Wave overtopping of sea dikes with very shallow foreshores

Wave overtopping is one of the key parameters for designing coastal structures: the crest level is usually determined using admissible overtopping discharges. Several formulae already exist for wave overtopping assessment that predict the average overtopping discharge per meter width of the coastal defence, generally for deep or intermediate water depths at the toe of the dike. However, the process of wave overtopping on sea dikes with shallow and very shallow foreshore is not yet fully understood. Gentle foreshores in combination with (very) shallow water conditions lead to heavy wave breaking and a significant change of the wave spectra from offshore to the toe of the dike. The wave steepness is assumed as one of the main criteria to identify cases of severe wave breaking on shallow and very shallow foreshores. For these conditions, Van Gent's formula, generally used for wave overtopping with shallow foreshores, has been implemented and validated against experimental data. It is the purpose of this paper to show that Van Gent's formula overestimates the average overtopping discharge for cases of very shallow foreshores. Moreover the existing formula cannot be applied to cases with an emergent toe. The present work therefore introduces a new “equivalent slope” concept to obtain an estimation of average wave overtopping discharges on sea dikes with shallow and very shallow foreshores. This study uses data from CLASH database and experimental campaigns, specifically carried out at Flanders Hydraulics Research (Belgium), in order to validate this approach. Results indicate that this concept shows better performance compared to other empirical formulae, which suggests that the influence of the very shallow foreshore on the average wave overtopping discharge should be included.