## 5 Results Analysis
### Tall Bridge Pier Under Multidimensional Ground Motions
To evaluate the different damping ratios, the variations in the peak displacement of the Z section and the peak shear stress of the YZ section of a tall bridge pier along the height subjected to multidimensional pulse ground motion are analysed. Figure 10 illustrates the trend in the displacement peak value of the Z section of a tall bridge pier structure with different damping ratios under multidimensional pulse ground motions. Figure 8: Time histories of the Z section displacement and YZ section shear stress response of tall bridge pairs subjected to multidimensional non-pulse ground motion: (**a**) displacement and (**b**) shear stress. The analysis is shown in Figure 10, and Table 2 demonstrates that the peak displacement at the Z section of a tall bridge pier increases as the bridge pier height increases under multidimensional pulse ground motions. When the damping ratios are set to 5% and 10%, the peak displacements for three-dimensional ground motions are nearly identical, indicating that the structure behaves similarly under these conditions. However, at a lower damping ratio of 3%, the peak displacement under three-dimensional ground motion is lower than that under one-dimensional or two-dimensional ground motions. These findings indicate that the damping ratio of a tall bridge structure has a notable effect on its seismic response to multidimensional ground motion actions. Furthermore, the interactions between the different directional components of the ground motion also significantly affect the displacement behaviour. As shown in Figure 11 and Table 3, the YZ section value of the peak shear stress of a tall bridge pier with different damping ratios under three-dimensional ground motion demonstrates a decrease with increasing bridge pier height. However, there is a sudden change point at the top, where the value abruptly increases. For damping ratios of 5% and 10%, the YZ section peak shear stress values of a tall bridge pier under three-dimensional ground motions are similar. When the damping ratio is 3%, the peak value of the YZ section shear stress of the tall bridge pier subjected to three-dimensional ground motions is less than that of one-dimensional and two-dimensional ground motions, indicating that the different damping ratios affect the input law for multidimensional ground motion of the tall bridge pier. Figure 11: Peak trends of the shear stress of the YZ section of the tall bridge pier structure with varying damping ratios under multidimensional pulse ground motion: (**a**) \(\xi\) = 3%; (**b**) \(\xi\) = 5%; and (**c**) \(\xi\) = 10%. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Pier** \\ **Heights** \\ **(m)** \\ \end{tabular}  } & \multicolumn{6}{c}{**Shear Stress (MPa)**} \\ \cline{2-10}  & \multicolumn{3}{c}{**\(\xi\) = 3\%**} & \multicolumn{3}{c}{**\(\xi\) = 5\%**} & \multicolumn{3}{c}{**\(\xi\) = 10\%**} \\ \cline{2-10}  & **1D** & **2D** & **3D** & **1D** & **  
A comparison of Figures 10 and 11 demonstrates that the multidimensional ground motions possess a negligible effect on the displacement of the Z section and the shear stress of the YZ section of the tall bridge pier under different damping ratios. This is because when the tall bridge pier is under multidimensional ground motion actions, the three directions of the earthquake interact with each other, which reduces both the displacement of the Z section and the shear stress of the YZ section. Under three-dimensional seismic input, the maximum peak acceleration in the Z direction (PGA = 2 m/s\({}^{2}\)) plays a predominant role in influencing the displacement in the Z-direction and shear stress in the YZ section of a tall bridge pier. The peak displacement values and time histories of the Z section, along with the shear stress responses in the YZ section, exhibit close trends, highlighting the substantial effect of the Z-direction ground motion on these structural parameters.