A model for fluvial bedrock incision by impacting suspended and bed load sediment

Abstract

A mechanistic model is derived for the rate of fluvial erosion into bedrock by abrasion from uniform size particles that impact the bed during transport in both bed and suspended load. The erosion rate is equated to the product of the impact rate, the mass loss per particle impact, and a bed coverage term. Unlike previous models that consider only bed load, the impact rate is not assumed to tend to zero as the shear velocity approaches the threshold for suspension. Instead, a given sediment supply is distributed between the bed and suspended load by using formulas for the bed load layer height, bed load velocity, logarithmic fluid velocity profile, and Rouse sediment concentration profile. It is proposed that the impact rate scales linearly with the product of the near‐bed sediment concentration and the impact velocity and that particles impact the bed because of gravitational settling and advection by turbulent eddies. Results suggest, unlike models that consider only bed load, that the erosion rate increases with increasing transport stage (for a given relative sediment supply), even for transport stages that exceed the onset of suspension. In addition, erosion can occur if the supply of sediment exceeds the bed load transport capacity because a portion of the sediment load is transported in suspension. These results have implications for predicting erosion rates and channel morphology, especially in rivers with fine sediment, steep channel‐bed slopes, and large flood events.