WATER TRANSPORT IN SOILS AS IN FRACTAL MEDIA

Fractal scaling laws of water transport were Found For soils. A water transport model is needed to describe this type of transport in soils. We have developed a water transport equation using the physical model of percolation clusters, employing the mass conservation law, and ass uming that hydraulic conductivity is a product of a focal component de pendent on water content and a scaling component depending on the dist ance traveled. The model predicts scaling of water contents with a var iable x/t(1/(2+beta)) where beta deviates from the zero value characte ristic for the Richards equation. A change in the apparent water diffu sivity with the distance is predicted if the apparent diffusivity is c alculated using the Richards equation. An equation for the time and sp ace invariant soil water diffusivity is obtained. Published data sets of five authors were used to test the scaling properties predicted by the model. The value of beta was significantly greater than zero in al most all data sets and typically was in the range from 0.05 to 0.5. Th is exponent was found from regression equations that had correlation c oefficients From 0.97 to 0.995. In some cases a dependence of beta on water content was found indicating changes in scaling as the water tra nsport progressed. (C) 1998 Elsevier Science B.V.