MODELS OF THE WATER-RETENTION CURVE FOR SOILS WITH A FRACTAL PORE-SIZE DISTRIBUTION

The relationship between water content and water potential for a soil is termed its water retention curve. This basic hydraulic property is closely related to the soil pore size distribution, for which it serve s asa conventional method of measurement. In this paper a general mode l of the water retention curve, is derived for soils whose pore size d istribution is fractal in the sense of the Mandelbrot number-size dist ribution. This model, which contains two adjustable parameters (the fr actal dimension and the upper limiting value of the fractal porosity) is shown to include other fractal approaches to the water retention cu rve as special cases. Application of the general model to a number of published data sets covering a broad range of soil texture indicated t hat unique, independent values of the two adjustable parameters may be difficult to obtain by statistical analysis of water retention data f or a given soil. Discrimination among different fractal approaches thu s will require water retention data of high density and precision.