# Effectiveness of LRB in Curved Bridge Isolation:
## 5 Sensitivity of Response Parameters
### Bi-Directional Loading  
Figure 11a-i depict the variation in bridge response for different damping ratios over all time periods for bi-directional Imperial Valley, Kobe, and Turkey ground motions, respectively. Similar to the uni-directional cases, the variation of responses with respect to the damping ratio is non-linear. The bearing displacement was decreased with an increase in the damping ratio. In Kobe and Turkey ground motions, the maximum decrease in bearing displacement was about 16% and 11%, respectively, for higher time periods from 2.5 to 3 s. In the case of Imperial Valley ground motion, the maximum variation (about a 16% decrease) was observed for a period of 2.0 s. For all the considered ground motions, the variation of bearing displacement with respect to the damping ratio was found to be almost the same at time periods of 1.5 s. Additionally, a steep variation of bearing displacement with respect to the damping ratio, as observed for the uni-directional case for Turkey ground motion, was reduced in bi-directional ground motions. Figure 11: Response sensitivity of the isolated bridge with respect to damping ratio of LRB for bi-directional (i) Imperial Valley (**a–c**), (ii) Kobe (**d–f**), and (iii) Turkey (**g–i**) ground motions. The variation of force transmitted to the pier is small (variations are 6-9%) with respect to the damping ratio for the Turkey ground motion in the time period range from 1.5 to 2.5 s. In the case of the time period of 3.0 s, the variation of force transmitted to the pier is about 13%. In the case of Kobe ground motion, the variation of force transmitted to the pier is found to be insensitive with respect to the damping ratio for the time period of 1.5 s, while for a 2 to 3 s time period, the variation is about 13-19%. In the case of Imperial Valley ground motion, the force transmitted to the pier is found to be sensitive (about 14% variation) with respect to the damping ratio corresponding to the 2 s time period. In contrast, for other time periods, the variation is almost insensitive. The variation of pier torsional moments is found to be insensitive to the Kobe and Turkey ground motions. The maximum variation (about 21%) of pier torsional moment with respect to damping ratio was observed for Imperial Valley ground motion for a 1.5 s time period. For bi-directional Imperial Valley, Kobe, and Turkey earthquakes, Figure 12a-i show the variation of the bridge response for varying time periods with all the considered damping ratios. Similar to uni-directional responses, the response parameters are more sensitive to the time period for all the damping ratios. Figure 12: Response sensitivity of the isolated bridge with respect to the time period of LRB for bi-directional (i) Imperial Valley (**a–c**), (ii) Kobe (**d–f**), and (iii) Turkey (**g–i**) ground motions. The bearing displacements are increased with respect to the time period for all the ground motions. The maximum increase in bearing displacement (about 125%) was observed for Imperial Valley ground motion, whereas, for Kobe and Turkey ground motions, the maximum increase was 56% and 85%, respectively. Moreover, the increase in bearing displacement is close to linear and steeper for Turkey's ground motion. The force transmitted is found to be decreased for every increase in the time period for all the ground motions. The maximum increase in force transmitted (about 69%) has been observed for Kobe ground motion, whereas, for Imperial Valley and Turkey ground motions, the maximum increase is 50% and 62%, respectively. Also, in Kobe and Turkey ground motions, the variations of force transmitted to the pier are found to be almost the same for all the considered damping ratios of the bearings. The variation of the pier torsional moment is non-linear and sensitive to all the ground motions. For Imperial Valley, Kobe, and Turkey ground motions, the pier torsional moment is decreased by about 63%, 72%, and 70%, respectively.