## 4 Parametric Study of Penetrator Structure on the Penetration Performance
### Effect of the Parameter of the Penetrating Head  
The results of the penetration resistance with different parameters combinations are presented in Figures 9-11. As \(d_{\text{p}}/D\) increased, \(F_{\text{end}}\) demonstrated a progressive increase and converged to a stable value, while \(F_{\text{side}}\) was positively correlated with \(d_{\text{p}}/D\) through the entire penetration process. This phenomenon could be attributed to the progressive increase in lateral contact area between the penetrator structure and the soil with advancing penetration depth, resulting in a positive correlation between \(F_{\text{side}}\) and penetration depth. In contrast, the basal contact area remained constant throughout the process, while the compressive pressure between the end face of the penetrator structure and the soil could be regarded as constant. Combining \(F_{\text{end}}\) and \(F_{\text{side}}\), the \(F_{\text{total}}\) on the \(15^{\circ}\) penetrating head angle penetrator structure became the smallest among all the penetrator structures when \(d_{\text{p}}/D\) was approximately 1.0.  
A boundary line was drawn to divide the penetration process into penetration area I and penetration area II, as shown in Figure 11. The value of the boundary line exhibited a continuous increase with the progressive augmentation of parameter \(b/D\). At penetration area I, the penetration resistance with the \(5^{\circ}\) penetrating head angle was the smallest and the \(30^{\circ}\) penetrating head angle was the largest. At penetration area II, the penetration resistance with the \(15^{\circ}\) penetrating head was the smallest, and that with the \(5^{\circ}\) penetrating head was the largest. The simulation results of this study were similar to those of [PERSON] [35], which focused on the penetration mechanics between a penetrator and the lunar  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Value** & **Normalized Value** \\ \hline \(\alpha\) & \(5^{\circ}\), \(15^{\circ}\), \(30^{\circ}\) & / \\ \(b\) & 2 mm, 4 mm, 6 mm, 10 mm & 0.027, 0.054, 0.081, 0.135 \\ \hline \end{tabular}
\end{table}
Table 2: Penetrating head parameters in cross-simulation.  
The mean pressure under different angles on the penetrating head is shown in Figure 12, when \(d_{\rm p}/D=1.89\). Under the same value of \(b/D\), the area of mean pressure for the \(30^{\circ}\) penetrating head angle penetrator structure was significantly larger than that of the \(5^{\circ}\) and \(15^{\circ}\) penetrating head angle penetrator structures, with the \(5^{\circ}\) penetrating head angle penetrator structure exhibiting the smallest extent. However, for Zone I, the area under the \(15^{\circ}\) penetrating head angle penetrator structure was the smallest (approximately half of that under the \(30^{\circ}\) penetrating head angle penetrator structure). This further indicated that the penetrator-soil interaction under the \(15^{\circ}\) penetrating head angle penetrator structure was more moderate.  
As shown in Figure 9, the larger the value of \(b/D\), the greater the \(F_{\rm end}\), and \(F_{\rm end}\) tended to converge. However, the value of \(F_{\rm end}\) showed no significant variation, which may be attributed to the low undrained shear strength of the soil, resulting in a decreased sensitivity to \(b/D\). Among the four different values of \(b/D\) in the current study, the \(F_{\rm end}\) under the \(5^{\circ}\) penetrating head angle penetrator structure was the largest. Furthermore, as \(b/D\) increased, the \(F_{\rm end}\) values for the three different penetrating head angle penetrator structures became closer.