# 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
The smaller the Y\({}_{1}\), the more obvious the effect. With the increase in Y\({}_{1}\), the influence degree of the boundary effect gradually decreases, and the influence difference between the two kinds of boundaries after 80 mm is reduced to less than 20 mm, indicating that the soil boundary effect will not be obvious after that. In addition to the areas studied above that are more prone to soil boundary effects, it is also necessary to determine which areas are relatively safe from the perspective of protective engineering. The residual velocity of fragment damage elements is used as the basis for measuring their killing power. Numerical simulations of fragment incidence are carried out at four distances of 50 mm, 150 mm, 250 mm, and 350 mm, and the calculated results of fragment residual velocities are shown in Table 7.  
From Table 7, it can be seen that as the incident and exit positions of fragments continue to move away from the original point O, the residual velocity of fragments decreases significantly, and the effective penetration depth of 1500 m/s fragments into soil media is approximately 400 mm. It can be seen from Figure 12 that with the increase in horizontal distance, the residual velocity of fragments shows a decreasing trend as a whole. However, when the vertical distance is too small, the residual velocity of fragments changes due to the influence of the boundary. When the vertical distance is within 100 mm, the residual velocity of fragments first decreases and then increases. In contrast, with the increase in vertical distance, the residual velocity of fragments shows an obvious decreasing trend as a whole. Figure 11: Relationship between the difference in residual velocity of fragments and boundary distances X\({}_{1}\) and Y\({}_{1}\). It can be seen from Figure 13 that with the increase in the initial velocity of fragments, the penetration depth of fragments increases and gradually slows down, and it is difficult for fragments to continue to penetrate after 500 mm. Taking the maximum speed of 2000 m/s as the standard, it can be concluded that a soil medium more than 500 mm away from the upper surface of the trench can achieve a useful protective effect. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Length from** & **Length from** & **Length of the** & **Angle of** & **Residual** \\  & **Point O in a** & **Point O in a** & **Penetration** & **Incidence (\({}^{\circ}\))** & **Velocity** \\  & **Horizontal** & **Vertical State (mm)** & **(mm)** & **Path (mm)** & **(m/s)** \\ \hline
11 & 50 & 50 & None & 45 & 1015 \\
12 & 50 & 150 & None & 18.43 & 500.7 \\
13 & 50 & 250 & None & 11.31 & 104.9 \\
14 & 50 & 350 & 376.5 & 8.13 & 0 \\
21 & 150 & 50 & None & 71.56 & 585.3 \\
22 & 150 & 150 & None & 45 & 373.5 \\
23 & 150 & 250 & None & 30.96 & 184.4 \\
24 & 150 & 350 & 367.9 & 23.20 & 0 \\
31 & 250 & 50 & None & 78.69 & 345.7 \\
32 & 250 & 150 & None & 59.04 & 194.9 \\
33 & 250 & 250 & None & 45 & 94.7 \\
34 & 250 & 350 & 376.5 & 35.53 & 0 \\
41 & 350 & 50 & Ricochet & 81.87 & 699.2 \\
42 & 350 & 150 & None & 66.80 & 76.65 \\
43 & 350 & 250 & 371.4 & 54.46 & 0 \\
44 & 350 & 350 & 378.9 & 45 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of fragment penetration into soil under different flying conditions. Figure 12: Changes in residual velocity of fragments with horizontal and vertical distances.