## 5 Conclusions  
To evaluate effects of different PSC systems on calculating \(D\). Mongolian pine plantations composed of _Pinus sylvestris_ var. _mongolica_ were used. By comparing top (0-5 cm) soil PSD across nine forest densities of _Pinus sylvestris_ var. _mongolica_ ranging from 900-2700 trees \(\mathrm{ha}^{-1}\) in the southern Mu Us Sandy Land, China. The differences as well as relationships among Soil PSD and \(D\) of soil PSD under China (1987), Katschinski (1957), USDA (1993), ISSS (1929), ISO14688 (2002), and Blott & Pye (2012) soil PSD classification systems were evaluated. The following conclusions were inferred from this study:1. The major soil particle-size was distributed within the sand classification, which accounted for more than 90% of the total volume. Clay and silt particle contents were much less prevalent. Blott & Pye (2012) PSC system had sufficient subdivisions of soil fractions classes, while other schemes did not provide sufficient basis for description and comparison of soil PSD. The order of volume fractal dimensions was USDA (1993) > ISO14688 (2002) > ISSS (1929) > Katschinski (1957) > China (1987) > Blott & Pye (2012) PSC systems.
2. There were significant positive correlations between \(D\)s and clay and silt fractions (\(R^{2}\) = 0.721-0.964 and 0.740-0.987, \(p\) < 0.01), and significant negative correlations between \(D\)s and sand fraction (\(R^{2}\) = 0.755-0.983, \(p\) < 0.01) under six PSC systems.
3. There were significant positive correlations among PSC systems with correlation coefficients ranging from 0.977 to 0.998 (\(p\) < 0.01), which also indicated they have close connection.
4. \(D\)s which were calculated by six PSC systems were sensitive to the desertification combating processes like MPPs establishment and forest densities by characterizing soil PSD and its variations. Compare to the other PSC systems, \(D\)s calculated by [PERSON] (1957) PSC systems had relatively weaker correlation with forest densities.
5. The variation of \(\mathrm{Lg}\) (\(V/V_{T}\)) and \(\mathrm{Lg}\) (\(R_{i}/R_{\mathrm{max}}\)) curve under different PSC systems indicated that refining clay and sand scales could increase \(D\) values, while refining silt scales could reduce \(D\) values.
6. Taking soil PSD data, \(D\) values, and the observed correlations into consideration, USDA (1993) and Blott & Pye (2012) PSC systems should be highly recommend optional PSC systems for calculating volume fractal dimensions of PSD. For the former PSC system, \(D\)s had the closest relationship with soil fractions, and latter PSC system had the most information of subdivision of soil fractions.  
This research was limited by the multifractal analysis was overlooked to capture the intrinsic variability of soil PSD and fractal dimensions under different PSC systems in order to retain more detailed information. Therefore, future studies should deal with these limitations.  
[PERSON] conceived the experiments; [PERSON] completed the experiments; [PERSON], [PERSON] and [PERSON] are responsible for managing and analyzing the data; [PERSON] is responsible for scientific paper writing.  
This work was supported in part by the National Natural Science Foundation of China (31800609), Doctoral Scientific Research Foundation of Liaoning Province (20170520247), Shenyang Agricultural University Startup Foundation for Introduced Talents (the year of 2015), and CFERN & GENE Award Funds on Ecological Paper.  
The authors declare no conflict of interest.