanof Islands,
Aleutian Islands
Japan
Russia
Colombia–Ecuador
Chile
USA
China
USA
March 11, 2011
November 4, 1952
January 31, 1906
February 27, 2010
February 4, 1965
August 15, 1950
March 9, 1957
9.0
9.0
8.8
8.8
8.7
8.6
8.6
1.2
Multi-approaches for Hazard Analysis
of Seismic Soil Liquefaction
It is very important to conduct comprehensive analysis of liquefaction hazards so as
to mitigate those hazards. The current analysis methods for liquefaction hazards
contain some difficulties. First, most liquefaction analysis only uses a single
method, which may lead to a lack of validation of the analysis results. Second, most
liquefaction analysis is semi-quantitative analysis; however, comprehensive quantitative analysis is required. Therefore, multi-approaches for liquefaction hazard
1.2 Multi-approaches for Hazard Analysis of Seismic Soil Liquefaction
3
Fig. 1.2 Widespread liquefaction in Disneyland parking area (reprinted from Bhattacharya et al.
(2011) with permission of Elsevier)
analysis are important. The main approaches of comprehensive analysis include
in situ testing and experimental analysis of liquefaction hazards, numerical simulation of liquefaction hazards, and liquefaction hazard evaluation.
1.2.1
In Situ Test Analysis
Typically, there are two methods for assessing soil liquefaction under dynamic
loads, namely, laboratory experiments and in situ testing (Iwasaki et al. 1984; Moss
et al. 2006; Zhou and Chen 2007; Seed and Lee 1966). Undisturbed soil samples
are very difficult to obtain owing to the difficulty of soil sampling and preservation,
which hinder laboratory testing in liquefaction studies. For this reason, the in situ
testing method has a wide range of project applications.
The in situ testing methods that can be used for site liquefaction evaluation
include the standard penetration test (SPT), cone penetration test (CPT), dynamic
cone penetration test (DPT) or Becker penetration test (BPT), and shear wave
velocity test (VS) (Moss et al. 2006; Idriss and Boulanger 2006; Lenz and Baise
2007; Sonmez and Gokceoglu 2005; Lin et al. 2004; Andrus et al. 2004). Among
them, SPT is currently the method most widely used worldwide to test the strength
and characteristics of in situ soil.
4
1
Introduction
Based on the in situ test results, the most highly recommended methods for
evaluating site liquefaction are introduced in this book, which includes three procedures: (I) assessment of “triggering” (initiation) of soil liquefaction;
(II) assessment of liquefaction resistance based on in situ testing; (III) assessment of
site liquefaction index and deformation of liquefiable sites. The safety factor is the
most important value for evaluating the liquefaction potential at engineering sites.
However, site investigation using one method is unsafe; if possible, two or more
test procedures should be applied to assure adequate data for evaluation of liquefaction resistance. In addition, for more detailed assessment, laboratory testing will
be introduced in Chap. 3. A deterministic analysis method is needed to determine
the safety factor of an entire site. However, probability analysis may therefore be
more reasonable; this method will be introduced in Chap. 7.
1.2.2
Experimental Analysis
In addition to in situ testing, dynamic characteristics and liquefaction probability
estimation can also be achieved by laboratory experimental methods and analysis,
which mainly include the laboratory dynamic test, dynamic centrifuge model test,
and shaking table test (Xenaki and Athanasopoulos 2008; Zhou and Chen 2005;
Popescu and Prevost 1993; Zhou et al. 2009; Dungca et al. 2006).
Laboratory soil dynamic experiments include the dynamic triaxial test, resonant
column test, simple shear test, torsion shear test, and shaking table test. Among
these, the dynamic triaxial and resonant column tests are the two main laboratory
methods used. The former is applied to a large strain scope range of more than 10−4
and the latter to a small strain scope range from 10−6 to 10−4. Many studies have
been conducted on the dynamic characteristics and liquefaction mechanisms of
liquefiable soils using laboratory dynamic tests such as liquefaction resistance,
shear modulus, and others. Seed and Lee (1966) proposed the definition of initial
liquefaction according to dynamic triaxial test results, namely, when the pore water
pressure is equal to the confining pressure for the first time, the soil achieves the
state of initial liquefaction.
Laboratory tests (such as dynamic triaxial and resonant column tests) focus on
small soil samples. To effectively reproduce the dynamic response of the earth’s
structure, physical model tests are useful because they enable the study and analysis
of various engineering problems by better control of material properties and
boundary conditions. Physical model tests such as shaking table tests and dynamic
centrifuge model tests are important for studying the seismic response of saturated
soil under controlled environments. Shaking table tests were developed in the
1970s, and large-scale dynamic tests are dedicated to the study of soil liquefaction
traits. Geotechnical centrifuge model test technology used to research seismic
dynamic problems was first conducted by the University of Cambridge in the late
1970s. Because the centrifuge can meet key similar conditions of the same stress
1.2 Multi-approaches for Hazard Analysis of Seismic Soil Liquefaction
5
level, continued improvement of this technology has gradually made the centrifuge
model test an important research tool in the field of geotechnical engineering.
In this book, the dynamic triaxial test is applied to a large strain scope range of
more than 10−4 and the resonant column test applied to a small strain scope range
from 10−6 to 10−4, because soil shear strain amplitude and its dynamic characteristics are closely related. After introduction of the experimental analysis method, a
case study is proposed in which both in situ and lab experimental methods (including the standard penetration test, dynamic triaxial test, and resonant column
test) are used to comprehensively analyze liquefaction potential and dynamic
characteristics. For laboratory model tests, we focus on the dynamic features of
seismic liquefaction of soil using centrifugal shaking tables. The principal and
scaling rules of dynamic centrifuge model tests are introduced in detail. A case
study of a constructed embankment subject to earthquake conditions is presented.
The physical modeling method is proved to be effective for researching the dynamic
characteristics of seismic liquefaction.
1.2.3
Numerical Simulation
Early research on seismic liquefaction placed greater emphasis on the likelihood of
liquefaction occurring than on deformation prediction of post-liquefaction soils.
With the accumulation of data on seismic liquefaction damage, it has been found
that large ground displacement caused by seismic liquefaction is one of the main
reasons for damage to highways, railways, bridges, and other lifeline engineering
(Huang and Yu 2013). Hence, the research on liquefaction analysis has gradually
transformed from liquefaction potential assessment to deformation analysis.
Therefore, it is necessary to develop an appropriate numerical modeling method for
evaluating the deformation of liquefiable soils.
The method for dynamic analysis of soil developed from the equivalent linear
seismic total stress analysis method in the 1970s to the undrained effective stress
analysis method of combining dynamic response analysis and soil liquefaction and
softening. The drainage effective stress analysis method was also developed, which
considers the diffusion and dissipation of pore water pressure of soil during
earthquakes in the 1980s. Since the 1990s, Dafalias and Popov (1975) and Pastor
et al. (1990) further developed the effective stress method using the approach of
elastic–plastic analysis from the perspective of the constitutive model. This analytical method has developed from 2D to 3D through the achievements of
researchers worldwide, which have mainly been aimed at investigation from the
aspect of the total stress method, effective stress analysis method, and selection of
the constitutive model.
Two schemes can be used for seismic response simulation: the total stress-based
method and the effective stress-based method. The total stress-based method has
6
1
Introduction
difficulties in describing the whole process of liquefaction because it cannot simulate the reduction in soil stiffness and strength after liquefaction (Biot 1941).
Hence, the total stress-based method is usually adopted to identify the initial liquefaction stage while the effective stress-based method, which can model the soil
skeleton and pore water interaction, can capture the subsequent stages of liquefaction. A fully coupled numerical procedure called UBCSAND is adopted to
model liquefaction and the resulting displacement of centrifuge tests (Byrne et al.
2004). The dynamic response of a clayey embankment built on a liquefiable
foundation was analyzed using a finite element method, DIANA-SWANYNE II,
which is based on effective stress (Aydingun and Adalier 2003). Di et al. (2008)
used a two-dimensional effective stress-based analysis code to simulate the seismic
performance of a river dike. These studies suggest that numerical schemes based on
effective stress can reliably assess the safety and antiliquefaction performance of
embankments.
The constitutive model can be divided into two broad categories: one is the
equivalent linear analysis method based on the equivalent viscoelastic model, and
the other is the nonlinear analysis method based on the viscoelastic–plastic model.
The equivalent linear analysis model, which can more reasonably determine the
acceleration, shear stress, and shear strain of soil during an earthquake, is widely
used in the dynamic analysis of soil. However, this model cannot consider the
cumulative deformation of soil under dynamic load owing to the disadvantage of
describing only nonlinearity and hysteresis in the dynamic stress–strain relationship
and using the same modulus during loading and unloading. To calculate the
residual deformation and permanent deformation of soil after an earthquake, the
residual deformation model must be established. The generalized elastic–plastic
model includes the following: the multiple yield surface model, bounding surface
model, and multiple shear mechanism model. Using the generalized elastic–plastic
model is closer to the actual soil dynamic response process and can fully characterize the dynamic stress–strain relationship of soil. Variations in the different states
of soil matter, such as compression, shear contraction, shear dilation, elastic
deformation, and others, can be reflected in the dynamic constitutive model.
Residual deformation and permanent deformation can be directly calculated using
the dynamic constitutive model of soil state. The disadvantages of the generalized
elastic–plastic model are that the model itself is more complex, parameters are not
easy to accurately obtain, and application is more difficult.
This book presents a numerical study on seismic performance of liquefiable soils
during earthquake loading. Analyses are carried out using an effective stress-based,
finite element program. Our group introduced a nonlinear constitutive model to
successfully simulate the constitutive behavior of the soils in Shanghai (Huang et al.
2009). Based on the cycle elastoplastic constitutive model (Oka et al. 1999) and
Biot dynamic consolidation theory, different engineering problems related to the
deformation of liquefiable soils are simulated and analyzed in detail in this book.
1.2 Multi-approaches for Hazard Analysis of Seismic Soil Liquefaction
Fig. 1.3 Main logical
structure of the book
7
Macroscopic characteristics of seismic liquefaction
Conventional characteristics
of seismic liquefaction
New liquefaction
phenomena during recentcentury earthquakes
Case study: 2008 Wenchuan
Earthquake
Multi-approaches for seismic liquefaction analysis
In-situ test for site
liquefaction evaluation
Laboratory study on
dynamic characteristics of
liquefiable soil
Physical model test for
dynamic characteristics of
liquefaction
Numerical simulation for
deformation of seismic
liquefaction
Comprehensive evaluation for liquefaction damages during
earthquakes
The finite element analysis method is thought to be able to capture the fundamental
aspects of the problems investigated, which can provide scientific references for
engineering design.
1.3
Book Outline
Recent seismic liquefaction-related damage to soils and foundations demonstrate
the need for comprehensive hazard analysis of seismic soil liquefaction, to reduce
such damage and protect human lives. Therefore, the aim of this book is to study
the disaster mechanisms and deformation evolution of seismic liquefaction so as to
provide a reference for risk assessment. First, macroscopic liquefaction phenomena
since the beginning of the century are summarized, and the liquefaction potential
evaluation based on in situ testing is discussed. Then, the study of dynamic
mechanisms of liquefaction using laboratory and model testing are presented. In
addition, numerical simulation for deformation analysis of liquefiable soils based on
finite element—finite difference method (FEM-FDM) is described. Finally, a
comprehensive evaluation for liquefaction damage during earthquakes is proposed.
The logical structure of this book is shown in Fig. 1.3.
8
1
Introduction
References
Andrus, R. D., Piratheepan, P., Ellis, B. S., et al. (2004). Comparing liquefaction evaluation
methods using penetration-V S relationships. Soil Dynamics and Earthquake Engineering, 24
(9), 713–721.
Aydingun, O., & Adalier, K. (2003). Numerical analysis of seismically induced liquefaction in
earth embankment foundations. Part I. Benchmark model. Canadian Geotechnical Journal, 40
(4), 753–765.
Bhattacharya, S., Hyodo, M., Goda, K., et al. (2011). Liquefaction of soil in the Tokyo Bay area
from the 2011 Tohoku (Japan) earthquake. Soil Dynamics and Earthquake Engineering, 31
(11), 1618–1628.
Biot, M. A. (1941). General theory of three-dimensional consolidation. Journal of Applied
Physics, 12(2), 155–164.
Byrne, P. M., Park, S. S., Beaty, M., et al. (2004). Numerical modeling of liquefaction and
comparison with centrifuge tests. Canadian Geotechnical Journal, 41(2), 193–211.
Cao, Z., Youd, T. L., & Yuan, X. (2011). Gravelly soils that liquefied during 2008 Wenchuan,
China earthquake, Ms = 8.0. Soil Dynamics and Earthquake Engineering, 31(8), 1132–1143.
Dafalias, Y. F., & Popov, E. P. (1975). A model of nonlinearly hardening materials for complex
loading. Acta Mechanica, 21(3), 173–192.
Di, Y., Yang, J., & Sato, T. (2008). Seismic performance of a river Dike improved by sand
compaction piles. Journal of Performance of Constructed Facilities, 22(6), 381–390.
Dungca, J. R., Kuwano, J. I. R. O., Takahashi, A., et al. (2006). Shaking table tests on the lateral
response of a pile buried in liquefied sand. Soil Dynamics and Earthquake Engineering, 26(2),
287–295.
Huang, Y., & Jiang, X. (2010). Field-observed phenomena of seismic liquefaction and subsidence
during the 2008 Wenchuan earthquake in China. Natural Hazards, 54(3), 839–850.
Huang, Y., Ye, W. M., & Chen, Z. C. (2009). Seismic response analysis of the deep saturated soil
deposits in Shanghai. Environmental Geology, 56, 1163–1169.
Huang, Y., & Yu, M. (2013). Review of soil liquefaction characteristics during major earthquakes
of the twenty-first century. Natural Hazards, 65(3), 2375–2384.
Huang, Y., Yu, M., & Bhattacharya, S. (2014). Characteristics of flow failures triggered by recent
earthquakes in China. Indian Geotechnical Journal, 44(2), 218–224.
Idriss, I. M., & Boulanger, R. W. (2006). Semi-empirical procedures for evaluating liquefaction
potential during earthquakes. Soil Dynamics and Earthquake Engineering, 26(2), 115–130.
Iwasaki, T., Arakawa, T., & Tokida, K. I. (1984). Simplified procedures for assessing soil
liquefaction during earthquakes. International Journal of Soil Dynamics and Earthquake
Engineering, 3(1), 49–58.
Lenz, J. A., & Baise, L. G. (2007). Spatial variability of liquefaction potential in regional mapping
using CPT and SPT data. Soil Dynamics and Earthquake Engineering, 27(7), 690–702.
Lin, P. S., Chang, C. W., & Chang, W. J. (2004). Characterization of liquefaction resistance in
gravelly soil: large hammer penetration test and shear wave velocity approach. Soil Dynamics
and Earthquake Engineering, 24(9), 675–687.
Moss, R. E., Seed, R. B., Kayen, R. E., et al. (2006). CPT-based probabilistic and deterministic
assessment of in situ seismic soil liquefaction potential. Journal of Geotechnical and
Geoenvironmental Engineering, 132(8), 1032–1051.
Oka, F., Yashima, A., Tateishi, A., et al. (1999). A cyclic elasto-plastic constitutive model for sand
considering a plain-strain dependence of the shear modulus. Geotechnique, 49(5), 661–680.
Pastor, M., Zienkiewicz, O. C., & Chan, A. H. C. (1990). Generalized plasticity and the modelling
of soil behaviour. International Journal for Numerical and Analytical Methods in
Geomechanics, 14(3), 151–190.
Popescu, R., & Prevost, J. H. (1993). Centrifuge validation of a numerical model for dynamic soil
liquefaction. Soil Dynamics and Earthquake Engineering, 12(2), 73–90.
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Seed, H. B., & Idriss, I. M. (1967). Analysis of soil liquefaction: Niigata earthquake. Journal of the
Soil Mechanics and Foundations Division, 93(3), 83–108.
Seed, B., & Lee, K. L. (1966). Liquefaction of saturated sands during cyclic loading. Journal of
Soil Mechanics & Foundations Division, 92(SM6), 105–134.
Sonmez, H., & Gokceoglu, C. (2005). A liquefaction severity index suggested for engineering
practice. Environmental Geology, 48(1), 81–91.
United States Geological Survey. (2016). Seismicity of the Earth 1900–2013. Retrieved September
20, 2016, from http://earthquake.usgs.gov/earthquakes/world/seismicity_maps/
Xenaki, V. C., & Athanasopoulos, G. A. (2008). Dynamic properties and liquefaction resistance of
two soil materials in an earthfill dam—laboratory test results. Soil Dynamics and Earthquake
Engineering, 28(8), 605–620.
Zhou, Y. G., & Chen, Y. M. (2005). Influence of seismic cyclic loading history on small strain shear
modulus of saturated sands. Soil Dynamics and Earthquake Engineering, 25(5), 341–353.
Zhou, Y. G., & Chen, Y. M. (2007). Laboratory investigation on assessing liquefaction resistance
of sandy soils by shear wave velocity. Journal of Geotechnical and Geoenvironmental
Engineering, 133(8), 959–972.
Zhou, Y. G., Chen, Y. M., & Shamoto, Y. (2009). Verification of the soil-type specific correlation
between liquefaction resistance and shear-wave velocity of sand by dynamic centrifuge test.
Journal of Geotechnical and Geoenvironmental Engineering, 136(1), 165–177.
Chapter 2
Macroscopic Characteristics
of Seismic Liquefaction
2.1
2.1.1
Characteristics of Seismic Liquefaction
Earthquakes Induced Widespread Liquefaction
since the Beginning of this Century
According to seismic data, seismic liquefaction and its damage to foundations and
upper structures since the beginning of this century were more frequent than before
in many places around the world. More liquefaction data have been acquired than
previously because of rapid development of science and technology, including
investigation methods and transportation facilities. To better understand macroscopic phenomena related to liquefaction, we examined several earthquakes in
the twenty-first century, considering the comprehensiveness and typicality of
earthquake liquefaction data acquired (Table 2.1).
2.1.2
Characteristics of Liquefaction Distribution
Liquefaction often occurs in areas with saturated and loose sandy soils, and is
distributed near the epicenter. In general, most liquefaction phenomena are
observed near rivers, lakes or coastal areas, owing to soil property and groundwater
level there.
For example, earthquake fountains were observed near the Gulf of Kachchh in
the 2001 Bhuj earthquake, and liquefaction phenomena were mainly reported along
the shore of Lake Pinios in the 2008 Greece earthquake (Margaris et al. 2010). In
the 2010 Chile earthquake, the northernmost liquefaction was in the tailings dam
Veta del Agua, while the southernmost liquefaction was in the Calafquén and
Panguipulli lakes (Verdugo 2011). According to observations of the 2010 Darfield
earthquake, the most serious liquefaction areas were near waterways such as rivers,
© Springer Nature Singapore Pte Ltd. 2017
Y. Huang and M. Yu, Hazard Analysis of Seismic Soil Liquefaction,
Springer Natural Hazards, DOI 10.1007/978-981-10-4379-6_2
11
12
2 Macroscopic Characteristics of Seismic Liquefaction
Table 2.1 General information on major earthquakes in the twenty-first century (reprinted from
Huang and Yu (2013) with permission of Springer)
Earthquake
Date (local
time)
Location
Magnitude
References
Bhuj
January
26, 2001
February
24, 2003
May 12,
2008
India
Mw = 7.6
Singh et al. (2005)
China
Ms = 6.8
Dong et al. (2010)
China
Ms = 8.0
Chen et al. (2009), Huang and Jiang
(2010), Hou et al. (2011), Yuan et al.
(2009)
Margaris et al. (2010)
Bachu
Wenchuan
June 8,
Greece
Mw = 6.4
2008
Chile
February
Chile
Mw = 8.8 Verdugo (2011), Villalobos et al. (2011)
27, 2010
Darfield
September New
Mw = 7.1 Wotherspoon et al. (2012)
4, 2010
Zealand
Yao et al. (2011)
Yingjiang
March 10, China
Ms = 5.8
2011
Tohoku
March 11, Japan
Mw = 9.0 Bhattacharya et al. (2011)
2011
Lushan
April 20,
China
Mw = 6.6 Liu and Huang (2013)
2013
Ms refers to surface wave magnitude, based on measurements of Rayleigh surface waves that
travel primarily along the uppermost layers of the earth; Mw refers to moment magnitude scale,
based on seismic moment of an earthquake (Huang and Yu 2013)
Greece
streams and swamps. In the 2011 Great East Japan Earthquake, Yamaguchi et al.
(2012) indicated that many liquefied sites were in old river beds and developed
areas near Tokyo Bay. In the 2008 Wenchuan earthquake, it was estimated that
70% of liquefied sites were on the Chengdu Plain, with 15% in the Mianyang area
(Cao et al. 2011). In the 2011 Yingjiang earthquake, liquefied areas were found on
both sides of the river, nearly parallel to the Dayingjiang fault. The liquefaction area
was about 2000 square km and was mainly in three areas—lowlands (even marsh
and desert), east of the earthquake region, and along rivers and to the northwest
along the tectonic line (Dong et al. 2010). Compared with the 2008 Wenchuan
earthquake, in the Lushan earthquake, liquefaction only occurred near river terraces
and alluvial flats along the Shuangshi-Dachuan fault, a sub-fault of the
Longmenshan fault (Shi et al. 2014).
2.1.3
Classification of Liquefaction Phenomena
Various liquefaction features have been observed, such as geometry, type, and
dimension. Wang et al. (1983) stated that for similar soil conditions, macro-features
2.1 Characteristics of Seismic Liquefaction
13
of liquefaction and damage on the ground depend on local geomorphic characteristics. Galli (2000) indicated that liquefaction features can be affected by many
factors, including amplification of seismic waves, anomalous propagation, and
geologic conditions (e.g., the grain distribution and density of soil, and groundwater
level). In spite of the various liquefaction features, Wang et al. (1983) pointed out
that macroscopic liquefaction topographic features that reveal various liquefaction
mechanisms can be divided into three categories, i.e., scattered stars, network and
tortile. In terms of liquefaction forms or phenomena, Fairless and Berrill (1984)
identified five types, namely, water ejection and sand boils, settlement, landslides
on moderate slopes, foundation failures, and flotation of light structures. Currently,
the latter three types are regarded as forms of liquefaction-induced damage.
Considering the above classification and data from recent field surveys or the
literature, macroscopic phenomena of liquefaction are classified into three types
here, i.e., sand boiling, ground cracking, and lateral spread based on seismic data
analysis.
2.1.3.1
Sand Boiling
Sand boiling, also called sand boils, sand blows or sand volcanoes, is regarded as
decisive evidence of liquefaction that occurs when void water pressure reaches a
certain value. The phenomenon is called sand boiling because water looks like it is
“boiling” up from the soil foundation. This boiling is actually a mixture of sand and
water that comes from shallow depths to form features of different shapes and sizes
on the ground surface during an earthquake. In general, it can be classified into two
categories based on its formation or the way that liquefied soils eject through the
weak upper soil layer. Both categories are described in the following.
The first formation category may be referred to as flat-cone sand volcanoes.
These volcanoes can be further divided into solitary and clustered cones, both of
which were observed in the 2005 Kashmir Earthquake (Sahoo et al. 2007). In the
2003 Bachu Earthquake, the typical sand boiling diameter was 1–2 m, with the
largest up to 3 m (Dong et al. 2010). Sand boiling was observed at many sites,
including farms where the water spouting was <1 m and the mixtures mainly
contained silty sand and water, according to field surveys. The shapes of sand
boiling holes can be separated into two types, circular and oval, with numerous
forms in the Bachu earthquake. In the 2011 Yingjiang earthquake, sand volcanoes
clustered with heights of no more than 30 cm, and diameters of 10–50 cm were
observed at some locales (Yao et al. 2011). In addition, various types of liquefied
materials that ejected in the shape of clustered cones were observed at certain spots
in the 2008 Greece earthquake (Margaris et al. 2010). In the 2013 Lushan earthquake, liquefaction in the form of sand boiling was observed and was mainly
distributed in a linear zone parallel to the Longmenshan front mountain fault zone.
The ejection holes were nearly 10 cm in diameter, and the ejection height
was *1.0 m (Zhang et al. 2013).
14
2 Macroscopic Characteristics of Seismic Liquefaction
Fig. 2.1 Sand boiling by
eruption on the surface
through existing cracks
(reprinted from Bhattacharya
et al. (2011) with permission
of Elsevier)
The second category refers to sands that erupt on the surface through cracks
while liquefied. Water and sediment mixtures eject immediately and violently to the
surface through preexisting cracks induced by seismic shaking, as seen in the 2005
Kashmir earthquake (Sahoo et al. 2007). This sand boiling category was also
observed in the 2011 Tohoku (Bhattacharya et al. 2011) and 2011 Yingjiang (Yao
et al. 2011) earthquakes. Figure 2.1 shows this type of sand boiling observed in the
Tohoku quake. In the 2001 Bhuj earthquake, a sand blow near Umedpur, 50 km
north of the epicenter, occurred with a crater *10 m long. In the Tohoku earthquake, liquefiable soil erupted from the bed of the Jukken-gawa River in Katori
City, and the riverbed floor was filled with erupted sand boils (Tsukamoto et al.
2012). This could be classified in the second category. In the 2008 Wenchuan
earthquake, sand boiling was accompanied by ground cracks, which caused secondary damage to structures (Huang and Jiang 2010).
2.1.3.2
Ground Cracks
Ground cracks, also called ground fissures, have been reported in almost every
earthquake because of highly uneven distributions of material in the soil layer.
According to field surveys, after the 2008 Wenchuan Earthquake, ground cracks
were reported at 70–80% of liquefaction sites, with elongation between tens and
thousands of meters (Chen et al. 2009). In the 2009 Olancha earthquake, the length
and width of fissures were reported at about 2–20 m and 1–4 cm, respectively
(Holzer et al. 2010). Similarly, the length, width, and depth of ground cracks were
30–50 m, 3–4.5 cm, and 60–130 cm, respectively, in the 2005 Kashmir earthquake
(Sahoo et al. 2007). Sometimes, ground cracks may occur with sand boiling, as
shown in Fig. 2.2. Ground cracks induced by the 2008 Greece earthquake may be
divided into two types, open or filled with sand, with widths of 2–8 cm (Margaris
2.1 Characteristics of Seismic Liquefaction
15
Fig. 2.2 Cracks observed with ejected sand (Pacific Earthquake Engineering Research Center
2001a)
et al. 2010). Cao et al. (2011) stated that in the 2008 Wenchuan earthquake, ground
fissures were found at many sites, and these damaged numerous buildings. In the
2011 Yingjiang earthquake, ground cracks were seen as the main cause of manufacturing damage. Ground cracking was seen everywhere in villages such as Heha
and Yunmao. Soil liquefaction also led to severe cracking of dykes. A crack in the
Yingjiang Dyke was *19 km in length, with average depth 1 m (Yao et al. 2011).
In the 2003 Bachu earthquake, fractures and cracks formed along the Bachu
Yarkand road slope direction, seriously damaging the highway (Dong et al. 2010).
2.1.3.3
Lateral Spread
Lateral spread refers to permanent horizontal displacement of the ground induced
by liquefaction. Bartlett and Youd (1992a, b) indicated that lateral spread produced
by liquefaction occurs mostly on mild slopes underlain by loose sand with a
shallow water table. Lateral spread may be classified into two types, lateral sliding
of mild sloping ground induced by liquefaction at relatively shallow depths, and
large horizontal movement associated with deep-seated liquefaction damage.
Generally, lateral spread has a fixed direction parallel to the course of rivers,
which then possibly generates tensile ground cracks in the same direction. In the
2005 Kashmir earthquake, there was lateral spread toward a bend in the Jhelum
River, 100 m in length, 50 m in width, and with a total displacement of 120–
160 cm. The direction of tensile cracks was parallel to the course of the river
(Aydan et al. 2009). Following the 2009 L’Aquila earthquake, liquefaction-induced
cracks extended toward the river embankment, with widths of 250–350 mm
(Kawashima et al. 2010). Lateral spread displacements generally increased toward
the sea in the 2008 Greece earthquake, with a maximum displacement of 60 cm
16
2 Macroscopic Characteristics of Seismic Liquefaction
Fig. 2.3 East–West view of lateral spread of embankment at Capitol Interpretive Center (Pacific
Earthquake Engineering Research Center, 2001b)
(Margaris et al. 2010). Figure 2.3 shows that lateral spread of an embankment at the
Capitol Interpretive Center occurred with damage length of *75 ft during the
Nisqually earthquake, and its direction was parallel to the river course (Pacific
Earthquake Engineering Research Center, 2001b). In addition, lateral spread is
frequent at relatively flat sites astride streams and other waterfronts, where saturated, recent sediments are common. In the 2001 Bhuj earthquake, lateral spreads
were observed over a wide area in Gujarat and on the border between India and
Pakistan (Tuttle and Hengesh 2002). Chatzipetros et al. (2008) reported that lateral
spread was observed in the 2008 Greece earthquake along the banks of Pinios
Reservoir, at the southern end of a fault. Papathanassiou et al. (2008) reported that
the banks of the Pinios River had a horizontal displacement of 1–2 cm toward the
river. Figure 2.4 shows the location of liquefaction along the Kaiapoi River and
lateral spread around the Kaiapoi Visitors Information Center and Coast Guard
building (identified by “1”), leading to the settlement and tilt of both structures in
the 2010 Darfield earthquake (Wotherspoon et al. 2012).
Fig. 2.4 Aerial photograph of central Kaiapoi River, indicating former river channel (reprinted
from Wotherspoon et al. (2012) with permission of Elsevier)
2.1 Characteristics of Seismic Liquefaction
2.1.4
17
Related Liquefaction Damage
Seismic liquefaction often causes great damage to houses, buildings, bridges,
routes, ports, railways, buried structures, and tailings dams. Such damage can be
distinguished as having three types, i.e., abject failure (including structure failure on
the ground), underground, and other facilities damage in ports or near rivers.
Regarding damage from liquefaction on the ground, damage to piles and bridges,
tilt or uneven settlement of buildings and wire poles, cracks in roads and high
buildings were generally observed. In the 2001 Bhuj earthquake, there were
widespread ground and structural failures at the port of Kandla, 50 km from the
earthquake epicenter, and more than 2300 piles in five berths were seriously
damaged (Hazarika and Boominathan 2009). Tile floors settled unevenly and there
were fine sand deposits around them, which may be seen as evidence of soil
liquefaction under the buildings during the earthquake (Hazarika and Boominathan
2009). In the 2010 Chile earthquake, some bridges suffered severe damage. For
example, noticeable pier settlements from liquefaction occurred at several locations
along Juan Pablo II Bridge, causing it to bend (Ledezma et al. 2012). According to
Yasuda et al. (2012), in the 2011 Tohoku earthquake, *27,000 houses were
damaged in the Tohoku and Kanto districts because of liquefaction, while 3680
houses were more than partially destroyed. Nakai and Sekiguchi (2011) indicated
that the type of surface soil and its amplification characteristics were the major
influences on the severity of liquefaction damage. Cao et al. (2011) stated that
fissures intersecting structures caused structural damage and sporadic collapse
during the 2008 Wenchuan earthquake. Serious damage to the Banqiao School
building was attributed to ground fissures generated by lateral spread toward a
nearby river and intersected building. In the 2011 Yingjiang earthquake, the
damage level of structures was strongly related to liquefied areas (Yao et al. 2011).
