# Simulation Study on the Installation of Helical Anchors in Sandy Soil Using SPH-FEM
## 3 Simulation Results and Discussion
### Influence of AR on Installation Force and Torque  
To study the influence of the \(AR\) on the installation force and torque of the helical anchor foundations, Figures 8 and 9, respectively, illustrate the relationship between the installation force \(F\) and installation torque \(T\) as a function of the installation depth \(z\) under various \(AR\) conditions for two helical anchors with different pitches. From Figures 8 and 9, it can be observed that both the installation force and torque gradually increase with the increase in installation depth, and the \(AR\) has a significant impact on both. Taking the installation depth \(z=1.20\) m as an example, compared to the \"pitch-matched\" installation mode (\(AR=1.0\)), when a low advancement ratio (\(AR=0.8\)) is used for installation, the required installation force decreases by an average of 94%, while the installation torque increases by an average of 13%. When a high advancement ratio (\(AR=1.2\), 1.5) is used for installation, the required installation force increases by an average of 94% and 234%, respectively, and the installation torque increases by an average of 28% and 69%. Furthermore, it is noteworthy that for the helical anchor with a pitch of 0.08 m, compressive installation force were negative at the depths of 1.10 to 1.50 m when the \(AR\) was 0.8, a phenomenon that is consistent with the indoor experimental results of [PERSON] et al. [10]. This indicates that the helical anchor foundation experienced a downward pull during the installation process. This phenomenon may be related to the special structure of  
Figure 8: Relationship between compressive installation force and installation torque versus installation depth for a pitch of 0.06 m (\(p_{\mathrm{w}}=0.06\) m). (**a**) Compressive installation force \(F\) vs. depth \(z\). (**b**) Installation torque \(T\) vs. depth \(z\). Figure 7: Resultant soil displacement vector diagram in disturbed area (m). the helical anchor plate. During installation, the helical anchor plate not only continuously shears the soil around the anchor but also lifts the soil above the plate, resulting in a downward reaction force from the soil on the plate. When the \(AR\) is low, this reaction force may be sufficient to cause the helical anchor to continue to screw into the soil, hence the installation pressure is zero or negative. This also explains why the helical anchor foundation can still screw into the soil at a slower speed when the compressive installation force provided by the installation equipment is insufficient. Comparing the installation torque curves for \(AR=0.8\) and \(AR=1.0\) reveals that the torque at \(AR=0.8\) is slightly higher than at \(AR=1.0\) when the depth is greater than 1.00 m. This suggests that the effect of \(AR\) on the installation may also depend on the depth of the installation. For this purpose, the installation forces and torques at the depths of 0.40 m, 0.80 m, and 1.20 m for each \(AR\) were extracted and normalized against the forces and torques (\(F_{1.0}\) and \(T_{1.0}\)) corresponding to the \(AR=1.0\) installation. The results are presented in Figures 10 and 11. Figure 10: Results of the influences of \(AR\) on the normalized compressive installation force for different values of the depth of installation \(z\). (**a**) \(z=0.40\) m. (**b**) \(z=0.80\) m. (**c**) \(z=1.20\) m.  
Figure 9: Relationship between compressive installation force and installation torque versus installation depth for a pitch of 0.08 m (\(p_{w}=0.08\) m). (**a**) Installation force \(F\) vs. depth \(z\). (**b**) Installation torque \(T\) vs. depth \(z\). Figure 10 shows that at each installation depth, there is a linear positive correlation between the installation force and \(AR\), meaning that the installation force increases linearly with the increase in \(AR\). The slope of the fitted line is defined as the influence coefficient of \(AR\) on the installation force.