## 3 Results
### Average Wave Overtopping Discharge  
Wave overtopping flows, as measured during the physical model tests, are herein compared with the main literature prediction methods. In the EurOtop Manual [30] the main predicting formulae to be adopted for estimating q\({}_{\text{rear}}\)* in steep structures hit by surging or non-breaking waves are resumed. In particular, q\({}_{\text{rear}}\)* is suggested to be calculated as follows:  
\[\text{q}_{\text{rear}}\text{*}=c_{1}\cdot\exp\{-[c_{2}\cdot\text{R}_{\text{c} }/\text{H}_{\text{m0}}\cdot(\gamma_{t}\cdot\gamma_{\text{P}}\cdot\gamma_{\text {P}})^{-1}]c_{3}\} \tag{3}\]where \(c_{1}\), \(c_{2}\) and \(c_{3}\) are empirical coefficients to be set equal to 0.2, 2.6 and 1.0, respectively, to derive the maximum wave overtopping for non-breaking waves [30]; \(\gamma_{\rm f}\) is the permeability and roughness factor; \(\gamma_{\beta}\) takes into account the oblique wave attack; and \(\gamma_{\rm b}\) should be retained to consider the presence of a berm in the structure. Equation (3) is applicable for \(0.5<R_{\rm c}/H_{\rm m0}<3.5\) and \(14^{\circ}<\alpha<45^{\circ}\). In the present case, no berm has to be considered (\(\gamma_{\rm b}=1.0\)), and only a perpendicular wave attack was simulated (\(\gamma_{\beta}=1.0\)). An uncertainty level affects the modeling of the structure roughness. Moreover, \(\gamma_{\rm f}\) is hardly to be accurately defined, indeed, due to the relevant differences in the effective roughness between the traditional breakwaters and the herein studied OBREC configuration. As demonstrated by [19], an equivalent roughness reduction on the passage from standard breakwaters to OBRECs is assumed by adopting \(\gamma_{\rm f}=0.70\). [PERSON] and [PERSON] [58] provided a new method to estimate \(q_{\rm rear}\) in dependence of \(\alpha\) and \(R_{\rm c}/H_{\rm m0}\) for steep low-crested structures, being in between mildly sloping dikes and vertical walls. If the geometry of the present physical model of OBREC is considered, then the following equation is applicable according to the following [58]:  
\[q_{\rm rear}*=0.2\cdot\exp(1.57\cdot\cot\alpha-4.88) \tag{4}\]  
Equation (4) is valid for \(0.8<R_{\rm c}/H_{\rm m0}<2.0\) and \(34^{\circ}<\alpha<90^{\circ}\). [PERSON] and [PERSON] [59] modified the approach indicated by [58], to define \(c_{1}\), \(c_{2}\) and \(c_{3}\) in Equation (3). In particular, \(c_{1}\) and \(c_{2}\) were assumed as a function of \(\alpha\). For \(\alpha\geq 26^{\circ}\), as in the present case, they can be derived as follows:  
\[c_{1}=0.09-0.01\cdot(2-\cot\alpha)^{2.1} \tag{5}\]  
\[c_{2}=1.50+0.42\cdot(2-\cot\alpha)^{1.5} \tag{6}\]  
Moreover, \(c3\) was made equal to 1.3, instead. This method is adoptable for \(0.0<R_{\rm c}/H_{\rm m0}<2.0\) and \(20^{\circ}<\alpha<90^{\circ}\), and it was included in [30] later. Figure 9 shows the measured values of \(q_{\rm rear}*\) as a function of \(R_{\rm c}/H_{\rm m0}\). As visible, \(q_{\rm rear}*\) decreases as \(R_{\rm c}/H_{\rm m0}\) augments. This demonstrates that, by making \(H_{\rm m0}\) constant, the larger is \(R_{\rm c}\), the smaller is the overtopped water volume beyond the structure. A comparison between the observed \(q_{\rm rear}*\) and the corresponding predicted values by [30; 58; 59] is also provided in Figure 9. All the predicting equations overestimate the observed \(q_{\rm rear}*\). This is clearly an effect of the nose, whose presence at the crest of the crown wall is not considered by [30; 58; 59]. The parquet limited the overtopping flows at the rear side of the OBREC, and, consequently, the measured values of \(q_{\rm rear}*\) are smaller than the corresponding computed values. Note that, according to the experimental data, \(R_{\rm c}/H_{\rm m0}\) varies between about 1.20 and 2.50. This implies that the relations suggested by [58; 59] cannot be indiscriminately applied to the herein experimental dataset.