Page - 1467 - in Book of Full Papers - Symposium Hydro Engineering

principal normal strain and risk of fracture in the grouting zone - max. plastic vertical strain, etc.  Performing nonlinear analyses of all necessary designs defined by the sampling method.  Evaluation and determination of the probability of failure 5.1. RESULTS OF THE STOCHASTIC ANALYSIS In this investigation two reliability analyses by means of probabilities of failure are carried out. To determine the exceedance probabilities, an adaptive response surface method (ARSM) was used in combination with the First Order Reliability Method (FORM). For each reliability analysis, more than 600 designs were calculated in individual (here three) iteration steps. With each iteration step, new designs are created that are closer to the limit state. The approximation quality of the generated response surfaces is 99%. The total displacement V (nodal mean value at the abutment) is used as the evaluation criteria. For the derivation of the limit values, limit load analyses were carried out (due to load increase and due to resistance reduction). Two threshold levels were derived for the rating criterion V, which are V_1 = 0.05 m (near system failure) and V_2 = 0.03 m (transition to non-linear system behavior) Fig. 7 Reliability analysis V_2, All Design points in the space of the most important parameters; red dots: V > 0.03 m; blue dots: below the limit of 0.03 m 1467