## Table of contents for Risk assessment in geotechnical engineering / Gordan A. Fenton , D.V. Griffiths.

Bibliographic record and links to related information available from the Library of Congress catalog

Information from electronic data provided by the publisher. May be incomplete or contain other coding.

PART 1: THEORY.
1. Review of Probability Theory.
1.1 Introduction.
1.2 Basic Set Theory.
1.2.1 Sample Spaces and Events.
1.2.2 Basic Set Theory.
1.2.3 Counting Sample Points.
1.3 Event Probabilities.
1.3.1 Event Probabilities.
1.4 Conditional Probability.
1.4.1 Total Probability.
1.4.2 Bayes' Theorem.
1.4.3 Problem-Solving Methodology.
1.5 Random Variables and Probability Distributions.
1.5.1 Discrete Random Variables.
1.5.2 Continuous Random Variables.
1.6 Measures of Central Tendency, Variability, and Association.
1.6.1 Mean.
1.6.2 Median.
1.6.3 Variance.
1.6.4 Covariance.
1.6.5 Correlation Coefficient.
1.7 Linear Combinations of Random Variables.
1.7.1 Mean of Linear Combinations.
1.7.2 Variance of Linear Combinations.
1.8 Functions of Random Variables.
1.8.1 Functions of a Single Variable.
1.8.2 Functions of Two or More Random Variables.
1.8.2.1 Linear Transformations.
1.8.3 Moments of Functions.
1.8.3.1 Arbitrary Function of One Variable.
1.8.3.2 Arbitrary Function of Several Variables.
1.8.4 The First Order Second Moment (FOSM) Method.
1.9 Common Discrete Probability Distributions.
1.9.1 Bernoulli Trials.
1.9.2 Binomial Distribution.
1.9.3 Geometric Distribution.
1.9.4 Negative Binomial Distribution.
1.9.5 Poisson Distribution.
1.10 Common Continuous Probability Distributions.
1.10.1 Exponential Distribution.
1.10.2 Gamma Distribution.
1.10.3 Uniform Distribution.
1.10.4 Weibull Distribution.
1.10.5 Rayleigh Distribution.
1.10.6 Student t-Distribution.
1.10.7 Chi-Square Distribution.
1.10.8 Normal Distribution.
1.10.8.1 The Central Limit Theorem.
1.10.8.2 Normal Approximation to the Binomial.
1.10.8.3 Multivariate Normal Distribution.
1.10.9 Lognormal Distribution.
1.10.9.1 Bivariate Lognormal Distribution.
1.10.10 Bounded Tanh Distribution.
1.11 Extreme Value Distributions.
1.11.1 Exact Extreme Value Distributions.
1.11.2 Asymptotic Extreme Value Distributions.
1.11.2.1 Type I Asymptotic Form.
1.11.2.2 Type II Asymptotic Form.
1.11.2.3 Type III Asymptotic Form.
1.12 Summary.
2. Discrete Random Processes.
2.1 Introduction.
2.2 Discrete-Time Discrete-State Markov Chains.
2.2.1 Transition Probabilities.
2.2.2 Unconditional Probabilities.
2.2.3 First Passage Times.
2.2.4 Expected First Passage Time.
2.3 Continuous-Time Markov Chains.
2.3.1 Birth and Death Processes.
2.4 Queueing Models.
3. Random Fields.
3.1 Introduction.
3.2 The Covariance Function.
3.2.1 Conditional Probabilities.
3.3 The Spectral Density Function.
3.3.1 Wiener-Khinchine Relations.
3.3.2 Spectral Density Function of Linear Systems.
3.3.3 Discrete Random Processes.
3.4 The Variance Function.
3.5 The Correlation Length.
3.6 Some Common Models.
3.6.1 Ideal White Noise.
3.6.2 Triangular Correlation Function.
3.6.3 Polynomial Decaying Correlation Function.
3.6.4 Autoregressive Processes.
3.6.5 Markov Correlation Function.
3.6.6 Gaussian Correlation Function.
3.6.7 Fractal Processes.
3.7 Random Fields in Higher Dimensions.
3.7.1 The Covariance Function in Higher Dimensions.
3.7.2 The Spectral Density Function in Higher Dimensions.
3.7.3 The Variance Function in Higher Dimensions.
3.7.5 Separable Correlation Structure.
3.7.6 Isotropic Correlation Structure.
3.7.7 Ellipsoidal Correlation Structure.
3.7.8 Anisotropic Correlation Structure.
