## 3 Results and Discussion
### Mechanical and Physical Parameters Analyses of Geogrids  
This section focuses on the mechanical and physical parameters of HDPE geogrids used for the reinforcement of slopes in an old sanitary landfill. The analyzed HDPE geogrid was installed more than 20 years ago (in 1993). The geogrid was excavated in November 2013 and was then tested by using several laboratory methods [27; 28; 29; 30; 31]. Three samples of geogrids were collected from the landfill after 20 years of exploitation, and the sample size had a width of approximately 1.0 m and length of about 1.20 m. The samples were excavated from the upper layer of the structure, which consists of five layers and is located at the access road to the landfill. Physical and mechanical compositional tests have been performed on the specimens, which were provided by the manufacturer and also on exhumed geogrid samples. The physical and mechanical test results are reported as arithmetic averages with standard deviation and are listed in Table 4. The tests were performed on multiple specimens: For physical properties testing, 10 samples were used, and to measure mass per unit area, only one sample was used. For the mechanical properties measurement, five samples were tested. The ultimate tensile strength falls in the range from 42.63 to 52.55 kN/m and the strain in maximum load ranges from 5.28% to 7.41%. The average values of the ultimate tensile strength for aged samples are 48.92 kN/m. Given that the geogrid is mostly exposed to mechanical factors during installation, the value is assumed to be high [32]. The comparison of laboratory tests of exhumed geogrid samples (Table 4), using typical values given by the geogrid supplier, indicates that the change in average value of the tensile strength was from 55 to 48.92 kN/m and the average value of elongation at maximum force was from 11.2% to 6.4%. The physical test results (i.e., rib and cross-machine direction (CMD) bar thickness, aperture size values) show no significant change in dimensional properties throughout the 20 years of service. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & \multicolumn{2}{c}{**FOS**} \\ \cline{3-4}
**Slope Cross-Section** & **Reinforcement** & \multicolumn{2}{c}{**Bishop Method**} \\ \cline{3-4}  & & **Without** & **With** \\  & & **Reinforcement** & **Reinforcement** \\ \hline
**Northern -I** & Inclination change (geogrid) & 1.04 & 1.36 \\
**Western -II** & Berm (tire mattress) & 1.14 & 1.27 \\
**Eastern -III** & Berm & 1.06 & 1.36 \\
**Further Western -IV** & Berm and retaining wall & 1.18 & 1.33 \\ \hline \end{tabular}
\end{table} 
Table 3: The results of the stability analysis for the Radiowo site according to Bishop method [22]. For the purpose of estimating the influence of geogrid strength changing over time on the landfill slope, analyses of local stability were performed. There were two scenarios considered. One when the slope was reinforced with a newly built-in geogrid and another for conditions where the geogrid was exploited on the landfill for 20 years. The analyses (Figure 8a,b) were performed by using LEM incorporating lateral reinforcements [33; 34]. The slope stability analyses incorporating reinforcements used the approach of the pull-out resistance, which can be specified if passive resistance is the dominant stress transfer mechanism. Passive resistance refers to the development of bearing-type stresses on relatively stiff members of the reinforcement that are situated normal to the direction of pull-out. The method of calculation applied [PERSON]'s method of slices. Incorporating reinforcements during the calculations is achieved by employing reduction factors.