Estimating Fractal Dimensions of Calcareous Soils Using Soil Texture Data

Mass-fractal models have been frequently used to quantify soil particles size distribution. Since fractal dimension has numerous capabilities to predict different soil properties, this study aimed to determine the best soil primary particles size groups in estimation of fractal dimension of soil primary particles size. This study was done with 186samples of calcareous soils in southern parts of Iran located in Fars province. Soil particles size distribution was determined using combination of wet sieving and modified hydrometer method. Fractal dimensions were calculated using three methods including Tyler and Wheatcraft (DT), Sepaskhah and Tafteh (DS), and Kravchenko and Zhang (DK). Then, the relationship between DT and DK with contents of soil primary particles in different size groups were established. Results showed that regression relationship (power 2) between DT and DK was very strong (with determination coefficient of 1). In addition, DS regression relationship (linear) with DT and DK was strong. Results also revealed that mean values of DK and DS were significantly higher and lower than DT, respectively.As the particles size became smaller, accuracy of regression relationships between smaller particles size percent of a specific diameter and soil fractal dimensions (DT and DK) becomes more, and the maximum accuracy was observed in logarithmic relationship between fractal dimensions and clay percent. R2 of training data and that of test data, normalized root mean square error (%), and Nash-Sutcliffe coefficient statistics were 0.99, 0.98, 0.6, and 0.95 for logarithmic model between clay content and DT, and 0.98, 0.99, 0.25, and 0.94 for logarithmic model between clay content and DK, showing very strong relationship between clay content and fractal dimensions. Therefore, it is possible to calculate Tyler and Wheatcraft and Kravchenko and Zhang fractal dimensions by using clay content and very simple equations in a wide range of calcareous soils with different mechanical components. Thus, those fractal dimensions can be used to estimate physical, chemical, and especially hydraulic properties of calcareous soils, whose measurements are complex, expensive, and time consuming.It should be pointed out that the proposed relations are valid when primary particle size distribution of soil is determined using the method used in the present study. Otherwise, the relations should be tested and validated.