# Limit Equilibrium Analysis of Landfill Instability Based on Actual Failure Surface
## 3 Results
### Parameter Analysis  
#### 3.2.1 Two-Wedge Model  
1. Slope scale and water level  
When the stability analysis of the actual landfill slope is carried out, the failure surface should be preliminarily judged according to the site topography, solid waste age and slope angle, etc. Then, based on the slope and displacement monitoring of the slope, the position of the failure surface and the angle of the most dangerous failure surface are determined; finally, the \(FS\) is calculated. This method of combining the measured data with the theoretical model can effectively improve the accuracy of the assessment of the \(FS\) of the slope. In this section, the failure surface data are obtained based on the centrifugal tests and the parametric analysis is conducted on the effect of the water level change and the failure surface angle on the \(FS\). In the parameter analysis of the two-wedge model, the slope ratio of 1:2 and the case without a dam were selected for calculation, and five values of water level ratios of 0.35, 0.375, 0.4, 0.425, and 0.45 were selected for analysis. It can be seen from Figure 7 that in the condition of constant water level ratio, with the increase in slope height, the \(FS\) tends to decrease and then increase. According to the proposed theoretical model, the stability changes of the slope with different water level ratios show good consistency. Therefore, it can be guessed that for a fixed water level ratio and failure mechanism, there might exist the most dangerous slope height range. It is an obvious conclusion that when the slope height is fixed, the stability of the landfill slope will decrease when the water level rises. This is consistent with the previous research conclusions. Taking the slope height of 20 m as an example, the water level rises from 7.5 m to 9 m, and the \(FS\) decreases by 0.1, which also explains the potential threats to slope stability caused by problems such as leachate accumulation or heavy rain. Figure 7: Variation curve of \(FS\) with slope height H for fixed water level ratio of two-wedge model. 2 Failure surface angle  
As shown in Figure 8, as the angle of the failure surface increases and the water level increases, the safety factor of the slope decreases. It can be found that the angle of the actual failure surface corresponds to the failure mode of the slope with a higher water level and the traditional method is conservative for the evaluation of _FS_. Further, the smaller the angle of the actual failure surface, the greater the influence of the water level change on the _FS_. That is to say, for the slope failure mode where the failure surface is not perpendicular to the ground, the traditional wedge method has a prudent evaluation of the _FS_ of the slope due to the water level. This leaves a larger design space for slope support and reinforcement engineering works. Soil properties  
Through sensitivity analysis, we evaluated the effect of cohesion and friction angle of active wedge and passive wedge, and different slope shapes (\(H\):\(L\) is 1:1, 1:2, and 2:3; \(L\) = 30 m; and water level ratio \(h\)/\(H\) = 0.4), on the stability of the slope [33]. It can be analyzed from Figure 9a that under the condition of a certain water level ratio, when the cohesion of the active wedge increases gradually from 0 to 25 kPa, the increase in the _FS_ is less than 0.05 and the decrease in the slope height will amplify the influence of cohesion of the active wedge. The cohesion of the passive wedge increases gradually from 0 to 25 kPa, and the increase in the safety factor is less than 0.03. The safety factor is not sensitive to the change in slope height. Figure 9b shows that the friction angle of the passive wedge significantly affects the stability of the whole slope. This is because the internal friction angle of the passive wedge contributes more to the overall anti-sliding force and the passive wedge occupies a large proportion of the sliding part in the test.