Analytical Study on Water and Heat Coupling Process of Black Soil Roadbed Slope in Seasonal Frozen Soil Region

The hydrothermal properties of black soils in seasonal frozen regions are more complex during the freezing process. In the context of the freezing and thawing cycles of black soil within seasonal freeze–thaw regions, there is a limited application of mathematical models to characterize the interplay between water and thermal dynamics. Therefore, existing models for analyzing water and heat in black soil in seasonal frozen regions may not be applicable or accurate. The application of existing models to the water and heat problems of black soil in seasonal frozen regions is important and innovative. This study is grounded in Darcy’s law pertaining to unsaturated soil water flow and is informed by principles of mass conservation, energy conservation, and conduction theory. The research begins with the establishment of definitions for relative saturation and the solid–liquid ratio through mathematical transformations. Subsequently, a theoretical model is developed to represent the water–heat coupling in black soil, utilizing relative saturation and temperature as field functions. The model’s validity is confirmed through its integration with experimental data from a black soil freezing and thawing model test. Furthermore, the analysis delves into the distribution of the temperature field, water field, and ice content that arise from the phase change processes occurring during the freezing and thawing of black soil roadbed slopes. There is a theoretical basis for the prevention and control of disasters associated with black soil roadbed slopes in seasonal frozen areas.