Reliability Analysis in Geotechnics with Finite Elements --- Comparison of Probabilistic, Stochastic and Fuzzy Set Methods

The finite element method is widely used for solving various problems in geotechnical engineering practice. The input parameters required for the calculations are generally imprecise. The paper is devoted to a comparison of probabilistic, stochastic and fuzzy set method for reliability analysis with respect to its applicability for practical problems in geotechnical engineering. Emphasis will be given by comparing the effects of modelling uncertainty using different methods, with special reference to the role of spatial correlation. After introducing some basic notions about the approaches, this article shows that the results obtained with the fuzzy set method for a simple bearing capacity problem agree with the outcomes by a probabilistic and a stochastic method. Advantages and shortcomings of either approach with respect to practical applications will be discussed.

[1]  Emilio Rosenblueth,et al.  Two-point estimates in probabilities , 1981 .

[2]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[3]  Helmut Schweiger,et al.  Reliability Analysis in Geotechnics with Deterministic Finite Elements Theoretical Concepts and Practical Application , 2001 .

[4]  M. Oberguggenberger,et al.  FROM PROBABILITY TO FUZZY SETS: THE STRUGGLE FOR MEANING IN GEOTECHNICAL RISK ASSESSMENT , 2022 .

[5]  R. Rackwitz,et al.  Reviewing probabilistic soils modelling , 2000 .

[6]  Gordon A. Fenton,et al.  Bearing Capacity of Spatially Random Soils , 2000 .

[7]  Arie Tzvieli.  Possibility theory: An approach to computerized processing of uncertainty , 1990, J. Am. Soc. Inf. Sci..

[8]  David H. Evans.  An Application of Numerical Integration Techniclues to Statistical Toleraucing , 1967 .

[9]  W. Jefferson Stroud,et al.  Probabilistic and Possibilistic Analyses of the Strength of a Bonded Joint , 2001 .

[10]  I. Elishakoff,et al.  Convex models of uncertainty in applied mechanics , 1990 .

[11]  H. Cudney,et al.  Comparison of Probabilistic and Fuzzy Set Methods for Designing under Uncertainty , 1999 .

[12]  M. Harr.  Probabilistic estimates for multivariate analyses , 1989 .

[13]  Christer Carlsson,et al.  On Possibilistic Mean Value and Variance of Fuzzy Numbers , 1999, Fuzzy Sets Syst..

[14]  T. Krishnamurthy,et al.  Optimized Vertex Method and Hybrid Reliability , 2002 .

[15]  R. B. J. Brinkgreve,et al.  Plaxis finite element code for soil and rock analyses , 2002 .

[16]  Andrzej S. Nowak,et al.  Integration formulas to evaluate functions of random variables , 1988 .

[17]  K. Phoon,et al.  Characterization of Geotechnical Variability , 1999 .

[18]  Erik H. Vanmarcke,et al.  Random Fields: Analysis and Synthesis. , 1985 .

[19]  K. S. Li.  Point-Estimate Method for Calculating Statistical Moments , 1992 .

[20]  Marco Savoia,et al.  Fuzzy number theory to obtain conservative results with respect to probability , 1998 .

[21]  S. Lacasse,et al.  Uncertainties in characterising soil properties , 1996 .

[22]  V. V. Sokolovskii,et al.  Statics of Granular Media , 1965 .