Reliability analysis with consideration of asymmetrically dependent variables: Discussion and application to geotechnical examples

Abstract

The consideration of multivariate models in the reliability analysis is quite essential from practical perspective. In principle, complete information regarding the joint probability distribution function should be known in prior to the analysis. However, in real practice, only the marginal distribution and covariance matrix are known in most cases. Such incomplete probabilistic information could lead to dubious results if dependences are not fully catered. Asymmetric dependence is one of these factors influencing the quality of reliability analysis. In this paper, the influences of asymmetric dependences to the reliability problem are investigated. The copula theory as well as the concept of asymmetric dependences is briefly introduced. The techniques of constructing asymmetric copulas are, thereafter, provided in details. Geotechnical problem is selected in this study as examples in the reliability analysis. Based on the given information, a group of symmetric and asymmetric copulas are selected to model the dependences between cohesion and friction angle, the parameters more commonly used to characterize soil strength. The reliability analysis of a continuous spread footing and an infinite slope are then presented to demonstrate the influence of asymmetric dependences on reliability. The results showed that the failure probabilities of the investigated geotechnical problems are very sensitive to the adopted dependence structure, either symmetrically or asymmetrically. The commonly applied one parameter symmetric copulas, such as Archimedean copulas, may underestimate the failure probabilities. Furthermore, the asymmetric copulas are more powerful in characterizing the tail dependences structures of variables especially for asymmetric dependent variables.