## 3 Results and Analysis
### Sensitivity Analysis of Anchored Clay Slope  
Case 2 analyzes the sensitivity of a clay slope. Figure 8 shows the profile and a simplified model of the Canggiiang bridge-Yingpan slope. It can be divided into three secondary slopes, where part I is critical stable, part II has local deformation in the shallow layer, part III is relatively stable compared with parts I and II. The bedrock is the Jurassic Bazhulu Formation (J3b). Table 10 shows the relevant basic parameters in the sensitivity analysis, including the internal friction angle, soil weight and thickness of sliding mass, and effective cohesion force. At the same time, the water head of the slope and slope inclination is also considered.  
\[F=\frac{\frac{mc^{\prime}}{\gamma^{2}}+\left(\cos^{2}\beta-\frac{\gamma_{2}ln }{\gamma^{2}}\right)\tan n\varphi^{\prime}}{\sin\beta\cos\beta} \tag{10}\]  
where \(F\) is the factor of safety, \(mc^{\prime}\) (\(m>1\)) is the effective cohesion force of the anchoring system (kPa), \(\gamma\) is the unit weight of sliding mass (kN/m\({}^{3}\)), and \(\beta\) is the slope inclination (\({}^{\circ}\)). Umbrella anchors can form an anchoring system in the slope, which influences the properties of the soil. The effective cohesion force (\(c\)) and effective internal friction angle (\(\varphi\)) could be increased by the anchoring system, and the pore water pressure (\(h\)) decreases. Therefore, \(c\), \(\varphi\), and \(h\) are described by adding coefficients \(l\), \(m\), and \(n\) (\(m>1\), \(n>1\), \(l<1\)), respectively, after the anchoring system is formed; \(mc^{\prime}\) (\(m>1\)) is the effective cohesion force of the anchoring system (kPa), \(n\varphi^{\prime}\) (\(n>1\)) is the effective internal friction angle of the anchoring system (\({}^{\circ}\)), and \(lh\) (\(l<1\)) is the water head height of the piezometer after the anchorage system is formed (m). [57]. Table 11 shows the assumed values of \(m\), \(n\), and \(l\).  
Figure 8: The Canggiiang bridge–Yingpan slope and geological section: (**a**) a photo, (**b**) a cross-section.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mass** & \(\gamma\) **(kN/m\({}^{3}\))** & \(\varphi\) (\({}^{\circ}\)) & \(c\) **(kPa)** \\ \hline Sliding mass & 20–21 & 20–24 & 20–40 \\ Soil mass in sliding & 18–20 & 19–23 & 15–20 \\ zone & & \\ \hline \hline \end{tabular}
\end{table}
Table 10: Related parameters in the study area.  
Moreover, the comprehensive influence of the fluctuation of the surface and groundwater level factors on the factor of safety should be analyzed for the clay slope. Due to the limitation of the model conditions, the sensitivity analysis did not consider the influence of factors such as the speed of water level changes and the groundwater seepage channels on slope stability.  
Conceptualization, J.L. and W.S.; methodology, J.L. and W.S.; software, J.L.; validation, J.L. and W.S.; formal analysis, J.L. and W.S.; investigation, J.L.; resources, J.L. and W.S.; data curation, J.L. and W.S.; writing--original draft preparation, J.L.; writing--review and editing, J.L. and W.S.; visualization, J.L.; supervision, W.S.; project administration, W.S.; funding acquisition, W.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Plan of China (No. 2017 YFC1501303) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant KYCX21_2317).  
Not applicable.  
The authors declare no conflict of interest.