分形渗透模型在饱和冻土中的应用

冻土中的渗透系数对于评估冻土工程中的水，热和溶质迁移至关重要。以往研究表明，渗透系数主要依赖孔隙结构，经常被描述为孔径大小和孔隙率，但是这两个参数并不能充分地表征孔隙结构。为加强对孔隙结构的描述，引用分形理论研究了冻土中的渗透系数。基于非均匀毛细管束模型和分形理论，提出了饱和冻土中渗透系数的分形模型，并提出通过土体冻结特征曲线获取冻土中孔径分布的理论方法。为了验证分形模型的有效性，对已有实验数据进行分析。分析表明，分形渗透系数模型是毛细管分维、最大孔径、黏度和迂曲度的函数，孔径分布变化是导致冻土渗透系数变化的根本原因。通过对比，计算值与实测值吻合较好。结果表明分形模型可以较好的预测冻土中的渗透系数，研究结果可为冻土渗透机理研究提供参考。

Application of the fractal hydraulic conductivity model in the saturated frozen soil

Hydraulic conductivity is crucial for the water, heat and solution migrations in the frozen soil engineering. 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 structures. To enhance the characterization ability of the pore structures, this study introduced fractal theory to investigate the influence of pore structures on hydraulic conductivity. In this study, a fractal hydraulic conductivity model for saturated frozen soil is proposed based on the non-uniform capillary bundle model and fractal model. The pore size distribution is determined by the soil freezing curve. To verify the validity of this model, several exiting experimental data were analyzed. The results indicate that the fractal model can be expressed as a function of the pore size dimension, the maximum pore size, the viscosity and the tortuosity. The change of the pore size distribution is the main reason for the changing of hydraulic conductivity of frozen soil. The predictions are in good agreement with the measured data. The fractal model can be used to predict the hydraulic conductivity of frozen soil and would be useful for studying infiltration mechanisms of frozen soils.