It was observed that ground cracking induced by soil liquefaction was the main
cause of building collapse. Damage to buildings, especially residential housing, was
caused by soil liquefaction and the seismic performance of those buildings (Zhang
et al. 2009). Most buildings in the Bachu-Jiashi area were constructed on soft soil,
where the water table was high. This unique geologic condition aggravated damage
from soil liquefaction. Liquefaction caused serious damage to highways. For example,
fractures and cracks formed along the Bachu Yarkand road slope direction in the 2003
Bachu earthquake (Dong et al. 2010). According to field investigations, damages to
structures and liquefaction-induced ground and building failures were widespread
throughout the town of Shuangshi. Damage from soil liquefaction accounted for a
certain proportion during the 2013 Lushan earthquake (Zhang et al. 2013).
Uplift is the main type of damage to underground structures from liquefaction. In
the 2010 Darfield earthquake, Orense (2011) indicated that liquefaction led to a
wide range of uplift of buried structures, including gasoline tanks, sewage tanks,
manholes, and buckled pipes. It is believed that damage from soil liquefaction there
may have been worsened by a high water table caused by a wet winter. In the 2003
Bachu earthquake, a pipeline was lifted *0.3 m in Qiongxiang, and the tilt of
18
2 Macroscopic Characteristics of Seismic Liquefaction
double utility poles led to uneven settlement of a foundation (Dong et al. 2010).
Damage to facilities in ports or near rivers was mainly in coastal areas. In the 2001
Bhuj earthquake, Mavroulis et al. (2010) reported that considerable coastal subsidence was generated by soil liquefaction, which induced secondary damage in
several coastal areas north of the epicentral area. Papathanassiou et al. (2008) stated
that there were small ground cracks in banks of the Pinios River, owing to the
ejection of coarse-grained material. Horizontal displacement of 1–2 cm toward the
river was observed. Structural damage from subsoil liquefaction was seen in the
waterfront area of Vrahneika village, at an epicentral distance of 25 km where the
pavement was cracked and lifelines were damaged.
2.2
2.2.1
Case Study: Field Investigation of Liquefaction
from the 2008 Wenchuan Earthquake
Introduction to Wenchuan Earthquake
The Wenchuan earthquake, also called the 2008 Sichuan or Great Sichuan
Earthquake, struck Sichuan Province in southwestern China on May 12, 2008. It
measured Ms 8.0 and Mw 7.9, with its epicenter in Wenchuan County, and resulted
in the deaths of more than 69,000 people. According to earthquake records, the
earthquake was the most destructive in China since the 1976 Tangshan earthquake.
The earthquake had widespread effects, and it was felt in most provinces of China
and even other countries in Asia.
2.2.2
Survey Area
The author did extensive site investigation of soil liquefaction and structural
damage, including residential buildings, libraries, dams, bridges, highways, tunnels,
underground structures, and other facilities. By combining information on earthquake geological conditions and forms of structural destruction, soil liquefaction
and related engineering damage were analyzed based on field investigation. The
survey area included six serious disaster zones—Wenchuan County, Beichuan
County, Mianzhu, Shifang, Qingchuan County, and Dujiangyan. This area is large
and the investigation scope was comprehensive. Table 2.2 shows investigation
subjects and Fig. 2.5 the distribution of survey sites.
2.2 Case Study: Field Investigation of Liquefaction from the 2008 …
19
Table 2.2 Earthquake damage survey list
Time
Investigation locations
Main investigation subjects
2008.6
Dujiangyan
2008.8
Dujiangyan, Wenchuan County,
Chengdu
2008.9–
11
Mianzhu, Shifang, Qingchuan County,
Beichuan County, Dujiangyan,
Wenchuan County
Mianzhu City, Shifang, Qingchuan
County, Beichuan County, Dujiangyan,
Wenchuan County, Deyang, Mianyang
Investigation of earthquake damage
phenomena
Earthquake damage phenomena of
Duwen Highway, Longxi Tunnel,
Chengdu metro line stations and
tunnels, railway station subway station
Investigation of geological condition
and phenomena of secondary disasters,
collapse, and slip flow
Investigation of foundation damage
phenomenon of housing construction,
reservoir dams, bridges, embankments
etc
Fig. 2.5 Map of investigation sites (modified from Jiang 2009)
2.2.3
Liquefaction Distribution and Characteristics
The earthquake liquefaction extent involves a region with area about 500 km long
and 200 km wide, including the areas of Suining, Meishan, Deyang, Chengdu,
Mianyang, Leshan, Ya’an and Guangyuan (Chen et al. 2009). The farthest district is
Suining in the east, about 210 km from the epicenter, and Hanyuan County in the
south, about 200 km away. Longnan in Gansu Province was the northernmost point
of liquefaction, about 280 km from the epicenter.
20
2 Macroscopic Characteristics of Seismic Liquefaction
Based on the field investigation of hydrology and geology after the Wenchuan
earthquake, the liquefaction distribution and characteristics were analyzed comprehensively as follows.
(1) As shown in Fig. 2.6, liquefaction sites were in a rectangular area about
160 km long and 60 km wide, with the long side in a northeast direction
(Yuan et al. 2009). Liquefied areas were mainly in the cities of Chengdu,
Deyang and Mianyang. The highest earthquake intensity areas (X, XI) were
mainly in the mountains, and a few liquefaction points were found there.
There were liquefaction points in areas of earthquake intensity VI, VII, VIII
and IX, but they were concentrated in area VIII. According to the survey, such
points concentrated in the Deyang area, Mianzhu, and Shifang, especially in
Mianzhu, which had serious damage. Liquefaction in the Chengdu area was
moderate, and was mainly in Dujiangyan. Liquefaction in Mianyang was slight,
mainly in Youxian and Jiangyou.
(2) Liquefaction points were mainly in rural areas, similar to the Tangshan earthquake. Unlike hydrologic conditions in rural areas, underground water depths
were 5–10 m in urban areas, such as southwest of Guanghan and west of
Deyang. Few liquefaction phenomena were observed there.
(3) Soil liquefaction was largely influenced by geologic conditions. By analyzing
the distribution of liquefaction points, it was seen that these points were
mainly in loose sediments of the Quaternary.
Fig. 2.6 Liquefaction points in the Wenchuan earthquake (modified from Yuan et al. 2009)
2.2 Case Study: Field Investigation of Liquefaction from the 2008 …
2.2.4
21
Foundation Damage Related to Liquefaction
in the Dujiangyan Area
To detail the soil liquefaction, a case study of that liquefaction and foundation
damage in the Dujiangyan area was undertaken, as follows. Dujiangyan County is
in a transition area between the south edge of the Longmenshan fault belt and the
Chengdu new-generation, depressed northwest edge of the Sichuan Basin.
2.2.4.1
Liquefaction and Related Damage
Huang and Jiang (2010) showed that sand boiling was observed at several sites in
Dujiangyan County, with maximum ejecta height >1.0 m. Sand boiling was generally accompanied by land subsidence, ground cracks, uneven settlement, and
ground collapse, which caused secondary damage to structures (Huang and Jiang
2010). Water ejection was reported at several sites, with heights from centimeters to
tens of meters. Cao et al. (2011) indicated that most investigated sites had ground
fissures, sand boil deposits, or wells clogged with intruded sand and gravel, which
evidence liquefaction.
At the locations of team numbers 17 and 18, i.e., Xingyi Village, Zhongxing
Town in Dujiangyan County, sand boiling appeared over a large area of cropland
and residences. Maximum ejecta height in these boils was >1.0 m. A large proportion of ejected material was made up of yellow and white sands and cobbles
(Fig. 2.7; Huang and Jiang 2010). Sand boiling was also observed in croplands at
the locality of Team No. 14—Huzhu Village, Puyang Town, Dujiangyan County.
Yellow sands and large cobbles were ejected from croplands and surrounding
roads, reaching a maximum height of *1.0 m. Localized sand deposits 10 cm in
depth were observed in fields after the earthquake (Fig. 2.8; Huang and Jiang
2010). Sand boiling was accompanied by land subsidence, uneven settlement,
ground cracks, and ground collapse. This damaged buildings, involving leaning,
cracking, and even collapse (Fig. 2.9; Huang and Jiang 2010). At the location of
team number 14, Huzhu Village in Puyang Town of Dujiangyan County, numerous
ground cracks were observed (Fig. 2.10; Huang and Jiang 2010), accompanied by
surface uplift. The broadest ground cracks were almost 30 cm wide, which were
partly hunched and shut in during aftershocks. In addition, surrounding buildings
suffered many cracks caused by leaning (Fig. 2.11; Huang and Jiang 2010).
In Dujiangyan Puyang Town, group 14, there was widespread ejected sand and
water, with a large number of ground fissures and ground swell. The earthquake
ground crack width was *30 cm. Some cracks were from uplift, and because of
aftershocks some cracks gradually closed. Figure 2.12 shows the uneven subsidence caused by liquefaction in Puyang Town. The uneven settlement cracked and
damaged foundations, causing some buildings to collapse. Figure 2.13 shows
bridge foundation displacement caused by liquefaction.
22
Fig. 2.7 Liquefaction of
fine-grained yellow sand
(ejection area *1094 m2)
(reprinted from Huang and
Jiang (2010) with permission
of Springer)
Fig. 2.8 Liquefaction of
white sand (ejection
area *294 m2) (reprinted
from Huang and Jiang (2010)
with permission of Springer)
Fig. 2.9 Subsidence caused
by liquefaction (length of
subsidence area *12 m,
mean width *3 cm)
(reprinted from Huang and
Jiang (2010) with permission
of Springer)
2 Macroscopic Characteristics of Seismic Liquefaction
2.2 Case Study: Field Investigation of Liquefaction from the 2008 …
23
Fig. 2.10 Cracks caused by
liquefaction (cracks
distributed over 8 5 m2
area) (reprinted from Huang
and Jiang (2010) with
permission of Springer)
Fig. 2.11 Building cracks
caused by liquefaction
(reprinted from Huang and
Jiang (2010) with permission
of Springer)
Quaternary sediments were widely distributed in the toes of dams and nearby
rivers, and mainly included fine-grained sand and silty clay. In such areas, pore
pressure can increase rapidly during an earthquake and the ground can become
liquefied because of a high groundwater level. Figure 2.14 shows buildings
downstream from the toe of the major dam of Boling Reservoir in the city of
Mianzhu (Huang and Jiang 2010). These buildings partially collapsed during the
earthquake, whereas those farther from the dam toe were only moderately or
slightly damaged. Figure 2.15 shows buildings near the Minjiang River at the
location of team number 10, Tongyi Village of Dujiangyan County (Huang and
Jiang 2010). These buildings were as close as 10 m to the levee, which was
severely damaged in the Wenchuan earthquake. As known from previous earthquakes, the major types of liquefiable soil are sandy silt and fine-grained sand
(Xenaki and Athanasopoulos 2003). However, in the Wenchuan earthquake,
24
2 Macroscopic Characteristics of Seismic Liquefaction
Fig. 2.12 Subsidence caused
by liquefaction
Fig. 2.13 Bridge foundation
displacement caused by
liquefaction
numerous larger-diameter cobbles were contained in the liquefaction ejecta. This
finding creates a new challenge to traditional liquefaction research, including criteria of liquefiable soil and liquefaction resistance measures.
2.2.4.2
Analysis of Liquefaction Mechanism
(1) Stratum distribution in Dujiangyan area
In the Dujiangyan area, the ground is flat and consists of Quaternary Holocene
artificial fill earth and Quaternary Holocene alluvium (Huang and Jiang 2010). This
strata is widely distributed in that area. From top to bottom are filled earth, silty
2.2 Case Study: Field Investigation of Liquefaction from the 2008 …
25
Fig. 2.14 Partially collapsed
buildings near dam (reprinted
from Huang and Jiang (2010)
with permission of Springer)
Fig. 2.15 Collapsed
buildings near Minjiang River
(reprinted from Huang and
Jiang (2010) with permission
of Springer)
clay, fine sand, loose cobble, slightly dense cobble, moderately dense cobble, and
dense cobble.
Dujiangyan is a geological transition area, located between the northwestern
edge of Chengdu Cenozoic in the Sichuan basin and Longmen Mountain tectonic
belt. The terrain is open, with few geologic disasters such as landslides or debris
flow. However, fine sand with medium liquefaction is widely distributed.
Quaternary Holocene artificial soil and Quaternary Holocene river alluvium
deposits are widespread in the area, and typical regional strata are as follows.
A. Fill soil: gray, grayish yellow, gray and black, mottled. Loose, slightly wet,
composed mainly of silt, gravel composite, with a thickness of 0.8–5.4 m.
B. Silt, silty clay: gray, brown gray. Slightly wet, loose, scattered distribution, with
a thickness of 0–3.0 m.
26
2 Macroscopic Characteristics of Seismic Liquefaction
C. Fine sand: gray, slightly wet, loose, lentoid distribution, with thickness 0.6–
1.9 m.
D. Loose gravel: yellow, pale yellow, slightly wet, gravel content 50–55%, with
diameters of 3–5 cm, with a maximum 15 cm, fine sand and silt filling a pebble
skeleton. Lentoid distribution with a thickness of 0–1.4 m.
E. Slightly dense gravel: yellow, pale yellow, close to saturation, gravel content
55–60%, diameters of about 3–18 cm, with some >30 cm; disarrayed, fine sand
and gravel fill between around 40 and 45% and a small amount of gravel, the
layer of which is continuously distributed over the dense gravel layer, with a
thickness of 0.8–4.1 m.
F. Dense gravel: yellow, pale yellow, saturation. Pebble content 60–70%, a
general diameter of 5–12 cm, a maximum diameter 40 cm, staggered
arrangement, most in contacts, pebble can form a skeleton, fine sand skeleton
filled between about 30 and 40% and a small amount of gravel, pebble content *30%, unknown hickness.
G. Compacted gravel: particle size of 8–20 cm, maximum size >40 cm, gravel
skeleton content about 70–85%, unknown thickness.
(2) Liquefaction factors (Huang and Jiang 2010)
In view of regional geological and ground conditions in Dujiangyan County, the
liquefaction of cobble layers was investigated by considering the following factors.
A. Seismic conditions
Dujiangyan is 16 km from the epicenter of the Wenchuan earthquake. The seismic
intensity at Dujiangyan during the earthquake was VIII, which means strong ground
motion and long seismic duration (China Earthquake Administration 2008). As is
commonly known, higher intensity and stronger peak ground acceleration is more
likely to result in soil liquefaction. In addition, longer duration means long cyclic
loading on soil, and therefore a greater risk of soil liquefaction.
B. Overlying earth pressure
In the Dujiangyan area, Quaternary Minjiang River alluvial deposits consist of
loose sand and cobbles distributed as lenses. Because the sediments have a top layer
of 0.5–5.0 m beneath the surface, overlying earth pressure is low. The ejection of
sands and cobbles from the ground occurred when pore pressure increased rapidly.
Investigations show that sand boiling occurred mostly in croplands and around
buildings, whereas it was seldom found inside buildings or in other locations with
additional load. This suggests that overlying pressure is one of the most crucial
factors in liquefaction.
As is well known, the stronger the overlying earth pressure, the greater the liquefaction resistance. This was verified by field investigation of macro phenomena.
Therefore, for low-rise buildings, if their site has liquefiable soil, it can be treated by
increasing overlying earth pressure by adding a certain thickness of earth fill. This
reduces the probability of liquefaction damage.
2.2 Case Study: Field Investigation of Liquefaction from the 2008 …
27
In the Dujiangyan area, the sand and silt are in a lentoid distribution, and are not
deep beneath the surface. Thus, in engineering design, removal of all liquefiable
soil is recommended.
C. Density
The top cobble layer in Dujiangyan County is generally loose and unconsolidated,
with an uneven thickness of 0–1.4 m over the entire area. Cobbles make up 50–
55% of the material in this soil layer by volume and have typical diameters of 3–
5 cm, with some as large as 15 cm. The cobbles are irregularly packed and most are
independent, not forming a skeleton. They are usually suspended with fine-grained
sands and silty soil.
Undrained cyclic triaxial tests showed that the liquefaction resistance of
sand-gravel composites increases with density. By increasing the amount of gravel
(Evans and Zhou 1995), the likelihood of liquefaction decreases with increasing
density of the sand-gravel composite. In contrast, the cobble layer has a lower
density, increasing the potential for liquefaction. Groundwater in Dujiangyan
County is found on the first terrace of the Minjiang River. This water is abundant
and the water table is shallow. Perched aquifers are common in silty soil and
fine-grained sand layers. The major regional aquifer has a shallow sand and gravel
layer. The groundwater is supplied by precipitation and underground transport, and
its distribution correlates well with the large number of liquefaction occurrences
along both sides of the Minjiang River.
For deep soil, methods like water-washed vibration and vibration-immersed
tubes can be used. Vibroflotation construction causes saturated loose sand particles
under forced vibration to have a high frequency; these particles rearrange and
became compact. This produces a strong horizontal vibration force in the surrounding soil, increasing relative density of the sand and reducing porosity. This
improves liquefaction resistance of the soil.
D. Fabric
The fabric of soils and buildings is also important in liquefaction. The cobble layer
in Dujiangyan County was loose and extremely porous. As a result, it had a lower
liquefaction resistance strength. Under these conditions, liquefaction takes place
much more easily through high-intensity shaking from an earthquake. Subsidence is
a common earthquake-induced phenomenon that results in the sinking of ground
and buildings. This is also known as permanent or residual deformation, and
accounts for some of the most substantial primary damage from earthquakes. The
extent of subsidence caused by past earthquakes has varied. Huang and Jiang
(2010) showed a building of brick column structure atop soft soil at Hanwang Town
in the city of Mianzhu, which did not have adequate bearing capacity. During the
earthquake, its columns sank by nearly 15 cm because of non-uniform ground
subsidence, which destroyed the structures supported by the columns. The steps of
a telecommunications building in Dujiangyan County show another example of the
effects of earthquake subsidence.
28
2 Macroscopic Characteristics of Seismic Liquefaction
Additionally, along the concreted edge of the building, nonuniform subsidence
occurred on the porch (Huang and Jiang 2010). Highways with soft roadbeds also
experienced non-uniform earthquake subsidence, which caused their substantial
damage.
2.3
New Liquefaction Phenomena During Recent
Earthquakes
In comparison to the conventional liquefaction characteristics mentioned above,
something different was found according to the 2008 Wenchuan earthquake survey
and other literature published in recent years. Yuan et al. (2009) listed three new
findings from analysis of liquefaction phenomena in that earthquake. Based on the
aforementioned survey, research findings, and the literature, the new characteristics
are summarized into four categories: Liquefaction occurred in areas of moderate
seismic intensity; liquefaction could occur in areas with gravelly soils; liquefaction
might also occur in deep-level sandy soils; re-liquefaction could occur during
aftershocks. These findings are explained as follows.
(1) Liquefaction in areas of moderate seismic intensity
In China, the Code for Seismic Design of Buildings (Ministry of Construction of
China 2001) stipulated that areas with seismic intensity VI or less could be treated
as free from liquefaction. However, liquefaction can occur in areas with moderate
seismic intensity. Chen et al. (2009) reported that although seismic intensity was
VI, liquefaction and serious related damage was observed at more than 10 sites.
Such a phenomenon was observed in mainland China for the first time, and reveals
that areas of moderate seismic intensity can liquefy because of relatively
high-amplitude ground motion and sufficient duration of shaking. Further, Shi et al.
(2014) discovered that in the Wenchuan earthquake, the threshold energy required
to induce liquefaction was just 5% that of the Lushan earthquake. This may be
related to two factors: (1) Liquefaction occurrence may be more sensitive to low
seismic frequencies; (2) the sensitivity of unconsolidated materials may have been
altered by the Wenchuan earthquake. Both of the above factors need further study.
(2) Liquefaction of gravelly soils
Liquefaction generally occurs in coarse silts and fine sands that are saturated. To
mitigate liquefaction potential in engineering practice, saturated coarse silts or fine
sands may be replaced by gravelly soil, which was once thought to be
non-liquefiable.
Until the 2008 Wenchuan earthquake, the aforementioned Code for Seismic
Design of Buildings held that gravels and gravelly soils may be treated as
non-liquefiable (Ministry of Construction of China 2001). However, Cao et al.
(2011) observed that gravelly soils with mean grain sizes from 1 to >30 mm were
2.3 New Liquefaction Phenomena During Recent Earthquakes
29
liquefied in the Wenchuan earthquake. In general, gravelly sand refers to cohesiveless, and individual gravel grains and cobbles suspended by fine-grained sand
and silty soil (Huang and Jiang 2010). The liquefied gravelly Holocene soils found
in the Wenchuan earthquake were shallow and loose, with low shear-wave
velocities. This may have increased the liquefaction potential (Hou et al. 2011).
Both sand boils and gravelly sand ejected from the surface were observed (Chen
et al. 2008), and gravelly soil liquefaction was also reported in Shuangshi Town
during the Lushan earthquake (Liu and Huang 2013). Owing to a lack of research
on liquefaction of gravels and gravelly soil, both the liquefaction mechanism or
conditions and method of evaluating liquefaction resistance of gravels and gravelly
soil require further study.
(3) Liquefaction of deep-level sandy soils
Sahoo et al. (2007) indicated that liquefaction occurs when a saturated sandy layer
is overlain by a certain thickness of confining medium, such as clay or silt. The
overlying medium reduces the overall hydraulic ability, preventing rapid drainage
and mitigating liquefaction potential. Moreover, according to the Code for Seismic
Design of Buildings (Ministry of Construction of China 2001), almost no liquefaction has been observed below a depth of 15 m.
In contrast with conventional experience, deep-level sandy soils were observed
to be liquefied in recent century earthquakes. For example, it was found in field
investigations that the depth of liquefaction reached *20 m in the large-magnitude
2008 Wenchuan earthquake (Ms = 8.0; Yuan et al. 2009), and 12–16 m in the 2011
Tohoku earthquake (Mw = 9.0) (Bhattacharya et al. 2011). There have been no
reports of soil liquefaction deeper than 30 m during recorded earthquakes (Youd
et al. 2001). However, it has been proven by centrifuge tests that medium-density
sand layers at depths >30 m can also fully liquefy under high confining stress.
Moreover, compared with surface soil, deposits at greater depths would require
more cycles of excitation to be liquefied (Gonzailez et al. 2005). Accordingly,
deep-level sandy soils may be liquefied under high-amplitude ground motion of
long duration.
(4) Re-liquefaction in aftershocks
In the 2008 Wenchuan Earthquake, an intensity-VII area liquefied following the
main shock on 12 May, and then re-liquefied during an aftershock of magnitude Ms
6.4 (Chen et al. 2009). By analyzing observational data of paleoseismic liquefaction, Ha et al. (2011) indicated that sand can liquefy again during aftershocks
following initial liquefaction during seismic shaking. Dong et al. (2010) held that
the most important feature of re-liquefaction is stacked sand volcanoes, with small
holes developing in larger holes. In the 2003 Bachu earthquake, diameters of large
and small holes were observed in ranges of 50–100 cm and 5–10 cm, respectively
(Dong et al. 2010). Following the 2010 Darfield Earthquake, liquefaction
30
2 Macroscopic Characteristics of Seismic Liquefaction
reoccurred in a Mw 6.3 aftershock on February 22, 2011, over a smaller part of the
region previously liquefied (Wotherspoon et al. 2012). Re-liquefaction during
aftershocks was also found following the 2011 Tohoku Earthquake (Onoue et al.
2012).
Research into the mechanism of re-liquefaction during aftershocks has received
much attention recently. After initial liquefaction, the soil fabric is destroyed and
becomes highly anisotropic and unstable (Ha et al. 2011). If excess pore water
pressure cannot be dissipated to a certain value before aftershocks, the liquefaction
assistance will reduce significantly. In such cases, soil may re-liquefy more readily
and lead to secondary damage (Oda et al. 2001).
2.4
Summary
Earthquakes occur in many locations worldwide every year, especially along plate
boundaries such as the one between the Pacific and North American plates.
Earthquakes can cause shaking and ground rupture, landslides, tsunamis, floods and
soil liquefaction, causing numerous injuries and loss of life. People have come to
recognize soil liquefaction over the past several centuries, from the discovery of its
related phenomena to its general characteristics.
This chapter examined several representative earthquakes around the world since
the beginning of this century and liquefaction phenomena in detail. These phenomena were classified into three types—sand boiling, ground cracks, and lateral
spread. Survey investigations of the 2008 Wenchuan earthquake were then
described in detail to determine seismic liquefaction. New liquefaction characteristics were discovered according to these surveys and other literature published in
recent years. Yuan et al. (2009) forwarded three new findings from analysis of
liquefaction phenomena in the Wenchuan earthquake. Based on the surveys
described above, research findings, and the literature, the new characteristics were
divided into one of four categories:
(1)
(2)
(3)
(4)
Liquefaction in areas of moderate seismic intensity
Liquefaction of gravelly soils
Liquefaction of deep-level sandy soils
Re-liquefaction during aftershocks
Most engineering design criteria in use are based on previous experience.
Because the new liquefaction characteristics were found in the recent field investigations, previous criteria of liquefaction and building design codes may not be
adequate and must be improved or revised. If this is not done, some areas may again
suffer serious loss of life and property. We should continually correct our understanding of nature through further surveys or study of new phenomena, and this is
precisely the intent of our work.
References
31
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Chapter 3
Liquefaction Potential Evaluation
Based on In Situ Testing
3.1
Introduction to Liquefaction Evaluation
Based on In Situ Testing
In Chap. 2, the liquefaction hazard caused by earthquakes was discussed. In this
chapter, four in situ tests widely used to evaluate the liquefaction potential of
engineering sites will be introduced. Three steps are needed to evaluate the liquefaction hazard, including the assessment of “triggering” (initiation) of soil liquefaction, assessment of liquefaction resistance based on in situ testing, and
assessment of the site liquefaction index and deformation of liquefiable sites.
3.1.1
Liquefaction Evaluation Procedure
Based on In Situ Testing
Figure 3.1 shows the three steps for evaluation of the liquefaction hazard.
Procedure I is the assessment of “triggering” (initiation) of soil liquefaction, procedure II the assessment of liquefaction resistance based on in situ tests, and procedure III the assessment of site liquefaction index and deformation of liquefiable
sites. It must be pointed out that current in situ testing methods are mainly for the
horizontal strata in the seismic codes.
3.1.2
Assessment of “Triggering” (Initiation)
of Soil Liquefaction
The first procedure in engineering is to assess the initiation of soil liquefaction.
Seed and Idriss (1982) modified the “Chinese Criteria” of Wang (1980) and pointed
© Springer Nature Singapore Pte Ltd. 2017
Y. Huang and M. Yu, Hazard Analysis of Seismic Soil Liquefaction,
Springer Natural Hazards, DOI 10.1007/978-981-10-4379-6_3
35
3 Liquefaction Potential Evaluation …
36
Engineering site
Procedure
Earthquake action
Assessment of “triggering” (initiation) of soil
liquefaction
No
Yes
Assessment of liquefaction
resistance base on in situ tests
SPT
CPT
Vs
BPT
No danger
danger
Liquefaction
treatment
Site liquefaction
index
Deformation estimation of
liquefied sites
The site is safe
Fig. 3.1 Analysis process of site liquefaction evaluation
out that soil type is very important for assessment of soil liquefaction initiation.
Soils with a flowing characteristic would be liquefied; these should include the
following criteria.
(1) Clay fines <15% (<0.005 mm)
(2) Liquid limit <35%
(3) In situ water content 90% of the liquid limit
Andrews and Martin (2000) determined that clay sizes should be defined as less
than 0.002 mm. They recommend a new criteria:
(1) Clay fines <10% (<0.002 mm) and liquid limit <32% should be considered
liquefiable soil
(2) Clay fines >*10% and liquid limit >32% are unlikely to be liquefied
(3) Soils between (1) and (2) should be sampled and tested to assess whether they
can be liquefied
According to the Code for Seismic Design of Buildings (Ministry of
Construction of China 2010), if one of the following conditions is present, the soil
can be identified as non-liquefiable or the impact of liquefaction can be disregarded:
(1) For geological age of Quaternary Pleistocene (Q3) and prior, with seismic
intensity VII and VIII.
(2) Clay content (particle size <0.005 mm) for seismic intensities VII, VIII and IX
is not less than 10, 13 and 16%, respectively.
(3) For construction of shallow buried natural foundation, when the thickness of
the overlying non-liquefied soil layer and depth of the underground water level
have one of the following conditions:
3.1 Introduction to Liquefaction Evaluation Based on In Situ Testing
37
du [ d0 þ db 2
ð3:1Þ
dw [ d0 þ db 3
ð3:2Þ
du þ dw [ 1:5d0 þ 2db 4:5;
ð3:3Þ
where dw is depth of the underground water level (m), which should be designed
according to the average annual maximum value in the design period
du is thickness of the overlying non-liquefied soil layer (m); the mud soil layer
should be deduced
db is the foundation depth (m), when <2 m we assume it is 2 m
d0 is the characteristic depth of liquefied soil (m) and is shown in Table 3.1.
The above methods are not always correct. They use empirical statistics based on
past earthquakes and may be correct for a degree of reliability. For example,
investigations of seismic damage have indicated that the methods are not very
convincing when the clay content is considered (Table 3.2).
Table 3.1 Characteristic
depth of liquefied soil
(m) (Ministry of Construction
of China 2010)
Soils
VII (0.1 g)
VIII (0.2 g)
IX (0.4 g)
silt
sand
6
7
7
8
8
9
Table 3.2 Cases of soil liquefaction containing fine clay particles (Based on: Bol et al. 2010;
Hwang and Yang 2001; Tan et al. 2013; Tokimatsu and Yoshimi 1983)
Year
Earthquake
Investigator
Soil characteristics
1964
1968
1971
1976
1979
1983
1987
1989
1993
1999
Niigata
Tokachi
San Fernando
Tangshan
Imperial Valley
Idaho
Chi-Toho-Oki
Loma Prieta
Hokkaido
ChiChi
70% fine, 10% clay
90% fine, 18% clay
Silty sand
20% clay
Silt with 15% clay
70% fine, 20% clay
Silt with clay
PI = 17, clay content 24%
48% fine, 18% clay
Fine content 36–53%
1999
Adapazari
2009
2010
Olanche
Christchurch
Kishida (1969)
Tohno and Yasuda (1981)
Seed et al. (1989)
Wang (1979)
Bennett et al. (1981)
Youd et al. (1985)
Ishihara et al. (1989)
Boulanger et al. (1997)
Miura et al. (1995)
Hwang and Yang (2001);
Ku et al. (2004)
Bray and Sancio (2006);
Bol et al. (2010)
Holzer et al. (2010)
Ward et al. (2010)
70% fine, PI = 0–25
Fine content 15 ± 8%
Silt
3 Liquefaction Potential Evaluation …
38
3.1.3
Assessment of Liquefaction Resistance
The safety factors in engineering seismic codes are similar in different countries.
This chapter introduces three codes (American, Japanese, and Chinese) for
assessment of liquefaction resistance, which represent the most advanced levels
worldwide. The value of the cyclic stress ratio (CSR in the National Center for
Earthquake Engineering Research (NCEER) recommended method and L in the
Japanese code) of the seismic action is calculated first, and the cyclic resistance
ratio (CRR in the NCEER recommended method and R in the Japanese code) of the
soil layer is calculated using SPT, CPT, BPT (DPT) and Vs. Finally, the liquefaction potential of the test point can be evaluated. It can be seen in Table 3.3 that
the safety factors are similar. The Chinese code is N=Ncr , the NCEER recommended method is Fs ¼ CRR=CSR, and the Japanese code is FL ¼ R=L. CSR and L
can be calculated using Eqs. 3.4–3.12. The Chinese code and cyclic resistance ratio
(CRR in Table 3.3) will be introduced in the next section, based on in situ tests.
