Theory of flow and deformation of swelling porous materials at the macroscale

We develop a theoretical foundations for a macroscale model for flow and deformation for a highly interacting porous media, i.e. a swelling porous media such as expansive soils by assuming the properties of the fluid phase are a function of the liquid volume fraction. We assume the porous material consists of a solid phase and liquid phase, that it swells when whetted and shrinks when dried, and that the process is isothermal. This is of interest when modeling settling due to the pumping of water or oil when there is a high clay content, compaction due to construction, or, in other fields, modeling soft bio-tissue, bones, or man-made porous materials. Here we review the assumptions and thermodynamical framework used to arrive at a generalized Darcy’s law for flow and then derive a generalized Terzaghi’s principle of effective stress.