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Open AccessArticle

A Fractal Model of Hydraulic Conductivity for Saturated Frozen Soil

by Lei Chen 1,2, Dongqing Li 1, Feng Ming 1,*, Xiangyang Shi 1,2 and Xin Chen 1,2
State Key Laboratory of Frozen Soil Engineering, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou 730000, China
University of Chinese Academy of Sciences, Beijing 100049, China
Author to whom correspondence should be addressed.
Water 2019, 11(2), 369;
Received: 10 December 2018 / Revised: 6 February 2019 / Accepted: 18 February 2019 / Published: 21 February 2019
(This article belongs to the Special Issue Environmental Hydraulics Research)
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. View Full-Text
Keywords: frozen soil; soil freezing curve; hydraulic conductivity; fractal model; Darcy’s law frozen soil; soil freezing curve; hydraulic conductivity; fractal model; Darcy’s law
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Chen, L.; Li, D.; Ming, F.; Shi, X.; Chen, X. A Fractal Model of Hydraulic Conductivity for Saturated Frozen Soil. Water 2019, 11, 369.

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