Failure of river dikes due to overtopping is a dangerous phenomenon to be avoided, and a complex unsteady sediment transport problem that is under intense scientific consideration. Mathematical modelling of these flows is conducted using one-dimensional families of models based on different conceptual approximations, including (i) a clear-water layer and bed-load layer approach; (ii) a mixture flow approach dividing the sediment transport into bed and suspended load transport modes; and (iii) a two-phase approach formulating the mass and momentum conservation equations for the water and sediment phases separately. These families of conceptual models involve a vertical momentum balance reducing to hydrostatic pressure distribution. As discussed in previous works, numerical results might be improved by relaxing this closure hypothesis. Herein, a vertically-averaged RANS model is presented for a water–sediment mixture, conceptually divided into suspended/bed-load layers, overtopping the erodible dike surface under non-equilibrium sediment transport and non-hydrostatic fluid pressure conditions. The model is critically compared with experimental data and Saint-Venant type simulations, resulting in improved predictions of the dike crest reach. However, the erosion at the dike toe is overpredicted, stating a limitation of depth-averaged modelling. © 2018, © 2018 International Association for Hydro-Environment Engineering and Research.