Reliability and Statistics in Geotechnical Engineering

Part I.

1 Introduction – uncertainty and risk in geotechnical engineering.

1.1 Offshore platforms.

1.2 Pit mine slopes.

1.3 Balancing risk and reliability in a geotechnical design.

1.4 Historical development of reliability methods in civil engineering.

1.5 Some terminological and philosophical issues.

1.6 The organization of this book.

1.7 A comment on notation and nomenclature.

2 Uncertainty.

2.1 Randomness, uncertainty, and the world.

2.2 Modeling uncertainties in risk and reliability analysis.

2.3 Probability.

3 Probability.

3.1 Histograms and frequency diagrams.

3.2 Summary statistics.

3.3 Probability theory.

3.4 Random variables.

3.5 Random process models.

3.6 Fitting mathematical pdf models to data.

3.7 Covariance among variables.

4 Inference.

4.1 Frequentist theory.

4.2 Bayesian theory.

4.3 Prior probabilities.

4.4 Inferences from sampling.

4.5 Regression analysis.

4.6 Hypothesis tests.

4.7 Choice among models.

5 Risk, decisions and judgment.

5.1 Risk.

5.2 Optimizing decisions.

5.3 Non-optimizing decisions.

5.4 Engineering judgment.

Part II.

6 Site characterization.

6.1 Developments in site characterization.

6.2 Analytical approaches to site characterization.

6.3 Modeling site characterization activities.

6.4 Some pitfalls of intuitive data evaluation.

6.5 Organization of Part II.

7 Classification and mapping.

7.1 Mapping discrete variables.

7.2 Classification.

7.3 Discriminant analysis.

7.4 Mapping.

7.5 Carrying out a discriminant or logistic analysis.

8 Soil variability.

8.1 Soil properties.

8.2 Index tests and classification of soils.

8.3 Consolidation properties.

8.4 Permeability.

8.5 Strength properties.

8.6 Distributional properties.

8.7 Measurement error.

9 Spatial variability within homogeneous deposits.

9.1 Trends and variations about trends.

9.2 Residual variations.

9.3 Estimating autocorrelation and autocovariance.

9.4 Variograms and geostatistics.

Appendix: algorithm for maximizing log-likelihood of autocovariance.

10 Random field theory.

10.1 Stationary processes.

10.2 Mathematical properties of autocovariance functions.

10.3 Multivariate (vector) random fields.

10.4 Gaussian random fields.

10.5 Functions of random fields.

11 Spatial sampling.

11.1 Concepts of sampling.

11.2 Common spatial sampling plans.

11.3 Interpolating random fields.

11.4 Sampling for autocorrelation.

12 Search theory.

12.1 Brief history of search theory.

12.2 Logic of a search process.

12.3 Single stage search.

12.4 Grid search.

12.5 Inferring target characteristics.

12.6 Optimal search.

12.7 Sequential search.

Part III.

13 Reliability analysis and error propagation.

13.1 Loads, resistances and reliability.

13.2 Results for different distributions of the performance function.

13.3 Steps and approximations in reliability analysis.

13.4 Error propagation – statistical moments of the performance function.

13.5 Solution techniques for practical cases.

13.6 A simple conceptual model of practical significance.

14 First order second moment (FOSM) methods.

14.1 The James Bay dikes.

14.2 Uncertainty in geotechnical parameters.

14.3 FOSM calculations.

14.4 Extrapolations and consequences.

14.5 Conclusions from the James Bay study.

14.6 Final comments.

15 Point estimate methods.

15.1 Mathematical background.

15.2 Rosenblueth’s cases and notation.

15.3 Numerical results for simple cases.

15.4 Relation to orthogonal polynomial quadrature.

15.5 Relation with ‘Gauss points’ in the finite element method.

15.6 Limitations of orthogonal polynomial quadrature.

15.7 Accuracy, or when to use the point-estimate method.

15.8 The problem of the number of computation points.

15.9 Final comments and conclusions.

16 The Hasofer–Lind approach (FORM).

16.1 Justification for improvement – vertical cut in cohesive soil.

16.2 The Hasofer–Lind formulation.

16.3 Linear or non-linear failure criteria and uncorrelated variables.

16.4 Higher order reliability.

16.5 Correlated variables.

16.6 Non-normal variables.

17 Monte Carlo simulation methods.

17.1 Basic considerations.

17.2 Computer programming considerations.

17.3 Simulation of random processes.

17.4 Variance reduction methods.

17.5 Summary.

18 Load and resistance factor design.

18.1 Limit state design and code development.

18.2 Load and resistance factor design.

18.3 Foundation design based on LRFD.

18.4 Concluding remarks.

19 Stochastic finite elements.

19.1 Elementary finite element issues.

19.2 Correlated properties.

19.3 Explicit formulation.

19.4 Monte Carlo study of differential settlement.

19.5 Summary and conclusions.

Part IV.

20 Event tree analysis.

20.1 Systems failure.

20.2 Influence diagrams.

20.3 Constructing event trees.

20.4 Branch probabilities.

20.5 Levee example revisited.

21 Expert opinion.

21.1 Expert opinion in geotechnical practice.

21.2 How do people estimate subjective probabilities?

21.3 How well do people estimate subjective probabilities?

21.4 Can people learn to be well-calibrated?

21.5 Protocol for assessing subjective probabilities.

21.6 Conducting a process to elicit quantified judgment.

21.7 Practical suggestions and techniques.

21.8 Summary.

22 System reliability assessment.

22.1 Concepts of system reliability.

22.2 Dependencies among component failures.

22.3 Event tree representations.

22.4 Fault tree representations.

22.5 Simulation approach to system reliability.

22.6 Combined approaches.

22.7 Summary.

Appendix A: A primer on probability theory.

A.1 Notation and axioms.

A.2 Elementary results.

A.3 Total probability and Bayes’ theorem.

A.4 Discrete distributions.

A.5 Continuous distributions.

A.6 Multiple variables.

A.7 Functions of random variables.

References.

Index.