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1999_an overview of probabilistic analysis for geotechnical_ETL

1999_an overview of probabilistic analysis for geotechnical_ETL

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ETL 1110-2-556 28 May 99 A-1 Appendix A An Overview of Probabilistic Analysis for Geotechnical Engineering Problems Table of Contents Page Purpose and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2 Probabilistic Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2 Background of Corps’ Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2 Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3 Risk Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3 Event Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-4 Time Basis of Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-5 Hazard Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-5 Fault Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-5 Further References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-5 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-6 Random Variables and Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-6 The Lognormal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-7 Moments of Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-7 Fitting Distributions and Moments to Test Data . . . . . . . . . . . . . . . . . . . . . . . A-7 Typical Coefficients of Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-8 Independent and Correlated Random Variables . . . . . . . . . . . . . . . . . . . . . . . . A-8 Spatial Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-9 First-Order Second-Moment Reliability Methods . . . . . . . . . . . . . . . . . . . . . . . A-10 The Reliability Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-10 Probability of Failure or Unsatisfactory Performance . . . . . . . . . . . . . . . . . . . A-11 Taylor’s Series Mean Value Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-11 Point Estimate Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-11 Hasofer - Lind Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-12 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-12 Some Comments on the Use and Meaning of or Pr(u) . . . . . . . . . . . . . . . . . . . A-13 Potential for Overlooking Some Performance Modes . . . . . . . . . . . . . . . . . . . A-13 Physical Meaning of Probability of Failure for Existing Structures . . . . . . . . A-13 Lack of Time Dimension in FOSM Methods . . . . . . . . . . . . . . . . . . . . . . . . . A-14 Frequency-based Reliability Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-14 Subjectively Determined Probability Values . . . . . . . . . . . . . . . . . . . . . . . . . . . A-14 System Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-15 Special Issues in Geotechnical Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-15 Some Differences Between Geotechnical and Structural Problems . . . . . . . . . A-15 Strength Parameters from Triaxial Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-16 Free-body and Critical Slip Surface Issues in Slope Stability Analysis . . . . . . A-16 Application of Spatial Correlation Theory to Slope Stability and Seepage Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-17 Application of Spatial Correlation Theory to Long Earth Structures . . . . . . . A-17 Examples of Probabilistic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-18 Wappapello Dam, St. Louis District . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-18 Shelbyville Dam, St. Louis District . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-18 Research on Navigation Structures for Guidance Development . . . . . . . . . . . A-18
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ETL 1110-2-556 28 May 99 A-2 Research on Levees for Guidance Development . . . . . . . . . . . . . . . . . . . . . . A-18 Hodges Village Dam, New England Division . . . . . . . . . . . . . . . . . . . . . . . . A-18 Walter F. George Dam, Mobile District . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-18 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-19 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-19 Purpose and Scope This appendix provides an overview of the application of probabilistic methods to geotechnical engineering problems of interest to the Corps of Engineers, with emphasis on methodology suitable for assessing the comparative reliability of dams, levees, and other hydraulic structures in the context of planning studies. A number of probabilistic methods that can and have been applied to the problems of interest are reviewed and discussed. These are drawn from Corps guidance, literature that led to Corps guidance, literature and methodology not yet in Corps guidance but considered state-of-the-art, case histories of past analyses by the Corps and by others for similar problems, and recent remarks made in state-of-the-art invited papers. The intent of this review is to introduce the reader to the diversity of methodology and issues that are encompassed in geotechnical probabilistic analysis, and their relationships to each other and Corps methodology, so that the relative
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