A triphasic model for unsaturated soil based on the theory of porous media

In the present contribution, the formulation of the governing equations of coupled flow and deformation processes in saturated and unsaturated soils is based on the well-founded theory of porous media (TPM). Embedded in this concept, the model under consideration represents a triphasic medium of a cohesive-frictional elastoplastic solid skeleton and a binary pore-fluid, which is composed of a materially incompressible liquid (wetting phase) and a materially compressible gas (nonwetting phase). The unsaturated domain (saturation in terms of liquid saturation) of the porous medium is included in the model by the application of a capillary-pressure-saturation relation, which takes into account the interaction of the solid skeleton and the two pore-fluids. Furthermore, the interaction is described by Darcyʹs filter law including a relative permeability, which depends on the deformation of the pore space and the degree of saturation. Finally, a corresponding finite element formulation is presented and applied to a volumetrically strongly coupled solid-fluid-problem.