UNSATURATED FLOWS IN SOILS WITH SELF-SIMILAR HYDRAULIC CONDUCTIVITY DISTRIBUTION

In this article, we are concerned with the statistics of steady unsatu rated flow in soils with a fractal hydraulic conductivity distribution . It is assumed that the spatial distribution of log hydraulic conduct ivity can be described as an isotropic stochastic fractal process. The impact of the fractal dimension of this process, the soil pore-size d istribution parameter, and the characteristic length scale on the vari ances of tension head and the effective conductivity is investigated. Results are obtained for one-dimensional and three-dimensional flows. Our results indicate that the tension head variance is scale-dependent for fractal distribution of hydraulic conductivity. Both tension head variance and effective hydraulic conductivity depend strongly on the fractal dimension. The soil pore-size distribution parameter is import ant in reducing the variability of the unsaturated hydraulic conductiv ity and of the fluxes.