Model of Isothermal Internal Erosion in Deformable Soil
In this paper, a mathematical model of isothermal internal erosion in a poroelastic medium is considered. Removal of moving solid particles from a flow region happens after achieving a certain value of a filtration rate. The equations of mass conservation and Darcy law for water, air and moving solids are taken as constitutive equations of the mathematical model. The motion of the solid skeleton is modeled by the equation of mass conservation with "solid skeleton-moving particles"phase transition, the law of momentum conservation for the entire system, and an equation for effective pressure and porosity in the form of Maxwell's rheological law. In section 1, a statement of the problem is given and a brief review of internal suffusion models is presented. In section 2, the hypotheses determining intensity of the phase transition are described. In section 3, development of the composite type system is discussed. A degenerate parabolic equation for the saturation of water phase, an elliptic equation for a so-called "reduced pressure and a first-order equation for the porosity and velocity of soil are the development results. It is shown that there is a similarity with the classical Musket-Leverett model of two-phase filtration.