## 6 Seismic Fragility Analysis of a High-Pier Bridge
### Seismic Fragility Analysis of the High-Pier Bridge  
It can be seen from Equations (16) to (20) that probability seismic fragility analysis is primarily dependent upon the parameters of limited stage capacity, \(LS\), the engineering demand parameter, \(EDP\), and the seismic intensity measure, \(IM\). Previous studies (such as those by the authors of [35]) have shown that there is no synchronous relationship between the curvature of the bottom cross-section and the displacement of the top cross-section for high piers under seismic loading, and the position of the contraflexure point is unstable. It can be seen that the displacement and displacement ductility ratio are not suitable for utilization as \(LS\) for assessing the damage characteristics of high piers. Therefore, the cross-sectional curvature is selected as the \(LS\), in order to assess the damage stage of the high piers in this study. The damage stages of high piers are classified into four damage stages, namely, slight, moderate, extensive, and collapsed damage stages, based on the damage stage division standard and the criteria proposed by [PERSON] et al. [25]. Nowadays, there are two main methods by which to establish the relationship between \(EDP\) and \(IM\) through nonlinear dynamic time-history analyses (NDTHA) and the probability of the seismic fragility analysis of structures [15; 33], namely, the incremental dynamic analysis (IDA) method and the cloud-based analysis method [20; 36]. The IDA method requires the selection of a series of ground motions, which are then scaled to generate a range of ground motions with specified intensity levels. Structural finite element models are then subjected to NDTHA under the influence of these scaled ground motions [37; 38]. However, unlike the IDA method, the cloud method does not require the scaling of the selected ground motions. Instead, the selected ground motions should demonstrate a wide range of intensity levels and good aleatory uncertainty. As a result, the cloud method can significantly reduce the necessary computational time, compared to the IDA method, as it only requires a few NDTHA runs under the influence of the selected unscaled ground motions [39]. However, to ensure the fitting accuracy of the exponential equation of \(EDP\)and _IM_ (as in Equation (18)), the cloud method requires a substantial number of unscaled ground motions to be selected [15]. As shown in Section 5.2, the numbers of the first class, second class, third class, and fourth class of pulse-like ground motions are 20, 38, 39, and 3, respectively. It can be seen that there are only three pulse-like ground motions in the fourth class. Therefore, the pulse-like ground motions in the fourth class should not be used for seismic fragility analysis due to their insufficient number. Meanwhile, the first class consists of only 20 pulse-like ground motions, which is insufficient to meet the requirements of the cloud method. However, 10 to 20 ground motions are sufficient to provide the required accuracy for the IDA method [38]. It can be deduced that the first class, second class, and third class pulse-like ground motions all satisfy the quantity requirement of the IDA method. Moreover, the study published by [PERSON] and [PERSON] [36] indicates that the IDA method is more accurate than the cloud method in terms of the seismic fragility analysis of bridge structures. Therefore, in this study, we used the IDA method to perform seismic fragility analysis for a five-span high-pier continuous rigid-frame bridge undergoing the original selected 100 pulse-like ground motions (original class), as well as the first class, second class, and third class pulse-like ground motions, respectively. As shown in Section 4.2, the correlation coefficient values of PGA exhibit a minimum mean value and greater dispersion, indicating that PGA is not the most suitable ground motion intensity measure for the seismic fragility analysis of high-pier bridges.