Fractal and multifractal characteristics of particle-size distributions in debris-flow deposits

Particle-size distribution is a fundamental characteristic of debris-flow deposits and provides important information on sediment transport, sorting, and depositional processes. This study investigates ten debris-flow deposit profiles along the sampled main-channel reach along Jiangjiagou, Yunnan Province, China. Mechanical sieving combined with laser diffraction was employed to obtain high-resolution particle-size data, and single-fractal and multifractal approaches were used to quantitatively characterize the spatial variability, structural complexity, and multiscale heterogeneity of particle-size distributions. The results reveal that the deposits were dominated by the coarse fraction (> 0.05 mm), which accounted for 95.75–99.82% of the total particle-size composition, whereas clay and silt contents varied among sampling sites, indicating clear spatial differentiation in particle-size organization. The global fractal dimension ranges from 2.09 to 2.40, reflecting substantial variability in particle mixing and granulometric complexity. The generalized dimension spectra exhibit a typical inverted S-shaped pattern, while D₀, D₁, and D₂ show marked spatial variations among sampling sites. The characteristic singularity strength (α₀) ranges from 0.768 to 1.714, and the spectrum width (Δα) varies from 1.19 to 2.49. D₁/D₀ values are consistently well below unity, further indicating pronounced heterogeneity and multiscale variability in particle-size distributions. Correlation analysis shows that the fractal and multifractal characteristics are closely related to particle-size composition, with fine-particle enrichment generally associated with higher granulometric complexity, whereas coarser deposits tend to exhibit relatively simplified fractal structures. These results demonstrate that fractal and multifractal parameters provide an effective quantitative framework for characterizing the complex particle-size architecture of debris-flow deposits and offer new insights into sediment sorting, transport, and depositional processes.