Better models for the wave overtopping flow and dike cover erosion that include the effect of several transitions to improve the design of flood defences.
Top: Road on a grass-covered sea-dike (photo by Vera van Bergeijk). Bottom-left: Wave overtopping on a grass-covered dike with a road on top (source: Tipner Lake Coastal Defences, 2019). Bottom-right: Erosion of the grass cover at the inner toe during field tests (source: Hoffmans, G. 2014).
Motivation and practical challenge
In the Netherlands, the introduction of multi-functional flood defences has led to an increase in the number of transitions on flood defences. Examples of these transitions are roads on grass-covered dikes (top photo) and geometrical changes such as berms and objects including stairs and trees. During storms, high waves can overtop the dikes and run down on the landward slope. The large forces of these overtopping waves lead to erosion of the grass cover (bottom-left photo). Once the cover is eroded, the core material of the dike starts to erode, weakening the dike and resulting in the end, in a dike breach. Wave overtopping was indeed one of the main failure mechanisms that led to dike failure during the flood of 1953. Recent experiments and numerical studies have shown that transitions are weak spots along with the dike profile (bottom-right photo). At these locations, the erosion by overtopping waves starts. However, we do not know how these transitions affect the overtopping flow and dike cover erosion, thus it is hard to include transitions in current calculation methods for dike failure.
Fascinated by the force of waves and their strength to erode, I develop analytical and numerical models for the wave overtopping flow and dike cover erosion. Using these models, I investigate how the wave overtopping forces and the cover strength are affected by transitions.
To address the above challenge, I develop two types of models. The first model is simple and fast, while the second numerical model calculates the forces pulling on the dike cover in more detail (top-left figure). In the models, locations are identified where the hydraulic forces are high resulting in erosion of the grass cover and failure of the dike. See the top-right figure for a zoom into the slope at a location with a high load that pulls hard on the grass cover leading to erosion.
Moreover, existing calculation methods can only be applied to one location of the dike profile. These new models calculate the forces along with the entire dike profile and therefore calculate the upstream and downstream effect of transitions on the flow. Lessons learned from the detailed model are simplified and implemented in the fast model. Thereby, I study three types of transitions (bottom-left figure):
- cover type: an asphalt road on a grass-covered dike.
- geometry: slope changes such as a horizontal berm.
- height differences: existing erosion holes or irregularities in the profile.
To determine the effect of transitions, we use the data of field tests on a grass-covered dike with a road on top near Millingen a/d Rijn. We further use the new green design of the Afsluitdijk to find vulnerable locations for grass-cover erosion (on the map below).
Relevant for whom and where?
Professionals or organizations involved in the design, assessment and maintenance of transitions on flood defences. The modelling approach developed in this study can be used to determine the failure probability of wave overtopping for complex flood defences with several transitions.
The models use dataset of experiments on a grass-covered dike near Millingen and are futher applied at Afsluitdijk.
Progress and practical application
In this study, two models are developed that are freely available and widely applicable. These models are more accurate than existing calculation methods and can be applied to flood defences with several transitions. To develop the models, I used a dataset of experiments on a grass-covered dike near Millingen aan de Rijn. A model study of the new design of the Afsluitdijk showed that transitions result in a lower critical overtopping discharge that is 10 times as small as flood defences without transitions. Furthermore, the inner toe was the weakest cross-dike location because of high flow velocities at this location. Numerical simulations have shown that the forces related to turbulence are high on the lower slope and the pressure increases at the inner toe. This means that the erosion at the inner toe is not only caused by high flow velocities, but also by an increase in the pressure and turbulence. Additionally, simulations with the fast model show that the failure probability increases significantly for damaged dikes as the result of cover erosion or slope instability.
Status for day-to-day practice
The effect of transitions on the overtopping flow and resulting cover erosion need to be taking into account during the design of flood defences to find the optimal location and design of the transitions.
The next steps include modelling the hydraulic forces near transitions using the detailed model to understand how the flow and cover erosion changes due to transitions. Additionally, simple design rules are developed for the maximum force and its location along the dike profile based on simulations with the detailed model.
Last modified: 27/04/2021
Vera van Bergeijk
University of Twente
Modelling the wave overtopping flow over the crest and the landward slope of grass-covered flood defenses
A new detailed model that is able to calculate the load of the overtopping waves on the grass cover and provides insights in how the load changes along the profile.
02/07/2020 by Vera van Bergeijk et al.
Bevat: Publication open access journal
An analytical model of wave overtopping flow velocities on dike crests and landward slopes
New formulas for the flow velocity over the dike crest and landward slope that can be applied to a wide range of geometries and dike covers.
Bevat: Publication upon journal access
Failure probability by wave overtopping over grass-covered and damaged dikes
We calculate the failure probability by wave overtopping of grass-covered and damaged dikes and show that damages to the dike cover, such as an animal burrowing or an erosion hole, can increase the failure probability significantly.
03/03/2021 by Vera van Bergeijk et al.
Bevat: Conference proceedings Publication open access journal
van Bergeijk, V.M., Warmink, J.J., Hulscher, S.J.M.H., 2020. Modelling the Wave Overtopping Flow over the Crest and the Landward Slope of Grass-Covered Flood Defences. JMSE 8, 489. https://doi.org/10.3390/jmse8070489
- van Bergeijk, V. M., Warmink, J. J., Frankena, M., & Hulscher, S. J. M. H. (2019). Modelling Dike Cover Erosion by Overtopping Waves: The Effects of Transitions. In N. Goseberg, & T. Schlurmann (Eds.), Coastal Structures 2019 Bundesanstalt für Wasserbau. https://doi.org/10.18451/978-3-939230-64-9_110
- van Bergeijk, V. M., Warmink, J. J., van Gent, M. R. A., & Hulscher, S. J. M. H. (2019). An analytical model of wave overtopping flow velocities on dike crests and landward slopes. Coastal engineering, 149, 28-38. https://doi.org/10.1016/j.coastaleng.2019.03.001
- Warmink, J. J., van Bergeijk, V. M., Chen, W., Van Gent, M. R. A., & Hulscher, S. J. M. H. (2018). Modelling wave overtopping for grass covers and transitions in Dike Revetments. International Conference Proceedings of Coastal Engineering, 1(36), 53. https://doi.org/10.9753/icce.v36.papers.53
- Warmink, J. J., van Bergeijk, V. M., Chen, W., Aguilar Lopez, J. P., Bomers, A., & Hulscher, S. J. M. H. (2018). Modelling wave overtopping for flood defense reliability. 1-5. Paper presented at 3rd International Conference on Protection against Overtopping 2018, Grange-over-Sands, United Kingdom.