Non-linear analysis of nearly saturated porous media: theoretical and numerical formulation Original Research Article

A formulation for a porous medium saturated with a compressible fluid undergoing large elastic and plastic deformations is presented. A consistent thermodynamic formulation is proposed for the two-phase mixture problem; thus preserving a straightforward and robust numerical scheme. A novel feature is the specification of the fluid compressibility in terms of a volumetric logarithmic strain, which is energy conjugated to the fluid pressure in the entropy inequality. As a result, the entropy inequality is used to separate three different mechanisms representing the response: effective stress response according to Terzaghi in the solid skeleton, fluid pressure response to compressibility of the fluid, and dissipative Darcy flow representing the interaction between the two phases. The paper is concluded with a couple of numerical examples that display the predictive capabilities of the proposed formulation. In particular, we consider results for the kinematically linear theory as compared to the kinematically non-linear theory.