(1) Cyclic stress ratio
The cyclic stress ratio can be calculated according to the method of Seed and Idriss
(1971) or the so-called NCEER recommended method (Eq. 3.4).
CSR ¼ sam r0mo ¼ 0:65ðamax =gÞ rmo r0mo rd
rd ¼
1:0 0:00765z
1:174 0:0267z
ð3:4Þ
z 9:15m
9:15 m\z 23 m
ð3:5Þ
where rmo and r0mo are the overlying total stress and effective stress at the penetration
point, respectively
amax is horizontal earthquake peak acceleration and cd is the stress reduction
coefficient; these can be calculated by Eqs. 3.5 and 3.7, respectively.
In the Japanese code for seismic design of roads and bridges (Japan Road
Association), L is equal to the cyclic stress ratio.
L ¼ rd khg rm r0m
ð3:6Þ
rd ¼ 1:0 0:015z
ð3:7Þ
where khg is the horizontal earthquake coefficient. Other coefficients are similar to
the NCEER recommended method.
Table 3.3 Safety factors of the three codes
Codes
NCEER recommended method
Japanese code
Chinese code
Safety factor
Fs ¼ CRR=CSR
FL ¼ R=L
N=Ncr
3.1 Introduction to Liquefaction Evaluation Based on In Situ Testing
39
(2) Magnitude scaling factors
The CRR of a clean sand base in the SPT or CPT only applies to an earthquake
magnitude of 7.5 (MSF = 1). Seed and Idriss (1982) introduced a correction factor
called the magnitude scaling factor (MSF) to correct the CSR for earthquake
magnitudes smaller or larger than 7.5. The safety factor should be corrected by
Eq. 3.8, and Eq. 3.4 should be corrected to Eq. 3.9.
Fs ¼ ðCRR=CSRÞMSF
ð3:8Þ
CSR ¼ sam r0mo ¼ 0:65ðamax =gÞ rmo r0mo rd MSF 1
ð3:9Þ
MSF can be obtained by Eq. 3.10 (Youd et al. 2001), Eq. 3.11 (Andrus and Stokoe
1997), and other recommended curves in Fig. 3.2. A similar magnitude scaling
factor rm in the Japanese code is shown in Eq. 3.12.
MSF ¼ 102:24 =Mw2
ð3:10Þ
MSF ¼ ðMw =7:5Þ2:56
ð3:11Þ
rm ¼ ½6:5=ðM 1Þ0:5ð1 þ Na=10Þ
ð3:12Þ
(3) Cyclic resistance ratio
There are many factors affecting liquefaction evaluation; in situ test methods can
consider those factors by empirical equations. Cyclic stresses can be calculated
using Eq. 3.9. The CRR calculated using in situ tests is the main subject of this
chapter. In addition, the site liquefaction index and deformation estimation are
introduced in the following sections.
Fig. 3.2 Magnitude scaling
factors derived by various
investigators (reprinted from
Youd et al. (2001) with
permission of American
Society of Civil Engineers)
40
3.2
3 Liquefaction Potential Evaluation …
In Situ Testing for Liquefaction Potential Evaluation
The methods that can be used for liquefaction evaluation are the standard penetration test (SPT), cone penetration test (CPT), dynamic cone penetration test (DPT
or BPT), and wave velocity test (VS). Liquefaction resistance is obtained by calculating the penetration resistance in empirical formulas. Compared with laboratory
tests, in situ testing has a notable feature that can basically maintain the formation
structure, humidity, and ground stress of soil. The data obtained by in situ tests can
represent the state of soil (e.g., relative density) and can be used to evaluate the
liquefaction potential of sites via empirical methods.
There are eight in situ tests that are most frequently used for geotechnical
investigation, which are listed below. Tests 2–5 can be used to evaluate the liquefaction potential:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Plate load test (PLT)
Standard penetration test (SPT)
Cone penetration test (CPT)
Dynamic cone penetration test or Becker penetration test (DPT or BPT)
Shear-wave velocity measurements (Vs)
Vane shear test (VST)
Flat dilatometer test (DMT)
Pressuremeter test (PMT)
Among these in situ tests, SPT, CPT, BPT and DPT are carried out in the soil,
which causes disturbance to the soil; therefore, the strain is larger than in the wave
velocity test (Vs), which produces nearly no disturbance to the soil. Although all of
these in situ tests are widely proposed in many codes for evaluating soil liquefaction
resistance, the SPT and CPT are generally preferred because there are many
databases for those methods. However, the other tests can be applied at sites of
gravelly sediment where the SPT and CPT cannot be used (Harder and Seed 1986).
Table 3.4 shows the advantages and disadvantages of these test methods (Youd
et al. 2001).
In this section, the SPT, CPT, Vs, BPT (DPT) will be introduced in two parts,
(1) the test apparatus and test procedure, and (2) data analysis for liquefaction
potential evaluation.
In addition to those methods proposed by different seismic codes, some in situ
tests have also been investigated for evaluation of liquefaction potential. For
example, Arulmoli et al. (1985) pointed out that electrical resistivity (ER) can be
used to investigate soil liquefaction. Banton et al. (1997) studied the spatial relationship between the saturated hydraulic conductivity, clay content, water content,
and electrical resistivity of soils and found that electrical resistivity can be used for
liquefaction sites. Investigation should be applied to large domains rather than to
small fields, a method that has been used by Yuan and Cao (2011b).
3.2 In Situ Testing for Liquefaction Potential Evaluation
41
Table 3.4 Advantages and disadvantages of field tests (reprinted from Youd et al. (2001) with
permission of American Society of Civil Engineers)
Feature
Past measurements at
liquefaction sites
Type of stress–strain
behavior influencing test
Quality control and
repeatability
Detection of variability
of soil deposits
Soil types in which test
is recommended
Soil sample retrieved
Test measures index or
engineering properties
3.2.1
Test type
Vs
BPT (DPT)
SPT
CPT
Abundant
Abundant
Limited
Sparse
Partially
drained, large
strain
Poor to good
Drained,
large strain
Small strain
Very good
Good
Partially
drained, large
strain
Poor
Good for
closely spaced
tests
Non-gravel
Very good
Fair
Fair
Non-gravel
All
Yes
Index
No
Index
No
Engineering
Primarily
gravel
No
Index
Standard Penetration Test
In engineering, the properties of soil can be determined by in situ tests, and the SPT
is a test method designed to provide soil information in geotechnical engineering.
Currently, the SPT is used worldwide for liquefaction evaluation (Bol et al. 2010;
Boulanger and Idriss 2012; Cetin et al. 2004; Hwang and Yang 2001; Kalantary
et al. 2009; Yalcin et al. 2008; Youd et al. 2001). At present, three corrections are
considered by research, namely, the confining pressure, the fine (clay) particle
content, and the hammer energy.
3.2.1.1
Test Apparatus and Procedure
The test apparatus includes the drilling equipment, sampling rods, a split-barrel
sampler and a drive weight assembly. According to the American Society for Testing
and Materials (ASTM D1586−2011) and Code for Investigation of Geotechnical
Engineering (Ministry of Construction of China 2009), the test apparatus and procedure are basically the same except for some differences in parameters. The tube
has an outside diameter of 50.8 mm, an inside diameter of 35 mm, and a
length >50 cm (Ministry of Construction of China 2009) or 45.7–76.2 cm (ASTM
D1586−2011). It is driven into the ground by a hammer with mass of 63.5 kg falling
through a distance of 760 mm.
The automatic free-drop hammer should be used and the rod should be kept
vertical. To avoid hammer eccentricity, the hammering rate should be less than
3 Liquefaction Potential Evaluation …
42
30 per minute. First, the penetrometer is imbedded in the soil to 15 cm, and then the
blow count is recorded each 10 cm. Finally, the total hammering number for 30 cm
is used as the SPT blow count. When more than 50 blow counts are reached and the
penetration depth is <30 cm the test is stopped, and Eq. 3.13 is used to convert the
equivalent penetration blow count (Ministry of Construction of China 2009).
N ¼ 30 50
DS
ð3:13Þ
where N is the equivalent penetration blow count for 30 cm;
DS is penetration depth upon stopping the test (<30 cm)
3.2.1.2
Data Analysis for Liquefaction Potential Evaluation
The SPT can be used to evaluate liquefaction potential, soil relative density, and
liquefaction settlement, as follows.
(1) Cyclic resistance ratio calculated by SPT
(a) NCEER recommended method
The NCEER recommended method was published in 2001 (Youd et al. 2001),
and is based on the research of Seed and Idriss (1972). Many scholars advanced the
method with correction (Boulanger and Idriss 2012; Cetin et al. 2004).
Equations 3.15 and 3.17 are recommended for correcting overburden effective
stress and fine content, and the CRR value can be calculated by the corrected SPT
count (Eq. 3.14). Equation 3.14 was obtained based on many earthquake liquefaction case histories (Fig. 3.3). We ultimately used Eq. 3.8 to evaluate soil liquefaction at the penetration point.
CRR7:5 ¼
ðN1 Þ60cs
1
50
1
þ
þ
2 34 ðN1 Þ60cs
200
135
10 ðN1 Þ60cs þ 45
ð3:14Þ
In engineering, N values of SPT should be corrected, among which the overburden
effective stress and fine content are most important. Because these values increase
with effective stress, Seed and Idriss (1982) recommended the overburden stress
correction. The correction factor can be calculated from Eqs. 3.15 and 3.16; the
correction factor CN can be calculated by Eq. 3.16.
ðN1 Þ60 ¼ Nm CN
(
0 0:5
0
CN ¼ P
200 kPa ;
a rmo 0 rmo
CN ¼ 2:2 1:2 þ rmo Pa r0mo [ 200 kPa
where (N1)60 is the blow count corrected by effective overburden stress
Nm is the blow count before correction for effective overburden stress
ð3:15Þ
ð3:16Þ
3.2 In Situ Testing for Liquefaction Potential Evaluation
43
Fig. 3.3 SPT clean sand base
curve for a magnitude‐7.5
earthquake, with data from
liquefaction case histories
(reprinted from Youd et al.
(2001) with permission of
American Society of Civil
Engineers)
CN is the correction factor;
Pa is *100 kPa (1 atm)
More detailed equations are in Youd et al. (2001).
The American and Japanese codes consider the influence of fine particles, and
the Chinese code considers that of clay content. The CRR curve in Fig. 3.3 for fine
contents <5% is a simplified procedure only for clean sand. For fine contents more
than 5 or 35%, Eq. 3.17 should be used to correct the SPT count.
ðN1 Þ60cs ¼ a þ bðN1 Þ60
a¼
b¼
ð3:17Þ
exp½1:76 ð190 Fc2 Þ
5
ð5% Fc\35%Þ
ðFc 35%Þ
ð3:18Þ
½0:99 þ ðFC 1:5 1000Þ
1:2
ð5% Fc\35%Þ
;
ðFc 35%Þ
ð3:19Þ
where (N1)60cs is the corrected blow count;
a and b are correction coefficients;
Fc is fine content
(2) Japanese code
There are many codes for seismic design in Japan, but the most used is the
design for roads and bridges (Japan Road Association 2002). The Japanese code is
similar to the American one, but varies in the correction of fine content. The safety
factor FL can be calculated by Eq. 3.20 and the entire calculation is similar to the
3 Liquefaction Potential Evaluation …
44
NCEER recommended method. Equations 3.22 and 3.23 are for correction of
effective overburden stress and fine content, respectively, and they and related
equations are as follows.
FL ¼ R=L
(
R¼
ð3:20Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0:0882 Na =1:7
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0:0882 Na =1:7 þ 1:6 106 ðNa 14Þ4:5
c1 ¼
ð3:21Þ
N1 ¼ 170 N=ðr0 þ 70Þ
ð3:22Þ
Na ¼ c1 N1 þ c2
ð3:23Þ
8
<
1
ðFc þ 40Þ=50
:
Fc =20 1
c2 ¼
ðNa \14Þ
ð14 Na Þ
ð0% Fc \10%Þ
ð10% Fc \60%Þ ;
ð60% Fc Þ
ð3:24Þ
ð0% Fc \10%Þ
;
ð10% Fc Þ
ð3:25Þ
0
ðFc 10Þ=18
where Na is the final corrected blow count;
c1 and c2 are correction coefficients for fine contents
N1 is the blow count before considering fine content
More detailed equations are in Japan Road Association (2002).
(3) Chinese code
According to the Chinese code for seismic design of buildings (Ministry of
Construction of China 2010), the ratio N=Ncr can be used to evaluate the liquefaction potential at the penetration point. The critical penetration blow count can be
attained by
sffiffiffiffiffiffiffi
3
Ncr ¼ N0 b½1n(0:6ds þ 1:5Þ0:1dw ;
qc
ð3:26Þ
where Ncr is the critical SPT blow count;
Table 3.5 Value of N0 for Chinese code (Ministry of Construction of China 2010 and Ministry of
Water Resources of China 2008)
Code
0.1 g
0.15 g
0.2 g
0.3 g
0.4 g
GB 50011–2010
GB 50487–2008
7
6
8
10
8
10
12
10
12
16
13
15
19
16
18
Epicenter distance (100–1000 km)
Epicenter distance (>1000 km)
3.2 In Situ Testing for Liquefaction Potential Evaluation
45
N0 is the reference blow count, which is associated with the earthquake (Table 3.5)
b is a coefficient;
ds is the penetration point depth
dw is underground water level
qc is clay content, when it is <3% it is assumed to be 3%
When N [ Ncr , the penetration point will not be liquefied and when N Ncr , it
will be liquefied.
According to the Chinese code for Engineering Geological Investigation of
Water Resources and Hydropower (Ministry of Water Resources of China 2008),
Ncr can be defined by Eq. 3.27. This code is consistent with the previous one
(Ministry of Water Resources of China 1999) for water resources and hydropower.
sffiffiffiffiffiffiffi
3%
;
Ncr ¼ N0 ½0:9 þ 0:1ðds dw Þ
qc
ð3:27Þ
where N0 is the reference N-value that depends on earthquake intensity and distance
(Table 3.6);
ds is depth from the ground surface (in meters) (set to 5 when ds is <5)
dw is underground water level
qc is clay content, when <3% it is assumed to be 3%
The measured N-value should be converted to an equivalent N-value using
0
N63:5 ¼ N63:5
ds þ 0:9dw þ 0:7
;
ds0 þ 0:9dw0 þ 0:7
ð3:28Þ
0
where N63:5 is the measured N-value;
N63:5 is the equivalent N-value;
0
0
ds and dw are depth from the ground surface and depth of the groundwater level,
respectively
(2) Evaluation of relative density of soils
According to the Code for Investigation of Geotechnical Engineering (Ministry
of Construction of China 2009), the SPT blow count can be used to evaluate the
relative density of sandy silt and sand (Table 3.6).
Table 3.6 SPT for sandy
silt and sand relative density
(Ministry of Construction of
China 2009)
SPT count
Relative density
N 10
10 < N 15
15 < N 30
N > 30
Loose
Slightly dense
Medium dense
Dense
3 Liquefaction Potential Evaluation …
46
The SPT can be used to evaluate sand relative density quantitatively according to
Eq. 3.29.
rffiffiffiffiffiffiffi
N1
Dr ¼ 21
1:7
N1 ¼ 170N=ðr0m þ 70Þ;
ð3:29Þ
ð3:30Þ
where Dr is relative density;
N1 is the corrected blow count considering effective overburden stress r′v in kPa.
3.2.2
Cone Penetration Test
The cone penetration tests are typically used in soft soil, clay, silt, sand, and sand
soil containing a small amount of gravel. The tests are not applicable to gravel soil
or very dense sand. The metal probe penetrates the soil at a standard speed, and then
penetration resistance is analyzed to evaluate soil mechanical properties. In contrast,
the cone penetration test penetrates the soil continuously, and the results can reflect
soil mechanical properties throughout the depth. Therefore, the latter test has two
functions, soil exploration and field testing, and is one of the most widely used
methods in geotechnical engineering investigation.
3.2.2.1
Test Apparatus and Procedure
According to the American Society for Testing and Materials (ASTM D5778
−2012) and Code for Investigation of Geotechnical Engineering (Ministry of
Construction of China 2009), the equipment for the cone penetration test includes a
friction cone penetrometer, measuring system, push rods, and friction reducer. The
test method pushes the cone with tip facing downward into the ground at a controlled rate (generally 1.5–2.5 cm/s). The typical cone tips have a cross-sectional
area of either 10 or 15 cm2, corresponding to diameters of 35.7 and 43.7 mm.
There are three types of electric probe. A single bridge probe can only acquire
the specific penetration resistance ps and a double bridge probe can obtain tip
resistance qc and side friction fs. The piezocone penetration test can also obtain data
of excess pore water pressure.
3.2.2.2
Data Analysis for Liquefaction Potential Evaluation
(1) Cyclic resistance ratio calculated by CPT
(a) NCEER recommended method
3.2 In Situ Testing for Liquefaction Potential Evaluation
47
Because of the poor repeatability and inherent difficulties of SPT, CPT penetration resistance has been proposed to estimate CRR of soils (Robertson and Wride
1998). The results of CPT are more consistent and repeatable, and it also permits a
more detailed definition of soil layers by a continuous soil profile. The CRR can be
determined by
CRR7:5 ¼
ðqc1N Þcs \50
0:833½ðqc1N Þcs =10003 þ 0:05
;
3
50\ðqc1N Þcs 160
93½ðqc1N Þcs =1000 þ 0:08
ð3:31Þ
where ðqc1N Þcs is clean-sand cone penetration resistance normalized to *100 kPa,
which can be calculated from Eq. 3.32. However, Kc and qc1N are still unknown,
but can be calculated from Eqs. 3.33 and 3.34.
ðqc1N Þcs ¼ Kc q1N
Kc ¼
0
0:403Ic4 þ 5:581Ic3 21:63Ic2 þ 33:75Ic 17:88
ð3:32Þ
Ic 1:64
Ic [ 1:6
ð3:33Þ
qc1N ¼ CQ ðqc =Pa Þ
ð3:34Þ
CQ ¼ ðPa =r0 m0 Þn ;
ð3:35Þ
where Kc is the correction factor for grain characteristics
qc is field cone penetration resistance measured at the tip
CQ = normalizing factor for cone penetration resistance
Pa = 1 atm of pressure (same units as r′v0)
n is an exponent that varies with soil type, from 0.5 to 1.0
Ic is the soil behavior type index in Table 3.7 (also from certain equations;
Robertson 1990).
(b) Chinese code for CRR based on CPT
According the Code for Investigation of Geotechnical Engineering (Ministry of
Construction of China 2009), the CPT can be used to evaluate liquefaction
Table 3.7 Boundaries of soil behavior type (reprinted from Robertson and Wride (1998) with
permission of NRC Research Press)
Soil behaviour type index, Ic
Soil behaviour type
Ic < 1.31
1.31 < Ic
2.05 < Ic
2.60 < Ic
2.95 < Ic
Ic > 3.60
Gravelly sand to dense sand
Sands: clean sand to silty sand
Sand mixtures: silty sand to sandy silt
Silt mixtures: clayey silt to silty clay
Clays: silty clay to clay
Organic soils: peats
<
<
<
<
2.05
2.60
2.95
3.60
3 Liquefaction Potential Evaluation …
48
potential. If qc < qccr , the soil will be liquefied. The critical penetration resistance
can be determined by
qccr ¼ qc0 aw au ap ;
ð3:36Þ
where qc0 is the reference value for critical penetration resistance (MPa); for
earthquake intensity 0.1 g, we assume it to be 4.6–5.5; for 0.2 g, 10.5–11.8; and for
0.4 g, 16.4–18.2
aw is a correction coefficient for groundwater level depth, 1.13 is the recommended
value
au is a correction coefficient for upper non-liquefied soil
ap is a correction coefficient for soil type, for sand = 1, for silt <1
3.2.3
Wave Velocity Test
The wave velocity test methods do not disturb soils and can be used at all types of
engineering sites. Andrus and Stokoe (1997, 2000) developed liquefaction resistance
criteria from field measurements of shear wave velocity (Vs). Vs values are proposed
for soils that are difficult to penetrate, such as gravelly ones or those where boring
may not be permitted. Another advantage of the Vs method is that it can calculate the
small-strain shear modulus of soils and be used to estimate the dynamics of soil
response and soil structure interaction. However, the test does not provide samples
for soil classification and should not be the only investigation method.
3.2.3.1
Test Apparatus and Procedure
According to the American Society for Testing and Materials (ASTM D7400
−2014) and Code for Investigation of Geotechnical Engineering (Ministry of
Construction of China 2009), the wave velocity test is a type of engineering geophysical prospecting that is a direct wave method and may be used as an in situ test
method. The wave proceeding from the source directly to the receiving point is
called a direct wave, the wave velocity of which can be obtained from the direct
wave of the time-distance curve and can be used to estimate dynamic properties of
rock mass parameters.
The velocity measurement is suitable for determination of the compression
wave, shear wave or Rayleigh wave of various rock and soil. The purpose of the test
is to determine the dynamic elastic modulus of rock and soil under small strain
(10−4–10−6), which is based on the propagation velocity of an elastic wave in rock
and soil. There are downhole, crosshole and surface wave methods. Figure 3.4
displays the apparatus of the wave velocity test and its schematic diagram for
downhole seismic testing.
3.2 In Situ Testing for Liquefaction Potential Evaluation
Fig. 3.4 Schematic diagram
of downhole seismic test
49
Data collection
The vibration source
Probes
3.2.3.2
Data Analysis for Liquefaction Potential Evaluation
(1) NCEER recommended method
Andrus and Stokoe (1997, 2000) developed liquefaction resistance criteria from
field tests of Vs. Vs is basically a mechanical property of soil materials. The procedures for Vs determination also need overburden stress correction using Eq. 3.37.
We then use the corrected Vs to calculate CRR by Eq. 3.38.
Pa 0:25
Þ
r0m0
ð3:37Þ
Vs1 2
1
1
Þ þ bð Þ
V S1 Vs1 Vs1
100
ð3:38Þ
Vs1 ¼ Vs ð
CRR ¼ að
Vs1
¼
8
<
215
Fc 5%
0:75Fc þ 218:75 5% Fc\35% ;
:
200
35% Fc
ð3:39Þ
where Vs1 is overburden-stress corrected shear wave velocity
Pa is atmospheric pressure, approximated by 100 kPa
r0m0 is initial effective vertical stress
V*s1 = limiting upper value of Vs1 for liquefaction occurrence, obtained by
Eq. 3.39
a and b are curve fitting parameters, 0.022 and 2.8, respectively
3 Liquefaction Potential Evaluation …
50
Table 3.8 Reference values
for critical shear wave
velocity (m/s) (Ministry of
Construction of China 2009)
Soil
0.1(0.15) g
0.2(0.3) g
0.4 g
Sand
Silt
65
45
95
65
130
90
(2) Chinese code for CRR based on Vs
The method of the Chinese code for CRR based on Vs is similar to the SPT and
CPT. There is critical shear wave velocity Vscr, which can be calculated by
Vscr ¼ Vs0 ðds 0:0133ds2 Þ0:25 ½1:0 0:185½
dw 3 0:5
ð Þ ;
d s qc
ð3:40Þ
where Vs0 is a reference value for critical shear wave velocity, shown in Table 3.8.
Other coefficients are the same as in Eq. 3.26.
3.2.4
Becker Penetration and Dynamic Penetration Tests
The BPT is not widely used for liquefaction evaluation because the mechanism of
gravel soil liquefaction is not well known. Liquefaction phenomena of sandy soil
containing gravel were introduced in the reference of Huang and Yu (2013). As is
known, the SPT blow count is larger for gravel soil, which causes error in liquefaction evaluation. Investigators have also used the heavy dynamic penetration test
(DPT) N120 to evaluate mechanical properties of gravel soil (Yuan and Cao 2011a).
There is no uniform standard for this method, however.
3.2.4.1
Test Apparatus and Procedure
In North America, the BPT is the primary field test to measure the penetration
resistance of gravels for liquefaction potential assessment. The BPT was developed
in Canada in the 1950s (Harder and Seed 1986). Penetration resistance is the same
as in the SPT and is defined as the blow count number through a depth of 30 cm.
Because very few liquefaction sites have had BPT data, the test has not been
very convincing in engineering. Cao et al. (2012) pointed out that the BPT has been
limited to high-cost investigations, and has not been used in many other parts of the
world. They thus used the Chinese dynamic penetration test for analysis of the
Wenchuan earthquake, and proposed more reliable and efficient methods for
gravelly soils. The DPT equipment consists of a 120-kg hammer with nominal
free-fall height of 100 cm dropped onto an anvil attached to 60-mm diameter drill
rods, which are attached to a solid cone tip 74 mm in diameter. Figure 3.5 shows
the apparatus of the DPT. N120 is the number of blows required to drive the tip
30 cm, which is used to calculate the CRR of the penetration point.
3.2 In Situ Testing for Liquefaction Potential Evaluation
51
Fig. 3.5 Apparatus for the dynamic penetration test (reprinted from Cao et al. (2012) with
permission of American Society of Civil Engineers)
3.2.4.2
Data Analysis for Liquefaction Potential Evaluation
The BPT data should be converted to an SPT N count, and then evaluation procedures based on the SPT applied. The relationship between BPT and SPT counts is
in Harder and Seed (1986), Harder and Idris (1997). Cao et al. (2012) also gave a
distinguishing standard for gravel soil based on N120.
3.3
3.3.1
Assessment of Site Liquefaction Potential
and Seismic Deformation
Assessment of Site Liquefaction Potential
Section 3.2 addressed liquefaction at each penetration point of the stratum.
However, the liquefaction magnitude of the entire stratum remains unknown. The
depth and thickness of the liquefiable soil layer should be considered. The site
liquefaction potential index (LPI) can be expressed as PL in Eq. 3.41 (Japan Road
Association 2002) or Ile in Eq. 3.42 (Ministry of Construction of China 2010). The
liquefaction magnitude of each boring hole is listed in Table 3.9.
Table 3.9 Assessment of site
liquefaction potential (Japan
Road Association 2002;
Ministry of Construction of
China 2010)
Liquefaction hazard
Equation 3.41
Equation 3.42
Slight liquefaction
Medium liquefaction
Severe liquefaction
PL 5
6 < PL 20
PL > 20
Ile 6
6 < Ile 18
Ile > 18
3 Liquefaction Potential Evaluation …
52
ZH
PL ¼
ð1 FL ðzÞÞw(z)dz
ð3:41Þ
0
I1e ¼
n
X
ð1 F1ei Þdi Wi ;
ð3:42Þ
i¼
where FL ðzÞ and Flei are safety factors at each depth, which can be obtained by
SPT, CPT, Vs, and BPT (DPT)
wðzÞ is the weight function, for 0 m < z < 10 m,wðzÞ = 10; for 10 m < z
< 20 m,wðzÞ ¼ 10 0:5z
di is thickness of the liquefied soil layer (m)
Wi is the weight function for Eq. 3.42, for 0 m < z < 5 m,wðzÞ = 10; for 10 m < z
zÞ
< 20 m, wðzÞ ¼ ð402
3
3.3.2
Assessment of Seismic Deformation
Besides the evaluation of liquefaction potential, another assessment of soil performance is soil seismic deformation, which includes liquefaction settlement and
lateral spread. Tokimatsu and Seed (1987), Shamoto et al. (1998), Cetin et al.
(2009) and others have researched this problem thoroughly in their pioneering
studies. In their methods, the equivalent volumetric strain should be evaluated first,
and then the settlement of an entire site can be calculated.
According to empirical formulae based on SPT and the shear stress ratio, liquefaction settlement can be calculated as shown in Fig. 3.6.
The assessment steps of the soil liquefaction settlement are as follows.
(1) Calculate shear stress ratio CSR by Eqs. 3.4 or 3.6.
(2) Calculate blow count (N1)60 after effective overburden stress correction by
Eqs. 3.15 or 3.23.
(3) Evaluate volumetric strain on the CSR and (N1)60 using Fig. 3.6 (Tokimatsu
and Seed, 1987).
(4) Calculate site liquefaction settlement by Eqs. 3.43 and 3.44
Si ¼ di e i
S¼
n
X
i¼1
where S is settlement of the entire site
Si
ð3:43Þ
ð3:44Þ
3.3 Assessment of Site Liquefaction Potential and Seismic Deformation
53
Fig. 3.6 Volumetric strain
for saturated sand based on
CSR and (N1)60 (reprinted
from Tokimatsu and Seed
(1987) with permission of
American Society of Civil
Engineers)
Si is the settlement of each layer
di is the thickness of each layer
ei is the volumetric strain of each layer
Lateral spread is liquefaction-induced deformation in which soil layers break
into blocks or flow, owing to gradients in the soil layer. The pioneering study of
Hamada et al. (1986) is widely accepted, and Faris et al. (2006) advanced a
field-calibrated model. An empirical equation based on 60 earthquake case histories
is proposed to predict liquefaction-induced lateral deformation (Hamada et al.
1986):
Dh ¼ 0:75H 0:5 h1=3 ;
ð3:45Þ
where Dh is predicted horizontal ground displacement (m)
H is thickness of the liquefied zone (m)
h is the larger slope of either the ground surface or liquefied zone lower boundary (%)
3 Liquefaction Potential Evaluation …
54
Faris et al. (2006) presented the following semi-empirical model:
Hmax ¼ expð1:0443 In(DPImax Þ þ 0:0046 In a þ 0:0029 Mw Þ;
ð3:46Þ
where Hmax is the lateral spreading in meters;
DPImax is the maximum cyclic shear strain potential
a is the slope or free-face ratio
Mw is the earthquake magnitude
3.3.3
Case Study of Liquefaction Evaluation Based on SPT
Here, we introduce the procedures of liquefaction potential evaluation based on
in situ testing, using a case study of those procedures. Figure 3.7 shows a site with
liquefiable soil from depths of 3–17 m; for B-1 the soil is sand and for B-2 it is silt.
The in situ test is used to evaluate liquefaction potential and calculate site liquefaction settlement. SPT boring holes in a section are used to evaluate the liquefaction potential of the site. Table 3.10 lists specific data of boring holes. The
seismic intensity is VII (0.1 g) for engineering design, and Eqs. 3.26 and 3.42 are
used to calculated Ilei. From the liquefaction evaluation based on SPT, it is seen that
the site has medium liquefaction. We determined a settlement of 22.5 cm for liquefiable soil layers.
Fig. 3.7 Stratum distribution
of case study
B-2
B-1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
N0
3.15
4.15
5.15
6.15
7.15
8.15
9.15
10.15
11.15
12.15
13.15
14.15
15.15
16.15
17.15
ds
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
dw
3.3
3
3
3
3
4.3
3.3
6.2
5.3
8.3
6.4
6.4
4.3
8.4
3.4
qc
8
13
6
10
5
9
11
9
5
6
11
10
13
12
13
N
6.2
7.41
8.2
8.89
9.5
8.39
10.06
7.66
8.61
7.12
8.36
8.59
10.76
7.88
12.66
Ncr
Table 3.10 Liquefaction potential evaluation based on SPT
10
10
9.9
9.23
8.57
7.9
7.23
6.57
5.9
5.23
4.57
3.9
3.23
2.57
1.9
Wi
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
di
No
No
Yes
No
Yes
No
No
No
Yes
Yes
No
No
No
No
No
Liquefied
or not
2.472
0.820
4.057
2.654
Ilei
Ile = 10
Medium liquefaction
Site liquefaction potential
0.225
Settlement (m)
3.3 Assessment of Site Liquefaction Potential and Seismic Deformation
55
3 Liquefaction Potential Evaluation …
56
3.4
Conclusions
The most highly recommended methods of various codes for routine evaluation of
liquefaction resistance were introduced in this chapter. Three steps are followed to
evaluate the liquefaction hazard, i.e., assessments of “triggering” (initiation) of soil
liquefaction, of liquefaction resistance based on in situ tests, and of the site liquefaction index and deformation of liquefiable sites. Four in situ tests were introduced to evaluate liquefaction potential.
