A numerical model for hydrothermal transport in unsaturated freezing soils considering thermodynamics equilibrium

The analysis of frost heave in unsaturated subgrade soils should consider the coupled movement of liquid water, vapor, and heat, accompanied by phase transition of water, vapor, and ice. In this paper, the equilibrium relationship of the three phases of water in soils was comprehensively considered, and the water head and vapor density were determined under frozen and unfrozen conditions from the perspective of thermodynamics. Based on that, the governing equations of mass and energy conservation were then derived and a new transient finite element model was developed, considering the behavior of the phase change and coupled hydrothermal transport under frozen as well as unfrozen conditions. Since the discontinuities between the frozen and the unfrozen zones may bring difficulties to the numerical solution, two kinds of smoothing techniques were proposed to solve the discontinuities at the phase transition interface, which guaranteed robust convergence and enhanced computational efficiency. The model proposed was verified by comparing with some available test results and applied to analyze the frost heave process of unsaturated subgrade under impermeable road pavements, demonstrating the model's accuracy and applicative prospect. It is revealed that the movement of liquid water and vapor in the frozen zones may still exist, and its mechanism and performance are different from that in unfrozen zones. The significance of vapor migration on the subgrade frost heave is also emphasized.