## 5 Example Analysis
### Example 2
#### 5.2.2 Stability Analysis  
Like example 1, the stability calculation method of this paper, strength reduction method and ultimate balance method are used to calculate the stability of example 2, respectively.  
(1) The method of this paper  
The stability of example 2 is calculated by using the stability analysis process in this paper, and the calculated results are shown in Figure 22. It can be clearly seen from Figure 22  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Layer Number**} & \multirow{2}{*}{**Original Method/kN**} & \multicolumn{2}{c}{**The Method of This**} & **Percentage of** \\  & & **Paper/kN** & **Difference** \\ \hline Fourth floor & 102.89 & 113.00 & 9.82\% \\ Third floor & 224.08 & 239.53 & 6.61\% \\ Second floor & 346.47 & 366.06 & 5.65\% \\ First floor & 408.26 & 492.59 & 5.20\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Calculation results of pullout force of anchor-plates in example 2.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Soil Layer Name**} & \multirow{2}{*}{\begin{tabular}{c} **Natural Heavy** \\ \(\gamma\)**(**/kN/m\({}^{3}\))** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Cohesive Force** \\ \(\sigma\)**(**/kPa**)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Angle of Internal Friction** \\ \(\varphi\)**(**/**c**)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Elastic Modulus** \\ \(E\)**/ kN/m\({}^{2}\))** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Friction Coefficient** \\ \(\mu\) \\ \end{tabular} } \\ \hline Fill soil & 17.5 & 20 & 22 & 30,000 & 0.35 \\ Foundation soil & 21 & 12 & 30 & 45,000 & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Soil parameters of example 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Layer Number**} & \multirow{2}{*}{\
\begin{tabular}{c} **Relative Ground** \\ **Height/m** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Length of Steel Tie** \\ **Rod/m** \\ \end{tabular} } & \multirow{2}{*}{**Prestress Value/kN**} \\ \hline Fourth floor & 10.5 & 13.5 & 50 \\ Third floor & 7.5 & 12.5 & 80 \\ Second floor & 4.5 & 11.5 & 110 \\ First floor & 1.5 & 10.5 & 140 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Parameters of anchor-plate of example 2.  
that the most dangerous slip surface is far from the foot of the slope, which belongs to the sliding mode of midpoint circle 1. The position of the most dangerous slip surface is 8 m away from point \(B\) at the top of the slope, the end position of the slip surface is 4 m away from point \(A\) at the foot of the slope, and the calculated stability factor is 1.612.  
(2) Strength reduction method  
The stability of example 2 is calculated with the help of PLAXIS 3D finite element software. The established three-dimensional model of the filled-slope with a slope ratio of 1:1 reinforced by the frame prestressed anchor-plates is shown in Figure 23.  
Figure 24 is the total displacement increment cloud map after the calculation of the model, from which it can be clearly see that the failure mode of the slope is circular sliding failure. When the slope is damaged, the slip surface may also be far away from the toe of the slope, except for the case where the slip surface passes through the toe of the slope, and failure may occur in the deformation area of the slope. The calculated stability factor is 1.665.  
Figure 23: The 1:1 model of filled-slope reinforced by frame with prestressed anchor-plates.  
Figure 22: Example 2 calculation results of the stability of this method.