We investigate the performance of a numerical model based on fully nonlinear depth-averaged equations for simulating wave propagation, transformation and overtopping over coastal structures. The model is based on the weakly-dispersive Serre-Green-Naghdi equations, solved with a high-order finite-volume/finite-difference scheme. Wave breaking is modelled either by locally switching to the nonlinear shallow water equations or by adding a diffusive-like term to dissipate energy, with a turbulent viscosity computed from the turbulent kinetic energy. Contrary to the former approach, the latter allows to perform computations with fine meshes, which is necessary to compute wave run-up and overtopping accurately. The model is used to reproduce experiments of solitary and irregular wave propagation, breaking, run-up and overtopping, with satisfactory results.