PREDICTION OF THE SATURATED HYDRAULIC CONDUCTIVITY POROSITY DEPENDENCE USING FRACTALS

Fractal theory has been used to quantify morphological properties of p ore systems in soil, but predictive capabilities of the derived fracta l dimensions have remained largely untested. The objective of this stu dy was to use morphologic ally derived fractal dimensions to predict a n exponent N in a power law relation between saturated hydraulic condu ctivity, K-sat, and porosity. A Kozeny-Carman equation was used to der ive N as a function of two fractal dimensions (pore volume, D-v, and p ore surface roughness, D-s) and a connectivity parameter, alpha. The a lpha parameter was used as a matching factor between fitted and calcul ated N values. Values of D-v and D-s characterizing pores in both undi sturbed 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, w hile 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-stai ned patterns of four undisturbed soils were used. Lower coefficients o f variation and lower absolute values of or were obtained with fractal dimensions from the 0.06-mm pixel images. Values of alpha were relate d to parameters from probability distributions of hydraulic radii as c alculated from the 0.06-mm pixel images, and to the connectivity of po res 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-arrive pores in the calc ulation of a fractal dimension. Methods to obtain such fractal dimensi ons were suggested.