Modelling of particles retention in a porous soil

Abstract

Construction of foundations and underground structures requires grouting the soil for groundwater protection. To select the technology of soil grouting and the type of grout, it is necessary to calculate the suspended particles retention for the filtration of bentonite or cement-based suspension in a porous soil in dependence of sizes of the soil pores and the grains of the injected mortar. The study of transport and retention of solid particles in the complex structure of a porous medium makes it possible to calculate the strength and impermeability of a grouted foundation at the stage of pre-construction preparation.The solid particles retention in the nonlinear process of deep bed filtration of a suspension in a porous medium is considered. It is assumed that the retained particles can not be detached from the frame of porous medium by a fluid flow or suspended particles. The purpose of the study is to calculate the dynamics of deposit formation for different types of variable filtration coefficients with the predominance of the size-exclusion mechanism of particles capture.The mathematical model of filtration is the system of mass transfer equation and the kinetic equation of deposit rate with the conditions of injection of a constant concentration suspension into an empty porous medium. In this paper an exact solution of the problem at the inlet of a porous medium is constructed. The dynamics of retained particles growth is studied by numerical modeling method, depending on the type of blocking filtration coefficient.The dependence of retained particles concentration on time at the inlet of a porous medium for various blocking filtration coefficients was obtained. Plots of the dependence of the deposit concentration on time for smooth and non-smooth filtration coefficients are constructed.When reducing the number of free pores of small sizes, the filtration rate slows down. It is shown that slowing down the filtration process and the growth rate of the deposit are determined by the multiplicity of the root of the blocking filtration coefficient. Depending on the type of filtration coefficient, the process of retention of solid particles in a porous medium can last indefinitely, or it may cease after some time with complete blocking of small pores by retained particles. The limiting time for the end of the filtration is given by a compact analytical formula.