A unified erosion formulation for fine sediments

Abstract

Different models of fine sediment transport often employ very different, frequently incompatible formulations for surface erosion of bottom sediment. In this paper, we develop a simple extension of the standard linear erosion formulation that allows it to be used to describe either Type I (depth-limited) erosion or Type II (unlimited) erosion, with a seamless transition between the two behaviors. The formulation is cast in terms of either the depth of erosion or eroded sediment mass. Assuming a locally constant rate of increase in critical stress with depth and direct proportionality between the erosion constant and sediment concentration at the interface, the model predicts the exponentially decaying erosion rate often observed in Type I erosion tests after application of each new shear stress step. The predicted decay rate is proportional to the rate of erosion per unit excess stress times the rate of increase in critical stress with depth. The formulation is tested by re-analyzing the data set presented by Maa et al. (1998) describing in situ erosion tests in Baltimore Harbor, MD, with generally favorable results. Solutions of the erosion formulation with time varying forcing show that erosion behavior is controlled by the ratio of the rate of change of shear stress to the rate of depletion of erodible sediment. If the time scale of shear stress change is long compare to the time scale of sediment depletion, then erosion rate is controlled by the time rate of increase in shear stress balanced against the depth rate of increase in critical stress (Type I behavior). If the time scale of shear stress change is short compared to the time scale of sediment depletion, then erosion rate is controlled by the instantaneous difference between bottom shear stress and critical shear stress (Type II behavior). A general algorithm for implementation in numerical sediment transport models is presented.