Estimation of the vertical diffusion coefficient of gas in compacted soils by means of mathematical modeling

The density properties of subsiding loess soils were studied within the framework of mathematical modeling of their compaction using the method of deep explosions. Soil compaction is carried out to eliminate subsidence properties. Loess soils are characterized by low density and high porosity. The density properties of loess depend on the parameters of the diffusion interaction of gas atoms formed as a result of the explosion and the soil being compacted. Solving inverse applied problems that arise when studying mathematical models of geological systems allows us to systematize knowledge about them. The work considers the inverse problem of estimating the diffusion coefficient. Mathematical modeling of the vertical diffusion coefficient in anisotropic and isotropic geological systems was carried out. The case of complete absorption of gas atoms by the surrounding soil has been studied. A numerical assessment of the coefficient of vertical diffusion in soil before and after compaction has been implemented, over time and with an accuracy sufficient for engineering calculations. Gas diffusion coefficients in soils of various densities were obtained. The constructed mathematical relationships for estimating the coefficient of vertical diffusion make it possible to predict the density properties of soils at the stage of designing the foundations of construction projects.