In this note we are interested in the modelling of sediment transport phenomena. We mostly focus on bedload transport and we do not consider suspension sediment processes. We first propose a coupled numerical scheme for the classical Saint-Venant -- Exner model. It is based on a relaxation approach and it works with all sediment flux function. We exhibit that this coupled approach is more stable than the splitting approach that is mostly used in industrial softwares. Then we derive an original three layers model in order to overcome the difficulties that are encountered when using the classical Exner approach and we write a related relaxation model.
