<p>In general, modelling bedload transport requires a full coupling between shallow water equations and sediment balance equations. Nevertheless, splitting approaches can be applied, depending on the time step size and the degree of interaction between flow and mobile bed. This work employs an implicit time discretisation to implement both a fully coupled and a splitting approach. The currently available approaches utilise an appropriate calculation of the numerical flux at the cell faces, e.g. Roe’s scheme, in order to ensure a full coupling. However, this work demonstrates that a fully coupled approach can also be achieved through an implicit time discretisation, as it combines the shallow water and the sediment balance equations into a system of non-linear equations, thereby ensuring full coupling between shallow water flow and bedload transport. The full coupling via implicit time discretisation has the advantage of being applicable to arbitrary bedload transport problems. In contrast, the existing fully coupled approaches are only applicable to uniform bedload transport and are not suitable for mixed size bedload transport with several grain classes or in situations where modifications to the bedload discharge rate are required, such as secondary currents or gravitational transport. Unlike the fully coupled approach, the splitting approach solves the shallow water equations and the sediment balance equations sequentially, resulting in two non-linear systems per time step. This work compares the two presented coupling approaches in terms of computational cost and with regard to the applicability of the splitting approach. The comparison indicates that, where applicable, the splitting approach often offers a superior performance compared to the presented fully coupled approach, particularly in cases involving several grain classes.</p>