Geoderma (Feb 2024)
A new hydraulic conductivity model of frozen soil considering the hysteresis effect based on fractal theory
Abstract
The hydraulic conductivity of frozen soil is crucial for predicting water migration and frozen heave. Many models have been proposed to estimate the hydraulic conductivity, which involves factors such as unfrozen water content, specific surface area, grain size distribution, and pore size distribution. However, the bottleneck effect on the hysteresis of unfrozen water has not been adequately considered. This study proposed a hydraulic conductivity model based on the fractal theory by assuming the capillary tubes with a pore throat. Subsequently, the hydraulic conductivity was expressed as the product of the saturated and relative hydraulic conductivity, both of which can be determined from the microscopic fractal characteristics. Finally, the proposed model was verified using the experimental data and existing models, and a sensitivity analysis of the relative hydraulic conductivity was conducted. The validation showed that the predicted results agree well with the experimental data. Meanwhile, the proposed model can better describe the hysteresis effect of unfrozen water content during the freezing-thawing process than other commonly used models. Relative hydraulic conductivity is sensitive to pore structure characteristics and unfrozen water content. Immobile water saturation evidently influenced the relative hydraulic conductivity when it reached 0.7. The proposed model can be simplified as a power function in which the exponent can be calculated using the fractal dimension. The results help simulate the dynamic process of unfrozen water in frozen soil and may help understand the complex mechanisms of hysteresis and transport processes in frozen soil.
