Extension of subset simulation approach for uncertainty propagation and global sensitivity analysis

The subset simulation (SS) method is a probabilistic approach which is devoted to efficiently calculating a small failure probability. Contrary to Monte Carlo Simulation (MCS) methodology which is very time-expensive when evaluating a small failure probability, the SS method has the advantage of assessing the small failure probability in a much shorter time. However, this approach does not provide any information about the probability density function (PDF) of the system response. In addition, it does not provide any information about the contribution of each input uncertain parameter in the variability of this response. Finally, the SS approach cannot be used to calculate the partial safety factors which are generally obtained from a reliability analysis. To overcome these shortcomings, the SS approach is combined herein with the Collocation-based Stochastic Response Surface Method (CSRSM) to compute these outputs. This combination is carried out by using the different values of the system response obtained by the SS approach for the determination of the unknown coefficients of the polynomial chaos expansion in CSRSM. An example problem that involves the computation of the ultimate bearing capacity of a strip footing is presented to demonstrate the efficiency of the proposed procedure. The validation of the present method is performed by comparison with MCS methodology applied on the original deterministic model. Finally, a probabilistic parametric study is presented and discussed.