# Working Face Stability of Box Shield Tunneling under Non-Uniform Support Pressure
## 3 Results
### Parametric Analysis  
In this part, a typical situation of \(D=6\) m and \(L/D=2\) is considered. The partially supported ratio \(B/L\) varies from 0.4 to 0.7. For shallowly buried tunnels, the depth ratio \(C/D\) varies from 1 to 2, and the total stress concept is accepted for calculating the soil stress. The soil weight was chosen as \(\gamma=19.8\) kN/m\({}^{3}\). The frictional angle \(\varphi^{\prime}\) varies from 15\({}^{\circ}\) to 45\({}^{\circ}\). Figure 13 shows the variation in \(N_{\gamma}\) depending on \(\varphi^{\prime}\). For \(C/D\)\(=1\) (in Figure 13a), \(N_{\gamma}\) decreases nonlinearly with an increasing \(\varphi^{\prime}\). When \(\varphi^{\prime}\)<30\({}^{\circ}\), \(N_{\gamma}\) increases with an increasing \(B/L\) at a constant \(\varphi^{\prime}\), and they become close to each other when \(\varphi^{\prime}\) is between 30\({}^{\circ}\) and 35\({}^{\circ}\). \(N_{\gamma}\) decreases with an increasing \(B/L\) at a constant \(\varphi^{\prime}\), which is less than 30\({}^{\circ}\). In Figure 13b, similar variations in \(N_{\gamma}\) at \(C/D\)\(=2\) can be observed. A comparison between Figure 13a and Figure 13b shows the influence of \(C/D\) on \(N_{\gamma}\). A higher \(C/D\) makes a higher coefficient \(N_{\gamma}\). Figure 14 shows the variations in \(N_{c}\) depending on \(\varphi^{\prime}\). For \(C/D\)\(=1\) (in Figure 14a), \(N_{c}\) decreases nonlinearly with an increasing \(\varphi^{\prime}\). As \(B/L\) becomes smaller, the change in \(N_{c}\) becomes more pronounced. When \(\varphi^{\prime}\) is relatively small, the discrepancy between \(N_{c}\) values associated with different \(B/L\) values becomes more significant. Figure 14b demonstrates a similar tendency of change in \(N_{c}\). A comparison between Figure 14a and Figure 14b shows that a higher \(C/D\) makes a higher a coefficient \(N_{c}\). Figure 11: Variations in \(s_{2}/s_{1}\) depending on \(B/L\) at typical \(\varphi=25^{\circ}\). Figure 12: Comparison of failure geometries obtained with the proposed mechanism and with the numerical model for different strength parameters. Figure 13: Variations in \(N_{\gamma}\) depending on \(\varphi^{\prime}\). In this part, typical non-cohesive soil \((c^{\prime}/(\gamma D)=0)\) is considered for the most adverse scenario. As a result, Equation (22) is simplified as \(s_{2}=\gamma DN_{\gamma}\). Table 3 shows the variation in \(\theta\), \(\alpha\), and \(V\) depending on \(\varphi^{\prime}\). \(V\) denotes the total volume of the wedge model, that is, the failure zone. \(V\) can be calculated by adding up the volumes of block I, II, and III, that is, \(V=2V_{1}+V_{2}\). It can be seen that with an increasing \(\varphi^{\prime}\), \(\theta\) increases, while \(\alpha\) and \(V\) decrease. In particular \((C/D=1,B/L=0.4)\), as \(\varphi^{\prime}\) increases from \(15^{\circ}\) to \(45^{\circ}\), \(\theta\) increases from \(55.9^{\circ}\) to \(71.0^{\circ}\), while \(\alpha\) decreases from \(48.5^{\circ}\) to \(29.8^{\circ}\), and \(V\) decreases from \(117.1\) m\({}^{3}\) to \(59.4\) m\({}^{3}\). The increase in \(\theta\) indicates that the wedge slope becomes larger. The decrease in \(\alpha\) indicates that the failure zone becomes smaller. Changes in \(\theta\) and \(\alpha\) both cause the volume of the failure zone to decrease. The decrease in \(V\) directly confirms the volume of failure zone decreases with an increasing \(\varphi^{\prime}\). The reason is that the increase in \(\varphi^{\prime}\) means that the soil has a greater shear strength, and the greater the self-stabilizing capacity of the soil, the better it is for the tunnel face to sustain stability by itself. At a constant \(\varphi^{\prime}\) and \(C/D\), the increasing \(B/L\) makes \(\theta\) decrease, but \(\alpha\) and \(V\) increase.