Analysis of the relationship between soil particle fractal dimension and physicochemical properties

Abstract

By examining the multifractal characteristics of soil particle size distribution (PSD), we can elucidate the distribution patterns of soil particles and identify their primary influencing factors. In this study, soil samples from different areas of a floodplain were analyzed for PSD, physicochemical properties, and heavy metal content. Multifractal parameters were calculated using multifractal theory. Subsequently, the relationships between soil PSD, fractal dimension, and soil physicochemical properties were investigated using correlation analysis, Mantel test, and random forest models. The results indicated that the soil particle size distribution in the study area was dominated by silt (2–20 μm) and sand (20–2000 μm) particles, with average contents ranging from 21.18% to 59.46% and 33.24% to 63.81%, respectively. The mean values of the single fractal dimension (D), which represents overall soil structure complexity rather than an average of D(0), D(1), and D(2), ranged from 2.27 to 2.54, indicating coarser soil particles. The multifractal dimensions revealed that the capacity dimension (D(0)) was greater than the information dimension (D(1)) and the correlation dimension (D(2)), i.e., D(0) > D(1) > D(2), confirming the multifractal nature of soil particle size distribution. The mean values of spectral width (Δα) ranged from 1.28 to 3.68, indicating a relatively complex soil fractal structure and significant variability in soil PSD inhomogeneity. Significant correlations (P < 0.05, |r| ≥ 0.35) were found between Zn and D, Δα, D(1), D(2), and D(1)/D(0), as well as between Pb and D(2) and D(1)/D(0), suggesting a relationship between heavy metals and fractal dimensions. Additionally, there was a significant correlation (P < 0.05, |r|≥ 0.35) between soil PSD and fractal dimensions. Mantel Test and RF analyses, with soil PSD and physicochemical properties as independent variables and soil fractal dimensions as the dependent variable, demonstrated the significant influence of soil PSD on soil fractal dimensions. Fractal dimensions reflect soil quality characteristics and weathering intensity, with multifractal dimensions offering more descriptive insights, as demonstrated by their significant correlations with key soil properties such as cation exchange capacity (CEC), amorphous aluminum oxide (Al_o), free iron oxide (Fe_d), and free aluminum oxide (Al_d). These findings highlight the critical role of soil fractal dimensions in representing soil particle composition and its spatial variability. By elucidating these relationships, this study enhances the understanding of soil structural variability, which is critical for informing targeted ecological management and restoration strategies in alluvial fan environments.