## 5 Results Analysis
### Tall Bridge Pier Under Pulse Ground Motion  
A damping ratio of 5% is adopted to simulate one-dimensional ground motion along the \(z\)-axis, characterized by a period of 0.45 s and a peak acceleration of 0.20 g. The dynamic behaviour of a tall bridge pier is studied under the influence of pulse and non-pulse ground motions. The displacement at the Z section (30 m) and shear stress at the YZ section (15 m) are selected for investigation. The time history curves of the displacement and shear stress under various earthquakes are shown in Figure 4, providing insights into the structural performance of the bridge pier under varying earthquake loading conditions. Figure 4: Time history curves of the response of tall bridge piers under pulse and non-pulse ground motion: (**a**) displacement and (**b**) shear stress. Figure 3: Acceleration time histories and acceleration spectrum curves of pulse ground motions. Figure 4 illustrates that tall bridge piers subjected to pulse ground motion exhibit a peak displacement of 0.1448 m, which is greater than the 0.0834 m displacement observed under non-pulse conditions, representing a 73.62% increase. The largest difference in displacement responses occurs during the 5-10 s interval, where the displacement time history under pulse motion is more complex and exhibits greater variability than that under non-pulse motion. This period is critical, highlighting the distinct influence of pulse ground motion on structural behaviour. These findings underscore the importance of considering the ground motion type evaluation of bridge pier structures. The peak shear stress response of a tall bridge pier subjected to pulse ground motion is greater than that under non-pulse ground motion. The peak shear stresses are 0.3987 MPa and 0.2260 MPa, respectively, with an error of 76.42%. In particular, at the 5-10 s interval, the peak shear stress error of the two earthquakes reaches a maximum. The shear stress response time history curves of tall bridge piers subjected to pulse ground motion are more complicated than those of tall bridge piers under non-pulse ground motion. In the range of 5-10 s, the time history curves of the two earthquakes exhibit notable dissimilarities. This is because the pulse signal applied in this interval alters the spectral characteristics of the original non-pulse ground motion. The analysis indicates that the displacement and shear stress responses of tall bridge piers are significantly greater when they are exposed to pulse ground motions compared to non-pulse motions. Additionally, the time history curves for displacement and shear stress exhibit greater complexity and variability when the structure is under pulse ground motion. These findings indicate the significance of considering pulse ground motion effects in the earthquake evaluation of tall bridge piers, as ignoring these effects may lead to inaccurate assessments of the structural performance. To investigate the underlying mechanisms by which pulsed ground motion affects the behaviour of bridge piers, this study used the fast Fourier transform to transform the time histories of the responses of tall bridge piers. This allowed these time-domain signals to be converted to frequency-domain representations, providing a clearer understanding of the structural dynamics under pulsed earthquake excitation, as illustrated in Figure 5.  
Figure 5 illustrates the responses of a tall bridge pier under pulse and non-pulse ground motions, specifically in terms of displacement and shear stress in the frequency domain. When the frequency is f1, the displacement and shear stress amplitudes for the tall bridge pier under pulse ground motion are significantly greater than those in the non-pulse scenario. Furthermore, the amplitude curves corresponding to displacement and shear stress under pulse ground motion exhibit greater complexity and variability, reflecting the more complicated frequency spectral characteristics of pulse ground motions.