Determination of site-specific soil-water characteristic curve from a limited number of test data – A Bayesian perspective

Determining soil–water characteristic curve (SWCC) at a site is an essential step for implementing unsaturated soil mechanics in geotechnical engineering practice, which can be measured directly through various in-situ and/or laboratory tests. Such direct measurements are, however, costly and time-consuming due to high standards for equipment and procedural control and limits in testing apparatus. As a result, only a limited number of data points (e.g., volumetric water content vs. matric suction) on SWCC at some values of matric suction are obtained in practice. How to use a limited number of data points to estimate the site-specific SWCC and to quantify the uncertainty (or degrees-of-belief) in the estimated SWCC remains a challenging task. This paper proposes a Bayesian approach to determine a site-specific SWCC based on a limited number of test data and prior knowledge (e.g., engineering experience and judgment). The proposed Bayesian approach quantifies the degrees-of-belief on the estimated SWCC according to site-specific test data and prior knowledge, and simultaneously selects a suitable SWCC model from a number of candidates based on the probability logic. To address computational issues involved in Bayesian analyses, Markov Chain Monte Carlo Simulation (MCMCS), specifically Metropolis-Hastings (M-H) algorithm, is used to solve the posterior distribution of SWCC model parameters, and Gaussian copula is applied to evaluating model evidence based on MCMCS samples for selecting the most probable SWCC model from a pool of candidates. This removes one key limitation of the M-H algorithm, making it feasible in Bayesian model selection problems. The proposed approach is illustrated using real data in Unsaturated Soil Database (UNSODA) developed by U.S. Department of Agriculture. It is shown that the proposed approach properly estimates the SWCC based on a limited number of site-specific test data and prior knowledge, and reflects the degrees-of-belief on the estimated SWCC in a rational and quantitative manner. Keywords: Soil–water characteristic curve, Bayesian approach, Unsaturated soils, Degrees-of-belief, UNSOD