基于多孔介质土体分形特征的渗透系数研究

堤坝工程渗流计算中确定土体渗透系数尤为重要。利用分形维数不同尺度域，分析渗透破坏试验土样无标度区，指出土体细颗粒含量是决定土体分形维数的主要因素。基于多孔介质毛管束模型，推导了渗透系数和孔隙率与分形维数之间分形关系解析式，阐释了多孔介质土体渗透系数影响因子包括分形系数、孔径大小、分形维数及流体黏滞系数。利用土体渗透破坏试验结果，进一步论证了渗透系数和孔隙率与分形维数之间的非线性关系。结果表明:当分形维数大于2.83时，孔隙率随着分形维数的增大而减小，但在颗粒吸着水和薄膜水形成的黏聚力影响下，渗透系数随着分形维数增大而减小的规律不明显。研究结果可为渗透破坏形成机制及发展过程分析提供理论依据，减少堤坝渗透破坏致灾隐患。

Permeability coefficient investigation based on fractal characteristics of porous media soil

Permeability coefficient of soil is extremely important to dike and dam engineering. Scale-invariant space of seepage failure testing soils were statistically analyzed by multifractal dimensions, which shows that fine particle content is the major factor of mass fractal dimension. Based on a pipe bundle model of porous medium, the theoretical relationship between permeability coefficient and porosity was deduced, indicating that the influence factors of permeability coefficient include fractal coefficient, particle size, fractal dimension and fluid viscosity coefficient. The nonlinear relationship of permeability coefficient, porosity and fractal dimension was verified for further studies based on seepage failure experimental results. The results show that when the fractal dimension value is greater than 2.83, porosity decreases obviously with the increase of the fractal dimension, while permeability coefficient decreases insignificantly under the cohesive force of hydroscopic water and film water. The results provide a theoretical base for seepage formation mechanism and evolution process, which can decrease the seepage disaster risk of dams.