Table Of ContentZijun Cao · Yu Wang
Dianqing Li
Probabilistic
Approaches for
Geotechnical Site
Characterization and
Slope Stability Analysis
Probabilistic Approaches for Geotechnical Site
Characterization and Slope Stability Analysis
Zijun Cao Yu Wang Dianqing Li
(cid:129) (cid:129)
Probabilistic Approaches
for Geotechnical Site
Characterization and Slope
Stability Analysis
123
Zijun Cao DianqingLi
State Key Laboratoryof Water Resources State Key Laboratoryof Water Resources
andHydropowerEngineering Science andHydropowerEngineering Science
WuhanUniversity WuhanUniversity
Wuhan, Hubei Wuhan, Hubei
China China
YuWang
City University of HongKong
Hong Kong
China
Jointlypublished with Zhejiang University Press
ISBN978-3-662-52912-6 ISBN978-3-662-52914-0 (eBook)
DOI 10.1007/978-3-662-52914-0
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Preface
In the last few decades, reliability-based design (RBD) approaches/codes and
probabilistic analysis methods, such as probabilistic slope stability analysis with
MonteCarlosimulation(MCS),havebeendevelopedforgeotechnicalstructuresto
deal rationally with various uncertainties (e.g., inherent spatial variability of soils
and uncertainties arising during geotechnical site characterization) in geotechnical
engineering. Applications of the RBD approaches/codes and probabilistic analysis
methods in turn call for the needs of probabilistic site characterization, which
describes probabilistically soil properties and underground stratigraphy based on
both prior knowledge (i.e., site information available prior to the project) and
project-specific test results. How to combine systematically prior knowledge and
project-specifictestresultsinaprobabilisticmanner,however,isachallengingtask.
This problem is further complicated by the inherent spatial variability of soils,
uncertainties arising during site characterization and the fact that geotechnical site
characterization generally only provides a limited number of project-specific test
data.
This book focuses on probabilistic characterization of uncertainties in geotech-
nicalpropertiesandtheirpropagationinslopestabilityanalysisusingMCS.Several
probabilistic approaches are developed and presented in this book for probabilistic
site characterization and reliability analysis of slope stability. These approaches
effectively tackle the following unresolved issues in geotechnical risk and relia-
bility,whichhampertheapplicationsofprobabilisticanalysisanddesignapproach
in geotechnical practice:
1. How to determine project-specific statistics and probability distributions of
geotechnicalpropertiesbasedonbothpriorknowledgeandalimitednumberof
project-specific test data obtained during geotechnical site characterization?
(Chaps. 3–6)
2. Howtoexpressengineeringjudgmentsinaquantitativeandtransparentmanner
during geotechnical site characterization? (Chap. 4)
v
vi Preface
3. How to delineate underground stratigraphy (including number and boundaries
ofsoillayers)probabilistically usingalimited numberofsiteobservationdata?
(Chap. 6)
4. How to efficiently incorporate various geotechnical-related uncertainties (e.g.,
uncertainties in geotechnical properties) into slope stability analysis using
MCS? (Chap. 7)
5. Howtoshedlightontherelativecontributionsofvariousuncertaintiestoslope
failure probability based on MCS? (Chap. 8)
6. How to make MCS-based probabilistic analysis approach of slope stability
accessible to geotechnical practitioners who are usually unfamiliar with prob-
ability theory and statistics? (Chaps. 7 and 8)
As far as the authors are aware, this is the first book to revisit geotechnical site
characterization from a probabilistic point of view and provide rational tools to
probabilistically characterize geotechnical properties and underground stratigraphy
using limited information obtained from a specific site. This book also develops
efficient MCS approaches for slope stability analysis and implements these
approaches in a commonly available spreadsheet environment by a package of
worksheets and functions/add-in in Excel. These approaches and the software
packagesarereadilyavailabletogeotechnicalpractitionersandalleviatethemfrom
reliability computational algorithms. The authors gratefully acknowledge the
financial support by the National Science Fund for Distinguished Young Scholars
(ProjectNo.51225903),theNationalNaturalScienceFoundationofChina(Project
Nos. 51329901, 51409196, 51579190, 51528901), the National Program on Key
Research Project (2016YFC0800208), and the Natural Science Foundation of
Hubei Province of China (Project No. 2014CFA001).
