SOLUTION TO FILTRATION PROBLEM WITH LINEAR POROSITY FUNCTION
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Abstract
Injection techniques are an effective tool for road construction, repair and maintenance. They allow solving a wide range of problems related to soil reinforcement, pavement rehabilitation and drainage improvement, ensuring durability and reliability of road infrastructure. Injection of various compositions (cement, polymer, silicatized) into weak soils (peat, clay, silt) can increase their bearing capacity, reduce deformations and prevent roadway subsidence. In addition, injection compositions fill voids and cracks formed as a result of erosion, soil erosion or vibration from traffic, which prevents further destruction of the road base. The study of depth filtration in injectable soil reinforcement techniques is a key aspect for optimizing and improving the effectiveness of these technologies. It helps to understand how injection solutions penetrate the soil, how they interact with the soil, and how this process can be controlled to achieve the best results. In this paper, the problem of suspension filtration in a heterogeneous porous medium with a linear porosity function varying as a function of spatial coordinate is solved. The exact solution to the problem is found. Asymptotic solutions of the concentrations of suspended and retained particles for the case of insignificant porosity measurement are obtained.
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