Modelling the Wave Overtopping Flow over the Crest and the Landward Slope of Grass-Covered Flood Defences

The wave overtopping flow can exert high hydraulic loads on the grass cover of dikes leading to failure of the cover layer on the crest and the landward slope. Hydraulic variables such as the near bed velocity, pressure, shear stress and normal stress are important to describe the forces that may lead to cover erosion. This paper presents a numerical model in the open source software OpenFOAM&reg: to simulate the overtopping flow on the grass-covered crest and slope of individual overtopping waves for a range of landward slope angles. The model provides insights on how the hydraulic forces change along the profile and how irregularities in the profile affect these forces. The effect of irregularities in the grass cover on the overtopping flow are captured in the Nikuradse roughness height calibrated in this study. The model was validated with two datasets of overtopping tests on existing grass-covered dikes in the Netherlands. The model results show good agreement with measurements of the flow velocity in the top layer of the wave, as well as the near bed velocity. The model application shows that the pressure, shear stress and normal stress are maximal at the wave front. High pressures occur at geometrical transitions such as the start and end of the dike crest and at the inner toe. The shear stress is maximal on the lower slope, and the normal stress is maximal halfway of the slope, making these locations vulnerable to cover failure due to high loads. The exact location of the maximum forces depends on the overtopping volume. Furthermore, the model shows that the maximum pressure and maximum normal stress are largely affected by the steepness of the landward slope, but the slope steepness only has a small effect on the maximum flow velocity and maximum shear stress compared to the overtopping volume. This new numerical model is a useful tool to determine the hydraulic forces along the profile to find vulnerable points for cover failure and improve the design of grass-covered flood defences.