Bedrock incision by bedload: insights from direct numerical simulations

Bedload sediment transport is one of the main processes that contribute to bedrock incision in a river and is therefore one of the key control parameters in the evolution of mountainous landscapes. In recent years, many studies have addressed this issue through experimental setups, direct measurements in the field, or various analytical models. In this article, we present a new direct numerical approach: using the classical methods of discrete-element simulations applied to granular materials, we explicitly compute the trajectories of a number of pebbles entrained by a turbulent water stream over a rough solid surface. This method allows us to extract quantitatively the amount of energy that successive impacts of pebbles deliver to the bedrock, as a function of both the amount of sediment available and the Shields number. We show that we reproduce qualitatively the behaviour observed experimentally by Sklar and Dietrich (2001) and observe both a "tool effect" and a "cover effect". Converting the energy delivered to the bedrock into an average long-term incision rate of the river leads to predictions consistent with observations in the field. Finally, we reformulate the dependency of this incision rate with Shields number and sediment flux, and predict that the cover term should decay linearly at low sediment supply and exponentially at high sediment supply.