Reinterpreting the segregation potential model for frozen soils

Abstract

For the past half-century, the segregation potential (SP) model has been extensively employed for characterizing heat and water transfer during soil freezing. However, the relation of SP with temperature and its applicability in unsaturated soils remains unclear, restricting the application scope of SP model to the thermal steady state of saturated frozen soil. To address the aforementioned issues, this study first reinterprets the classical SP model using thermodynamics, yielding the general SP function G(T). After that, the dynamic G(T) model is proposed for saturated-unsaturated soils. Moreover, by adopting the proposed G(T) function, the steady thermal profile of freezing soil column is analytically solved. Finally, an extended SP model is proposed based on the aforementioned insights. The main findings were as follows. (1) The newly introduced G(T) function extends the classical SP into a continuous function with temperature, which can be transformed from the hydraulic conductivity function of frozen soils. The classical SP parameter is essentially an average value of G(T) among frozen fringe. (2) The proposed dynamic G(T) model can uniformly express G(T) curves amidst varying degrees of saturation. (3) At the stable freezing state, the temperature profile is analytically nonlinear in the frozen fringe. (4) The extended SP model refines the governing equations and applicable scenarios of SP model, bringing new understandings regarding soil freezing and ice segregation process. In summary, this study not only clarifies the ambiguities but also strengthens the theoretical foundation and mathematical expression of the SP model.