Introducing different approaches to determine fractal dimension of soil using particle size distribution

It is not possible to describe the irregular shapes. From a geometric point of view, fractal is a complicated form, pattern and geometrical structure. Unlike usual forms, enlarging a fractal does not make it simpler. In Euclidean geometry, dimension of point, straight line, plane and volume are 0, 1, 2, and 3, respectively. Euclidean geometry describes simple structures like cube, parallelepiped and sphere but is not useful for describing irregular lines, planes, and volumes. Opposite of Euclidean geometry, dimension of fractal bodies is not integer. There is several approaches to determine fractal dimension like Tyler and Wheatcraft (1992), Kravchenko and Zhang (1998) and Sepaskhah and Tafteh (2013).Fractal dimension can be considered as an easily available parameter that may be used to estimate the soil properties like specific surface area, saturated and unsaturated hydraulic properties, soil moisture retention curve, and cation exchange capacity, etc which need great amounts of energy, cost and time to determine. Therefore, determining the fractal dimension of soils may be useful in terms of predicting soil properties