Series capillary bundle model for simultaneously estimating the hydraulic conductivity for saturated frozen soil and unfrozen unsaturated soil

Estimation of the hydraulic conductivity of saturated frozen soil (SFS) and unsaturated unfrozen soil (UUS) is crucial for understanding the water flow process. This study proposed a new model for simultaneously estimating the hydraulic conductivity of the SFS and UUS based on a series capillary bundle model wherein the radius of the capillaries varies along the length and an assumption that the soils in different temperature or suction conditions were regarded as a series of independent porous media. The model does not require consideration of the probability of the connection between the pores with different diameters. Given the relation between the pore size distribution (PSD) and the soil freezing characteristic curve (SFCC) and the soil water characteristic curve (SWCC), the model was expressed as a function of temperature, suction, liquid water content, and saturation. To examine the model’s validity, the predictions of 12 SFS and 18 UUS samples were calculated and compared with the measured data. The results revealed the model validity and significance of tortuosity. To attain appropriate tortuosity, empirical formulas for the SFS and UUS were determined by the inversion method and performed better than the previous three tortuosities. Additionally, the influences of hysteresis, saturated water content, and ice lens on hydraulic conductivity are discussed. The proposed model is more realistic and proves that the model developed based on the PSD can simultaneously predict hydraulic conductivity for the SFS and UUS.