## 1 Introduction  
The soil particle-size distributions (PSD) has a great influence on soil hydraulic properties such as water retention characteristics, saturated and unsaturated hydraulic conductivities, bulk density, permeability, porosity, thus it is known as the result of geological, chemical, and biological processes [1; 2; 3; 4; 5; 6]. Characteristics of PSD has a good relationship with the changes of soil structure, which is affected by management practices, erosion and desertification [4; 7; 8; 9; 10; 11; 12; 13]. Therefore, characterizing changes in the soil PSD is an inevitable issue in environmental research [1]. Quantity of studies have been carried out to estimate soil PSD, these approaches basically require the PSD to be quantified by parameters like average particle diameter, weight, and volume, etc. And the latest developments in the studies have focused on the extensively accepted descriptive tool of use of fractal geometry [14; 15]. The way of fractal measures is to characterize PSDs with parameters that retain most information [9; 16; 17; 18; 19]. Fractal theory (fractal model) has been applied to soil systems and associated with fractal parameters has become crucial in understanding the dynamics of soil movement. Many scientists used fractal theory to estimate \(D\) of the PSD and discussed its pros and cons [5; 20; 21; 22; 23]. Recent studies on the various soil textures showed that \(D\) tend to increase with the clay content is increasing [18; 24; 25], and \(D\) decreased with the sand content is increasing [26; 27]. Thus, the fractal analysis is sensitive to soil coarsening process, which related to the degree of soil desertification [16]. The size of an individual soil particle can be described and measured in different ways and various methods [28]. Till now, though numerous particle-size scales and classification systems have been presented and vary considerably between scientific disciplines and regions, but no unified terminology is used to reach agreement to describe the PSDs of soils [28]. The most scientists currently use a descriptive terminology for size classes proposed by [PERSON] (1922), usually in combination with the 'texture' classification proposed by [PERSON] (1954), or a variant of it [28; 29], which were also adopted by [PERSON] (1957) and China (1987) particle-size classification (PSC) systems. In the former PSC system, soil classification mainly focused on agropedology use [29; 30], while forestry and urban soil characteristics were represented in the latter PSC system. The recent USDA (1993) (United States Department of Agriculture) provides a subdivision of the \(>\)2 mm fraction into fine, medium and coarse gravel, cobbles, stones and boulders. This PSC system is now adopted by United States and other scientists worldwide [18; 19; 31]. [PERSON] who is European agricultural scientist decided to use an upper size limit of 2 mm for sand, with all size classes above and below that size assigned on scale to log\({}_{10}\) (i.e., at 2000 \(\upmu\)m, 630 \(\upmu\)m, 200 \(\upmu\)m, 63.0 \(\upmu\)m, etc.). Such a class definition was adopted by ISSS (1929) known as \"International Society of Soil Science\" and ISO14688 (2002) referred as \"International Organization for Standardization\". And the merit of this PSC system is set class boundary by using the number 6.3 instead of 6.0 to create more even classes' spacing and almost true logarithmic scale [28; 29]. [PERSON] (1932, 1936) improved the scheme, which proposed by [PERSON] (1898) and [PERSON] (1922), suggested by using the formula \(-\)log\({}_{2}\)\(\xi\) (\(\xi\), referred to the particle size in millimeters), size in phi (\(\phi\)) units could be converted and obtained [29]. In 2012, Blott & Pye scholars revised the PSC system of [PERSON]'s and according to this scheme, they provide more logical framework with limits defined at one \(\phi\) intervals [28].