3.7.9 Cross-Correlated Random Fields.
3.7.10 Common Higher-Dimensional Models.
3.7.10.1 White Noise and Triangular Correlation Function.
3.7.10.2 Markov Correlation Function.
3.7.10.3 Gaussian Correlation Function.
4. Best Estimates, Excursions, and Averages.
4.1 Best Linear Unbiased Estimation.
4.1.1 Estimator Error.
4.1.2 Geostatistics: Kriging.
4.1.2.1 Estimator Error.
4.2 Threshold Excursions in One Dimension.
4.2.1 Derivative Process.
4.2.2 Threshold Excursion Rate.
4.2.3 Time to First Upcrossing: System Reliability.
4.2.4 Extremes.
4.3 Threshold Excursions in Two Dimensions.
4.3.1 Local Average Processes.
4.3.2 Analysis of Realizations.
4.3.3 Total Area of Excursion Regions.
4.3.4 Expected Number of Isolated Excursions.
4.3.5 Expected Area of Isolated Excursions.
4.3.6 Expected Number of Holes Appearing in Excursion Regions.
4.3.7 Integral Geometric Characteristic of 2-D Random Fields.
4.3.8 Clustering of Excursion Regions.
4.3.9 Extremes in Two Dimensions.
4.4 Averages.
4.4.1 The Arithmetic Average.
4.4.2 The Geometric Average.
4.4.3 The Harmonic Average.
4.4.4 Comparison.
5. Estimation.
5.1 Introduction.
5.2 Choosing a Distribution.
5.2.1 Estimating the Distribution Parameters.
5.2.1.1 Method of Moments.
5.2.1.2 Maximum Likelihood Estimators.
5.2.2 Goodness-of-Fit.
5.2.2.1 Heuristic Procedures.
5.2.2.2 Goodness-of-Fit Tests.
5.2.2.3 Chi-Square Test.
5.2.2.4 Kolmogorov-Smirnov Test.
5.2.2.5 Anderson-Darling Test.
5.3 Estimation in the Presence of Correlation.
5.3.1 Ergodicity and Stationarity.
5.3.2 Point versus Local Average Statistics.
5.3.3 Estimating the Mean.
5.3.4 Estimating the Variance.
5.3.5 Trend Analysis.
5.3.6 Estimating the Correlation Structure.
5.3.7 Example: Statistical Analysis of Permeability Data.
5.4.1 Second Order Structural Analysis.
5.4.1.1 The Sample Correlation Function.
5.4.1.2 The Sample Semivariogram.
5.4.1.3 The Sample Variance Function.
5.4.1.4 The Wavelet Coefficient Variance.
5.4.1.5 The Sample Spectral Density Function.
5.4.2 Estimation of First and Second Order Statistical Parameters.
5.4.2.1 Finite-Scale Model.
5.4.2.2 Fractal Model.
5.4.3 Summary.
6. Simulation.
6.1 Introduction.
6.2 Random Number Generators.
6.2.1 Common Generators.
6.2.2 Testing Random Number Generators.
6.3 Generating Non-Uniform Random Variables.
6.3.1 Introduction.
6.3.2 Methods of Generation.
6.3.2.1 Inverse Transform Method.
6.3.2.2 Convolution.
6.3.2.3 Acceptance-Rejection.
6.3.3 Generating Common Continuous Random Variates.
6.3.3.1 Generating Discrete Random Variates.
6.3.3.2 Generating Arrival Process Times.
6.3.4 Queueing Process Simulation.
6.4 Generating Random Fields.
6.4.1 Moving Average Method.
6.4.2 Covariance Matrix Decomposition.
6.4.3 Discrete Fourier Transform Method.
6.4.4 The Fast Fourier Transform Method.
6.4.5 The Turning Bands Method.
6.4.6 The Local Average Subdivision Method.
6.4.6.1 One-Dimensional Local Average Subdivision.
6.4.6.2 Multi-Dimensional Local Average Subdivision.
6.4.6.3 Implementation and Accuracy.
6.4.7 Comparison of Methods.
6.5 Conditional Simulation of Random Fields.
6.6 Monte Carlo Simulation.
7. Reliability-Based Design.
7.1 Acceptable Risk.
7.2 Assessing Risk.
7.2.1 The Hasofer-Lind First Order Reliability Method (FORM).
7.2.2 Point Estimate Method.
7.3 Background to Design Methodologies.
7.4 Load and Resistance Factor Design.
7.4.1 Calibration of Load and Resistance Factors.
7.4.2 Characteristic Values.
7.5 Going Beyond Calibration.
7.5.1 Level III Determination of Resistance Factors.
7.6 Risk-Based Decision Making.
PART 2: PRACTICE.
