# Simulation Study on the Installation of Helical Anchors in Sandy Soil Using SPH-FEM
## 2 Establishment of SPH-FEM Model
### Initial Boundary Conditions and Sensitivity Analysis of Installation Speed  
The SPH-FEM computational model is set up with a total of three analysis steps: the first step simulates geostatic stress equilibrium, the second step simulates the installation process of the helical anchor, and the third step simulates the uplift bearing process of the helical anchor.  
The geostatic stress equilibrium is achieved by modifying key words. The vertical stress is determined by the height and unit weight of the soil, while the horizontal stress is determined based on the soil pressure coefficient \(K_{0}\) and the vertical stress, where \(K_{0}\) = 1-sin\(\varphi\). The displacement boundary conditions for the soil are set as follows: the two lateral boundaries perpendicular to the x-direction restrict movement in the x-direction, the two lateral boundaries perpendicular to the y-direction restrict movement in the y-direction, and the bottom boundary of the soil model restricts movement in all three x, y, and z directions. The upper surface is free and unconstrained.  
The movement of the helical anchor is controlled by a reference point at its top. During the installation process, a constant rotational speed is applied to the reference point while maintaining the anchor body in a vertical downward motion (with lateral displacement constrained) until the helical anchor is installed to the specified depth. In field construction, the typical rotation speed for the installation of helical anchors is 10-30 rpm. However, in the explicit dynamics module of ABAQUS, the duration of the analysis step is set to the actual physical process time. If the typical rotation speed is directly used, it will result in excessively long analysis steps, which in turn leads to significant computational costs. To reduce computation time, the rotation speed adopted in this paper is higher than the typical speed in the specifications. To ensure that the simulation rotation speed is selected appropriately, ensuring that the installation process is a quasi-static process, a sensitivity analysis of the rotation speed was conducted before the formal calculations using the SPH-FEM model.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & **Young’s** & **Poisson’s** & **Internal** & **Dilatancy** & **Density** \\
**Type** & **Modulus** & **Ratio** & **Friction** & **Angle** & **\(\rho\) (kg/m\({}^{3}\))** \\  & **\(\mathbf{\
u}\) (-)** & **Angle \(\mathbf{\varphi}\) (\({}^{\circ}\))** & \(\mathbf{\psi}\) (\({}^{\circ}\))** & \(\mathbf{\rho}\) (kg/m\({}^{3}\))** \\ \hline Helical Anchor & 2.06 \(\times\) 10\({}^{5}\) & 0.30 & - & - & \(7.85\times 10^{3}\) \\ Soil & 60.00 & 0.25 & 37.00 & 7.00 & \(1.69\times 10^{3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of helical anchor and soil.  
Three rotational speeds of 0.5\(\pi\) rad/s, \(\pi\) rad/s, and 2\(\pi\) rad/s were used to simulate the installation of a helical anchor with an 0.08 m pitch, with an advance of one pitch per rotation (\(AR\) = 1.0), and the results are shown in Figure 3. It can be seen that as the installation depth increases, both the installation torque and compressive installation force show a gradual increase. Under the conditions of three different rotational speeds, the curves of installation torque versus installation depth and compressive installation force versus installation depth exhibit differences in the amplitude of oscillation, yet they maintain a consistent overall trend. This indicates that the impact of rotational speed on installation torque and compressive installation force is relatively minor. Considering computational cost and accuracy, a rotational speed of \(\pi\) rad/s was used for the subsequent simulations. Additionally, for the simulation of the pulling-up process of the helical anchor, displacement loading control was adopted with an upward pull displacement load of 0.2D applied at the reference point, and the loading speed was \(2\times 10^{-3}\) m/s.