## 3 Test Results
### Model of Compressive Strength Response Surface
According to statistical conventions, a _p_-value < 0.0001 indicates very significant (***); a _p_-value < 0.05 indicates significant (**); and a _p_-value > 0.05 indicates not significant (*). To further evaluate the accuracy and reliability of the model, a variance analysis was used to test its significance, and the results are presented in Table 4. The P-value of the compressive strength model for the third grouting was 0.0162, which was less than 0.0500, indicating that the model item was significant. The F-value was 4.30, indicating that the model is reasonable. The P-value of the compressive strength model for the seventh round of grouting was less than 0.0001 with an F-value of 22.47, which indicates that the model is extremely significant and credible. First, the regression model of unconfined compressive strength of the three grouting rounds was analyzed, and the complex correlation coefficient \(R^{2}\) was 0.7947 and \(R^{2}\) was greater than 0.8, indicating that the model had a good correlation; thus, the correlation type of the model was general. The corrected correlation coefficient \(R^{2}{}_{Adj}\) was 0.6100, whereas the predicted correlation coefficient \(R^{2}{}_{Per}\) was 0.1451; the difference between the two values is greater than 0.2, indicating that the accuracy of the model is not high, and the error is large. The signal-to-noise ratio was 6.3051, which was greater than 4, indicating the high level of confidence of the trial. Similarly, the regression model of the unconfined compressive strength of seven grouting rounds was analyzed, and the complex correlation coefficient \(R^{2}\) was 0.9529, indicating that the model had a good correlation. The adjusted correlation coefficient \(R^{2}{}_{Adj}\) was 0.9105, whereas the predicted correlation coefficient \(R^{2}{}_{Per}\) was 0.8827. The difference between these two values is less than 0.2, indicating that the model has high accuracy and \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Source**} & \multirow{2}{*}{**df**} & \multicolumn{3}{c}{**3 Rounds of Grouting**} & \multicolumn{3}{c}{**7 Rounds of Grouting**} \\  & & _F-Value_ & _p-Value_ & **Significance** & _F-Value_ & _p-Value_ & **Significance** \\ \hline Model & 9 & 4.30 & 0.0162 & ** & 22.47 & \textless{}0.0001 & *** \\ A & 1 & 0.0758 & 0.7887 & * & 4.69 & 0.0555 & * \\ B & 1 & 0.6379 & 0.4430 & * & 32.71 & 0.0002 & ** \\ C & 1 & 0.1452 & 0.7111 & * & 18.98 & 0.0014 & ** \\ AB & 1 & 1.60 & 0.2339 & * & 0.0379 & 0.8496 & * \\ AC & 1 & 0.1834 & 0.6775 & * & 2.37 & 0.1547 & * \\ BC & 1 & 0.0651 & 0.8037 & * & 0.0353 & 0.8546 & * \\ A\({}^{2}\) & 1 & 0.0040 & 0.9509 & * & 0.0181 & 0.8955 & * \\ B\({}^{2}\) & 1 & 7.83 & 0.0189 & ** & 0.6760 & 0.4301 & * \\ C\({}^{2}\) & 1 & 3.08 & 0.1096 & * & 2.24 & 0.1655 & * \\ \hline \multirow{6}{*}{Note: A _p_-value < 0.0001 indicates very significant (***); a _p_-value < 0.05 indicates significant (**); and a _p_-value > 0.05 indicates not significant (*).} & \multicolumn{3}{c}{\(R^{2}=0.9529\)} \\  & & & \(R^{2}{}_{Adj}=0.6100\) & \multicolumn{3}{c}{\(R^{2}{}_{Adj}=0.9105\)} \\  & & & \(R^{2}{}_{Per}=0.1451\) & \multicolumn{3}{c}{\(R^{2}{}_{Per}=0.8827\)} \\ \cline{1-1}  & & & Noise Ratio = 6.3051 & \multicolumn{3}{c}{Noise Ratio = 13.9100} \\ \hline \hline \end{tabular} Note: A _p_-value < 0.0001 indicates very significant (***); a _p_-value < 0.05 indicates significant (**); and a _p_-value > 0.05 indicates not significant (*).  
\end{table} 
Table 4: Variance analysis of compressive strength response surface regression mode. small error. The signal-to-noise ratio was 13.9100, which was greater than 4, indicating the high reliability of the experiment. Figure 4 shows the normal probability distribution of the unconfined compressive strength residuals for three and seven grouting rounds. If the model is adaptable, the normal probability distribution of the residuals should be a straight line.