## 5 Response of Pulse Seismic Waves to Bridge Piers
### Influence of Pulse Ground Motion on the Hydrodynamic Effect of Bridge Piers  
This study investigates the effects of water levels on the dynamic behavior of bridge piers, focusing on acceleration at a 5 m height and stress at a 1 m height. By comparing water depths of 0 m and 10 m, the analysis reveals that the existence of water, especially at higher levels, generally amplifies the dynamic behavior of the pier under non-pulse seismic motion. This consequence is primarily attributed to the low height-to-size ratio of the bridge piers [36]. However, various factors influence the dynamic behavior, including the spectral characteristics of the seismic motion [38], the dimensions of the bridge, and the water level. Higher water levels are found to increase the forces acting on the bridge, altering the natural frequency and damping properties. Consequently, a thorough understanding of these dynamic interactions is crucial for assessing the seismic resilience of bridges, particularly in areas with fluctuating water levels [39]. Figure 7 illustrates the acceleration and stress behavior time histories of bridge piers at different water levels under non-pulse ground motions with distinct characteristic periods. Figure 8 shows the acceleration and stress behavior time histories of bridge piers with varying water levels subjected to pulse ground motion with distinct characteristic periods. From Figure 7, showing that when the bridge pier is under non-pulse seismic motion action, when Tg = 0.45 s, the peak acceleration rates of the bridge pier in the anhydrous environment and the water environment are 0.4629 m/s\({}^{2}\) and 0.5129 m/s\({}^{2}\), respectively. The hydrodynamic effect of acceleration is 10.80%; the peak stress values are 13.2089 MPa and 12.9822 MPa, and the hydrodynamic effect of stress is \(-\)1.72%. When Tg = 0.40 s, the peak acceleration values of the pier structure in an anhydrous environment and the water environment are 0.4941 m/s\({}^{2}\) and 0.5126 m/s\({}^{2}\), respectively, and the hydrodynamic effect of the acceleration is 3.74%. The peak stress values are 13.3561 MPa and 13.3728 MPa, respectively, and the hydrodynamic effect of stress is 0.13%. When Tg = 0.30 s, the peak acceleration values of the pier structure in the anhydrous environment and the water environment are 0.5903 m/s\({}^{2}\) and 0.5612 m/s\({}^{2}\), respectively, and the hydrodynamic effect of the acceleration is \(-\)4.93%. The peak stresses are 15.5085 MPa and 15.0731 MPa, respectively, with a corresponding hydrodynamic effect of the stress of \(-\)2.81%. From Figure 8, where the bridge pier is under pulse ground motion action, when Tg = 0.45 s, the peak acceleration values of the bridge pier in an anhydrous environment and a water environment are 0.5422 m/s\({}^{2}\) and 0.6074 m/s\({}^{2}\), respectively. The hydrodynamic effect of acceleration is 12.03%; the peak stress values are 21.2677 MPa and 21.3105 MPa, and the hydrodynamic effect of stress is 0.2%. When Tg = 0.40 s, the peak acceleration values of the bridge pier structure in the anhydrous environment and the water environment are 0.5422 m/s\({}^{2}\) and 0.6074 m/s\({}^{2}\), respectively. The hydrodynamic effect of acceleration is 12.03%; the peak stress values are 21.2677 MPa and 21.3105 MPa,  
0.6392 m/s\({}^{2}\) and 0.6616 m/s\({}^{2}\), respectively, and the hydrodynamic effect of the acceleration is 3.5%. The peak stress values are 21.1582 MPa and 21.1707 MPa, respectively, and the hydrodynamic effect of stress is 0.06%. When Tg = 0.30 s, the peak acceleration values of the bridge pier in the anhydrous environment and the water environment are 0.6951 m/s\({}^{2}\) and 0.6358 m/s\({}^{2}\), respectively, and the hydrodynamic effect of the acceleration is, thus, calculated to be \(-\)8.53%. The peak stress values are 21.2333 MPa and 21.2878 MPa, respectively, with a hydrodynamic effect of stress of 0.26%. From Figures 7 and 8, the water has a relatively minor effect on the acceleration and displacement time histories.