Physical model tests have been performed to study wave overtopping at rubble mound breakwaters, including breakwaters with a crest wall, breakwaters with a berm, and breakwaters with a crest wall and a berm. For rubble mound structures with a protruding crest wall or with a stable berm, limited information is available in literature even though protruding crest walls and berms clearly affect wave overtopping discharges. Adding a crest wall to an existing structure, increasing the height of a crest wall, adding a berm, or increasing the width or height of a berm, can be effective measures to account for effects of sea level rise if the sea level rise appears to be more severe than the amount of sea level rise for which the structure was designed for. The present wave flume tests were used to develop guidelines for rubble mound breakwaters, including breakwaters with a crest wall or with a berm. The relative height of the protruding part of a crest wall dominates the effect of a crest wall. The berm width, berm level and wave steepness all affect the influence of a berm on the wave overtopping discharge. Moreover, it was confirmed that the wave steepness also affects wave overtopping discharges for rubble mound breakwaters without a berm or without a crest wall. The developed set of expressions for rubble mound structures has also been validated based on existing data for oblique wave attack on rubble mound breakwaters with a crest wall.

This paper describes a method of determining the reaction forces of a vertical structure with an overhang to impulsive wave impacts. The aim is to develop a method to design a hydraulic structure exposed to the impulsive wave impact. At present, there is a lack of guidelines on the designing and verification with such a purpose. The impulse of the impact is taken as the primary design variable to estimate the impulsive reaction force instead of peak impact forces. By using extreme value analysis (EVA), the characteristic impulse (e.g., I _im,0.1% ) can be determined. Then a simple structure model is used for obtaining reaction forces to the characteristic impact impulse. The sum of the impulsive reaction force and the quasi-steady wave force could represent the total reaction force, which can be used as a design load on the structure. The advantage of using the impact impulse could give an approach in which several aspects of the impulsive wave impact force can be incorporated better, like determining the exceedance probability of a certain load, incorporating the flexibility of the structure and correcting possible scale effects in small scale hydraulic models. The proposed method based on the characteristic value of the I _im,0.1% is applied to forces measured in a small scale model of the Afsluitdijk discharge sluice, and compared well to a full-time domain solution. The results indicate the initial assumption that using the impact impulse of the impact as the primary design variable, it is possible to estimate the dynamic response of the structure.

Wave loads on crest walls on top of rubble mound structures determine the size of these crest walls. For the design of crest walls some design guidelines exist, but their validity is limited to particular designs of the cross section (berm, no berm, toe, armour layout, protruding crest element, etc). The present work addresses the validation of OpenFoam/waves2Foam for the prediction of integrated forces on crest wall elements against a new set of experimental data in order to obtain a numerical model that can be applied for a wider field of application than the existing empirical guidelines. One key concern for the accurate modelling of wave loads is the spurious entrapment of air between the water surface and structural elements. The solution developed for this problem is a boundary condition that allows for air ventilation, while enforcing a predefined head loss characteristic. Compared to the existing technique of introducing small meshed tubes through the structure, the new method does not lead to excessive time-step limitations and is therefore more efficient (a practical case was accelerated by a factor 20). The new boundary condition is validated against experimental data of forces on bridge decks with girders. Subsequently, the numerical model is validated against experimental data for loads on crest wall elements from new experiments conducted in a wave flume. The comparison between numerical and experimental data is made both in the time domain and as probability of exceedance. Special emphasis is given to the openness of the faces of the crest wall to mimic the effect of mixing of water and air during the wave impact. Finally, the validated model is applied to evaluate the forces on crest walls as a function of the elevation of the crest wall with respect to the still-water level. This effect is of interest, since the level of the crest wall element is only tested to a limited extent in laboratory experiments and the bottom face was mainly wetted or submerged during these tests (existing empirical formulations). The numerical results are compared to an empirical design formulation [Pedersen, 1996] and conclusions on the general applicability of this particular empirical design formulation are presented. The effect of the shape of the wave spectrum on the resulting forces is investigated in a preliminary fashion.