Modeling soil water retention curve with fractal theory

A three-dimensional fractal model for soil water retention curve (SWRC) is derived with Menger Sponge model on the basis of Tyler and Wheatcrafts' theory,which is related to the intrinsic nature of the fractal porous structure. The fractal dimension is calculated with experimental data for soil retention curve of ten soils. And the fractal dimension of SWRC is then compared to the fractal dimension of particle-size distribution (PSD) which is calculated on the basis of accumulative mass distribution of soil particles. The resups indicate that the fractal dimension of SWRC increases with clay content but decreases with sand content,and the fractal dimension of SWRC shows slightly different from and is linear related to the fractal dimension of PSD. This implies that the soil water retention curve can be predicted by the powerlaw function incorporating with the mass based fractal dimension of PSD. It can be seen that the predicted soil water retendon curve agrees well with the measured data.