8. Groundwater Modeling.
8.1 Introduction.
8.2 Finite Element Model.
8.2.1 Analytical form of finite element conductivity matrices.
8.3 One-Dimensional Flow.
8.4 Simple Two-Dimensional Flow.
8.4.1 Parameters and Finite Element Model.
8.4.2 Discussion of Results.
8.5 Two-Dimensional Flow Beneath Water Retaining Structures.
8.5.1 Generation of Permeability Values.
8.5.2 Deterministic Solution.
8.5.3 Stochastic Analyses.
8.5.3.1 Single Realization.
8.5.3.2 Statistics of the Potential Field.
8.5.3.3 Flow Rate, Uplift, and Exit Gradient.
8.5.4 Summary.
8.6 Three-Dimensional Flow.
8.6.1 Simulation Results.
8.6.2 Reliability-Based Design.
8.6.3 Summary.
8.7.1 Simulation Results.
8.7.2 Comparison of Two- and Three-Dimensions.
8.7.4 Concluding Remarks.
9. Flow Through Earth Dams.
9.1 Statistics of Flow Through Earth Dams.
9.1.1 The Finite Element Model.
9.1.2 Simulation Results.
9.1.3 Empirical Estimation of Flow Rate Statistics.
9.1.4 Summary.
9.2.1 The Stochastic Model.
9.2.2 The Finite Element Model.
9.2.3 Downstream Free Surface Exit Elevation.
9.2.5 Summary.
10. Settlement of Shallow Foundations.
10.1 Introduction.
10.2 Two-Dimensional Probabilistic Foundation Settlement.
10.2.1 The Random Finite Element Model.
10.2.2 Single Footing Case.
10.2.3 Two Footing Case.
10.2.4 Summary.
10.3 Three-Dimensional Probabilistic Foundation Settlement.
10.3.1 The Random Finite Element Model.
10.3.2 Single Footing Case.
10.3.3 Two Footing Case.
10.3.4 Summary.
10.4 Strip Footing Risk Assessment.
10.4.1 Settlement Design Methodology.
10.4.2 Probabilistic Assessment of Settlement Variability.
10.4.3 Prediction of Settlement Mean and Variance.
10.4.4 Comparison of Predicted and Simulated Settlement Distribution.
10.4.5 Summary.
10.5 Resistance Factors for Shallow Foundation Settlement Design.
10.5.1 The Random Finite Element Model.
10.5.2 Reliability-Based Settlement Design.
10.5.3 Design Simulations.
10.5.4 Simulation Results.
10.5.5 Summary.
11. Bearing Capacity.
11.1 Strip Footings on soils.
11.1.1 The Random Finite Element Method.
11.1.2 Bearing Capacity Mean and Variance.
11.1.3 Monte Carlo Simulation.
11.1.4 Simulation Results.
11.1.5 Probabilistic Interpretation.
11.1.6 Summary.
11.2 Load and Resistance Factor Design of Shallow Foundations.
11.2.1 The random soil model.
11.2.2 Analytical approximation to the probability of failure.
11.2.3 Required resistance factor.
11.3 Summary.
12. Deep Foundations.
12.1 Introduction.
12.2 The Random Finite Element Model.
12.3 Monte Carlo Estimation of Pile Capacity.
12.4 Summary.
13. Slope Stability.
13.1 Introduction.
13.2 Probabilistic Slope Stability Analysis.
13.2.1 Probabilistic Description of Shear Strength.
13.2.2 Preliminary Deterministic Study.
13.2.3 Single Random Variable Approach.
13.2.4 Spatial Correlation.
13.2.5 The Random Finite Element Method.
13.2.6 Local Averaging.
13.2.7 Variance Reduction over a Square Finite Element.
13.2.8 Locally Averaged Single Random Variable Approach.
13.2.9 Results of Random Finite Element Method Analyses.
13.2.10 Summary.
13.3 A Slope Stability Reliability Model.
13.3.1 The Random Finite Element Method.
13.3.2 Parametric Studies.
13.3.3 A Failure Probability Model.
13.3.4 Summary.
14. Earth Pressure.
14.1 Introduction.
14.2 Passive Earth Pressures.
14.2.1 Numerical Approach.
14.2.2 Refined Approach Including Second Order Terms.
14.2.3 Random Finite Element Method.
14.2.4 Parametric Studies.
14.2.5 Summary.
14.3 Active Earth Pressures: Retaining Wall Reliability.
14.3.1 Introduction.
14.3.2 The Random Finite Element Method.
14.3.3 Active Earth Pressure Design Reliability.
14.3.4 Monte Carlo Results.
14.3.5 Summary.
15. Mine Pillar Capacity.
15.1 Introduction.
15.2 Literature.
15.3 Parametric Studies.
15.3.1 Mean of.
15.3.2 Coefficient of Variation of.
15.4 Probabilistic Interpretation.
15.4.1 General Observations on the Probability of Failure.
15.4.2 Results from Pillar Analyses.
15.5 Summary.
16. Liquefaction.
16.1 Introduction.
16.2 Model Site: Soil Liquefaction.
16.2.1 Stochastic Soil Model.
16.2.2 Stochastic Earthquake Model.
16.2.3 Finite Element Model.
16.2.4 Measures of Liquefaction.
16.3 Monte-Carlo Analysis and Results.
16.4 Summary.
References.
Appendices.
A Tables.
A.1 Standard Normal Distribution.
A.2 Inverse Student-T Distribution.
A.3 Inverse Chi-Square Distribution.
B Numerical Integration.
C Computing Variances and Covariances of Local Averages.

Library of Congress subject headings for this publication:
Soil mechanics.
Rock mechanics.
Risk assessment.