Vertical and horizontal land deformation in a desaturating porous medium

Soil deformation due to the flow of two immiscible fluids can be described by a general three-dimensional deformation field coupled with a three-dimensional hydrologic flow field. The resulting system of equations provides the components of displacement, the pressure and the fluid saturations. The equations governing saturated-unsaturated soil deformation are obtained as a simplified subset of a more general multiphase formulation. These equations can be solved numerically using an iterative Galerkin finite element technique with a weighted implicit finite difference approximation of the time derivative. A mixed stress-displacement formulation of the governing equations provides the flexibility necessary to consider both stress and displacement boundary conditions. The model predicts the commonly ignored horizontal displacements in a variably saturated system undergoing simultaneous desaturation and deformation. This is accomplished using completely coupled stress and pressure fields. The model provides vertical and horizontal displacement and changes in pressure (head) and saturation as a result of fluid withdrawal in a phreatic aquifer.