Vera M. van Bergeijk

Salt marshes protect coastlines by attenuating wind waves with their elevated marsh platform and above-ground vegetation¹. Confidence in the persistence of this service under a changing climate requires knowledge on how extreme storms damage the platform and vegetation; however, a comprehensive, quantified understanding of salt marsh–wave interactions under extreme events is lacking. A unique experiment was conducted by transferring intact salt marsh to one of the world’s largest wave flumes, and subsequently exposing it to increasingly higher waves that reach up to 2 m significant wave height. We show that marsh substrates can persist with negligible erosion, despite cumulative wave exposure. By contrast, the vegetation was progressively damaged during continued wave exposure, gradually reducing vegetation-related wave attenuation. Results emphasize that vegetation was most effective in attenuating waves at low-energy marsh coasts (up to 1 m), where attenuation exceeded 10% (up to 50%), whereas attenuation at high-energy marsh coasts (wave height > 1 m) does not exceed 10%. Our global assessment supports the differentiation between low- and high-energetic conditions resulting from the flume experiment. Our results suggest that the marsh platform remains stable under extreme wave events and that substantial wave attenuation by marsh vegetation is limited to low-energy marsh coasts.

Wave overtopping on grass-covered dikes results in erosion of the dike cover. Once the dike cover is eroded, the core will be washed away and the dike breaches, leading to flooding of the hinterland. Transitions between grass covers and revetments or geometric transitions are vulnerable for cover erosion and are therefore the most likely locations to initiate dike breach. These transitions affect the overtopping flow and thereby the hydraulic load on the dike cover. For example, bed roughness differences can create additional turbulence and slope changes can result in the formation of a jet that increases the load at the jet impact location. Although it is known that dike cover failure often starts at transitions, the effect of transitions on the hydraulic load remains unknown.We developed a detailed numerical 2DV model in OpenFOAM for the overtopping flow over the crest and the landward slope of a grass-covered dike. This model is used to study the effects of transitions on the overtopping flow variables including the flow velocity, shear stress, normal stress and pressure. Several types of transitions are studied such as revetment transitions, slope changes and height differences. The results show that the shear stress, normal stress and pressure increase significantly at geometric transitions such as the transition from the crest to the slope and at the landward toe. The increase depends on the wave volume and the geometry of the dike such as the steepness and length of the landward slope. Furthermore, the results show that roughness changes at revetment transition on a grass-covered crest has no influence on the maximum shear stress, maximum normal stress and maximum pressure. The flow velocity increases from a rough to a smooth revetment, while the opposite occurs for the transition from a smooth to a rough revetment. The variation in the flow velocity is well described by analytical formulas for the maximum flow velocity along the dike profile. These formulas are also able to describe the variation in flow velocity for a revetment transition on a berm on the landward slope. In this case, the shear stress increases from a smooth to a rough revetment and decreases from a rough to a smooth revetment. This means that a rough revetment can locally reduce the shear stress, however the transitions have no effect on the shear stress downstream.These model results are used to obtain relations for the increase in the hydraulic variables at transitions. These relations can be used to describe the effect of transitions on the hydraulic load in models for grass cover failure by overtopping waves. Accurate descriptions of the hydraulic load in these models will improve the failure assessment of grass-covered dikes with transitions.

A probabilistic framework is developed to calculate the cross-dike failure probability by overtopping waves on grass-covered dikes. The cross-dike failure probability of dike profiles including transitions and damages can be computed to find the most likely location of failure and quantify the decrease in the failure probability when this location is strengthened. The erosion depth along the dike profile is calculated using probability distributions for the water level, wind speed and dike cover strength. Failure is defined as the exceedance of 20 cm erosion depth when the topsoil of the grass cover is eroded. The cross-dike failure probability shows that the landward toe is the most vulnerable location for wave overtopping. Herein, the quality of the grass cover significantly affects the failure probability up to a factor 1000. Next, the failure probability for different types of damages on the landward slope are calculated. In case of a damage where the grass cover is still intact and strong, the dike is most likely to fail at the landward toe due to high flow velocity and additional load due to the slope change. However, when the grass cover is also damaged, the probability of failure at the damage is between 4 and 125 times higher than for a regular dike profile.

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.