
12(85) 2015 MATHEMATICS
I.G. Akhmerova
Selfsimilar Solution of Moving Water and Air Problem in a Deformed Soil
This paper describes the process of water and air filtering in a deformed soil. Soil is a threephase medium consisting of water (i = 1), air (i = 2), and a solid deformable porous medium (i = 3). The mathematical model is presented by the equation of the conservation of mass and momentum of the porous medium at saturation with water and air. The equation of motion and the law of deformation of the porous matrix take into account the effect of capillary forces. The problem is formulated, and the modification of the system of equations is carried out. As a result of the modification, the law of conservation of momentum for water and air is written as Darcy’s law, the law of conservation of momentum for a solid matrix is formulated with consideration of Terzaghi’s principle, the generalized Hooke’s law, and the effect of capillary forces. The solution to the problem of motion of air and water in a deformed medium in the form of a traveling wave is investigated. The equations for saturation and porosity are derived. This model can be used to calculate critical values of saturations, wherein on the free surface under the action of capillary forces tension cracks arise. This is the effect of the surface soil degradation during drought.
DOI 10.14258/izvasu(2015)1.214
Key words: multiphase flow, porous medium, saturation, deformed soil, destruction of soil
