## 5 Analysis of Dominant Factors Influencing Surface and Roof Settlement
### Quantification of Influential Factors and Analysis of Dominant Variables  
Variance analysis can decompose the total sum of squares of deviations in experimental results into the sum of squares of deviations due to factors and the sum of squares of deviations due to experimental errors. By constructing the F-statistic and conducting an F-test, the magnitudes of the influence of various factors on the target indicators can be quantified [17]. We define the null hypothesis H0 as follows [27]: if there is no significant difference in the mean values of the observed variable under different levels of the control variable, then the effects at different levels of the control variable are simultaneously zero, denoted as  
\[H_{0}:\alpha_{1}=\alpha_{2}=\cdots=\alpha_{r}=0 \tag{4}\]  
In other words, the variation in the control variable at different levels does not have a significant impact on the observed variable. The alternative hypothesis \(H_{1}\) posits that the effects are not simultaneously zero. Utilizing the \(F\)-statistic, its mathematical definition is [27]:  
\[F=\frac{SSA/(k-1)}{SSE/(n-k)}=\frac{MSA}{MSE} \tag{5}\]  
where \(n\) represents the total sample size, \(k-1\)and \(n-k\) are the degrees of freedom for \(SSA\) and \(SSE\), \(MSA\) is the mean square between groups, and \(MSE\) is the mean square within groups. The purpose is to eliminate the impact of the number of levels and sample size on the analysis. The rejection region for \(H_{0}\) is [28]:  
\[W=\left\{ \begin{array}{l}f<F_{\alpha/2}(k-1,n-k),\text{ or }\\ f>F_{1-\alpha/2}(k-1,n-k)\end{array} \right\} \tag{6}\]  
Here, \(f\) represents the observed value of the \(F\)-statistic in the test. Its corresponding \(p\)-value is:  
\[P=2\text{min}\left\{P_{H_{0}}\{F>f\},P_{H_{0}}\{F<f\}\right\} \tag{7}\]  
Using significance levels \(\alpha\) = 0.01, 0.05, and 0.1, the influence of each factor was quantified into four levels: highly significant, significant, somewhat influential, and no influence. The observed values of the \(F\)-statistic and the corresponding probability \(p\)-values were calculated using SPSS Statistics 26 software. If the probability \(p\)-value was less than the significance level \(\alpha\), the null hypothesis was rejected, and it was concluded that the different levels of the control variable have an impact on the observed variable. Conversely, if the \(p\)-value was greater than the significance level, the null hypothesis was accepted, and it was assumed that the different levels of the control variable had no impact on the variable. Tables 4 and 5 present the quantified impact of fill parameters on ground surface and immediate roof displacements, respectively. The factors influencing ground subsidence, in descending order of impact, are fill cohesion, strip spacing, fill friction angle, fill Poisson's ratio, fill strip width, and fill elastic modulus. Notably, fill cohesion and strip spacing have a considerable effect on ground subsidence. Regarding immediate roof subsidence, the factors' impact decreases in the following order: fill cohesion, strip spacing, fill friction angle, fill Poisson's ratio, fill elastic modulus, and fill strip width. Fill cohesion has a highly significant influence, while strip spacing and friction angle have a substantial effect. Since the fill undergoes plastic deformation after bearing overburden load, the influence of the fill's elastic modulus is minimal. Additionally, the fill strip width primarily affects the fill's stability, and the immediate roof subsidence mainly occurs above the extracted area; thus, the fill width has a marginal impact on the immediate roof subsidence. Consequently, to control the immediate roof and ground surface subsidence within a limited range, the fill strength parameters must meet specific requirements, and the mine structure parameters must be rationally designed. In summary, the influence of fill strength parameters, deformation parameters, and structural parameters on ground surface subsidence and immediate roof subsidence follows a similar order.