A Statistical Model for the Relative Hydraulic Conductivity of Water Phase in Unsaturated Soils

Abstract

Permeability coefficients of fluids occupying the pore space of a porous medium have significant influence on the flow of these fluids through the porous medium. In the case of unsaturated soils, in addition to other parameters such as void ratio, void distribution, particle size distribution and initial density the degree of saturation also affects the permeability coefficient of water. The degree of saturation, in unsaturated soil, is directly related to the matric suction of the soil through soil water characteristic curve. Matric suction is one of the two stress state variables widely used to characterize the deformation behavior of unsaturated soils. Therefore, it can be stated that both flow and deformation behaviors of unsaturated soil are affected by the permeability coefficient of water. Numerical modeling of coupled deformation-flow behavior of unsaturated soil requires a mathematical equation that relates the permeability coefficient to the degree of saturation. Since the parameters that affect the permeability coefficient of water in unsaturated soil have similar direct or indirect effects on the soil water characteristic curve, permeability can be effectively predicted using the soil water characteristic curve as done in statistical models. In this paper, a statistical model is proposed for the permeability of water in unsaturated soil using soil water characteristic curve of the soil. The calibrated parameters of the soil water characteristic curve are directly used in the prediction of permeability with- out additional calibration using measured permeability data. The predictive capability of the new equation is verified by matching the measured data of eight different soils found in the literature.