A Fractal Model of Hydraulic Conductivity for Saturated Frozen Soil

Lei Chen,Xiangyang Shi,Feng Ming,Dongqing Li,Xin Chen

doi:10.3390/w11020369

Abstract

In cold regions, hydraulic conductivity is a critical parameter for determining the water flow in frozen soil. Previous studies have shown that hydraulic conductivity hinges on the pore structure, which is often depicted as the pore size and porosity. However, these two parameters do not sufficiently represent the pore structure. To enhance the characterization ability of the pore structure, this study introduced fractal theory to investigate the influence of pore structure on hydraulic conductivity. In this study, the pores were conceptualized as a bundle of tortuous capillaries with different radii and the cumulative pore size distribution of the capillaries was considered to satisfy the fractal law. Using the Hagen-Poiseuille equation, a fractal capillary bundle model of hydraulic conductivity for saturated frozen soil was developed. The model validity was evaluated using experimental data and by comparison with previous models. The results showed that the model performed well for frozen soil. The model showed that hydraulic conductivity was related to the maximum pore size, pore size dimension, porosity and tortuosity. Of all these parameters, pore size played a key role in affecting hydraulic conductivity. The pore size dimension was found to decrease linearly with temperature, the maximum pore size decreased with temperature and the tortuosity increased with temperature. The model could be used to predict the hydraulic conductivity of frozen soil, revealing the mechanism of change in hydraulic conductivity with temperature. In addition, the pore size distribution was approximately estimated using the soil freezing curve, making this method could be an alternative to the mercury intrusion test, which has difficult maneuverability and high costs. Darcy’s law is valid in saturated frozen silt, clayed silt and clay, but may not be valid in saturated frozen sand and unsaturated frozen soil.

Highlights

Hydrology in cold regions is a rapidly progressing research field, representing an important sub-discipline of hydrology
The present model was applied to existing literature on the measured hydraulic conductivity of saturated frozen soil to test its validity
Figure presents the cumulative pore size distribution estimated by the soil freezing curve (SFC), with the solid line representing the cumulative cumulative pore size distribution estimated by the SFC, with the solid line representing the volume of pores and the dashed line representing the cumulative number of pores

Summary

Introduction

Hydrology in cold regions is a rapidly progressing research field, representing an important sub-discipline of hydrology. To solve the problem of the water melting the frozen soil, different fluids other than water have been used to measure hydraulic conductivity; for example, Horiguchi and Miller [8] used distilled water; Wiggert et al [9] used dacane, octane, heptane and NaCl brine; McCauley et al [10] used diesel; and Seyfried and Murdock [11] used air. All of these studies tended to overestimate hydraulic conductivity because the fluids could flow due to air-filled porosity, making it difficult to obtain an accurate hydraulic conductivity measuring by such experiments alone

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