Reliability Analysis in Geotechnics with Deterministic Finite Elements — Theoretical Concepts and Practical Application

Abstract

A comprehensive procedure for combining probabilistic concepts and deterministic finite element methods for geotechnical analysis is presented. Bayes’ theorem is employed to arrive at input parameters for the calculations combining different sources of information. A Taylor Series is adopted to identify the most important input parameters, and, consequently, a point estimate method (PEM) together with a finite element model is used to obtain a density distribution of a limit state function for a particular problem. A brief description of the theoretical background is given and an illustrative example analyzing a sheet pile wall supporting an excavation is presented to demonstrate the general applicability of the proposed approach. Finally, the application to numerical analyses of tunnel excavation is discussed in some detail. A NATM tunnel construction is analyzed, and the results obtained from the suggested approach are compared with the ones obtained from conventional finite element analyses. The results clearly reveal the applicability of the proposed concept for solving practical problems, and it is argued that the validity of finite element analyses is extended by introducing stochastic properties of input parameters. Finally, it is shown that the method provides a tool for decision making in optimizing support measures.