# Seismic Study of An Isolated Cable-Stayed Bridge under Near-Fault Ground Motions
## 4 Pounding Mitigation Performance of Seismic-Reduction System
### Pounding Mitigation Performance  
To investigate the impact of the bounding effect between the cable-stayed bridge and the approach bridge, and the bounding mitigation effect of FPBs and FVDs, four cases are set as follows:  
* Case I: Prototype bridge without considering bounding effect;
* Case II: Prototype bridge considering bounding effect;
* Case III: Isolated bridge without considering bounding effect;
* Case IV: Isolated bridge considering bounding effect. In this context, the term \"prototype bridge\" refers to a bridge without any isolation devices, while the term \"Isolated bridge\" refers to the bridge where FPBs are installed at the bridge piers and towers, and FVDs are assembled between the bridge towers and the main beam. Full transient dynamic analysis techniques, in conjunction with the Newmark algorithm are applied in the time history analyses. These analyses meticulously account for substantial deflection effects, ensuring a comprehensive assessment of structural response. Note that the wave velocity of 800 m/s is considered in the non-uniform excitation. Figure 6 shows the seismic response of the bridge under the above four cases. Figure 6a shows the bounding force of the cable-stayed bridge and the approach bridge at expansion joint 1 and expansion joint 2. The bounding force at expansion joint 1 is 1.30 \(\times\) 10\({}^{5}\) kN in Case II, which is reduced to 6.46 \(\times\) 10\({}^{4}\) kN in Case IV equipped with FPBs and FVDs. The bounding force at expansion joint 2 is 5.48 \(\times\) 10\({}^{4}\) kN in Case II and is reduced to 3.02 \(\times\) 10\({}^{4}\) kN in Case IV. The reduction rates of FPBs and FVDs on the bounding force at expansion joints 1 and 2 are 50.4% and 44.8%, respectively. Figure 6b illustrates the longitudinal bearing deformation of the cable-stayed bridge. Due to the consideration of the wave passage, the deformation of the bearings on both sides of the cable-stayed bridge is asymmetrical. As seismic waves propagate from the north side to the south side, the deformation of the bearings on the north side of the bridge is greater than that on the south side. On the north side of the bridge, the deformation of the bearings in Case I and Case II is not significantly different. However, on the south side, the deformation of the bearings in Case II is noticeably smaller than that in Case I. The reason is that the approach bridge on the south side collides with the main bridge, impeding the movement of the main bridge. Similar patterns can be found through comparison of Case III and Case IV. By comparing Case I with Case III and Case II with Case IV, it can be observed that, regardless of whether bounding is considered, the displacement of the bearings in the isolated bridge equipped with FPBs and FVDs is significantly smaller than that of the prototype bridge. To better visually observe the bounding mitigation effect of the longitudinal seismic-reduction system, Figure 7 provides time-history curves of bounding forces and bearing displacements at expansion joint 2 under the action of the sixth seismic wave for four cases. Figure 7 illustrates that the longitudinal seismic reduction system reduces the maximum bounding force at expansion joint 2 from 1.48 \(\times\) 10\({}^{5}\) kN to 7.25 \(\times\) 10\({}^{4}\) kN. By examining the bounding force and bearing displacement time-history curves together in  
Figure 6: Average maximum responses in different cases: (**a**) bounding force at each expansion joint; (**b**) longitudinal bearing displacement. Figure 7: Sample time histories at EJ2 under GM6: (**a**) bounding force; (**b**) bearing displacement of main bridge at Tower 2; (**c**) bearing displacement of south approach bridge at Pier 9. Figure 7, it can be observed that each peak in bounding force corresponds to a peak in displacement. In Case I, without considering promoting effects, when the bridge moves southward, the maximum deformation of the cable-stayed bridge is 148 cm, while the bearing deformation of the approach bridge is only 11 cm.