Some free-boundary problems in deformable porous media

For nonlinear viscous and viscoplastic porous media with free-boundary surface, a mathematical model is proposed. The free-boundary surface is a priory unknown surface, which separates the parts of the porous body with a different properties. Typical examples of free-boundary are the phase interface, which separates the phases of material, in the theory of phase transformations and the surface between saturated and unsaturated parts of a porous body. The variational set up of problen is given that allow us to consider discontinuous solution of the problem. The boundary conditions on the unknown surface are obtained by using this variational formulation These conditions are required to determine the free-boundary surface. The results obtained in the paper can be used to model transport phenomena in saturated soils.