# Seismic Vulnerability Assessment of Hybrid Mold Transformer Based on Dynamic Analyses
## 4 Dynamic Analyses and Development of Seismic Fragility Curves
### Characteristics of Input Ground Acceleration Time Histories Used for Dynamic Analyses  
In order to assess the seismic vulnerability of the mold transformer using fragility curves, the selection of input ground motion for time history analyses is a key parameter. [PERSON] and [PERSON] [35] proposed the use of 10-20 input acceleration time histories when performing TIDA, while [PERSON] [36] recommended 20 time histories. Thus, in this study, 20 ordinary records of natural ground motion with both horizontal and vertical components were selected from the PEER database [37]. The time history ground motions were derived from historical recordings so that their mean response spectrum matched the target design acceleration spectrum evaluated according to the Korean Building Code (KBC 2016) [38]: \(S_{ds}\) = 0.497 and \(S_{d1}\) = 0.287, and their shear wave velocity (\(V_{s,30}\)) in a range of 180 m/s to 760 m/s, which was complied with the soil type C and D [38]. The SRSS-based pseudo-acceleration response spectrum of selected ground motion was demonstrated in Figure 12. The selected earthquake ground motions were presented in detail in Table 5. These earthquake records cover the ranges of magnitude from 5.5 to 7.5, of shear wave velocity (\(V_{s,30}\)) from 198.77 to 634.33 m/sec, and of closet ruptured distance (\(R_{rup}\)) from 4.06 to 199.84 km. Scatter diagrams of magnitude versus closet ruptured distance (\(R_{rup}\)) and magnitude versus peak ground acceleration of the selected ground motions are illustrated in Figures 13 and 14, respectively. Figure 11: Flowchart of seismic vulnerability assessment process. Intensity Measure, Intensity Levels, and Uncertainty in Modeling Parameters Used for Dynamic Analyses  
In order to construct the fragility curves using the TIDA approach, a series of time history analyses have been performed for a set of acceleration records, which were scaled to varying and increasing levels of seismic intensity. The parameter that informs the scaling of the acceleration records is typically known as the intensity measure (IM), while the degree of seismic intensity is referred to as the intensity level (IL). A common IM that has been widely used in seismic fragility analysis, peak ground acceleration (PGA) [16; 39; 40; 41], was chosen in the present study. In particular, various levels of PGA with a range of 0.05 to 2 g were used as IL. This range of PGA was considered to ensure that the mold transformer could exhibit different performance levels to exceed the limit states. Moreover, in reality, the mold transformers can be manufactured with different configurations and specifications, which can lead to variations in performance when subjected to the same earthquake. In order to consider such uncertainty in the modeling parameters of the mold transformer when estimating the fragility curves, various dynamic parameters of the mold transformer were investigated in terms of the effective stiffness and the coil mass. Specifically, three cases of effective translational stiffness (0.8 \(K_{t}\), 1.0 \(K_{t}\), and 1.2 \(K_{t}\)), three cases of effective rotational stiffness (0.8 \(K_{\theta}\), 1.0 \(K_{\theta}\), and 1.2 \(K_{\theta}\)), and three cases of coil mass (0.6 M\({}_{\text{C}}\), 1.0 M\({}_{\text{C}}\), and 1.2 M\({}_{\text{C}}\)) were investigated for each time history analysis; based on the test results, 1.0 \(K_{t}\), 1.0 \(K_{\theta}\), and 1.0 M\({}_{\text{C}}\) were the values of the modeling parameters chosen for the prototype analytical model. Figure 12: Response spectrum of selected ground motions.