## 3 Results and Discussion
### Geometric Parameter Analysis  
In order to investigate the effects of the slope geometry of the redesigned soil nail support system and the geometric properties of the elements used, one parameter was changed in the Hoek-Brown constitutive model, provided that all other parameters were kept constant. A total of 81 numerical analyses were performed. The factor-of-safety values of the model created using the moderately weathered parameters given in Table 10 were examined using different geometric variations (Table 11). The results are shown in Figure 20.  
Factor-of-safety values were compared in the geometric parameter analyses. When the effect of slope inclination on determining the safety number was examined, it was found that the highest safety numbers were obtained under all conditions on slopes with a slope of 65\({}^{\circ}\). In this case, it can be said that reducing slope inclination significantly enhanced overall stability. According to the results, the most important structural element affecting slope stability was long soil nails. The positive effect of increasing soil nail length on stability is most clearly seen in the slope system with a 65\({}^{\circ}\)-incl \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Highly Weathered to Completely** & **Moderately Weathered Sandstone** \\  & **Weathered Sandstone** & **Moderately Weathered Sandstone** \\ \hline Average qu (MPa) & 12 & 25 \\ RMR Score & 2 & 4 \\ \hline RQD (\%) & 0–25 & 25–50 \\ RMR Score & 3 & 8 \\ \hline Discontinuity Spacing (mm) & \textless{}60 & 200–600 mm \\ RMR Score & 5 & 10 \\ \hline Discontinuity Status & Fault filling and 1–5 mm open joints &
\begin{tabular}{c} Slightly rough surfaces, separation of \\ \textless{}1 mm, hard joint surfaces \\ \end{tabular} \\ RMR Score & 10 & 15 \\ \hline Groundwater & Moist & Trickle \\ RMR Score & 10 & 4 \\ \hline Total RMR Score & 30 & 41 \\ \hline Total GSI Score (RMR-5) & 25 & 36 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Evaluation of RMR and GSI scores. A parametric study has found that the soil nail inclination angle yields the highest performance for slopes with soil nail inclinations of between 10 and 20\({}^{\circ}\)[43]. In this context, \begin{table}
\begin{tabular}{c c c c c} \hline
**Parameter** & **Symbol** & **Unit** & **Moderately Weathered Sandstone** & **Completely Weathered Sandstone** \\ \hline Unit weight & \(\gamma\) & kN/m\({}^{3}\) & 26 & 21 \\ Elasticity modulus & E & MPa & 280 & 100 \\ Poisson’s ratio & \(\gamma\) & - & 0.25 & 0.25 \\ Uniaxial compressive strength & \(|\epsilon_{\mathrm{G}}|\) & MPa & 25 & 12 \\ Material constant for intact rock & m\({}_{\mathrm{s}}\) & - & 17 & 13 \\ Geological strength index & GSI & - & 36 & 25 \\ Disturbance factor & D & - & 0.7 & 0.7 \\ \hline \end{tabular}
\end{table} 
Table 10: Parameter data pertaining to the Hoek–Brown constitutive model for weathered sandstone units. Figure 20: Results of geometric parameter analysis using the Hoek–Brown constitutive model. studies were conducted with soil nail inclinations of 10-15-20\({}^{\circ}\) to determine the effect of the inclination angle of soil nails at different spacings on stability. The results of a study carried out on weathered granite rock suggested that soil nail spacing should not exceed 2.00 m. The use of soil nails at very frequent intervals increases the safety of a design [38]. As part of the geometric analysis, the influence of soil nail length on stability was systematically evaluated (Figure 20). The factor-of-safety (FoS) values for 4.00 m long soil nails ranged from 1.911 to 2.156, while those for 6.00 m long soil nails varied between 2.285 and 2.599. For 8.00 m long soil nails, the FoS values were observed to range from 2.559 to 3.024. Despite these variations, the 4.00 m long soil nails were considered potentially adequate in terms of the FoS. However, nail pull-out tests indicated that the applied loads were effectively dissipated at a depth of 4.00 m, suggesting that longer soil nails may be necessary to improve load distribution.