(1) Generally, the assessment of liquefaction resistance based on in situ tests is the
main component of the liquefaction evaluation. The SPT, CPT, and Vs measurements are widely used in worldwide. For gravelly sites, the BPT (DPT) is
recommended. Each test has its advantages and limitations.
(2) The SPT has a longer record of application and provides disturbed soil samples
from which fine contents and other grain characteristics can be determined.
The CPT can provide the most detailed soil stratigraphy and liquefaction
resistance curves. Measured Vs provides fundamental information on
small-strain soil and is also applicable to sites with gravelly sediments where
the CPT and SPT may not be possible or reliable. The BPT (DPT) test is
recommended for gravelly sites, but this method has not been standardized.
(3) Safety is the most important factor in the evaluation of liquefaction potential at
an engineering site. However, site investigation using only one method is
unsafe. If possible, two or more tests should be used to ensure adequate data to
evaluate liquefaction resistance. For a more detailed evaluation, laboratory tests
are introduced in the next chapter. For an entire site, the safety factor is
addressed by deterministic analysis. Therefore, probability analysis may be
more reasonable. This analysis is introduced in Chap. 7.
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2010). Beijing: China Building Industry Press. (in Chinese).
Ministry of Water Resources of China. (1999). Code for water resources and hydropower
engineering geological investigation (GB 50287–1999). Beijing: China Water Power Press. (in
Chinese).
Ministry of Water Resources of China. (2008). Code for engineering geological investigation of
water resources and hydropower (GB 50487–2008). Beijing: China Water Power Press. (in
Chinese).
Miura, S., Kawamura, S., & Yagi, K. (1995). Liquefaction damage of sandy and volcanic grounds
in the 1993 Hokkaido Nansei-Oki earthquake. In Proceeding 3rd international conference on
recent advances in geotechnical earthquake engineering and soil dynamics, St. Louis, MO
(Vol. 1, pp. 193–196).
Robertson, P. K. (1990). Soil classification using the cone penetration test. Canadian Geotechnical
Journal, 27(1), 151–158.
Robertson, P. K., & Wride, C. E. (1998). Evaluating cyclic liquefaction potential using the cone
penetration test. Canadian Geotechnical Journal, 35(3), 442–459.
Seed, H. B., & Idriss, I. M. (1971). Simplified procedure for evaluating soil liquefaction potential.
Journal of Soil Mechanics & Foundations Div, 97, 1249–1273.
Seed, H. B., & Idriss, I. M. (1982). Seed H B, Idriss I M. Ground motions and soil liquefaction
during earthquakes. Earthquake Engineering Research Institute.
Seed, H. B., Seed, R. B., Harder, L. F., & Jong, H. L. (1989). Re-Evaluation of the lower San
Fernando Dam, Report 2. Examination of the Post-Earthquake Slide of February 9, 1971.
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post-liquefaction ground settlement and horizontal displacement. Special Issue on the
Geotechnical Aspects of the January 17 1995 Hyogoken-Nambu Earthquake, No. 2, pp 69–83
Tan, C. S., Marto, A., Leong, T. K., & Teng, L. S. (2013). The role of fines in liquefaction
susceptibility of sand matrix soils. Electronic Journal of Geotechnical Engineering, 18,
2355–2368.
Tohno, I., & Yasuda, S. (1981). Liquefaction of the ground during the 1978 Miyagiken-Oki
earthquake. Soils and Foundations, 21(3), 18–34.
Tokimatsu, K., & Seed, H. B. (1987). Evaluation of settlements in sands due to earthquake
shaking. Journal of Geotechnical Engineering, 113(8), 861–878.
Tokimatsu, K., & Yoshimi, Y. (1983). Empirical correlation of soil liquefaction based on SPT
N-value and fines content. Soils and Foundations, 23(4), 56–74.
Wang, W. (1979). Some findings in soil liquefaction. Research Report, Water conservancy and
hydroelectric power scientific research Institute, Beijing, China
Wang, W. S. (1980). Some findings in soil liquefaction. Chinese Journal of Geotechnical
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Proceedings of the ninth pacific conference on earthquake engineering building an
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center (Central Anatolia, Turkey). Natural Hazards and Earth System Science, 8(4), 641–649.
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References
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Youd, T. L., Idriss, I. M., Andrus, R. D., et al. (2001). Liquefaction resistance of soils: summary
report from the 1996 NCEER and 1998 NCEER/NSF workshops on evaluation of liquefaction
resistance of soils. Journal of Geotechnical and Geoenvironmental Engineering, 127(10),
817–833.
Yuan, X., & Cao, Z. (2011a). Fundamental method and formula for evaluation of liquefaction of
gravel soil. Chinese Journal of Geotechnical Engineering, 33(4), 509. (in Chinese).
Yuan, X., & Cao, Z. (2011b). Features and new aspects of liquefaction in the Wenchuan
Earthquake. World Earthquake Engineering, 27(1), 1–8. (in Chinese).
Chapter 4
Laboratory Experimental Study
on Dynamic Characteristics
of Liquefiable Soil
4.1
Introduction
In addition to in situ tests, dynamic characteristics and liquefaction probability
estimation can be achieved by laboratory experimental methods and analyses. The
dynamic characteristics of soil refer to direct or indirect responses or effects of soil
under all types of dynamic loading, mainly modulus and damping ratio, dynamic
strength, and liquefaction resistance. The shear strain amplitude of soil and its
dynamic characteristics are closely related. When that amplitude is in the range of
10−6–10−4, the soil is in the elastic stage. When the amplitude is in the range of
10−4–10−2, it is in the elastic-plastic stage, and when the amplitude is >10−2, the
soil enters a state damage stage. A strain amplitude of 10−4 is used as the threshold
for large and small strain (Georgiannou et al. 1991).
Within the scope of small strain, soil deformation parameters such as the
dynamic modulus, Poisson’s ratio and damping ratio have been the main topics of
research (Clayton and Heymann 2001; Sun and Yuan 2003; Xu et al. 2012). Within
the scope of large strain, soil dynamic strength parameters such as dynamic strength
and liquefaction resistance have been principally researched (Huang et al. 2012).
The essence of the approach is to estimate the stress ratio and residual pore water
pressure ratio, which produce soil liquefaction and alter the seismic stress ratio of
the soil layer. Moreover, one estimates the liquefaction probability by comparing
the liquefaction stress and seismic stress ratios. With changes in shear strain, the
deformation and strength parameters of soil are obtained by various test methods.
These parameters include dynamic strength parameters or liquefaction strength, the
relationship between dynamic shear modulus and dynamic shear strain and that
between damping ratio and dynamic shear strain, and the law of growth and dissipation of pore pressure in soil.
The soil dynamic property tests refer to generic terms in research of those
properties using indoor experiments. First, soil samples are prepared in accord with
requirements of humidity, density, structure and stress state in a sample container,
© Springer Nature Singapore Pte Ltd. 2017
Y. Huang and M. Yu, Hazard Analysis of Seismic Soil Liquefaction,
Springer Natural Hazards, DOI 10.1007/978-981-10-4379-6_4
61
4 Laboratory Experimental Study …
62
to which different forms and strengths of dynamic loading are applied. Stress and
strain of the soil samples are then measured under the loadings, resulting in qualitative and quantitative determination of soil dynamic properties and related change
rules. The laboratory soil dynamic experiments include the dynamic triaxial, resonant column, simple shear, torsion shear and shaking table tests, as shown in
Table 4.1. Among these, the dynamic triaxial and resonant column tests are the two
main laboratory methods. The former is applied in the large strain scope range
(>10−4) and the latter in the small strain scope range (10−6–10−4).
Table 4.1 Laboratory soil dynamic experiments
Experiments
Test principle
Characteristic
Dynamic
triaxial test
The cylindrical specimen sealed in
the rubber membrane is consolidated
under a given axial and lateral
compressive stress, and then
applying vibration force at the axial
or lateral direction to make shear
stress on the shear surface of the soil
sample periodic alternating
The cylindrical specimen is applied
longitudinal and torsional vibration
at one end of the specimen with
changing its frequency to measured
its resonant frequency
The sample sealed in rubber
membrane is supported in the sample
container, on which the sample is
applied by the vertical pressure to
make a pair of side wall operate
reciprocating motion under
alternating shear effect
The sample presents a hollow ring
and different height inside and
outside; the ratio of the inner and
outer heights is equal to the ratio of
inside and outside diameters. Under
the certain side pressure, the sample
is applied periodic alternating torque
on the end
The sealed flask containing saturated
sand is put on shaking table and
applied by forced vibration through
the shaking table. The vibration
frequency and amplitude can be
adjusted according to requirements
and the pore water pressure and the
stress change can be measured at the
same time
Dynamic triaxial tests are mostly
limited to vertical vibration, and a
few vibrating at lateral direction.
Hence, the difference between
experimental loading condition and
the real seismic condition is very big.
Dynamic triaxial test is currently the
most widely used
Resonant column test is restricted to
small strain range and
non-destructive
Resonant
column test
Simple
shear test
Torsion
shear test
Shaking
table test
Sample is confined and applied by
the horizontal vibration. The
instrument is simple and easy to
operate, but the side wall stress
cannot be measured and the stress
concentration cannot be avoided
The shear stress of the sample is
uniform and the stress state and
drainage conditions can be
controlled, but the sample
preparation and test operation are
complex, only suitable for disturbed
soil
Boundary conditions and the stress
of the sample are not in conformity
with the actual situation and the test
is high-cost and difficult
4.2 Dynamic Triaxial Tests of Soil Dynamic Properties for Large Strain Range
4.2
4.2.1
63
Dynamic Triaxial Tests of Soil Dynamic Properties
for Large Strain Range
Introduction of Dynamic Triaxial Tests
(1) Test principle
A dynamic triaxial apparatus can be used to simulate natural stress conditions and
conduct soil liquefaction experiments. Its basic principle is shown in Fig. 4.1. The
cylinder sample in the pressure chamber used in a dynamic triaxial test is consolidated under isobaric condition r′0 in all directions. After the consolidation stage is
complete, periodic pressure +rd in the axial direction is applied by an excitation
device under undrained conditions. At the same time, the cell pressure is keep
invariant so that a periodic shear stress +rd/2 is applied to the 45° direction plane of
a sand sample, and the normal stress increases +rd/2.
The basic principle differential consolidation test is shown in Fig. 4.2. In the
initial stage, the cylinder sample in the pressure chamber is consolidated under
isobaric condition r′3 in all directions. After the isobaric condition stage, deviatoric
stress (r′1 − r′3) is applied in the axial direction. Then the cylinder sample is
consolidated under anisobaric conditions in which the axial stress is r′1 and lateral
stress is r′3. There is thus an initial shear stress in the 45° direction plane until the
consolidation stage is complete. Other conditions such as drainage and dynamic
stress are the same as in the isobaric consolidation test.
Figure 4.3 shows a typical dynamic triaxial stress path diagram of the sample in
the 45° direction plane under cycle loading. The effective principal stress p’ decays
gradually until finally approaching zero.
Fig. 4.1 Stress change of dynamic triaxial specimen at under isobaric consolidation conditions
(Modified on Seed and Lee 1966)
64
4 Laboratory Experimental Study …
Fig. 4.2 Stress changes of dynamic triaxial specimen under anisobaric consolidation conditions
(Modified on Seed and Lee 1966)
Fig. 4.3 Dynamic triaxial stress path diagram under cycle loading
(2) Advantages and limitations
For natural saturated sand or silt layers under horizontal ground, normal stresses in
the vertical and lateral are the maximum and minimum principal stress respectively.
Shear stress of the horizontal surface is zero, which means that initial shear stress is
zero. In addition, because lateral deformation of soil cannot occur, the saturated soil
unit is under the K0 compression state. During an earthquake, the seismic wave is
given shear movement priority with upward propagation, and the saturated soil unit
4.2 Dynamic Triaxial Tests of Soil Dynamic Properties for Large Strain Range
65
only bears the horizontal shear stress from back and forth. Under the action of
cyclic shear stress, the direction of main stress changes continuously between
a+ and a−, and the normal stress of the horizontal plane is constant during the
earthquake.
The advantages of the dynamic triaxial test are as follows.
1. The test principle is clear and maneuverability is strong. The stress, strain and
pore water pressure change states can be synchronously measured.
2. Under the isobaric consolidation condition, the soil specimen plane in the 45°
direction can simulate actual natural soil during the earthquake.
Despite the many advantages of the test, it still has some limitations:
1. The dynamic triaxial test under cycle loading cannot treat the K0 consolidation
state of natural soil.
2. The principal stress axis of the specimen during vibration cannot rotate in accord
with the actual soil situation under vibration.
3. Necking in lateral or bulge phenomena always takes place when the soil sample
approaches damage. This can redistribute the density, which affects the precision of the strain measurement.
4. The stress state of the entire unit is simulated by the stress state of the sample in
the 45° direction simulation.
5. The rubber membrane’s influence on test results is not considered.
4.2.2
Laboratory Tests
(1) Experimental apparatus
We used a GDS dynamic triaxial apparatus and associated software (Fig. 4.4). Its
vibration system is one-directional and its frequency, amplitude and waveform can
be adjusted according to requirements. Stress control is used and the maximum load
force is 2.5 kN, with maximum confining pressure 1.2 MPa. The main component
on the left is the pressure chamber of the triaxial apparatus in which the soil sample
is tested. On the right side there are two devices, which control confining pressure
and back pressure.
(2) Sample preparation
There are two types of samples tested in the dynamic triaxial test—undisturbed and
reconstituted soil. The sand specimen preparation method was followed based on
national standard procedures (GB/T50123-1999).
Undisturbed soil sample preparation
The main instruments used for undisturbed soil sample preparation were a soil
cutter, soil-fixed knife, fretsaw, half-open mold, labels, and glass pane (Figs. 4.5,
4.6 and 4.7).
66
4 Laboratory Experimental Study …
Fig. 4.4 GDS dynamic triaxial apparatus
Fig. 4.5 Soil cutter
The soil sample size in the triaxial experiment was 39.1 mm in diameter and
80 mm in height. First, we removed the undisturbed soil samples gently from the
soil sampler after cutting packing tape with scissors or knives and opening
wax-sealed lids at both ends and placing on a glass pane. According to the required
numbers of sample preparation, we carefully cut undisturbed soil into corresponding segments. Then we put the cut undisturbed soil sample carefully into the
soil cutter and extracted the uneven portion of the sample by observing the
up-and-down level and layer state of the sample. The next step was to cut the
sample into a desired size using soil-fixed knives and fretsaw. During this procedure, we maintained a cutting direction perpendicular to the natural soil layer.
Finally, we put the correct-size sample into a half-open mold immediately after
4.2 Dynamic Triaxial Tests of Soil Dynamic Properties for Large Strain Range
67
Fig. 4.6 Soil-fixed knives
and fretsaw
Fig. 4.7 Half-open mold
weighing, recording and placing corresponding sample labels. We also weighed and
dried residual soil to measure sample moisture content and made corresponding
records.
Reconstituted soil sample preparation
The main instruments used for reconstituted soil sample preparation were a rubber
hammer, sieve, mortar, oven, compaction device, vernier caliper, electronic scales,
and half-open mold (Figs. 4.8, 4.9, 4.10, 4.11, 4.12, 4.13 and 4.14).
First, we dried a certain amount of soil in a drying oven for more than 10 h
(Fig. 4.15). We then ground the dried soil with a mortar and sieved it with a
corresponding aperture sieve, given its grain size distribution (Fig. 4.16). We then
weighed a certain quality of sifted soil using electronic scales controlling for dry
density, and allocated a certain quantity of water to soil in order to revert the soil
sample to its natural water content. The water quantity was evenly sprayed on the
surface of the soil and the water–soil mixture was stirred adequately, and then left to
stand for a period of time to reach uniform moisture content. Four equal-quantity
68
4 Laboratory Experimental Study …
Fig. 4.8 Rubber hammer
Fig. 4.9 Sieve
Fig. 4.10 Mortar
Fig. 4.11 Oven
water–soil mixtures were weighed and compacted in a sample compaction container
composed of a three-way split former, one layer at a time. Cylindrical soil samples
were prepared with a height of 39.1 mm and a diameter of 80 mm. Filter paper
strips were cut and soaked in water. Soaked filter drains were placed at both ends of
the sample (wrapped around the specimen if necessary) to increase the rate of
consolidation. A plain-ended top cap was placed on top of the sample, which was
4.2 Dynamic Triaxial Tests of Soil Dynamic Properties for Large Strain Range
Fig. 4.12 Compaction
device
Fig. 4.13 Electronic scales
Fig. 4.14 Vernier caliper
69
70
4 Laboratory Experimental Study …
Fig. 4.15 Dried soil
Fig. 4.16 Grinded and
sieved soil
then covered by a very thin membrane. O-rings under tension were used to seal the
membrane to the pedestal and top cap (Craig 1983). A set of the samples tested in
one liquefaction resistance experiment had the same skeletal relative density, and
density differences were <0.02 g/cm3.
(3) Experimental procedures
The consolidation undrained test is commonly used in the dynamic triaxial test to
evaluate the dynamic characteristics of typical liquefiable soil. Specimens were
saturated by vacuum pumping equipment. All samples were immersed in deionized
de-aired water and air was exhausted continuously for 2 h, and let it sit in a vacuum
status for 10 h. Skempton’s pore pressure parameter (B parameter) was then
checked before testing. If this parameter was found to be less than the desired value
(0.95), back pressure was applied to saturate the sample. The B parameter was
checked in several stages during saturation. In all cases, a parameter 0.95 was
achieved, indicating satisfactory saturation (Hong and Ting 1991).
After ensuring saturation, the specimens were consolidated to the expected
effective consolidation stress by being isotropically consolidated at an effective
confining stress, which corresponds to the normally consolidated state of soil in the
field. The complete consolidation standard was such that for sand samples under an
isotropic consolidation state, the pore pressure did not increase for 5 min after
4.2 Dynamic Triaxial Tests of Soil Dynamic Properties for Large Strain Range
71
closing the drain valve; under an anisotropic consolidation state, the axial deformation was not >0.005 mm within 5 min.
Undrained conditions were chosen because they are closer to the actual situation
in which the pore water cannot drain in time under dynamic earthquake loading.
A sinusoidal wave was selected with frequency 0.1 Hz in all tests and the applied
stress was reversed, starting with compression loading. Pore pressure generation
was monitored continuously by a transducer at the base of the soil specimen. Test
procedures were based on the industrial standard of China Specification of Soil Test
(SL237-1999). Different criteria were used to identify the number of cycles to
liquefaction, mainly including porewater pressure-related and strain-related criteria.
The various criteria affected the liquefaction analysis, and specific differences are
discussed in Sect. 4.2.3.
4.2.3
Test Analysis of Test Results
(1) Seed–Idriss simplified method
Seed’s simplified method (Seed et al. 1983) is a theoretical discriminant method
based on lab experiments and the first proposed discriminant of sand liquefaction
potential. There are five factors affecting liquefaction taken into consideration, i.e.,
overlying pressure, average particle diameter, relative density, ground motion
intensity, and earthquake duration. The basic concept is that the irregular force
produced by an earthquake is converted into an equivalent cyclic shearing stress
and is a function of soil depth. This facilitates quantification of earthquake intensity
and duration. Laboratory experiments are then conducted, applying overlying
pressure to soil samples according to depth. At a certain depth, a certain cyclic shear
force is applied to simulate earthquake effects on the soil samples until soil liquefaction. In addition, other factors such as average particle diameter and relative
density can also be considered to affect the soil samples. In this way, the function
between cyclic shear stress that causes liquefaction (that means liquefaction resistance) and soil layer depth can be mapped. Then, by comparing the two stresses,
liquefied soil area can be determined (Amini and Sama 1999).
Under seismic action, the soil has a periodic shear force that is the seismic shear
stress. In sandy and silty soil layers, when this shear stress overcomes liquefaction
resistance, such soil liquefies. This type of sandy and silty soil loses stability, and
there is failure because of liquefaction. Seismic shear stress can be represented by
the equivalent average shear stress during the earthquake. According to the Seed–
Idriss simplified method in the Engineering Geology Manual, seismic shear stress
can be calculated by
sav ¼ 0:65cz cd a max
g
cd ¼ 1 0:0133z;
ð4:1Þ
4 Laboratory Experimental Study …
72
where sav is the equivalent average shear stress (kPa)
c is the unit weight of sandy and silty soil (kN/m3)
amax is peak ground acceleration (PGA) (m/s2)
z is the depth of sandy and silty soil (m)
rd is the stress reduction factor
Liquefaction resistance can be calculated by
sd ¼ Cr ð
rd
Þ r0 ;
2rc Nf m
ð4:2Þ
rd
where ð2r
Þ is the stress ratio of soil liquefaction determined by the dynamic
c Nf
triaxial test
Cr is the correction factor of the stress ratio of soil liquefaction
0
rv is the overlying effective pressure (kPa)
Soil that satisfies the following equation is determined as liquefiable:
sam [ sd
ð4:3Þ
For foundation soil that is potentially liquefiable, further assessments including a
liquefaction index and liquefaction level of that soil can be calculated according to
the ratio sd =sav and buried depth of liquefaction of the soil. The determination of
that index and level can refer to relevant provisions of Code for Seismic Design of
Buildings (DGJ08-9-2013) as shown in Table 4.2. The liquefaction index can be
calculated by
Ile ¼
Xn
i¼1
ð1 sdi
Þdi Wi
sami
ð4:4Þ
where Ile is the liquefaction index
savi and sdi are equivalent cycle shear stress (kPa) and liquefaction resistance,
respectively. Their ratio is 1 when the liquefaction resistance is greater than
equivalent cycle shear stress.
di is soil layer thickness (m) at point i, using half of the depth differences
between adjacent upper and lower sampled layers. The upper bound is not higher
than the depth of the underground water level and the lower bound is not deeper
than the depth of liquefiable soil.
Table 4.2 Determination of liquefaction index and liquefaction level (code for Seismic Design of
Buildings (DGJ08-9-2013))
Liquefaction level
Slight
Medium
Severe
Liquefaction index of 20-m depth liquefiable soil
0 < Ile 6
6 < Ile 18
Ile > 18
4.2 Dynamic Triaxial Tests of Soil Dynamic Properties for Large Strain Range
73
Wi is the horizon-effect weight function value of unit soil thickness at point
i (m−1). If the depth of the soil layer is 20 m, the midpoint depth is not >5 m, and
Wi is 10. If the midpoint depth is 20 m, Wi is 0 and, if it is 5–20, Wi should be
according to linear interpolation.
Earthquake magnitude refers to the absolute magnitude of the earthquake itself
and is related to the magnitude of released energy. Earthquake intensity refers to the
degree to which the ground surface and buildings are affected by the earthquake.
Therefore, the magnitude that represents earthquake size is only one certain value,
but the intensity varies because earthquake effects vary by region. The closer to the
epicenter, the stronger the vibration and the greater the seismic intensity. The Seed–
Idriss simplified method is used within the saturated soil liquefaction and determination method based on existing seismic liquefaction data. The method considers
the effect of magnitude on saturated soil liquefaction but does not consider varying
earthquake intensity effects. Therefore, when earthquake liquefaction discrimination is done using this method, it is only for a given earthquake magnitude, considering various seismic intensities (accelerations).
(2) Liquefaction criteria
In the dynamic triaxial tests, there are two main types of soil liquefaction criteria to
determine the number of cycles to liquefaction. One is the initial liquefaction
standard proposed by Seed et al. (1983). In this criterion, the number of cycles to
liquefaction is defined as that corresponding to pore water pressure in excess of
confining pressure. The other criterion is the strain standard proposed by Castro
(1975), characterized by deformation. Because some liquefiable soil contains a
certain amount of clay particles having cohesion, such soil retains shear strength
when the effective stress decreases to zero (Zhuang 2008; Huang et al. 2010).
Therefore, the number of cycles to liquefaction is defined by magnitude of strain.
Taking a reconstituted sample of silty sand in the same layer as an example, its
temporal history curves of pore pressure, dynamic stress and axial strain are shown
in Fig. 4.17.
When the dynamic force was large (dynamic stress = 11.4 kPa), the first-stage
duration of liquefaction deformation was short. Then liquefaction deformation
proceeded rapidly into the second stage and the strain had a trend of sustained
growth. In that stage, pore pressure increased rapidly and tended to be stable, as
shown in Fig. 4.17a. When the dynamic force was small (dynamic
stress = 7.8 kPa), the first-stage duration of liquefaction deformation was long.
After reaching a certain number of cycles, the deformation amplitude increased and
entered the second stage. During that stage, the strain again had a trend of sustained
growth. The pore pressure increased until deformation amplified and then tended
toward stabilization, as shown in Fig. 4.17c.
The time-series curves shown in Fig. 4.17 indicate that a certain pore pressure
persisted after each stress cycle, causing that pressure to build gradually with the
increase in cycles. At the same time, effective stress declined as pore pressure
increased, until that stress became zero such that soil stiffness decreased abruptly
and there was initial liquefaction of the soil sample. The change of axial strain
4 Laboratory Experimental Study …
74
Fig. 4.17 Time series data of pure silty sand sample for varying CSR
Table 4.3 Cycles to liquefaction according to two criteria
Confining
pressure
(kPa)
Back
pressure
(kPa)
Effective
pressure
(kPa)
Dynamic
stress
(kPa)
Cyclic stress
ratio (CSR)
Cycles to liquefaction
Initial
Strain
liquefaction
standard
standard
130
130
130
100
100
100
30
30
30
0.19
0.15
0.13
11.4
9
7.8
3
31
124
5
34
127
amplitude was small at the initial stage, and dynamic stress had a constant
amplitude until pore pressure rose to near or equal to the confining pressure after a
certain cycle. Then, the amplitude of axial strain sharply amplified, but that of
dynamic stress began to weaken.
The number of cycles to liquefaction determined according to the strain standard
was greater than that determined by the stress standard (Table 4.3). However, the
evaluation standard of strain failure was related to the evaluation standard of pore
pressure. Because when pore pressure was reached after initial liquefaction of the soil
mass, the stiffness decreased and dynamic stress weakened. Therefore, the strain could
not continue increasing and entered the shear stage, and the amplitude of the strain
time history curve no longer extended to both sides, but developed in one direction.
4.2 Dynamic Triaxial Tests of Soil Dynamic Properties for Large Strain Range
0.2
0.18
Cyclic Stress Ratio, CSR
Fig. 4.18 CSR versus
number of cycles to
liquefaction according
to two criteria
75
0.16
0.14
0.12
0.1
0.08
0.06
0.04
initial liquefaction standard
0.02
Axial strain standard
0
1
10
100
Number of Cycles to Liquefaction
1000
The smaller the dynamic stress was, the smaller the increase in strain; according
to dynamic stress from strong to weak, the corresponding strain was 4.5, 2 and
1.5%. Liquefaction strength increases in accord with the standard strain from the
liquefaction strength curve and pore pressure in accord with the standard from that
curve. However, this increase is not great and, in terms of safety, the failure time of
the vibration pore pressure standard according to the initial liquefaction discrimination standard was adopted in this study (Fig. 4.18).
4.3
4.3.1
Resonant Column Tests of Soil Dynamic Properties
for Small Strain Range
Introduction of Resonant Column Tests
(1) Test principle
Many case studies of earthquake damage show that site soil conditions have a
strong influence on earthquake damage. Resonance, filtering and amplification
effects of the soil layer have been treated in earthquake engineering. Onsite soil
conditions include the soil distribution structure and dynamic properties of each soil
layer, which constitute basic soil conditions. For example, earthquake damage in
the Caracas earthquake were primarily caused by the resonance of soil vibration and
seismic oscillation. Earthquake damage in the Mexico City earthquake were jointly
caused by unique dynamic characteristics of a deep soft soil layer and basin effects.
Whatever the resonance and amplification or filtering effects of the soil layer, they
are all closely related to the dynamic characteristics of the soil itself. Therefore,
these characteristics are among the main factors affecting ground motion at a site.
4 Laboratory Experimental Study …
76
The dynamic modulus and damping ratio of soil are two major parameters. In
soil seismic response analysis, the dynamic characteristics, dynamic shear modulus
and damping ratio make up a parameter and two curves. The latter are curves
G/Gmax-c and D-c, which are used in the equivalent linearization method to consider nonlinear soil properties. The dynamic characteristics of soil, including the
initial shear modulus and soil nonlinear attenuation relationship, must be considered
in nonlinear soil analysis. The analysis of soil dynamics parameter effects on soil
dynamic response uses data from standard and experimental results of dynamic
shear modulus ratio and damping ratio in Yuan et al. (2000). They stated that a
different soil dynamic shear modulus and damping ratio affected seismic response
analysis results, especially for strong earthquakes.
The dynamic shear modulus and damping ratio of soil are essential parameters
for seismic safety evaluation and seismic response analysis for engineering sites
(Huang et al. 2002, 2005). Whether the choices of these two parameters conform to
an actual situation is important with respect to the reliability of calculation results.
In China, the seismic design of major projects is based on site design ground
motion parameters. As these parameters are obtained from seismic response analysis, the validity of analysis results directly affects the safety and economic efficiency of engineering structures (Chen et al. 1995).
(2) Advantages and limitations
Laboratory experiments measuring the soil dynamic modulus and damping ratio
generally include four main instruments, namely, resonant column, torsional shear,
shear and triaxial shear apparatus. The resonant column has advantages and limitations compared with other instruments.
The advantages of a resonant column test can be summarized as follows.
The test based on one-dimensional wave theory is relatively ideal for measuring
soil dynamic characteristic parameters under the condition of small strain. Its
experimental results have small discreteness and operation is easy.
Limitations of the test are as follows.
1. The resonant column apparatus is suitable for measuring the dynamic shear
modulus and damping ratio within a small strain scope (10−6–10−4), but the
other experimental apparatuses, such as dynamic triaxial test, simple shear test
and torsion shear test, can measure parameters from medium to large deformation strain scope.
2. The test cannot treat the K0 consolidation state of natural soil.
4.3.2
Laboratory Tests
(1) Experimental apparatus
The experimental apparatus is fixed at one end and free at the other (with lumped
mass block). Stress control is used, and the maximum confining pressure is
0.7 MPa. The strain measurement range is 10−6–10−3. The soil sample tested in the
4.3 Resonant Column Tests of Soil Dynamic Properties for Small Strain Range
77
Fig. 4.19 V. P. Drnevich resonant column apparatus
resonant column test has a diameter of 35.7 mm and a height of 71.2 mm. The
measurable parameters include dynamic shear modulus Gd and damping ratio D
(Fig. 4.19).
(2) Sample preparation
There are also two types of soil sample tested by resonant column—undisturbed
and reconstituted. The sample is 35.7 mm in diameter and 70 mm in height. The
sand specimen preparation method follows national standard procedures
(GB/T50123-1999). Specific steps are similar to the dynamic triaxial test.
(3) Experimental procedures
The consolidation undrained test is commonly used in the dynamic triaxial test to
evaluate the dynamic characteristics of typical liquefiable soil. The specimens are
saturated by vacuum pumping equipment. All samples in this experiment were
immersed in deionized, de-aired water, air was exhausted continuously for 2 h, and
they were kept in a vacuum state for 10 h. After full saturation, the specimens were
consolidated to the desired effective consolidation stress. This was done by isotropic consolidation at an effective confining stress representing soil field conditions. We used the steady forced vibration method (Fig. 4.20). Specific test
procedures were based on the industrial standard of China Specification of Soil Test
(SL237-1999).
