Numerical model for saturated-unsaturated flow in deformable porous media 1. Theory

A theory is presented for numerically simulating the movement of water in variably saturated deformable porous media. The theoretical model considers a general three‐dimensional field of flow in conjunction with a one‐dimensional vertical deformation field. The governing equation expresses the conservation of fluid mass in an elemental volume that has a constant volume of solids. Deformation of the porous medium may be nonelastic. Permeability and the compressibility coefficients may be non‐linearly related to effective stress. Relationships between permeability and saturation with pore water pressure in the unsaturated zone may be characterized by hysteresis. The relation between pore pressure change and effective stress change may be a function of saturation. In the transition zone where pore water pressure is less than atmospheric but greater than air entry value, soil moisture diffusivity as used in soil physics and coefficient of consolidation as used in soil mechanics are shown to be conceptually equivalent. It is believed that this model will be of practical interest in studying saturated‐unsaturated systems undergoing simultaneous desaturation and deformation.