A Mathematical Model for the Hydraulic Properties of Deforming Porous Media

Abstract

AbstractA new and relatively simple mathematical model is presented to predict the changes in porosity and saturated hydraulic conductivity that result from the skeletal deformation of porous media. A mathematical expression for the deformation‐dependent porosity is derived from the relationship between porosity and volumetric strain, assuming that the individual solid grains are relatively incompressible or less deformable compared to the solid skeleton of a porous medium. A mathematical expression for the deformation‐dependent saturated hydraulic conductivity is then obtained by substituting the deformation‐dependent porosity into the Kozeny‐Carman equation, assuming that the shape factor of the saturated hydraulic conductivity is independent of the skeletal deformation of the porous medium. To evaluate the effects of the deformation‐dependencies of the hydraulic properties on poro‐elastic consolidation, the mathematical model is applied to two different numerical experiments on fully saturated porous media. The simulation results show that the deformation‐dependencies of the hydraulic properties intrinsically induce hydraulic heterogeneity and nonlinear consolidation, and hence produce different trends than those obtained from analytical or numerical solutions with an assumption of constant hydraulic properties. Although the mathematical model presented in this paper is not applicable to all hydrogeomechanicai phenomena, the methodology should have useful application in many consolidation problems.