## 2 Materials and Methods
### Numerical Investigation
#### 2.2.2 Mesh Details  
Simulation of helical piles subjected to uplift and lateral loading conditions requires sufficiently large enough model space to minimize boundary effects. According to the previous literature, the normalized model dimensions in the X and Y directions are 20 to 80D, and in the Z direction, ranges between 0.5 and 2L were used to avoid boundary effects. Figure 4 shows the generated mesh with mesh dimensions. It was decided to conduct a mesh independence study (MIS) in order to avoid subjectivity in the determination of model dimensions. The MIS was carried out in order to analyze the relationship between the number of elements and the computed response (for example, predicted resistance). In the current study, a model with X and Y = 25D and Z = 2L is considered for the MIS study. In Plaxis-3D software, the available mesh distribution options say very coarse, coarse, medium, fine, and very fine mesh responses were computed and compared. As a result, no significant benefit is achieved from very fine meshing compared to fine mesh, so the fine element distribution option was chosen for all analyses, along with local refinement for the pile geometry (local element refinement factor = 0.125) to gradually reduce the element size near the pile geometry in order to obtain accurate results [19].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Element** & **Soil** & \begin{tabular}{c} **Soil Volume** \\ **for Pile** \\ \end{tabular} & **Shaft Plate** & **Helical Plates** & **Interfaces** \\ \hline \multirow{3}{*}{Purpose} & \multirow{3}{*}{Simulate Soil Block} & \begin{tabular}{c} Simulate Rigid \\ Elements Inside \\ the Soil and Act \\ as a Pile \\ \end{tabular} & \begin{tabular}{c} Simulate Shaft \\ Behavior and \\ Connect Helical \\ Plates \\ \end{tabular} & \begin{tabular}{c} Simulate \\ Helical Plates \\ as a Planar \\ Element \\ \end{tabular} & \
\begin{tabular}{c} Allow \\ Separation \\ Separation \\ between Soil \\ and Anchors \\ \end{tabular} \\ \hline Material model & Hardening soil model & Linear elastic & Linear elastic & Linear elastic & Mohr coulomb \\ \hline Drainage type & Undrained B & Non-porous & - & - & Drained \\ \hline Unit weight, \(\gamma\) & \(\gamma\)\({}_{\text{unast}}\) = 16 & \multirow{2}{*}{78.5} & \multirow{2}{*}{0.0785} & \multirow{2}{*}{78.5} & \(\gamma\)\({}_{\text{unast}}\) = 17 \\ (kN/m\({}^{3}\)) & \(\gamma\)\({}_{\text{sat}}\) = 17 & & & \\ \hline \multirow{3}{*}{Young’s modulus, E (kN/m\({}^{2}\))} &
\begin{tabular}{c} Secant stiffness, \\ E\({}_{\text{50}}\)ref = 24,550 \\ Oedometer stiffness, \\ E\({}_{\text{oed}}\)ref = 28,000 \\ Unloading/reloading stiffness, \\ E\({}_{\text{ur}}\)ref = 73,650 \\ \end{tabular} & \multirow{2}{*}{200} & \multirow{2}{*}{200} & \multirow{2}{*}{200 \(\times\) 10\({}^{6}\)} & \multirow{2}{*}{24,550} \\  & \multicolumn{2}{c}{} & & \\ \hline Poisson ratio, \(\mu\) & 0.3 & 0.3 & 0.3 & 0.3 & 0.3 \\ \hline Soil strength, \(S_{\text{u}}\) & \multirow{2}{*}{7.5} & \multirow{2}{*}{-} & \multirow{2}{*}{-} & \multirow{2}{*}{-} & \multirow{2}{*}{7.5} \\ (kN/m\({}^{2}\)) & & & & \\ \hline Friction angle, \(\phi_{\text{u}}\) & 0 & - & - & - & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Element parameters and properties to simulate helical anchor model.