Probabilistic Analysis of Soil-Water Characteristic Curve of Bentonite: Multivariate Copula Approach

Abstract

Measurement of the soil-water characteristic curve (SWCC) is time-consuming for soils such as bentonites. It is desirable to develop a first-hand estimate of SWCC from a statistical generalization of the available data. A database for SWCCs of bentonite was compiled from the literature. The proposed approach entails the parameterization of SWCCs and constructing a multivariate probability distribution for the SWCC parameters. The choice of parameter constraints has a significant impact on SWCC quantification, which has not been studied for bentonites. Therefore, a database from this study was used to investigate the effect of van Genuchten (vG) model constraints on SWCC parameter statistics of bentonite. The three-parameter vG model with parameters α,n, and m provided the best choice. Subsequently, trivariate probability distributions of parameters α,n, and m were constructed using Gaussian and t copulas. The proposed trivariate copula is suitable for modeling the asymmetric dependence structure of vG parameters. It was demonstrated that the proposed approach can be used to construct the confidence intervals for SWCCs of bentonites. In the absence of measured data, the trivariate distribution provides a first-hand estimate of the SWCC. It also can be used as an informative prior for updating site-specific limited data using a Bayesian approach.