Phase Front Perturbations in Unsaturated Soils under the Rainwater Infiltration
Abstract
The paper is devoted to the study of rainwater infiltration influence on temperature, water saturation, and permafrost thawing. In general case, the problem is very complicated due to a lot of factors to be taken into account. We consider here a one-dimensional problem without including evaporation, vegetative layer, and radiation. The domain between a daylight surface and a thawing front is filled with soil that is considered as porous media with immovable skeleton and pores containing water and air. The domain ahead of phase change boundary is occupied with frozen soil with pores containing ice and air. The model is constructed under the following assumptions: water and ice are incompressible, air is a perfect viscous gas; temperature and pressure are common for skeleton and pores; the soil surface is under the action of falling rain with given temperature and rate. The system of governing equations in frozen and thawing soil consists of mass and energy conservation laws completed with generalized Darcy’s law and the Clapeyron equation. The conditions on phase change boundary that coincides with the line of discontinuity of water saturation are obtained in a standard way from the conservation laws under the assumption of temperature and pressure continuity. The velocity of rain on the ground surface is assumed to be given, and that leads to assuming the condition for the pressure. Nonlinear system of equation with the free boundary is considered to be linearized on the stationary solution of the problem with the absence of rain. The numerical simulation algorithm for a linear problem is elaborated, and the numerical results are provided.
DOI 10.14258/izvasu(2015)1.1-18
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