# Damage Characteristics and Dynamic Response of RC Shells Subjected to Underwater Shock Wave
## 4 Numerical Investigation
### Numerical Model
The semi-spherical RC shell is not damaged when the explosive equivalent is less than or equal to 100 kg at a 5 m explosive distance. The bottom of the semi-spherical RC shell is in a state of complete damage when the explosive  
Figure 9.1 The curves of center vertical displacements of semi-cylindrical RC shells change with time under 7 m explosive distance and 300 kg explosive equivalent. Figure 9.2 The curves of center vertical displacements of semi-spherical RC shells change with time under 7 m explosive distance and 300 kg explosive equivalent. equivalent is greater than or equal to 200 kg at a 5 m explosive distance. In addition, the damage appears in the center, besides the damage at the bottom of the semi-spherical RC shell when the explosive equivalent is greater than or equal to 300 kg at a 5 m explosive distance, and the damage gradually increases with an increase in explosive equivalent. As shown in Figure 18, the damage to the inner surface of the semi-spherical RC shell is more severe than to the outer surface when the explosive equivalent is greater than 200 kg. It is primarily because the outer surface of the semi-spherical RC shell mainly bears the pressure and the concrete has great compressive capacity, but the inner surface of the semi-spherical RC shell mainly bears the tension, and the concrete has poor tensile capacity. In addition, the inner and outer surface of the bottom of the semi-spherical RC shell are significantly damaged due to the large deformation when the explosive equivalent is greater than or equal to 200 kg. As shown in Figure 19, the vertical compression deformation of the semi-spherical RC shell gradually increases with an increase in explosive equivalent. As shown in Figure 20, the vertical displacement of the center of the semi-spherical RC shell increases in a quadratic function form with an increase in explosive equivalent at 0.015 s. The vertical displacement of the center of the semi-spherical RC shell has a maximum value of \(-\)0.2462 m when the explosive equivalent is 500 kg. The center displacement of the semi-spherical shell is small and also tends to be stable with time when the explosive equivalent is less than or equal to 100 kg within 0.015 s.  
As shown in Figure 21, the overall damage of the semi-cylindrical RC shell gradually increases with an increase in explosive equivalent at a 5 m explosive distance. The damage is mainly concentrated in the junction of the semi-cylindrical RC shell and the side walls at both ends, the constraint position of the semi-cylindrical RC shell, and the center of the semi-cylindrical shell. The damaged area gradually extends from the junction between the semi-cylindrical RC shell and side walls at both ends, and the restraint on both sides of the semi-cylindrical shell to the center of the semi-cylindrical shell with an increase in explosive equivalent. Figure 9.3 The damage of the outer surface of semi-spherical RC shells at a 5 m explosive distance under different explosive equivalents: (**a**) 25 kg; (**b**) 50 kg; (**c**) 100 kg; (**d**) 200 kg; (**e**) 300 kg; (**f**) 500 kg. Figure 9.4 The curves of center vertical displacements of semi-spherical RC shells changing with time at a 5 m explosive distance under different explosive equivalents. Figure 9.5 The curves of center maximum vertical displacements of semi-spherical RC shells changing with explosive equivalent at a 5 m explosive distance. The damaged area of the semi-cylindrical RC shell is small when the explosive equivalent is 25 kg and 50 kg, and the damage begins to appear in the junction of the semi-cylindrical RC shell and side walls at both ends, and the bottom restraint of side walls at both ends. The damage begins to appear in the bottom restraint of both sides of the semi-cylindrical shell when the explosive equivalent is 100 kg. The damage starts to appear in the center of the semi-cylindrical shell when the explosive equivalent is 300 kg.