A note on the soil-water conductivity of a fractal soil

We show that for a fractal soil the soil-water conductivity, K, is given by K/K-epsilon = (Theta/epsilon)(2D/3+2/(3-D)) where K-epsilon is the saturated conductivity, theta the water content, epsilon its saturated value and D is the fractal dimension obtained from reinterpreting Millington and Quirk's equation for practical values of the porosity epsilon, as D = 2 + 3 epsilon(4/3) + (1 - epsilon)(2/3) - 1/2 epsilon(4/3)In, epsilon(-1) + (1 - epsilon)In-2/3 (1- epsilon)(-1).