多孔介质非饱和导水率预测的分形模型

多孔介质非饱和导水率是地下水污染预测与评价的重要参数。根据分形几何的基本原理和方法,推导出了与Campbell经验公式在形式上完全一致的多孔介质非饱和导水率的预测公式。公式中的幂指数为介质孔隙分维和随机行走分维的函数,分别体现了多孔介质的静态性质与动态性质对其中水分运动的影响,但静态性质的影响是主要的,即导水率主要受多孔介质的结构控制。根据文献中报道的大量数据,利用笔者推导的预测公式计算得到的幂指数的统计值与试验测定的幂指数的统计值基本一致,说明推导的理论公式预测多孔介质非饱和导水率是较为可靠的。

Fractal model for predicting of unsaturated hydraulic conductivity of porous media

The unsaturated hydraulic conductivity is a key parameter of porous media applied to groundwater pollution prediction and assessment. The fractal approach is employed in derivation of a power law equation consistent with the empirical Campbell's Law to predict unsaturated conductivity of porous media. The power exponent is a function of the pore-volume fractal dimension and random walk dimension, which respectively characterize the static and dynamic properties of the media, but the contribution of the static property to water movement is dominant. The analytical comparison of the reported experimental data of fractal dimensions with the corresponding power exponents indicates that the derived power law equation is valid for predicting the unsaturated conductivity of porous media.