In this study, the mean wave overtopping characteristics of vertical-type and return-type crown walls installed on rubble-mound breakwaters armored with tetrapods were experimentally investigated, and the applicability and limitations of the mean over...
In this study, the mean wave overtopping characteristics of vertical-type and return-type crown walls installed on rubble-mound breakwaters armored with tetrapods were experimentally investigated, and the applicability and limitations of the mean overtopping formula proposed in EurOtop (2018) were evaluated. The original reduction coefficient in the EurOtop formulation was derived primarily from experiments with irregularly placed tetrapods; however, the present results demonstrate that under the double-layered, regularly placed conditions commonly adopted in Korea, the formula consistently underestimates mean overtopping rates. To improve the predictive accuracy of mean overtopping, four types of reduction coefficients—fixed, exponential, inverse, and linear—were proposed and optimized using the Levenberg–Marquardt (LM) algorithm. Comparative analyses of both vertical and return-type crown walls revealed that the inverse-type reduction coefficient performed best overall. The inverse-type coefficient produced the smallest error values in terms of RMSE, SI, and SD, while achieving a Nash–Sutcliffe Efficiency (NSE) exceeding 0.93, indicating substantially higher predictive reliability compared with the other coefficient forms. Scatter-plot analyses of predicted and measured overtopping rates also showed that the inverse-type model yielded the least under- and overestimation across both low- and high-overtopping conditions. Similar trends were observed for the return-type crown wall, implying that a single reduction coefficient in the existing EurOtop formula is insufficient to capture the influence of crown-wall geometry on overtopping behavior. The inverse-type reduction coefficient proposed in this study effectively reflects the nonlinear dependence of overtopping reduction on wave steepness and structural configuration, offering a more realistic and reliable approach for evaluating overtopping discharge in Korean coastal and port structures. The findings of this study are expected to supplement the limitations of the existing EurOtop formulation and serve as essential reference data for establishing overtopping prediction frameworks tailored to domestic coastal conditions.