4 Laboratory Experimental Study …
78
Fig. 4.20 Experimental procedures of resonant column test
4.4
Comprehensive Liquefaction Potential
and Dynamic Characteristic Analysis
of a Reservoir Dam Foundation
In general, the in situ tests in Chap. 3 and laboratory tests in Chap. 4 are used
together to evaluate liquefaction potential. Next, we propose a case study in which
in situ and laboratory experimental methods including the standard penetration,
dynamic triaxial and resonant column tests are used to comprehensively analyze
liquefaction potential and dynamic characteristics.
4.4.1
Site Introduction
There is a reservoir in the western part of the town of Wangqingtuo in Tianjin,
China, for which the local geology is North China Plain Quaternary silt. To the east
and west of this project site are two important seismotectonic zones (Tangshan–
Cixian and Linqiu–Huailai) (Fig. 4.21), and soil layers under the reservoir dam are
mainly silt and silty soil (Fig. 4.22). It is thus evidently important to study the
liquefaction potential and dynamic characteristics of the dam foundation for the
safety of reservoir operation.
4.4 Comprehensive Liquefaction Potential and Dynamic Characteristic Analysis …
79
Fig. 4.21 Map showing the location of the project in Tianjin (reprinted from Huang et al. 2012
with permission from Springer)
Fig. 4.22 Typical dam and soil layer distribution under a dam body (reprinted from Huang et al.
2012 with permission from Springer)
4.4.2
Analysis of Standard Penetration Test Results
The onsite liquefaction evaluation was done using the standard penetration test
based on the precise test procedures described in Sect. 3.2.1. A total of 115 SPT
tests were conducted at 14 boreholes. The number of blows (N-value) were measured to estimate liquefaction resistance, using a 63.5-kg hammer. Figure 4.23
shows five typical boreholes around the dam that were chosen to assess the liquefaction potential of the dam foundation.
4 Laboratory Experimental Study …
80
Fig. 4.23 Location of SPT
boreholes (reprinted from
Huang et al. 2012 with
permission from Springer)
Table 4.4 Liquefaction evaluation results for selected boreholes by SPT (seismic intensity VII)
(reprinted from Huang et al. 2012 with permission from Springer)
0
No.
Type of
soil
ds (m)
qc (%)
N63:5
Liquefaction
evaluation
H1
Loam
and silt
Silt
Loam
and silt
Silt
Silt
4
11.4
17
Possible
5.4
Moderate
3
3
5.8
6.5
14
28
Possible
Possible
12.7
3.5
Moderate
Low
3
2
3.9
6.4
17
5
Possible
Possible
9.6
10.1
Moderate
Moderate
H2
H3
H4
H5
LPI
Liquefaction
potential
The liquefaction assessment compared the equivalent N-value (N63:5 ) and the
critical N-value Ncr for each soil layer. If Ncr > N63:5 , soil liquefaction is likely. Ncr ,
N63:5 , and liquefaction potential index (LPI) are calculated in Eqs. 3.26–3.28 and
3.42, respectively. The groundwater level is assumed to be 0 m and the seismic
fortification intensity is VII. The test points are at depths from 1.15 to 4.15 m.
Table 4.4 shows specific SPT results for the five typical holes. Nearly all of the
boreholes have the potential for liquefaction, but this potential is moderate, or even
low.
4.4 Comprehensive Liquefaction Potential and Dynamic Characteristic Analysis …
4.4.3
81
Analysis of Dynamic Triaxial Test Results
(1) Results of liquefaction evaluation
The liquefaction evaluation by the dynamic triaxial test was done based on Seed’s
simplified method as described above. Groundwater level was assumed to be 0 m
and the seismic fortification intensity was VII. Peak ground acceleration was
0.15 g. The test points were at depths 1–4 m. Table 4.5 shows results for five
typical boreholes. The liquefaction potentials of most boreholes were characterized
as very low to moderate.
(2) Influence of dynamic stress
When the dynamic force is strong (dynamic stress = 90 kPa), the first-stage duration of liquefaction deformation was short. Then, liquefaction deformation proceeded rapidly into the second stage and the strain had a trend of sustained growth.
In that stage, pore pressure increased rapidly and tended toward stabilization, as
shown in Fig. 4.24.
When the dynamic force was weak (dynamic stress = 65 kPa), the first-stage
duration of liquefaction deformation was long. After reaching a certain number of
cycles, the deformation amplitude increased and entered the second stage. During
that stage, the strain again had a trend of sustained growth. Pore pressure increased
until deformation amplified, then tended toward stabilization, as shown in
Fig. 4.25.
Figures 4.24 and 4.25 compare time-series data of porewater pressure, dynamic
axial strain and dynamic stress. When cycle stress increased, so did the rate of the
strain growth, and porewater pressure increased at a nearly linear rate. However, the
number of cycles to liquefaction declined.
Table 4.5 Results of liquefaction evaluation by Seed’s simplified method (seismic intensity VII)
(reprinted from Huang et al. 2012 with permission from Springer)
rd
Liquefaction
LPI
Liquefaction
sd
No.
d
Type of soil
2rc N
f
(kPa)
evaluation
potential
(m)
F-H1
4
Loam and
0.3
5.1
Possible
5.4
silt
F-H2
2
Silt
0.2
1.4
Possible
6.1
F-H3
2
Loam and
0.3
2.7
Possible
1.9
silt
F-H4
2
Silt
0.2
1.7
Possible
10.0
F-H5
2
Silt
0.3
2.5
Possible
5.8
Groundwater table was at 0 m relative to ground surface
F-Hi means that soil sample was from Hi borehole (i = 1, 2, 3, 4, and 5)
Moderate
Moderate
Low
Moderate
Moderate
82
4 Laboratory Experimental Study …
Fig. 4.24 Time series data for dynamic stress = 90 kPa (reprinted from Huang et al. 2012 with
permission from Springer)
Fig. 4.25 Time series data for dynamic stress = 65 kPa (reprinted from Huang et al. 2012 with
permission from Springer)
4.4 Comprehensive Liquefaction Potential and Dynamic Characteristic Analysis …
83
(3) Influence of consolidation pressure
Figures 4.26 and 4.27 compare dynamic strength (rd) and cyclic stress ratio
(CSR) versus change of consolidation pressure (r′0) under the same cycles of
loading (Nf). The results show that the greater the consolidation pressure, the larger
the dynamic stress amplitude and number of cycles needed to cause liquefaction, as
shown in Fig. 4.26. r′0 has some effect on liquefaction CSR, but the effect is not
great, as shown in Fig. 4.27.
(4) Influence of initial shear stress
No initial shear stress
Saturated sand permanent volume densification deformation takes place under
cycle shear stress. For loose and moderately dense sand, the same volume of water
drains from soil voids because of such deformation. The water drainage speed
depends on the permeability coefficient of soil and seepage path length. When the
permeability coefficient of soil is small or there is an aquiclude, the permanent
volume pressure deformation rate caused by cycle shear stress is greater than pore
water drainage speed. Thus, porewater in the blocked state and pore water pressure
increase. Under cycle shear stress, the total normal stress remains constant, so the
increase of pore water pressure can only be balanced by decreasing the effective
normal stress of soil. However, a decrease of effective normal stress may cause a
loss of shear strength, which means a decrease or complete loss of shear deformation resistance. This phenomenon is liquefaction (Zhou et al. 2011;
Stamatopoulos 2010). However, for dense sand, owing to dilatancy, porewater
Fig. 4.26 Dynamic stress change with consolidation pressure (reprinted from Huang et al. 2012
with permission from Springer)
84
4 Laboratory Experimental Study …
Fig. 4.27 CSR versus number of cycles to liquefaction change with consolidation pressure
(reprinted from Huang et al. 2012 with permission from Springer)
pressure rises slowly under cycle shear stress. Although soil produces some
deformation, liquefaction does not take place.
Because silt is a special soil between cohesive and sandy soils, it has a unique
nature. It has crumb structure characteristics and a structural strength greater than
sand, and thus tends to have greater liquefaction resistance than sandy soil.
However, the permeability of silt is weak, preventing pore water from draining over
time. Therefore, pore water pressure increases continuously and the shear resistance
of silt grains is thereby lost. When that pressure increases until the shear strength
becomes zero, the silt reaches the liquefaction state. In this process, clay particles in
the silt may mainly act as lubrication and reduce liquefaction resistance.
Test results show that the deformation of saturated silt samples under cycle shear
stress has two stages. Figure 4.28 shows dynamic triaxial experimental results
under isobaric consolidation conditions. From time series data of the strain, in the
first stage, the deformation amplitude is small and basically remains constant. After
reaching a certain number of cycles, this amplitude increases and enters the second
stage. In that stage, porewater pressure accumulates under cycle shear stress and
shear strength and shear deformation resistance gradually decline until that pressure
equals the consolidation pressure. In this state, liquefaction occurs and there is
complete loss of shear strength and shear deformation resistance.
After applying cyclic stress, the pore water pressure rises sharply in the initial
stage, but the growth rate slows in the later stage and tends toward final stability.
This is because the permeability coefficient of silt is generally small compared with
fine sand. Therefore, the pore water pressure is not readily dissipated at the
beginning of the vibration. The generated large volume change potential causes a
4.4 Comprehensive Liquefaction Potential and Dynamic Characteristic Analysis …
85
Fig. 4.28 Time series data of stress, strain, and porewater pressure (isobaric consolidation)
sharp rise in initial pore water pressure, leading to rapid structural destruction of the
soil sample. However, as silt has a small amount of clay particles, it has a certain
structural strength and cohesive force that limits the increase of volume change
potential. This causes pore water pressure to increase slowly until reaching stabilization (Huang et al. 2010), as shown in Fig. 4.28.
Initial shear stress
When there is initial shear stress, strain develops along the direction of that stress
under cycle shear stress. The pore water pressure continues rising until reaching a
certain number of cycles, and then this growth slows and tends to be steady;
however, the deformation continues to increase. When pore water pressure equals
the consolidation pressure, liquefaction occurs and there is complete loss of shear
strength and shear deformation resistance. Influenced by the initial shear stress,
deformation properties and pore pressure growth under cycle shear stress are shown
in Fig. 4.29.
(5) Influence of density
Experimental results show that liquefaction CSR increases with dry density,
because the greater that density, the denser the silt is. As a result, silt with high dry
density is not easily liquefied (Fig. 4.30).
(6) Influence of soil structure
The effect of soil structure on silt liquefaction resistance cannot be ignored.
Xenakia and Athanasopoulos (2008) discussed structural property influences on
86
4 Laboratory Experimental Study …
Fig. 4.29 Time series data of stress, strain, and porewater pressure (anisobaric consolidation)
Fig. 4.30 Liquefaction resistance of silts with three different dry densities (owing to the loss of
clay content during sample preparation, there is error of 15%)
4.4 Comprehensive Liquefaction Potential and Dynamic Characteristic Analysis …
87
Fig. 4.31 Liquefaction resistance of undisturbed and reconstituted soil
dynamic characteristics of liquefiable silt. Reconstituted silt samples changed the
original structure of undisturbed soil such that its strength decreased. However, in
the present study, the liquefaction resistance of reconstituted and undisturbed soil
samples saw no obvious change (Fig. 4.31), in contrast to expected results and the
literature. The reason may be disturbance during acquisition of the undisturbed soil
samples, leading to weak structural planes, or that there were weak structural planes
in the undisturbed soil itself. Considering that liquefaction prevention measures
such as dynamic compaction have a great impact on the structure of surface soil, the
liquefaction resistance of reconstituted soil samples are recommended as the design
standard, given the properties of reconstituted soil samples are closer to actual site
condition.
(7) Influence of grain composition
Varying grain composition has a substantial influence on soil liquefaction resistance
(Baziar and Sharafi 2011; Dimitrova and Yanful 2012; Xenakia and
Athanasopoulos 2003). Table 4.6 shows that the higher sand content in the soil, the
less soil liquefaction resistance. Examples are N12 (the dynamic shear stress ratio
causing liquefaction for 12 equivalent cycles of loading) and N30 (30 equivalent
cycles). Silt and clay contents also affect the silt liquefaction strength N12 and N30.
The higher the silt and clay contents, the stronger the liquefaction strength for N12
and N30. This is because for higher sand content, the soil has the liquefaction
characteristics of sandy soil. That sand has a kind of single-grain structure, and
particles tend to move easily under the action of vibration. For high silt and clay
4 Laboratory Experimental Study …
88
Table 4.6 Relation between grain composition and liquefaction resistance
Soil
sample
No.
Granulometric composition
Sand
Silt
0.25–0.075 mm 0.075–0.005 mm
%
%
Clay
<0.005 mm
%
QZK2-1
QZK2-2
QZK3-1
QZK4-1
QZK5-1
QZK7-1
QZK8-1
QZK9-1
9.0
4.0
26.5
23.5
4.5
2.0
26.5
10.0
7.5
5.6
4.4
6.7
3.6
11.1
3.2
3.6
83.5
90.4
69.1
69.8
91.9
86.9
70.3
86.4
Liquefaction
resistance
N12
Liquefaction
resistance
N30
0.260
0.280
0.148
0.420
0.360
0.300
0.190
0.270
0.245
0.268
0.136
0.400
0.310
0.290
0.185
0.240
contents, the silt has some aspects of a granular structure and behaves differently
from sand. Moreover, owing to physical and chemical effects, porewater bonding,
soil structural strength and other factors, silt is more difficult to liquefy than sand.
4.4.4
Analysis of Resonant Column Test Result
Figure 4.32 shows the relationship between dynamic modulus Gd and shear strain c
(Gd-c curve) of silt in the western Tianjin region under different confining pressures. It is seen that the curve shapes of silt are very similar under different pressures. Gd is a function of c. In the elastic deformation stage (c < l0−6), their
relationship is linear. Thus, the deformation is recoverable and Gd is constant.
However, in the elastoplastic deformation stage (l0−6 < c < l0−4), the relationship
between Gd and c is no longer linear. Gd decreases with the increase of c. In the
plastic deformation stage (l0−4 < c ), Gd decreases with a larger gradient. These
trends reflect the general rule of the dynamic stress–strain relationship, such as
nonlinearity and hysteresis.
For a constant c, Gd increases with increased effective consolidation stress
(Fig. 4.32). This is because the void ratio of soil decreases with the increase of that
stress and the relative density rises, increasing soil particle contact. Therefore, the
stress wave propagation is faster in soil and Gd increases.
The initial dynamic shear modulus G0 increases with confining pressure r3. For
the same soil samples, the higher the consolidation pressure, the larger the G0.
Different soil samples have different G0 under certain confining pressure conditions.
However, for the same stratum and soil property, G0 changed little for a given
pressure condition.
Gd of soil with the same property in each layer is normalized by G0, and the
results are shown in Fig. 4.33. Points under different initial confining pressure are
4.4 Comprehensive Liquefaction Potential and Dynamic Characteristic Analysis …
89
Fig. 4.32 Relationship between dynamic shear modulus Gd and shear strain c (Gd-c curve) of silt
in the west of Tianjin
Fig. 4.33 Relationship between shear modulus ratio Gd/G0 and shear strain c (Gd/G0 − c curve)
of silt in western Tianjin
90
4 Laboratory Experimental Study …
Fig. 4.34 Relationship between damping ratio D and shear strain c (D-c curve) of silt in western
Tianjin
concentrated within a very narrow strip and their discreteness is small, but the
confining pressure has a impact on the Gd/G0-c curve. Gd/G0 decreases with the
increase of c. Overall, Gd has a good normalization to its G0.
Figure 4.34 shows the relationship between D and c (D-c curve) of silt in
western Tianjin under different confining pressures. It is seen that the curve shapes
and trends of both sandy silt and silt are very similar under varying pressure.
D increased with c. In the elastic deformation and elastoplastic deformation stage
(c < l0−4), the change of D was slight. However, in the plastic deformation stage
(l0−4 < c ), D rapidly increased with c. Although there was some discreteness, the
effect of confining pressure on the D-c curve is still evident.
For constant c, D decreased with increased effective consolidation stress
(Fig. 4.34). This is because the void ratio of soil decreases with increasing effective
consolidation stress and the relative density increases, enhancing soil particle
contact. Thus, the dissipation of energy during propagation in soil is small and D
declines. However, as c increased, the effect of confining pressure on the D-c curve
was not obvious.
According to the above results based on resonance column tests, the dynamic
characteristics (D-c curve) of silt in western Tianjin were analyzed. These characteristics conform to the general rule of nonlinearity and hysteresis. With the
increase of c, Gd decreased nonlinearly. The Gd/G0-c curve has good normalization.
Under small amplitude strain, D did not change much. However, under large
amplitude strain, D increased with c, and D results were discrete. However, the
4.4 Comprehensive Liquefaction Potential and Dynamic Characteristic Analysis …
91
variation range of D was smaller than that of Gd. It should be noted that the resonant
column tests do not consider the natural soil K0 consolidation state.
4.5
Summary
Based on the dynamic triaxial and resonant column tests, the dynamic characteristics of liquefiable soils were comprehensively analyzed for both large and small
strain. Major conclusions are as follows.
(1) Soil shear strain amplitude and its dynamic characteristics are closely related:
when c amplitude of the soil is in the 10−6–10−4 range, it is in the elastic stage;
when the amplitude is 10−4–10−2, it is in the elastic-plastic stage; when the
amplitude is >10−2, the soil enters a state damage stage. A c amplitude of 10−4
is used as the threshold of large and small strain.
(2) For large strain, dynamic triaxial tests were conducted to study the liquefaction
mechanism of saturated liquefiable soil under dynamic loading. The Seed–
Idriss simplified method was used to obtain the liquefaction resistance of such
soil and assess the liquefaction potential.
(3) Numerous factors affecting the liquefaction susceptibility of liquefiable sands,
including dynamic force, consolidation pressure, initial shear stress, density and
soil structure were discussed.
(4) For small strain, resonant column tests were conducted to study the relationship
between dynamic stress and dynamic strain of liquefiable soil under undrained
conditions. In addition, damping characteristics were analyzed.
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Chapter 5
Physical Model Testing for Dynamic
Characteristics of Seismic Soil
Liquefaction
5.1
Introduction
Liquefaction of loose cohesionless soils seriously damages earth structures during
strong seismic motion (Elgamal et al. 2002). With the rise of pore pressure, soil
stiffness and strength dramatically decrease, which generates large deformations
such as cracking, settlement, lateral spread and slump (Huang et al. 2008).
Laboratory tests (such as the dynamic triaxial and resonant column tests) focus on
small soil samples. These tests are widely used for determining dynamic soil
characteristics, including liquefaction resistance and shear modulus. To reproduce
well the dynamic response of earth structures, physical model tests are important
and useful means, because they enable the analysis of various engineering problems
via better control of material properties and boundary conditions. Physical model
methods such as shaking table and seismic centrifuge model tests are useful for
studying the seismic response of saturated soil under controlled environments. Most
shaking table tests are performed under normal gravity conditions using scaled
models and have produced some promising results (Wang and Lin 2011; Kokusho
et al. 2011). However, these tests are limited by scale effects because of differences
in stress level between model and prototype and a lack of rational scaling laws.
Fortunately, centrifuge modeling can overcome these deficiencies. In centrifuge
model testing, the scale model is subjected to preconcerted high gravity, which can
preserve the stress–strain relationship as the prototype. Centrifugal shaking table
tests combine the shaking table and centrifuge, and are widely used in liquefaction
modeling. The seismic response of soil liquefaction has been modeled using
dynamic centrifuge devices in prior research (Adalier and Sharp 2004; Phillips et al.
2002; Saleh and Madabhushi 2010). Hence, dynamic centrifuge model tests based
on well-designed scale rule can predict the dynamic characteristics of seismic soil
liquefaction.
© Springer Nature Singapore Pte Ltd. 2017
Y. Huang and M. Yu, Hazard Analysis of Seismic Soil Liquefaction,
Springer Natural Hazards, DOI 10.1007/978-981-10-4379-6_5
93
94
5.2
5.2.1
5 Physical Model Testing for Dynamic Characteristics …
Principles and Scaling Relationships in Geotechnical
Centrifuge Modeling
Principles of Geotechnical Centrifuge Modeling
A geotechnical centrifuge represents the gravity of a prototype using centrifugal
force. Considering that gravity is equivalent to inertia force, the physical effect of
gravity in the prototype is the same as that generated by centrifugal force in the
scale model. The essential properties of material are determined by electromagnetic
force. Because gravity or centrifugal force is not significant to electromagnetic
force, soil properties will not change when exposed to a centrifugal field. The
centrifuge models gravity using centrifugal force, which can recreate the same
stress and strain level of the scale model with prototype. The principle is illustrated
using a dam. Figure 5.1 presents the stress level of soil in a prototype under normal
gravity and in a 1/N scale model under an Ng environment. The stress is the same
between prototypes and models if we ignore error caused by the direction of the
centrifugal force. The coordinate system is shown in Fig. 5.2 and acceleration
components caused by centrifugal rotation are presented in Fig. 5.3. When the
geotechnical centrifuge reaches a pre-set acceleration and is kept rotating at constant speed, angular acceleration is zero (d2h/d2t = 0) and radial velocity near zero
(dr/dt 0). Hence, the centrifugal acceleration of the scale model is r(dh/dt)2, and
this force creates an artificial force field for that model.
Fig. 5.1 Stress in prototype and scale model
5.2 Principles and Scaling Relationships in Geotechnical Centrifuge Modeling
95
Fig. 5.2 Coordinate system in 1/N scale model
Fig. 5.3 Acceleration of point A′ in local coordinate system
Because of the difference of centrifugal force exerted on the scale model, the
stress level is slightly different between scale model and prototype. The centrifugal
acceleration is
Ng ¼ x2 re ;
ð5:1Þ
where ɷ is the angular acceleration of the rotation arm and re is the effective radius
of the centrifuge.
Vertical stress of the prototype is
rmp ¼ qghp ¼ qgNhm ;
ð5:2Þ
5 Physical Model Testing for Dynamic Characteristics …
96
where q is soil density, and hp and hm is depth in the prototype and scale model,
respectively.
Vertical stress of the scale model is
Zz
rmm ¼
z
qx2 ðrt þ zÞdz ¼ qx2 z rt þ ;
2
ð5:3Þ
0
where rt is distance from the model surface to the rotation axis and z is height of the
model from the model surface.
We assume that the vertical stress level of the prototype is equal to that of the
scale model at depth hi (i.e., z = hi). We obtain from Eqs. (5.1)–(5.3) that
re ¼ rt þ 0:5hi
ð5:4Þ
When z < hi, rmp [ rmm , while z [ hi ,rmp \rmm . We assume that
ru ¼ max rmp rmm =rmp
ð5:5Þ
ro ¼ max rmm rmp =rmp
ð5:6Þ
When ru = ro, we obtain
2
hi ¼ hm
3
ð5:7Þ
ro ¼ ru ¼
hm
6Re
ð5:8Þ
re ¼ rt þ
hm
3
ð5:9Þ
To minimize the error of stress, the effective radius should be set as the distance
from the rotation axis to 1/3 the height of the scale model. The actual stress
relationship between prototype and scale model is presented in Fig. 5.4.
We take the TJL-150 centrifuge as an example to calculate stress error. The
radius of this centrifuge is 3 m and height of the laminar model box is 0.55 m. The
stress error of the centrifuge is
maxðr0 Þ ¼ maxðru Þ ¼ maxð
hm
0:55
3:49%
Þ¼
6 ð3:0 0:37Þ
6re
ð5:10Þ
Hence, stress error of the TJL-150 is very small, and thus this centrifuge can
accurately recreate the actual stress level of the prototype.
5.2 Principles and Scaling Relationships in Geotechnical Centrifuge Modeling
97
Fig. 5.4 Stress relationship
between prototype and scale
model
5.2.2
Scaling Relationships in Geotechnical Centrifuge
Modeling
During centrifuge model tests, it is important to develop a set of suitable scale rules
between prototype and scale model to ensure that the mechanical behavior of the
two are the same and that the experimental data can be used to predict the dynamic
response of the prototype.
When a physical process contains p variables, among which r variables are basic,
there are a total of (p–r) independent dimensionless parameter combinations; this is
referred to as the p constant. If we assume that a physical process has p variables
(X1, X2, X3,… Xp), then
fðX1; X2; X3; . . . XpÞ ¼ 0
ð5:11Þ
Assuming r basic variables, Eq. (5.11) can be changed to Eq. (5.12), which
contains p–r p constants:
u p1 ; p2 ; . . .; ppr ¼ 0
ð5:12Þ
Thus, any physical process that can be expressed as an equation can be defined
by dimensionless variable p. Similar physical processes have the same p constants.
Hence, similar rules can be determined from the above law, which is referred to as
5 Physical Model Testing for Dynamic Characteristics …
98
the Bockingham p theory. Similar laws of quality that ignore gravity based on the
Bockingham p theory are widely used in seismic model tests.
The design of scaling rules is a process to determine similar constants between
prototype and scale model, based on similar conditions. Scaling rules can be
determined through equation or dimensional analyses. We know only the variables
and their dimensions in the investigated physical process when in dimensional
analysis. However, it is complicated to perform equation analysis to calculate
scaling rules in dynamic centrifuge model tests. We must know the functional
relationship of different physical variables involved in such tests. A scaling rule
designed by equation analysis is more credible than that from dimensional analysis.
Hence, the former analysis is presented as follows.
For seismic dynamic centrifuge modeling, the scale rule can be determined by
analyzing dynamic functions. The dynamic function of the prototype can be
expressed as
up ¼ Ap sinð2pfp tp Þ;
ð5:13Þ
in which f is vibrational frequency, A denotes amplitude and subscript p represents
the prototype. The vibration velocity can be obtained through derivation of
Eq. (5.13):
mp ¼
dup
¼ 2pfp Ap cosð2pfp tp Þ
dtp
ð5:14Þ
The vibration acceleration is obtained through derivation of Eq. (5.14):
ap ¼
d 2 up
¼ ð2pfp Þ2 Ap sinð2pfp tp Þ
dtp2
ð5:15Þ
In centrifuge model tests, the scale rule of length and acceleration between prototype and scale model is 1:N and N:1, respectively. The frequency relationship is
fm ¼ Nfp
ð5:16Þ
up ¼ Ap ¼ NAm ¼ Num
ð5:17Þ
The displacement relationship is
The velocity relationship is
mp ¼ 2pfp Ap ¼ 2p
fm
NAm ¼ 2pfm Am ¼ mm
N
ð5:18Þ
5.2 Principles and Scaling Relationships in Geotechnical Centrifuge Modeling
99
The acceleration relationship is
fm
ð2pfm Þ2 am
¼
;
ap ¼ ð2pfp Þ2 Ap ¼ ð2p Þ2 NAm ¼
N
N
N
ð5:19Þ
in which the subscript m donates model.
Scaling relationships for centrifuge modeling are well known, and are shown in
Table 5.1.
From Table 5.1, it is evident that most of the scaling rules are compatible and
adequate in static and dynamic situations. However, in some cases, a scale rule
obtained from different functions is contradictory, such as the time scale during a
dynamic physical process. From dimensional similarity, the scale for time is
rffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffi
Lp =N
tp
Lm
tm ¼
¼ ;
¼
ap N N
am
ð5:20Þ
in which L is length, a represents acceleration, N is the g-level, and subscripts p and
m denote prototype and model, respectively. However, the time scale derived from
the consolidation equation is (Stewart et al. 1998)
tm ¼
Table 5.1 Scaling
relationship (Based on Ko
1988)
dm2
cmm
dp
¼
N
cmp
2
¼
tp
N2
ð5:21Þ
Quantity
Model
Prototype
Acceleration (LT−2)
Length (L)
Area (L2)
Volume (L3)
Angle (◦)
Displacement (L)
Stress (FL−2)
Dynamic time (T)
Consolidated time (T)
Creep time (T)
Diffusion time (T)
Permeability factor
Density (ML−3)
Moisture content (%)
Cohesion (FL−2)
Friction angle (◦)
Compression modulus(FL−2)
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1/N
N
N2
N3
1
N
1
N
N2
1
1
1/N
1
1
1
1
1
100
5 Physical Model Testing for Dynamic Characteristics …
where d is a relevant dimension and cv.m and cv.p are consolidation coefficients of
the model and prototype. The time-scale conflict can be addressed by reducing the
permeability of soil, either using smaller particles in the test model or viscous liquid
as a substitute pore fluid (Dewoolkar et al. 1999). The first method is seldom used,
because it is difficult to ensure that mechanical properties are unchanged.
5.3
5.3.1
Physical Model Testing for Dynamic Characteristics
of a Reservoir Dam Foundation
Problem Description
The prototype reservoir is the first erected in the middle of a tidal estuary in China
and the largest one for retaining freshwater while preventing saltwater in the world
(Huang et al. 2014; Chen et al. 2014). The reservoir is at the mouth of the Yangtze
River in Shanghai. The reservoir supplies nearly half the raw water for the Shanghai
urban area. Hence, it is a major infrastructure for the development and social
stability of that city. Unfortunately, backfill of the embankment and two saturated
soil layers (① silty sand and ② sandy silt in Fig. 5.5) under the reservoir
embankment are prone to liquefaction. It is important to evaluate the seismic
response of this dam to maintain reservoir safety. The width of the embankment
is *64 m. It is impossible to construct a model of the entire embankment in a
laminar box, owing to the size of the box and the centrifuge capacity under dynamic
conditions. Krinitzsky and Hynes (2002) investigated damage to the Tapar,
Fatehgadh and Kaswati dams, finding that the Bhuj earthquake triggered shallow
sliding and lateral spread, especially around the bottom part of upstream slopes.
Localized liquefaction around the toes of the dams caused this damage (Singh et al.
2005). Therefore, seismic response of the toe area should be addressed. Attention
Fig. 5.5 Cross-section diagram of embankment foundation (reprinted from Huang and Zhu
(2017) with permission from American Society of Civil Engineers)
5.3 Physical Model Testing for Dynamic Characteristics …
101
should also be paid to the body area, which is not as reinforced as the toe area. In
this chapter, dynamic response of a dam foundation is studied using two separate
physical model tests, one for the body area and the other for the toe area.
5.3.2
Dynamic Centrifuge Modeling Tests
(1) Dynamic centrifuge modeling test system
The dynamic centrifuge model tests were carried out at Tongji University in
Shanghai, using the TJL-150 geotechnical centrifuge and electro-hydraulic shaking
table (Fig. 5.6). The nominal ratio of the arm was 3 m and the centrifuge capacity
was 150 gt. The maximum acceleration is 50 g with a full load of 300 kg under
dynamic model testing. The shaking table (Fig. 5.7) can produce exact sinusoidal
and earthquake waves with maximum amplitude 20 g, maximum duration 1 s, and
frequency 20–200 Hz. The laminar model box (Fig. 5.8), which is composed of 22
rectangular cross-sectional aluminum frames, was used to reduce boundary effects
(Chen and Shen 2014). The size of the box was 500 mm 400 mm 550 mm.
Maximum relative displacement between adjacent layers was 6 mm. The inner wall
Fig. 5.6 Overview of the TJL-150 geotechnical centrifuge (reprinted from Huang and Zhu (2017)
with permission from American Society of Civil Engineers)
102
5 Physical Model Testing for Dynamic Characteristics …
Fig. 5.7 Overview of the shaking table
Fig. 5.8 Configuration of the laminar model box
5.3 Physical Model Testing for Dynamic Characteristics …
103
of the box was wrapped in high-strength flexible latex film to provide an impervious boundary condition.
(2) Model test materials
It is essential to substitute prototype materials according to scaling factors in the
dynamic centrifuge model test. As mentioned above, a viscous liquid is needed to
address the conflict of time scale. The substitute pore fluid should behave like
water, with very similar density and mechanical properties. Moreover, the substitute
liquid should have operational qualities such as easy acquisition and preparation,
relatively stable properties, and environmental safety (Dewoolkar et al. 1999).
