Жуковська, Н. А. та Жуковський, В. В. та Zhukovska, N. А. та Zhukovskyі, V. V. (2020) МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ НАПРУЖЕНО-ДЕФОРМОВАНОГО СТАНУ БАГАТОШАРОВОГО ҐРУНТОВОГО МАСИВУ З ВРАХУВАННЯМ ФІЛЬТРАЦІЇ ЗАБРУДНЕНИХ РЕЧОВИН У НЕІЗОТЕРМІЧНИХ УМОВАХ. Вісник Національного університету водного господарства та природокористування (3(91)). с. 181-191.

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Анотація

В статті здійснено математичне моделювання просторового напружено-деформованого стану фільтруючого багатошарового ґрунтового масиву з вільною поверхнею. Знайдено зміщення, нормальні та дотичні деформації і напруження в досліджуваній області. Проведено аналіз отриманих результатів.

Title in English

MATHEMATICAL MODELING OF MULTILAYER SOIL MASSIF STRESS-STRAIN STATE UNDER POLLUTANTS FILTRATION IN NON-ISOTHERMAL CONDITIONS

English abstract

The article presents a mathematical modeling of the spatial stressstrain state of a filtering multilayer soil massif with a free surface. The mathematical model includes the following equations: the system of Lamé equations describing stress-strain state for displacements, equations of mass forces components, the equation of convective diffusion in the presence of mass and heat transfer for a watersaturated area of a soil massif, the equation of convective heat transfer, the generalized equation of filtration of salt solutions in nonisothermal conditions and the equation of continuity of a process in a water-saturated area of a soil massif, the specific flow of dissolved salts in the case of non-isothermal conditions in a water-saturated soil massif, the generalized Fourier law in the case of convective mass and heat transfer, the normal and shear strains, the normal and shear stresses. The basic equations are supplemented by boundary conditions for temperature, concentration of pollutants, pressures, displacements and stresses. For the numerical solution of the set boundary value problem is used the method of finite differences. Displacements, normal and tangential deformations and stresses, temperature, concentration of pollutantas, pressures in the study area were found. The analysis of the obtained results is carried out. As an example, the soil mass is considered, consisting of three subregions (clay water is saturated, sandy water is saturated and the soil is in its natural state (dry)). It is shown that the largest values of spatial displacements are achieved in the subregions of water-saturated sandy soil. In the sub-areas of clay soil, the displacements are smaller than in sandy water-saturated ones due to the slow passage of pollution filtration and mass and heat transfer.

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