## 4 Study on the Blast Resistance of Ultra-Wide Concrete Twin-Edge Box Girders Coated with Polyurea
### Parametric Analysis
#### 4.2.3 Analysis of the Impact of Different Repeated Explosion Patterns
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Specimen**} & \multirow{2}{*}{**Condition**} & \multirow{2}{*}{\begin{tabular}{c} **Number of** \\ **Blasts** \\ \end{tabular} } & \multicolumn{2}{c}{**Blast**} & \multirow{2}{*}{\begin{tabular}{c} **TNT** \\ **Direction** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Scaled Standoff** \\ **Height/m** \\ \end{tabular} } \\  & & & & & & & \\ \multirow{4}{*}{PG and PPCG} & \multirow{2}{*}{15} & First blast and second blast & \
\begin{tabular}{c} Center of the top \\ plate of box \\ chamber 2 \\ \end{tabular} & Mid-span & 1 & 100 & 0.171 \\ \cline{2-8}  & & First blast and second blast &
\begin{tabular}{c} Center of the top \\ plate of box \\ chamber 2 \\ \end{tabular} & Mid-span & 1 & 200 & 0.171 \\ \hline \end{tabular}
\end{table} 
Table 9: Single-point repeated detonation scenarios. Figure 36: Comparison of damage patterns in the ultra-wide box girder subjected to repeated and single blasts. As shown in Figure 37b, the peak vertical displacement in chamber 2 of specimen PG under the first 200 kg explosion was 8.67 mm, and under the second explosion of the same charge, it was 7.61 mm, with a total displacement of 16.28 mm. Under a single 400 kg explosion, the peak displacement was 15.52 mm. For specimen PPCG, the peak vertical displacement was 8.45 mm under the first 200 kg explosion and 8.94 mm under the second explosion, resulting in a total displacement of 17.39 mm. The peak displacement under a single 400 kg explosion was 14.37 mm. Thus, compared with a single 400 kg explosion, the displacement increases for PG and PPCG specimens under two 200 kg repeated explosions were 4.67% and 17.37%, respectively. Comparing the PG and PPCG specimens under two 200 kg repeated explosions, the displacement decreased by 11.73%. The results show that after the first explosion, the top plate located directly beneath the blast center formed a rupture, allowing the shockwave from the second blast to enter the box girder, intensifying the impact on the baseplate. After applying the polyurea coating, the energy-absorption mechanism of polyurea dissipated much of the direct impact on the baseplate by converting internal energy into the fracture energy of the top plate's concrete. Consequently, the baseplate's displacement was reduced. Furthermore, polyurea's protective impact improved with higher explosive charges under repeated explosions. (2) Multiple points and multiple detonations  
From the aforementioned studies, it has been observed that when explosive loads act on the surface of an ultra-wide box girder, the typical failure mode involves localized punching shear failure. In military strikes, missiles and armor-piercing projectiles can cause explosions inside the box. These warheads, composed of high-strength material cores, penetrate the top plate due to the high velocity provided by the detonation of the propellant. Figure 37: Comparison of vertical-displacement time–history curves of ultra-wide box girder under repeated explosion and single explosion. The projectile cores use their kinetic energy and material strength to pierce the top plate, allowing them to enter the chamber and explode, causing more extensive damage to the box girder. Additionally, in terrorist attacks, successive explosions may take place both externally and internally within the box. To further investigate the damage characteristics and dynamic response of ultra-wide box girders during internal explosions, the restart function of LS-DYNA was employed. The first explosion was set at the upper surface center, creating a localized penetration hole in the top plate. Afterward, a second explosion was placed inside the chamber.