## 6 Parametric Study  
### Discussion on Effects of Seismic Parameters  
In this section, considering the numerical results under NP motion with positive incident angles, the impact of the seismic intensity and pulse parameters on the damage and displacement response is discussed to determine the optimal characterization parameters at different incident angles. Figure 13 shows the fitting line between seismology parameters (including the peak value and duration) of NF motion and the dynamic response of concrete dams for incident angles of 15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), and 75\({}^{\circ}\). Because the PGA was adjusted to 0.6 g, the numerical results show some discreteness and the corresponding \(R^{2}\) has a moderate correlation with the seismic input at various incident angles. Additionally, the composite parameter (\(I_{\mathrm{c}}\)) exhibits the highest correlation coefficient with the dynamic responses under different incident angles by combining all seismic indices related to the seismic peak and duration. Moreover, it should be noted that the seismic parameters PGV and \(I_{\mathrm{c}}\) have a greater fitting slope, affecting the dynamic response of such concrete dams enormously. Specifically, the dynamic response increases with the incident angle, reaching its peak at 60\({}^{\circ}\) or 75\({}^{\circ}\), consistent with the trend of the average response results shown in Figure 8. However, the \(R^{2}\) value between the pulse parameters and duration (including the PGV/PGA, \(T_{\mathrm{P}}\), and \(T_{90}\)) and structural responses is small. The fitting results show that the dynamic response of the concrete dam exhibits a good correlation with the seismic intensity parameters.  
Figure 14 shows the relationship between the seismic parameters related to the acceleration, velocity time history, and dynamic response under the five incident-angle conditions. It is evident from the fitting lines that the response indices correlate well with the seismic intensity parameters, with \(R^{2}\) almost exceeding 0.6. Between the incident angles of 15\({}^{\circ}\) and 45\({}^{\circ}\), the slope of the fitting line for damage and displacement responses increases relatively steadily. However, as the angle increases from 45\({}^{\circ}\) to 75\({}^{\circ}\), the growth rate of the fitting line gradually decelerates until it reaches its maximum value. Additionally, compared to the displacement response, the DVR response is more sensitive to the incident angle. Combining all the numerical results, the spectral acceleration \(S_{\mathrm{a}}(T_{\mathrm{1}})\) has a high correlation with the response indices and can be employed as the optimal seismic parameter for subsequent analysis.  
Figure 12: Difference in dynamic response for different seismic cases: (a) difference in DVR response; (b) difference in displacement response.  
Figure 14: Relationship between the seismic parameters (related to acceleration and velocity time history) and dam dynamic responses: (**a**) \(A_{\rm rms}\); (**b**) \(Al\); (**c**) \(CAV\); (**d**) \(ASI\); (**e**) \(S_{\rm a}(T_{1})\); (**f**) \(V_{\rm rms}\); (**g**) \(SED\); (**h**) \(HI\); (**i**) \(VSI\).  
Figure 13: Relationship between the seismic parameters (related to the peak value and duration) and dam dynamic responses: (**a**) PGA; (**b**) PGV; (**c**) PGV/PGA; (**d**) \(T_{90}\); (**e**) \(I_{\rm c}\); (**f**) \(T_{\rm p}\).