Cover -- Title Page -- Copyright Page -- Table of Contents -- Preface -- Introduction -- PART 1. QUALITATIVE METHODS FOR EVALUATING THE RELIABILITY OF CIVIL ENGINEERING STRUCTURES -- Introduction to Part 1 -- Chapter 1. Methods for System Analysis and Failure Analysis -- 1.1. Introduction -- 1.2. Structural analysis -- 1.2.1. The sub-systems -- 1.2.2. Environments -- 1.2.3. Bounding the analysis -- 1.2.4. Scales of a study -- 1.3. Functional analysis -- 1.3.1. Principles of functional analysis -- 1.3.2. External functional analysis -- 1.3.3. Internal functional analysis -- 1.4. Failure Modes and Effects Analysis (FMEA) -- 1.4.1. Principles of FMEA -- 1.4.2. Process FMEA -- 1.4.3. Product FMEA -- 1.5. Bibliography -- Chapter 2. Methods for Modeling Failure Scenarios -- 2.1. Introduction -- 2.2. Event tree method -- 2.3. Fault tree method -- 2.3.1. Information acquisition -- 2.3.2. Fault tree construction -- 2.4. Bow-tie method -- 2.5. Criticality evaluation methods -- 2.5.1. Criticality formulation -- 2.5.2. Civil engineering considerations -- 2.6. Bibliography -- Chapter 3. Application to a Hydraulic Civil Engineering Project -- 3.1. Context and approach for an operational reliability study -- 3.2. Functional analysis and failure mode analysis -- 3.2.1. Functional analysis of the system -- 3.2.2. Failure mode analysis, and effects -- 3.3. Construction of failure scenarios -- 3.4. Scenario criticality analysis -- 3.4.1. Hydrological study -- 3.4.2. Hydraulic model and quantitative consequence analysis -- 3.4.3. Evaluation of probability of technological failure -- 3.4.4. Representing the criticality of a scenario -- 3.5. Application summary -- 3.6. Bibliography -- PART 2. HETEROGENEITY AND VARIABILITY OF MATERIALS: CONSEQUENCES FOR SAFETY AND RELIABILITY -- Introduction to Part 2 -- Chapter 4. Uncertainties in Geotechnical Data.

4.1. Various sources of uncertainty in geotechnical engineering -- 4.1.1. Erratic terrain, light disorder and anthropogenic terrain -- 4.1.2. Sources of uncertainty, errors, variability -- 4.1.3. Correlations between material properties -- 4.2. Erroneous, censored and sparse data -- 4.2.1. Erroneous data -- 4.2.2. Bounded data -- 4.2.3. Sparse data -- 4.3. Statistical representation of data -- 4.3.1. Notation -- 4.3.2. Spatial variability of material properties -- 4.4. Data modeling -- 4.4.1. Probabilistic and possibilistic approaches -- 4.4.2. Useful random variables (Gaussian, Weibull) -- 4.4.3. Maximum likelihood method -- 4.4.4. Example: resistance measurements in concrete samples -- 4.5. Conclusion -- 4.6. Bibliography -- Chapter 5. Some Estimates on the Variability of Material Properties -- 5.1. Introduction -- 5.2. Mean value estimation -- 5.2.1. Sampling and estimation -- 5.2.2. Number of data points required for an estimate -- 5.3. Estimation of characteristic values -- 5.3.1. Characteristic value and fractile of a distribution -- 5.3.2. Example: resistance measurements for wood samples -- 5.3.3. Optimization of number of useful tests -- 5.3.4. Estimate of in situ concrete mechanical strength -- 5.4. Principles of a geostatistical study -- 5.4.1. Geostatistical modeling tools -- 5.4.2. Estimation and simulation methods -- 5.4.3. Study of pressuremeter measurements in an urban environment -- 5.5. Bibliography -- Chapter 6. Reliability of a Shallow Foundation Footing -- 6.1. Introduction -- 6.2. Bearing capacity models for strip foundations - modeling errors -- 6.3. Effects of soil variability on variability in bearing capacity and safety of the foundation -- 6.3.1. Methodology -- 6.3.2. Purely frictional soil -- 6.3.3. Soil with friction and cohesion.

6.4. Taking account of the structure of the spatial correlation and its influence on the safety of the foundation -- 6.4.1. Spatial correlation and reduction in variance -- 6.4.2. Taking account of the spatial correlation, and results -- 6.5. Conclusions -- 6.5.1. Conclusions drawn from case study -- 6.5.2. General conclusions -- 6.6. Bibliography -- PART 3. METAMODELS FOR STRUCTURAL RELIABILITY -- Introduction to Part 3 -- Chapter 7. Physical and Polynomial Response Surfaces -- 7.1. Introduction -- 7.2. Background to the response surface method -- 7.3. Concept of a response surface -- 7.3.1. Basic definitions -- 7.3.2. Various formulations -- 7.3.3. Building criteria -- 7.4. Usual reliability methods -- 7.4.1. Reliability issues and Monte Carlo simulation -- 7.4.2. FORM -- 7.5. Polynomial response surfaces -- 7.5.1. Basic formulation -- 7.5.2. Working space -- 7.5.3. Response surface expression -- 7.5.4. Building the numerical experimental design -- 7.5.5. Example of an adaptive RS method -- 7.6. Conclusion -- 7.7. Bibliography -- Chapter 8. Response Surfaces based on Polynomial Chaos Expansions -- 8.1. Introduction -- 8.1.1. Statement of the reliability problem -- 8.1.2. From Monte Carlo simulation to polynomial chaos expansions -- 8.2. Building of a polynomial chaos basis -- 8.2.1. Orthogonal polynomials -- 8.2.2. Example -- 8.3. Computation of the expansion coefficients -- 8.3.1. Introduction -- 8.3.2. Projection methods -- 8.3.3. Regression methods -- 8.3.4. Post-processing of the coefficients -- 8.4. Applications in structural reliability -- 8.4.1. Elastic engineering truss -- 8.4.2. Frame structure -- 8.5. Conclusion -- 8.6. Bibliography -- PART 4. METHODS FOR STRUCTURAL RELIABILITY OVER TIME -- Introduction to Part 4 -- Chapter 9. Data Aggregation and Unification -- 9.1. Introduction -- 9.2. Methods of data aggregation and unification.

