Probabilistic analysis of soil-water characteristic curve using limited data

Abstract

Soil-water characteristic curve is an essential constitutive relationship required for modelling unsaturated soil behaviour. Earlier supposed to be characteristic or unique for a particular soil, it is now well established that there are various sources of uncertainty which lead to different curves for the same soil. Hence it becomes necessary to probabilistically characterize soil-water characteristic curve for the purpose of reliability based design in unsaturated geotechnical engineering projects. Popular approach is to parametrize the soil-water characteristic curves into a set of curve fitting parameters and evolve the joint distribution of these parameters. However, a satisfactory probabilistic characterization requires large number of realizations and is practically not feasible since experimental measurement of soil-water characteristic curve is an expensive, time intensive and difficult task. For all practical purposes, it is impossible to obtain a large number of curves to arrive at the site-specific probability distribution. Therefore, this study proposes a Bayesian approach integrated with copula theory to obtain the joint probability distribution of soil-water characteristic curve parameters from limited number of curves. Limited number of curves are incorporated with prior knowledge to obtain the updated probability distribution of soil-water characteristic curve parameters. Efficacy of the proposed approach is demonstrated on three databases, one each for loam, fly ash and bentonite. Finally for demonstrating a practical application of the proposed approach, a site specific reliability based design of unsaturated slope is conducted.