One‐dimensional numerical modeling of sediment transport and bed deformation in open channels

Abstract

A one‐dimensional numerical model for simulating unsteady flow and sediment transport in open channels is presented and tested. The flow hydrodynamics is represented by the shallow water equations, and the bed morphodynamics is represented by the Exner equation and an additional equation describing the nonequilibrium sediment transport. Sediment size distribution is represented by the median grain diameter and the standard deviation, instead of the usual modeling with multiple particle size classes. Various methods for computing bed elevation changes at a cross section due to erosion or deposition of sediment are proposed and tested, including an innovative approach that relates the spatial pattern of erosion and deposition rates to boundary shear stress distribution, which is calculated by the Merged Perpendicular Method. An explicit finite difference scheme is employed for solving the water and sediment governing equations. The pertinence of the model is examined for two hypothetical cases. The model is then tested on one set of laboratory experiments on bed degradation under steady flow, showing excellent model data fit, and indicating that incorporating a nonequilibrium sediment transport equation into the model structure is an important element in reproducing the bed degradation process. Finally, the model is applied to simulate the morphological changes taking place in the Ha!Ha! River (Quebec) after the failure of the Ha!Ha! Dyke on July 1996. Relevant results can be obtained in terms of changes in longitudinal bed profile and cross‐sectional geometry as well as water levels, although some discrepancies are obtained between the simulated and surveyed cross‐sectional geometries, mainly because bank failure and channel widening are not modeled.