RISK AND RELIABILITY IN GEOTECHNICAL ENGINEERING

Transcription

1 RISK AND RELIABILITY IN GEOTECHNICAL ENGINEERING EDITED BY KOK-KWANG PHOON JIANYE CHING CRC Press Taylor & Francis Group Boca Raton London New York CRC Press Is an Imprint of the Taylor & Francis Croup, an informa business A SPON BOOK

2 Preface Acknowledgments Editors Contributors xix xxi xxiii xxv PART I Properties I 1 Constructing multivariate distributions for soil parameters 3 JIANYE CHING AND KOK-KWANG PHOON 1.1 Introduction Normal random variable Random data Normal random variable Probability density function Cumulative distribution function Estimation of normal parameters Method of moments Percentile method Maximum likelihood method Normal probability plot Statistical uncertainties in the p. and a estimators Simulation of a normal random variable Simulating standard uniform random variable U Simulating standard normal random variable X Simulating normal random variable Y Bivariate normal vector Bivariate data Bivariate normal distribution Bivariate standard normal Correlation coefficient Estimation of 5j Method of moments Maximum likelihood method 25

3 Rank correlation method Statistical uncertainties in the 8,2 estimate Goodness-of-fit test (the line test) Simulation of bivariate standard normal random variables Multivariate normal vector Multivariate data Multivariate normal distribution Estimation of correlation matrix C Positive definiteness of the correlation matrix C Goodness-of-fit test Simulation of multivariate standard normal random vector X Conditional normal and updating Non-normal random variable Non-normal data Non-normal distribution Lognormal and shifted lognormal distributions Johnson system of distributions Selection and parameter estimation for the Johnson distribution Probability plot and the goodnessof-fit test (K-S test) Simulation of the Johnson random variable Some practical observations Choice of z Parameter estimation under prescribed lower and/or upper bound Multivariate non-normal random vector Multivariate non-normal data CDF transform approach Estimation of the marginal distribution of Y Estimation of the correlation matrix C Simulation Some practical observations Real example Clay/10/7490 database Construction of multivariate distribution Fit a Johnson distttbution to eacb component (^j) Convert Y, into standard normal X, Compute the correlation matrix for (X X2,...,X,o) Problem of nonpositive definiteness Conditioning: Bayesian analysis Future challenges 72 List of symbols 72 References 74

4 vii 2 Modeling and simulation of bivariate distribution of shear strength parameters using copulas 77 DIAN-QING LI AND XIAO-SONG TANG 2.1 Introduction Copula theory Definition of copulas Dependence measures Pearson's rho Kendall's tau Four selected copulas Modeling bivariate distribution of shear strength parameters Measured data of cohesion and friction angle Identification of best-fit marginal distributions Identification of best-fit copula Simulating bivariate distribution of shear strength parameters Algorithms for simulating bivariate distribution Gaussian copula Plackett copula Frank and No.16 copulas Simulation of copulas and bivariate distribution Impact of copula selection on retaining wall reliability Retaining wall example Probability of failure using direct integration Nominal factor of safety for retaining wall stability Reliability results produced by different copulas Effect of geometrical parameters on probability of failure Effect of GOV of shear strength parameters on probability of failure Effect of correlation between cohesion and friction angle on probability of failure Discussions Summary and conclusions 115 Acknowledgments 115 Appendix 2A: MATLAB codes 115 List of symbols 125 References 126 PART II Methods Evaluating reliability in geotechnical engineering 131 J. MICHAEL DUNCAN AND MATTHEW D. SLEEP 3.1 Purpose of reliability analysis Probability of failure and risk 132