Theauthorswouldliketoexpressmyheartfeltgratitudetowardmanycolleagues
who give invaluable advice and insightful comments on this book. We would also
thankMissShuoZhengforherassistanceinwordprocessingofthemanuscriptand
Mr.FupingZhang,Mr.JianHe,Mr.XinLiu,andMs.MiTianfortheirhelponthe
proofread of the manuscript. Last but not least, the authors’ deep gratitude goes to
theirfamiliesfortheirlovingconsiderationandcontinuoussupporttoencourageus
to finish this book.
Wuhan, China Zijun Cao
Hong Kong, China Yu Wang
Wuhan, China Dianqing Li
March 2016
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Uncertainties in Soil Properties . . . . . . . . . . . . . . . . . . 1
1.1.2 Probabilistic Analysis of Geotechnical Structures. . . . . . 1
1.1.3 Reliability-Based Design of Geotechnical Structures. . . . 2
1.1.4 Geotechnical Site Characterization. . . . . . . . . . . . . . . . 3
1.2 Objectives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Uncertainty Propagation During Geotechnical Site
Characterization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 Bayesian Framework for Geotechnical Site
Characterization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.3 Prior Knowledge and Prior Distribution . . . . . . . . . . . . 5
1.2.4 Probabilistic Site Characterization Using Limited
Site Observation Data. . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.5 Probabilistic Site Characterization Using a Large
Number of Site Observation Data . . . . . . . . . . . . . . . . 6
1.2.6 Probabilistic Slope Stability Analysis Using Subset
Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.7 Probabilistic Failure Analysis of Slope Stability. . . . . . . 7
1.3 Layout of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Geotechnical Site Characterization. . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 Desk Study and Site Reconnaissance . . . . . . . . . . . . . . 11
2.1.2 In Situ Investigation. . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.3 Laboratory Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.4 Interpretation of Observation Data and Inferring
the Site Subsurface Conditions . . . . . . . . . . . . . . . . . . 15
2.1.5 Challenges in Geotechnical Site Characterization. . . . . . 16
vii
viii Contents
2.2 Uncertainties in Soil Properties . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 Inherent Variability . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.2 Measurement Errors. . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.3 Statistical Uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.4 Transformation Uncertainties. . . . . . . . . . . . . . . . . . . . 24
2.2.5 Uncertainty Propagation . . . . . . . . . . . . . . . . . . . . . . . 26
2.3 Bayesian Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.1 Bayesian Mathematical Framework . . . . . . . . . . . . . . . 27
2.3.2 Prior Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.3 Likelihood Function. . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3.4 Posterior Distribution. . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3.5 Updating the Probability of an Event . . . . . . . . . . . . . . 33
2.4 National Geotechnical Experimentation Site (NGES) at Texas
A&M University. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.5 Probabilistic Slope Stability Analysis. . . . . . . . . . . . . . . . . . . . 37
2.5.1 First-Order Second-Moment Method (FOSM) . . . . . . . . 38
2.5.2 First-Order Reliability Method (FORM) . . . . . . . . . . . . 38
2.5.3 Direct Monte Carlo Simulation (Direct MCS) . . . . . . . . 39
2.5.4 Subset Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Appendix 2.1: Several Empirical Correlations Reported by Kulhawy
and Mayne (1990). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3 Bayesian Framework for Geotechnical Site Characterization. . . . . . 53
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2 Uncertainty Propagation During Geotechnical Site
Characterization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3 Uncertainty Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3.1 Inherent Spatial Variability . . . . . . . . . . . . . . . . . . . . . 55
3.3.2 Transformation Uncertainty. . . . . . . . . . . . . . . . . . . . . 56
3.4 Bayesian Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.5 Probability Distribution of the Design Soil Property. . . . . . . . . . 58
3.6 The Most Probable Number of Soil Layers. . . . . . . . . . . . . . . . 58
3.6.1 Bayesian Model Class Selection Method. . . . . . . . . . . . 58
3.6.2 Calculation of the Evidence. . . . . . . . . . . . . . . . . . . . . 59
3.6.3 Calculation of Prior Probability. . . . . . . . . . . . . . . . . . 59
3.6.4 Calculation of Probability Density Function
of Site Observation Data. . . . . . . . . . . . . . . . . . . . . . . 60
3.7 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4 Quantification of Prior Knowledge Through Subjective
Probability Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Uncertainties in Prior Knowledge. . . . . . . . . . . . . . . . . . . . . . . 64
Contents ix
4.3 Subjective Probability Assessment Framework (SPAF). . . . . . . . 64
4.4 Specification of Assessment Objectives. . . . . . . . . . . . . . . . . . . 66
4.5 Collection of Relevant Information and Preliminary
Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.6 Synthesis of the Evidence. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.6.1 Evaluation of the Strength of Evidence. . . . . . . . . . . . . 69
4.6.2 Evaluation of the Weight of Evidence . . . . . . . . . . . . . 70
4.6.3 Assembling the Evidence and Statistical Analysis . . . . . 71
4.6.4 Reassembling the Relevant Evidence for Each
Sub-objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.7 Numerical Assignment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.7.1 Equivalent Lottery Method . . . . . . . . . . . . . . . . . . . . . 72
4.7.2 Verbal Descriptors of the Likelihood . . . . . . . . . . . . . . 74
4.7.3 Implementation of the Equivalent Lottery Method . . . . . 75
4.7.4 Prior Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.8 Confirmation of Assessment Outcomes. . . . . . . . . . . . . . . . . . . 76
4.9 Scenario I: Uninformative Prior Knowledge . . . . . . . . . . . . . . . 77
4.9.1 Assessment Objectives. . . . . . . . . . . . . . . . . . . . . . . . 77
4.9.2 Relevant Information and Prior Uncertain Estimates. . . . 78
4.9.3 Strength and Weight of the Evidence
and Statistical Analysis. . . . . . . . . . . . . . . . . . . . . . . . 78
4.9.4 Results of Subjective Probability Assessment . . . . . . . . 80
4.9.5 Final Confirmation. . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.10 Scenario II: Informative Prior Knowledge. . . . . . . . . . . . . . . . . 84
4.10.1 Assessment Objectives. . . . . . . . . . . . . . . . . . . . . . . . 84
4.10.2 Relevant Information and Prior Uncertain Estimates. . . . 84
4.10.3 Strength and Weight of the Evidence and Statistical
Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.10.4 Results of Subjective Probability Assessment . . . . . . . . 89
4.10.5 Final Confirmation. . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.11 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Appendix 4.1: Questionnaire for Implementing the Equivalent
Lottery Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Questionnaire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5 Probabilistic Characterization of Young’s Modulus of Soils
Using Standard Penetration Tests. . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.2 Uncertainty Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.2.1 Inherent Variability . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.2.2 Transformation Uncertainty. . . . . . . . . . . . . . . . . . . . . 98
5.3 Bayesian Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
x Contents
5.4 Probability Density Function of Undrained Young’s
Modulus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.5 Markov Chain Monte Carlo Simulation and Equivalent
Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.5.1 Metropolis–Hastings (MH) Algorithm. . . . . . . . . . . . . . 102
5.5.2 Equivalent Samples . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.6 Implementation Procedures. . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.7 Illustrative Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.7.1 Equivalent Samples . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.7.2 Probability Distribution of Undrained Young’s
Modulus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.7.3 Estimates of the Mean, Standard Deviation, and
Characteristic Value. . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.8 Sensitivity Study on Project-Specific Test Data . . . . . . . . . . . . . 111
5.8.1 Effect of Data Quantity on the Mean of ln(Eu). . . . . . . . 113
5.8.2 Effect of Data Quantity on the Standard Deviation
of ln(Eu). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.9 Sensitivity Study on Prior Knowledge . . . . . . . . . . . . . . . . . . . 115
5.9.1 Effect of the Ranges of Uniform Prior Distributions. . . . 117
5.9.2 Effect of Different Types of Prior Distributions . . . . . . . 119
5.10 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6 Probabilistic Site Characterization Using Cone Penetration
Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.2 Random Field Modeling of Inherent Spatial Variability . . . . . . . 124
6.3 Regression Between Cone Tip Resistance and Effective
Friction Angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.4 Bayesian System Identification . . . . . . . . . . . . . . . . . . . . . . . . 127
6.5 Posterior Knowledge and Boundaries of Statistically
Homogenous Layers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.5.1 Posterior Knowledge on Model Parameters. . . . . . . . . . 129
6.5.2 The Most Probable Thicknesses and Boundaries
of Statistically Homogenous Layers . . . . . . . . . . . . . . . 130
6.6 The Most Probable Number of Layers . . . . . . . . . . . . . . . . . . . 130
6.6.1 Calculation of the Evidence for Each Model Class. . . . . 131
6.7 Implementation Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.8 Illustrative Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.8.1 The Most Probable Number of Sand Layers . . . . . . . . . 135
6.8.2 The Most Probable Thicknesses or Boundaries . . . . . . . 136
6.8.3 The Posterior Knowledge on Model Parameters. . . . . . . 137
6.9 Sensitivity Study on Confidence Level of Prior Knowledge. . . . . 138
6.9.1 Effect on the Most Probable Number
of Sand Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
