## 5 Results Analysis
### Varying Damping Ratios Affect the Dynamic Response  
This study investigated the dynamic behaviour of a tall bridge pier under different damping ratios (3%, 5%, and 10%) when subjected to synthetic earthquake waves. The ground motion, which was characterized by a 0.45 s period and a peak acceleration of 0.20 g, was modelled in the Z direction. The principal aim was to assess the influence of the damping ratio on the bridge pier's response to both pulse and non-pulse seismic actions. The displacement at 35 m in the Z direction and the shear stress at 10 m in the YZ section of the tall bridge pier were identified as the key parameters for analysis.  
Figure 6 illustrates the time histories of the displacement and shear stress for tall bridge pier with different damping ratios (3%, 5%, and 10%) under non-pulsed ground motion. The peak displacement values for the three damping ratios are 0.1301 m, 0.1070 m, and 0.0732 m, respectively, showing a 77.73% maximum variation in displacement. The corresponding peak values for the peak shear stress are 0.2931 MPa, 0.2412 MPa, and 0.1800 MPa, respectively, with a maximum variation of 62.83%. As the damping ratio increases, the peak displacement and shear stress of the tall bridge pier decrease.  
When the time is within the range of 1-18 s, the time histories are nearly identical with three damping ratios. When the time exceeds 18 s, the time histories exhibit discrepancies. The results demonstrated that the influence of non-pulse ground motion on displacement and shear stress is relatively minor in comparison with the influence of the damping ratio. These findings demonstrate the more significant role of the damping ratio in controlling the structural responses of tall bridge pier  
Figure 6: Time history curves of the response of tall bridge pier with varying damping ratios under non-pulse ground motion: (**a**) displacement and (**b**) shear stress.  
Figure 7 presents the time histories for the displacement and shear stress of a tall bridge pier with different damping ratios subjected to pulse ground motions. As shown in Figure 7, the peak displacement values for the three different damping ratios of the tall bridge pier are 0.1973 m, 0.1836 m, and 0.1566 m, respectively, with the maximum error in peak displacement being 25.99%. For the peak shear stress, the corresponding values are 0.4558 MPa, 0.4307 MPa, and 0.3806 MPa, resulting in a maximum error of 19.76%. These findings indicate that as the damping ratio increases, both the peak displacement and peak shear stress of the bridge pier decrease gradually under pulse ground motion. The difference in peak displacement and peak shear stress for pulse ground motion is much smaller than that under non-pulse motions. This is mainly due to the frequency effect, because if the main frequency of the pulse is far from the sensitive frequency band of the structure, the energy input efficiency is reduced, resulting in a small difference between the dynamic stress amplitude and the static stress. When the time exceeds 18 s, the displacement and shear stress time histories converge for the three damping ratios, showing no significant differences. This suggests that the effect of the damping ratio is small compared to that of pulse earthquakes, and that pulse ground motion exerts a more substantial influence on the dynamic behaviour of tall bridge pier.  
In summary, pulse ground motion substantially influences the dynamic behaviour of tall bridge pier, resulting in significant variations in displacement and shear stress, whereas the effects of different damping ratios are less pronounced over time. The results highlight the dominant role of pulse ground motion in shaping the structural response, with diminishing effects on the damping ratios.