Fast Monte Carlo Simulations and Safety Index Checking

by A. Sellier, Cent Natl de la Recherche, Scientifique, Cachan, France,
A. Mébarki, Cent Natl de la Recherche, Scientifique, Cachan, France,

Document Type: Proceeding Paper

Part of: Analysis and Computation


This paper presents recent techniques which require a small number of simulations to assess the structural reliability. They combine both the concept of importance zones in the random operating space and conditioning technique. The procedures developed herein are also a helpful tool to check the accuracy of the safety index: β value. Actually, in presence of non convex failure domains, the usual procedures used to locate the design point P*, defined as the nearest point on the limit state surface to the origin of the standardized gaussian operating space, may give erroneous results. The authors have developed probabilistic methods that can check whether the obtained design point is actually the true point. These procedures are ran in the case of RC structures involving several random variables. The collected results show that: *Monte carlo simulations may require a small number simulations, less than 100, to evaluate probabilities of failure which order ranges within the interval 10-6 to 10-5. *by conditioning technique (ie simulations performed outside hyperspheres centered on the space origin), the true design point P* and therefore the safety index β are correctly calculated. Any local minimum might then be detected and corrected.

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