## 3 Findings and Discussion  
### The Effect of the Distance between Helixes  
The effect of the distance between helixes was expressed with the spacing ratio between helixes (S/D\({}_{1}\)), which is a dimensionless term, where S and D\({}_{1}\) refer to the distance between helixes and the diameter of the lower helix, respectively. The effect of this parameter on the bearing capacity of the helical piles was investigated using physical model tests and compared to the results obtained from 2D and 3D finite element models. In accordance with this purpose, the multiple helical pile (N = 2) was used in this series of tests by considering the diameters of helixes of D\({}_{1}\) = D\({}_{2}\) = 60 mm. While examining the spacing ratio between helixes, the diameter of helixes was kept constant to eliminate the effect of other parameters on the results. The physical model tests were conducted for eight different spacing ratios as S/D\({}_{1}\) = 1-8. The reason as to why such different spacing ratios are considered in this study is that there is still uncertainty on the subject. Several researchers have stated that if the buried depth is between 3 and 8 times the foundation diameter, these types of foundations can be considered deep foundations. On the other hand, the recommended minimum buried depth of helical piles was expressed as 5 times the upper helix diameter [47]. Therefore, the aim of this section, both the optimum spacing ratio between helixes and the efficient depth of the upper helix specified. In this study, the \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Values** \\ \hline
**Soil** & \\ Material model & Hardening Soil \\ Drainage type & Drained \\ Unit weight above phreatic level, \(\gamma_{\text{unsat}}\) (kN/m\({}^{3}\)) & 15.2 \\ Unit weight below phreatic level, \(\gamma_{\text{sat}}\) (kN/m\({}^{3}\)) & 18.0 \\ Secant stiffness, \(\text{E}_{\text{M}}^{\text{ref}}\) (kN/m\({}^{2}\)) & 9000 \\ Tangent stiffness, \(\text{E}_{\text{ced}}^{\text{ref}}\) (kN/m\({}^{2}\)) & 9000 \\ Unloading/reloading stiffness, \(\text{E}_{\text{ur}}^{\text{ref}}\) (kN/m\({}^{2}\)) & 27,000 \\ Power, m & 0.68 \\ Poisson’s ratio, \(v\) & 0.3 \\ Friction angle, \(\phi\) (\({}^{\circ}\)) & 30 \\ Dilatancy angle, \(\Psi\) (\({}^{\circ}\)) & 0 \\ Failure ratio, \(\text{R}_{\text{f}}\) & 0.99 \\ Strength reduction factor, \(\text{R}_{\text{inter}}\) & 0.4 \\
**Pile** & \\ Thickness, d (mm) & 2.5 \\ Unit weight, \(\gamma\) (kN/m\({}^{3}\)) & 77 \\ [PERSON]’s modulus, E (kN/m\({}^{2}\)) & \(2.1\times 10^{8}\) \\ [PERSON]’s ratio, \(v\) & 0.3 \\ \hline \end{tabular}
\end{table} 
Table 3: Material properties used in the numerical analysis. physical model tests were continued until the displacement of 10% of the helix diameter, and the failure load was determined as the load corresponding to this displacement. The results of the load-displacement relationship obtained from the physical model tests and 2D/3D finite element models are presented in Figure 5; also, the failure mechanism results obtained from the 3D finite element model, which shows better agreement with the physical model test results, are given in Figure 6.  
Figure 5: The effect of the distance between helixes on the load–displacement relationship. The load-displacement results acquired from the physical model tests were more consistent with the 3D finite element model results compared to the 2D finite element model results (see Figure 5). The reason for this result can be shown in the more realistic modelling for helixes in the 3D analyses compared to the 2D analyses. However, from all results, it was seen that even if the approach of modelling the helix as a horizontal plate in two dimensions is not good enough, this approach shows that it is possible to have a rough idea about the behavior of helical piles. In addition, the pile capacity increased with the increase in the distance between helixes, and this increase continued up to a certain ratio.