5 viii Contents 3.3 Language of statistics and probability Variables Correlated and uncorrected variables Standard deviation Coefficient of variation Histograms and relative frequency diagrams Probability and probability theory Probability density function Normal and lognormal distributions Lognormal distribution Cumulative density function Probability of failure Reliability Reliability index Probability of failure on the CDF curve Reliability index for normally distributed factor of safety Reliability index for a lognormally distributed factor of safety Effect of standard deviation on estimated value of probability of failure Probability of failure and factor of safety What is "failure/" Assumed distribution of the factor of safety Methods of estimating standard deviations Computation from data Published values The "three-sigma rule" The "N-sigma rule" Graphical N-sigma rule Computing probability of failure Deterministic analyses Factor of safety against sliding on top of the silty sand layer Factor of safety against sliding on the clay foundation Factor of safety against bearing capacity failure Monte Carlo analysis Accuracy of calculations Hasofer Find method Summary of the 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 Summary of the Taylor Series method PEM with a normal distribution for the factor of safety PEM with a lognormal distribution for the factor of safety Summary of the PEM Comments on the methods 176

6 ix Significance of the variables Accuracy Summary 177 References Maximum likelihood principle and its application in soil liquefaction assessment 181 CHARNG HSEIN JUANG, SARA KHOSHNEVISAN, AND JIE ZHANG 4.1 Introduction Principle of maximum likelihood Independent observations Correlated observations Censored observations Ranking of competing models Limitations of the maximum likelihood method Liquefaction probability based on generalized linear regression Predicting liquefaction probability based on generalized linear models Calibration database Evaluation of sampling bias Calibration of liquefaction models Ranking of liquefaction models Converting a deterministic liquefaction model into a probabilistic model Probabilistic model Calibration and ranking of P^-F, relationships Estimation of liquefaction-induced settlement Probabilistic model for predicting liquefaction-induced settlement Calibration database Maximum likelihood estimation of statistics of model bias factor 210 -*.6 Summary and conclusions 213.Acknowledgments 214.Appendix 4A: Model of Robertson and Wride (1998) and Robertson (2009) 215 Appendix 4B: Notation 216 References Bavesian analysis for learning and updating geotechnical parameters and 3 with measurements 221 LMNiEL STRAUB AND lason PAPAIOANNOU 5.1 Introduction Z Bayesian analysis Geotechnical reliability based on measurements: Stepby-step procedure for Bayesian analysis Initial probabilistic model: Prior distribution Modeling spatially variable parameters Computing the reliability and risk based on the prior model 230

7 X Contents Describing observations and data: The likelihood Measurement Xi of a parameter X Samples of a spatially variable parameter Measurement of site performance parameters Updating the model Conjugate priors Numerical integration to determine the proportionality constant Advanced sampling methods Multinormal approximation of the posterior Direct updating of the reliability Predictive distributions Updating reliability and risk estimates Communicating the results Advanced algorithms for efficient and effective Bayesian updating of geotechnical models Markov chain Monte Carlo Sequential Monte Carlo Bayesian updating with structural reliability methods Application: Foundation of transmission towers under tensile loading Prior probabilistic model Reliability analysis based on the prior model Updating with CRT test outcomes Updating with survived loading conditions Application: Finite-element-based updating of soil parameters and reliability Prior probabilistic model Updating the soil parameters with deformation measurements Updating the reliability with deformation measurements Concluding remarks 261 Acknowledgment 261 References Polynomial chaos expansions and stochastic finite-element methods 265 BRUNO SUDRET 6.1 Introduction Uncertainty propagation framework Introduction Monte Carlo simulation Polynomial chaos expansions Mathematical setting Construction of the basis Univariate orthonormal polynomials Multivariate polynomials Practical implementation Isoprobabilistic transform 270

