The overtopping flow velocity and layer thickness are closely related to the stability of coastal structures. Some empirical formulas are available for estimating the overtopping flow velocities and layer thicknesses. However, these empirical equations were derived based on experiments where only limited amount of wave conditions and dike configurations (mostly smooth straight waterside slopes) were tested. Therefore, the extrapolation of existing empirical equations to cases that are outside of the applicable ranges remains uncertain. Numerical modelling has become an important complementary tool to physical experiments. In this study, we developed a 2DV numerical model based on the OpenFOAM framework to simulate the overtopping flow velocity and layer thickness at the waterside edge of the dike crest. This model is validated by comparing the modelled overtopping flow parameters with the measured ones from physical experiments. The model validation shows that the 2DV OpenFOAM model is capable of predicting the overtopping flow parameters with a low probability (2%) of exceedance reasonably well although the overtopping layer thickness is slightly overestimated.

The average overtopping discharge is an important parameter for the design and reinforcement of dikes. Rock armour on the waterside slopes and berms of dikes is widely used to reduce the wave overtopping discharge by introducing slope roughness and dissipation of energy in the permeable armour layer. However, methods for estimating the influence of a rock berm and roughness of rock armour at dikes on the average overtopping discharge still need to be developed and/or validated. Therefore, this study aims to develop empirical equations to quantify the reductive influence of rock armour on wave overtopping at dikes. Empirical equations for estimating the effects of rock berms and roughness are derived based on the analysis of experimental data from new physical model tests. The influence of roughness of the rock armour applied on parts of waterside slopes is estimated by introducing the location weighting coefficients. Results show that the newly derived equations to predict the average overtopping discharge at dikes lead to a significantly better performance within the tested ranges compared to existing empirical equations.

The average overtopping discharge is an important parameter for the design of flood defences. Several empirical formulas are available for predicting the overtopping discharge at dikes. However, these empirical formulas often have their specific applicable conditions. To complement with the empirical methods, a numerical model has been developed using the open source CFD package OpenFOAM to model the wave overtopping at dikes. Systematic calibration and validation of the numerical model are performed. The influences of the mesh, solver, turbulence model and roughness height on the modelled results of the average overtopping discharge have been investigated during the model calibration. The simulations show that the turbulence model increases the accuracy of the numerical model for predicting the average overtopping discharge under wave breaking conditions. The calibrated model is then validated by comparing the modelled average overtopping discharges with the measured ones from the physical model tests. Results show that the OpenFOAM model is capable of predicting the average overtopping discharge accurately at dikes that have a smooth straight waterside slope.

Transitions in the dike revetment or in the grass cover can significantly affect the wave overtopping discharge and the dike cover erosion. At the University of Twente, two PhD students recently started on the challenge of quantifying the effect of (1) waterside transition on the wave overtopping discharge and (2) transitions in grass covered dikes on dike erosion. In this paper we present their preliminary results and outline their future plans. Firstly, new laboratory experiments show that the existing wave overtopping formulas are not able to accurately predict the overtopping discharge in case of transitions on the waterside slope. Secondly, the analytical dike cover erosion model shows that transitions in grass covers significantly affect the location of maximum flow velocity and potential dike cover erosion. In future work, detailed numerical models will be developed for both the waterside slope and the landward slope to further increase our understanding of the effects of transitions on the wave overtopping discharge and the dike cover erosion.