A new integral model for predicting the hydraulic conductivity of saturated frozen soil

Hydraulic conductivity of frozen soil is indispensable for describing water flow process in freezing soils. However, this conductivity is difficult to measure in the laboratory. So, the objective of this study is to propose a simple and smooth hydraulic conductivity model for saturated frozen soil based on the soil freezing characteristic curve (SFCC). Considering that the volume of pore water approximately represents the pore volume, the distribution of effective pore radii changed as a function of temperature was determined by combining the SFCC and the Gibbs-Thomson equation. Based on the distribution of effective pore radii, Hagen-Poiseuille equation, Darcy's law, relative hydraulic conductivity and tortuosity, a simple and smooth hydraulic conductivity model for saturated frozen soil based on the SFCC was proposed. To illustrate the model performance, eight existing experimental cases were analyzed. The results showed that predictions considering the three different tortuosity formulations were in good agreement with the tested data; the results were worse when not considering the tortuosity and the results were best when considering the tortuosity tau(F) = (B/r(b))(2). Moreover, the predictive modeling power was related to the tortuosity function. Furthermore, the model was further compared with the previous models, the results of which showed the better performance of the proposed model. The model is quite simple and timesaving to use when the SFCC and the saturated hydraulic conductivity are available. This result provides a new idea for developing the hydraulic conductivity model of saturated frozen soil.