Prediction and modeling of permeability function and its application to the evaluation of breakthrough suction of a two-layer capillary barrier

Different empirical formulas have been proposed to describe the water retention curve (WRC) and relative permeability (kr) of soils. This paper presents a Bayesian framework that evaluates not only the most probable empirical fitting constants, but also their joint probability density function. A dataset containing two soil classes — sand and silty loam — compiled from the UNSODA database is used for illustration. First, model constants of the van Genuchten’s WRC formula are calibrated and subsequently used to predict kr of the studied soils using two existing formulas based on Mualem’s and Burdine’s models. The best estimated kr in both formulas is found to skew towards the lower side of the measurement. Then, a new three-parameter empirical formula is proposed to describe kr with suction while the model constants are calibrated from the permeability data. Using the proposed framework, the statistical distribution of kr and subsequently the unsaturated permeability (kunsat), as a function of suction, can be obtained. The results are then applied to a hypothetical two-layer capillary barrier composed of soils of the compiled dataset to determine the breakthrough suction (ψBT) of the barrier. The proposed Bayesian approach gives a probabilistic distribution of ψBT instead of a single value in the traditional deterministic method.