# Seismic Study of An Isolated Cable-Stayed Bridge under Near-Fault Ground Motions
## 5 Influence of Various Factors  
### Influence of Wave Passage Effect  
This section takes near-fault ground motion in Section 4.1 to investigate the effects of the traveling wave phenomenon to isolated bridge. Seven scenarios are analyzed, including six incident waves ranging from 200 m/s to 1200 m/s, with uniform intervals of 200 m/s, and one consistent excitation case. Figure 8a depicts the average bounding force at the two expansion joints under the influence of near-fault waves for all apparent wave velocities and consistent excitation (represented by v =\(\infty\)). The deformation requirements at different expansion joints in the Figure 8 exhibit a consistent trend with wave speed, despite having different absolute values. Figure 8: Average maximum responses considering different wave passage effect: (**a**) bounding force at each expansion joint; (**b**) longitudinal bearing displacement; (**c**) longitudinal bending moment of tower. Figure 8b illustrates the deformation of the bearings of the cable-stayed bridge under the influence of different wave passage velocities. On the one hand, considering the wave passage effects, the bearing deformation significantly increases compared to uniform excitation. The smaller the wave velocity, the larger the bearing deformation. For instance, when \(\
u=\infty\), the bearing deformation at pier 4 is 48.3 cm, increasing to 76.8 cm at \(\
u=200\) m/s, with a growth rate of 62.7%. On the other hand, when uniform excitation is considered, the deformations of the bearings on the north and south sides of the cable-stayed bridge are symmetric and consistent. However, when non-uniform excitation considering traveling wave effects is considered, there are notable differences in the longitudinal bearing deformations, becoming more pronounced as the wave velocity decreases. For example, at \(\
u=200\) m/s, when non-uniform excitation is considered, the bearing deformation on the north side, where the seismic wave arrives first, is greater than on the south side, resulting in a 21.6% difference in bearing deformation between pier 4 and 9. As the seismic wave velocity increases, this difference gradually decreases. Figure 8c illustrates the distribution of tower moments along the height direction at different wave velocities. As the tower position descends, the moments become larger, with a significant discontinuity occurring at a height of 82.2 m, where two tower columns merge in the design. The graph indicates that as the wave velocity decreases, the moments in the cable-stayed bridge equipped with a damping system become larger. This suggests that traveling wave effects not only increase bearing deformation but also magnify the internal forces in the bridge towers, thereby exerting unfavorable effects on the structure. To better illustrate the impact of traveling wave effects on bounding, taking GM6, GM7, and GM8 as examples, Figure 9 provides time-history curves of bounding forces at two expansion joints for wave velocities \(\
u=\infty\), \(\
u=800\) m/s, and \(\
u=200\) m/s. Under the action of GM6, the bounding frequency and peak force at the expansion joint 1 are consistent across all cases, occurring at t = 12.54 s. However, with a decrease in wave velocity, the bounding force significantly increases, with peak values of 29,625 kN, 42,112 kN, and 101,125 kN at the expansion joint 1 for \(\
u=\infty\), \(\
u=800\) m/s, and \(\
u=200\) m/s, respectively. At expansion joint 2, the reduction in wave velocity not only increases the bounding force but also the bounding frequency. Under GM7, no bounding occurs at expansion joints 1 and 2 when \(\
u=\infty\), but they do occur at \(\
u=800\) m/s and \(\
u=200\) m/s.