## 3 Sensitivity Analysis of Influencing Factors
### Analysis of Variance (ANOVA)  
The analysis of variance (ANOVA) method involves analysing the sources of error in the data and thereby determining whether the means of the different aggregates are equal or not, and ultimately analysing whether or not the respective variables have a significant effect on the response variable. The \(p\)-value method of hypothesis testing is adopted to measure the statistical significance of the results observed through range analysis method, and the F-test method is applied to determine whether the difference between two or more sample variances is significant, thus measuring the difference between the sample data and inferring the significance of the overall parameter.  
When \(F>F_{\alpha}(r-1,n-r)\), it is considered that there is a significant difference in the calculation of this impact factor. The significance level is usually taken as 0.05. With reference to the F-test table, it can be concluded that:  
\[F_{\alpha}(r-1,n-r)=F_{0.05}(2,24)=3.40 \tag{5}\]  
The meaning of each symbol in the expression is as follows: \(\alpha\)--significance level, \(r\)--factor level, \(n\)--total number of samples achieved in independent trials.  
As illustrated in Table 5, significance tests were carried out for each of the influencing factors through an analysis of variance (ANOVA). After statistical analysis of the collected original data with vertical displacement as the target variable, among the calculated F-value  
Figure 8: Range analysis of the principal stress difference.  
and \(p\)-value of each influencing factor, the F-value of the influencing factor A6 (tunnel diameter) is 9.53 with a \(p\)-value of 0.001, and the F-value of A10 (tunnel buried depth) is 3.50 with a \(p\)-value of 0.046. This indicates that the results observed by the influencing factors A6 (tunnel diameter) and A10 (tunnel buried depth) may be statistically significant due to accidental factors. The F-values of the other nine influences were less than the corresponding critical values at a significance level of 0.05, and the \(p\)-values were greater than the significance level of 0.05. The F-values of the other nine influencing factors were less than the corresponding critical values at a significance level of 0.05, and the \(p\)-values were greater than the significance level of 0.05. Considering the first principal stress S1 as the target variable, among the calculated F-values and \(p\)-values of the influencing factors, only the influencing factor A10 (tunnel buried depth) has an F-value of 452.50 and a \(p\)-value of 0.00. The F-values and \(p\)-values of the other 10 influencing factors were smaller than the corresponding critical values at a significance level of 0.05. It illustrates that the results resulting from the influence factor A10 (tunnel buried depth) are statistically significant. Adopting the principal stress difference S1-S3 as the target variable, from the calculated F-value and \(p\)-value of each influencing factor, the F-value of influencing factor A10 (tunnel buried depth) is 161.58 and the \(p\)-value is 0.00. The F-values and \(p\)-values of the remaining 10 influencing factors were less than the corresponding critical values at a significance level of 0.05. The results observed for the influencing factor A10 (tunnel buried depth) are also statistically significant in this situation.