# Risk and Reliability in Geotechnical Engineering

DOI link for Risk and Reliability in Geotechnical Engineering

Risk and Reliability in Geotechnical Engineering book

# Risk and Reliability in Geotechnical Engineering

DOI link for Risk and Reliability in Geotechnical Engineering

Risk and Reliability in Geotechnical Engineering book

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**Establishes Geotechnical Reliability as Fundamentally Distinct from Structural Reliability**

Reliability-based design is relatively well established in structural design. Its use is less mature in geotechnical design, but there is a steady progression towards reliability-based design as seen in the inclusion of a new Annex D on "Reliability of Geotechnical Structures" in the third edition of ISO 2394. Reliability-based design can be viewed as a simplified form of risk-based design where different consequences of failure are implicitly covered by the adoption of different target reliability indices. Explicit risk management methodologies are required for large geotechnical systems where soil and loading conditions are too varied to be conveniently slotted into a few reliability classes (typically three) and an associated simple discrete tier of target reliability indices.

Provides Realistic Practical Guidance

**Risk and Reliability in Geotechnical Engineering** makes these reliability and risk methodologies more accessible to practitioners and researchers by presenting~~ ~~soil statistics which are necessary inputs, by explaining how calculations can be carried out using simple tools, and by presenting illustrative or actual examples showcasing the benefits and limitations of these methodologies.

With contributions from a broad international group of authors, this text:

- Presents probabilistic models suited for soil parameters
- Provides easy-to-use Excel-based methods for reliability analysis
- Connects reliability analysis to design codes (including LRFD and Eurocode 7)
- Maximizes value of information using Bayesian updating
- Contains efficient reliability analysis methods

Accessible To a Wide Audience

**Risk and Reliability in Geotechnical Engineering** presents all the "need-to-know" information for a non-specialist to calculate and interpret the reliability index and risk of geotechnical structures in a realistic and robust way. It suits engineers, researchers, and students who are interested in the practical outcomes of reliability and risk analyses without going into the intricacies of the underlying mathematical theories.

Part I

Properties

**Constructing multivariate distributions for soil parameters**; *Jianye Ching and Kok-Kwang Phoon*

Introduction

Normal random variable

Bivariate normal vector

Multivariate normal vector

Non-normal random variable

Multivariate non-normal random vector

Real example

Future challenges

List of symbols

References

**Modeling and simulation of bivariate distribution of shear strength parameters using copulas; ***Dian-Qing Li and Xiao-Song Tang*

Introduction

Copula theory

Modeling bivariate distribution of shear strength parameters

Simulating bivariate distribution of shear strength parameters

Impact of copula selection on retaining wall reliability

Summary and conclusions

Acknowledgments

Appendix 2.1: MATLAB® codes

List of symbols

References

Part II

Methods

**Evaluating reliability in geotechnical engineering; ***J. Michael Duncan and Matthew D. Sleep*

Purpose of reliability analysis

Probability of failure and risk

Language of statistics and probability

Probability of failure and factor of safety

Methods of estimating standard deviations

Computing probability of failure

Monte Carlo analysis using @Risk™

Hasofer Lind method

Taylor Series method with assumed normal distribution of the factor of safety

Taylor Series method with a lognormal distribution of the factor of safety

PEM with a normal distribution for the factor of safety

PEM with a lognormal distribution for the factor of safety

Comments on the methods

Summary

References

**Maximum likelihood principle and its application in soil liquefaction assessment; ***Charng Hsein Juang, Sara Khoshnevisan, and Jie Zhang*

Introduction

Principle of maximum likelihood

Liquefaction probability based on generalized linear regression

Converting a deterministic liquefaction model into a probabilistic model

Estimation of liquefaction-induced settlement

Summary and Conclusions

Acknowledgments

Appendix 4.1: Model of Robertson and Wride (1998) and Robertson (2009)

Appendix 4.2: Notation

References

**Bayesian analysis for learning and updating geotechnical parameters and models with measurements; ***Daniel Straub and Iason Papaioannou*

Introduction

Bayesian analysis

Geotechnical reliability based on measurements: Step-by-step procedure for Bayesian analysis

Advanced algorithms for efficient and effective Bayesian updating of geotechnical models

