# The Influence of Metro Tunnel Construction Parameters on the Settlement of Surrounding Buildings
## 3 Results
### Stage 1: Primary Regression Model  
The first analysis of variance was conducted on a sample of 201 observations. The parameters presented in Section 2. were considered for the first iteration, except for parameter v. The assessment of the results of the analysis of variance allows for the conclusion that the equation is statistically significant, as the F-significance in this sample is 8.66285 \(\times\) 10\({}^{-34}\) << 0.05 = \(\alpha\). The coefficient of determination R\({}^{2}\) = 0.62, which, according to [PERSON]'s scale [30], cannot be considered as a high value. The standard error of the model was 2.37 mm. Nevertheless, when analyzed in conjunction with other metrics, within the scope of this study, this value may be sufficient for determining significant parameters. It should be noted that, out of the eleven parameters claimed in this model, the following parameters were found to be significant:  
* Depth from surface to vault (H), m, \(p\)-value = 4.37412 \(\times\) 10\({}^{-6}\) << 0.05 = \(\alpha\);  
Figure 1: Flowchart of the methodology for selecting significant parameters. * Average ground pressure for 10 m (Pavg.10), bar, \(p\)-value = 1.13748 \(\times\) 10\({}^{-27}\)\(<<\) 0.05 = \(\alpha\);
* Average ground output for installing one ring (V\({}_{10}\)), t, \(p\)-value = 0.001014007 \(<\) 0.05 = \(\alpha\);
* Deformation modulus in the tunnel face (E\({}_{1}\)), kPa, \(p\)-value = 0.023281021 \(<\) 0.05 = \(\alpha\). Additionally, a correlation matrix, presented in Table 2, was obtained, from which several conclusions can be drawn. Firstly, the correlation coefficient R = 0.65 indicates a moderate relationship between the investigated variables, absolute subsidence (S), and average ground pressure for 10 m (Pavg.10). Secondly, of interest within this sample is the positive relationship between the parameters number of floors (L) and depth from the surface to the tunnel vault (H), which is supported by a correlation coefficient of R = 0.63. One possible explanation for this relationship could be the increase in the depth of compressible stratum depending on the number of building floors and the potential consistent matching of the depth of the compressible stratum with the depth of the tunnel vault. In other words, digging a tunnel at a depth of 10 m under a two-story building corresponds to digging a tunnel at a depth of 20 m under a five-story building. However, the study of the relationship between the parameters number of floors (L) and depth from the surface to the tunnel vault (H) is not the subject of this study, and the parameter characterizing the surrounding buildings will not be used in the final equation due to multicollinearity with the parameter depth from the surface to the tunnel vault (H) and \(p\)-value \(>\) 0.05 = \(\alpha\). The third conclusion that can be drawn regarding the multicollinearity of parameters is the relationship between the parameters of the 3 rd group of the sample, which relates to the characteristics of the soil mass. An analysis of Table 2 shows that the highest correlation is observed between the parameters of cohesion and the internal friction angle for the soils both in the tunnel face and above the tunnel. There is also a relationship between the deformation modulus itself and the deformation modulus with the strength characteristic. These patterns are presumably explained by the laws of soil mechanics, but it is necessary to note this in order to justify the use of one parameter from group No. 3 in the final regression model, in combination with the \(p\)-values obtained from the analysis of variance, from an econometric perspective. Therefore, to establish the final equation, it is necessary  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Parameter** & **S, mm** & **r, m** & **H, m** & **Pavg.10, bar** & **V10, t** & **L, f f.**  
and sufficient to use only one parameter from group No. 3, the soil deformation modulus at the tunnel face (E\({}_{1}\)) with a \(p\)-value = 0.023281021 \(<\) 0.05 = \(\alpha\).