# Damage Characteristics and Dynamic Response of RC Shells Subjected to Underwater Shock Wave
## 4 Numerical Investigation
### Numerical Model
As shown in Figure 27, the vertical displacement of the center of the semi-spherical RC shell decreases in a power function form with an increase in explosive distance at 0.015 s. The vertical displacement of the center of the semi-spherical RC shell has a minimum value of 0.0302 m when the explosive distance is 9 m. In addition, the vertical displacement of the center of the semi-spherical RC shell at a 3 m explosive distance is larger than at 5 m, 7 m, and 9 m explosive distance. Figure 12.0 The damage of the outer surface of semi-spherical RC shells with a 300 kg explosive equivalent under different explosive distances: (**a**) 3 m; (**b**) 5 m; (**c**) 7 m; (**d**) 9 m.  
As shown in Figure 28, the damage of the semi-cylindrical RC shell significantly decreases with an increase in the explosive distance. The damaged area has the most significant value when the explosive distance is 3 m. The damage mainly occurs in the junction of the semi-cylindrical RC shell and side walls at both ends, the constraint position of the semi-cylindrical RC shell, and the center of the semi-cylindrical shell. The center of the semi-cylindrical shell remains undamaged at a 9 m explosive distance. As shown in Figure 29, the center displacement of the semi-cylindrical RC shell significantly decreases with an increase in explosive distance. As shown in Figure 30, the vertical displacement of the center of the semi-cylindrical RC shell decreases in a power function form with an increase in explosive distance at 0.015 s. The vertical displacement of the center of the semi-cylindrical RC shell has a minimum value of 0.0869 m when the explosive distance is 9 m. In addition, the vertical displacement of the center of the semi-cylindrical RC shell at a 3 m explosive distance is larger than at 5 m, 7 m, and 9 m explosive distance. Figure 12.1 The curves of center maximum vertical displacements of semi-spherical RC shells changing with explosive distance with a 300 kg explosive equivalent. Figure 12.2 The curves of vertical displacements of the center of semi-spherical RC shells changing with time with a 300 kg explosive equivalent under different explosive distances. Figure 12.3 The damage of the outer surface of semi-cylindrical RC shells with a 300 kg explosive equivalent under different explosive distances: (**a**) 3 m; (**b**) 5 m; (**c**) 7 m; (**d**) 9 m.  
Figure 12.4 The curves of center maximum vertical displacements of semi-cylindrical RC shells changing with explosive distance with a 300 kg explosive equivalent. Figure 12.5 The curves of center vertical displacements of semi-cylindrical RC shells changing with time with a 300 kg explosive equivalent under different explosive distances. Effects of Bottom Reinforcement on the Damage Characteristics and Dynamic Response of Semi-Spherical and Semi-Cylindrical Bottom-Sitting RC Shells  
The tensile properties of ordinary concrete materials are inadequate, and the reinforcement located in the main tensile area of the concrete significantly affects the damage characteristics and dynamic response of semi-spherical and semi-cylindrical bottom-sitting RC shells. Therefore, the damage characteristics and dynamic response of semi-spherical and semi-cylindrical shells with different reinforcement are studied under 200 kg explosive equivalent and 5 m explosive distance. As shown in Figure 31, the surface damage area of unreinforced semi-spherical concrete shells is significantly larger than RC shells. Additionally, the surface damage area of the semi-spherical RC shell with 10 mm steel reinforcement is significantly larger than with 16 mm steel reinforcement when the explosive equivalent is 200 kg and the explosive distance is 5 m. The semi-spherical concrete shell exhibits large damage cracks extending upwards from the bottom damage area compared with the RC shell. It suggests that the reinforced semi-spherical shell has better ductility and bottom reinforcement can narrow the large cracks of the semi-spherical RC shell into smaller cracks.