9.2.1. Data unification methods -- 9.2.2. Data aggregation methods -- 9.3. Evaluation of evacuation time for an apartment in case of fire -- 9.4. Conclusion -- 9.5. Bibliography -- Chapter 10. Time-Variant Reliability Problems -- 10.1. Introduction -- 10.2. Random processes -- 10.2.1. Definition and elementary properties -- 10.2.2. Gaussian random processes -- 10.2.3. Poisson and rectangular wave renewal processes -- 10.3. Time-variant reliability problems -- 10.3.1. Problem statement -- 10.3.2. Right-boundary problems -- 10.3.3. General case -- 10.4. PHI2 method -- 10.4.1. Implementation of the PHI2 method - stationary case -- 10.4.2. Implementation of the PHI2 method - non-stationary case -- 10.4.3. Semi-analytical example -- 10.5. Industrial application: truss structure under time-varying loads -- 10.6. Conclusion -- 10.7. Bibliography -- Chapter 11. Bayesian Inference and Markov Chain Monte Carlo Methods -- 11.1. Introduction -- 11.2. Bayesian Inference -- 11.2.1. Bayesian estimation of the mean of a Gaussian distribution -- 11.3. MCMC methods for weakly informative data -- 11.3.1. Weakly informative statistical problems -- 11.3.2. From prior information to prior distributions -- 11.3.3. Approximating a posterior distribution -- 11.3.4. A popular MCMC method: Gibbs sampling -- 11.3.5. Metropolis-Hastings algorithm -- 11.3.6. Assessing the convergence of an MCMC algorithm -- 11.3.7. Importance sampling -- 11.4. Estimating a competing risk model from censored and incomplete data -- 11.4.1. Choosing the prior distributions -- 11.4.2. From prior information to prior hyperparameters -- 11.4.3. Gibbs sampling -- 11.4.4. Adaptive Importance Sampling (AIS) -- 11.5. Conclusion -- 11.6. Bibliography -- Chapter 12. Bayesian Updating Techniques in Structural Reliability -- 12.1. Introduction.

12.2. Problem statement: link between measurements and model prediction -- 12.3. Computing and updating the failure probability -- 12.3.1. Structural reliability - problem statement -- 12.3.2. Updating failure probability -- 12.4. Updating a confidence interval on response quantities -- 12.4.1. Quantiles as the solution of an inverse reliability problem -- 12.4.2. Updating quantiles of the response quantity -- 12.4.3. Conclusion -- 12.5. Bayesian updating of the model basic variables -- 12.5.1. A reminder of Bayesian statistics -- 12.5.2. Bayesian updating of the model basic variables -- 12.6. Updating the prediction of creep strains in containment vessels of nuclear power plants -- 12.6.1. Industrial problem statement -- 12.6.2. Deterministic models -- 12.6.3. Prior and posterior estimations of the delayed strains -- 12.7. Conclusion -- 12.8. Acknowledgments -- 12.9. Bibliography -- PART 5. RELIABILITY-BASED MAINTENANCE OPTIMIZATION -- Introduction to Part 5 -- Chapter 13. Maintenance Policies -- 13.1. Maintenance -- 13.1.1. Lifetime distribution -- 13.1.2. Maintenance cycle -- 13.1.3. Maintenance planning -- 13.2. Types of maintenance -- 13.2.1. Choice of the maintenance policy -- 13.2.2. Maintenance program -- 13.2.3. Inspection program -- 13.3. Maintenance models -- 13.3.1. Model of perfect maintenance: AGAN -- 13.3.2. Model of minimal maintenance: ABAO -- 13.3.3. Model of imperfect or bad maintenance: BTO/WTO -- 13.3.4. Complex maintenance policy -- 13.4. Conclusion -- 13.5. Bibliography -- Chapter 14. Maintenance Cost Models -- 14.1. Preventive maintenance -- 14.2. Maintenance based on time -- 14.2.1. Model I -- 14.2.2. Model II -- 14.2.3. Model III -- 14.3. Maintenance based on age -- 14.4. Inspection models -- 14.4.1. Impact of inspection on costs -- 14.4.2. The case of imperfect inspections -- 14.5. Structures with large lifetimes.

14.6. Criteria for choosing a maintenance policy.