## 5 Parameter Sensitivity Analysis
### Sensitivity Analysis  
The five-factor and five-level orthogonal test was selected. There are twenty-five cases for the orthogonal test. The stability factors were calculated using the FLAC\({}^{\rm 3D}\) software for every case. The orthogonal test scheme and stability factors are shown in Table 5.  
\(K_{ij}\) is the sum of all test results for each factor at the same level. \(R_{j}\) is the range of the factor \(j\). It can be calculated as followed  
\(R_{j}=\max\{K_{1j},\,K_{2j},\,K_{3j},\,K_{4j},\,K_{5j}\}-\min\{K_{1j},\,K_{2 j},\,K_{3j},\,K_{4j},\,K_{5j}\}\).  
The range \(R_{j}\) is a variable. If the \(R_{j}\) value is larger, the influences of factor \(j\) on the subgrade stability are greater. Therefore, a larger range \(R_{j}\) value indicates that the subgrade stability is more sensitive to the factor \(j\). The range \(R_{j}\) can be used to determine the sensitivity order of every factor. The range analysis results are shown in Table 6.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Level**} & \multicolumn{5}{c}{**Parameters**} \\ \cline{2-6}  & **Width B/m** & **Height H/m** & \begin{tabular}{c} **Density** \\ \(\rho\)**/kg/m\({}^{3}\)** \\ \end{tabular} & \
\begin{tabular}{c} **Cohesion** \\ _c/kPa_ \\ \end{tabular} &
\begin{tabular}{c} **Internal** \\ **Friction \(\varphi l^{\circ}\)** \\ \end{tabular} \\ \hline level 1 & 2.5 & 2 & 1700 & 10 & 8 \\ level 2 & 5 & 3 & 1800 & 12.5 & 12 \\ level 3 & 7.5 & 4 & 1900 & 15 & 16 \\ level 4 & 10 & 5 & 2000 & 17.5 & 20 \\ level 5 & 12.5 & 6 & 2100 & 20 & 24 \\ \hline \hline \end{tabular}
\end{table}
Table 4: ELB parameter values for every level.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{5}{c}{**Factors**} \\ \cline{2-7}  & **Factor A** & **Factor B** & **Factor C** & **Factor D** & **Factor E** & \multirow{2}{*}{\(F_{s}\)} \\ \cline{2-7}  & **Width** & **Height** & **Density** & **Cohesion** & **Internal** & \\  & **B/m** & **H/m** & \(\rho\)**/kg/m\({}^{3}\)** & _c/kPa_ & **Friction \(\varphi l^{\circ}\)** & \\ \hline
1 & 2.5 & 2 & 1700 & 10 & 8 & 1.11 \\
2 & 5 & 2 & 1800 & 12.5 & 12 & 1.13 \\
3 & 7.5 & 2 & 1900 & 15 &  
Table 6 and Figure 11 demonstrate that \(R_{\rm A}\) is the biggest, \(R_{\rm B}\), \(R_{\rm C}\), and \(R_{\rm D}\) are next, and \(R_{\rm E}\) is the smallest. These suggest that the ELB width is the most sensitive parameter and the internal friction is the least sensitive parameter. The ELB width's sensitivity to the stability factors is higher than that of ELB height. This is consistent with the simulation results in Section 4.  
The \(R_{\rm B}\) is higher than \(R_{\rm C}\). This means the sensitivity of the geometric parameters (width, height) is higher than that of the physical and mechanical parameters. The \(R_{\rm C}\) is higher than \(R_{\rm D}\), which shows the ELB density's sensitivity to the stability factors is higher than that of ELB cohesion. The ELB parameter sensitivity order is as follows. Width > height > density > cohesion > internal friction.  
In the ELB designing process, the width and height should be focused on and the density, cohesion, and internal friction can be ignored.