## 7 Conclusions  
This study investigated the seismic dynamic response of concrete dams under NF obliquely incident P waves using finite element numerical simulations. Nonlinear time-history analyses were conducted on a typical concrete gravity dam. Various seismic input scenarios were considered, including PL and NP motion under 13 different incident angles and 2 peak ground acceleration conditions. By examining the combined effects of the pulse characteristics, incident angle and direction, and seismic intensity, the damage and displacement responses clarified the seismic behavior and failure mechanism of concrete gravity dams under obliquely incident P waves. Additionally, a nonlinear 3D predictive model was proposed to evaluate the seismic response of concrete dams. The findings of this study offer insights into dynamic response predictions for arbitrary NF earthquake input, underscoring the importance of considering the seismological characteristics and oblique incidence on the seismic performance of concrete dams in regions susceptible to NF seismic activity. The conclusions can be summarized as follows:  
1. The numerical results demonstrated that the oblique incidence angle of the P waves significantly influenced the damage to and displacement of the dam. As the incident angle of the P waves increased, the average response also increased, reaching a peak at approximately 60\({}^{\circ}\) with a slightly smaller average response at 75\({}^{\circ}\). The damage response value for positive incidence was considerably greater than that for negative oblique incidence. In contrast, the displacement response results exhibited greater symmetry in the positive and negative incidence directions. Moreover, PL motion could cause heightened levels of dynamic response and potential damage compared to NP motion. Figure 18: Three-dimensionally fitted surfaces of the displacement response by incident angle and seismic parameter for four seismic conditions: (**a**) NF pulse-like motion with positive direction; (**b**) NF pulse-like motion with negative direction; (**c**) NF non-pulse motion with positive direction; (**d**) NF non-pulse motion with negative direction. 2. The Ratio\({}_{\rm{EDP}}\) index assessed discrepancies in the response induced by the pulse characteristics. Owing to the upstream and downstream asymmetry of the dam body, the PL ground motion tended to exhibit considerably higher response values under negative oblique incidence. In the presence of strong earthquakes 0.6 g, the variation in the response between the PL and NP ground motions was more pronounced, with the maximum ratio increasing by up to 1.5 times, indicating that strong earthquakes further excite the effect of pulse components on the dam structure. 3. The influence of the incident direction on the dynamic response was determined using the proposed Diff\({}_{\rm{EDP}}\) index. The differences in the damage response caused by positive and negative incidents were nearly identical under NF earthquakes with or without pulse characteristics. Furthermore, the response difference was considerably larger when the PGA was at 0.6 g as opposed to when it was at 0.3 g, with the damage response difference reaching its maximum value at an incident angle of 45\({}^{\circ}\). Regarding displacement response, variations in Diff\({}_{\rm{UC}}\) were evident under PL and NP ground motion at 0.6 g, with the maximum value being reached at an incident angle of 15\({}^{\circ}\). 4. The optimal seismic parameter \(S_{\rm{a}}(T_{1})\) was determined by analyzing the effect of the seismic intensity and pulse parameters on the dynamic response. The coupled effects of the pulse characteristics and oblique direction were examined by establishing the relationship between \(S_{\rm{a}}(T_{1})\) and the dynamic response at various angles. As the incident angle was varied, the fitting results exhibited variations under different working conditions. The slope and intercept of the fitting line exhibited a quadratic polynomial relationship with the incident angle.