# Working Face Stability of Box Shield Tunneling under Non-Uniform Support Pressure
## 3 Results
### Parametric Analysis
In particular (\(\varphi^{\prime}=25^{\circ}\)), as \(B/L\) increases from \(0.4\) to \(0.7\), \(\theta\) decreases from \(61.7^{\circ}\) to \(59.4^{\circ}\), while \(\alpha\) increases from \(41.9^{\circ}\) to \(63.1^{\circ}\), and \(V\) increases from \(92.9\) m\({}^{3}\) to \(114.9\) m\({}^{3}\). In addition, at a constant \(\varphi^{\prime}\) and \(B/L\), \(\theta\)  
Figure 14: Variations in \(N_{c}\) depending on \(\varphi^{\prime}\). \(\alpha\), and \(V\) remain virtually constant when \(C/D\) increases from 1 to 2. The failure zone is hardly affected by \(C/D\). In this part, typical non-cohesive soil (\(c^{\prime}/(\gamma D)=0\)) is considered. Figure 15 shows the variation in support pressure \(s_{2}\) depending on the angle of internal friction \(\varphi^{\prime}\). In Figure 15a (\(C/D=1\)), the proposed model predicts that \(s_{2}\) decreases nonlinearly as \(\varphi^{\prime}\) increases, and changes gradually flatten out. The change in \(s_{2}\) becomes more apparent with a higher \(B/L\). The discrepancy between \(s_{2}\) values associated with different \(B/L\) values becomes more significant at a lower \(\varphi^{\prime}\). In Figure 15b (\(C/D=2\)), a similar variation in \(s_{2}\) depending on \(\varphi^{\prime}\) can be seen. A comparison between Figure 15a and Figure 15b shows that a higher \(C/D\) makes a higher \(s_{2}\). This is because the higher the \(C/D\), the greater the pressure of the overburden, and therefore, the more likely it is to slide unstably. In Figure 16a (\(C/D=2\)), the proposed model predicts that \(s_{2}/\gamma D\) decreases nonlinearly with an increasing \(\varphi^{\prime}\). \(s_{2}/\gamma D\) associated with a higher \(B/L\) has a larger variation. Compared to Figure 15b (\(C/D=2\)), due to \(s_{2}=S_{2}/BD\) (Equation (15)), the change in \(s_{2}/\gamma D\) is related to \(B/L\) when \(\gamma D\) and \(L\) are constant. Thus, the variation in \(s_{2}/\gamma D\) is different from that of \(S_{2}\) depending on \(\varphi^{\prime}\). Assuming that the \(S_{2}\) associated with a lower \(B/L\) (assumed to be \(B_{1}/L\)) is named as \(\left.S_{2}\right|_{B_{1}/L}\), the \(S_{2}\) associated with \(B_{2}/L\)(\(B_{2}\)>\(B_{1}\)) is named as \(\left.S_{2}\right|_{B_{2}/L}\), named in the same way as \(\left.s_{2}/\gamma D\right|_{B_{1}/L}\) and \(\left.s_{2}/\gamma D\right|_{B_{2}/L}\). A simple calculation (\(s_{2}=S_{2}/BD\)) leads to the conclusion that at a constant \(\varphi^{\prime}\), when \(\left.S_{2}\right|_{B_{2}/L}\)\(\left.S_{2}\right|_{B_{1}/L}\), \(\left.s_{2}/\gamma D\right|_{B_{2}/L}\)>\(s_{2}/\gamma D\right|_{B_{1}/L}\). For example, two scenarios are shown in Figure 16b. The calculation about \(S_{2}\) shows that when \(\varphi^{\prime}\)<35\({}^{\circ}\) and \(\left.S_{2}\right|_{B_{2}/L=0.7}\)>\(\frac{7}{4}S_{2}|_{B_{1}/L=0.4}\) (condition 1), \(\left.s_{2}/\gamma D\right|_{B_{2}/L=0.7}\)>\(s_{2}/\gamma D\)\(\left|_{B_{1}/L=0.4}\). The opposite (condition 2) happens when \(\varphi^{\prime}\)>30\({}^{\circ}\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{\(\varphi^{\prime}\) /\({}^{\circ}\)} & \multicolumn{3}{c}{**B/L = 0.4**} & \multicolumn{3}{c}{**B/L = 0.7**} \\ \cline{2-7}  & \(\theta\) /\({}^{\circ}\) & \(\alpha\) /\({}^{\circ}\) & \(V\)/m\({}^{3}\) & \(\theta\)/\({}^{\circ}\) & \(\alpha\)/\({}^{\circ}\) & \(V\)/m\({}^{3}\) \\ \hline
15 & 55.9 & 48.5 & 117.1 & 53.4 & 68.0 & 144.5 \\
20 & 58.99 & 45.1 & 104.2 & 56.5 & 65.6 & 128.8 \\
25 & 61.7 & 41.9 & 92.9 & 59.4 & 63.1 & 114.9 \\
30 & 64.3 & 38.7 & 83.0 & 62.2 & 60.4 & 102.5 \\
35 & 66.7 & 35.6 & 74.3 & 64.8 & 57.5 & 91.5 \\
40 & 69.0 & 32.7 & 66.5 & 67.2 & 54.5 & 81.6 \\
45 & 71.0 & 29.8 & 59.4 & 69.5 & 51.2 & 72.6 \\ \hline \end{tabular}
\end{table} 
Table 3: Variations in the optimal \(\theta\), \(\alpha\), and \(V\) depending on \(\varphi^{\prime}\). Figure 15: Variations in \(S_{2}\) depending on \(\varphi^{\prime}\).