Silicon oil has often been used in model tests (Ko 1994; Madabhushi 1994). The
density of silicon is similar to that of water. However, it is difficult to clean up and
deal with saturated soil samples, because silicon oil is hazardous (Kutter 1995). The
solution of glycerin has also been used in centrifuge experiments. Unfortunately,
the density of glycerin is much lower than that of water (Kutter 1995). In the
present work, the solution of carboxyl methyl cellulose (CMC) was used as model
fluid to conduct dynamic centrifuge tests. The fine white powder of CMC is
tasteless, non-toxic and environment-friendly. CMC can be mixed easily with water
to produce needed viscosities with small amounts of powder. Hence, density of the
Fig. 5.9 Rotational viscometer used in experiment
5 Physical Model Testing for Dynamic Characteristics …
104
CMC solution is very similar to that of water. Moreover, CMC is inexpensive and
readily available. The viscosities of CMC solutions are determined using a rotational viscometer, which is shown in Fig. 5.9.
The relationship between CMC concentration and viscosity under indoor temperatures is shown in Fig. 5.10. Before model preparation, a 60 cSt CMC solution
was prepared with *0.78% concentration by weight. The solution can be diluted to
45 cSt by adding distilled, de-aired water.
At a scaling factor of 45, it is difficult to simulate the flexural rigidity of a
three-axis, cement mixing pile diaphragm wall in a prototype using original
material, considering wall thickness. Hence, an aluminum plate is often used to
model concrete-face slabs and the diaphragm wall in dynamic centrifuge tests (Hou
et al. 2004; Bolton and Powrie 1987). Thickness of the substitute material was
calculated as
rffiffiffiffiffiffi
3 Ep tp
tm ¼
Em N
ð5:22Þ
Here, m represents the model, p the prototype, E Young’s modulus, and
t thickness. Young’s modulus is *400 MPa and the thickness is 850 mm for the
prototype. The elastic modulus of the aluminum plate is *69 GPa. Therefore, the
required thickness of the model is *3 mm according to the scale law.
To ensure stability of the embankment, the dam toe was reinforced using geotextiles. Geotextiles used in the model must be N times weaker than the prototype
geotextiles to satisfy the similarity ratio. Tensile strength of the prototype geotextile
was 58 kN/m. Medical gauze was used as the model geotextile. Tensile strength
of this gauze was measured using a tensile testing machine (Fig. 5.11) according to
Chinese code for measurement of geosynthetics (Nanjing Hydraulic Research
Institute 2012). The tensile strength of the model geotextile was *1.53 kN/m.
90
test data
linear fitting
Kinematic viscosity(cSt) at 15 C
80
°
70
60
50
y = 114.93*x - 28.96
R2 = 0.9963
40
30
20
0.5
0.55
0.6
0.65
0.7
0.75
0.8
CMC concentration(%)
0.85
0.9
0.95
Fig. 5.10 Relationship between concentration of CMC and viscosity (at indoor temperature)
1
5.3 Physical Model Testing for Dynamic Characteristics …
105
Fig. 5.11 Geotextile tensile testing machine
(3) Input seismic waves
Considering the importance of the input earthquake wave for seismic response of
the embankment foundation during both experimental and numerical analyses, that
wave was selected discreetly. Strong motion records for Shanghai is lacking. The
Shanghai Seismic Geological Engineering Technology Research Institute evaluated
seismic safety of the research site in 2006, considering the importance of the
reservoir. The geologic profile, compounded bedrock acceleration, and ground
acceleration are provided in their report. Owing to the size of the model box, the
study depth of the foundation was only 24.75 m. Hence, the SHAKE91 code (Idriss
and Sun 1992) was used to analyze seismic response of the soil column of the site
to obtain the input earthquake wave. The thickness of soil deposits is 150–400 m in
Shanghai, with an average of *280 m in the city (Huang et al. 2009). However,
the borehole was only 100 m deep. Therefore, soil properties below that depth were
unknown. In the present work, soil from the bottom of the borehole to the surface of
the bedrock was assumed to be the same as the last soil layer of the borehole.
Moreover, thickness was adjusted to make the simulated ground excitation agree
well with the one in the aforementioned report. The calculated earthquake wave at
18.25-m depth (dam height is 6.5 m) was taken as the input motion for the physical
experiments. Soil properties (soil type, layer depth, maximum shear wave velocity,
and total unit weight) are presented in Table 5.2.
5 Physical Model Testing for Dynamic Characteristics …
106
Table 5.2 Parameters of soil deposits of embankment foundation
Layer
Type
Embedment
(m)
Thickness
(m)
Unite Density
(g/cm3)
S-Wave velocity
(m/s)
1
2
3
4
5
6
6’
7
Sandy backfill
Sandy silt
Clay
Silty clay
Silty sand
Medium sand
Medium sand
Bedrock
0
4.0
14.0
33.0
65.0
83.0
100.0
276.0
4.0
10.0
19.0
22.0
18.0
17.0
176.0
–
1.71
1.89
1.79
1.82
1.90
1.95
1.95
2.44
90.0
160.0
170.0
290.0
330.0
380.0
380.0
800.0
The relationship used herein between shear modulus ratio G/Gmax and shear
strain cn, and that between damping ratio D and cn for sand and clay (Fig. 5.12), are
empirical equations that are widely used for Shanghai (Huang and Zhu 2016).
The numerical and compounded ground accelerations agree relatively well in
tendency and quantity (Fig. 5.13), which indicates that the simulation was effective
and accurate. The input earthquake wave is presented in Fig. 5.14. Considering that
the seismic wave value after 15 s is near zero, only 15 s of records were inputted in
dynamic centrifuge model tests.
(4) Instrumentation and test procedures
Three pore pressure transducers were placed in the middle of each liquefiable soil
layer. Four horizontal accelerometers were installed at the surface of each soil layer.
Settlement was measured by a laser displacement sensor. All transducers used in
1
0.8
0.6
0.4
0.8
G/Gmax-γ n for clay
G/Gmax-γ n for sand
λ - γ n for sand
λ - γ n for clay
0.6
0.4
0.2
0
3.16E-6
Δαμπινγ ρατιο λ
Shear module ratio G/Gmax
1
0.2
1.00E-5
3.16E-5
1.00E-4
3.16E-4
1.00E-3
3.16E-3
0
1.00E-2
Shear strain γ n
Fig. 5.12 Relationship of shear modulus ratio and damping ratio with shear strain for Shanghai
soil (reprinted from Huang and Zhu (2017) with permission from American Society of Civil
Engineers)
5.3 Physical Model Testing for Dynamic Characteristics …
107
0.15
The Offical Data
SHAKE Simulated
Acceleration(g)
0.10
0.05
0
-0.05
-0.10
-0.15
0
5
10
15
20
25
30
35
40
45
Time(s)
Fig. 5.13 Comparison of ground acceleration between official data and SHAKE91 simulated
result (reprinted from Huang and Zhu (2017) with permission from American Society of Civil
Engineers)
0.15
Acceleration(g)
0.10
0.05
0
-0.05
-0.10
-0.15
0
5
10
15
20
25
30
35
40
45
Time(s)
Fig. 5.14 Input earthquake wave of dynamic centrifuge model tests (reprinted from Huang and
Zhu (2017) with permission from American Society of Civil Engineers)
these tests were carefully calibrated before testing. The instrumentation layout is
presented in Fig. 5.15. A saturated sample was prepared layer-by-layer using a
vacuum mixer and centrifuge. Masses of de-aired water and stoving soil were
calculated according to prototype soils. Soil and water were blended sufficiently
using the vacuum mixer. Saturated soil was poured into the model box and
transducers were installed at specific locations. The saturated soil was consolidated
5 Physical Model Testing for Dynamic Characteristics …
108
using a centrifuge, which was operated at an acceleration of 45 g until pore pressure
remained stable. We repeated this procedure to build the entire model.
5.3.3
Model Test Result Analysis
(1) Accelerations
The time history of acceleration at different nodes of the embankment body is
shown in Fig. 5.16. Although the figures are simplified because of limitations of
sample frequency in this model test, we still obtained useful information. The
experimental and calculated ground horizontal accelerations were *0.1 g, which
indicates that the input seismic wave from the SHAKE91 code was adequate.
Attenuation of the earthquake wave from the bottom to surface was not obvious,
especially in the numerical results. This illustrates that the liquefiable soil layers did
not sufficiently liquefy.
Acceleration records at the embankment toe are presented in Fig. 5.17. The
tendency is similar to seismic response of the embankment body, which indicates
that it is suitable to study the large embankment foundation using two separate
Fig. 5.15 Model dimensions
and instrumental layout (unit
mm) (reprinted from Huang
and Zhu (2017) with
permission from American
Society of Civil Engineers)
j4
g1
k1
Backfill
g2
Diaphragm wall
k2
1 Silty sand
g3
k3
2 Sandy silt
g4
k4
3 Silty clay
Acceleration sensor
Displacement sensor
Pore pressure sensor
(a) Embankment body model
5.3 Physical Model Testing for Dynamic Characteristics …
109
J4
G1
Reinforced area
K1
Backfill
G2
1 Silty sand
K2
G3
2 Sandy silt
K3
G4
3 Silty clay
Acceleration sensor
Displacement sensor
Pore pressure sensor
(b) Embankment toe model
Fig. 5.15 (continued)
typical positions. Acceleration was magnified from the ground surface to the top of
the dam toe.
(2) Excess pore water pressures
The time history of excess pore pressure at the specific locations of liquefiable soil
in the body and toe model is presented in Figs. 5.18 and 5.19, respectively. The
excess pore pressure ratio remained near zero before seismic excitation and began
to rise when the shake table started to move. That pressure maximized at the end of
the earthquake and remained stable for a period of time. With rotation of the
centrifuge, the excess pore water pressure declined slowly by transferring the
seismic load to the soil skeleton via the drainage of pore water. The physical
simulations captured the tendency in the time history of excess pore pressure ratio.
Therefore, it is appropriate to claim that the CMC solution is a suitable substitute in
the dynamic centrifuge tests and can reproduce the full evolution of excess pore
pressure ratio. There was insufficient liquefaction (i.e., excess pore pressure was
equal to 1.0) in both models. The maximum excess pore water ratio was *0.6–0.7.
However, the peak value of k1 was lower than expected. The location of the k1
transducer may have been responsible for this. It was installed too close to the
5 Physical Model Testing for Dynamic Characteristics …
110
0.15
Acceleration(g)
0.1
0.05
0
-0.05
-0.1
-0.15
0
3
6
9
12
15
9
12
15
9
12
15
9
12
15
Time(s)
(a) g1
0.15
Acceleration(g)
0.1
0.05
0
-0.05
-0.1
-0.15
0
3
6
Time(s)
(b) g2
0.15
Acceleration(g)
0.1
0.05
0
-0.05
-0.1
-0.15
0
3
6
Time(s)
(c) g3
0.15
0.1
Acceleration(g)
Fig. 5.16 Time history of
acceleration in embankment
body model test (reprinted
from Huang and Zhu (2017)
with permission from
American Society of Civil
Engineers)
0.05
0
-0.05
-0.1
-0.15
0
3
6
Time(s)
(d) g4
5.3 Physical Model Testing for Dynamic Characteristics …
0.15
Acceleration(g)
0.1
0.05
0
-0.05
-0.1
-0.15
0
3
6
9
12
15
9
12
15
9
12
15
9
12
15
Time(s)
(a) g1
0.15
Acceleration(g)
0.1
0.05
0
-0.05
-0.1
-0.15
0
3
6
Time(s)
(b) g2
0.15
Acceleration(g)
0.1
0.05
0
-0.05
-0.1
-0.15
0
3
6
Time(s)
(c) g3
0.15
0.1
Acceleration(g)
Fig. 5.17 Time history of
acceleration in embankment
toe model test (reprinted from
Huang and Zhu (2017) with
permission from American
Society of Civil Engineers)
111
0.05
0
-0.05
-0.1
-0.15
0
3
6
Time(s)
(d) g4
5 Physical Model Testing for Dynamic Characteristics …
112
0.7
Excess pore pressure ratio
0.6
0.5
0.4
0.3
0.2
0.1
0 -1
10
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Time(s)
(a) k1
0.7
Excess pore pressure ratio
0.6
0.5
0.4
0.3
0.2
0.1
0 -1
10
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Time(s)
(b) k2
Excess pore pressure ratio
0.5
0.4
0.3
0.2
0.1
0 -1
10
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Time(s)
(c) k3
Fig. 5.18 Time history of excess pore pressure ratio in embankment body model test (reprinted
from Huang and Zhu (2017) with permission from American Society of Civil Engineers)
5.3 Physical Model Testing for Dynamic Characteristics …
113
Excess pore pressure ratio
0.4
0.3
0.2
0.1
0 -1
10
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Time(s)
(a) k1
0.8
Excess pore pressure ratio
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-1
10
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Time(s)
(b) k2
Excess pore pressure ratio
0.5
0.4
0.3
0.2
0.1
0
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Time(s)
(c) k3
Fig. 5.19 Time history of excess pore pressure ratio in embankment toe model test (reprinted
from Huang and Zhu (2017) with permission from American Society of Civil Engineers)
5 Physical Model Testing for Dynamic Characteristics …
114
diaphragm wall. Hence, the small k1 value may have been caused by boundary
effects. The generation of excess pore pressure was found to have started from the
ground to the base, while the dissipation of that pressure proceeded from the base to
the surface. This is reasonable, because the effective stress increases with depth.
The excess pore pressure in the upper soil layer reaches the effective stress quickly.
The excess pore pressure is continuously higher in the deep soil layers than in the
upper layers, although the excess pore pressure ratio may be smaller. Therefore, the
dissipation initiated from the deep soil layer toward the upper layer, according to
the second law of thermodynamics.
(3) Displacements
The experimental time history of vertical displacement of the embankment body
and toe after excitation are shown in Figs. 5.20 and 5.21, respectively.
From dynamic centrifuge model tests, the final vertical displacement was *24 cm
0
Displacement(mm)
-50
-100
-150
-200
-250
-300
0
0.5
1
1.5
2
Time(s)
2.5
x 10
5
Fig. 5.20 Time history of vertical displacement in embankment body model test
0
Displacement(mm)
-50
-100
-150
-200
-250
0
0.5
1
1.5
T ime(s)
2
2.5
x 10
5
Fig. 5.21 Time history of vertical displacement in embankment toe model test (reprinted from
Huang and Zhu (2017) with permission from American Society of Civil Engineers)
5.3 Physical Model Testing for Dynamic Characteristics …
115
in the body model and *17.6 cm in the toe model. Settlement in the body model
was greater than that in the toe model, because the settlement of backfill was
considered in the former model test. The deformation belongs to the pattern of
settlement without slip failure. The settlement is acceptable and the embankment is
safe, because of no overtopping. Consequently, the reservoir can fulfill its expected
design function under seismic intensity VII.
5.3.4
Discussion
The dynamic response of earthquake-induced liquefaction was presented above.
The dynamic centrifugal results were compared with dynamic triaxial tests to
validate the accuracy of the model tests. The laboratory tests were conducted using
a GDS dynamic triaxial apparatus to determine the liquefaction strength curve of
undisturbed soil samples. The liquefaction of various soil layers can be evaluated
according to Seed’s simplified method (Seed et al. 1983). The equivalent cyclic
shear stress during shaking is
sam ¼ 0:65 cz rd amax
;
g
ð5:23Þ
in which c is the unit weight of soil, z is depth from the ground surface, rd ¼
1 0:0133 z is the stress reduction factor, amax represents maximum horizontal
acceleration, and g is gravity.
The liquefaction resistance shear stress based on the dynamic triaxial tests is
sd ¼ Cr ð
rd
Þ r0 ;
2rc Nf m
ð5:24Þ
rd
where Cr is a correction coefficient, ð2r
Þ is the ratio of shear stress, and r0m is
c Nf
effective vertical stress.
From Eqs. (5.3) and (5.4), the liquefaction resistance factor FL is defined by
FL ¼
sd
sam
ð5:25Þ
If FL is <1, the soil may liquefy during shaking. When FL is >1, soil may not
liquefy. However, the excess pore pressure ratio will still increase to some extent. The
greater the FL, the smaller the excess pore pressure ratio during an earthquake
(Tokimatsu and Seed 1984). Table 5.3 presents results of the liquefaction evaluation
based on triaxial tests under seismic intensity VII. From the triaxial tests, only the
backfill layer may liquefy during an earthquake. However, the excess pore pressure
ratio of backfill reached only 0.51 and 0.27 in the body and toe models, respectively.
In the body model, pore transducer k1 was placed too close to the diaphragm wall.
The boundary effects produced this result. In the toe model, k1 was put in the
5 Physical Model Testing for Dynamic Characteristics …
116
Table 5.3 Evaluation of liquefaction potential based on dynamic triaxial tests (seismic intensity
VII)
Soil layer
Soil type
d(m)
Cr
rd
ð2r
Þ
c Nf
r0m (kPa)
sav
(kP)
sd
(kP)
FL
①
②
③
Backfill
Silty sand
Sandy silt
4
11
19
0.57
0.57
0.57
0.16
0.27
0.29
42
98
162
4.43
10.99
16.61
3.83
15.08
26.78
0.86
1.37
1.61
geotextile, which accelerated the dissipation of excess pore pressure. Thus, excess
pore water pressure did not accumulate because of the geotextile, which caused the
small excess pore pressure ratio. The triaxial tests cannot take into consideration
geotextile effects. Hence, the difference of backfill liquefaction between the triaxial
and centrifuge model tests is reasonable. Soil layer ② and ③ will not liquefy from
the standpoint of either model test. Moreover, soil layer ② will have more serious
liquefaction than layer ③. It is reasonable that the excess pore pressure ratio of the toe
model is larger than that of the body model, given the existence of initial deviatoric
stress around the toe area. However, the triaxial test cannot consider the effect of that
stress and geotextiles. Hence, the discrepancy is acceptable.
Although further calibration and validation are needed for the dynamic response
of embankment liquefaction, current model tests are capable of providing preliminary assessments of embankment safety.
5.4
Summary
In this chapter, dynamic characteristics of seismic soil liquefaction were captured
through physical modeling tests. Centrifugal shaking-table model tests are widely
used to research aspects of earthquake-induced liquefaction, considering that it can
reproduce the stress field of the prototype. The following conclusions were drawn.
(1) The principle and scale rule of dynamic geotechnical centrifuge model tests
were analyzed. The scale rule was obtained by equation analysis. Most of the
scaling rules were compatible, except for that of time scaling. The time scaling
rule is important in the study of liquefaction. Improved viscosity of the pore
fluid is a feasible way to address the time scaling conflict.
(2) The seismic wave is an important factor in soil liquefaction. The SHAKE 91
code can be applied to select the earthquake wave during centrifugal
shaking-table tests. This code can consider site effects on propagation of the
earthquake wave.
(3) Materials and structures should be substituted according to scaling rules when
dynamic centrifuge model tests are used in engineering projects. Geotextiles,
the diaphragm wall and other structures are always involved in the actual
projects to improve the seismic stability of structures. Hence, these elements
should be taken into consideration in experiments.
5.4 Summary
117
(4) The seismic response of soil is important in the study of liquefaction.
Acceleration, the excess pore water pressure ratio, and settlement can be used to
evaluate the liquefaction performance of soil. From these indexes, the liquefaction can be quantitatively described.
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behavior and densification remediation. Journal of Geotechnical and Geoenvironmental
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Chen, Z. Y., & Shen, H. (2014). Dynamic centrifuge tests on isolation mechanism of tunnels
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Dewoolkar, M. M., Ko, H. Y., & Pak, R. Y. S. (1999). Centrifuge modeling of models of seismic
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Elgamal, A., Parra, E., Yang, Z., et al. (2002). Numerical analysis of embankment foundation
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Chapter 6
Numerical Simulation for Deformation
of Liquefiable Soils
6.1
Numerical Method
Since Biot (1956) put forward the theory of elastic wave propagation through a
saturated fluid porous medium, a variety of analyses using finite element methods in
the time domain have been established, such as the formations us-uw-pw, us-uw,
us-ww, and us-pw (us is displacement of the solid phase, uw is absolute displacement
of the liquid phase, pw is pore-water pressure, and ww is speed of the liquid phase
relative to the solid phase). Xie and Zhang (1995) and Huang et al. (2002, 2004)
have incisively summarized these methods.
As is well known, liquefied sand is a type of saturated fluid–solid coupling
medium. Therefore, it is more reasonable and practical to use effective stress
numerical analysis of a two-phase porous media model than the total stress method
of a one-phase solid medium. Owing to the low frequency of earthquake load, we
chose the dynamic coupling equation, whose formation is us-pw (Biot 1956). In the
numerical method, solid displacement and pore-water pressure are the basic variables. The motion equation and continuity equation are described in the following
forms.
q€ui ¼ rij;j þ qbi
q f €ui;i pi;i cw
nc
e_ ii þ wf p_ ¼ 0
k
kK
ð6:1Þ
ð6:2Þ
€i is soil acceleration, rij is total stress,
where q is soil density, q f is water density, l
bi is the body force, p is pore pressure, n is soil porosity, cw is the unit weight of
water, e_ ii is the volumetric strain of soil, and k and K f are the permeability coefficient and the volumetric compressibility of water, respectively.
To overcome the incompressibility problem that may arise in numerical solution,
the FEM-FDM (Akai and Tamura, 1978) is used to solve the governing equations
described previously. The liquid and solid are discretized by the finite difference
© Springer Nature Singapore Pte Ltd. 2017
Y. Huang and M. Yu, Hazard Analysis of Seismic Soil Liquefaction,
Springer Natural Hazards, DOI 10.1007/978-981-10-4379-6_6
119
120
6 Numerical Simulation for Deformation of Liquefiable Soils
and finite element methods, respectively. That is, the finite element method is used
to spatially discretize pore-water pressure in the continuity equation and the finite
difference method to discretize displacement in the motion equation. The
Newmark-b method is adopted as the time integration program. It effectively avoids
the difficulty caused by inconsistency of the shape function between displacement
and pore pressure. The validity of the method in numerical analysis of soil
dynamics problems was verified by Oka et al. (1994). They compared analytical
and numerical solutions of transient dynamic response of a saturated two-phase
medium.
6.2
Constitutive Models for Liquefiable Soils
The constitutive model can be divided into two categories, an equivalent linear
method (e.g., Schnabel et al. 1972) based on an equivalent viscoelastic model, and a
nonlinear method (e.g., Lee and Finn 1978) based on an elastoplastic or viscoelastic
model. The equivalent linear analysis model has been widely used in the dynamic
analysis of soil. The same modulus was used for the processes of loading and
unloading. Thus, it only describes the nonlinear and hysteresis quality of the
dynamic stress–strain relation and cannot consider the cumulative deformation
characteristics of soil under dynamic loads. The elastoplastic model is more
appropriate to characterize soil dynamic response. It can not only fully describe the
dynamic stress–strain relationship but also calculate residual and permanent
deformation. The model is more complex, and accurate parameters are not easily
obtained.
To effectively describe the dynamic evaluation of liquefiable soil, we introduce
two main models in this chapter—nonlinear constitutive and cycle elastoplastic
constitutive.
6.2.1
Nonlinear Constitutive Model
The successful simulation of soil dynamic response in Shanghai proves the effectiveness of the nonlinear constitutive model. The results were given in Huang et al.
(2009b).
Data analysis of the numerous experimental findings showed that soils in
Shanghai have nonlinear and hysteretic characteristics. Based on a series of nonlinear viscoelastic concepts, the stress–strain relationship of the soil is deduced
(Seed and Idriss 1969). All parameters used in the constitutive model are obtained
from representative experiments. Here, parameters of the soil dynamic model are
analyzed according to existing data of soil dynamic tests in Shanghai, as follows
(Huang 1999).
6.2 Constitutive Models for Liquefiable Soils
121
(1) Maximum dynamic shear modulus
Maximum shear modulus Gmax is also called the initial shear modulus or
low-amplitude shear modulus. It represents the stress–strain backbone curve’s slope
at the origin. Laboratory tests have shown that soil stiffness is influenced by the
cyclic strain amplitude, void ratio, mean principal effective stress, plasticity index,
overconsolidation ratio, and number of loading cycles. The following empirical
expression is often used in laboratory tests during determination of the maximum
shear modulus of soils (Hardin 1978):
Gmax ¼ D
OCRk
r00 0:5
p
ð
Þ ;
a
0:3 þ 0:7e2
pa
ð6:3Þ
where D is a dimensionless parameter, e is the void ratio, OCR is the overconsolidation ratio, r00 is confining pressure, pa is atmospheric pressure, and k is a
coefficient related to the plasticity index of soil. Based on the above relationship and
experimental data of Shanghai saturated soils, suitable values are: D = 353 for clay,
451 for silty clay, and 485 for sand (Huang et al. 2009b).
(2) Strain-dependent modulus and damping
Both the shear modulus and damping ratio of soil strongly depend on the amplitude
of shear strain under cyclic loading. The secant shear modulus G at strain amplitude
c is calculated by the expression proposed by Martin and Seed (1982):
G
G
¼ 1 HðcÞ
¼ 1 HðcÞ
Gmax
Gmax
ð6:4Þ
In the model, the function HðcÞ is
HðcÞ ¼ ½
ðjcj=cr Þ2B
1 þ ðjcj=cr Þ2B
A ;
ð6:5Þ
where cr is the reference or yield strain and A and B are two dimensionless
parameters. The values of cr for the Shanghai saturated soils may be determined by
the following empirical relationship:
cr ¼ C qffiffiffiffiffi
3
r00 ;
ð6:6Þ
where r00 is effective mean principal stress in kPa and C is an empirical parameter.
Table 6.1 lists experimental numerical values for parameters A, B, and C, obtained
for Shanghai saturated soft soil. The curve of the shear modulus ratio G/Gmax of the
Shanghai clay with c is compared with the experimental data in Fig. 6.1.
For the Shanghai saturated soil, variation of the damping ratio D with strain level
is estimated from a Hardin–Drnevich type equation (Hardin and Drnevich 1972):
122
6 Numerical Simulation for Deformation of Liquefiable Soils
Table 6.1 Reference values
of A, B, and C (reprinted from
Huang et al. (2009b) with
permission of Springer)
Type
A
B
C
Clay
Silty clay
Sand
1.62
1.12
1.10
0.42
0.44
0.48
0.00013
0.00017
0.00022
1.0
Fig. 6.1 Relationship
between shear modulus ratio
and shear strain of Shanghai
clay (reprinted from Huang
et al. (2009b) with permission
of Springer)
G/Gmax
0.8
0.6
0.4
0.2
0.0
1E-6
1E-5
1E-4
1E-3
D
G
¼1
;
Dmax
Gmax
0.01
ð6:7Þ
where Dmax = 0.30 for the clay and 0.25 for the silty clay and sand. A comparison
between the proposed model and experimental data is shown in Fig. 6.2.
(3) Pore-water pressure buildup
On the basis of results from undrained cyclic-triaxial test data, the excess
pore-water pressure buildup of the Shanghai clay and silty clay may be expressed as
p
b
0 ¼ aN ;
r0
ð6:8Þ
where p is the excess pore-water pressure, N is the equivalent number of uniform
stress cycles, and a and b are two experimental parameters that are determined by
the dynamic shear stress ratio r. Table 6.2 shows reference values of a and b for the
0
Shanghai clay and silty clay. Curves of the excess pore-water pressure ratio p r0
and N of the Shanghai clay are compared with the experimental data in Fig. 6.3.
0.30
0.25
0.20
D
Fig. 6.2 Relationship
between damping ratio and
shear strain of Shanghai clay
(reprinted from Huang et al.
(2009b) with permission of
Springer)
0.15
0.10
0.05
0.00
1E-6
1E-5
1E-4
1E-3
0.01
6.2 Constitutive Models for Liquefiable Soils
Fig. 6.3 Relationship
between pore-water pressure
ratio and N of Shanghai clay
(reprinted from Huang et al.
(2009b) with permission of
Springer)
Type
a
b
Clay
0:247c0:767
0:375c0:431
Silty clay
0:273c0:711
0:348c0:394
0.7
0.6
Pore water pressure ratio
Table 6.2 Reference values
of a and b (reprinted from
Huang et al. (2009b) with
permission of Springer)
123
0.5
0.4
0.3
r=0.16
r=0.20
r=0.23
r=0.25
r=0.354
0.2
0.1
0.0
0
200
400
600
800
1000
1200
Cyclic number N
For the Shanghai sand, the development of excess pore-water pressures in cyclic
loading is of the following form (Seed et al. 1976):
p
2
N 1
arcsinð Þ2h ;
0 ¼ ð1 ms1 Þ
p
Nf
r0
ð6:9Þ
where s1 is the static stress level, m and h are two experimental parameters (for the
Shanghai sand m = 1.1 and h = 0.7), and Nf is the accumulative number of cycles at
the same stress level required to produce a peak cyclic pore-water pressure ratio of
100% under undrained conditions.
6.2.2
Cycle Elastoplastic Constitutive Model
Based on the work of Oka et al. (1999), liquefiable saturated sand was represented
by a cyclic elastoplastic constitutive model, which was mainly composed of an
overconsolidation boundary surface, Armstrong–Frederick-type nonlinear kinematic
hardening rule, and non-associated flow rule. The nonlinear expression of stress
dilatancy characteristic relationships and cumulative strain-dependent characteristics
of the plastic shear model were also considered. All related parameters were defined
by considering typical experimental values or in situ tests (Table 6.3). Under seismic
loading, it has been proven that the constitutive law could well describe the
responses of features such as cyclic mobility, liquefaction strength, effective stress
path, and the stress–strain relationship (Sugito et al. 2000; Huang et al. 2004, 2005).
Controlling reduction of elastic modulus after phase transformation
cP
ref
cE
ref
Cd
D*0
n
Reference strain parameters
Disappearance of anisotropy
Dilatancy parameters
Controlling the rate of disappearance of initial anisotropy
Controlling entire amount of dilatancy
Controlling sensitivity of dilatancy to stress amplitude
Stress ratio for phase transformation line
Stress ratio for failure line
Related to initial plastic shear modulus
Related to ultimate plastic shear modulus
Controlling reduction of plastic modulus after phase transformation
M*m
M*f
B*0
B*1
Phase transformation stress ratio
Failure stress ratio
Hardening parameters
Density of mixture
Coefficient of permeability
Related to bulk modulus and overconsolidation boundary surface
Elastic modulus
Related to overconsolidation boundary surface
Related to bulk modulus and overconsolidation boundary surface
Related to overconsolidation boundary surface
Related to initial shear modulus
Physical role
q (t/m3)
k (um/s)
e0
m
k
j
OCR*
0
G0 rm
Density
Coefficient of permeability
Initial void ratio
Poisson ratio
Compression index
Swelling index
Quasi-overconsolidation ratio
Initial shear modulus ratio
Name of parameters
Table 6.3 Parameters of E-P model
Data adjusting method based on
liquefaction strength curves,
strain-dependent shear modulus
and damping factor
Monotonic shear test
Volume change characteristics
PS logging
Density test
Permeability test
Density test
Monotonic shear test
Isotropic compression test,
Isotropic swelling test
Determination method
124
6 Numerical Simulation for Deformation of Liquefiable Soils
6.2 Constitutive Models for Liquefiable Soils
15
10 Experiment
5
0
-5
-10
-15
-5
-2.5
0
2.5
Shear strain (%)
15
10
Theory
5
0
-5
-10
-15-5
-2.5
0
2.5
Shear strain (%)
Shear stress (kPa)
Shear stress (kPa)
Fig. 6.4 Comparison of
theoretical and experimental
results of undrained torsional
shear tests (after Matsuo et al.
