Impedance Factor of Hydraulic Conductivity for Frozen Soil Based on Ice Segregation Theory and Its Application

The necessity and rationality of using an impedance factor in the calculation of hydraulic conductivity of frozen soil has been an ongoing debate. To address this issue, ice segregation theory was used to analyze the physical meaning of the impedance factor. Based on assumptions sourced from segregation theory, experimental evidence regarding the hydraulic conductivity of frozen soil and the Gibbs-Thompson effect, a relationship between the impedance factor and soil parameters was deduced. The necessity of the impedance factor was discussed under closed unsaturated and open saturated freezing systems. Finally, the derived impedance factor was compared with the current empirical impedance factor. The results showed the following: (a) The impact of the impedance factor on closed unsaturated freezing systems was small. However, an impedance factor was necessary for water migration in freezing systems with a high degree of ice segregation, such as open saturated freezing systems. (b) The derived impedance factor combined with the VG model had good performance for simulating water migration under different freezing conditions. (c) Compared with the empirical impedance factors, the derived impedance factors considered the effect of segregation acceleration caused by the pore expansion, improving the simulation accuracy of water migration at the freezing front. The parameters used to derive the impedance factor were only the initial porosity and the accumulative curve of the particle size grading, which was easily applied and combined with a VG model as a general method for computing the hydraulic conductivity of frozen soil.