Relationship between fractal characteristics of grain-size and physical properties: Insights from a typical loess profile of the loess Plateau

The fractal characteristics of soil grain-size in thick loess profile are closely related to its physical and hydrological characteristics. To reveal the relationship between loess grain-size distribution and its hydrological and physical characteristics, a profile of about 60 m was selected as the material. Systematic collection of samples along profile at 1 m intervals, and grain-size, moisture content, porosity, specific surface area, organic matter content and soil permeability were tested. The spatial heterogeneity of physical properties and grain-size fractal characteristics were analyzed using geostatistical methods and single and multifractal theories, respectively. The results showed that there was a strong spatial correlation between soil physical properties, but the moisture content was affected by certain human factors. The variation of fractal parameters with depth was affected by the climatic environment during its accumulation and development period. During loess accumulation period, the content of coarse particles in loess layers increased, and the concentration and symmetry of GSD increased, making D1, D2 and D1/D0 increase, and D, α0, Δα and Δf(α) decrease. The relative content of fine particles and coarse particles in the soil affected the fractal characteristics and parameter sizes of GSD. Increase of singular spectrum parameters characterized the increase of soil heterogeneity, leading to the increase of specific surface area. The correlation between multifractal parameters and water content and organic matter was greatly affected by the depth and formation age of strata. There was a mutual response between GSD fractal characteristics and the soil permeability. The increase of D1, D2 and D1/D0 indicated strong soil permeability; the increase of α0, Δα and Δf(α) reflected the high soil uniformity, which was not conducive to the occurrence of seepage process. The research results provided a case study and theoretical basis for the engineering construction and ecological restoration of the Loess Plateau.