Solution of the problem of temperature field distribution in a soil massif by numerical methods

Introduction. Almost a quarter of the Earth’s landmass and two thirds of the territory of the Russian Federation, including significant areas with a high concentration of natural resources and minerals, are located in the permafrost zone. These soils have structural instability: temperature fluctuations lead to a radical decrease in their strength characteristics and the development of significant deformations, which can critically affect the safety and reliability of buildings and structures. The geographical features of the Russian Federation necessitate the development and refinement of computational methods for determining temperature fields in the bases of cryolithozone soils. This paper discusses the implementation of the problem of freezing and thawing of a soil mass using numerical methods.

Materials and methods. The main provisions of a nonlinear mathematical model describing temperature transformations in a soil body, taking into account the phase transition of a pore liquid into ice and the corresponding thermophysical processes, are presented. The model was implemented in a specialized software package developed by the authors that implements the finite element method.

Results. As part of the study, numerical calculations of the temperature effects of buildings and structures under construction on the soil mass in a flat substitution were carried out. Numerical models were considered taking into account the impact of boundary conditions of various types on the computational domain. The results of numerical calculations were compared in detail with the results of similar calculations performed in proven software packages.

Conclusions. In this paper, the main mechanisms of a numerical model describing temperature transformations in a soil body are formulated and their implementation using the finite element method is proposed. Additionally, recommendations are presented on the further development of the numerical model, including the solution of the deformation problem of determining the precipitation of thawing of a soil body.

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