# Stability Analysis of the Landfill Slope with an Engineered Berm Under Composite Failure Mode
## 3 Results
### Error Analysis
#### 3.1.2 Analysis of the Safety Factor When Under-Berm Failure Occurs  
Figure 13a shows that \(FS_{\text{max}}\), \(FS_{\text{min}}\), and \(FS_{\text{ave}}\) all increase as \(H_{\text{B}}\) increases. When \(H_{\text{B}}\) increases from 3 m to 15 m, \(FS_{\text{max}}\), \(FS_{\text{ave}}\), and \(FS_{\text{min}}\) increase by 6.59%, 6.35%, and 6.10%, respectively. The rate of increase in these safety factors gradually diminishes, but the differences in their rates are not significant.  
From Figure 13b, it can be seen that \(\Delta\) increases with the increase in \(H_{\text{B}}\). And it can be determined that when \(H_{\text{B}}\) = 3 m, 6 m, 9 m, 12 m, 15 m, \(\Delta\) = 2.75%, 2.80%, 2.86%, 2.94%, 2.99%. It can be concluded that the maximum value of \(\Delta\) is 2.99%.  
Figure 14a shows that that \(FS_{\text{max}}\), \(FS_{\text{min}}\) and \(FS_{\text{ave}}\) all decrease with the increase in \(\xi\). When \(\xi\) increases from 15\({}^{\circ}\) to 45\({}^{\circ}\), \(FS_{\text{max}}\), \(FS_{\text{ave}}\), and \(FS_{\text{min}}\) decrease by 3.62%, 3.57%, and 3.53%, respectively. It can be seen that the increase above three safety factors is gradually decreasing, but their decrease rates is similar to the impact of \(H_{\text{B}}\) on the safety factor.  
From Figure 14b, it can be seen that \(\Delta\) increases with the increase in \(\xi\). And it can be determined that when \(\xi\) = 15\({}^{\circ}\), 20\({}^{\circ}\), 25\({}^{\circ}\), 30\({}^{\circ}\), 35\({}^{\circ}\), 40\({}^{\circ}\), 45\({}^{\circ}\), \(\Delta\) = 2.867%, 2.837%, 2.831%, 2.826%, 2.822%, 2.818%, 2.815%. It can be concluded that the maximum value of \(\Delta\) is 2.867%.  
Figure 15a shows that \(FS_{\text{max}}\), \(FS_{\text{min}}\), and \(FS_{\text{ave}}\) all increase as \(\delta_{\text{B}}\) increases. When \(\delta_{\text{B}}\) increases from 15\({}^{\circ}\) to 40\({}^{\circ}\), \(FS_{\text{max}}\), \(FS_{\text{ave}}\), and \(FS_{\text{min}}\) increase by 5.38%, 5.19%, and 4.98%, respectively. The rate of increase in these safety factors gradually diminishes, but the differences between them are not significant.  
From Figure 15b, it can be seen that \(\Delta\) first slightly decreases and then increases with the increase in \(\delta_{\text{B}}\). And it can be determined that when \(\delta_{\text{B}}\) = 15\({}^{\circ}\), 20\({}^{\circ}\), 25\({}^{\circ}\), 30\({}^{\circ}\), 35\({}^{\circ}\), 40\({}^{\circ}\), \(\Delta\) = 2.742%, 2.741%, 2.792%, 2.815%, 2.855%, 2.938%. It can be concluded that the maximum value of \(\Delta\) is 2.938%.  
Figure 16a shows that \(FS_{\text{max}}\), \(FS_{\text{min}}\) and \(FS_{\text{ave}}\) all increase with the increase in \(c_{\text{B}}\). When \(c_{\text{B}}\) increases from 0 to 20 kN/m\({}^{2}\), \(FS_{\text{max}}\), \(FS_{\text{ave}}\), and \(FS_{\text{min}}\) increase by 1.45%, 1.47%, and 1.49%, respectively. It can be seen that there is almost no difference in the increase in the above three safety factors.  
From Figure 16b, it can be seen that \(\Delta\) decreases approximately linearly with the increase in \(c_{\rm B}\). And it can be determined that when \(c_{\rm B}=0\), 4 kN/m\({}^{2}\), 8 kN/m\({}^{2}\), 12 kN/m\({}^{2}\), 16 kN/m\({}^{2}\), 20 kN/m\({}^{2}\), \(\Delta=2.839\%\), 2.834%, 2.829%, 2.824%, 2.819%, 2.814%. It can be concluded that the maximum value of \(\Delta\) is 2.839%.  
Through the analysis of \(\Delta\) above, it can be found that the maximum value of \(\Delta\) is 4.89%. In other words, the values of \(\Delta\) are all within 5%. Therefore, it is feasible to use \(FS_{\rm ave}\) to approximate \(FS_{\rm true}\) to evaluate the degree of stability of the landfill with an engineered sperm against composite failure modes.