Granular controls of hillslope deformation and creep

Abstract:

Sediment transport on hillslopes has been described as "creep", and has been modeled as a "diffusive" process by invoking random disturbance of soil in the presence of a gradient. In this framework, physical and biological agents are envisioned to cause dilation of the soil that is greatest at the surface and decays with depth. Thus, there is a kind of internal energy of the sediment that allows flow, even below the angle of repose. This transport has not yet been connected, however, to the more general phenomenon of creep in disordered, particulate systems. Work in such "soft matter" materials has shown that disordered solids are fragile, and may deform slowly by localized particle rearrangement under static loads much smaller than the yield stress at which fluid-like flow occurs. The transition from creep to granular flow has not been thoroughly examined. Here we use particle dynamics simulations to examine creep and granular flow dynamics and the transition between them, and to test the ability of a granular physics model to describe observations of hillslope soil creep. We employ a well-developed discrete element model, with frictional and over-damped interactions among grains to approximate the conditions of earth hillslopes. Transient and equilibrium particle dynamics are described for a range of inclination angles that transit the angle of repose. We verify that sub-threshold creep occurs, even in the absence of internal energy, and describe its dynamic signature. Moreover, simulations show that the transition from creeping to a sustained granular flow is continuous as the angle of repose is crossed. We then perturb the granular system with acoustic vibrations, to directly compare the model with previously-reported laboratory experiments of acoustically-driven hillslope transport. We test the ability of the model to reproduce the heuristic nonlinear hillslope flux law. Results reveal that the bulk movement of hillslope sediment over long timescales may be accomplished by intermittent and localized particle motion - i.e., creeping of a disordered solid - for sub-critical slopes. Further, they suggest that the nonlinear flux law is a consequence of a continuous transition between two limits; creep at low angles and fluid-like granular flow at the angle of repose.