Reliability Analyses in Geotechnics with Finite Element Method

It is well known that material parameters of geomaterials may scatter within a considerable range. Thus, a high degree of uncertainty may be introduced in any type of analysis if material parameters are treated as deterministic values. There is no agreement about what method should be used for solving geotechnical problems, where only little information is available about uncertainties, because site investigation and laboratory testing performed for practical projects are usually not sufficient for a stochastic description of the material. In the developed methodology point estimate methods (PEM) for probabilistic analyses and fuzzy set method for possibilistic analyses together with a finite element model are used to obtain a density distribution of a limit state function or a membership function for a particular problem. Both variability and spatial correlation lengths of material properties can affect the reliability of geotechnical systems. The finite element analysis has been combined with theories mentioned above to investigate the influence of material variability and spatial correlation lengths on different practical geotechnical problems. The developed methodology will be applied for a bearing capacity problem, for slope stability analysis, deep excavations and for the analysis of tunnel excavations according to the principles of the New Austrian Tunnelling Method (NATM).