## 4 Characterization of Damage Under Blast Loading
### Analysis of Damage Parameters and Main Influencing Factors  
#### 4.3.1 Effect of TNT Equivalent on Damage  
Figure 11 gives the relationship between the failure characterization of the top and base plates and the TNT equivalent. The areas of the top plate cracks were 0.5512 m\({}^{2}\), 1.1532 m\({}^{2}\), and 1.653 m\({}^{2}\) (location 1); 0, 0.7904 m\({}^{2}\) and 1.6048 m\({}^{2}\) (location 2); and 1.6653 m\({}^{2}\), 2.3805 m\({}^{2}\), and 2.7404 m\({}^{2}\) (location 3). The results show that with the rise in TNT equivalent, the range of the cracks in the top plate under the explosion load expands, but this expansion trend gradually slows down. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Cases**} & \multicolumn{2}{c}{**Crack Length of**} & \multirow{2}{*}{**Crack Length of Base Plate**} & \multirow{2}{*}{**Displacement of**} & \multirow{2}{*}{**Displacement of**} \\  & \multicolumn{2}{c}{**Top Plate**} & & & & **Transverse** & **Longitudinal** \\  & **Crosswise** & **Vertically** & **Crosswise** & **Vertically** & **Partitions** & **Partitions** \\ \hline
1 & 0.52 & 1.06 & - & - & 0.12 & 0.04 \\
2 & 0.93 & 1.24 & 0.12 & 0.14 & 0.23 & 0.04 \\
3 & 1.14 & 1.45 & 0.15 & 0.16 & 0.46 & 0.06 \\
4 & - & - & - & - & 0.05 & 0.03 \\
5 & 0.76 & 1.04 & 0.12 & 0.12 & 0.04 & 0.04 \\
6 & 1.18 & 1.36 & 0.13 & 0.13 & 0.06 & 0.06 \\
7 & 0.91 & 1.83 & 0.15 & 0.15 & 0.15 & 0.1 \\
8 & 1.15 & 2.07 & 0.16 & 0.17 & 0.28 & 0.24 \\
9 & 1.24 & 2.21 & 0.18 & 0.17 & 0.49 & 0.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Main damage parameters of steel box girder (unit: m). Figure 11: Relationship between failure characterization of top and base plates and TNT equivalent. (**a**) Length of top plate crack and equivalent. (**b**) Maximum crack area of base plate and equivalent. There are several reasons for this: firstly, because of the increase in TNT equivalent, the shock wave arrives at the top plate earlier and faster, producing the cracks faster. As a result, the shock wave propagates rapidly through the cracks and manholes inside the steel box girder. Secondly, the partitions and stiffening ribs in the steel box girders provide resistance. Table 7 shows that the maximum length of the longitudinal crack in the top plate is larger than the maximum length of the transverse crack, which is due to the restraining effect of the U-ribs on the bridge deck slab. The base plate fracture area increases with the increase in TNT equivalent, and the change is more obvious for 100-200 kg; for example, in location 3, the base plate fracture area increases by 20.88% and 12.5%, respectively, and the growth degree decreases gradually. However, the base plate fracture area is subject to the double effect of the shock wave and top plate fragmentation, and the size of the fragmentation produced is random, so the size of the base plate fracture may be random. The relationship between the displacement of the transverse and longitudinal partitions and the amount of TNT equivalent is shown in Figure 12. From the figure, it can be seen that the displacement of the longitudinal partitions increases with an increase in explosion equivalent. At position 3, due to the explosion location not being in the bulk-head, this results in the largest displacement of the longitudinal plate; with an increase in TNT equivalent, the longitudinal plate transverse displacement increased by 86.67% and 103.57%. At location 2 and location 1, the displacements were similar, and the change in the transverse displacement of the longitudinal partitions was not significant. The displacements of the partitions at locations 1 and 3 increase by 91.67% and 100% (location 1) and 86.67% and 75% (location 3), respectively, and the displacements are similar at both locations.