Equilibrium Cross-section for River Channel with Cohesive Erodible Banks

Bank erosion processes represent an important factor in driving planform changes, meander development and channel width adjustments in alluvial rivers. Recent literature of the last decade has shown that bank retreat process often involves combination of fluvial erosion and mass wasting, giving important contribution to the amount of sediment delivered downstream. In particular fluvial (or hydraulic) erosion involves the removal of bank materials by the direct erosive action of the flow, and it is one on the triggering factors of mass wasting such that the long-term rate of bank retreat is controlled by the rate of hydraulic erosion at the toe. A theoretical framework is here proposed to investigate the equilibrium cross-section in a river channel with cohesive erodible bank: the equilibrium width and the near-bank shear stress are predicted, given the channel and bank roughness characterization and the hydraulic variables which define the flow in the central region (slope, discharge, depth at bankfull condition). In this approach the solution for the flow obtained with a simple 1D model is coupled with a theoretical model to derive the boundary shear stress. The Kean and Smith (2006) model, which predicts the flow over the irregular bank topography that is characteristic of fine-grained riverbanks, provides a means to partition the form and skin drag components of bank boundary shear stress and thus determine the extent to which form drag influences bank erosion rates and channel equilibrium width. In this work, the hydraulic bank erosion rates are quantified using an excess shear stress formula; hence, the river channel is supposed to widen if the banks are unstable under the given hydraulic conditions, while the shape of the bank profile is conserved. The procedure is repeated until the equilibrium width associated with stable bank is reached. The results showed that form roughness induced by bank topographic features is a major component of the spatially averaged total shear stress, and as such it can be viewed as an important factor that self-limits bank erosion. The above theoretical model is preliminarily applied to the equilibrium conditions of sand-bed rivers with cohesive erodible bank, using the dataset of Wilkerson and Parker (2011), describing bankfull hydraulic geometry of sand-bed rivers. This approach could be generalized to include the more sophisticated bank failure mechanisms and the effect of channel curvature.