## 3 Results and Discussion of the Physical Experiment
### Wave Overtopping
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **State of** \\ **Movable Barrier** \\ \end{tabular} } & **Designed Sea** & **Return Period** & \multicolumn{2}{c}{**Overtopping Discharge (q, m\({}^{3}\)/(m s))**} \\ \cline{3-5}  & **Level** & **(year)** & **Model Scale** & **Full Scale** \\ \hline \multirow{4}{*}{Non-standing} & Approx. H.H.W. & 10 & \(1.366\times 10^{-4}\) & 0.0295 \\  & Approx. H.H.W. & 50 & \(5.043\times 10^{-4}\) & 0.1089 \\  & Sea level during & 10 & \(5.572\times 10^{-4}\) & 0.1204 \\  & storm surge + SLR & & & \\  & Sea level during & 50 & \(1.598\times 10^{-3}\) & 0.3453 \\  & storm surge + SLR & & & \\ \hline \multirow{4}{*}{Standing} & Approx. H.H.W. & 10 & 0 & 0 \\  & Approx. H.H.W. & 50 & \(1.749\times 10^{-5}\) & 0.0038 \\ \cline{1-1}  & Sea level during & 10 & \(1.106\times 10^{-5}\) & 0.0024 \\ \cline{1-1}  & storm surge + SLR & & & \\ \cline{1-1}  & Sea level during & 50 & \(4.602\times 10^{-5}\) & 0.0099 \\ \cline{1-1}  & storm surge + SLR & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the measured overtopping discharge. Figure 7: Photographs of the overtopping water for the maximum water surface elevation; (**a**) non-standing barrier for the 10-year return period and the approx. H.H.W. (No. 1, Table 2); (**b**) standing barrier for the 50-year return period and the sea level during the storm surge with the SLR (No. 4, Table 2). not placed in front of the vertical wall. When the mound influence is significant (i.e., \(d<0.6\) h), the prediction equations are suggested to be  
\[\frac{q}{\sqrt{gH_{m0}^{3}}}=1.3\left(\frac{d}{h}\right)^{0.5}0.0014\left(\frac{H _{m0}}{h\cdot s_{m-1,0}}\right)^{0.5}\left(\frac{R_{c}}{H_{m0}}\right)^{-3}\ \ \ \text{Valid for}\ R_{c}/H_{m0}\geq 1.35 \tag{6}\]  
\[\frac{q}{\sqrt{gH_{m0}^{3}}}=1.3\left(\frac{d}{h}\right)^{0.5}0.011\left(\frac {H_{m0}}{h\cdot s_{m-1,0}}\right)^{0.5}exp\left(-2.2\ \frac{R_{c}}{H_{m0}}\right)\ \ \text{Valid for}\ R_{c}/H_{m0}<1.35 \tag{7}\]  
where \(q\) is the overtopping discharge per meter of the structure's width, \(g\) is the acceleration of gravity, \(H_{m0}\) is the significant wave height from the spectral analysis, \(d\) is the water depth above the toe mound or the perm in front of the vertical wall, \(h\) is the water depth in front of the toe of the structure, \(R_{c}\) is the crest freeboard of the structure, and \(s_{m-1,0}\) is the wave steepness with \(L_{m-1,0}\). The wave steepness is given by  
\[s_{m-1,0}=\frac{H_{m0}}{L_{m-1,0}}=\frac{2\pi H_{m0}}{gT_{m-1,0}^{2}} \tag{8}\]  
where \(L_{m-1,0}\) is the spectral wave length in deep water, and \(T_{m-1,0}\) is the spectral wave period. Equations (6) and (7) can predict overtopping discharge under conditions where impulsive overtopping is expected. An occurrence of impulsive overtopping is determined as  
\[\frac{d}{H_{m0}}\cdot\frac{h}{L_{m-1,0}}\leq 0.65. \tag{9}\]  
Figure 8 shows the definitions of the parameters related to Equations (6) and (7). The parameters for the movable barrier are defined similar to EurOtop's definitions, even though armor units (i.e., T.T.Ps) are placed in front of the vertical wall and the revetment. Table 4 shows detailed parameters at the model scale. The case where the overtopping discharge is zero in Table 3 is excluded. As shown in Table 4, for all cases, the mound has a significant influence (i.e., \(d<0.6\) h), and the impulsive overtopping conditions are less than 0.65. Thus, Equations (6) and (7) can be used to compare the overtopping discharge in this study. Figure 9 shows the relative overtopping discharge with respect to the relative free board. Based on the relative free board, the standing barrier is compared with Equation (6), and the non-standing barrier is compared with Equation (7).