# The Influence of Metro Tunnel Construction Parameters on the Settlement of Surrounding Buildings
## 3 Results
### Stage 2: Optimized Regression Model  
The next step is the development of a regression model using only significant parameters identified as a result of the analysis of variance. A re-analysis of the results of the analysis of variance allows us to conclude that this equation is also statistically significant, just like the previous one, with an F-significance of 1.08371 \(\times\) 10\({}^{-37}\)\(<<\) 0.05 = \(\alpha\) and a coefficient of determination R\({}^{2}\) = 0.60. The standard error of the model was 2.39 mm. The combination of these metrics allows us to state that the equation is statistically significant and explains approximately 60% of the variability in the data. All model parameters are statistically significant, with the \(p\)-value of each parameter being less than \(\alpha\) = 0.05. Furthermore, according to Table 3, there is no multicollinearity between the parameters, while the relationship between the response and the parameter of the average face-support pressure for 10 m intervals (Pavg10) with the highest weight coefficient b\({}_{3}\) = 6.98 is maintained. Figure 2: Histogram of the distribution of average face-support pressure (Pavg10). Therefore, the equation for multiple linear regression to determine surface settlement looks as follows:  
\[\text{S}=-14.82-0.20\cdot\text{H}+6.98\cdot\text{P}_{\text{avg}10}-0.16\cdot \text{V}_{10}+0.00049\cdot\text{E}_{1} \tag{3}\]  
By analyzing the signs of the regression coefficients, we can conclude that an increase in the average face-support pressure for a 10 m section (Pavg10) and the weighted average deformation modulus of the tunnel face (E1) lead to a decrease in the absolute settlement of the monitoring object. At the same time, an increase in the tunnel depth and the average volume of ground output for a 10 m section (V10) results in an increase in the absolute settlement. It is also important to note that the low value of the regression coefficient b4 is associated with higher values of the deformation modulus compared to other parameters. Figure 3 shows the influence of each regression coefficient of the significant parameter at the average values of the independent variables. In many works on related topics, the authors [28; 29; 32; 33; 34; 35; 36; 37] resort to this regression model due to its ease of interpretation of results, ease of implementation, and robustness to new data (this type of model is less prone to overfitting). Stage 3: Determining the Significance of the Grouting Pressure Parameter into the Space between the Living and Soil Mass for Surface Settlement  
Data on the volumes of grout injection into the space between the lining and soil mass are only available for the construction of the left tunnel of the RAL, consisting of 92 rows of data. In light of the above, a decision has been made to use the data on grouting volumes in combination with the optimized regression model presented in Section 3.2 to ensure an optimal balance of the number of data rows and regression parameters. The average volume of injected grout when installing one ring, consisting of precast reinforced concrete blocks with a width of 1.4 m, is 4.02 m\({}^{3}\). The mode is 4.04 m\({}^{3}\). The maximum volume encountered during the excavation of this branch is 4.76 m\({}^{3}\), while the minimum is 3.68 m\({}^{3}\). Figure 3: The overall contribution of significant factors to the magnitude of deformation. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **S, mm** & **H, m** & **Pavg10, bar** & **V10, t** & **E1, kPa** \\ \hline S, mm & 1.00 & - & - & - & - \\ \hline H, m & 0.06 & 1.00 & - & - & - \\ \hline Pavg10, bar & 0.65 & 0.33 & 1.00 & - & - \\ \hline V10, t & \(-\)0.05 & 0.21 & 0.15 & 1.00 & - \\ \hline E1, kPa & 0.47 & 0.45 & 0.32 & 0.17 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Correlation matrix of parameters for the model with only significant parameters.