## 5 Collapse Failure Analysis of the BC System  
Because the shaking table test does not study the seismic performance of the specific site, considering the duration, acceleration amplitude, and spectral composition of various seismic records, four kinds of seismic waves were tested. The Landers seismic wave, Cerro Prieto seismic wave, El Centro seismic wave, and Chi-Chi seismic wave, which represent four kinds of soil types: hard, medium-hard, medium soft, and weak, respectively.  
In order to save space, only two kinds of longitudinal wave input cases in collapse analysis are analyzed below, and the original seismic wave information is shown in Table 4. The seismic waves used in the shaking table test and the collapse analysis need to be compressed 0.408 times of the original seismic record to satisfy the similarity relationship. Longitudinal test seismic wave with peak ground acceleration (PGA) of 0.05 g is depicted in Figure 8. The PGA of seismic waves input in collapse analysis rose gradually from 0.1 g until the bridge specimen collapsed.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Wave** & **Observation Station** & **Year** & **Duration/s** & **PGA/m-s-2** & **Predominant Period/s** \\ \hline El Centro & Imperial Valley, USGS & 1940 & 53.460 & 3.4 & 0.19 \\ Chi-Chi & TCU117 & 1999 & 89.995 & 1.2 & 0.57 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Original shaking wave details.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Direction** & **Mode Order** & **Test Frequency** & **Calculated Frequency** & **Mode Shape** \\ \hline Vertical & 1 & 7.941 & 7.887 & \\  & 2 & 12.140 & 12.464 & \\ Vertical & 3 & 20.805 & 20.606 & \\  & 4 & 30.702 & 30.591 & \\ \hline Longitudinal & 1 & 3.514 & 3.495 & \\  & 2 & 7.963 & 7.887 & \\  & 3 & 12.105 & 12.464 & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Natural Vibration Characteristics of the Bridge Specim with HDR Bearings.  
The bridge specimen of the BC system collapsed under the action of the El Centro wave with a longitudinal PGA of 1.2 g. Figure 9 depicts the whole damage process from slight damage to the final collapse, which is described as follows: when \(t\) was 0.81 s, at the bottom of the middle pier the cracks started, and when \(t\) was 0.84 s, the failure at the bottom of the pier intensified and some hoops were exposed; when \(t\) was 1.05 s, the laminated rubber bearings on the middle pier failed, and the failure of the middle pier resulted in the loss of girder support and the cracking at the bottom of the girder; when \(t\) was 1.13 s, the ribs of the T beam continued to crack; finally, when \(t\) was 1.44 s, the girder was destroyed and the bridge collapsed.  
Besides, the bridge specimen of the BC system collapsed under the conditions of the Chi-chi seismic wave input longitudinal with a PGA of 1.2 g (see Figure 10). The specific process is as follows: when \(t\) was 8.9 s, the middle bearings failed and caused damage at the bottom of the T beam; when \(t\) was 16.91 s, the superstructure was almost detached from the pier, and Figure 11 demonstrated that the relative displacement between the upper and lower structures above 40 cm occurred at this time; when \(t\) was 17.45 s, one end of the upper main beam fell down from the cap beam, which could be determined by the collapse of the bridge specimen.  
Figure 8: Longitudinal test seismic wave: (**a**) El Centro wave, (**b**) Chi-chi wave.  
Figure 9: Longitudinal collapse mode of bridge specimen under the El Centro wave.