## 6 Seismic Fragility Analysis of a High-Pier Bridge
### Seismic Fragility Analysis of the High-Pier Bridge
However, due to the ease of obtaining peak ground acceleration values, PGA is one of the earliest and most commonly used indicators for characterizing the intensity of ground motions in seismic studies. Furthermore, as previously mentioned, this study utilized the IDA method to conduct seismic fragility analysis for the research bridge, necessitating the scaling of ground motions to encompass the various levels of specified _IM_. The ground motion intensity measure, PGA, is commonly selected as the specified _IM_, and a series of ground motions within a wide range of intensity levels are generated by scaling the PGA values. NDTHA is then conducted at various intensity levels. PGA was identified as the optimum _IM_ by [PERSON] et al. [40] for performing the seismic fragility analysis of bridge structures. Many studies utilize PGA as the ground motion intensity measure when performing seismic fragility analysis for bridge structures, as in the studies by [PERSON] and [PERSON] [36] and [PERSON] et al. [41]. Elsewhere, [PERSON] et al. [35] also investigated the variable characteristics of seismic damage probability for a high-pier bridge under various PGA levels. As the primary objective of this study was to investigate and establish the need for utilizing the PCA-K-means method to cluster ground motions and conduct seismic fragility analysis, PGA was chosen as the ground motion _IM_ for analyzing the seismic fragility analysis of the research object, a five-span, high-pier, continuous rigid-framed bridge. Selecting the bottom cross-sections of Pier 1# and Pier 2# (cross-sections 1-1 and 6-6) and the top cross-sections of Pier 1# and Pier 2# (cross-sections 5-5 and 10-10) as the research cross-sections (as shown in Figure 3), seismic fragility analysis was performed for each research cross-section, subject to the original class and the first class, second class, and third class pulse-like ground motions along the longitudinal direction. The fragility curves for each research cross-section were derived by following the main procedural steps, as follows. Step 1: Establish the finite element model of the five-span, high-pier, continuous rigid-frame bridge, following the modeling methodology outlined in Section 2.2. Step 2: The original class, first class, second class, and third class pulse-like ground motions are scaled using PGA and ranging from 0.1 g to 1.0 g, with 0.1 g increments. Step 3: Perform NDTHA of the finite element model by inputting each class of ground motions along the longitudinal direction to obtain the corresponding maximum cross-sectional curvature values of each research cross-section. Step 4: Using the Xtract software to calculate the critical curvature values of each damage stage for each research cross-section along the longitudinal direction. The critical cross-sectional curvature values of each research cross-section are shown in the literature [42]. It can be seen from Figures 14 and 15 that the damage probability to cross-sections 1-1 and 5-5 at each damage stage increased with increasing PGA for each of the original class, first class, second class, and third class pulse-like ground motions. For the bottom cross-section of Pier 1# (cross-section 1-1), when the PGA value reached 1.0 g, the damage probabilities of the slight and moderate damage stages undergoing the first class of ground motions reached maximum values of 0.94 and 0.92, while the damage probabilities of the  
Figure 16: Fragility curves of cross-section 6-6. Figure 17: Fragility curves of cross-section 10-10.  
third class pulse-like ground motions were 0.93 and 0.90. Thus, the fragility curves of the slight and moderate damage stages under the first class and third class ground motions were generally consistent with the increase in PGA, while the damage probability values were larger than the original class pulse-like ground motions.