## 4 Simulation Results and Discussion  
The simulation was run and the Factor of Safety (FoS) was determined for four different slope angles of 30\({}^{\circ}\), 35\({}^{\circ}\), 40\({}^{\circ}\), and 45\({}^{\circ}\). We found that the FoS decreases as the slope angle increases, which was expected, and additionally, the FoS for a similar slope angle is lower for Material 1--non-associative plasticity--compared to Material 2--associative plasticity. These results are graphically shown in Figure 6, and are consistent with those reported in [77,78]. Figure 5: The finite element mesh of the model. Figure 6: FoS as a function of the slope angle. The equivalent plastic strain for all of the different slope angles, just before failure, is shown in Figures 7 and 8 for the two considered materials. The localization of the plastic strain nuclei in these figures provides an indication of the failure surfaces for the different slope angles. For smaller slope angles, multiple failure surfaces develop within the rock mass. A 3D visualization of the displacement is shown for a slope angle of 45\({}^{\circ}\) for both material types in Figures 9 and 10. This slope angle was chosen for the tridimensional presentation as it has the lowest corresponding FoS of 1.45 for the non-associative flow rule and 1.56 for the associative flow rule. The qualitative results are supported by previous research conducted using LEM [91; 92; 93]. The obtained values also show how parts of the sloped rock mass outside the slip surface begin to slide once the material becomes unstable. Figure 8: Equivalent plastic strain as a function of slope angle, Material 2. Figure 7: Equivalent plastic strain as a function of slope angle, Material 1. Next, Figure 11 shows the 2D section displacements of the slope corresponding to Material 1, for the four slope angles considered, while Figure 12 shows the displacements for the same angles, but for Material 2. Regarding the quantitative results, Table 4 summarizes the results obtained for all four slope angles considered and for both the non-associative flow rule and the associative flow rule. It is observed that the FoS values corresponding to the same angle are higher for the case of the associative flow rule compared to the non-associative flow rule, which was also demonstrated by [PERSON] et al. [94]. Figure 10: Displacement magnitude for a slope angle of 45\({}^{\circ}\), Material 2. Figure 9: Displacement magnitude for a slope angle of 45\({}^{\circ}\), Material 1. Figure 11: Slope displacements for Material 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Result**} & \multirow{2}{*}{**Unit**} & \multicolumn{5}{c}{**Non-Associative Flow Rule**} \\ \cline{3-6}  & & **A = 30\({}^{\circ}\)** & **A = 35\({}^{\circ}\)** & **A = 40\({}^{\circ}\)** & **A = 45\({}^{\circ}\)** \\ \hline FOS & 1 & 2.03 & 1.79 & 1.61 & 1.45 \\ Equivalent plastic strain & 1 & 0–0.26 & 0–0.26 & 0–0.26 & 0–0.26 \\ Displacement magnitude & m & 0–0.072 & 0–0.072 & 0–0.072 & 0–0.072 \\ \hline \multicolumn{6}{c}{**Associative flow rule**} \\ \cline{3-6}  & 1 & 2.11 & 1.89 & 1.71 & 1.56 \\ Equivalent plastic strain & 1 & 0–0.23 & 0–0.23 & 0–0.23 & 0–0.23 \\ Displacement magnitude & m & 0–0.072 & 0–0.072 & 0–0.072 & 0–0.072 \\ \hline \end{tabular}
\end{table} 
Table 4: Results obtained after simulation in all scenarios. Figure 12: Slope displacements for Material 2. The difference in FoS value increases with an increasing friction angle but the differences between the results are relatively small. It can also be seen from Table 4 that the values corresponding to the equivalent plastic strain and the displacement magnitude do not differ between the two flow rules considered. Also, in regard to the flow rule, the FoS and the locations of the critical failure surfaces are not greatly affected by the dilatation angle.