# Mechanical Mechanism and Dynamic Characteristics of Barge-Whole Bridge Collision Behaviours
## 2 Materials and Methods
### Mesh Generation and Contact Definition  
Meshing quality directly determines the validity of an FE simulation. High-quality meshing is conducive to controlling the extent of system hourglass energy [30]. Consequently, it is extremely necessary to consider the mesh convergence of FE models so as to achieving high- quality meshing. In this model, the minimum mesh size of the model was set 200 mm to endow the ship-_whole bridge_ collision simulation with high efficiency and precision in convergence. As presented in Table 5, SHELL163 element was adopted for the outer plate of the barge bow, BEAM161 element was used in the internal trusses of barge bow, and SOLID164 element was adopted to model the barge hull. During the collision process, the barge bow produces a large deformation that needs refined meshes to depict details of the deformation. Therefore, we set 200 mm for each side of barge-bow elements while 1000 mm for the length of the hull elements (Figure 4a). For the bridge, SHELL163 element was utilized to reflect the bridge superstructure, BEAM161 element was adopted for the steel reinforcement, and the rest of bridge, such as the pier and pile foundation, was modelled with SOLID164 element, as displayed in Table 6. In terms of the meshing of the _whole bridge_, the common-node method was used to connect the circular pile foundation with the rectangular pile cap (Figure 4c), and the pile cap with the pier column. This method can effectively reduce the contact setting, improve the calculation efficiency, and enable the converge of numerical calculation. The mesh size of the pier as well as pile cap that is involved in the collision is 200 mm, and that of the rest portions is 1000 mm. Collectively, there are 247,A19 elements in the barge-_whole bridge_ FE model with 42,107 barge elements and 205,312 _whole bridge_ elements. The barge-_whole bridge_ FE model is illustrated in Figure 4.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Size Label** & **AASHTO (m)** & **The Barge Model (m)** \\ \hline Total Length (L) & 195 & 59.5 \\ Profile Width (W) & 35 & 11 \\ Type Depth (D) & 13 & 4 \\ Hull Length (L\({}_{1}\)) & 175 & 53 \\ Barge-Bow Length (L\({}_{2}\)) & 20 & 6.5 \\ LongitudinalLength of & 3 & 0.6 \\ Barge-Bow (D\({}_{1}\)) & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: The size of JH barge.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Structure** & **Element Type** & **Material Parameters** \\ \hline Hull & SOLID164 & Density varies with barge \\ Outer Plate & SHELL163 & See Table 2 \\ Trusses & BEAM161 & See Table 2 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Element types and material parameters of barge model.  
There were two contact types set in this FE model to prevent mutual penetration of barge and _whole bridge_ models and excessive sliding energy during the course of collision [31]. The contact type between barge bow and bridge pier was the surface-to-surface contact [22], with the barge bow being the contact surface and the pier being the target surface. The kinetic and static friction coefficients were 0.3 and 0.28, respectively. The contact type between the internal trusses and outer plate of barge bow was the single-surface contact, exhibiting high calculation efficiency. The kinetic and static friction coefficients of this contact type were both 0.3.