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

Abstract

<jats:p>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® 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.</jats:p>

Modelling of Wave Overtopping Flow Over Complex Dike Geometries: Case Study of the Afsluitdijk

“…Computational fluid dynamics models can compute the flow velocity, pressure, shear stress and normal stress of the overtopping waves (Bomers et al, 2018;Van Bergeijk et al, 2020). Additionally, the turbulence is solved within the models and therefore the effect of transitions on the hydraulic load can be studied directly.…”

“…Additionally, the turbulence is solved within the models and therefore the effect of transitions on the hydraulic load can be studied directly. Previous model studies have shown that geometric changes are vulnerable locations for grass cover erosion due to an increase in near-bed turbulence (Bomers et al, 2018) and high shear forces (Van Bergeijk et al, 2020). However, solely one type of transition has been studied with these models and the effect of multiple transitions along a dike profile is still unknown.…”

“…Two formulations for the turbulence parameter are studied to show the effect of an additional load factor at transitions in a flow-velocity based erosion model. Next, the recently developed 2DV model for the wave overtopping flow over a grass-covered dike (Van Bergeijk et al, 2020) is used to compute the flow velocity, pressure, shear and normal stress along the dike profile for four overtopping volumes. The hydraulic load along the dike profile is analyzed to gain insights in the effect of transitions on the overtopping flow and the hydraulic load near transitions.…”

“…The 2DV model is developed in the open-source software OpenFOAM and simulates the flow from the start of the dike crest to the end of the inner slope (Van Bergeijk et al, 2020). The Nikuradse roughness height K s of grass was calibrated to 8 mm and the roughness of asphalt is set to 10.1 mm, corresponding to a friction factor f of 0.01 and 0.02 for a layer thickness of 20 cm, respectively.…”

“…The horizontal grid size is 5 cm and the vertical grid size is 3 cm. The required boundary conditions at the start of the crest are the depth-averaged flow velocity and layer thickness of the overtopping wave as function of time which are generated from the overtopping volume (Van Bergeijk et al, 2020). The k − ω SST turbulence model is used to simulate the turbulence in the flow.…”