6. Governing Equations in Porous Media

The equations governing deformation of single-phase materials and the associated finite element formulations have been presented in Chaps. 3 and 5, respectively. While all materials are porous at some scale, they may be modeled as single-phase materials when the pores in the materials are macroscopically homogeneous and empty. In some cases, the stresses in the skeleton may be so much greater than those in the fluid that the effect of the fluid on the behavior of the skeleton may be neglected (e.g., dry concrete used in members supporting a bridge where the pores are filled with air). In a two-phase material (e.g., saturated soil), if the conditions (e.g., high permeability and/or slow loading) allow full drainage, the loading does not cause pressure build up and hence the fluid phase does not influence the behavior of the skeleton (i.e., the behavior of the skeleton under fully saturated and dry conditions are the same). At the other extreme, in a fully saturated material, if the conditions are such that relative movement of the fluid with respect to the skeleton is negligible (as in undrained behavior), the material may be modeled as a single-phase material. The theories presented in Chaps. 3 and 5 may then be used to model such problems.