Velocity and water-layer thickness of overtopping flows on sea dikes: Report of measurements and formulas development
The study aims to establish a set of formulas estimating velocity and depth of overtopping flows at sea dikes including seaward-side slope, crest and landward-side slope. These formulas are applicable to flows which are generated by natural waves and the simulator giving associated characteristics of any arbitrary value of exceedance probability. Note that the probability is based on the total number of incident waves and not to be confused with the total number of overtopping events. The difference between the fictitious wave run-up level and the crest level (Ru2% - Rc) is widely considered as a measure of the (potential) energy of wave overtopping. This term is therefore used to estimate values of the mean overtopping discharges, ow velocities, water-layer thickness and overtopping volumes. In line with many existing research works and guidelines, the potential term is crucial to derive other parameters. Experimental data of Van Gent [2002] is reanalyzed with a slightly different perspective to achieve the study objective. The analysis procedure basically consists of three main steps:  from wave conditions and dike cross-section to calculate wave run-up levels;  from wave run-up levels to estimate flow parameters on the dike crest;  from flow parameters on the dike crest to further compute the corresponding parameters on the landward slope. The obtained equations are verified with flow measurements of the simulator on real dike slopes. Consequently, feasible values representing the roughness of different grass coverings are determined.
Flow depths and velocities at crest and landward slope of a dike, in theory and with the wave overtopping simulator
Wave overtopping discharges at coastal structures are well described in the EurOtop Manual (2007), including the distribution of overtopping wave volumes. Each volume that overtops a dike or levee will have a certain flow velocity and depth record in time, often given by the maximum velocity and flow depth. This paper describes some further development of the theory on flow depth and velocities on the crest, but will also show an inconsistency with respect to the mass balance. The second part of the paper gives an analysis of measured values on real dikes, simulated by the Wave Overtopping Simulator. It gives also the method of "cumulative hydraulic load" to compare overtopping discharges for different wave conditions. A large wave height with less overtopping waves, but larger overtopping wave volumes, is more damaging than a small wave height with more, but smaller overtopping volumes, even if the overtopping discharge is similar. The reasons to develop the cumulative hydraulic load have been compared with the recently in the US developed method of erosional equivalence.
Wave overtopping resistance of grassed dike slopes in Vietnam
The resistance of various grassed slopes against wave overtopping has been appraised by means of the Wave Overtopping Simulator in situ for a couple of years in Viet Nam. Destructive test results show that a dike slope covered with grass could suffer a certain overtopping discharge not smaller than 20 l/s per m. During testing it was difficult to predict when a slope starts to be damaged, however, damages tend to follow a more or less similar process of development. The concept of “erosional indices” and the method of “cumulative overload” (van der Meer et al., 2010) are applied to the simulator tests in Viet Nam. Critical velocities were then estimated for different kind of grassed slopes.