Modeling soil water retention curve with a fractal method

Many empirical models have been developed to describe the soil water retention curve(SWRC). Applications of the fractal theory may provide a useful tool to fill the gap between the use of empirical models and the physical meaning of their parameters. In this paper, a fractal model for the SWRC was derived with a special constructed Menger sponge. The model is in a power-law form, similar to the empirical functions of Brooks-Corey( 1964) and Compbell ( 1974). Experimental data of particle size distribution, texture, soil water retention for 10 soils collected at different places in China were used to estimate the fractal dimension of SWRC and the mass fractal dimension. The fractal dimension of SWRC and the mass fractal dimension are linearly related. Both of the fractal dimensions are dependent on the soil texture, i.e., the clay and sand contents. Expressions were proposed to quantify the relationships. Based on the relationships, four methods were used to determine the fractal dimension of SWRC and the model was applied to estimate soil water contents at a wide range of tension values. The estimated results were well compared with the measured data with relative errors less than 10% for most of the soils. The model offers an alternative to predict the SWRC with the fractal dimension estimated using soil texture data.