# Stability of MSW Landfill Slopes Reinforced with Geogrids
## 2 Materials and Methods
As a result of the analyses carried out, no significant change was observed in the results in the case of the fine mesh, and the model was created in a fine mesh structure. In the unreinforced case, the analyses were carried out using two phases. In the first phase, the initial stresses due to the soil self-weight were created, and in the second stage, the phi-c reduction analysis was performed. In the reinforced case, the geogrid reinforcement was activated, and the analyses were carried out. For the finite element analysis, the slope geometries considered in the reinforced and unreinforced conditions are shown in Figure 2.  
In this study, limit equilibrium analyses were performed using the SLOPE/W computer program. With the LEM, the behavior of the soils was modeled based on certain assumptions, and geotechnical problems could be solved according to these assumptions. In this method, assuming that the slip circle was formed on a certain surface, FS values were obtained by comparing the forces sliding along this surface with the forces resisting the slip. With these analysis methods, the static equilibrium equation of the slope was attempted to be obtained using the Mohr-Coulomb stress criteria. There are three main types of limit equilibrium analyses used in slope stability calculations. These are: the slice \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Soil** & **MSW** \\ \hline Unit weight, \(\gamma\) (kN/m\({}^{3}\)) & 17.0 & 9.0 \\ Elasticity moduli, E (kPa) & 14,000 & 6500 \\ [PERSON]’s ratio, \(\
u\) (\(\cdot\)) & 0.25 & 0.45 \\ Internal friction angle, \(\phi\) (\(\cdot\)) & 25 & 15 \\ Cohesion, \(c\) (kPa) & 15.0 & 10.0 \\ Dilatation angle, \(\psi\) (\(\cdot\)) & 0.0 & 0.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: MC model parameters. Figure 2: (a) Unreinforced; (b) reinforced. Slope geometry used in finite element analyses. method, the wedge method, and the infinite slope method. The most widely used method in slope stability analysis is the slice method. The slice methods used in practice are based on dividing the slip surface into sufficient vertical slices. Many approaches have been developed using the slice method, such as those by [PERSON] [33], [PERSON] [34], [PERSON] [35], and [PERSON] [36]. Although there are some differences in practice between these methods, the common feature is the investigation of the slip mass equilibrium on a known or accepted critical slip surface. The slice method was used in the analyses performed in this study. The Bishop and half-sine function methods were selected in the calculations. Figure 3 shows the geometry of the unreinforced and reinforced models considered in the limit equilibrium analysis. The Mohr-Coulomb model (MCM) was used as the material model in the analysis. The values in Table 1 were used for the material parameters required in this model. After the material properties were entered into the program, the slip surface model was defined. There are two types of failures in the SLOPE/W program: circular and block slip. The circular slip surface model was used in the slope analysis. Although there are many methods to determine the circular slip surface, the entry and exit method was used. The reason for using this method was that the boundaries of the slip surface could be determined clearly.