2000) a shear stress—shear
strain b effective stress paths
125
5
5
Shear stress (kPa)
Shear stress (kPa)
(a) Shear stress – shear strain
15
15
10
10
5
5
0
0
-5
-5
-10
-10
-15
-15
0 10 20 30 40 50 60 70
0 10 20 30 40 50 60 70
Mean effective stress (kPa)
Mean effective stress (kPa)
(b) Effective stress paths
In the above model, the nonlinear kinematic hardening rule can reveal the
nonlinear characteristics of the stress–strain process. The overconsolidation
boundary was used to describe expansion under alternating loads. The constitutive
model can simulate the simple shear response of soil in the state of initial anisotropy
and initial stress and strain.
Figure 6.4 shows the performance of the constitutive model in undrained torsional shear tests of Toyoura standard sand under the condition of vertical strain
constraint (Matsuo et al. 2000). The simulated shear stress–shear strain relationship
and effective stress path are show to coincide well with the experimental results.
(1) Overconsolidation boundary surface
The overconsolidation boundary surface fb is used to depict the stress history state
of the soil. When fb 0, soil is in a state of normal consolidation. If fb < 0, soil is in
a state of overconsolidation. Similar to the general boundary models, the purpose of
the overconsolidation boundary surface is to describe plastic deformation of the
yield surface under cyclic loading, which is defined as
fb ¼ g0 þ Mm ln
r0m
¼0
r0mb
ð6:10Þ
1
g0 ¼ fðgij gijð0Þ Þðgij gijð0Þ Þg2
1
g ¼ ðgij gij Þ2 ;
ð6:11Þ
ð6:12Þ
where ηij is the stress ratio, gij ¼ sij r0m ; ηij(0) is the initial value of ηij; r0m is the
mean effective stress, r0m ¼ 13 dij r0ij ; dij is the Kronecker sign; r0ij is the effective
stress; sij is the deviatoric stress, sij ¼ r0ij dij r0m ; Mm is the phase transformation
126
6 Numerical Simulation for Deformation of Liquefiable Soils
stress ratio; r0mb is the value of r0m at the intersection of the ηij(0) line and overconsolidation boundary surface.
r0mb ¼ r0mbi expð
1þe P
t Þ;
kj
ð6:13Þ
where r0mbi is the initial value of r0mb , known as the mean value of the initial
consolidation effective stress; e is the void ratio; k is the compression index; j is the
swell index; tP is the plastic volumetric strain.
(2) Yield surface
The yield surface is composed of two functions, fy1 and fy2. fy1 reflects the change
of stress ratio and fy2 describes the change of mean effective stress. fy1 is defined as
fy1 ¼ fðgðijÞ vij ÞðgðijÞ vij Þg1=2 k ¼ 0;
ð6:14Þ
where k is a numerical parameter that controls the size of the elastic region and vij
is the kinematic hardening parameter, known as the back stress parameter.
Regarding the translation of the yield surface, in classical plasticity, it is common to
use linear kinematic hardening rules, such as the models of Prager and Ziegler.
Here, for more accurate prediction of the multiaxial Bauschinger effect, a modified
Armstrong and Frederick nonlinear kinematic hardening rule was adopted, as follows (Lemaitre and Chaboche 1990):
dvij ¼ BðMf dePij vij dcP Þ
ð6:15Þ
dcP ¼ ðdePij dePij Þ1=2
ð6:16Þ
B ¼ ðB0 B1 Þ expðCf cpn Þ þ B1 ;
ð6:17Þ
where Mf is the failure ratio; dePij is the deviatoric plastic strain increment; dcP is the
second invariant of dePij ; cpn is accumulated value of cP between two sequential stress
reversal points in a previous cycle; B0, B1 and Cf are material parameters.
Therefore, this rule generalizes the Prager linear hardening rule by adding an
evanescent strain-memory term (dynamic recovery term) to overcome the shortcoming of linear proportion between dvij and dePij in the Prager model. This shows
excellent correlation with experimental results for monotonic and cyclic loading.
The other yield function fy2 is defined as
r0m
fy2 ¼ Mm lnð 0 ym Þ Rd ¼ 0;
r
ð6:18Þ
m0
where ym is the scalar kinematic hardening parameter; r0m0 is the unit value of mean
effective stress; Rd is the scalar parameter. Because the effective stress in soils
6.2 Constitutive Models for Liquefiable Soils
127
decreases gradually during liquefaction in earthquakes, the yield state of fy2 could
not be reached in the present work.
(3) Plastic potential function
Using the non-associated flow rule, the plastic potential function g is defined as
~ lnð
g ¼ fðgðijÞ vij ÞðgðijÞ vij Þg1=2 þ M
r0m
Þ ¼ 0;
r0ma
ð6:19Þ
~ is calculated by
where r0ma is a constant and M
~ ¼
M
8
<
:
g
ln ðr0m
fb \0
r0mc Þ
fb 0
Mm
r0mc ¼ r0mb expð
ð6:20Þ
gð0Þ
Þ
Mm
ð6:21Þ
After determining the constitutive model and corresponding parameters, the
liquefaction analysis based on the finite element method can be accomplished as
follows.
After determining the constitutive model and corresponding parameters, the
liquefaction analysis based on the finite element method can be accomplished as
follows.
First, the finite element model can be set up according to the geologic model and
structure conditions. Specifically, the strata are divided and the boundary and initial
conditions are determined. Then, the seismic motion condition is inputted. In this
way, the liquefaction can be analyzed.
6.3
6.3.1
Simulation and Analysis of Various
Engineering Problems
Earth Embankment Foundation on Liquefiable Soils
(1) Problem description
The target project was a plane strain seismic analysis of part of a new river dike in
the Kansai area of western Japan. Because Japan is prone to frequent earthquakes,
there is a great need for the stability of earth embankments under strong seismic
design motions to be verifiable. Figure 6.5 demonstrates the configuration of an
earth embankment. Soil at the site is composed of *9 m of mixed hydraulic sand
fill overlying *17 m of alternating bands of clays and sands. The groundwater
table was *1.2 m below ground level. Consequently, most of the soil deposits
were fully saturated below the ground surface. It is apparent that this type of
128
6 Numerical Simulation for Deformation of Liquefiable Soils
385.547
A
C
3.75
0.00
-2.85
B
S1a
5.00
D
B
S1b
C1
-8.60
-13.40
-16.00
-20.00
C2
Y
S2
S3
X
Unit: m
Fig. 6.5 Configuration of earth embankment (unit: m) (reprinted from Huang et al. (2009a) with
permission of Springer)
saturation affects the earthquake response of soil layers related to liquefaction and
softening. The finite element model was composed of 2848 nodes and 2732
four-node quadrilateral elements.
The following constitutive models were used for plane strain elements in the
analysis.
(1) Shallow sand layers B, S1a and S1b were modeled by the elastoplastic constitutive law for sand, which was mentioned previously. Shallow sand layers were
in the upper part of the site and comprised of recent fill and alluvia soils with
thickness *9 m. As the 1995 Hyogoken Nambu earthquake revealed, these
soils were prone to liquefy. Fill material of the embankment consisted of sand B.
(2) Under the aforementioned sand layers were alluvial clays C1 and C2. They
belong to a homogeneous group, for which they were modeled by a similar
cyclic elasto-viscoplastic constitutive law for clay (Oka et al. 2004). The clay
and sand models had a similar frame. However, the clay model was distinguished from the sand model by the viscous effect of clays.
(3) The lower underlying geology of the site was composed of over 6 m of dense
sand layers, S2 and S3. They were considered stable bearing layers during
earthquakes, and were modeled by the Ramberg-Osgood model.
Tables 6.4 and 6.5 list material parameters used in the analysis. Figure 6.6
shows the simulated liquefaction strength curves of liquefiable sand layers (B, S1a
and S1b) with 5% double-amplitude of axial strain in the triaxial test. All of these
soil parameters were defined by considering typical experimental values for liquefiable sand, based on the results of geotechnical investigations. The procedures of
parameter selection for soils are found in Oka et al. (1999).
A horizontal earthquake time history with maximum acceleration 1.5 m/s2 was
used as excitation in the analysis (Fig. 6.7), and a severe earthquake corresponding
to the ultimate limit state of a collapse event specified for the river embankment is
6.3 Simulation and Analysis of Various Engineering Problems
129
Table 6.4 Parameters used for sands and clays (elastoplastic model) (reprinted from Huang et al.
(2009a) with permission of Springer)
B
S1a
S1b
C1
C2
Density
Coefficient of permeability
Initial void ratio
Poisson ratio
Compression index
Swelling index
Quasi-overconsolidation ratio
Initial shear modulus ratio
q (t/m3)
k (um/s)
e0
m
k
k
OCR*
0
G 0 rm
1.83
20
0.808
0.3
0.015
0.0015
1.0
700
1.74
10
1.089
0.3
0.015
0.0015
1.0
550
1.82
10
0.728
0.3
0.015
0.0015
1.0
600
1.68
18
1.410
0.4
0.25
0.0500
1.0
300
1.78
45
1.170
0.4
0.34
0.0600
1.0
350
Phasetransformation stress ratio
Failure stress ratio
Hardening parameters
M*m
M*f
B*0
B*1
Reference strain parameters
cP
ref
0.91
1.25
2500
30
0.005
0.91
1.25
2800
30
0.005
0.91
1.30
3000
30
0.005
1.30
1.30
–
–
–
1.35
1.35
–
–
–
0.010
0.010
0.010
–
–
2000
1.0
4.0
–
–
–
2000
1.0
4.0
–
–
–
2000
1.0
4.0
–
–
–
–
–
–
17
3.0
7.5
–
–
–
17
3.0
7.5
Soil layer
Disappearance of anisotropy
Dilatancy parameters
Viscoplastic parameters
cE
ref
Cd
D*0
n
m′0
C01/10−7 s−1
C02/10−8 s−1
Table 6.5 Parameters used for sands (Ramberg-Osgood model) (reprinted from Huang et al.
(2009a) with permission of Springer)
Soil layer
Density
Coefficient of permeability
Initial void ratio
Compression index
Shear modulus parameters
Cohesion
Angle of internal friction
q (t/m3)
k (um/s)
e0
m
a
b
C (kPa)
/(°)
a
r
S2
S3
1.97
10
0.643
0.30
7000
0.50
0
38
3
2
2.00
20
0.600
0.30
8000
0.50
0
45
3
2
Fig. 6.6 Simulation of
liquefaction strength of
liquefiable sand layers
(reprinted from Huang et al.
(2009a) with permission of
Springer)
6 Numerical Simulation for Deformation of Liquefiable Soils
0.50
Cyclic shear stress ratio
130
0.40
B
S
0.30
S
1a
1b
0.20
0.10
DA=5%
0.00
1
10
100
Number of cycles
3.00
Acceleration (m/s2)
Fig. 6.7 Input earthquake
wave with maximum
acceleration 1.5 m/s2
(reprinted from Huang et al.
(2009a) with permission of
Springer)
2.00
Max. Acc. = 1.500 m/s 2
1.00
0.00
-1.00
-2.00
-3.00
0
10
20
30
40
50
60
70
Time (s)
represented. An input motion of 70 s was applied synchronously across the base of
the model.
(2) Results and analysis
Predicted accelerations at points A through D (Fig. 6.5) are shown in Fig. 6.8. The
results show the damping effect of soils. The soil deposits act as a damper when the
bedrock earthquake acceleration is transmitted through soil. Owing to liquefaction
of shallow sand deposits, the frequency content of soil ground acceleration has a
tremendous difference relative to that of bedrock acceleration. The soil deposit
attenuates a substantial portion of the high-frequency content of the bedrock
acceleration. The isolation and damping effects of liquefied soil on earthquake
acceleration response of the embankment are proven.
Both points A and C are above the groundwater table, where the soils do not
experience tremendous stiffness reduction and degradation during an earthquake.
Therefore, compared with the underlying liquefied saturated soil, they show similar
acceleration responses as a quasi-rigid body.
Predicted displacements at points A through D are shown in Fig. 6.9.
Figure 6.10 shows the configuration of the earth embankment at the end of the
earthquake, where the displacements were magnified by a factor of three for easy
comparison.
The above results show that liquefaction occurs in the free field, producing large
deformation of the embankment by lateral flow of the base ground. There
6.3 Simulation and Analysis of Various Engineering Problems
3.00
2.00
Acceleration (m/s)
A
2
2
Acceleration (m/s )
3.00
1.00
0.00
2.00
B
1.00
0.00
-1.00
-1.00
-2.00
-3.00
131
-2.00
0
10
20
30
40
50
60
-3.00
70
0
10
20
Time (s)
2.00
Acceleration (m/s)
C
2
2
Acceleration (m/s)
50
60
70
3.00
3.00
1.00
0.00
2.00
D
1.00
0.00
-1.00
-1.00
-2.00
-2.00
-3.00
30
40
Time (s)
-3.00
0
10
20
30
40
Time (s)
50
60
70
0
10
20
30
40
Time (s)
50
60
70
Fig. 6.8 Accelerations at points A through D (reprinted from Huang et al. (2009a) with
permission of Springer)
is *1.0 m of lateral spread of foundation soil toward the free field at the toe. Upper
soils have larger displacements compared with lower ones during excitation.
Moreover, seismic displacements of embankment soils are much larger than those
of free-field soils. The crest undergoes large settlement >60 cm because of the
combined action of migration of the underlying foundation soil and deformation of
the embankment itself. This agrees satisfactorily with conclusions based on
observations in earthquake case histories. Total deformation increases continuously
until the full dissipation of excess pore-water pressure.
The time histories of excess pore-water pressure ratios (ηEPWPR) at points B and
D are shown in Fig. 6.11. The final distribution of ηEPWPR in the earth embankment
is shown in Fig. 6.12. During the earthquake, in the shallow sand layers, ηEPWPR
approached 1.0 after *30 s and remained large thereafter. The maximum ηEPWPR
was equal to or near 1.0 at the end of earthquake. In the portion beneath the
embankment, owing to the initial stress state, seismic pore-water pressure ratios
were less than those of the free field at the same depths.
6.3.2
Mitigation of Liquefaction-Induced Soil Deformation
of Sandy Ground Improved by Cement Grouting
(1) Problem description
The target project was a sluice gate called Yahatagawa, which has a reinforced
concrete footing of thickness 2.1 m (Fig. 6.13). This gate is at the downstream
mouth of the Yahata River at Minamisanriku Town in Miyagi Prefecture, on the
Horizontal Displacement (m)
6 Numerical Simulation for Deformation of Liquefiable Soils
Horizontal Displacement (m)
132
1.50
1.00
A
0.50
0.00
-1.00
Vertical Displacement (m)
1.00
10
20
30 40
Time (s)
50
1.00
60
C
0.00
10
20
30 40
Time (s)
50
60
20
30 40
Time (s)
50
60
70
1.50
1.00
D
0.50
0.00
A
0.50
-1.50
70
Vertical Displacement (m)
0
0.00
-0.50
0
10
20
30 40
Time (s)
50
60
70
1.00
B
0.50
0.00
-0.50
0
10
20
30 40
Time (s)
50
60
70
1.00
C
0.50
-1.00
Vertical Displacement (m)
Vertical Displacement (m)
10
-1.00
-1.00
0.00
0
10
20
30 40
Time (s)
50
60
70
1.00
D
0.50
0.00
-0.50
-0.50
-1.00
0
-0.50
-0.50
-1.00
0.00
-1.50
70
0.50
-1.50
B
0.50
-1.00
0
Horizontal Displacement (m)
Horizontal Displacement (m)
1.50
1.00
-0.50
-0.50
-1.50
1.50
0
10
20
30 40
Time (s)
50
60
70
-1.00
0
10
20
30 40
Time (s)
50
60
70
Fig. 6.9 Horizontal and vertical displacement at points A through D (reprinted from Huang et al.
(2009a) with permission of Springer)
Fig. 6.10 Configuration of earth embankment at end of earthquake (reprinted from Huang et al.
(2009a) with permission of Springer)
6.3 Simulation and Analysis of Various Engineering Problems
1.00
1.00
B
0.80
Pressure Ratio
Pressure Ratio
133
0.60
0.40
0.20
0.60
0.40
0.20
0.00
0.00
-0.20
-0.20
0
10
20
30 40
Time (s)
50
60
70
D
0.80
0
10
20
30 40
Time (s)
50
60
70
Fig. 6.11 Time histories of excess pore-water pressure ratios (ηEPWPR) at points B and
D (reprinted from Huang et al. (2009a) with permission of Springer)
0.0
0.2
0.4
0.6
0.8
1.0
Fig. 6.12 Excess pore-water pressure ratio of earth embankment at end of earthquake (reprinted
from Huang et al. (2009a) with permission of Springer)
northeastern Pacific coast of Japan. Unfortunately, this area is in a seismically
active region where tsunami may be triggered by earthquakes. For example, tsunami generated by the 1933 Sanriku-Oki Earthquake (M 8.1) along the Japan
Trench inundated the coast of Miyagi, causing serious damage and loss of life.
Therefore, the sluice gate is an important infrastructure for tsunami prevention and
river management in the area.
The alluvial sand layer classified as ‘‘As’’ in Japan is in the upper portions of the
site, with a thickness of 5.85 m. This layer is liable to liquefy, as shown during the
1995 Hyogoken-Nambu earthquake. This type of sand usually has an average
diameter D50 of 75 lm–2.0 mm, with a relative density Dr < 70%. The underlying
soils comprised *10.2 m of volcanic ash, alluvial clay and gravel lying on a
strongly weathered conglomerate, which constitutes the lower boundary. The
groundwater table is at the ground surface and soil deposits are fully saturated.
Because of the high risk of severe earthquake liquefaction at the site, suitable
countermeasures were adopted to reduce liquefaction-induced soil deformations of
the foundation during the design earthquake. As a result, there is a need for an
assessment of the effectiveness of various mitigation designs. The liquefaction
mitigation schemes for the foundation are as follows: (1) No treatment and (2) use
of a cement-grouting containment enclosure adjacent to the foundation. The
problem was considered as plane strain and the selected finite element mesh consisted of 700 nodes and 646 quadrilateral elements.
134
6 Numerical Simulation for Deformation of Liquefiable Soils
7.50 m
SPT-N
Depth-m
0
0
Gravel
N=14
As
Sand
N=5
Av
Volcanic
ash
Ac
Clay
N=3
Ag
Gravel
N=14
Rock
N=50
0.79
7.71 m
Footing
10 20 30 40 50
6.64
7.50
N=22
2.00 m
Cement grouting
14.35
16.85
18.00 WCg
Fig. 6.13 Schematic cross-section showing ground improvement constructed as a liquefaction
countermeasure for a sluice gate (reprinted from Huang et al. (2008b) with permission of Springer)
The constitutive relation of the liquefiable soil layer (As) was simulated using
the aforementioned cyclic elastoplastic model, with parameters indicated in
Table 6.6. All of these parameters were defined by considering typical experimental
values for liquefiable sand. Figure 6.14 shows the simulated undrained response of
Table 6.6 Soil parameters
used for numerical analysis of
the case (reprinted from
Huang et al. (2008b) with
permission of Springer)
Name of soil profile
As
3
Density
Coefficient of permeability
Initial void ratio
Compression index
Swelling index
Quasi-overconsolidation ratio
Initial shear modulus ratio
q (t/m )
k (m/s)
e0
k
k
OCR*
0
G0 rm
1.8
1 10−6
0.8
0.015
0.0015
1.0
800
Phase transformation stress ratio
Failure stress ratio
Hardening parameter
M*m
M*f
B*0
B*1
Reference strain parameter
cP
ref
0.91
1.25
2500
50
0.005
Disappearance of anisotropy
Dilatancy parameter
cE
ref
Cd
D*0
n
0.010
2000
1.0
4.0
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.03 -0.02 -0.01
0
0.01
Axial strain
Deviator stress ratio
Deviator stress ratio
6.3 Simulation and Analysis of Various Engineering Problems
0.02
0.03
135
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
0
0.2
0.4
0.6
0.8
Mean effective stress ratio
1
Fig. 6.14 Numerical simulation of undrained response of foundation soil, As (reprinted from
Huang et al. (2008b) with permission of Springer)
saturated foundation soil under symmetric stress-controlled cyclic triaxial loading
conditions, in terms of shear stress-strain and effective stress path.
The numerical simulation was run with the following boundary conditions.
1. For the solid phase, a horizontal input motion was specified along the base. All
base nodes were fixed in both vertical and horizontal directions. A simplified
pseudo-free field boundary condition was applied at the lateral boundaries,
where displacements of the lateral side nodes were forced to equal those of
corresponding nodes at the same depths in the free field.
2. For pore pressures, the base and the two lateral sides were impervious. The
ground surface was assumed to be drainage boundary.
A 30-s-long horizontal earthquake wave was used as excitation in the analysis,
which represents a rare, extreme earthquake corresponding to the ultimate limit
state of collapse event specified for the sluice gate. Its maximum amplitude was
3.19 m/s2. The input motion was applied synchronously across the base of the
model.
In addition to hysteresis damping described by the cyclic elastoplastic constitutive model, Rayleigh damping proportional to the system-stiffness matrix was
used with a damping ratio of 5%. For the time-stepping scheme, the Newmark
method was used with b = 0.3025 and c = 0.6. The time step was taken as 0.001 s.
(2) Results and analysis
A static elastic-perfectly plastic analysis with the Drucker-Prager yield criterion was
performed to determine the distribution of initial stress field under gravity before
seismic excitations.
Figures 6.15 and 6.16 show time histories of horizontal and vertical displacements at the center of the footing, respectively. Based on the deformation pattern,
we can conclude the following: (1) the extensive liquefaction causes a typical lateral
spread of the foundation soil toward the free field, as indicated by permanent
deformation of as much as 90.2 cm at the foundation center; (2) deformations
occurring with cement grouting are very small compared with those without any
Fig. 6.15 Time histories of
horizontal displacements
(reprinted from Huang et al.
(2008b) with permission of
Springer)
6 Numerical Simulation for Deformation of Liquefiable Soils
Horizontal Displacement (m)
136
1.5
1
0.5
0
-0.5
Vertical Displacement (m)
-1.5
Fig. 6.16 Time histories of
vertical displacements
(reprinted from Huang et al.
(2008b) with permission of
Springer)
0
5
10
15
20
Time (s)
25
30
1.5
1
0.5
0
-0.5
-1
-1.5
Cement Grouting
No Countermeasure
0
5
10
15
20
Time (s)
25
30
6
2
Acceleration (m/s )
Fig. 6.17 Time histories of
accelerations (reprinted from
Huang et al. (2008b) with
permission of Springer)
Cement Grouting
No Countermeasure
-1
4
2
0
-2
Cement Grouting
No Countermeasure
-4
-6
0
5
10
15
20
Time (s)
25
30
countermeasures. Specifically, the horizontal permanent deformation is
only *0.05 cm.
The accelerations at the foundation center are depicted in Fig. 6.17. It shows an
increase in acceleration caused by soil amplification effects under the condition of
cement grouting, a result of soil stiffness improvement by the liquefaction mitigation method.
Time histories of excess pore-water pressure (EPWP) ratio (the ratio of excess
pore-water pressure to initial effective vertical stress) in the sand layer at the end of
the earthquake are shown in Fig. 6.18. It is obvious that the seismic loading produces a typical pattern of liquefaction response of the soil layer, with EPWP ratios
Fig. 6.18 Time histories of
excess pore-water pressure
ratios (reprinted from Huang
et al. (2008b) with permission
of Springer)
Pore Water Pressure Ratio
6.3 Simulation and Analysis of Various Engineering Problems
137
1
0.8
0.6
0.4
0.2
0
Cement Grouting
No Countermeasure
-0.2
-0.4
0
5
10
15
20
Time (s)
25
30
approaching 1.0 after *9 s and remaining large thereafter. The response of EPWP
in the foundation soil still reaches the liquefaction state even after the ground
improvement by cement grouting. This result is in keeping with the mechanisms of
the liquefaction mitigation method as mentioned in previous sections, i.e., not
preventing EPWP generation but reducing liquefaction-induced deformations.
6.4
Summary
Deformation of liquefiable soils is a major concern for construction safety. This
chapter presented a numerical study of seismic performance of liquefiable soils
during earthquake loading. Analyses were conducted using an effective stressbased, finite element program.
(1) Sandy soil behavior was described by two constitutive models, a nonlinear
constitutive and cyclic elastoplastic constitutive model.
(2) The first constitutive model that was developed within the framework of the
nonlinear viscoelastic concept was mainly composed of three parts—maximum
shear modulus, strain-dependent modulus and pore-water pressure buildup. The
second constitutive model that was developed within the framework of a
nonlinear kinematic hardening concept was mainly composed of an overconsolidation boundary surface, Armstrong–Frederick-type nonlinear kinematic
hardening rule, and non-associated flow rule.
(3) Two types of engineering problem were described and analyzed in detail, such
as earthquake embankment foundations on liquefiable soils, and mitigation of
liquefaction-induced soil deformation on sandy ground improved by cement
grouting. Special emphasis was given to computed results of excess pore-water
pressure, displacement, and acceleration during seismic excitation.
(4) Generally, the effectiveness of the approaches to soil deformation caused by
liquefaction was clearly demonstrated by the analytical methods. The method in
this chapter is capable of capturing the fundamental aspects of the investigated
problems, and its results are useful for design.
138
6 Numerical Simulation for Deformation of Liquefiable Soils
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Matsuo, O., Shimazu, T., Uzuoka, R., Mihara, M., & Nishi, K. (2000). Numerical analysis of
seismic behavior of embankments founded on liquefiable soils. Soils and Foundations, 40(2),
21–39.
Oka, F., Yashima, A., Tateishi, A., et al. (1999). A cyclic elasto-plastic constitutive model for sand
considering a plain-strain dependence of the shear modulus. Geotechnique, 49(5), 661–680.
Oka, F., Kodaka, T., & Kim, Y. S. (2004). A cyclic viscoelastic-viscoplastic constitutive model for
clay and liquefaction analysis of multi-layered ground. International Journal for Numerical
and Analytical Methods in Geomechanics, 28(2), 131–179.
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porous soil using an elasto-plastic model. Applied Scientific Research, 52(3), 209–245.
Schnabel, P. B., Lysmer, J., & Seed, H. B. (1972). SHAKE: A computer program for earthquake
response analysis of horizontally layered sites. In Tech Rep UCB/EERC-71/12, University of
California, Berkeley.
Seed, H. B., & Idriss, I. M. (1969). Influence of soil conditions on ground motions during
earthquakes. Journal of the Soil Mechanics and Foundations Division, 95(1), 99–138.
Seed, H. B., Martin, P. P., & Lysmer, J. (1976). Pore-water pressure changes during soil
liquefaction. Journal of Geotechnical and Geoenvironmental Engineering, 102. (Proc. Paper#
12074).
Sugito, M., Oka, F., Yashima, A., et al. (2000). Time-dependent ground motion amplification
characteristics at reclaimed land after the 1995 Hyogoken Nambu Earthquake. Engineering
Geology, 56(1), 137–150.
Xie, D. Y., & Zhang, J. M. (1995). Transient dynamic characteristics and mechanism analysis of
saturated sand. Xian: Shanxi Science and Technology Press. (in Chinese).
Ye, G. L., Miyaguchi, H., Huang, Y., et al. (2004). Dynamic behavior of group-pile foundation
evaluated by simplified model and sophisticated model. In 13th World Conference on
Earthquake Engineering (pp. 28). Vancouver, B.C., Canada.
Chapter 7
Comprehensive Evaluation of Liquefaction
Damage During Earthquakes
7.1
Introduction
Based on the preceding chapters, in the soft soil engineering field, it is necessary to
evaluate the damage to engineering structures after field liquefaction during an
earthquake. Therefore, this chapter is based on the previous chapters and investigates the evaluation of seismic liquefaction security in geotechnical problems.
Comprehensive evaluation methods for liquefaction damage during earthquakes
include field tests, a laboratory dynamic test, a dynamic centrifugal model test, and
a performance-based seismic design evaluation method.
Multilevel seismic design principles are used in traditional seismic theories in
countries worldwide, including China (e.g., the Chinese seismic code). Properly
engineered structures cannot be ruined in small earthquakes, can be repaired in
moderate earthquakes, and do not collapse in strong earthquakes. When structures
designed according to the aforementioned seismic concepts experience a devastating earthquake, damage will be allowed to disappear, but the major structure will
not collapse, ensuring the safety of people. This seismic design theory does not
ensure that the structures (and especially non-structural elements) will avoid
destruction in moderate or minor earthquakes, and does not consider how to reduce
pecuniary loss or social effects of earthquake disasters. We can say that this design
method has the single seismic fortification goal of protecting human life to the
extent possible. However, recently, experiences of seismic damage in cities during
numerous earthquakes give us new clarification and recognition. That is, although
engineered structures do not collapse and guarantee the basic security of life, and
are designed and constructed in light of current seismic design methods with the
global aim of protecting human life, earthquake damage causes huge economic
losses. What, therefore, are the main reasons for such losses under the situation of
© Springer Nature Singapore Pte Ltd. 2017
Y. Huang and M. Yu, Hazard Analysis of Seismic Soil Liquefaction,
Springer Natural Hazards, DOI 10.1007/978-981-10-4379-6_7
141
142
7 Comprehensive Evaluation of Liquefaction Damage …
light seismic damage? These are largely because every required function of the
building structure is affected by its destruction; other engineered structures have
similar problems. Technically, current seismic design cannot determine the nonlinear dynamic behavior of structures well during strong earthquakes. It is also
unclear regarding the mechanism of the influence of nonlinear properties on
structural function. Therefore, the single seismic performance design standard
based solely on security of human life obviously cannot satisfy structural seismic
performance demands of society. Seismic design should also ensure that the
function of engineering structures is somewhat protected during strong earthquakes.
In other words, seismic resistance design must be sufficiently economical and
credible to assure that the structure function can survive an earthquake.
In light of the above understanding, the new seismic resistance concept of
performance-based seismic design (PBSD) philosophy was proposed by American
scientists and engineers in the early 1990s. This chapter mainly addresses liquefaction damage evaluation of engineering structures based on PBSD criteria.
In the research field of seismic liquefaction, it is widely accepted that
geotechnical materials and seismic ground motions have enormous variability.
Moreover, the interaction of stochasticity and nonlinearity make the responses of
geotechnical engineering structures random. Therefore, it is necessary to investigate
the seismic liquefaction performance of geotechnical projects from the stochastic
point of view. For this reason, this chapter addresses seismic liquefaction performance problems in the geotechnical engineering field with the PBSD criteria and
reliability analysis. To treat the stochastic seismic response of engineered structures,
a newly developed stochastic dynamic response analysis method, the probability
density evaluation method (PDEM) (Li and Chen 2009), is introduced to investigate
stochastic seismic liquefaction performance and dynamic reliability in geotechnical
engineering.
On the whole, this chapter mainly addresses a seismic liquefaction performance
evaluation of geotechnical engineering at a soft soil site.
7.2
Comprehensive Evaluation Methods of Seismic
Liquefaction Performance
In the liquefaction performance evaluation, common methods include in situ
measurements and indoor testing. Among the former measurements are the standard
penetration (SPT), static cone penetration (CPT), and wave velocity tests. The
indoor testing includes the dynamic triaxial test, which has recently been introduced
in the field of liquefaction potential evaluation. Nevertheless, Seed’s simplified
method is the most widely used measure in indoor testing and stress analysis of
liquefaction potential. In the complicated engineering field, multiple evaluation
methods are used for that evaluation.
