A theoretical model on unfrozen water content in soils and verification

•Premelting theory and crystallization theory are developed to solving water freezing in soil.•A theoretical model for unfrozen water content in soil is proposed and verified.•The correlation between nucleation rate and physical property of soil is built.•The contribution of influence factors for unfrozen water content is analyzed. Phase transition of pore water is a fundamental reason for frost heave in cold regions. Therefore, studying the variation in unfrozen water content is of great significance for understanding the freezing process of pore water and revealing the freezing mechanism in soils. In this study, a prediction model for unfrozen water content was established based on a probabilistic ice-forming model. To determine the heterogeneous nucleation rate, which is the key variation in the probabilistic model, the relationship between the water film thickness and temperature variation in the soil was characterized based on the improved premelting theory. In this process, the equivalent particle size and density of impurities on the surface of the particles were determined by introducing the particle size distribution curve and average accumulation mode of the particles. Based on the heterogeneous nucleation mechanism of ice crystals and the variation in the water film, a relationship between the heterogeneous nucleation rate and temperature was established. Subsequently, a method for calculating the equivalent contact angle related to pore water in soils was presented. The results showed that the heterogeneous nucleation rate and equivalent contact angle are positively and negatively correlated with the equivalent particle size at the same temperature, respectively, and the angle decreases with increasing solution concentration. Furthermore, the experimental data of 10 different soils showed that the variation in water content obtained by our model was in good agreement with the experimental values, particularly during the stage of rapid water phase change. The study developed an effective correlation among heterogeneous nucleation rate and equivalent contact angle of pore water and physical properties of soil, by combining crystallization theory and premelting theory, which provided a new way to explain water freezing and predict unfrozen water content in soils.