The performance of fractal models in estimating soil particle size distribution

Particle size distribution (PSD) is one of the most important soil physical properties. Determining soil PSD using low-cost, rapid, and accurate methods is of interest to researchers. In this research, performance of seven fractal models to estimate PSD characteristics of 40 samples in five soil textural classes, including clay, clay loam, silty clay, sandy loam, and sandy clay loam was investigated using different statistical indices. For this purpose, 28 points of the soil PSD curve were measured using either sieve or hydrometric method for each soil sample. Fitting of the PSD models was performed by nonlinear regression using the Matlab program. The results showed the effect of soil texture on the fractal dimension value. Among the models studied, Perrier et al. (1999) model had the most fitting error for all soil textures. Also, Bird et al. (2000), Perrier & Bird (2002) and Kravchenko & Zhang (1998) models had the best performance in fractal dimension estimation. The statistical indices showed that two-parameter fractal models have a better fit for the soil PSD curve than single-parameter ones. The studied PSD models were relatively accurate in estimating D60 and D50 values. The results of this study indicated that fractal models can be reasonably capable of estimating soil PSD characteristics.