## 4 Seismic Vulnerability and Sensitivity Analysis
### Effect on Global Response  
Figure 7 presents the seismic vulnerability curves of the selected RC structures and sensitivity swings for each uncertain variable. The solid line of each limit state shown in Figure 6 indicates the fragility curve derived by considering all EDPs of each modeling group (e.g., the CS, YS, LR, and TR models detailed in Table 1). For example, in the case of the CS models, all of the structural responses from five RC frame models with different concrete strengths were considered to be the EDPs, and the single fragility curve for the CS models was derived. The dotted line indicates the fragility curve of the reference model. In particular, the seismic vulnerability of each group's models was analyzed by comparing it with that of the reference model. As shown in Figure 7a, the seismic vulnerability of the CS models, which considers the uncertainty of concrete strength, increased slightly at the lower value of \(\mathrm{S_{a}}\), when compared with that of the reference model. However, it decreased at the higher value of \(\mathrm{S_{a}}\). Figure 7 also clearly indicates that the sensitivity swings at the damage control and collapse prevention levels of the CS models were higher than those of other groups. For example, for the CS model, the exceedance probability at an \(\mathrm{S_{a}}\) of 1.5 g of the collapse prevention state varied from 0.31 to 0.77, resulting in a swing of 0.46. However, the corresponding swings of the YS and LR models were 0.06 and 0.05, respectively. Thus, the impact of concrete strength on the structural response was significant when compared with other variables. In addition, the width of the sensitivity swing of the CS models increased as the limit state changed from the serviceability to collapse prevention level. Figure 7b shows the seismic vulnerability of the YS group, which considers the varying yield strength of longitudinal reinforcement. The sensitivity swings for the fragility curves of the YS model were significantly lower than those of the CS models at the collapse prevention level. Conversely, their swings were higher than those of other groups at the serviceability level. This is because the serviceability level is defined when a longitudinal reinforcement reaches yielding, and thus it is significantly affected by the yield strength variability. Furthermore, it was observed that the sensitivity swings of LR models are notably lower than other groups except the serviceability level, indicating less impact on the seismic vulnerability of RC frames (Figure 7c). The fragility curves of TR models, which are associated with the variability in the volumetric ratio of transverse reinforcement, are illustrated in Figure 7d. The results indicate the high sensitivity of the selected uncertain variable to the seismic vulnerability of the TR models at the damage control and collapse prevention level. The swing at an \(\mathrm{S_{a}}\) of 1.5 g of the collapse prevention level is 0.4, which indicates a significant impact on the structural response. In particular, the overall trend of their sensitivity swings is similar to those of the CS models. Figure 8 shows the relative sensitivity of material properties and structural details on the seismic vulnerability curve at each limit state. The relative sensitivity is estimated as the ratio of the sensitivity swing of each variable to the sum. In all cases, the sensitivity of concrete strength was high at very low S\({}_{a}\), and those of the serviceability, damage control, and collapse prevention states decreased until the \(S_{a}\) reached 0.5 g, 0.78 g, and 1.15 g, respectively. After that, it was observed that the sensitivity of concrete strength dominated, particularly for the damage control and collapse prevention limit states. In addition, the sensitivity of the volumetric ratio of transverse reinforcement was notably high as it reached 0.4 at an \(Sa\) of 1.5 g for the collapse prevention limit state.