Analysis of heat–moisture coupling transfer for unsaturated soil under freezing and thawing based on fractal theory

Frost heave- and thaw settlement-induced frost damage in cold regions is related to moisture–heat transfer. Various mathematical models have previously been proposed. Numerical simulation largely depends on the forms of mathematical descriptions and appropriately determined model parameters, which have yet to be further investigated. In this paper, unsaturated soils under closed-form freezing and thawing were adopted as study objects, while frost heave or thaw settlement was ignored, and only heat and moisture transfer was considered. Seepage parameters of partially frozen soil characterized by fractal theory were introduced. The relative saturation concept was constructed, and the solid–liquid ratio was defined. A new heat-moisture coupled model was proposed for soil freezing and thawing through mathematical transformation of a previously proposed well-recognized coupled model. The model, with the relative saturation and temperature as field variables, was integrated into COMSOL software via secondary development. The feasibility and effectiveness of the model were verified by comparing the calculated and measured temperature and moisture results in the freezing and thawing process. Furthermore, the proposed mathematical model was evaluated considering three error indices. The temporal evolution of moisture and influence of the boundary temperature on the coupled process were examined. The findings of this study could provide a reference for practical engineering applications.