## 4 Parametric Study of Penetrator Structure on the Penetration Performance
### Effect of the Length/Diameter Ratio of the Penetrator Structure  
To study the effect of penetration performance on length-to-diameter ratio of the penetrator structure, four different length-to-diameter ratios, \(L/D=3.45\), 2.65, 1.85, and 1.05, were considered by adjusting \(D\), \(D=57\) mm, 74 mm, 106 mm, and 187 mm, based on the diameter of drill pipes for the mineral resource exploration mission described above. The penetration resistance at four different \(L/D\) ratios is shown in Figure 15, when the other parameters remained the same as in Section 3. It is evident that in different penetrator structures, the penetration resistance increased with the depth of penetration. The trend in \(F_{\rm total}\) aligned with \(F_{\rm side}\), and \(F_{\rm end}\) tended to converge. However, the smaller the \(L/D\) ratio, the greater the penetration resistance, and the more pronounced its growth. At \(d_{\rm p}/D=1.89\), the \(F_{\rm total}\) for the minimum \(L/D\) ratio was 4.8 times that of the maximum \(L/D\) ratio. Figure 12: Mean pressure (\(\sigma\)) distribution with different penetrating head parameters at the maximum penetration depth: (**a**) \(\alpha\) = 5\({}^{\circ}\), 15\({}^{\circ}\), 30\({}^{\circ}\) and \(b/D\) = 0.027; (**b**) \(\alpha\) = 5\({}^{\circ}\), 15\({}^{\circ}\), 30\({}^{\circ}\) and \(b/D\) = 0.054; (**c**) \(\alpha\) = 5\({}^{\circ}\), 15\({}^{\circ}\), 30\({}^{\circ}\) and \(b/D\) = 0.081; (**d**) \(\alpha\) = 5\({}^{\circ}\), 15\({}^{\circ}\), 30\({}^{\circ}\) and \(b/D\) = 0.135. The penetration resistance is governed by the contact area between the penetrator and the soil. The following relationships can be formulated in this case, including the area of the end face on the penetrating head and the area of the side of the penetrating head, as shown in Equation (3). \[\left\{ \begin{array}{l}S_{end}=\pi b(D-b)\\ S_{side}=2\pi\cdot d_{p}\big{(}D-d_{p}\tan\alpha\big{)}\sqrt{4\tan^{2}\alpha+1}+ \pi D\big{(}d_{p}-L_{1}\big{)}\end{array} \right. \tag{3}\]  
However, the relationship between the penetration resistance and penetrator diameter from the FEM results was not the simple linear relationship shown in Equation (3). As shown in Figure 16, the growth rate of penetration resistance relative to diameter varied: when the diameter was smaller (or _L/D_ was greater), the growth rate was lower; when the diameter was larger (or _L/D_ was smaller), the growth rate was higher. While Equation (3) could explain the overall trend of increasing force, it could not account for all aspects of the penetrator-soil interaction mechanism, such as differences in the compression deformation process on the penetrator end face under different _L/D_ ratios. The mean pressure at maximum penetration depth for four different diameters is shown in Figure 17. As the \(L/D\) ratio decreased, the area of mean pressure gradually increased, while Zone I progressively diminished. When \(L/D=1.05\), Zone I nearly disappeared. Under a larger \(L/D\) ratio, the interaction between the penetrator structure and the soil tended to increase, while the unit action intensity increased, resulting in higher mean pressure. For a smaller \(L/D\) ratio, although Zone I (the primary interaction zone) was minimized, the penetrator structure influenced a significantly larger soil area. The resistance acting on the penetrator structure could be considered as an integration of the  
Figure 14: Mean pressure (\(\sigma\)) variations with the penetrator structure, where \(\alpha=15^{\circ}\) and \(b/D=0.135\), under 20.0 kPa \(\mathrm{S_{\mathrm{um}}}\) condition: (**a**) \(d_{\mathrm{P}}/D=0.026\); (**b**) \(d_{\mathrm{P}}/D=0.037\); (**c**) \(d_{\mathrm{P}}/D=0.074\); (**d**) \(d_{\mathrm{P}}/D=0.095\). in situ mean pressure.