This text presents a thorough examination of the theories and methodologies available for risk assessment in geotechnical engineering, spanning the full range from established single–variable and "first order" methods to the most recent, advanced numerical developments. In response to the growing application of LRFD methodologies in geotechnical design, coupled with increased demand for risk assessments from clients ranging from regulatory agencies to insurance companies, authors Fenton and Griffiths have introduced an innovative reliability–based risk assessment method, the Random Finite Element Method (RFEM). The authors have spent more than fifteen years developing this statistically based method for modeling the real spatial variability of soils and rocks. As demonstrated in the book, RFEM performs better in real–world applications than traditional risk assessment tools that do not properly account for the spatial variability of geomaterials.
This text is divided into two parts:
- Part One, Theory, explains the theory underlying risk assessment methods in geotechnical engineering. This part′s seven chapters feature more than 100 worked examples, enabling you to develop a detailed understanding of the methods.
- Part Two, Practice, demonstrates how to use advanced probabilistic tools for several classical geotechnical engineering applications. Working with the RFEM, the authors show how to assess risk in problems familiar to all geotechnical engineers.
All the programs used for the geotechnical applications discussed in Part Two may be downloaded from the authors′ Web site at [external URL] at no charge, enabling you to duplicate the authors′ results and experiment with your own data. In short, you get all the theory and practical guidance you need to apply the most advanced probabilistic approaches for managing uncertainty in geotechnical design.
PART 1: THEORY.
Chapter 1: Review of Probability Theory.
1.2 Basic Set Theory.
1.4 Conditional Probability.
1.5 Random Variables and Probability Distributions.
1.6 Measures of Central Tendency, Variability, and Association.
1.7 Linear Combinations of Random Variables.
1.8 Functions of Random Variables.
1.9 Common Discrete Probability Distributions.
1.10 Common Continuous Probability Distributions.
1.11 Extreme–Value Distributions.
Chapter2: Discrete random Processes.
2.2 Discrete–Time, Discrete–State Markov Chains.
2.3 Continuous–Time Markov Chains.
2.4 Queueing Models.
Chapter 3: Random Fields.
3.2 Covariance Function.
3.3 Spectral Density Function.
3.4 Variance Function.
3.5 Correlation Length.
3.6 Some Common Models.
3.7 Random Fields in Higher Dimensions.
Chapter 4: Best Estimates, Excursions, and Averages.
4.1 Best Linear Unbiased Estimation.
4.2 Threshold Excursions in One Dimension.
4.3 Threshold Excursions in Two Dimensions.
Chapter 5: Estimation.
5.2 Choosing a Distribution.
5.3 Estimation in Presence of Correlation.
5.4 Advanced Estimation Techniques.
Chapter 6: Simulation.
6.2 Random–Number Generators.
6.3 Generating Nonuniform Random Variables.
6.4 Generating Random Fields.
6.5 Conditional Simulation of Random Fields.
6.6 Monte carlo Simulation.
Chapter 7: Reliability–Based Design.
7.1 Acceptable Risk.
7.2 Assessing Risk.
7.3 Background to Design Methodologies.
7.4 Load and Resistance Factor Design.
7.5 Going Beyond Calibration.
7.6 Risk–Based Decision making.
PART 2: PRACTICE.
Chapter 8: Groundwater Modeling.
8.2 Finite–Element Model.
8.3 One–Dimensional Flow.
8.4 Simple Two–Dimensional Flow.
8.5 Two–Dimensional Flow Beneath Water–Retaining Structures.
8.6 Three–Dimensional Flow.
8.7 Three Dimensional Exit Gradient Analysis.
Chapter 9: Flow Through Earth Dams.
9.1 Statistics of Flow Through Earth Dams.
9.2 Extreme Hydraulic Gradient Statistics.
Chapter 10: Settlement of Shallow Foundations.
10.2 Two–Dimensional Probabilistic Foundation Settlement.
10.3 Three–Dimensional Probabilistic Foundation Settlement.
10.4 Strip Footing Risk Assessment.
10.5 Resistance Factors for Shallow–Foundation Settlement Design.
Chapter 11: Bearing Capacity.
11.1 Strip Footings on c–ø Soils.
11.2 Load and Resistance Factor Design of Shallow Foundations.
Chapter 12: Deep Foundations.
12.2 Random Finite–Element Method.
12.3 Monte Carlo Estimation of Pile Capacity.
Chapter 13: Slope Stability.
13.2 Probabilistic Slope Stability Analysis.
13.3 Slope Stability Reliability Model.
Chapter 14: Earth Pressure.
14.2 Passive Earth Pressures.
14.3 Active Earth Pressures: Retaining Wall Reliability.
Chapter 15: Mine Pillar Capacity.
15.3 Parametric Studies.
15.4 Probabilistic Interpretation.
Chapter 16: Liquefaction.
16.2 Model Size: Soil Liquefaction.
16.3 Monte Carlo Analysis and Results.
PART 3: APPENDIXES.
APPENDIX A: PROBABILITY TABLES.
A.1 Normal Distribution.
A.2 Inverse Student t–Distribution.
A.3 Inverse Chi–Square Distribution
APPENDIX B: NUMERICAL INTEGRATION.
B.1 Gaussian Quadrature.
APPENDIX C. COMPUTING VARIANCES AND CONVARIANCES OF LOCAL AVERAGES.
C.1 One–Dimensional Case.
C.2 Two–Dimensional Case
C.3 Three–Dimensional Case.