Amplified transport variability in granular slope flows near the critical angle

Abstract

Mechanical disturbances such as seismic shaking can set a granular slope in motion. Understanding the resulting transport before arrest is important for predicting topographic change, assessing landslide hazards and controlling powder flows in industrial processes. Experiments show that smaller disturbances can trigger avalanches and larger areas are mobilized as slopes approach their stability limit. Yet how much transport varies between events under the same macroscopic conditions and forcing remains unclear. Here we use numerical simulations to show that transport variability is amplified near the critical angle. We apply identical basal pulses to static granular layers with the same macroscopic conditions but different initial particle configurations. Although the mean transport increases approximately in inverse proportion to the angular distance from the critical angle, the standard deviation increases even faster and can exceed the mean. Thus, identical forcing can produce widely different transport amounts. Deterministic constitutive laws that assign a unique response to given macroscopic conditions cannot capture this variability. We introduce fluctuations into the energy balance to develop a stochastic model that captures the main features of the broadening transport distribution. These results show that assessing transport near the critical angle requires considering its distribution, not just its mean, and motivate constitutive descriptions that incorporate fluctuations.