An idealised model to study the effects of transitions on wave overtopping flow and dike
cover erosion
V.M. van Bergeijk1, J.J. Warmink1, S.J.M.H. Hulscher1
1 University of Twente, Marine and Fluvial Systems. Corresponding author: v.m.vanbergeijk@utwente.nl
Introduction
The major part of the Dutch flood defence system consists of dikes. One of the main failure mechanisms of dikes is wave overtopping. Waves that overtop the dike crest, run down on the landward slope and cause erosion on landward side of the dike cover. Once the cover is eroded, the dike core material starts to erode resulting in weakening of the dike which may result in a dike breach. Dike covers typically contain many transitions in roughness (e.g. from grass to asphalt; Fig. 1). Also, changes in slope angle are classified as transitions. Experiments and numerical simulations identified transitions as weak spots resulting in a local increase of dike cover erosion (Bomers et al, 2018). We want to investigate the sensitivity of various transitions in dike cover for erosion due to overtopping waves. Idealised model
As a first step, we formulate an idealised model extending the formulas of the maximum flow velocity and layer thickness of Van Gent (2002). Dike cover erosion occurs when the maximum flow velocity exceeds the critical flow velocity, the erosion depth is calculated following Hoffmans (2012) using a critical flow velocity of 4.5 m/s corresponding to an average grass cover quality. Subsequently, the idealised model is used to study the effects of several types of transitions on the overtopping flow and dike cover erosion. For example, Fig. 2 shows the effect of the slope angle on the overtopping flow velocity and the dike cover erosion maintaining a constant dike height of 4 m. The flow velocity decreases on top of the dike crest due to friction and increases on the landward slope due to the effect of gravity. The flow velocity increases with increasing slope angle while the slope length decreases with increasing slope angle. For comparison, the sum is taken of the amount of erosion along the slope to obtain the total cumulative erosion depth. The cumulative erosion depth increases with increasing slope angle even though the slope is much shorter. We compare the cumulative erosion depth of a change in slope with placing a berm on the landward slope and roughness transitions to find which measure is most effective in the reduction of erosion.
Acknowledgements
This work is part of the research programme All-Risk, with project number P15-21, which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO).
References
Bomers, A., Lopez, J. A., Warmink, J. J., & Hulscher, S. J. (2018). Modelling effects of an asphalt road at a dike crest on dike cover erosion onset during wave overtopping. Natural hazards, 1-30.
Van Gent, M. R. A. (2002). Low-exceedance wave overtopping events: Measurements of velocities and the thickness of water-layers on the crest and inner slope of dikes. Delft Cluster Report DC030202/H3803. Delft Hydraulics, Delft.
Hoffmans, G. J. (2012). The influence of turbulence on soil erosion (Vol. 10). Eburon Uitgeverij BV. Figure 1: Wave overtopping on a dike with a road on top of the dike crest resulting in roughness transitions.
Figure 2: (a) The maximum flow velocity as function of the cross-dike direction for various steepness’s of the landward slope with a crest height of 4 m. The critical flow velocity is shown in red dashed. (b) The cumulative erosion depth as function of the slope angle of the landward slope.
