Purpose: Mathematical model for studying the process of soil freezing given moisture migration is developed. Numerical modeling of temperature mode of railway subgrade at non-stationary pro-cess in cold climate conditions is performed. Methods: Numerical implementation of the model is performed by mathematical module processing in COMSOL Multiphysics program, which’s based on partial differential equations (PDE), with finite element method. The model reliability is con-firmed by the comparison with previous experimental data and the results of simulation by other authors. Results: Calculation results on the developed model basis show the best correlation with experimental data in comparison with the results for other models. Calculation example and calcu-lation results for subgrade temperature mode in freezing-thawing fifth cycle are presented. The analysis of soil freezing depth change and soil temperature fluctuation change by depth by fifth year are carried out. Practical significance: The developed mathematical model makes it possible to predict soil freezing depth, taking into account moisture migration, including freezing and thawing depth changes caused by climate warming. The developed model can be used both, to study the mechanism of subgrade temperature mode distribution at freezing and thawing, and to improve subgrade construction for to protect it from soil frost heaving.

Purpose: Methods for calculating soil freezing depth of high-speed railway subgrade are de-veloped given its multilayer structure. Methods: Existing methods for soil freezing depth calculation have been reviewed, advanced Berggren method for calculating soil freezing depth of HSR subgrade and numerically modeling method for subgrade temperature regime on the basis of mathematical model given moisture migration are proposed. The calculation reliability is confirmed by comparison with numerical simulation results and the results of the calculation by method based on Chinese and Russian railway construction standards. Re-sults: The results of soil freezing depth calculations by different methods are similar. It is reasonable to use advanced Berggren method to calculate soil freezing depth for multilayer system. Numerical modeling method makes it possible to predict soil freezing depth includ-ing depth change of freezing and thawing caused by climate warming. Practical signifi-cance: To calculate soil freezing depth of HSR subgrade, it is advisable to use advanced Berggren method. The developed model can be used both to study the logic of subgrade thermal regime distribution at freezing and thawing and to project the thickness of protec-tive layers against a frost for HSR subgrade construction.