# Braking Performance and Response Analysis of Trains on Bridges Under Seismic Excitation
## 3 Calculation and Analysis of Emergency Braking of Subway on Bridge During Earthquake
### Analysis of Calculation Results  
Through the calculation and analysis, Figures 4 and 5 show the changes in derailment coefficient and lateral acceleration of the car body generated during the operation of subway trains under different working conditions. In Figure 4, the two non-earthquake cases are shown with lighter, semi-transparent colors to highlight the contrast between the earthquake without braking (+EQ, -BK) and the earthquake with braking (+EQ, +BK) curves. The results show that the derailment coefficient and lateral acceleration of the train increase significantly after considering the seismic factor, both in the decelerating braking condition and in the uniform speed driving condition, indicating that the seismic excitation significantly amplifies the lateral response of the vehicle, which constitutes a potential threat to the lateral stability of the train and the safety of the train operation. Further comparison of the responses under different operating conditions shows that under the same seismic excitation, the derailment coefficient and lateral acceleration of the train are lower than those of the uniform speed driving condition when the train applies deceleration braking. This indicates that the deceleration braking process can effectively suppress the lateral vibration of the train caused by the earthquake and improve the smoothness of operation. The time-course curve of car body vertical acceleration shown in Figure 6 further illustrates that the effect of earthquake on car body vertical acceleration is relatively small, and the response in the case of no deceleration is slightly larger than that in the state of deceleration braking, which indicates that the deceleration also has a certain inhibition effect on the vertical response. It can be concluded that the implementation of deceleration braking under the effect of an earthquake not only helps to reduce the risk of derailment but also effectively reduces the vibration acceleration of the car body, thus improving  
Figure 7 compares lateral bridge acceleration for the four operating conditions--no-earthquake constant speed (\(-\)EQ, \(-\)BK), no-earthquake braking (\(-\)EQ, \(+\)BK), earthquake constant speed (\(+\)EQ, \(-\)BK), and earthquake braking (\(+\)EQ, \(+\)BK). The two no-earthquake curves remain within \(\pm\)0.05 m/s\({}^{2}\), confirming that braking alone induces negligible lateral vibration. With earthquake loading, the constant-speed case peaks at about \(\pm\)1.8 m/s\({}^{2}\) around 23 s, whereas applying braking lowers those peaks to roughly \(\pm\)1.4 m/s\({}^{2}\) and shortens the decay period. Figure 8 shows that all four vertical acceleration curves nearly overlap; the earthquake introduces broadband vertical motion of up to \(\pm\)0.75 m/s\({}^{2}\), and braking has little additional effect because of the bridge's high vertical stiffness. These observations demonstrate that the earthquake markedly amplifies lateral response, while emergency braking cuts those lateral peaks by roughly 15-20%, with only minor changes in the vertical direction. Table 2 summarizes the peak bridge accelerations and derailment coefficients for the four operating conditions. Under earthquake loading, emergency braking reduces the lateral bridge peak by approximately 22% and the derailment coefficient by about 19% compared with the constant speed case. Figure 8: Bridge vertical acceleration. Figure 7: Bridge lateral acceleration. The comparative analysis shows that the presence of an earthquake significantly enhances the dynamic response of the bridge, especially in terms of higher local peaks and valleys in the acceleration time histories. Compared with the no-earthquake conditions, the lateral and vertical accelerations of the bridge under earthquake conditions are enhanced to different degrees, which indicates that an earthquake poses a potential threat to the overall stability of the bridge.