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.