Nonlinear problem of unsaturated frozen soil thawing in the presence of capillary forces

The problem of ice melting in unsaturated frozen soil in the presence of the capillary pressure in the water-air zone is formulated. The complete system of boundary conditions on the phase transition front is derived. For solving the nonlinear problem a numerical method is proposed. The dependence of the water saturation distribution on the form of the Leverett function, the capillary pressure, and the external pressure and temperature gradients is investigated. In the limiting case of saturated frozen soil the numerical and analytical solutions are compared.