## 5 Results and Discussion
### Comprehensive Evaluation of Bridge Response Under Combined Seismic and Train Loadings  
This section comprehensively analyzes the prestressed concrete bridge under the combined effects of seismic ground motions, train-induced vibrations, soil-structure interaction, and the traveling wave phenomenon. Considering these multiple concurrent dynamic loads and phenomena provides a more realistic and holistic assessment of the bridge's structural behavior and demands, which is crucial for ensuring the safety and reliability of such critical infrastructure assets.  
Two different train speeds were considered in the analysis: 30 km/h and 300 km/h. For the 400 m bridge, the train passage times were 48 s and 4.8 s for speeds of 30 km/h and 300 km/h, respectively. However, any other intermediate case regarding the speed of the train was non-trivial, especially when considering the soil-structure interaction and traveling wave effects.  
By incorporating the soil-structure interaction and traveling wave effects, a more accurate representation of the bridge's dynamic response can be obtained, enabling the development of robust design considerations that can withstand the complex loading conditions. Without loss of generality, it was assumed that the train began crossing the bridge at exactly time t = t(5%), corresponding to the time that 5% of Arias Intensity was released [43; 44].  
Thus, the bending moments' time histories at the bridge deck, just above the left pier, are shown in Figures 13 and 14. The black dashed line represents the response due to the train loading alone; the red dotted line represents the seismic loading alone; the continuous cyan line includes the combined effect of seismic and train loadings. It should be mentioned that the examined problem is nonlinear (due to the material and geometric nonlinearities); therefore, the third case cannot be considered a direct, linear combination of the two other cases.  
The bending moment time histories provide valuable insights into the bridge's dynamic response under the combined effects of seismic and train-induced loadings. At the lower 30 km/h train speed (Figure 15), the combined loading case (cyan line) exhibited significantly more pronounced peaks compared to the individual train (black dashed) or seismic (red dotted) load cases. This indicates that the increased length of time that the train was present on the bridge allowed for greater interaction with the seismic excitation, leading to amplified combined effects despite the relatively low results obtained for the train-induced loads alone.  
Figure 13: Influence of traveling wave effect on bridge displacement–base shear hysteretic response.  
Figure 14: Time–history of the bending moment of the bridge’s deck (above the left pier): train loading, seismic loading, and train–seismic loading for a train speed of 300 km/h.  
Figure 15: Time–history of the bending moment of the bridge’s deck (above the left pier): train loading, seismic loading, and train–seismic loading for a train speed of 30 km/h.  
Interestingly, at the higher 300 km/h speed (Figure 14), the combined loading case showed only a modest 10% increase in peak moments over the individual load cases. This suggests that higher speed train vibrations do not resonate as strongly with the seismic response, despite the shorter bridge occupancy time.  
The analysis underscores the sensitivity of the bridge's behavior to the train speed and the importance of considering intermediate speed scenarios, as the 30 km/h case appeared more critical than the 300 km/h condition. The increase in the length of time for which the train is present at lower speeds provides a greater opportunity for superposition with the seismic excitation, potentially leading to more severe combined effects. This nuanced understanding is crucial for accurately assessing the demands on critical infrastructures like this prestressed concrete bridge.