# Damage Characteristics and Dynamic Response of RC Shells Subjected to Underwater Shock Wave
## 4 Numerical Investigation
### Numerical Model
Also, the damage in the junction of the semi-cylindrical RC shell and side walls at both ends, and the damage in the bottom restraint of both sides of the semi-cylindrical shell are connected with the damage in the center of the semi-cylindrical shell. The semi-cylindrical shell is damaged, except for the center of side walls at both ends and the part of the two sides of the semi-cylindrical shell when the explosive equivalent is 500 kg. As shown in Figure 22, the damage to the inner surface of the semi-cylindrical RC shell is more severe than the outer surface when the explosive equivalent exceeds 200 kg. It is primarily because the outer surface of the semi-cylindrical RC shell mainly bears the pressure and the concrete has great compressive capacity, whereas the inner surface of the semi-cylindrical RC shell mainly bears the tension and the concrete has low tensile strength. In addition, the inner and outer surfaces in the junction of the semi-cylindrical RC shell and side walls at both ends, the bottom restraint of side walls at both ends, and the bottom restraint of both sides of the semi-cylindrical shell are all seriously damaged due to the large deformation when the explosive equivalent is greater than or equal to 200 kg. As shown in Figure 23, the vertical compression deformation of the RC shell gradually increases with an increase in explosive equivalent. As shown in Figure 24, the vertical displacement of the center of the semi-cylindrical 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-cylindrical RC shell has a maximum value of 0.36444 m when the explosive equivalent is 500 kg. The center displacement of the semi-cylindrical shell is small when the explosive equivalent is less than or equal to 50 kg within 0.015 s.  
Figure 9.6 The damage of the outer surface of semi-cylindrical 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 9.7 The curves of center vertical displacements of semi-cylindrical RC shells changing with time at a 5 m explosive distance under different explosive equivalents. Figure 9.8 The curves of center maximum vertical displacements of semi-cylindrical RC shells changing with explosive equivalent at a 5 m explosive distance. Figure 9.9 The damage comparison of the outer surface and inner surface of semi-cylindrical RC shells at a 5 m explosive distance under different explosive equivalents: (**a**) 200 kg; (**b**) 300 kg; (**c**) 500 kg. Effects of Explosive Distance on the Damage Characteristics and Dynamic Response of Semi-Spherical and Semi-Cylindrical Bottom-Sitting RC Shells  
The explosive distance is an essential factor affecting the structural damage characteristics and dynamic response. Therefore, the explosive distance is set to 3 m, 5 m, 7 m, and 9 m, and the verified numerical model is used to study the damage characteristics and dynamic response of semi-cylindrical and semi-spherical bottom-sitting RC shells under underwater shock waves with a 300 kg explosive equivalent. As shown in Figure 25, the damage of the semi-spherical RC shell significantly decreases with an increase in the explosive distance. The damage primarily occurs at the center and bottom of the semi-spherical RC shell, and the damaged area has the most significant value when the explosive distance is 3 m. The center of the shell remains undamaged at an explosive distance of 7 m and 9 m. There is minor damage to the semi-spherical RC shell around one-third of its vertical height when the explosive distance is 9 m. As shown in Figure 26, the center displacement of the semi-spherical RC shell decreases significantly with an increase in explosive distance.