Application: Foundation of transmission towers under tensile loading

Application: Finite-element-based updating of soil parameters and reliability

Concluding remarks

Acknowledgment

References

**Polynomial chaos expansions and stochastic finite-element methods; ***Bruno Sudret*

Introduction

Uncertainty propagation framework

Polynomial chaos expansions

Postprocessing for engineering applications

Sensitivity analysis

Application examples

Conclusions

Acknowledgments

Appendix 6.1: List of symbols

Appendix 6.2: Hermite polynomials

References

**Practical reliability analysis and design by Monte Carlo Simulation in spreadsheet; ***Yu Wang and Zijun Cao*

Introduction

Subset Simulation

Expanded RBD with Subset Simulation

Probabilistic failure analysis using Subset Simulation

Spreadsheet implementation of MCS-based reliability analysis and design

Illustrative example I: Drilled shaft design

Illustrative example II: James Bay Dike design scenario

Summary and concluding remarks

Acknowledgment

List of symbols

References

Part III

Design

**LRFD calibration of simple limit state functions in geotechnical soil-structure design; ***Richard J. Bathurst*

Introduction

Preliminaries

Bias value distributions

Calculation of β, ϒ_{Q}, and φ

Example

Additional considerations

Conclusions

References

**Reliability-based design: Practical procedures, geotechnical examples, and insights; ***Bak-Kong Low*

Introduction

Example of reliability-based shallow foundation design

SORM analysis on the foundation of FORM results for a rock slope

Probabilistic analyses of a slope failure in San Francisco Bay mud

Reliability analysis of a Norwegian slope accounting for spatial autocorrelation

System FORM reliability analysis of a soil slope with two equally likely failure modes

Multicriteria RBD of a laterally loaded pile in spatially autocorrelated clay

FORM design of an anchored sheet pile wall

Reliability analysis of roof wedges and rockbolt forces in tunnels

Probabilistic settlement analysis of a Hong Kong trial embankment on soft clay

Coupling of stand-alone deterministic program and spreadsheetautomated reliability procedures via response surface or similar methods

Summary and conclusions

References

**Managing risk and achieving reliable geotechnical designs using Eurocode 7; ***Trevor L.L. Orr*

Introduction

Geotechnical complexity and risk

Reliability requirements in designs to Eurocode 7

Verification of designs to Eurocode 7

Reliability levels

Conclusions

Acknowledgments

References

Part IV

Risk and decision

**Practical risk assessment for embankments, dams, and slopes; ***Luis Altarejos-García, Francisco Silva-Tulla, Ignacio Escuder-Bueno, and Adrián Morales-Torres*

Introduction

Estimation of conditional probability as a function of safety factor

Role of fragility curves to evaluate the uncertainty in probability estimates

Mathematical roots and numerical estimation of fragility curves

From fragility curves to annualized probability of failure commonly used in risk analysis

Summary of main points

Acknowledgments

List of main symbols and acronyms

References

**Evolution of geotechnical risk analysis in North American practice; ***Gregory B. Baecher and John T. Christian*

Introduction

Beginnings

Geotechnical reliability (1971–1996)

Mining engineering (1969–1980)

Offshore reliability (1974–1990)

Environmental remediation (1980–1995)

Dam safety (1986–Ongoing)

Systems risk assessment (2005–Ongoing)

Emerging approaches: System simulation, stress testing, and scenario appraisals

Ten unresolved questions

Concluding thoughts

Acknowledgments

References

**Assessing the value of information to design site investigation and construction quality assurance programs; ***Robert B. Gilbert and Mahdi Habibi*

Introduction

Value of information framework

Insights from Bayes’ theorem

Implementation of value of information assessment

Case-history applications

Summary

Acknowledgments

References

**Verification of geotechnical reliability using load tests and integrity tests; **

*Limin Zhang*

Introduction

Within-site variability of pile capacity

Updating pile capacity with proof load tests

Updating pile capacity with integrity tests

Reliability of piles verified by proof load tests

Reliability of piles verified by integrity tests

Summary

Acknowledgment

List of symbols

References

Part V

Spatial variability

**Application of the subset simulation approach to spatially varying soils; ***Ashraf Ahmed and Abdul-Hamid Soubra*

Introduction

Karhunen–Loève expansion methodology for the discretization of a random field

Brief overview of the subset simulation approach

Method of computation of the failure probability by the SS approach in the case of a spatially varying soil property

Example applications

Conclusion

Appendix 15.1: Modified M–H algorithm

List of symbols

References

Index