A hydraulic conductivity model incorporating adsorption and capillarity for unsaturated/frozen soil

Hydraulic conductivity is a key parameter for describing seepage-related issues in soils. The soil water retention, soil water freezing, and soil water flow are essentially dominated by adsorption and capillarity. However, these mechanisms have not been effectively incorporated into a unified hydraulic conductivity model. This study proposes a hydraulic conductivity model based on the Navier-Stokes equations and capillary bundle model, which is applicable to both unsaturated and frozen soils. By considering the different influences of adsorption and capillarity on water flow and water freezing, the model can predict the hydraulic conductivities of soils in different states and distinguish the contributions of capillary flow and film flow to the total permeability. Benefiting from the consideration of physical mechanisms, the proposed model can use any of the soil water characteristic curve, the soil freezing characteristic curve, or the particle size distribution as input. The model achieves better prediction accuracy than existing models that do not consider the film flow and its reliability is validated through extensive experimental data including various sands, silts, and lean clays. This study not only provides an effective tool for predicting hydraulic conductivity but also highlights the underlying physical connections between soil water retention, soil water freezing, and seepage.