A mathematical model of freezing of unsaturated soils in the presence of capillary pressure

A mathematical model of freezing of soils saturated with a heterogeneous mixture of water and air in the presence of capillary pressure is proposed. The derivation of the diffusion equation for the redistribution of moisture from the laws of conservation of mass and momentum is given. This allows us to define the diffusion coefficient through the parameters of the porous medium and fluids. Balance relations through the water crystallization front is derived. A self-similar solution of the problem in the linear approximation is obtained. It is shown that the growth of capillary forces reduces the amount of ice formed, and a more intensive freezing regime leads to an increase in the saturation with ice.