Fully coupled poroelastic governing equations for groundwater flow and solid skeleton deformation in variably saturated true anisotropic porous geologic media

Abstract

The governing equation for solid skeleton deformation in a variably saturated true anisotropic porous geologic medium is derived from the macroscopic momentum balance equation for variably saturated solid skeleton. The governing equation for groundwater flow in a deforming variably saturated true anisotropic porous geologic medium is then derived from the macroscopic mass balance equations for water and solid constituent. Finally, these two governing equations constitute a set of fully coupled poroelastic governing equations for groundwater flow and solid skeleton deformation in variably saturated true anisotropic porous geologic media with appropriate constitutive mathematical equations, which are available from the literature, for the changes in the unsaturated hydraulic properties (i.e., degree of water saturation and relative hydraulic conductivity) by unsaturated water flow and the changes in the saturated hydraulic properties (i.e., porosity and saturated hydraulic conductivity tensor) by solid skeleton deformation.