## 3 Seismic Fragility Assessment Procedure
### Ground Motion for Incremental Dynamic Analysis  
Three ground motion suites were used in the IDA of each analytical model, respectively. All the selected ground motions in each suite have earthquake magnitudes between 6.0 and 7.0 and epicenter distance between 10 and 50 km. The mean shear wave velocities for the upper 30 m of the site profile at the record station is between 150-420 m/s, which are similar to the condition of site class S\({}_{4}\) applied to the design of the analytical models. Ground motions were chosen from the NGA-West2 ground motion database of the PEER, as in the design [13]. The ground motion records comprising a single suite were matched to the probability distribution as well as the median of the conditional spectrum by amplitude scaling in accordance with [PERSON] and [PERSON]'s study [33]. The fundamental mode period of each analysis model was chosen for the control period of the conditional spectra. Figure 8 shows the target and matched ground motion spectra for analytical Model B. The individual ground motion suite is comprised of 30 pairs of horizontal components, much more than the seven pairs used for the design phase. Similar to the design of the analytical models, only the single horizontal component of ground motion was applied to the in-plane horizontal direction in a single IDA. Each component comprising a ground motion pair was applied to the IDA alternately, considering the randomness in the azimuth of ground motion. Therefore, total 60 IDA's were conducted in the in-plane direction for a total of 60 ground motion components, respectively. Regarding the number of ground motion records, 22 pairs of horizontal components are used in FEMA P695 [4]. [PERSON] et al. conducted a study on an adequate number of ground motion records necessary to predict the collapse of moment-resisting frames with nonlinear dynamic analysis [34]. According to their research result, 40 to 100 ground motion records are required to achieve a coefficient of variation below 10% with respect to the result using 200 records. The 60 ground motion components used in this study is a reasonable choice considering both computational efforts and accuracy in collapse probability. It was assumed that the target spectrum was defined in the direction of the maximum spectral acceleration and GMRotD100 spectrum of each ground motion suite is used in amplitude scaling of each suite. The GMRotD100 spectrum is the 100-percentile of the geometric mean dependent on period [35; 36]. Figure 9a shows the GMRotD100 spectra of individual ground motion pairs and the target MCE spectrum for the Model B. Figure 9b,c compare the target spectrum and the individual ground motion spectra for each horizontal component, respectively, for the Model B. The median  
Figure 8: Target conditional spectrum and scaled GMRotD100 spectra for incremental dynamic analysis (Model B). spectrum and the target MCE spectrum for each direction have considerable difference in the spectral acceleration ordinate, but the difference is only slight at the control period. The ground motion suites for the design of the analytical models were scaled so that the mean SRSS spectrum is fit to 1.3 times the MCE spectrum, while those for IDA was scaled so that individual GMRotD100 spectrum has the same Sa(T1) as that of the MCE spectrum itself. The mean SRSS spectra of the ground motion suites for design and IDA is plotted, respectively, and compared to 1.3 times the MCE spectrum in Figure 10. The mean SRSS spectrum of the ground motion suite for IDA is lower than that for design at most periods longer than 0.2 s. For consistency between the design and performance evaluation, \(S_{MT}\), the spectral acceleration at \(T_{1}\) for MCE spectrum itself, is modified into \(S^{\prime}_{MT}\) using a scale factor defined by the ratio of spectral accelerations at \(T_{1}\) on the mean SRSS spectra for design and IDA.