Prediction of the saturated hydraulic conductivity-porosity dependence using fractals

Fractal theory has been used to quantify morphological properties of pore systems in soil, but predictive capabilities of the derived fractal dimensions have remained largely untested. The objective of this study was to use morphologically derived fractal dimensions to predict an exponent N in a power law relation between saturated hydraulic conductivity, K(sat) and porosity. A Kozeny-Carman equation was used to derive N as a function of two fractal dimensions (pore volume, D(v), and pore surface roughness, D(s)) and a connectivity parameter, α. The α parameter was used as a matching factor between fitted and calculated N values. Values of D(v) and D(s) characterizing pores in both undisturbed and packed soil were obtained from images with pixel sizes of 0.06 and 0.29 mm. Porosity was measured on the 0.29-mm pixel images, while K(sat) was measured in undisturbed cores and packed soil columns. Also, published data on porosity, K(sat), and D(v) and D(s) from dye-stained patterns of four undisturbed soils were used. Lower coefficients of variation and lower absolute values of α were obtained with fractal dimensions from the 0.06-mm pixel images. Values of α were related to parameters from probability distributions of hydraulic radii as calculated from the 0.06-mm pixel images, and to the connectivity of pores as inferred from dye-stained patterns. Fractal characterization of pore structure proved useful for predicting N, but predictions would probably be improved by considering only flow-active pores in the calculation of a fractal dimension. Methods to obtain such fractal dimensions were suggested.