# Stability of MSW Landfill Slopes Reinforced with Geogrids
## 3 Results and Discussion
### Unreinforced Analyses
#### 3.1.4 Effect of Slope Angle  
Analyses were performed for different slope angle values (\(\beta\) = 45\({}^{\circ}\)-26.56\({}^{\circ}\)-18.43\({}^{\circ}\)-14.04\({}^{\circ}\)-11.31\({}^{\circ}\)) In the analysis, the other parameters were selected as c = 10 kPa, \(\psi\) = 0\({}^{\circ}\), E = 6500 kN/m\({}^{2}\), \(\
u\) = 0.45, \(\phi\) = 15\({}^{\circ}\), and \(\gamma\) = 9 kN/m\({}^{3}\). Table 5 and Figure 7 present the FS values for different slope angle values obtained as a result of the FEM and LEM analyses. As seen from Table 5 and Figure 7, as expected, the FS values decrease with the increasing slope angle. It is clear that the FS values obtained by FEM and LEM are very close to each other. Slope geometry is one of the major parameters affecting the stability calculations. The FS of the slope decreases depending on the increase in height and slope angle. Increasing the slope angle can trigger movement in the slope mass. The slope may become too steep to balance the shear stress, and as a result, the angle of repose can be exceeded, and mass movement may occur. Landfill designers often choose safe slopes such as 1V/3H and 1V/4H to design the slopes in conventional landfills. In other words, stability problems that may occur in MSW slopes due to the increase in moisture content and decrease in interlocking properties are eliminated by designing low-angle slopes. However, low-angle slopes are not economical because of the reduction in storage capacity [37]. Due to the uncertainties in the prediction of parameters, it is recommended that the FS determined to ensure long-term stability should be between 1.5-3.0 [38]. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Unit Weight (\(\gamma\)) (kN/m\({}^{3}\))**} & \multicolumn{2}{c}{**Factor of Safety (FS)**} \\ \cline{2-3}  & **FEM** & **LEM** \\ \hline
9 & 1.52 & 1.55 \\
10 & 1.46 & 1.50 \\
11 & 1.42 & 1.45 \\
12 & 1.37 & 1.42 \\
13 & 1.34 & 1.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Analysis results for different unit weight values. Figure 6: Variation in FS with \(\gamma\). When the analysis results are examined, it is seen that the necessary FS values cannot be obtained in cases where the slope is 1V/1H and 1V/2H. When the FS values obtained as a result of the FEM and LEM analyses are compared, it is seen that the FS obtained with LEM are generally higher. There are many studies in the literature that perform slope stability analysis using LEM and FEM and compare the results [39, 40, 41, 42, 43, 44]. When the results obtained from these studies are examined, it is seen that although the FS values obtained by LEM and FEM analyses are in general agreement, there are differences of up to 10%. According to [PERSON] et al. [44], although there are acceptable differences between the FS values obtained from the LEM and FEM analyses, this reveals a fundamental difference in the principles of approach between the analyses. While LEM is based on a static force or moment equilibrium analysis, the formulations used in FEM depend on the stress-strain relationship. Due to the differences in the assumptions and approaches made in the analysis methods, there are differences between the FS values obtained from the LEM and FEM analyses. The failure planes obtained as a result of the FEM and LEM analyses are shown in Figures 8 and 9, respectively. In FEM analysis, failure planes are shown as shear strain increments. As can be seen from Figures 8 and 9, the failure planes contact the toe of the slopes in the analyses performed without reinforcements at different slope angles. Figure 7: Variation in FS with \(\beta\).