# Limit Equilibrium Analysis of Landfill Instability Based on Actual Failure Surface
## 3 Results
### Parameter Analysis
#### 3.2.2 Three-Wedge Model  
In order to make the calculation of the factor of safety easier, we simplified the geometric model as follows: in the parameter analysis of the three-wedge model, the intersection of the failure surface and the slope bottom is flush with the slope shoulder,  
Figure 8: Two-wedge model: profile of _FS_ with water level of different failure surface angles \(\alpha\). as shown in Figure 10, where \(d_{1}=3\) m, \(D=16\) m, \(H=16\) m, \(h_{B}=3\) m, dam angle \(\theta=60^{\circ}\), \(\beta=50.9^{\circ}\), \(L\) can be obtained according to the geometric relationship in the figure, and the mechanical parameters of the soil are consistent with those in Two-Wedge Model analysis. We analyze the influence of water level, angle of the failure surface, soil parameters, height and angle of the dam to the \(FS\). 4. Failure surface angle and water level  
Considering the failure mode in the centrifugal model tests, the failure surface angle \(\alpha\) is around \(90^{\circ}\) and the water level h increases from 5 m to 9 m. The factor of safety improved quickly but the assumption that the safety factor of the active wedge and the passive wedge are equal and the assumption that \(\alpha\) is too large or too small is obviously unrealistic; so, in the analysis of the angle of the failure surface, \(\alpha\) is only in the range of \(75\)-\(115^{\circ}\). Figure 11 shows that as the angle of the failure surface increases, the \(FS\) of the slope increases gradually. It is conservative to evaluate the situation where the actual failure surface is greater than \(90^{\circ}\) and it is relatively dangerous for the actual failure surface angle to be less than \(90^{\circ}\); so, it is necessary to analyze the slope stability based on the actual failure mode for safety. Compared with the case where the angle of the actual failure surface is less than \(90^{\circ}\), the safety factor fluctuates less with the change in the angle. Therefore, the traditional method is relatively reliable for the evaluation of the instability mode of a failure surface angle less than \(90^{\circ}\). However, once the angle exceeds \(90^{\circ}\), the difference between the safety factors of \(95^{\circ}\) and \(115^{\circ}\) can reach about 0.5. In addition, it can be seen that with the increase in water level, the change in the failure surface angle has no apparent effect on the slope stability. Figure 10: Simplified diagram of three-wedge model. Figure 9: Sensitivity analysis: the effects of (**a**) cohesion and (**b**) friction angle. Soil properties  
We consider the case where the angle of the failure surface is 100\({}^{\circ}\) under the condition of water level \(h=6\) m. By changing the cohesion and friction angle of the soil of active wedge and passive wedge, the influence of soil property change on slope stability is analyzed. The other parameters are the same as in the previous section. The active wedge and passive wedge friction angles of 15\({}^{\circ}\), 20\({}^{\circ}\), and 25\({}^{\circ}\) and the cohesion forces of 0 kPa, 5 kPa, 10 kPa, 15 kPa, and 20 kPa are calculated, respectively. It can be seen from Figure 12 that the change in the cohesion of the active wedge and the passive wedge has little effect on the overall stability, and the \(FS\) does not change more than 0.1 when the cohesion increases by 5 kPa. The \(FS\) is more sensitive to the cohesion of the active wedge than the passive wedge. Similar to the conclusion obtained from the two-wedge model, the change in the friction angle has a significant impact on slope stability. The friction angle in the active wedge soil increases from 15\({}^{\circ}\) to 25\({}^{\circ}\); the safety factor increases by about 0.2; and the passive wedge increases by about 0.5, which is relatively more obvious. Figure 11: Three-wedge model: profile of \(FS\) with water level of different failure surface angles \(\alpha\). Figure 12: Three-wedge model: profile of \(FS\) with cohesion of different friction angle in active and passive wedge.