The effects of hillslope gradient and environmental disturbances on sediment flux along soil-mantled hillslopes: A granular dynamics approach

Sediment flux across and out of soil-mantled hillslopes controls the volume and rate of sediment delivery to rivers, the rate of rock exhumation and the topographic evolution of hillslopes. Recent experimental, theoretical and field-based studies have inferred a nonlinear relation between the hillslope gradient and the sediment flux. However, the proposed functional forms generally lack mechanistic explanations. Furthermore, environmental disturbances have been invoked as facilitating sediment mobilization across soil-mantled hillslopes that reside below the angle of repose and would otherwise remain static, but the links between the properties of the disturbances and the sediment flux have received little investigation.

Here, we develop and employ a discrete element granular dynamics numerical model to study the relations between flux, slope, and disturbance characteristics at the grain scale. The choice of the granular dynamics approach is rooted in the inherent particulate nature of the mobile regolith layer that mantle hillslopes, and in the potential role of grain-scale interactions in controlling the long-term evolution of hillslopes. In our model, the numerical grains are subjected to gravitational body forces, to contact forces, and to random external perturbation forces, which are used to represent natural disturbances. Despite their random nature, in each simulation, the external perturbations are characterized by a maximum magnitude and a wavelength.

Simulation results reveal an abrupt transition between two kinematic regimes. Under low and intermediate hillslope gradients, granular creep is observed, where grain velocity rapidly decays with depth. High hillslope gradients, albeit still below the angle of repose, show deep, granular slides, where all the available material participates in the sliding motion. In this regime, the velocity-depth profile partly follows Bagnold's rheology that was developed for grain layers that reside above the angle of repose. This means that the external perturbations effectively reduce the angle of repose, which allows relatively rapid evacuation of deep layers of mobile regolith downslope.

A nonlinearity between the flux and the hillslope gradient emerges from each of the kinematic regimes separately, but from the transition between them in particular. The simulation results further show a systematic relation between the characteristics of the external perturbations and the sediment flux, whereby the flux increases both with the perturbations maximum magnitude and with the perturbations wavelength.