Modeling multivariate cross-correlated geotechnical random fields using vine copulas for slope reliability analysis

Abstract

Modeling multivariate cross-correlated random fields plays an important role in reliability analysis of geotechnical systems. The cross-correlation among random fields is commonly characterized by the Nataf transformation using a correlation coefficient matrix, which is equivalent to considering the Gaussian dependence structure from the perspective of the copula theory. In this study, a generic approach for modeling multivariate cross-correlated geotechnical random fields based on vine copulas is proposed. This approach can incorporate the diversity and non-Gaussianity of dependence structures in the cross-correlation characterization. A four-variate geotechnical dataset is used to verify the proposed approach and the results illustrate that the statistics of generated random field realizations are comparable with the predefined values. Furthermore, the application of the proposed approach to reliability analysis of soil slopes with spatially varying soil parameters (cohesion, friction angle, and unit weight) is presented. The results indicate that considerably different probabilities of slope failure are produced by different vine-copula models. The conventional Nataf transformation (i.e., vine-Gaussian copula model) may considerably underestimate the probability of slope failure. The difference of reliability results for different vine models is generally enlarged as the level of the failure probability becomes lower. The proposed approach provides a more flexible way for geotechnical practitioners to characterize the cross-correlation among geotechnical random fields compared with the Nataf transformation, and is applicable to reliability analysis of various geotechnical systems.