Modeling multivariate distribution of multiple soil parameters using vine copula model

Abstract

This study introduces the vine copula model to model the multivariate distribution of multiple soil parameters. First, the conventional bivariate and multivariate copulas are presented to model the joint probability distribution of soil parameters. Then, the procedure for modeling the multivariate distribution of soil parameters using the vine copula model is explained. Finally, two soil databases (CLAY/5/345 and CLAY/6/535) containing complete multivariate data of multiple soil parameters are studied to demonstrate the validity of the vine copula model. The results indicate that there exist different levels of correlation between all pairs of soil parameters. The dependence structure among multiple soil parameters shows obvious diversity and non-Gaussianity, which cannot be adequately characterized by the commonly-used multivariate normal distribution. The vine copula model performs well in modeling the multivariate distribution of multiple soil parameters. It can effectively consider the diversity and non-Gaussianity in the dependence structure among multiple soil parameters. In comparison with the original distributions, the coefficients of variation (COVs) for the conditional distributions of soil parameters may be significantly reduced. The incorporation of more information may produce smaller COVs for the conditional distributions. The reduced COVs for soil parameters can be eventually converted to cost savings in the reliability-based design of geotechnical structures, which provides an incentive for geotechnical engineers to collect more information of soil parameters from various sources.