The wave overtopping load on landward slopes of grass-covered flood defences: Deriving practical formulations using a numerical model

Overtopping waves exert a high hydraulic load on the landward slopes of flood defences leading to erosion of the grass cover and finally to a dike breach. The hydraulic load is an important variable in erosion models and a detailed description of the load is necessary to determine where and when the grass cover erodes. We use a numerical model to simulate the flow of a single overtopping event over a flood defence with a grass-covered crest and landward slope. The model results show that the flow velocity, the shear stress and the pressure are maximal at the landward toe and can be used to describe grass erosion by shear forces. For steep slopes, the flow separates at the crest line and impacts on the upper slope. The normal stress is maximal at the location of impact and describes the grass erosion by normal forces. Practical formulations are developed for the maximum flow velocity, the maximum pressure, the maximum shear stress, the maximum normal stress and the impact location using three main design parameters for the landward slope: the overtopping volume, the slope steepness and the slope length. The formulations are able to accurately predict the overtopping load with Nash–Sutcliffe model efficiency factors between 0.41 and 0.90. The model output and these new formulations are used to calculate the erosive power of the overtopping waves predicted by eight erosion indices to show how the simulated load can be used in erosion models.