# Damage Characteristics and Dynamic Response of RC Shells Subjected to Underwater Shock Wave
## 4 Numerical Investigation
### Numerical Model
Figure 12: The reinforcement diagram of \(1/4\) semi-spherical and semi-cylindrical RC shells: (**a**) the reinforcement of semi-spherical RC shells; (**b**) the reinforcement of semi-cylindrical RC shells. Effects of Shock Wave Transmission Medium on the Damage Characteristics and Dynamic Response of Semi-Spherical and Semi-Cylindrical Bottom-Sitting RC Shells  
The attenuation law for shock waves in water is different from that in air, which affects the explosion response of the structure. The density of water is approximately 835 times greater than air. The compressibility of water is 1/30,000-1/2000 that of the air. In addition, shock wave attenuation in water is slow and the capacity of water to store energy is not strong. Therefore, water becomes a good carrier for the propagation of shock waves. The damage caused by water shock waves on surrounding objects surpasses that of air shock waves due to the above factors. The physics of underwater explosions is more complex than that of air explosions, and an equivalent quantity of explosives will cause greater damage to a structure underwater. Figures 13 and 14 demonstrate the comparative damage distribution on the outer surface of semi-spherical and semi-cylindrical RC shells under 7 m explosive distance and 300 kg explosive equivalent. The annular damage occurs at the bottom of the semi-spherical RC shell near the constraint when subjected to underwater shock waves, whereas there is hardly any damage observed in the semi-spherical RC shell when subjected to air shock waves. The semi-cylindrical RC shell is most prone to damage in the junction of the semi-cylindrical RC shell and side walls at both ends, and the constraint position of the semi-cylindrical RC shell under underwater shock waves. Conversely, the semi-cylindrical RC shell is hardly damaged at all under air shock waves. The structure remains in the elastic deformation stage under air shock waves. Because the resistance of water is greater than air, the attenuation rate of shock waves in water is slow, and the pressure reaching the structure is relatively large, resulting in more significant structural damage. The curves of center vertical displacements of the  
Figure 14: The damage on the outer surface of semi-cylindrical RC shells under 7 m explosive distance and 300 kg explosive equivalent: (**a**) the air explosion; (**b**) the water explosion. Figure 9.0 The damage on the outer surface of semi-spherical RC shells under 7 m explosive distance and 300 kg explosive equivalent: (**a**) the air explosion; (**b**) the water explosion. semi-spherical and semi-cylindrical RC shell changing with time under 7 m explosive distance and 300 kg explosive equivalent are shown in Figures 15 and 16, respectively. The vertical displacement of the center of the semi-spherical and semi-cylindrical RC shell under underwater shock waves is more significant than under air shock waves. Therefore, the damage and center deformation of semi-spherical and semi-cylindrical RC shells under underwater shock waves are significantly greater than those under air shock waves. Effects of Explosive Equivalent on the Damage Characteristics and Dynamic Response of Semi-Spherical and Semi-Cylindrical Bottom-Sitting RC Shells  
The explosive equivalent is an essential factor affecting the dynamic response of structures. Therefore, the explosive equivalent is set as 25 kg, 50 kg, 100 kg, 200 kg, 300 kg, and 500 kg, and the verified numerical model is used to study the damage characteristics and dynamic response of semi-spherical and semi-cylindrical RC shell structures under underwater shock waves at a 5 m explosive distance. As shown in Figure 17, the overall damage of the semi-spherical RC shell gradually increases with an increase in explosive equivalent at a 5 m explosive distance. The damage is mainly concentrated in the lower part and the center of the semi-spherical RC shell, and gradually extends from the lower part to the center of the semi-spherical RC shell with an increase in explosive equivalent.