document: Non-linear analysis of nearly saturated porous media : theoretical and numerical formulation 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
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