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This paper considers the artificial freezing of an argillite-like clay layer containing a NaCl salt solution in its pore space. The experimental results of the thermophysical properties of the clay with various salinities and water content in soil samples are presented. We determine the parameters of the soil freezing characteristic curves, the dependences of the specific heat capacity, and thermal conductivity based on temperature and salinity. These parameters are used in the formulation of a simple thermodynamic model for the artificial freezing of a clay layer with a single freezing pipe. The model includes diffusive transfer of heat and salt concentration, as well as salt precipitation when the eutectic point is reached. The motivation for using the simplified model is to understand the general patterns of soil freezing when considering the effect of salinity, as well as to test the proposed numerical finite-difference algorithm for solving the problem of freezing a clay layer based on the method of equivalent heat capacities. Using the algorithm, we analyzed the regularities of the redistribution of dissolved and precipitated salt in frozen soil, and also evaluated the effect of diffusive salt transfer on the numerical solution. [ABSTRACT FROM AUTHOR]