## 5 Example Analysis
### Example 1
#### 5.1.2 Stability Analysis  
The stability calculation method of this paper, strength reduction method and ultimate balance method are used to calculate the stability of example 1, respectively. (1) The method of this paper  
The stability of example 1 is calculated by using the stability analysis process in this paper, and the calculated results are shown in Figure 18. It can be clearly seen from Figure 18 that the most dangerous slip surface passes over the toe of the slope, which belongs to the sliding mode of toe circle 1. The position of the most dangerous slip surface is 7 m away from point \(B\) at the top of the slope, and the calculated stability factor is 1.710. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Layer Number**} & **Relative Ground** & **Length of Steel Tie** & \multirow{2}{*}{**Prestress Value/kN**} \\  & **Height/m** & **Rod/m** & \\ \hline Fourth floor & 10.5 & 12.5 & 60 \\ Third floor & 7.5 & 11.0 & 90 \\ Second floor & 4.5 & 9.5 & 120 \\ First floor & 1.5 & 8.0 & 150 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of anchor-plate of example 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Layer Number**} & **Original Method/kN** & \
\begin{tabular}{c} **The Method of This** \\ **Paper/kN** \\ \end{tabular} &
\begin{tabular}{c} **Percentage of** \\ **Difference** \\ \end{tabular} \\ \hline Fourth floor & 151.64 & 168.81 & 11.32\% \\ Third floor & 326.94 & 351.12 & 7.40\% \\ Second floor & 502.23 & 533.43 & 6.21\% \\ First floor & 677.52 & 715.74 & 6.08\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calculation results of pullout force of anchor-plate in example 1. (2) Strength reduction method  
PLAXIS 3D finite element software can establish a three-dimensional slope model and calculate its stability, so PLAXIS 3D finite element software is used to calculate the stability of example 1. The anchor-plate is simulated by a large area rectangular beam in the \"Embedded beam\" element, the frame beam is simulated by the \"Beam\" element, and the tension bar is simulated by the \"Node to node anchor\" element. The established three-dimensional model of the filled-slope with a slope ratio of 1:0.5 reinforced by the frame with prestressed anchor-plates is shown in Figure 19.  
Figure 20 shows the total displacement increment cloud map after the calculation of the model, which can reveal the possible failure mechanism. From Figure 20, it can be clearly seen that the slope failure is an arc sliding failure, and the slip surface will pass over the foot of the slope. Failure may occur in the deformation area of the slope, but the location of the most dangerous slip surface cannot be clearly known. The calculated stability factor is 1.790. Figure 19: The 1:0.5 model of filled-slope reinforced by a frame with prestressed anchor-plates. Figure 18: Example 1 calculation results of the stability of this method. 3. Ultimate balance method  
The slope stability results simulated by PLAXIS 3D are very close to those calculated by this algorithm, but it is not very convincing to verify the rationality of the algorithm in this paper by only relying on the stability results of a slope simulated by a finite element software. Thus, the Bishop method in the SLOPE module of GeoStudio 2012 finite element software is used to calculate the stability of example 1. The anchor-plate is simulated by the \"anchor\" unit, the specific calculation results are shown in Figure 21. From Figure 21, it can be seen that the most dangerous slip surface passes through the toe of the slope, and the starting point of the slip surface is 6.5 m away from the starting point of the top of slope. The stability factor is 1.840. (4) Comparative analysis  
By using the above three methods to calculate the stability of example 1, it is not difficult to see that the slip surfaces obtained by the three methods all pass over the toe of the slope.