# Stability Analysis of the Landfill Slope with an Engineered Berm Under Composite Failure Mode
## 5 Conclusions  
This paper established a static calculation model for evaluating the stability of a landfill with an engineered berm against composite failure mode. Through relevant assumptions,  
Figure 22: \(FS_{\text{ave}}\) against translational and composite failure modes, respectively, in different cases.  
implicit function equations for the maximum and minimum safety factors under different failure modes of the engineered berm were obtained. The maximum and minimum safety factor values were calculated through MATLAB programming. Through error analysis, it was verified that using the average safety factor instead of the true safety factor to evaluate the static stability of the landfill with an engineered berm against composite failure modes is feasible. Furthermore, the influence of relevant parameters of the engineered berm on the landfill stability and the critical slip surface was analyzed, and the following conclusions were drawn:  
(1) When the height of berm remains constant, the ability of the landfill slope to resist over-berm failure can be improved by increasing the value of the angle of the back slope of the berm. In addition, for the over-berm failure mode, a larger value of interface friction angle of liner components beneath the block combined with appropriate apparent cohesion between liner components beneath the block is more conducive to improving the stability of the landfill slope.  
(2) Unlike the situation when over-berm failure occurs, a specific height of berm requires a smaller value of the angle of the back slope of the berm to resist under-berm failure. At this point, the combination of the interface friction angle of liner components beneath the block and the apparent cohesion between liner components beneath the block has the opposite effect on the stability of the landfill slope compared to the situation when over-berm failure occurs.  
(3) Regardless of over-berm failure or under-berm failure, as the interface friction angle of liner components beneath the block or the apparent cohesion between liner components beneath the block increases, the critical log-spiral slip surface gradually shifts to the right. In addition, the changes in the mechanical parameters of the engineered berm have a significant impact on the horizontal spacing of the critical log-spiral slip surfaces corresponding to the maximum and minimum safety factors in the over-berm failure mode while having little effect on the corresponding horizontal spacing in the under-berm failure mode.  
(4) Whether it is over-berm failure or under-berm failure, the geometric and mechanical parameters of the engineered berm have little effect on the transition between translational and composite failure of the landfill slope, while the mechanical parameters of the waste mass have a significant effect.  
Conceptualization, X.R. and Y.-S.L.; methodology, X.R. and H.W.; software, Y.L. and H.W.; validation, Y.L., Y.-S.L. and H.W.; writing--original draft preparation, X.R. and Y.L.; writing--review and editing, Y.-S.L., J.C. and Z.D.; supervision, X.R.; funding acquisition, Y.-S.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Shanghai Rising-Star Program, grant number 21 QB1404400.  
Not applicable.  
Data Availability Statement: Data can be acquired upon reasonable request.  
[PERSON] was employed by the Shanghai Shen Yuan Geotechnical Engineering Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.