Efficient Geotechnical Reliability Analysis Using Weighted Uniform Simulation Method Involving Correlated Nonnormal Random Variables

Abstract

In the context of probabilistic analysis involving uncertain factors, efficient reliability methods play an important role for promoting a wider application in engineering practice. Although the ordinary Monte Carlo simulation (MCS) can simulate the probabilistic performance of a complex engineering system well and has been widely-employed in reliability analysis because of its simplicity and accuracy, the unavoidable computational burden to ensure sufficient accuracy often limits its use as a reference tool only for academic purposes. This paper proposes a modified weighted uniform simulation (WUS) method for reliability analysis involving nonnormal random variables, in which the Nataf transformation is adopted to effectively transform the correlated nonnormal variables into independent standard normal variables. This method takes into account the correlations between random variables, while the sample size is greatly reduced under the same accuracy requirements. Four examples of reliability analysis are presented to demonstrate the feasibility of the WUS method. It is shown that the proposed method can yield sufficiently accurate reliability analysis results with a reasonably small sample size compared to ordinary MCS. In particular, the most probable failure point (MPP), which is the basis for reliability-based design works, can also be directly obtained during the simulation process.