8 xi Truncation scheme Application example Computation of the coefficients Introduction Projection Least-square minimization Validation Error estimators Leave-one-out cross-validation Curse of dimensionality Adaptive algorithms Post-processing for engineering applications Moment analysis Distribution analysis and confidence intervals Reliability analysis Sensitivity analysis Sobol decomposition Sobol indices Sobol indices from PC expansions 286 r-5 Application examples Load-carrying capacity of a strip footing Independent input variables Correlated input variables Settlement of a foundation on an elastic two-layer soil mass Settlement of a foundation on soil mass with spatially varying Young's modulus Conclusions Summary and outlook 295 Aektiowledgments 296 Afpendix 6A: Hermite polynomials 296 List of symbols 297 References 297 Practical reliability analysis and design by Monte Carlo Simulation m ^readsheet 301 TCWANG AND ZIJUN CAD "J Introduction 301 ~_Z Subset Simulation Algorithm Simulation procedures 303 ~J Expanded RBD with Subset Simulation Expanded RBD approach Desired sample number in direct MCS Integration of expanded RBD approach with Subset Simulation 306 ~-t Probabilistic failure analysis using Subset Simulation 307

9 xii Contents Hypothesis testing Bayesian analysis Integration of probabilistic failure analysis tvith Subset Simulation Spreadsheet implementation of MCS-based reliability analysis and design Deterministic modeling Uncertainty modeling Uncertainty propagation Illustrative example I: Drilled shaft design Deterministic model worksheet Uncertainty model worksheet Subset Simulation and RBD Add-In Determination of feasible designs Results comparison Effects of the driving variable Illustrative example II: James Bay Dike design scenario Subset Simulation results Hypothesis test results Bayesian analysis results Summary and concluding remarks 331 Acknowledgment 332 List of symbols 332 References 334 PART III Design 8 LRFD calibration of simple limit state functions in geotechnical soil-structure design RICHARD J. BATHURST 8.1 Introduction Preliminaries Bias value distributions Calculation o/p, Tq, and cp Generation of bias values Selection of load factor Selection of target reliability index Calculation of tp MC simulation Closed-form solutions Example General Load data Pullout (resistance) data Calibration 351

10 xiii Resistance factor using MC simulation Resistance factor using closed-form solution Additional considerations Conclusions 353 References Reliability-based design: Practical procedures, geotechnical examples, and insights 355 BAK-KONG LOW 9.1 Introduction Three spreadsheet FORM procedures and intuitive dispersion ellipsoid perspective Example of reliability-based shallow foundation design RBD compared with EC7 or LRFD design, and complementary roles of RBD to EC7 and LRFD design SORM analysis on the foundation of FORM results for a rock slope Constrained optimizational FORM spreadsheet approach with respect to the u vector Positive reliability index only if the meanvalue point is in the safe domain 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 Illustrative example of multicriteria RBD of a laterally loaded pile 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 ESS and performance functions g(x) pertaining to magnitude and rate of soft clay settlement Distinguishing positive and negative reliability indices Reliability analysis for different limiting state surfaces Obtaining probability of failure (Pfi and CDF from P indices Obtaining PDF curves from P index Coupling of stand-alone deterministic program and spreadsheetautomated reliability procedures via response surface or similar methods Summary and conclusions 390 References Managing risk and achieving reliable geotechnical designs using Eurocode TREVOR L.L. ORR 10.1 Introduction Geotechnical complexity and risk 395

11 xiv Contents Factors affecting complexity Levels of risk and Geotechnical Categories Risks due to adverse water pressures Geotechnical investigations and geotechnical risks Reliability requirements in designs to Eurocode Basic requirement Measures to achieve reliable designs Design assumptions for reliable designs Verification of designs to Eurocode Limit state design method Verification by use of calculations Design equations and their components Design geometrical data Design actions Design geotechnical parameters 407 i;, Design effects of actions and design resistances Characteristic parameter values Definition and selection of characteristic values Aleatory variability and epistemic uncertainty Selection of aleatory characteristic parameter values Example 10.1: Selection of characteristic parameter values Characteristic pile compressive resistances Partial factors, safety levels and reliability Types of ultimate limit state and recommended partial factor values Example 10.2: Determination of the design soil resistance on walls against uplift Example 10.3: Design of a basement against uplift Reliability levels Partial factors, uncertainty, calibration, and target reliability Partial factors in spread and pile foundations designs Reliability differentiation Conclusions 430 Acknowledgments 431 References 432 PART IV Risk and decision Practical risk assessment for embankments, dams, and slopes 437 LUIS ALTAREJOS-GARCfA, FRANCISCO SILVA-TULLA, IGNACIO ESCUDER-BUENO, AND ADRIAN MORALES-TORRES 11.1 Introduction Estimation of conditional probability as a function of safety factor FS versus p(f) charts for slope instability and soil transport 438

