Although fractal mathematics has been commonly used to quantify particle size distribution (PSD), limited attention has been paid to the fractal dimension of the infiltration curve (D_I). Therefore, it is necessary to determine whether the D_I and fractal dimensions of PSD (D_m, D_clay, D_silt and D_sand) can reflect the infiltration process, and soil erodibility and degradation. Accordingly, this study aimed to provide new information on the quantification of infiltration processes, and soil erodibility and degradation, using D_I and D_m in the Soorak basin in the northern part of Iran. The soil and infiltration properties were calculated by field and laboratory practices on 46 topsoil samples and 34 infiltrometer double‐ring tests. Correlation, regression and redundancy analysis (RDA) were used to identify relationships between the infiltration curve and PSD coordinates with soil and infiltration properties. Results indicated that the D_I was significantly linearly correlated with other infiltration curve characteristics, with the correlation coefficient ranging from −0.737 to −0.403 (sig. = 0.000–0.037). However, there was no significant correlation between D_I and D_m, D_clay, D_silt and D_sand. Different erodibility factors, especially K_USLE, had significant relations with D_m, D_clay, D_silt, D_sand and D_I (p < .01), suggesting that these fractal dimensions are indicators of soil degradation. Other findings indicated that the land use had no significant effect on D_I and infiltration properties, whereas K_USLE, D_m, D_clay, D_Silt and D_Sand were significantly affected by land‐use patterns (p < .01). These findings demonstrate that fractal dimensions of PSD and infiltration can be practicable indices to analyse soil degradation under different land‐use types.

中文翻译：

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半湿润小流域入渗曲线和土壤粒径的分形分析

尽管分形数学通常用于量化粒度分布（PSD），但对渗透曲线的分形维数（D _I）的关注却很少。因此，有必要确定PSD的D _I和分形维数（D _m，D_黏土，D_淤泥和D_沙）是否能够反映入渗过程以及土壤的易蚀性和降解性。因此，本研究旨在提供利用D _I和D _m定量分析入渗过程以及土壤易蚀性和降解性的新信息。在伊朗北部的Soorak盆地。通过田间和实验室实践，对46个表土样品和34个浸润仪双环试验计算了土壤和入渗特性。使用相关，回归和冗余分析（RDA）来确定入渗曲线和PSD坐标与土壤和入渗特性之间的关系。结果表明，D _I与其他入渗曲线特征线性相关，相关系数范围为-0.737至-0.403（sig。= 0.000-0.037）。但是，D _I和D _m，D_黏土，D_淤泥之间没有显着相关性。和D_沙。不同的_侵蚀性因素，特别是K _USLE，与D _m，D_黏土，D_淤泥，D_沙和D _I有显着关系（p  <.01），表明这些分形维数是土壤退化的指标。其他发现表明，土地利用对D _I和入渗特性没有显着影响，而K _USLE，D _m，D_黏土，D _Silt和D_沙土受到土地利用方式的显着影响（p  <.01）。这些发现表明，PSD的分形维数和入渗量可以作为分析不同土地利用类型下土壤退化的可行指标。