## 3 Results and Analysis
### Sensitivity Analysis of Anchored Sand Slope
#### 3.1.1 Sensitivity of a Single Factor
Figure 5: Response graphs for the main effects according to Table 4.  
Table 7 lists the results of the orthogonal experiment of sand slope stability under water level fluctuation. The factors of safety of trials 27, 28, 31, and 32 are negative; however, according to the principle of model derivation, under these four sets of parameters, the anchoring force provided by the umbrella anchor is greater than the sliding force of the slope element, and the value is negative. In practice, the slope is still stable at this time. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Factor** & **Symbol** & **Range** \\ \hline Layout density & \(n\) & 1-2 rows \\ Anchorage angle & \(\alpha\) & 5–65\({}^{\circ}\) \\ Average buried depth & \(h\) & 2–8 m \\ Distance between surface water level and the top of the slope & \(L_{1}\) & 16–19 m \\ Distance between groundwater level and the top of the slope & \(L_{2}\) & 0–6 m \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The variation range of parameters. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **1** & **2** & **3** & **4** & **5** & \\ \hline
**Trial No.** & \(n\) **(Row)** & \(\alpha\) **(\({}^{\circ}\))** & \(h\) **(m)** & \(L_{1}\) **(m)** & \(L_{2}\) **(m)** & F \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 7: Results of the orthogonal experiment of sand slope stability under water level fluctuation. Figure 6: Sand slope model diagram considering the factors of anchorage. Table 8 shows the results of the range analysis, and Figure 7 shows the response graph of the relationship among various factors and stability. The order of sensitivity of each factor is \(n>h>L_{2}>a>L_{1}\). Table 9 shows the results of the analysis of variance; the order of the analysis of variance is as follows: \(n>h>a>L_{2}>L_{1}\). The \(p\)-value of \(n\) is 0.043, less than 0.05. This implies that the layout density of the umbrella anchors \(n\) has a more significant influence on slope stability. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **1** & **2** & **3** & **4** & **5** & \\ \hline
**Trial No.** & \(n\) **(Row)** & \(\alpha\) (\({}^{\circ}\)) & \(h\) **(m)** & \(L_{1}\) **(m)** & \(L_{2}\) **(m)** & \(F\) \\ \hline
24 & 2 & 25 & 8 & 19 & 4 & 60.12 \\
25 & 2 & 45 & 2 & 17 & 4 & 1.41 \\
26 & 2 & 45 & 4 & 16 & 6 & 7.21 \\
27 & 2 & 45 & 6 & 19 & 0 & \(-\)5.13 \\
28 & 2 & 45 & 8 & 18 & 2 & \(-\)2.47 \\
29 & 2 & 65 & 2 & 17 & 6 & 1.76 \\
30 & 2 & 65 & 4 & 16 & 4 & 15.60 \\
31 & 2 & 65 & 6 & 19 & 2 & \(-\)1.63 \\
32 & 2 & 65 & 8 & 18 & 0 & \(-\)0.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: _Cont._ \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Factor**} & **1** & **2** & **3** & **4** & **5** \\ \cline{2-5}  & \(n\) & \(\alpha\) & \(h\) & \(L_{1}\) & \(L_{2}\) \\ \hline \(K_{1j}\) & 1.70 & 1.39 & 0.98 & 1.39 & 1.14 \\ \(K_{2j}\) & 2.66 & 2.19 & 2.16 & 2.00 & 2.10 \\ \(K_{3j}\) & & 3.04 & 2.80 & 2.14 & 1.60 \\ \(K_{4j}\) & & 1.88 & 3.11 & 2.61 & 3.05 \\ \(R_{j}\) & 2.18 & 1.65 & 2.12 & 1.23 & 1.91 \\ Rank & 1 & 4 & 2 & 5 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Range analysis of various factors. Figure 7: Response graph for the main effects according to Table 8.