Stochastic seepage and slope stability analysis using vine-copula based multivariate random field approach: Consideration to non-Gaussian spatial and cross-dependence structure of hydraulic parameters

Abstract

Stochastic seepage and slope stability analysis is conventionally performed in a random field framework. However, most of the studies are limited to Gaussian spatial and cross-dependence structure of hydraulic parameters. Using a well documented hydraulic conductivity (k) data from Borden aquifer, Canada (Sudicky, 1986), evidence of non-Gaussian spatial dependence is provided within a copula framework. It is shown that the non-Gaussian spatial dependence structure is a field reality for k. To handle the non-Gaussian spatial as well as cross-dependence structure, a multivariate random field framework based on vine copula theory is presented. It is shown that the vine-copula approach can efficiently model the non-Gaussian dependence structure of hydraulic parameters. For investigating the practical engineering importance of dependence structure, stochastic seepage and slope stability analysis under steady and transient seepage conditions is conducted. It is shown that the assumption of arbitrary spatial dependence structure, can significantly affect (by a factor of 100) the failure probability of slopes across the entire acceptable range (Salgado and Kim, 2014) of 10-4 to 10-2. It is also shown that the choice of spatial dependence structure is more crucial than the cross-dependence for stochastic seepage and slope stability analysis.