# Evaluating Collapse Fragility Curves for Existing Buildings Retrofitted Using Seismic Isolation
## 5 Results
On the other hand, a significant reduction of the number of superstructure failures is observed at each IM. This is mainly due to a different seismic response of the isolation system in the two modeling approaches. As a matter of fact, for each ground motion, a larger displacement of the isolation system (\(\Delta_{\text{IS}}\)) is obtained using the Kikuchi bearing element. On the contrary, the corresponding top displacement of the superstructure (\(\Delta_{\text{top}}\)) remains substantially the same. As a consequence, a reduction of the relative displacement (\(\Delta_{\text{top}}-\Delta_{\text{IS}}\)) is observed in the revised model (see Figure 8a), thus reducing the probability of collapse of the superstructure. In other words, the horizontal cyclic behavior of the Kikuchi bearing element is characterized by larger displacement demand and lower shear force level towards those exhibited by the HDR element subjected to the same ground motion, especially at large deformations. Figures 4b and 6b show the CFFs for the SLD case-study building derived adopting the two aforementioned modeling approaches. As can be observed, small differences (of the order of 10%) are obtained in terms of median collapse capacity (\(\mathbb{S}_{\text{a,C}}\)) and record to record dispersion (\(\mathbb{P}_{\text{RTR}}\)). A significant increase in terms of number of failures (from 0 to 1 at IM6, from 2 to 10 at IM7, from 5 to 14 at IM8 and from 14 to 20 at IM9) is observed adopting the revised model for the GLD case-study building (see Figures 5a and 7a). As mentioned before, larger displacement demands are obtained adopting the Kikuchi bearing element in lieu of the HDR element. However, in this specific case, the displacement demand level is so larger to produce the attainment of the deformation threshold associated to shear failure for a several number of ground motions (see Figure 8b). The CFFs for the  
Figure 8: (**a**) Relative displacement vs time for the SLD case-study at IM7—ground motion n. 5 (**b**) Isolation system base displacement vs time for the GLD case-study at IM7—ground motion n. 6. Figure 7: (**a**) Number of collapses for each IM and (**b**) corresponding collapse fragility curve obtained for the GLD case-study adopting the revised model. GLD case-study building, associated to the two different modeling approaches, are shown in Figures 5b and 7b. Significant differences are observed in the GLD case study. In particular, a reduction of approximately 30% is obtained in terms of median collapse capacity, \(\text{S}_{\text{a,C}}\) passing from the RINTC research project modeling approach to the revised model. Table 4 summarizes the collapse fragility function parameters derived for the case-studies examined and the corresponding values of the collapse margin ratio (CMR, median collapse capacity \(\text{S}_{\text{a,C}}\), divided by the design spectral acceleration at Collapse Prevention limit state). Values of CMR larger than 1 have been obtained in each case. Larger values are observed for the GLD case-study building due to a more prudential design of the isolation system. Finally, record-to-record dispersion values ranging between 0.19 and 0.27 have been obtained. These results are aligned with those proposed by [PERSON] et al. [6] for similar building typologies.