# 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 Influence of Boundary Effects on Fragment Penetration on Finite Thick Soil of Different Trajectories  
This part of the content is based on practical considerations. As shown in Figure 9, there are two hypothetical scenarios: (a) is the simulation of the protective effect of sandbags on personnel, and (b) is the simulation of the protective effect of bunkers on personnel. Based on the similarity between the two scenarios, the sandbags and bunkers are equivalent to a rectangular boundary block of soil. The equivalent diagram of sandbags and bunkers is shown in Figure 9.  
Figure 8: Deviation angle of fragments with different velocities as a function of attack angle. Figure 7: Stress cloud map of a fragment moving at 1000 m/s at different angles of attack. From Figure 9, it can be seen that when determining the source of fragments in a certain direction, people located behind sandbags and in bunkers can only consider the protective effect on one side (the other side is the same). The soil parts located above and to the left are exposed areas that are easily affected by soil-free boundary effects, while the lower and right sides of the soil are non-exposed infinite areas that are less affected by the effects of free interfaces. Based on this assumption, the authors conducted numerical simulation calculations on the penetration of prefabricated fragments with different initial conditions into the soil. The intersection point of two free interfaces was selected as the origin, and the distances X\({}_{1}\) and Y\({}_{1}\) from the origin O were selected as the entry and exit points of the fragments. The initial velocity of the fragments was 1500 m/s. The working conditions of the numerical simulation are shown in Figure 10.  
Figure 9: Illustrated schematic diagram of two scenarios. (**a**) is a schematic diagram of sandbag protection; (**b**) is a schematic diagram of bunker protection. In Table 6, the length of the penetration trajectory is used as the standard for measuring the remaining velocity of prefabricated fragments. If there is a clear functional relationship between the residual velocity and the length of the fragment penetration trajectory, but there is no significant relationship between it and the distances \(X_{1}\) and \(Y_{1}\) from the origin, it can be concluded that the soil does not have a significant boundary effect. Figure 11 shows the three-dimensional relationship between the absolute difference in residual velocity of fragments and the boundary distances \(X_{1}\) and \(Y_{1}\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**No. **} & \multirow{2}{*}{\(X_{1}\) (mm)} & \multirow{2}{*}{\(Y_{1}\) (mm)} & \multirow{2}{*}{ \begin{tabular}{c} **Length of the** \\ **Penetration** \\ **Trajectory (mm)** \\ \end{tabular}  } & \multicolumn{2}{c}{**Residual**} & \multicolumn{2}{c}{**Comparison of**} & \multicolumn{1}{c}{**Proportion of**} & \multicolumn{1}{c}{**Speed**} \\  & & & **Penetration** & **Velocities of** & **Residual** & **Differences** & **Difference** \\  & & & & **Trajectory (mm)** & **Fragments (m/s)** & **Velocities (m/s)** & **(\%)** & **(m/s)** \\ \hline
11 & 25 & 25 & 35.4 & 1294 & 1238 & 4.52 & 56 \\
12 & 25 & 50 & 55.9 & 1145 & 1111 & 3.06 & 34 \\
13 & 25 & 75 & 79.1 & 997.4 &  
It can be seen from Figure 10 that although the residual velocity of fragments has a relatively obvious inverse proportional relationship with the length of the penetration trajectory as a whole, we have noticed that within the small value range of X\({}_{1}\) and Y\({}_{1}\), the reduction in fragment velocity is relatively small. It is obvious that this is because it is close to the free boundary of the soil, which affects the structural strength of this part of the soil and reduces the resistance of fragments penetrating the soil, resulting in this situation. Therefore, it can be seen from Figure 10 that under the initial condition of 1000 m/s, with the increase in X\({}_{1}\), the influence of boundary action gradually increases, and the growth rate slows down after 70 mm.