## 3 Results and Analysis
### Sensitivity Analysis of Anchored Sand Slope
#### 3.1.1 Sensitivity of a Single Factor  
Sensitivity analysis is carried out on soil weight (\(\gamma\)), the distance between surface water level and the crown level of the slope (\(L_{1}\)), the distance between groundwater level and the crown level of the slope (\(L_{2}\)), the internal friction angle of soil (\(\varphi\)), slope inclination (\(\beta\)), the anchorage angle of the umbrella anchor (\(\alpha\)), and the average buried depth of the umbrella anchor (\(h\)). Table 2 shows the range of each factor. Figure 3 shows that the stability of the sand slope is negatively correlated with \(\beta\) and the factor of \(L_{1}\) and positively correlated with other factors. Figure 4 shows that the water level fluctuation factors \(L_{1}\) and \(L_{2}\) have exactly the opposite effects on the factor of safety. This implies that landslides will be triggered easily with a large amount of precipitation in a short time, because this results in a sudden change in the surface water level, while the groundwater level changes lag, depending mainly on the hydraulic conductivity of the soil [52]. The fluctuation of the water level is caused by impoundment or discharge in a short time. This is similar to the fact that the minimum factor of safety occurs during the rapid declination period of the reservoir water level and rainy season [53]. When the surface water level is more than one quarter of the slope height, a sudden drop in the surface water level is more likely to trigger instability [54; 55]. If the surface water level rises suddenly, the factor of safety will increase first and then decrease when the surface water level is less than 10% of the slope height. The water levels have the greatest impact on the factor of safety when the surface water level is 20-30% of the slope height. This result is close to that of [PERSON] and [PERSON] [56]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Factor** & **Symbol Reference Value** & **Range** \\ \hline Soil weight & \(\gamma\) & 19 kN/m3  & 16–22 kN/m3  \\ Distance from surface water level to the crown level of the slope & \(L_{1}\) & 17 m & 14–20 m \\ Distance from groundwater level to the crown level of the slope & \(L_{2}\) & 2 m & 0–6 m \\ Internal friction angle & \(\varphi\) & 35\({}^{\circ}\) & 20–40\({}^{\circ}\) \\ The inclination of the slope & \(\beta\) & 30\({}^{\circ}\) & 26–34\({}^{\circ}\) \\ Anchorage angle & \(\alpha\) & 25\({}^{\circ}\) & 16–34\({}^{\circ}\) \\ Average buried depth & \(h\) & 4 m & 1–7 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The variation range of each factor. Figure 3: Comprehensive graph of the single factor sensitivity analysis. Table 5 shows that the order of sensitivity of each factor is as follows: \(\beta>h>\gamma>\varphi>L_{2}>L_{1}\). The factors of water level fluctuation and anchor arrangement are mainly considered. We change the slope inclination from 30\({}^{\circ}\) to 34\({}^{\circ}\), keep the other parameters consistent (Figure 6), and analyze the sensitivity of the factors of the umbrella anchor layout and water level fluctuation. According to the specification of the layout of the anchor, the horizontal spacing of the anchor layout should not be less than 2 m. Therefore, the horizontal spacing of the umbrella anchor layout is selected as 2 m in this analysis, and \(n\) is the number of umbrella anchor rows, which can be understood as the number of umbrella anchors arranged in the vertical direction of slope within the unit width (2 m). Table 6 shows the variation range of each factor. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Source** & **Sum Sq.** & **Mean Sq.** & **Rank** \\ \hline \(\gamma\) & 117.80 & 29.45 & 3 \\ \(L_{1}\) & 87.14 & 21.79 & 6 \\ \(L_{2}\) & 104.47 & 26.12 & 4 \\ \(\varphi\) & 102.54 & 25.63 & 5 \\ \(\beta\) & 810.61 & 202.65 & 1 \\ \(h\) & 132.65 & 33.16 & 2 \\ Total & 1357.58 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of the variance analysis of sand slope stability.