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

The Cross-Dike Failure Probability by Wave Overtopping over Grass-Covered and Damaged Dikes

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

Risk-based maintenance and inspection of riverine flood defence systems

The condition of flood defence revetments is influenced by many different degradation processes such as animal burrowing, rutting and growth of weeds. Many of these processes are shock-based rather than progressive continuous. As shocks can cause a drop in performance, this means that the condition of a revetment can suddenly decrease, meaning that revetments can have significant initial damage at the beginning of a storm. Combined with the limited detection probability of common visual inspections of flood defences, this can have a significant influence on the reliability of flood defence systems, something typically not considered in reliability analysis. In this paper we study the reliability of a flood defence system subject to shock-based degradation. Various maintenance concepts are compared for a case study of a riverine flood defence of 20 kilometres length. This demonstrates that the current maintenance concept is insufficient to satisfy the reliability requirements for failure of the revetment. Overall, the joint influence of degradation and the existing maintenance concept leads to a 20 times higher failure probability estimate compared to a typical assessment without these aspects. Next, we demonstrate that both additional inspections, and targeted interventions to reduce the impact of for instance animal burrowing, can significantly reduce total cost and improve robustness of the considered flood defence system.Hydraulic Structures and Flood RiskEngineering Structure

Hydrodynamic Modelling of Wave Overtopping over a Block-Covered Flood Defence

Wave overtopping can cause erosion on the landward slope due to high flow velocities and turbulence that cause high stresses on the cover. Innovative block revetments such as Grassblocks protect the subsoil of the dike against erosion. The blocks are permeable, which reduces the flow velocity and the pressures along the landward slope. The performance of these blocks is assessed in physical tests, which provides insights into the stability of the blocks. However, such experiments are expensive and accurate measurements are difficult due to highly turbulent conditions. Therefore, the goal of this study is to determine the hydrodynamic conditions at the dike cover caused by the wave run-up on the seaward slope and by the overtopping flow over the crest and landward slope. The geometry and wave conditions from the physical test at the Deltares Delta flume are implemented in an OpenFOAM® numerical model. Using the porousWaveFoam solver, a porous layer on the crest and landward slope is implemented, where the flow resistance of this porous layer largely depends on the resistance coefficients α [-] and β [-]. The numerical model is calibrated based on resistance coefficients as introduced earlier in the literature, which showed that the resistance coefficients of α=500 and β=2.0 performed best for the peak flow velocities and the peak pressures. The numerical model is evaluated by using these resistance coefficients in other time series of the physical tests. The evaluated model is then used to determine the hydrodynamic conditions on the landward slope, which showed that the pressure was the most influential hydrodynamic condition at the time of failure. Finally, the model showed that a porosity of n=0.6 and the porous layer thickness η=36mm reduced the peak pressure the most