Combined Thermal-Hydraulic-Mechanical Frost Heave Model Based on Takashi’s Equation

The purpose of this study is to establish a numerical simulation model that addresses the combined thermal-hydraulic-mechanical process of frost heave. Of the several practical frost heave estimation theories, the authors adopt Takashi’s equation, which has been successfully applied to one-dimensional frost heave estimation. In this paper, Takashi’s equation is used to assess the frost heave ratio during freezing. Takashi’s equation is expanded for a two-dimensional evaluation by introducing an anisotropic parameter to distribute the frost heave ratio in different directions. This model couples Fourier’s law for heat transfer and Darcy’s law for unfrozen water flow. Latent heat is seriously evaluated by equivalent heat capacity method. For the thermal and hydraulic processes, this model considers temperature- and pressure-dependent hydraulic conductivity by an empirical equation. Both saturated and unsaturated conditions are addressed in this model. A finite-element method is adopted, and the time domain solution employed is the widely accepted Crank–Nicolson method. Specifically, it is assumed that the pore water pressure head and water content at freezing are zero. In this situation, it is not necessary to consider the hydraulic condition during the freezing process because it is accepted that Takashi’s equation can deal with the hydraulic process of freezing. Future complex and detailed models will require a more complete understanding and formulation of the processes in freezing zone; however, this is outside the scope of this paper. Finally, in order to demonstrate the applicability of this model, simple examples and simulations are provided.