Numerical modelling of wave overtopping-induced erosion of grassed inner sea-dike slopes

Recent field wave overtopping experiments on grassed sea-dikes indicate that a moderate-quality grass cover can surprisingly resist severe overtopping rates. This high erosion-resistant capacity against wave overtopping of grass covers is owing to the root reinforcement of grass in the subsoil. Inspired by this finding, the present study makes first attempt to develop a numerical model of wave overtopping-induced erosion of the inner slope of grassed sea-dikes, considering the effect of the root reinforcement. The critical velocity for grass erosion is described as a function of the root cohesion and thus decreases with the erosion depth. This depth-dependent strength of grass allows for a better description of the nature of grass erosion, especially eligible for modelling erosion initiated from a naturally or artificially weak spot in a grass slope. Wave overtopping on grass slopes exhibits high turbulence with entrained air bubbles, for which the bed shear stress determined according to the conventional approach for ordinary open-channel flows is underestimated. To resolve this, it is assumed that the structure of wave overtopping resembles that in a bubbly turbulent wall jet, so that the bed shear stress can be determined in connection with the degree of flow turbulence. Model validation against the data from field overtopping experiments conducted in the Netherlands shows that main features of grass erosion on landward dike slopes are successfully simulated. Numerical experiments on various aspects of grass erosion are carried out which give some new insights into the nature of wave overtopping-induced grass erosion. Also, if the process of breach initiation of a grassed dike can be divided into subprocesses, erosion of the grass turf and erosion of the bare clay cover, an attempt is successfully made to roughly anticipate the breach initiation time of grassed sea-dikes composed of a sand core and a grassed clay cover. Copyright Springer Science+Business Media B.V. 2012