Fractal-statistical analysis of grain-size distributions of debris-flow deposits and its geological implications

Breakage models and particle analyses have been widely used as tools for describing and interpreting various deposits and providing parameters for assessing the particle-size distribution of the deposits. Debris flows can be seen as a two-phase rheological fluid with a clay-fluid composition, and debris-flow deposits comprise mud, silt, sand, and boulders, with grain sizes ranging from less than one μm to more than several meters. As a consequence, according to fractal theory, the particles in debris-flow deposits have self-similarity in geometrical shape and scale invariance in size. In this paper, the fractal dimensions of particles in various debris-flow deposits are calculated and corresponding fractal features are determined based on fractal-statistical theory. The aims of the study are: to provide a quantitative grain parameter that reflects both the grain composition and grain-size distribution in debris-flow deposits; to compare the fractal dimensions of grains in different types of debris-flow deposits and the degree of self-organization of debris flows; as well as to discuss the geological implications of fractal dimensions and fractal features of particles in debris-flow deposits.