# Stability Analysis of the Landfill Slope with an Engineered Berm Under Composite Failure Mode
## 4 Discussion  
In order to investigate the reliability of the method proposed in this paper in analyzing the stability of the landfill with an engineered berm, the average safety factor, \(FS_{\rm ave}\), against composite failure mode was compared with that against translational failure mode. Figure 21: The influence of \(\delta_{\rm B}\) and \(c_{\rm B}\) on critical log-spiral slip surface, respectively. Referring to Technical code [36], the shear strength values of four types of liner interfaces are shown in Table 1. The shear strength of the liner interface can generally reach its peak value at the bottom of the landfill slope, while only residual values can be exerted at its back slope [29]. For the shear strength value of waste mass, any type can be selected according to Technical code [34], i.e., \(\phi_{\text{SW}}\) = 12\({}^{\circ}\), \(\phi_{\text{SW}}\) = 15 kN/m\({}^{2}\) (WM-1), while the other type can be selected according to the paper by [PERSON] et al. [37], i.e., \(\phi_{\text{SW}}\) = 17\({}^{\circ}\), \(\phi_{\text{SW}}\) = 6 kN/m\({}^{2}\) (WM-2). For the comparison of safety factors under the action of the engineered berm, the over-berm and under-berm failure modes were considered separately. Under these two failure modes, parameter value combinations for five working conditions are provided as shown in Tables 2 and 3, respectively. The other unchanged parameter values are as follows: \(H\) = 70 m, \(B\) = 100 m, \(\alpha\) = 18.4\({}^{\circ}\), \(\omega\) = 14\({}^{\circ}\), \(\theta\) = 1.1\({}^{\circ}\), \(D_{\text{B}}\) = 3 m, \(\eta\) = 63.4\({}^{\circ}\), \(\gamma_{\text{SW}}\) = 10.2 kN/m\({}^{3}\), \(\gamma_{\text{B}}\) = 18 kN/m\({}^{3}\). When analyzing the stability of the landfill slope in Figure 22, T indicates translational failure while C indicates composite failure. In addition, considering the type of failure of the engineered berm, Subscript o represents the over-berm failure mode, and Subscript u represents the under-berm failure mode. The bold font in the above tables suggests that the safety factor calculated for resisting the composite failure mode is lower than the value calculated for resisting the translational failure mode, and the italic bold font implies that the safety factors calculated for resisting the two failure modes are no different. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No**} & **Liner** & \multicolumn{2}{c}{**Peak Shear Strength**} & \multicolumn{2}{c}{**Residual Shear Strength**} \\ \cline{3-5}  & **Interface** & \(\delta_{\text{P}}\) (\({}^{\circ}\)) & \(c_{\text{P}}\) (kN/m\({}^{2}\)) & \(\delta_{\text{A}}\) (\({}^{\circ}\)) & \(c_{\text{A}}\) (kN/m\({}^{2}\)) \\ \hline LI-I & GMX1/GT2 & 30 & 5 & 15 & 2 \\ LI-II & GMX/CCL3 & 27 & 10 & 18 & 10 \\ LI-III & GMX/GCL & 28 & 3 & 16 & 0 \\ LI-IV & GT/GN4 & 27 & 0 & 14 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Peak and residual shear strength values of four types of liner interfaces at bottom and back slope, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Case I** & **Case II** & **Case III** & **Case IV** & **Case V** \\ \hline \(H_{\text{B}}\) (m) & 3 & 10 & 3 & 3 & 3 \\ \(\xi\) (\({}^{\circ}\)) & 26.6 & 26.6 & 18.4 & 26.6 & 26.6 \\ \(\delta_{\text{B}}\) (\({}^{\circ}\)) & 18 & 18 & 18 & 10 & 18 \\ \(c_{\text{B}}\) (kN/m\({}^{2}\)) & 11.5 & 11.5 & 11.5 & 11.5 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Geometric and mechanical parameters for the engineered berm when over-berm failure occurs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Case I** & **Case II** & **Case III** & **Case IV** & **Case V** \\ \hline \(H_{\text{B}}\) (m) & 3 & 10 & 3 & 3 & 3 \\ \(\xi\) (\({}^{\circ}\)) & 26.6 & 26.6 & 18.4 & 26.6 & 26.6 \\ \(\delta_{\text{B}}\) (\({}^{\circ}\)) & 32 & 32 & 32 & 20 & 32 \\ \(c_{\text{B}}\) (kN/m\({}^{2}\)) & 8 & 8 & 8 & 8 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Geometric and mechanical parameters for the engineered berm when under-berm failure occurs.