7.2 Comprehensive Evaluation Methods of Seismic Liquefaction Performance
7.2.1
143
Field Tests
Field test methods of the mechanical properties of soils include the SPT, CPT, and
wave velocity test.
According to the Chinese code (Code for Engineering Geological Investigation
of Water Resources and Hydropower GB50487-2008), it is unnecessary to consider
the liquefaction of field soil, or the soil does not liquefy when saturated sand or silt
meet one of the following conditions.
(i) The geologic age of saturated sand is the late Pleistocene (Q3) period or
before.
(ii) When the grain content of soil particle size >5 mm is 70%, it will not
liquefy. If this content is <70% and there is no other full discriminant
method, one may evaluate liquefaction performance according to soil particle
size <5 mm.
(iii) When the grain content of soil particle size <5 mm is >30%, among which if
the content of soil particle size <0.005 mm corresponding to seismic fortification intensities VII, VIII and IX is not >16, 18 and 20%, respectively,
liquefaction cannot be determined.
(iv) After operation of the project, unsaturated soil above the groundwater level
will not liquefy.
(v) When the ground soil layer shear wave velocity is not greater than the upper
limit shear wave velocity, the ground soil will not liquefy.
(1) SPT test
SPT technology was a 1950s development, and it is convenient and widely used in
the United States and Japan. In China, it was implemented in the Huaihe River
recovery project by the Nanjing Hydraulic Research Institute in the 1950s, and
considerable experience has been accumulated. It was popularized in the 1960s. For
liquefaction performance assessment, the SPT test can obtain the following information on liquefiable sites.
(i) Evaluation of the physical conditions of foundation soil (e.g., stratigraphic
section and weak intercalated layer)
(ii) Evaluation of mechanical property parameters of foundation soil (e.g.,
deformation modulus and physical and mechanical parameters)
(iii) Calculation of the bearing capacity of natural foundations
(iv) Calculation of the ultimate bearing capacity of a single pile and selection of
the bearing layer of pile tips
(v) Assessment of the liquefaction potential and grade of sandy and silty soils in
the field
(2) CPT test
CPT test technology originated in Sweden in 1917. Recently, this measuring and
testing technique has been listed as a state technological criterion in most design
7 Comprehensive Evaluation of Liquefaction Damage …
144
codes, and it is widely used worldwide. The CPT test is mainly suitable for conditions of cohesive soil, silt soil, and sandy soil with moderate density. For liquefaction performance evaluation, the CPT can obtain the following information of
engineering fields.
(i)
(ii)
(iii)
(iv)
Classification of soil layers
Evaluation of the bearing capacity of foundation soil
Estimation of the physical and mechanical parameters of foundation soil
Selection of bearing strata of piles, estimation of bearing capacity of a single
pile, and determination of the possibility of pile sinking
(v) Evaluation of the liquefaction potential of engineering sites
(3) Wave velocity test
The wave velocity test is an in situ test method for determining the physical and
mechanical properties of soil and engineering indexes in light of the wave test,
which can indirectly determine the dynamic modulus and other parameters of rock
and soil mass under small strain according to the velocity of elastic waves in rock
and soil mass. The propagation velocity of a wave is an engineering character of
foundation soil under dynamic load, and is the main seismic parameter of engineering structures. For liquefaction performance evaluation, the wave velocity test
can attain the following engineering field information.
(i) Classification of site category and calculation of the fundamental period at an
engineering site
(ii) Provision of the dynamic parameters of foundation soil for seismic response
analysis (e.g., dynamic shear modulus, damping ratio, and dynamic shear
stiffness)
(iii) Provision of the dynamic parameters of foundation soil for dynamic machine
foundation design (e.g., parameters of compression, shear, anti-torque,
damping and stiffness)
(iv) Determination of the liquefaction performance of foundation soil
(v) Classification of soil category and evaluation of the reinforcement effect of
the foundation soil.
As all the field test methods are described in detail in Chap. 3, this content will
not be presented in this chapter.
7.2.2
Laboratory Dynamic Test
The dynamic triaxial test is the most common means for saturated sand soil seismic
liquefaction evaluation in the laboratory. It can determine cyclic liquefaction
resistance curves and time-history curves of stress, strain, and vibration pore water
pressure.
7.2 Comprehensive Evaluation Methods of Seismic Liquefaction Performance
145
Under earthquake action, periodic change shear stress appears in soil layers, i.e.,
earthquake shear stress. In sand or silt layers, the soil mass will undergo liquefaction failure when the seismic shear stress exceeds the con-liquefaction shear
stress of the sand or silt soil. The seismic shear stress can be represented as the
equivalent average shear stress during the earthquake. Thus, the liquefaction
potential of the soil layers can be distinguished by the Seed–Idriss simplified
method based on the laboratory dynamic test.
The liquefaction evaluation method uses the comparison between the seismic
site shear stress and con-liquefaction shear stress as tested in a laboratory. During
an earthquake, the saturated sand or silt loses shear strength and the foundation
loses bearing capacity, resulting in saturated sand liquefaction. Comparison
between shear stress of the dynamic triaxial test and equivalent average shear stress
may be used for the evaluation of sand liquefaction potential. This method is
rigorous in theory and has several parameters with definite physical meaning.
Moreover, it has become the most common method for saturated sand in North
America and many countries.
The equivalent average shear stress and liquefaction shear stress equations are
respectively
P
ci h i
sc ¼ 0:65dz
amax
ð7:1Þ
g
rd
sd ¼ C r
r0 ;
ð7:2Þ
2rc Nf m
in which sc is the equivalent average shear stress; sd is the critical liquefaction
shear stress; dz is the correction coefficient of seismic shear stress with dz ¼
1 0:0133z; ci and hi are the saturated bulk density and thickness
of the ith soil
layer; amax is the maximum horizon earthquake acceleration;
rd
2rc N
f
is the lique-
faction shear stress ratio of the soil layer as determined by the dynamic triaxial test;
Cr is a correction factor of the soil layer liquefaction shear stress; r0m is the effective
stress of overlying soil layer.
The saturated sand soil may be classified as liquefaction soil when it satisfies the
following condition:
sc [ sd
ð7:3Þ
Seed’s simplified method is an experimental analysis method for liquefaction
evaluation of saturated sand soil. This method uses existing seismic liquefaction
data. It considers the influence of earthquake magnitude in saturated sand liquefaction evaluation, but does not take into account the effect of seismic intensity on
that liquefaction. Therefore, the method only works for a certain earthquake
magnitude.
7 Comprehensive Evaluation of Liquefaction Damage …
146
7.2.3
Dynamic Centrifuge Model Test
According to a previous chapter’s description of the dynamic centrifuge model test,
this test is known to be the most advanced physical means to reflect seismic
liquefaction performance in geotechnical engineering. The geotechnical centrifuge
can produce the same self-weight stress as prototypes in model soil by increasing
the weight through high-speed rotation. The deformation and failure mechanism in
the models are similar to the prototypes, and they can directly simulate complicated
geotechnical problems. Therefore, we can evaluate seismic liquefaction performance for geotechnical problems using the dynamic centrifuge model test. As
details of the dynamic centrifuge model are included in Chap. 5, they are not
repeated here.
7.2.4
Security Evaluation of Seismic Liquefaction Based
on the PBSD Criteria
(1) PBSD concept
Structural seismic design based on the PBSD concept holds that structural performance is determined based on the importance and function of an engineered
structure, and earthquake fortification levels are selected according to structural
performance. This ensures that designed structures have the intended function
during future earthquakes.
The purpose of the traditional theory of seismic design is to ensure human safety
in seismic design code, as is the case in China and almost every other country in the
world. Performance-based criteria represent a new seismic design concept, and
were put forward by American scholars in the 1990s (Priestley 2000). The concept
spread widely worldwide, and its completely different traditional seismic design is
based on the seismic design code. In light of the PBSD, the appropriate structural
system, engineering material, and design methods are chosen according to the
engineering function and objective performance for the owners and users in engineering seismic design. Although traditional seismic design principles of
“three-standard” and “two-phase” include partial performance design concepts, it is
very difficult for their operation and implementation in actual engineering seismic
design, and they still do not form a complete PBSD system. The basic concept of
PBSD is such that designed engineering structures satisfy various predetermined
performance objectives during the application period. Specific performance
requirements can be determined by the importance of engineering structures and
proprietor requirements. In 1992, the PBSD concept was applied in the field of
building structure reinforcement by the Applied Technology Council (ATC-33). In
1995, the Structural Engineers Association of California completed the
7.2 Comprehensive Evaluation Methods of Seismic Liquefaction Performance
147
development of Vision 2000, which was entrusted by the Federal Emergency
Management Agency. Vision 2000 provided details on the concept and implementation framework of PBSD, including the selection and definition of performance levels. PBSD was extended to the design of new buildings. In recent
decades, the PBSD concept has been gradually introduced into Chinese seismic
code. The concept has also been increasingly integrated in the seismic codes of
most countries.
(2) Deterministic evaluation from PBSD perspective
Performance is essential to the response of structures, components, and systems to
outside disturbance. In the earthquake engineering field, seismic performance
means the reaction of structures and components under earthquake loading. For
instance, acceleration, velocity, displacement and shear forces can be defined as
seismic performance. Currently, the general view is that seismic design theory
based on PBSD mainly includes the following content, which forms the basic
framework of PBSD theory.
(a)
(b)
(c)
(d)
(e)
(f )
(g)
Determination of earthquake protection levels
Division of performance levels of engineering structures
Selection of appropriate performance objectives
Determination of seismic performance criteria
Study of seismic performance analysis methods
Study of seismic design methods
Formulation of the seismic design code in light of PBSD
For seismic liquefaction performance in geotechnical engineering, performance
objectives are determined according to requirements of the owners, and earthquake
protection and performance levels are determined by seismic design codes.
(3) Reliability evaluation in light of PBSD
Reliability evaluation of the PBSD method is still based on deterministic PBSD
philosophy. According to the above deterministic evaluation of PBSD criteria,
random seismic response analysis and dynamic reliability evaluation are based on
the recently developed PDEM (Li and Chen 2008; Chen and Li 2007, 2009, 2010).
This is according to objective physical laws, and transforms random dynamic
seismic analysis into a series of deterministic analyses based on dynamic time
history analysis. For stochastic analysis, the performance index is the same as in
deterministic analysis, and dynamic reliability of the performance objective is used
for safety evaluation of the engineered structures. Generally, seismic displacement
of the structures is selected for the performance index.
(a) PDEM and dynamic reliability
Generally, the dynamic balance equation of soil slope under earthquake action can
be expressed as
148
7 Comprehensive Evaluation of Liquefaction Damage …
€ þ CX_ þ f ðXÞ ¼ MI€xg ðH; tÞ;
MX
_ 0 Þ ¼ x_ 0 ;
Xðt
Xðt0 Þ ¼ x0 ;
ð7:4Þ
where M and C are the mass and damp matrices, respectively; f ðXÞ is the nonlinear
€ X_ and X are acceleration, velocity and displacement
restoring force vector; X,
vectors, respectively; I is the unit vector; €xg is the earthquake ground motion
process; H is a random vector. Obviously, only the randomness of seismic ground
motion is considered in this chapter.
The vector is composed by relevant physical quantities, which can be represented by
Z ¼ ðZ1 ; Z2 ; . . .; Zm ÞT
ð7:5Þ
Based on the probability conservation principle, the stochastic system is conservative and composed of ðZðtÞ; HÞ : Therefore, its joint probability pZH ðz; h; tÞ
satisfies the generalized probability density evolution equation:
m
@pZH ðz; h; tÞ X
@p ðz; h; tÞ
þ
¼0
Z_ j ðh; tÞ ZH
@t
@zj
j¼1
ð7:6Þ
The initial condition of Eq. (7.6) is
pZH ðz; h; t0 Þ ¼ pH ðh; tÞdðz z0 Þ;
ð7:7Þ
in which z0 is the initial value of ZðtÞ and dðÞ is the Dirac function. The probability
density function pZ ðz; tÞ of ZðtÞ is given by
Z
pZH ðz; h; tÞdh
ð7:8Þ
pZ ðz; tÞ ¼
XH
Although the PDEM is based on objective laws of physics, it is very challenging
to obtain its exact solution. Therefore, the PDEM Eq. (7.6) may be solved by
numerical methods with detailed steps as follows.
(i) Select representative discretized points hq ðq ¼ 1; 2; . . .; npt Þ in the basic
random variable space H and determine the corresponding given probability
(ii) For the determined hq , solve the dynamic Eq. (7.4) with certain earthquake
excitations and obtain the velocity of seismic response
(iii) Introduce the velocity into the PDEM equation and solve it
(iv) Accumulate the results of q ¼ 1; 2; . . .; npt and obtain the required probability density function (PDF)
Finally, combined with the equivalent extreme event and solution of the PDEM,
the dynamic reliability can be obtained.
7.2 Comprehensive Evaluation Methods of Seismic Liquefaction Performance
149
(b) Stochastic seismic ground motion
Dynamic time history analysis is one of the most widely used dynamic analyses in
current earthquake engineering. The appropriate seismic ground motion input
should be chosen when pursuing this analysis. For stochastic vibration based on the
dynamic time history method, there is a great challenge to obtain sufficient seismic
ground motion samples satisfying the same set of features, which makes it difficult
to carry out strict statistical analysis of seismic response. Therefore, stochastic
seismic ground motion samples are generated by orthogonal expansion and a
random function concept.
According to previous research findings, for earthquake ground motion,
non-stationary characteristics are mainly intensity and frequency. Therefore,
non-stationary stochastic earthquake ground motions are mainly divided into two
categories, i.e., only intensity in non-stationary stochastic seismic models and
intensity and frequency of fully non-stationary ground motion. In this chapter, we
only address the intensity, non-stationary stochastic ground model. Generally,
non-stationary earthquake stochastic processes can be assumed as a mean of zero
real stationary random process times with envelope function, which is introduced to
express the non-stationary intensity (Li and Chen 2009).
Based on the above assumption, the seismic ground motion acceleration process
can be written simply as (Liu et al. 2016)
Ug ðtÞ ¼ AðtÞ UðtÞ;
ð7:9Þ
where UðtÞ is the zero-mean real stationary stochastic process and SU ðxÞ is its
power spectrum density function (PSDF). AðtÞ is a deterministic intensity envelope
function, written as
AðtÞ ¼
ht
t id
exp 1 ;
c
c
ð7:10Þ
where c is the average time instant of the intensity decay of peak ground acceleration (PGA), and d is the shape control parameter of AðtÞ. Here, c = 4 s and d = 1.
We used the Clough and Penzien acceleration power spectrum density:
x4g þ 4n2g x2g x2
x4
S0 ;
SU ðxÞ ¼ x2 x2g þ 4n2g x2g x2 x2 x2f þ 4n2f x2f x2
ð7:11Þ
where in the general soft soil engineering location (e.g., Shanghai), xg ¼ 3prad=s
and ng ¼ 0:9 are the site circle frequency and damping ratio. The secondary filtering frequency parameter and damping ratio (xf ¼ 3prad=s and nf ¼ 0:9,
respectively) are used to simulate the low-frequency energy of earthquake ground
motion (Code for Seismic Design of Buildings 2010).
150
7 Comprehensive Evaluation of Liquefaction Damage …
Hence, the intensity non-stationary evolutionary PSDF of the non-stationary
stochastic ground motion can be expressed as
SUg ðx; tÞ ¼ A2 ðtÞ SU ðxÞ
ð7:12Þ
In Eq. (7.11), the perturbation factor of the bedrock white noise can be calculated according to
S0 ¼
a2max
;
f 2 xe
ð7:13Þ
where amax is the mean PGA of the seismic ground motion. According to
Eq. (7.11), the spectrum area xe ¼ 49:26rad/s is calculated when the perturbation
factor of the bedrock white noise S0 ¼ 1 and the peak factor f ¼ 3:1.
We now examine the validity of the above-proposed stochastic seismic ground
motion and seismic acceleration time history generation method. In the Shanghai
area, the duration of a strong earthquake T = 30 s was selected, based on seismic
design experience in choosing design seismic ground motion parameters at soft soil
sites. This duration is not fully established in the above process of artificially
generated ground motion; it can be altered based on different engineering structures
and seismic zoning requirements. With the same interval time, the number of
sampling points varies for different earthquake durations. This means that too long a
duration of ground motion will increase the calculation time of the dynamic time
history analysis. The intensity of non-stationary seismic ground motion proposed
was selected as an example for demonstration. In the first step, the standard
orthonormal basis function and autocorrelation function expressions were simultaneously used to calculate the autocorrelation matrix, and eigenvalues and corresponding feature vectors were obtained. In the second step, the dispersed typical
sample point set fhn ¼ 0:025n 3:1625; n ¼ 1; 2; ; 987g of the random variable
H in domain [−1,1] was obtained along with the preset probability Pn ðn ¼
1; 2; ; 987Þ of every dispersed representative point hn . According to Eq. (7.11),
certain representative sample point sets of the normal orthogonal random variables
nj ð1; 2; ; NÞ were then obtained. Finally, a series of seismic ground motion time
history acceleration samples with corresponding probabilities were generated.
Typical acceleration samples are shown in Fig. 7.1.
Figure 7.2 shows a comparison of mean and standard deviation between
non-stationary intensity earthquake acceleration samples with a target power density spectrum.
There were 987 seismic acceleration time history samples obtained, and
ensemble-average second-order characteristics (mean and standard deviation) of the
representative samples and targets were virtually identical. This demonstrates the
validity and excellent performance of the orthogonal expansion method used to
generate the intensity of non-stationary seismic ground motion.
7.2 Comprehensive Evaluation Methods of Seismic Liquefaction Performance
151
0.8
0.6
0.4
Acceleration(m/s 2)
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1.2
0
5
10
15
Time(s)
20
25
30
Fig. 7.1 Typical intensity non-stationary earthquake acceleration sample
Combined with the PDEM and construction of equivalent extreme value event,
we determined the seismic dynamic reliability of the engineering structures.
7.3
Case Study
To illustrate the aforementioned comprehensive evaluation methods, this section
describes a numerical example based on PBSD. This case study targets an actual
engineering project, namely an earthen dam. For aseismic problems of earthen and
rockfill dams, a seismic performance evaluation system based on PBSD criteria is
illustrated in Fig. 7.3. Given the PBSD method, the major content of the performance evaluation system has three parts:
(1) Determining the performance objective of earthen and rockfill dams
(2) Performance verification
(3) Performance description
7 Comprehensive Evaluation of Liquefaction Damage …
152
Mean(m/s2)
0.5
Samples
Target
0.25
0
-0.25
-0.5
0
5
10
15
20
25
30
Time(s)
2
Std.D(m/s )
0.8
Samples
Target
0.6
0.4
0.2
0
0
5
10
15
20
25
30
Time(s)
Fig. 7.2 Characteristics of typical non-stationary seismic accelerations for sample ensembles and
targets
According to the performance evaluation system, various components of concrete seismic safety assessment for existing dams were reported in the previous
research (Wieland and Brenner 2008). The PBSD criteria were used for the security
evaluation of seismic liquefaction in this chapter.
Based on the seismic liquefaction performance evaluation methods, this section
introduces real applications combined with actual engineering.
In this section, we discuss the security evaluation of seismic liquefaction for an
actual engineering project (earthen dam), both certain and uncertain. The structure
is a zoned earthen dam in Chongming County, Shanghai, eastern China. According
to the Earthquake Ground Motion Parameter Zonation Map of China (GB183062001) and Code for Seismic Design of Buildings (GB50011-2010), classification of
the design earthquake is the first group. This has a seismic fortification intensity of
7-degree, a site characteristic period of 0.9 s, and the peak ground acceleration with
exceedance probability 10% in 50 years is 0.1 g in the earthen dam engineering
field. The main cross section of the dam is illustrated in Fig. 7.4.
7.3 Case Study
153
Determining the performance
objective of earth and rockfill dam
The basic performance of structures
Security, reparability, applicability
Performance evaluation items
Limit state
Ground motion and loads
Determining the limit state
Determining ground motion
performance
by each performance
and loads by each
levels
evaluation item of earth
performance evaluation item
and rockfill dam
of earth and rockfill dam
Performance verification
Assessment principles for performance:
Response value should not be higher than limit value
<Performance evaluation criteria>
Probability
Res ≤ Lim
Res: response value
Lim: limit value
Res
Lim
Value
(i) Ground motion and loads;
(ii) Determining the engineering quantity
of response value and limit value;
(iii) Analyzing the response value;
(iv) Speculating the limit value;
(v) Comparing the response value with
limit value.
Performance description
Principle: describing the performance of the earth and rockfill dam according to
the each performance assessment item. For example, the earth and rockfill dam
doesn't appear the phenomenon of water storage overflow and dam break, and the
dam keeps the function of float downstream.
Fig. 7.3 Performance evaluation system of earthen and rockfill dam
7 Comprehensive Evaluation of Liquefaction Damage …
154
Backfill
Free water surface
drain
Drainage boundary
1.00m
Water
Non-liquefiable part
5.50m
Silty sand 8.20m
Sandy silty 8.40m
Drainage wall
Silty clay 11.40m
Clay
9.00m
Silty clay 11.00m
Silty sand 6.00m
Fig. 7.4 Main cross section of earthen dam (reprinted from Huang and Xiong (2016) with
permission from John Wiley and Sons)
(1) Security evaluation of earthen dam seismic liquefaction based on PBSD criteria
with deterministic seismic ground motions
Based on the PBSD concept, the first step is to determine seismic fortification
levels. According to ICOLD Bulletin 72 (1989) and Specifications for Seismic
Design of Hydraulic Structures, the security evaluation of the earthen dam involves
two seismic design levels:
(I) Operation basic earthquake (OBE) with the following criteria
The OBE indicates that an earthquake is likely during the operational period, with a
return period of *145 years. The OBE is not related to dam safety but represents a
serviceability limit state and is basically an economic criterion, which is of major
interest to the dam owner. The performance requirement of the earthen dam is no
structural damage or only light earthquake damage, and if the dam meets the
requirement, it can continue normal operation. According to the performance
objective of Chinese design earthquakes, earthquake damage to the dam can be
repaired and water retention and storage are not limited.
The acceleration-time history of the OBE for the earthen dam is shown in
Fig. 7.5, according to Chinese seismic code (GB50011-2010) and field seismic risk
analysis. Based on PBSD, performance of the earthen dam during OBE loading is
quantified as dam crest permanent settlement. Hynes-Griffin and Franklin (1984)
7.3 Case Study
155
0.1
0.08
0.06
Acceleration(g)
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
0
5
10
15
Time(s)
Fig. 7.5 The acceleration-time history corresponding to the OBE
indicated that earthen dams did not sustain damage (with respect to water tightness)
when this settlement was <1% of the maximum embankment height. This value can
be used as a plausible limit threshold to assess dam performance. Since 2004,
seismic evaluation standards have been implemented coercively in Switzerland,
where the allowable permanent deformation is 20 cm for shallow sliding and 50 cm
for deep sliding. In China, Shen et al. (1984) proposed a seismic permanent
deformation of 2% of the maximum height for 100-meter-tall earthen dams in the
8th Five-Year Plan. For seismic performance evaluation of the targeted earthen
dam, an allowable dam crest permanent settlement of 35 cm was chosen.
Seismic response of the earthen dam under the OBE was analyzed by FEM
software FLIP (Iai and Ichii 2010; Iai et al. 1990; Huang et al. 2015). The vertical
displacement time history of the dam crest is shown in Fig. 7.6. The maximum
seismic permanent settlement was 0.1730 m, less than the allowable limit dam crest
permanent settlement. Therefore, the dam satisfied the seismic performance target
of the OBE.
7 Comprehensive Evaluation of Liquefaction Damage …
156
0.02
0
-0.02
Displacement(m)
-0.04
-0.06
-0.08
-0.1
-0.12
-0.14
-0.16
-0.18
0
5
10
15
Time(s)
20
25
30
Fig. 7.6 Vertical displacement time history of dam crest under OBE
(II) Safety evaluation earthquake (SEE) with the following criteria
The SEE is relevant to dam safety. It represents a limit state of ultimate load; its
return period is not specified, but is typically 10,000 years. As an earthen dam, its
main function is water storage, with performance measured by water tightness.
Earthen and rockfill dams are completely different from concrete dams; they cannot
withstand current scour, but can bear hydrostatic pressure. When reservoir water
overtops the dam crest, it damages that crest. This reduces the crest height, which
causes more water to erode the newly formed crest, finally causing a dam break.
Therefore, the limit state of the earthen dam is overtopping, and thus such dams do
not have a limit state under SEE earthquake loading.
In this chapter, the SEE was selected for earthquake ground motion with 2–3%
transcendental probability over 50 years, according to the Chinese seismic
(Standard 2001) and field seismic risk analysis, that is, the SEE seismic intensity is
increased by one degree based on the design ground motion. The acceleration time
history of the SEE is shown in Fig. 7.7. According to the aforementioned performance objective of the earthen dam under the SEE, its quantitative description is
such that the dam does not have the limit state of overtopping. For that dam, the
7.3 Case Study
157
0.15
0.1
Acceleration(g)
0.05
0
-0.05
-0.1
-0.15
-0.2
0
5
10
15
Time(s)
Fig. 7.7 Acceleration time history corresponding to SEE
Table 7.1 Seismic security
grade classification of SEE
Safety margin
Security grade
>75%
75 * 50%
50 * 25%
<25%
Safe
Comparative safe
Comparative dangerous
Dangerous
allowable dam crest permanent settlement is *1 m, which is the height difference
between the crest and normal pool level. The safety margin is defined in Eq. (7.14)
for the safety evaluation, and security is classified into five grades (Table 7.1)
according to the safety margin.
Fs ¼
1x
100%;
x
in which x is the dam crest permanent settlement under the SEE.
ð7:14Þ
7 Comprehensive Evaluation of Liquefaction Damage …
158
0.05
0
-0.05
Displacement(m)
-0.1
-0.15
-0.2
-0.25
-0.3
-0.35
-0.4
0
5
10
15
Time(s)
20
25
30
Fig. 7.8 The vertical displacement-time history of the dam crest under the SEE
Seismic response of the earthen dam under the SEE was analyzed using the FLIP
software. The vertical displacement time history of the dam crest is shown in
Fig. 7.8. Maximum permanent settlement was 0.3997 m, less than the allowable
limit dam crest permanent settlement. Therefore, the dam satisfied the seismic
performance of the SEE. Moreover, according to the security grade classification of
the SEE, the dam is comparatively safe.
(2) Security evaluation of earthen dam seismic liquefaction based on PBSD and
reliability criteria
It is well known that earthquake ground motions have remarkable randomness, and
thus it is necessary to investigate the seismic performance of earthen and rockfill
dams from a stochastic perspective. Therefore, this section reports on a new attempt
to assess such performance based on PBSD and reliability criteria. The seismic
response analysis is based on the following two earthquake types.
7.3 Case Study
159
0.8
0.6
0.4
Acceleration(m/s 2)
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1.2
0
5
10
15
Time(s)
20
25
30
Fig. 7.9 Typical sample curve of OBE seismic ground motion
(I) OBE with the following criteria
The seismic performance of the earthen dam under the OBE is the same as
described above, and OBE ground motion is generated by the stochastic function
method (Liu and Zeng 2014). The stochastic seismic ground motion is composed of
a series of acceleration time histories with numerous assigned probabilities. There
were 987 samples of acceleration time history in the stochastic seismic ground
motion set. Figure 7.9 shows a typical sample curve of the sample set.
The series of deterministic seismic responses were obtained using the FLIP
software, with acceleration-time history sample inputs of stochastic seismic ground
motion. The stochastic seismic responses were obtained by introducing deterministic seismic responses such as velocity into Eq. (7.6). The probability density
evolution surface of the vertical displacement history is shown in Fig. 7.10.
7 Comprehensive Evaluation of Liquefaction Damage …
160
60
50
PDF
40
30
20
10
0
-10
0.1
6.5
6.4
0.05
S et
tlem
en t
( m)
6.3
6.2
0
6.1
6
s)
Tim e(
Fig. 7.10 Probability density evolution surface for settlement of earthen dam under OBE
It demonstrates that the PDF of settlement evolved with time and the settlement had
remarkable variability. The probability density evolution surface also shows that it
is necessary to analyze seismic response of the earthen dam.
Combined with the PDEM and equivalent extreme event, the cumulative distribution function (CDF) of permanent settlement is illustrated in Fig. 7.11.
According to the allowable limit permanent settlement of the OBE, the reliability of
the earthen dam is 0.9827. This clearly shows that the dam satisfies the seismic
performance for the OBE.
(II) SEE with following criteria
The stochastic seismic ground motion of the SEE was also generated by the
stochastic function. There were 987 acceleration time history samples in the
stochastic ground motion set of the SEE. A typical acceleration time history sample
curve is shown in Fig. 7.12.
7.3 Case Study
161
1
0.9
0.8
0.7
CDF
0.6
0.5
0.4
0.3
0.2
0.1
0
0.1
0.15
0.2
0.25
0.3
0.35
Settlement(m)
Fig. 7.11 CDF for permanent settlement of earthen dam under OBE (reprinted from Huang and
Xiong (2016) with permission from John Wiley and Sons)
As above, deterministic responses were obtained by the FEM, and we let the
seismic motion be introduced in the PDEM equation as the velocity. By solving the
PDEM equation, the stochastic seismic response of the earthen dam under the SEE
was determined. The probability density function evolution surface is illustrated in
Fig. 7.13. It also shows the variability of seismic response of the dam under the
SEE. By constructing the equivalent extreme event with maximum permanent
settlement, the CDF is shown in Fig. 7.14. Thus, the reliability of the earthen dam
was determined. The reliability is 1.0 when the threshold of permanent settlement is
1 m, which is the height difference between the dam crest and normal pool level.
Therefore, per the safety grade, the dam is safe under the SEE.
7 Comprehensive Evaluation of Liquefaction Damage …
162
3
Acceleration(m/s 2)
2
1
0
-1
-2
-3
0
5
10
15
Time(s)
20
25
30
Fig. 7.12 The typical sample curve of the seismic ground motion of the SEE
7.4
Summary
This chapter described a comprehensive evaluation of liquefaction damage during
earthquakes. It comprised two parts: a liquefaction potential evaluation and a liquefaction damage evaluation.
(1) The first part addressed the liquefaction potential evaluation by the comprehensive method, and mainly introduced the field tests, laboratory dynamic test,
dynamic centrifuge model test, and PBSD evaluation.
(2) The second part treated the evaluation of liquefaction damage, taking an actual
earthen dam as an example. For security evaluation of that dam under earthquake loading, the PBSD concept was introduced. Based on that concept,
seismic performance of the dam engineering was assessed: earth dam; and
7.4 Summary
163
25
20
PDF
15
10
5
0
0.2
6.5
0.15
Set
6.4
6.3
0.1
tlem
6.2
ent
0.05
(m)
0
6.1
6
s)
Tim e(
Fig. 7.13 The probability density evolution surface of the settlement of the earth dam under the
SEE
seismic performance of the dam under two design earthquake levels (OBE and
SEE) was determined. The stochastic dynamic method was also presented, and
seismic evaluation of the earthen dam was analyzed by PBSD and reliability
methods.
(3) In geotechnical problems, because of intrinsic and very complicated variabilities of rock and soil material properties, earthquake ground motion appears
random. Therefore, it is necessary to analyze these problems based on
stochastic criteria. The stochastic seismic response and reliability analyses may
be regarded as a new approach to earthquake liquefaction damage evaluation.
7 Comprehensive Evaluation of Liquefaction Damage …
164
1
0.9
0.8
0.7
CDF
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Settlement(m)
Fig. 7.14 CDF of permanent settlement of earthen dam under SEE (reprinted from Huang and
Xiong (2016) with permission from John Wiley and Sons)
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