Application of Fractal Mathematics to Soil Water Retention Estimation

Abstract In this paper, we present an analysis correlating the fitting parameter α in the Arya and Paris (1981) soil water retention model to physical properties of the soil. Fractal mathematics are used to show that α is equal to the fractal dimension of the pore trace and expresses a measure of the tortuosity of the pore trace. The fractal dimension of the particle‐size distribution can be easily measured and related to the α parameter of the Arya and Paris model. By suggesting a physical significance of the coefficient, the universality of the model is greatly improved. Soil water retention data, estimated strictly from particle‐size distributions, are proven to match measured data quite well. The fractal dimension of pore traces range from 1.011 to 1.485 for all but one soil tested.