# Working Face Stability of Box Shield Tunneling under Non-Uniform Support Pressure
## 3 Results
### Comparisons of the Support Pressure
Figure 9 shows the variation in \(S_{2}\) depending on \(B/L\) for a typical \(\varphi^{\prime}=25^{\circ}\) and \(L/D=2\). \(S_{2}\) grows rapidly with an increasing \(B/L\); the change curve is steep, and the range of change is large. Figure 10 shows the variation in \(s_{2}/\gamma D\) depending on \(B/L\) for a typical \(\varphi^{\prime}=25^{\circ}\). In Figure 10a (\(C/D=1\)), both models predict that \(s_{2}/\gamma D\) increases with an increasing \(B/L\). The curves are relatively flat with less variation. Comparing Figures 9 and 10, it can be found that under the same conditions, \(S_{2}\) increases by almost 100%, while \(s_{2}/\gamma D\) increases by approximately 10%. Due to \(s_{2}=S_{2}/BD\) (Equation (15)), the change in \(s_{2}/\gamma D\) is related to \(B\) when \(\gamma D\) is constant. When the increase in \(S_{2}\) is apportioned to the increase in \(B\), the change in \(s_{2}/\gamma D\) will be relatively small. This is the reason why \(s_{2}/\gamma D\) is less sensitive to \(B/L\) compared to \(S_{2}\). In Figures 10 and 11, both \(s_{2}/\gamma D\) and \(s_{2}/s_{1}\) increase in a similar pattern with an increasing \(B/L\). The curves indicating the results of the proposed model are mostly above the curves of the numerical model results. The comparison indicates that the proposed model agrees well with the numerical model and predicts higher and safer pressures. The error mainly comes from the assumption that the support pressure acting on block I is known and can be obtained by the active earth pressure coefficient \(K_{\rm a}\), which is shown in Equation (6). This assumption makes \(s_{1}\) smaller and \(s_{2}\) larger. The findings from the proposed model are larger than those from the numerical model. It can also be found that at an identical \(B/L\), the results increase with a higher ratio of \(L/D\). This probably occurs because the increase in the width of the working surface weakens the soil arching effect, making the overlying soil pressure increase, and the area partially supported increases accordingly, and it will be more difficult to maintain soil stability. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{6}{c}{\(C\)/D = 1, \(L\)/D = 2} \\ \hline \multirow{2}{*}{\(\varphi^{\prime}/\mathrm{o}\)} & \multicolumn{3}{c}{\(s_{2}\)/\(s_{1}\)(Proposed Model)} & \multicolumn{3}{c}{\(s_{2}\)/\(s_{1}\)(Numerical Model)} \\ \cline{2-7}  & \multicolumn{2}{c}{\(B\)/\(L\) = 0.5} & \multicolumn{2}{c}{\(B\)/\(L\) = 0.6} & \multicolumn{2}{c}{\(B\)/\(L\) = 0.7} & \multicolumn{2}{c}{\(B\)/\(L\) = 0.5} & \multicolumn{2}{c}{\(B\)/\(L\) = 0.6} & \multicolumn{2}{c}{\(B\)/\(L\) = 0.7} \\ \hline
15 & 0.609 & 0.627 & 0.642 & 0.504 & 0.539 & 0.563 \\
25 & 0.489 & 0.502 & 0.512 & 0.342 & 0.369 & 0.387 \\
35 & 0.451 & 0.448 & 0.448 & 0.272 & 0.291 & 0.305 \\
45 & 0.475 & 0.452 & 0.437 & 0.235 & 0.251 & 0.263 \\ \hline \multicolumn{7}{c}{\(C\)/D = 2, \(L\)/D = 2} \\ \hline \multirow{2}{*}{\(\varphi^{\prime}/\mathrm{o}\)} & \multicolumn{3}{c}{\(s_{2}\)/\(s_{1}\)(Proposed Model)} & \multicolumn{3}{c}{\(s_{2}\)/\(s_{1}\)(Numerical Model)} \\ \cline{2-7}  & \multicolumn{2}{c}{\(B\)/\(L\) = 0.5} & \multicolumn{2}{c}{\(B\)/\(L\) = 0.6} & \multicolumn{2}{c}{\(B\)/\(L\) = 0.7} & \multicolumn{2}{c}{\(B\)/\(L\) = 0.5} & \multicolumn{2}{c}{\(B\)/\(L\) = 0.6} & \multicolumn{2}{c}{\(B\)/\(L\) = 0.7} \\ \hline
15 & 0.395 & 0.420 & 0.441 & 0.322 & 0.350 & 0.372 \\
25 & 0.257 & 0.270 & 0.281 & 0.204 & 0.220 & 0.234 \\
35 & 0.223 & 0.216 & 0.214 & 0.164 & 0.176 & 0.184 \\
45 & 0.254 & 0.225 & 0.