Wave overtopping

Wave overtopping is the time-averaged amount of water that is discharged (in liters per second) per structure length (in meters) by waves over a structure such as a breakwater, revetment or dike which has a crest height above still water level. When waves break over a dike, it causes water to flow onto the land behind it. Excessive overtopping is undesirable because it can compromise the integrity of the structure or result in a safety hazard, particularly when the structure is in an area where people, infrastructure or vehicles are present, such as in the case of a dike fronting an esplanade or densely populated area. Wave overtopping typically transpires during extreme weather events, such as intense storms, which often elevate water levels beyond average due to wind setup. These effects may be further intensified when the storm coincides with a high spring tide. Excessive overtopping may cause damage to the inner slope of the dike, potentially leading to failure and inundation of the land behind the dike, or create water-related issues on the inside of the dike due to excess water pressure and inadequate drainage. The process is highly stochastic, and the amount of overtopping depends on factors including the freeboard, wave height, wave period, the geometry of the structure, and slope of the dike.

Overtopping factors and influences Overtopping can transpire through various combinations of water levels and wave heights, wherein a low water level accompanied by high waves may yield an equivalent overtopping outcome to that of a higher water level with lower waves. This phenomenon is inconsequential when water levels and wave heights exhibit correlation; however, it poses difficulties in river systems where these factors are uncorrelated. In such instances, a probabilistic calculation is necessary. The freeboard is the height of the dike's crest above the still water level, which usually corresponds to the determining storm surge level or river water level. Overtopping is typically expressed in litres per second per metre of dike length (L/s/m), as an average value. Overtopping follows the cyclical nature of waves, resulting in a large amount of water flowing over a structure, followed by a period with no water. The official website of the EurOtop Manual, which is widely used in the design of coastal engineering structures, features a number of visualisations of wave overtopping. In the case of overtopping at rubble-mound breakwaters, recent research using numerical models indicates that overtopping is strongly dependent on the slope angle. Since present design guidelines for non-breaking waves do not include the effect of the slope angle, modified guidelines have also been proposed. Whilst these observed slope effects are too large to be ignored, they still need to be verified by tests using physical models. Overtopping behaviour is also influenced by the geometry and layout of different coastal structures. For example, seawalls (which are typically vertical, or near-vertical, as opposed to sloping breakwaters or revetments), are often situated behind natural beaches. Scour at the base of these structures during storms can have a direct impact on wave energy dissipation along their frontage, thus influencing wave overtopping. This phenomenon assumes critical importance when storms occur in such quick succession that the beach doesn't have sufficient time for sediments removed by the storm to be re-established. Experimental results show that, for near-vertical structures at the back of a beach, there is an increase in wave overtopping volume for a storm that starts from an eroded beach configuration, rather than a simple slope.

Calculation of overtopping

Wave overtopping predominantly depends on the respective heights of individual waves compared to the crest level of the coastal structure involved. This overtopping doesn't occur continuously; rather, it's a sporadic event that takes place when particularly high waves within a storm impact the structure. The extent of wave overtopping is quantified by the volume of water that overflows onto the adjacent land. This can be measured either as the volume of water per wave for each unit length of the seawall, or as the average rate of overtopped water volume per unit length during the storm wave period. Much research into overtopping has been carried out, ranging from laboratory experiments to full-scale testing and the use of simulators. In 1971, Jurjen Battjes developed a theoretically accurate equation for determining the average overtopping. However, the formula's complexity, involving error functions, has limited its widespread adoption in practical applications. Consequently, an alternative empirical relationship has been established:

Q = a ⋅ exp ⁡ ( − b R γ ) {\displaystyle Q=a\cdot \exp \left(-b{\frac {R}{\gamma }}\right)}

in which Q {\displaystyle Q} is the dimensionless overtopping, and R {\displaystyle R} is the dimensionless freeboard:

Q = q g H s 2 h / L 0 tan ⁡ α {\displaystyle Q={\frac {q}{\sqrt {gH_{s}^{2}}}}{\sqrt {\frac {h/L_{0}}{\tan \alpha }}}}

R = h c H s 1 ξ {\displaystyle R={\frac {h_{c}}{H_{s}}}{\frac {1}{\xi }}}

in which:

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