# Damage Characteristics and Dynamic Response of RC Shells Subjected to Underwater Shock Wave
## 4 Numerical Investigation
### Numerical Model
As shown in Figure 32, the central displacement of the unreinforced semi-spherical shell is significantly greater than that of the reinforced semi-spherical shell, and the central displacement of the semi-spherical RC shell decreases significantly with an increase in the diameter of the steel bar. Therefore, the overall damage and center vertical deformation of the semi-spherical shell can be reduced by bottom reinforcement and an increase in the diameter of the steel bar within the diameter range of 10-16 mm. As shown in Figure 33, the surface damage area of unreinforced semi-cylindrical shells is significantly larger than that of RC semi-cylindrical shells. Additionally, the surface damage area of the semi-cylindrical RC shell with 10 mm steel reinforcement is significantly larger than with 16 mm steel reinforcement. The damage in the center of the unreinforced semi-cylindrical shell is greater than that of the reinforced semi-cylindrical shell. The outer surface of the reinforced semi-cylindrical RC shell has hardly any damage in the central area, and the inner surface has a small amount of damage. As shown in Figure 34, the central displacement of the unstiffened semi-cylindrical shell is more significant than the reinforced semi-cylindrical shell, and the central displacement of the semi-cylindrical RC shell slightly decreases with an increase in the diameter of the steel bar. Therefore, the overall damage and vertical deformation of the semi-cylindrical shell can be reduced by bottom reinforcement and an increase in the diameter of the steel bar within the diameter  
Figure 12.6 The surface damage of semi-spherical RC shells under different reinforcement diameters with 200 kg explosive equivalent and 5 m explosive distance: (**a**) unreinforced; (**b**) reinforced—10 mm; (**c**) reinforced—16 mm. range of 10-16 mm, but the diameter of the steel bar has little effect on the vertical center deformation of the semi-cylindrical RC shell. Figure 12.7 The curves of center vertical displacements of semi-cylindrical RC shells changing with time with 200 kg explosive equivalent and 5 m explosive distance under different reinforcement diameters. Figure 12.8 The curves of center vertical displacements of semi-spherical RC shells changing with time with 200 kg explosive equivalent and 5 m explosive distance under different reinforcement diameters. Effects of Hydrostatic Pressure on the Damage Characteristics and Dynamic Response of Semi-Spherical and Semi-Cylindrical Bottom-Sitting RC Shells  
The coupling of hydrostatic pressure and underwater shock waves may lead to structural damage to underwater structures. Therefore, the initial hydrostatic pressure is set as 0 MPa, 0.50225 MPa, 1.0045 MPa, and 2.009 MPa, to study the damage characteristics and dynamic response of semi-spherical and semi-cylindrical bottom-sitting RC shells with 7 m explosive distance and 300 kg explosive equivalent. As shown in Figure 35, the damage is mainly concentrated in the lower part of the shell, and relatively severe annular damage occurs near the bottom of the shell. As shown in Figure 36, the damaged area and center displacement of the semi-spherical RC shell slightly decrease with an increase in hydrostatic pressure within the hydrostatic pressure range of 0-2.0092 MPa. The schematic diagram of the deformation in semi-spherical RC shell cross-section is shown in Figure 12.9 The curves of horizontal displacements of the semi-spherical RC shell changing with \(\alpha\) with 300 kg explosive equivalent and 7 m explosive distance under different hydrostatic pressures are shown in Figure 7:0 The maximum horizontal displacement is located in the damaged area of the semi-spherical shell. The maximum horizontal displacement of the semi-spherical shell under a hydrostatic pressure of 0 MPa is more significant than under a hydrostatic pressure of 2.0092 MPa.