Using fractal models for quantifying soil structure and comparison with classical methods

Soil structure is of great importance from both crop production and water resources management point of views. Since soil structure is often expressed qualitatively, the so-called fractal geometry, as a novel method, can be used to describe the soil structure in a quantitative manner. Using fractal concept and its comparison with the classical aggregate stability methods can assist to better understanding of soil structure. This research was aimed to quantitatively assess the soil aggregate stability by using some fractal and classical models. To attain this purpose, a number 30 soil samples were collected from topsoil of an agricultural area. Then, the mean weight diameter MWD and geometric mean diameter GMD of soil samples were determined by using wet and dry sieving method. The fractal dimensions of soil samples were determined for four fractal models including the number-size and mass-size of Rieu and Sposito, number-size of Mandelbrot, and mass-size of Tyler and Wheatcraft. Results indicated that the range of fractal dimensions for mass-size model of Rieu and Sposito in dry condition varies from 2.86 to 2.92 and in wet condition from 2.90 to 2.99., this range for Tyler and Wheatcraft model was 2.52 to 2.78 and 2.24 to 2.55, for dry and wet conditions, respectively. Results further showed that for the number-size model of Rieu and Sposito the fractal dimension varied from 2.77 to 3.59 in the dry and from 2.35 to 3.18 in wet conditions. These ranges for Mandelbrot model were obtained to be 2.89 to 3.72 and 2.21 to 3.22 for the dry and wet sieves, respectively. The largest standard deviation was obtained for MWD, while the lowest belonged to the mass-size model of Rieu and Sposito. The obtained results further indicated that by increasing the fractal dimension, aggregate stability decreases and aggregate instability tend to increase. It can be then concluded that by using fractal dimensions one can more precisely describe the aggregate stability compares to the classical methods.