IMPORTANCE ZONE AND IMPORTANCE SAMPLING IN RELIABILITY-ANALYSIS OF CIVIL STRUCTURES

The authors present an efficient method to reduce the number of simula tions when dealing with small values of the probability of failure. Th is technique combines the attractive features of the importance sampli ng procedures with the properties of the importance zone, located arou nd the design point in the random operating space. This method can be ran in the context of implicit form of the limit state surface (finite element context for instance). A theoretical approach is developed in order to adapt the statistical distributions to the size of the mesh in the case of uniform stress. The proposed methods have been applied to analyse the reliability of civil structures: reinforced concrete st ructures. The obtained results show that probabilities of failure, eve n small in the order of 10(-5), may be obtained with accurate precisio n with only 30 to 100 simulations, once the design point is located. T he sensitivity of the reliability to the concrete quality, for instanc e (expressed through the standard deviation of the concrete compressiv e strength) shows that the distribution parameters must be fitted to t he size of the mesh. Otherwise the probability of failure may be dange rously under-estimated. The results concerning the volume effect are i n good accordance with the experimental results.