# Impact of Soil on the Penetration of Prefabricated Spherical Fragments and Its Protective Effect
## 2 Experiments on Fragment Penetration into Soil
### Impact of the Initial Attack Angle of Fragments on Soil Penetration Depth  
Based on the numerical model of fragment penetration into soil mentioned above, the authors observed the vertical penetration depth and trajectory penetration depth of the fragment from the surface by changing its initial incidence angle. The initial velocities of the fragments were selected as 500 m/s, 1000 m/s, and 1500 m/s. At each fragment velocity, a total of nine attack angles were conducted, including \(0^{\circ}\), \(10^{\circ}\), \(20^{\circ}\), \(30^{\circ}\), \(40^{\circ}\), \(50^{\circ}\), \(60^{\circ}\), \(70^{\circ}\), and \(80^{\circ}\). The final penetration position of fragments in numerical simulation is shown in Figure 5.  
Figure 5: Different directional depths of spherical fragments penetrating soil at different angles of attack and velocities. It can be seen from Figure 5 that with the increase in the initial incident angle of fragments, the absolute value of the penetration depth perpendicular to the soil surface gradually and linearly decreases from 0\({}^{\circ}\) to 30\({}^{\circ}\). However, the depth value gradually increases after 30\({}^{\circ}\). With the increase in the initial velocity of fragments, the maximum depth difference in the vertical direction is 91.94 mm (60\({}^{\circ}\)\(\sim\)70\({}^{\circ}\)) at 1500 m/s, and the depth in the horizontal direction is 83.4 mm (20\({}^{\circ}\)-30\({}^{\circ}\)). However, the length of the penetration trajectory at the end point first decreases and then increases under various velocity gradients, as shown in Figure 6.  
It can be seen from Figure 6 that the fragment trajectory length of different initial velocities reaches the minimum value between 30\({}^{\circ}\)\(\sim\)40\({}^{\circ}\) in the range of 0\({}^{\circ}\)\(\sim\)70\({}^{\circ}\), indicating that the soil has a greater impact on fragment penetration at this time. The main reason for the reduction in the vertical depth and penetration trajectory depth of fragments penetrating into the soil is that the angle of attack reduces the vertical partial velocity and causes the fragments to approach the surface area of the soil. From Figure 7, the stress state of the soil on fragments under the penetration trajectory at different angles can be seen. With the increase in the angle of attack, the angle between the force direction of the fragment at the bottom and the velocity direction of the fragment increases, resulting in a gradual increase in the trajectory offset of the fragment, which affects the penetration ability of the fragment into the soil. The deviation angle is mainly related to the initial attack angle of the fragments. Figure 8 shows the variation in fragment deviation angle with attack angle under three velocity gradients. Regardless of the initial velocity of fragments, the variation trend of the deviation angle of fragments has similar regularity. As the initial angle of attack increases, the vertical velocity of fragments decreases rapidly while the horizontal velocity increases. With the increase in the angle of attack, the thickness of the soil above the fragment in the process of penetration gradually decreases. This is affected by the free interface effect on the upper surface of the soil medium, causing the upper and lower parts of the fragment to be subjected to different sizes of stress. Consequently, there is a gradual increase in the deflection angle in the process of fragment movement. The speed reduction in the horizontal direction is relatively low. It can be seen from Figure 8 that the deviation angle of fragments is negative in the range of 0\({}^{\circ}\)\(\sim\)40\({}^{\circ}\) and reaches its maximum value at 20\({}^{\circ}\). The deviation angle of fragments is positive in the range of 40\({}^{\circ}\)-80\({}^{\circ}\), and the maximum value is obtained near 80\({}^{\circ}\). Figure 6: Penetration depth of fragments at different speeds based on variations in penetration trajectory length with initial angle of attack.