# Instability Characteristics of and Control Techniques for Mudstone-Clay Composite Roof Roadways
## 4 Deformation and Instability Law and Prevention Technology of Double Soft Composite Roof
### Sensitivity Analysis of Influencing Factors  
#### 4.2.1 Orthogonal Experiment Range Analysis  
Using the range analysis method, the experimental results from Table 6 were used to evaluate the influence and ranking of clay layer moisture content, thickness, and type on roof subsidence [39; 40]. Following range analysis, variance analysis was conducted to verify the results and assess the reliability of parameter optimization. (1) For roadway roof subsidence analysis, the \(K_{1}\) value for layer thickness is the sum of experimental results corresponding to the number \"1\" in that column as follows:  
\[K_{1}=1407.16\]  
Therefore, \(K_{2}=2121.27\) and \(K_{3}=2874.57\). The average layer thickness is obtained by dividing \(K_{1}\) value for layer thickness by its corresponding horizontal repetition number as follows:  
\[\overline{K_{1}}=\frac{1407.16}{9}=156.35\]  
Similarly, the average layer thickness is \(\overline{K_{2}}=235.70\) and \(\overline{K_{3}}=319.40\). A larger range (R) indicates a greater impact from factor level changes on the indicator, signifying the factor's \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{Index} & Layer & Moisture & \multirow{2}{*}{Horizon} & \multirow{2}{*}{Index} & Layer & Moisture & \multirow{2}{*}{Horizon} \\  & Thickness & Content & & & Thickness & Content & \\ \hline \(K_{1}\) & 469.05 & 149.26 & 1210.13 & \(\overline{K_{1}}\) & 156.35 & 49.75 & 201.52 \\ \hline \(K_{2}\) & 23.70 & 39.70 & 45.30 & \(\overline{K_{2}}\) & 235.70 & 234.65 & 139.30 \\ \hline \(K_{3}\) & 958.20 & 1140.40 & 321.37 & \(\overline{K_{3}}\) & 319.40 & 380.13 & 159.18 \\ \hline \(K_{4}\) & & & 1348.32 & \(\overline{K_{4}}\) & & & 448.10 \\ \hline \(K_{5}\) & & & 1061.02 & \(\overline{K_{5}}\) & & & 352.00 \\ \hline \(K_{6}\) & & & 550.10 & \(\overline{K_{6}}\) & & & 181.36 \\ \hline \(K_{7}\) & & & 964.31 & \(\overline{K_{7}}\) & & & 319.10 \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{Range \(R\)} & \multirow{2}{*}{163.05} & \multirow{2}{*}{330.38} & \multirow{2}{*}{308.80} & Primary & \multirow{2}{*}{3} & \multirow{2}{*}{1} & \multirow{2}{*}{2} \\  & & & and & secondary & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Range analysis of roof subsidence. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline Test & \begin{tabular}{c} Roof \\ Subsidence \\ \end{tabular} & \begin{tabular}{c} Test \\ Number \\ \end{tabular} & \begin{tabular}{c} Roof \\ Subsidence \\ \end{tabular} & \
\begin{tabular}{c} Test \\ Number \\ \end{tabular} &
\begin{tabular}{c} Root \\ Subsidence \\ \end{tabular} \\ \hline
1\# & 44.29 mm & 10\# & 54.60 mm & 19\# & 37.11 mm \\ \hline
2\# & 32.50 mm & 11\# & 31.97 mm & 20\# & 40.70 mm \\ \hline
3\# & 47.70 mm & 12\# & 65.09 mm & 21\# & 93.83 mm \\ \hline
4\# & 116.32 mm & 13\# & 162.07 mm & 22\# & 225.40 mm \\ \hline
5\# & 137.91 mm & 14\# & 252.15 mm & 23\# & 206.97 mm \\ \hline
6\# & 176.03 mm & 15\# & 419.66 mm & 24\# & 415.36 mm \\ \hline
7\# & 157.34 mm & 16\# & 302.92 mm & 25\# & 465.60 mm \\ \hline
8\# & 251.25 mm & 17\# & 239.85 mm & 26\# & 286.40 mm \\ \hline
9\# & 443.82 mm & 18\# & 592.96 mm & 27\# & 1103.20 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation results of maximum deformation of roadway in orthogonal experimental scheme. greater importance. Conversely, a smaller range suggests the factor is less significant [41; 42]. Taking roadway roof subsidence as an example, the range for layer thickness is the difference between the maximum and minimum values of \(\overline{K_{1}}\), \(\overline{K_{2}}\), and \(\overline{K_{3}}\), which equals \(R_{A}=\overline{K_{3}}-\overline{K_{1}}=163.05\). Similarly, the K value \(\overline{K_{3}}\), average \(\overline{K_{1}}\), and range R for each factor affecting roadway roof subsidence can be determined, as shown in Table 4. The mean main effects for each factor are illustrated in Figure 12. In Figure 12, (A), (B), and (C) respectively represent the main effects of thickness, moisture content and layer position.