Parameterized Modeling of Unfrozen Water in Frozen Soil Based on the Freezing Characteristics of Multicomponent Cation Solutions and the Electrical Double-Layer Theory of Clay Colloids

Soil freezing characteristics are predominantly governed by the mechanism of bound water, which essentially constitutes a multicomponent cations distribution within the electrical double-layer (EDL) on clay particles. The freezing behavior of bound water is determined by two critical factors: (a) the distribution characteristics of cation solutions; (b) the quantitative relationship between cation concentration and freezing point. Although EDL-based unfrozen water model has been proposed, the freezing characteristics of multicomponent cation solutions remain poorly understood. Our findings indicate that: (a) The synergistic effect of multicomponent cations increases the freezing point depression coefficient of bound water (i.e., the degree of freezing point lowering per unit concentration) by several-fold compared to NaCl solution; (b) For typical mineral soils with low Na⁺ content (<15%), a linear freezing point depression equation can accurately characterize the freezing process of multicomponent cation solutions; (c) typical mineral soils exhibit highly similar cation distribution characteristics. By integrating the freezing point depression equation with EDL theory, this study not only improves the EDL-based unfrozen water model but also develops a parameterized model applicable to typical mineral soils, and elucidating the intrinsic mechanisms of the model's robustness. Validation using measured data from 12 typical soil types demonstrates that this parameterized model can accurately predict unfrozen water content in sands, silts, and clays with low to moderate clay content within the temperature range of −0.263°C to −20°C. The study establishes a theoretical framework distinct from conventional water potential theory, thereby deepening the understanding of freezing characteristics in frozen soils.