Numerical and Asymptotic Solutions for Multi Particle Bridging in Filtration Process

Abstract

The preservation of cultural and historic buildings is an important task for society. Historical buildings are prone to the appearance of numerous cracks and damage, therefore they require strengthening of their foundations and soils. Strengthening the foundations of historic buildings using injection methods is a technique used to improve and restore the foundations of old or damaged buildings. This method involves injecting special injection materials into the soil or foundation structure to improve its bearing capacity, stability and durability. The study of suspension flow with suspended solids in a porous medium is an integral part of ensuring the effectiveness of injection techniques. The paper considers a classical filtration model with a nonlinear filtration function. As a concentration function, a fifth-degree polynomial is used, describing the dimensional mechanism of particle capture in combination with the formation of arched partitions consisting of three or five particles blocking the pores. The considered problem with nonlinear filtration function and concentration function does not have an analytical solution, the paper presents its numerical solution using finite difference schemes. In addition to the numerical solution, expressions of analytical asymptotic solutions are obtained, which approximate the numerical solutions quite well even at sufficiently large values of time.