## 3 Sensitivity Analysis of Penetration Velocity  
Empirical evidence from [PERSON] et al. [34] demonstrates that the performance of the CEL method is affected by the penetration velocity, as it can be very time-consuming to simulate the actual penetration process with the real penetration velocity. Thus, sensitivity analysis of the CEL method on penetration velocity needs to be conducted to identify the optimum penetration velocity. Four different penetration velocities, \(v=7.4\) mm/s, 5.55 mm/s, 3.7 mm/s, and 1.85 mm/s, were considered in this study. The penetration resistance of the penetrator structure is shown in Figure 6, where \(\alpha=15^{\circ}\), \(b/D=0.027\), and \(L_{2}=160\) mm. \(F_{\text{end}}\) exhibited identical behavior for \(d_{\text{p}}/D=0.25\); however, beyond a normalized depth of 0.25, \(F_{\text{end}}\) exhibited a positive correlation with velocity and demonstrated asymptotic convergence toward a stable value. The interaction between the end face of the penetrator and the soil could be regarded as a process of compression deformation. Since the soil was modelled as an elastic-perfectly plastic material, the soil was elastically deformed when \(d_{\text{p}}\) was low at the beginning of the penetration process, and \(F_{\text{end}}\) presented a linear relationship with \(d_{\text{p}}\) rather than penetration velocity. When \(d_{\text{p}}\) was larger than the elastic deformation displacement limit of the soil, the soil was compressed due to plastic deformation. As the kinetic energy of the penetrator structure increased with its velocity, the interaction  
Figure 5: Validation of the CEL method. \(V\) (N) represents vertical resistance. \(D_{\text{p}}\) (m) represents pipe diameter. \(S_{\text{u}}\) (Pa) represents the soil’s undrained shear strength. \(W\) (m) represents pipe displacement. Figure 6: The penetration resistance of the penetrator structure, where \(\alpha=15^{\circ}\), \(b/D=0.027\), and \(L_{2}=160\) mm, at four different penetration velocities: (**a**) \(F_{\text{end}}\); (**b**) \(F_{\text{side}}\); (**c**) \(F_{\text{total}}\). between the penetrator and the soil became more intense, resulting in an increase in soil deformation and the resistance of the end face on the penetrator, \(F_{\text{end}}\). The trend in \(F_{\text{side}}\) was consistent before \(d_{\text{p}}/D=1.0\). When \(d_{\text{p}}/D>1.0\), \(F_{\text{side}}\) showed positive correlations with velocity. \(F_{\text{side}}\) is mainly the friction between the side face of the penetrator structure and the hole wall of the soil during the penetration process. As shown in the above analyses, the normal pressure between the side face of the penetrator structure and the hole wall of the soil increased as its normal pressure increased when the soil was plastically deformed beyond its elastic deformation displacement limit. Combined with the parameters of the penetrator structure, the coring tube was in contact with the hole wall to create friction when \(d_{\text{p}}/D=1\). When \(d_{\text{p}}/D>1\), \(F_{\text{side}}\) was positive with respect to penetrating velocity due to the increase in friction. However, the interaction between the side face of the penetrator structure and the hole wall of the soil was instability due to the flow of the soil during the penetration process. As a result, the increase in \(F_{\text{side}}\) presented a disturbing phenomenon. The value of \(F_{\text{total}}\) was not significantly different, as the maximum average deviation of penetration resistance did not exceed 10%, which showed that the resistance was slightly influenced by the velocity effect. The mean pressures at maximum penetration depth at four different penetration velocities were analyzed, as shown in Figure 7. Based on the pressure variations in the soil induced by penetration, Zone II can be meticulously subdivided into Zone II-1, Zone II-2 and Zone II-3. Zone I presents the most pronounced soil compression with the highest pressure, with its minimum pressure being 13.2 times \(\sigma_{\text{m}}\).