# Effectiveness of LRB in Curved Bridge Isolation:
## 5 Sensitivity of Response Parameters
### Uni-Directional Loading  
Figure 9a-i show the bridge response variation with the variation of damping ratio for the considered time period ranges for uni-directional Imperial Valley, Kobe, and Turkey earthquakes, respectively. It can be seen from the figures that most of the response parameters are non-linear with respect to changes in damping ratios. A higher damping ratio reduces the bearing displacement for all the considered earthquakes. The yield force  
Figure 8: Effect of incidence angle (\(\alpha\)) on response parameter of the isolated bridge under bi-directional Imperial Valley (**a–d**), Kobe (**e–h**), and Turkey (**i–I**) Ground Motions. of the seismic isolation bearing increases as the damping ratio increases. The reduction in bearing displacement was observed in Imperial Valley (15-20%) and Turkey (8-19%) ground motions, especially in higher time periods exceeding 1.5 s. For Kobe ground motion, it was found that the bearing displacement changed very little relative to the damping ratio (3-5%). It was also found that in the case of Turkey ground motion, the variation of bearing displacement was linear and steeper for the higher time periods ranging from 2.5 to 3.0 s which might be due to the forward directivity effect that causes a sharp decrease in the bearing displacement for higher time periods. It was observed that the force transmitted to the pier was not sensitive (0-4%) to the damping ratio for Kobe ground motion. In the case of Imperial Valley, the force transmitted to the pier was sensitive to the damping ratio (10-19% reduction) in the lower time period ranges of 1.5 to 2.0 s. However, in the case of Turkey ground motions, the force transmitted to the pier was sensitive (9-17% decrease) with respect to the damping ratio, especially for higher time periods from 2 to 3 s.  
In the case of Imperial Valley ground motion, pier torsional moments were found to be more sensitive with respect to damping ratio for a 1.5 s time period, while for time periods from 2.0 to 3.0 s, the same was found to be almost insensitive and found to be in the range of 5-10%. In the case of Kobe and Turkey ground motions, the pier torsional moment was found to be small (0-8%). Figure 10a-i show the variation of the bridge response for variation of the time period with all considered damping ratios for uni-directional Imperial Valley, Kobe, and Turkey  
Figure 9: The Bridge Response sensitivity with respect to the damping ratio of LRBs under uni-directional (i) Imperial Valley (**a–c**), (ii) Kobe (**d–f**), and (iii) Turkey (**g–i**) ground motions. earthquakes, respectively. It was found that with respect to the time period, the response parameters are more sensitive for all the considered damping ratios. The bearing displacements increased with respect to the time period for all the considered ground motions. The increased time period imparted additional flexibility to the structure, which increased the bearing displacement. It was observed that in the case of the Imperial Valley and Kobe earthquakes, the increase in bearing displacement is non-linear, while for Turkey's ground motion, the same is almost linear, which might be because of the forward directivity effect. The transmitted force to the pier was found to be decreased significantly with respect to the increase in the time period for all the ground motions. The maximum decrease (about 67%) in force transmitted to the pier was observed for Kobe's ground motion. However, for Kobe's ground motion, the variations are almost the same for all the considered damping ratios of the bearings. For the Imperial Valley and Turkey earthquakes, the maximum decrease in force transmitted to the pier is about 60% and 47%, respectively. Figure 10: Response sensitivity of the isolated bridge with respect to the time period of LRB under uni-directional (i) Imperial Valley (**a–c**), (ii) Kobe (**d–f**), and (iii) Turkey (**g–i**) ground motions. Pier torsional moment is sensitive with respect to the increase in the time period.