Scaling relation between fluctuating stress and basal friction in granular flows down rough inclines

The basal friction coefficient, defined as the ratio of basal shear to normal stress, is fundamental to understanding granular avalanche dynamics. Normalized stress fluctuations, quantifying deviations from the mean stress, capture grain-scale interactions, yet their link to bulk friction remains unclear. Through inclined-chute experiments using uniform glass beads under varying slopes and flow thicknesses, we show that the fluctuation intensity systematically decreases as the flow becomes thicker and increases with slope. When both basal friction and stress fluctuations are rescaled by geometric parameters, the data collapse onto a unified curve, revealing a robust power-law trend. This scaling demonstrates that frictional resistance strengthens with enhanced stress variability but weakens with flow depth, offering a quantitative framework for modeling the mobility of landslides and debris flows.