# Mechanical Mechanism and Dynamic Characteristics of Barge-Whole Bridge Collision Behaviours
## 4 Factors Influencing Behaviors of Barge-_Whole Bridge_ Collision
### Influence of Superstructure on Collision  
The existing researches of a ship impacting a bridge mainly focus on analyzing the evaluation of impact force. The barge-pier FE model is substantially identical to the barge-_whole bridge_ FE model in peak value of impact force. Furthermore, the barge-pier FE model has fewer meshes, reducing operation calculation time. Hence, for studying the ship-_whole bridge_ collision problem, many scholars ignore the superstructure of the _whole bridge_ or use the equivalent idea to simplify the constraint effect of the superstructure on the pier  
Figure 21: Collision durations under different barge masses. Figure 22: Barge-_whole bridge_ stress nephograms under different barge masses. top [37]. Based on this situation, it is critical to study the effect of the bridge superstructure on the dynamic response and damage evolution of ship-_whole bridge_ collisions. The barge-pier FE model is established, which is consistent with the barge-_whole bridge_ FE model except that there is no superstructure, as illustrated in Figure 23.  
The influence of the superstructure on the dynamic response of the collision is analyzed from the two aspects: impact force and the displacement of pier top. The barge with 6000 dwt impacts the pier column at a velocity of 2 m/s. In this situation, three broadly applied methods of superstructure simplification in the current study of pier model were selected, and four cases were set: (1) it is the _whole bridge_; (2) it ignores the superstructure without any simplification; (3) it simplifies the superstructure and exerts a restraint of equivalent surface force on the upper part of the pier during the barge-_whole bridge_ collision. The loading curve of equivalent surface force is illustrated in Figure 24, including the lateral surface force of equivalent friction and the vertical pressure of simplified superstructure mass; and (4) it simplifies the superstructure and makes it equivalent to a mass point, which is applied to the center of the pier top. Figure 25 displays the settings under different cases. Figure 23: The barge–pier FE model. Figure 24: Diagram of equivalent surface force of superstructure. The displacement of pier top is a key factor to reflect the performance of post-collision bridge. At case 2 3 and 4, the collision simulations of barge and pier were implemented and the results of top displacement were compared with that of the _whole bridge_ in case 1, with differences presented in Figure 26a-c, respectively. The displacement of pier top varies with different cases. The peak value of the positive displacement in the case 2 is 2.37 times that of the _whole bridge_ in the case 1, as  
Figure 26: Comparison of pier-top displacement under different working conditions: (**a**) case 1 and case 2; (**b**) case 1 and case 3; (**c**) case 1 and case 4. Figure 25: Simplified description of superstructure in case 2, 3 and 4 (from left to right). depicted in Figure 26a. Meanwhile, a large negative displacement of pier top occurs in the case 2, inconsistent with the forced vibration phase in the case 1. This is because the top of the single pier is free and unconstrained. The amplitude of pier-top displacement is markedly higher than that in the case 1. The peak value of the positive displacement in the case 3 is significantly smaller than that in the case 2, consistent with the amplitude of the case 1. However, due to the direction of equivalent surface force, the negative pier-top displacement significantly increases. In the Figure 26c, the mass of the superstructure is converted into a mass point, and the peak value of the positive displacement is about 1.5 times than the case 1. The trend of the displacement of pier top in the forced vibration phase is more consistent with the _whole bridge_, but in the subsequent free vibration phase, the vibration of pier is suppressed and the amplitude of displacement decreases, with obvious differences with the case 1.