Predicting the Soil Freezing Curve via a Modified Clapeyron Equation

The soil freezing curve (SFC) is a constitutive equation describing unfrozen soil-water content and temperature under subzero conditions (below 273.15 K). The SFC governs various mechanical and hydrological behaviors of frozen soils. Most existing SFC frameworks attribute pore water freezing temperature depression to capillarity and model it using the capillary pressure-based Clapeyron equation. A theoretical synthesis based on the water phase diagram is performed and identifies that adsorption, rather than capillarity, is the dominant mechanism governing pore water freezing in soil. Under this premise, a novel closed-form SFC equation is developed, fully underpinned by adsorptive water retention and its local positive pore water pressure. The equation is formulated through three physical links: (1) linking water content to water potential using a soil-water retention curve (SWRC) equation for adsorptive water; (2) linking water potential to local pore water pressure via soil sorptive potential; and (3) linking local pore water pressure to freezing temperature using a modified Clapeyron equation. Experimental evaluations demonstrate that the proposed equation significantly outperforms existing models in predicting SFC from SWRC, while achieving comparable performance with existing models in fitting the SFC dataset for a wide range of soil types. Practical implication is demonstrated through predicting SFC directly from the soil-water isotherm or SWRC for representative soil types.