# 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
#### 4.2.2 Orthogonal Experiment's Analysis of Variance
For a certain factor \(A\), when \(a=0.05\), if \(p<a\), there is a confidence level of \((1-a)\times 100\%\), that is, a 95% confidence that factor \(A\) is significant. Conversely, if \(p>a\), factor \(A\) cannot be considered significant at the \(a\) level [44]. Generally, if \(a=0.05\) and \(p<a\), factor \(A\) is significant; if \(a=0.01\) and \(p<a\), factor \(A\) is highly significant. The significance criteria are shown in Figure 12:2  
Based on Table 9, the influence of various factors on the roof subsidence of the tunnel can be determined. Among them, the \(p\)-value of the water content in the clay layer is 0.000, which is less than 0.01, indicating that the water content is a level I factor, and its influence on the roof subsidence is highly significant. The \(p\)-value for the thickness and position of the clay layer is greater than 0.05, which indicates that thickness and position are level III factors, and their influence on the roof subsidence is not significant. These findings are consistent with some previous studies, while also offering new insights. For example, researchers have investigated the effect of water content on the mechanical properties of clay-bearing sandstone and found that increasing water content significantly reduced the rock strength and increased deformation [45]. However, this study focused on a single rock type and did not consider the influence of clay layer thickness or position in a composite roof system. In another study, the deformation behavior of a composite roof consisting of mudstone and coal layers was studied using numerical simulations [46]. They found that the thickness of the weak coal layer had a significant \begin{table}
\begin{tabular}{c c c c c c} \hline \hline Source & Class III Sum & Freedom & Mean Square & F & \(p\) \\ \hline Corrected model & 986,377.617  & 10 & 98,637.762 & 4.101 & 0.006 \\ \hline Intercept & 1,491,457.930 & 1 & 1,491,457.930 & 62.007 & 0.000 \\ \hline Layer thickness & 91,080.828 & 2 & 45,540.414 & 1.893 & 0.183 \\ \hline Moisture content & 644,248.955 & 2 & 322,124.477 & 13.392 & 0.000 \\ \hline Layer & 251,047.835 & 6 & 41,841.306 & 1.740 & 0.176 \\ \hline Error & 384,847.126 & 16 & 24,052.945 & & \\ \hline Total & 2,800,921.645 & 27 & & \\ \hline Revised total & 1,371,224.743 & 26 & & \\ \hline \hline \end{tabular} \(R^{2}=0.719\) (After adjustment \(R^{2}=0.544\))  
\end{table} 
Table 8: SPSS analysis of roadway roof subsidence. \begin{table}
\begin{tabular}{c c c} \hline \hline \(p\)**-Value Range** & **Level** & **Significance** \\ \hline \(p<0.01\) & I & Highly significant \\ \hline \(0.01<p<0.05\) & II & Remarkable \\ \hline \(p>0.05\) & III & Not significant \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Significance criteria. impact on roof subsidence, with thicker coal layers leading to greater deformation. But this study did not consider the effect of moisture content or the presence of clay layers. The current study extends these previous findings by investigating the combined effects of moisture content, clay layer thickness, and position in a mudstone-clay composite roof system. The moisture content is identified as the dominant factor influencing roof subsidence, even more significant than the thickness and position of the clay layer. The sensitivity analysis in this study highlights the importance of considering the interactions between different factors in composite roof systems. While previous studies have often focused on individual factors in isolation, this work demonstrates that the relative significance of each factor can vary depending on the specific combination of geological and environmental conditions. In summary, the sensitivity analysis results in this study offer a new perspective on the factors influencing roof subsidence in mudstone-clay composite roofs. By comparing these findings with previous research and highlighting novel contributions, this manuscript provides a clearer understanding of the significance and implications of the current work in the field of coal mine roadway support design.