Modeling hydraulic conductivity function of frozen soil

Hydraulic conductivity function for frozen soils (HCFF) is crucial for accurately simulating the water transfer process in cold regions, impacting hydrological states and frost heave diseases. However, the absence of HCFF model capturing the relation between hydraulic conductivity and unfrozen water content (θ) or temperature (T) has significantly impeded the numerical calculation of freezing seepage. To address this challenge, this study delves into HCFF encompassing both empirical and prediction models. This study begins with introducing θ-form and innovative T-form empirical HCFF models, showcasing their solid performance in fitting measured hydraulic conductivity data. Furthermore, the extension of the T-form empirical model to incorporate vapor flow and bimodal soils, through the introduction of maximum vapor conductivity and weighting factors, demonstrates a closer alignment with physical mechanisms and observed trends. In terms of predicting HCFF, the study provides a theoretical foundation through statistical hydraulic conductivity models and thermodynamic equilibrium in frozen soils. Additionally, it clarifies three routes for HCFF prediction—single Soil Freeze Characteristic Curve (SFCC), single Soil Water Characteristic Curve (SWCC), and a combination of the two—and validates their effectiveness through test results and comparison of HCFF prediction outcomes using SWCC and SFCC data from specific soil samples. In practice, the empirical and prediction models are recommended for available hydraulic conductivity data and available SFCC or SWCC data, respectively. Overall, this study not only lays the theoretical groundwork for most prediction models but also presents a valid empirical equation for modeling hydraulic conductivity function tailored specifically for frozen soils.