Equations for soil freezing characteristics curves based on the thermodynamics principles

Experimental studies related to the thermo-hydro-mechanical-chemo (THMC) behaviors of unsaturated frozen soils are cumbersome, expensive, and time consuming. For this reason, several researchers suggested mathematical models exploiting the strong relationships between the soil freezing characteristics curve (SFCC) and the THMC behavior of unsaturated frozen soils. However, the physical meanings of parameters in the available models are not clearly defined; hence there are limitations in providing rational interpretation of the frozen unsaturated soils behavior. In the present study, SFCC models with well-defined model parameters are developed extending thermodynamics principles and are linked to well-known soil–water characteristics curves (SWCC) models from the literature. Various zones in the SFCC are discussed along with providing rational explanation for the hysteretic effects using the proposed models. In addition, comparisons are provided between the measured results from experimental studies and the predicted results using the proposed models successfully highlighting the effects of salinity and the initial water content on the frozen unsaturated soils. The SFCC models proposed in this paper are promising and can be used for rigorous interpretation and in the prediction of the complex THMC behaviors of frozen unsaturated soils.