Experimental Study on Regular Wave Overtopping over a Sloping Dike with a Flexible Vegetated Foreshore

Accurate prediction of wave overtopping at vegetated sloping dikes is essential for nature-based coastal defense design. This study presents laboratory experiments investigating the influence of a flexible vegetated foreshore on regular wave overtopping. The results indicate that, for a fixed dike height, increased crest freeboard enhances wave attenuation by submerged vegetation. Compared with unvegetated conditions, vegetation reduces both wave height and mean water level. Wave nonlinearity diminishes across vegetated foreshores, as evidenced by increasingly negative asymmetry — a characteristic of forward-leaning waves, marked by a rapid rise and slow fall. The impact of vegetation on overtopping discharge depends strongly on its physical characteristics: greater submergence, higher density, and larger relative width lead to more pronounced reductions. On average, vegetation reduces overtopping by 14.6%, with a maximum reduction of 59.9% under optimal conditions. A new empirical formula incorporating relative vegetation submergence, density, and width is proposed to quantify overtopping reduction. The formula shows good agreement with experimental data, yielding a geometric mean (GM) of 1.02 and a geometric standard deviation (GSD) of 1.345. This model provides a practical tool for designing ecosystem-based coastal defenses.