# Stability of MSW Landfill Slopes Reinforced with Geogrids
## 2 Materials and Methods  
For the slope stability analyses in landfills, a model with a width of 210 m and a height of 45 m was created (Figure 1). The geometry was reconstructed for different slope angles in the analyses. The symmetry of the geometric model was used for convenience in the analyses. Slope stability analyses of the model were performed with PLAXIS using FEM, and SLOPE/W using LEM. Unreinforced and reinforced analysis results obtained by both methods were compared. In the analysis, the waste material and soil were modeled with the Mohr-Coulomb model (MCM). The input parameters were obtained from previous experimental studies. The most important issue in the slope stability analysis of MSW landfills is the realistic estimation of the parameters of the waste material including unit weight, internal friction angle, and cohesion. Due to the natural properties of solid waste materials, such as moisture content, degree of degradation, waste composition, and particle size, it is very difficult to determine these parameters in the laboratory. When the existing studies in the literature are examined, it is seen that the mentioned shear strength parameters and unit weight values are in a wide range. Many investigations have been performed on the geotechnical properties of landfills to examine the settlement and stability of landfills [19; 20; 21; 22; 23; 24]. Average in-place unit weights, \(\gamma\), used by owners and operators for landfill capacity estimates are typically in the range of 8.6 to 10.2 kN/m\({}^{3}\). Values in this range have also been used for seismic analyses by [25; 26; 27]. [PERSON] et al. [28], in their study, presented a summary of the unit weight values obtained in situ by various researchers for MSW. Accordingly, the unit weight values were between 2.9 kN/m\({}^{3}\) to 14.4 kN/m\({}^{3}\). The shear strength values of the MSW landfills presented in the studies carried out on the subject are very variable, with internal friction angles, \(\phi\), as low as 10 degrees and as high as 53 degrees and cohesion values, c, varying from 0 to 67 kPa [29]. In the study performed by [PERSON] et al. [30] in an existing MSW landfill, Poisson's ratio value was obtained as 0.49. [PERSON] and [PERSON] [31] carried out an experimental study to estimate the deformation properties of MSW materials. The results obtained from this study show that Poisson's ratio value varies between 0.35 and 0.49. The modulus of elasticity, E, of waste materials is not constant and depends on the average stress [28; 32]. Therefore, the modulus of elasticity value is in a wide range. In the stability analysis, the material parameters presented in Table 1, obtained as a result of the literature study, were used for the modeling of the solid waste material and soil. Figure 1: Landfill geometry for \(1\mathrm{V}/3\mathrm{H}\) (dimensions are in meters). The geometric model of the MSW landfill was created in the PLAXIS computer program as two-dimensional. Slope analyses were performed according to plane strain conditions. In the modeling, triangular elements with 15 nodes were chosen to obtain more accurate and sensitive results. In the analyses, the standard boundary conditions available in the PLAXIS program were selected. Vertical and horizontal displacements at the base of the geometric model (u\({}_{x}\) = 0, u\({}_{y}\) = 0) were assumed to be zero, while on the vertical side of the slope, only vertical displacements were taken into account (u\({}_{x}\) = 0, u\({}_{y}\) = free). In the analyses, geogrid elements were used to model the geogrid reinforcement layers. The EA value of 1100 kN/m was entered into the program as the material property of the geogrid reinforcement layers. While creating the finite element mesh, the most suitable mesh structure that gives the most accurate result in the optimum time where the analysis results do not change much was investigated. For this purpose, the effect of the mesh structure on the FS was investigated by performing analyses for medium, fine, and very fine mesh.