Equilibrium bank geometry and the width of shallow sandbed streams

Cross-sections of 16 straight sandbed streams in Minnesota, Iowa, and Nebraska were surveyed. Two stratigraphic horizons were found in the banks at each site, an upper cohesive unit usually composed of silt and clay and a lower unit composed of sand. Bank erosion on these rivers occurs when the upper cohesive unit is undercut by scour at bends. The overhanging cohesive block fails by beam or cantilever failure. As upper bank failure is a direct result of undercutting, the stability and rate of retreat of the bank are largely determined by erosion of the sandy part of the bank. The cohesive layer has little influence on bank retreat and width adjustment on the rivers studied here. A quantitative lateral sediment transport model developed by Parker (1978a) is used to calculate the steady-state geometry of the sandy part of the bank. Results are obtained for the shape, length, and height of the sandy part of the bank. The model predicts the length of the bank fairly well, and the theoretical equation for the height of the bank is of the correct form. The model, however, overestimates the slope of the bank. The height of the sandy part of the bank (D_b) is approximately equal to the depth of the mean annual flow. Since D_b is determined by the lateral sediment transport model, the width (W) may be obtained from the equation of continuity (Q = WD_bV), published flow (Q) data, and a resistance equation for the mean velocity, V. The calculated widths are similar to those measured in the field.