# Stability of MSW Landfill Slopes Reinforced with Geogrids
## 3 Results and Discussion
### Reinforced Analyses
#### 3.2.1 Effect of Geogrid Number
In the study carried out by [PERSON] and [PERSON] [37], it was stated that the FS of the slope could be increased by 1.63 times if five geogrids were placed in the 25 m high 1V/3H MSW landfill slope. Table 8 and Figure 12 present the FS changes depending on the number of geogrids in the case of the N = 4 geogrid in the MSW landfill with a 1V/2H slope. \begin{table}
\begin{tabular}{c c} \hline \hline
**Number of Geogrids, N** & **Factor of Safety, FS** \\ \hline
0 & 0.99 \\
3 & 1.49 \\
4 & 1.84 \\
5 & 2.08 \\
6 & 2.35 \\
10 & 3.32 \\
15 & 4.68 \\
30 & 4.74 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of reinforced analysis. Figure 11: (**a**) Shear strain increment (without geogrids); (**b**) shear strain increment with one geogrid; (**c**) shear strain increment with two geogrids; (**d**) shear strain increment with three geogrids; (**e**) shear strain increment with four geogrids. Shear strain increment in FEM analysis. Figure 12: Variation in FS with N (1V/2H slope) (FEM). Table 8 and Figure 12 show that the FS value can be increased up to FS = 1.84 by placing the geogrid reinforcements in the MSW landfill slope with h = 7.5 m spacings. In this case, the FS value increases by approximately 1.86 times compared to the unreinforced condition. By using the optimum number of geogrids (N = 4) obtained by the finite element method, limit equilibrium analyses were carried out with the SLOPE/W program. In the analyses, other parameters were \(\phi\) = 15\({}^{\circ}\); c = 10 kN/m\({}^{2}\); \(\psi\) = 0\({}^{\circ}\); E = 6500 kN/m\({}^{2}\); \(\gamma\) = 0.45; \(\gamma\) =9 kN/m\({}^{3}\); and \(\beta\) = 26.56\({}^{\circ}\). In the case where the geogrid reinforcement layers are placed in the MSW landfill slope as h = 7.5 m, the FS values obtained for N = 4 geogrids are shown in Table 9, and the geogrid number (N)-safety number (FS) relationship is shown in Figure 13.  
From Table 9 and Figure 13, it is seen that the FS value can be increased up to FS = 1.89 by placing geogrid reinforcements at 7.5 m spacings in the MSW landfill slope. In this case, the FS value increases by approximately 1.85 times compared to the unreinforced condition (FS = 1.02). Figure 14 presents the slip surfaces obtained from the LEM analysis. Figure 15 presents the factor of safety-number of geogrids relationship obtained as a result of the FEM and LEM analyses for N = 4 geogrids. It can be seen from Figure 15 that for geogrid-reinforced MSW landfill slopes, the FS values obtained by LEM are greater  
Figure 13: Variation in FS with N (1V/2H slope) (LEM). \begin{table}
\begin{tabular}{c c} \hline \hline
**Number of Geogrids, N** & **Factor of Safety, FS** \\ \hline
0 & 1.02 \\
1 & 1.05 \\
2 & 1.30 \\
3 & 1.57 \\
4 & 1.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: LEM analysis results for the reinforced slope (1V/2H slope, N = 4). than those obtained by FEM. It is thought that the reason for this is due to some limitations in some local stresses occurring at the top and toe of the slope in limit equilibrium methods. In this study, the FS values obtained by LEM are on average 2% greater for the unreinforced case and 8% for the reinforced case than those obtained by FEM.