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Abstract. The structure of underground waters and water permeability of rocks must be taken into account when choosing the location of construction objects, the design of tunnels, hydraulic and underground structures. The model of filtration for suspension in solid porous medium during its displacement with clean water is considered. The numerical calculation of boundary of two phases is carried out and concentrations of suspended and retained particles are calculated for different values of porosity and permeability of the porous medium.

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The filtration problem is one of the most relevant in the design of retaining hydraulic structures, water supply channels, drainage systems, in the drainage of the soil foundation, etc. Construction of transport tunnels and underground structures requires careful study of the soil properties and special work to prevent dangerous geological processes. The model of particle transport in the porous rock, which is based on the mechanical-geometric interaction of particles with a porous medium, is considered in the paper. The suspension particles pass freely through large pores and get stuck in small pores. The deposit concentration increases, the porosity and the permissible flow of particles through large pores changes. The model of one-dimensional filtration of a monodisperse suspension in a porous medium with variable porosity and fractional flow through accessible pores is determined by the quasi-linear equation of mass balance of suspended and retained particles and the kinetic equation of deposit growth. This complex system of differential equations has no explicit analytical solution. An equivalent differential equation is used in the paper. The solution of this equation by the characteristics method yields a system of integral equations. Integration of the resulting equations leads to a cumbersome system of transcendental equations, which has no explicit solution. The system is solved numerically at the nodes of a rectangular grid. All calculations are performed for non-linear filtration coefficients obtained experimentally. It is shown that the solution of the transcendental system of equations and the numerical solution of the original hyperbolic system of partial differential equations by the finite difference method are very close. The obtained solution can be used to analyze the results of laboratory research and to optimize the grout composition pumped into the porous soil.

Abstract. The filtration problem describes the process of concreting loose soil with a liquefied concrete solution. The filtration of 2-types particles suspension in a homogeneous porous medium with a size-exclusion particles retention mechanism is considered. The difference in the filtration coefficients of 2-types particles leads to the separation of the filtration domain into two zones, in one of which two types of particles are deposited and in another -only particles of one type are deposited. In this paper, the mobile boundary of two zones is calculated, and numerical solution of the problem is calculated.

The injection method of soil stabilization is one of the methods to improve the soil base during the road construction. This method consists in the introduction of special compounds into the ground with the help of special equipment. Such compositions, as a rule, are solutions of polymers or cement, which harden, forming a solid base. The advantages of the injection method of soil stabilization for roads include rapid completion of work, minimal environmental impact, the possibility of application in difficult geological conditions, as well as strengthening the soil base at great depth. Injection solutions penetrate into microcracks and micropores of soils, forming a deposition. The study of liquid filtration in a porous soil system is of great practical importance. The paper considers the filtration of liquid in a porous medium with three types of particles. In the considered problem, each of the three types of suspension particles is characterized by its linear filtration function. It determines the size-exclusion particle capture mechanism, in which particles whose diameter exceeds the size of the pores get stuck in them, the rest pass through them unhindered. Numerical solutions are obtained for the concentrations of suspended particles of three types, as well as the total deposition. Depending on the initial parameters of the problem, the concentrations of suspended particles are either monotonic functions or non-monotonic, reaching the maximum value. In this paper, asymptotic solutions are constructed for the concentrations of suspended and retained particles near the concentration front, which are compared with numerical ones. The solution is obtained at infinity using a traveling wave.

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The filtration problem of a suspension in a porous medium is relevant for the construction industry. In the design of hydraulic structures, construction of waterproof walls in the ground, grouting the loose soil, it is necessary to calculate the transfer and deposition of solid particles by the fluid flow. A one-dimensional filtration problem of a monodisperse suspension in a porous medium with a size-exclusion capture mechanism is considered. It is assumed that as the deposit grows, the porosity and admissible flow of particles through the porous medium change. The solution of the initial filtration model and the equivalent equations are calculated. For the numerical calculation of the problem, both standard first-order finite difference formulas and more accurate second-order schemes were used. The obtained solutions are compared with the results given by the TVD-scheme.