12 xv Example of risk assessment for an earth dam based on the empirical FS versus p(f) charts Estimation of failure probabilities versus peak pool elevation: Example from engineering practice Estimation of peak pool elevation annual exceedance probabilities Estimation of potential loss of life versus peak pool elevation at time of failure Comparison of results with risk evaluation guidelines Role of fragility curves to evaluate the uncertainty in probability estimates Concept of uncertainty Concept of fragility curves Role of fragility curves in risk analysis Mathematical roots and numerical estimation of fragility curves Introduction Conditional probability of failure versus ES Building fragility curves Example of fragility analysis for stability failure mode of an earth dam Erom fragility curves to annualized probability of failure commonly used in risk analysis Summary of main points 467 Acknowledgments 467 List of main symbols and acronyms 467 References Evolution of geotechnical risk analysis in North American practice 471 GREGORY B. BAECHER AND JOHN T. CHRISTIAN 12.1 Introduction Beginnings Geotechnical reliability ( ) Probabilistic veneer on deterministic models Variability of soil-engineering properties Slope stability analysis Lumped versus distributed parameter models Aleatory versus epistemic uncertainty Mining engineering ( ) Offshore reliability ( ) Environmental remediation ( ) Dam safety (1986-ongoing) Systems risk assessment (2005-ongoing) New Orleans California delta Risk registers Emerging approaches: System simulation, stress testing, and scenario appraisals 482

13 xvi Contents Systems simulation methods Stress testing and scenario analysis Dynamic risk analysis and management Ten unresolved questions Concluding thoughts 487 Acknowledgments 487 References Assessing the value of information to design site investigation and construction quality assurance programs 49. ROBERT B. GILBERT AND MAHDI HABIBI 13.1 Introduction Value of information framework Decision analysis Illustrative example: Remediation of contaminated lagoon Insights from Bayes' theorem Prior probabilities Likelihood functions Illustrative example: Design of pile foundation Implementation of value of information assessment Analytical methods Illustrative example: Design quality control program for compacted fill Numerical methods Illustrative example: Pile foundation load tests Case-history applications Site investigation for foundation design Remedial investigation for a contaminated site Exploration program for resources QA/QC testing Summary 529 Acknowledgments 531 References Verification of geotechnical reliability using load tests and integrity tests 533 LIMIN ZHANG 14.1 Introduction Within-site variability of pile capacity Updating pile capacity with proof load tests Proof load tests that pass Proof load tests that do not pass Proof load tests conducted to failure Multiple types of tests Updating pile capacity with integrity tests Reliability updating based on integrity tests Updating occurrence probability of toe debris 540

14 xvii Updating mean thickness of toe debris Cases of test outcome Reliability of piles verified by proof load tests Calculation of reliability index Example: Design based on SET and verified by proof load tests Accuracy effect of design methods Reliability of piles verified by integrity tests Worked example Survey of toe debris Updating the priors based on interface coring tests Updating reliability of piles based on interface coring tests Summary 555.Acknowledgment 556 List of symbols 556 References 557 nurrv Spatial variability Application of the subset simulation approach to spatially varying soils 561 RSHKAF AHMED AND ABDUL-HAMID SOUBRA IJ.l Introduction Karhunen-Loeve expansion methodology for the discretization of a random field 561 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 J Example applications Example 1: Generation of a random field by K-L expansion Example 2: Computation of the failure probability by SS approach in the case of random variables Example 3: Computation of the failure probability by an SS approach in the case of random fields 572 Zonclusion 574 Itx 15A: Modified M-H algorithm 575 symbols 576 a.s'erences 577 imux 579