# Stability Analysis of Box Tunnel Working Face under Non-Uniform Support Pressure
## 3 Results  
### Parametric Analysis  
The influence of soil shear strength parameters (\(\varphi^{\prime}\),\(c^{\prime}\)), tunnel geometry parameters (\(C\)/\(D\),\(L\)/\(D\)), and open silo parameters (unsupported ratio \(B\)/\(L\)) on the stability was analyzed. The calculation parameters are shown in Table 1.  
As shown in Table 2, when \(c^{\prime}\)/\(\gamma D=0.15\) and \(L\)/\(D\) is 1.5 and 2, respectively, \(\theta\) and \(f_{s}\) change with \(\varphi^{\prime}\). It can be seen that, as \(\varphi^{\prime}\) increases, \(\theta\) increases, and \(f_{s}\) increases, indicating that the increase in the self-stabilization capacity of the soil causes the volume of the damage area to decrease, and the safety factor is increased. When \(\varphi^{\prime}\) and \(L\)/\(D\) are certain, the larger that \(B\)/\(L\) is, the smaller that \(f_{s}\) is. For example, with \(L\)/\(D\) = 1.5, \(\varphi^{\prime}\) = 30, the increase in \(B\)/\(L\) is from 0.45 to 0.75, and a decrease in fs occurs of approximately 21.9%, which is due to the increase in the risk of instability of the working face caused by the increase in the unsupported area. \begin{table}
\begin{tabular}{c c c c c c c} \hline \(\gamma\) & \(\varphi^{\prime}\) & \(c^{\prime}\)/\(\gamma D\) & \(D\) & \(C\)/\(D\) & \(L\)/\(D\) & \(B\)/\(L\) \\ \hline
19.8 kN/m & 15\({}^{\circ}\)–40\({}^{\circ}\) & 0.10–0.20 & 6 m & 1,2 & 1–2 & 0.25–0.75 \\ \hline \end{tabular}
\end{table} 
Table 1: Calculation parameters. As shown in Figure 5, \(f_{s}\) increases with \(\varphi^{\prime}\) when other conditions are certain. For example, with \(L/D=1.0\) and \(c^{\prime}/\gamma D=0.15\), when \(\varphi^{\prime}\) increased from 20\({}^{\circ}\) to 40\({}^{\circ}\), \(f_{s}\) increased by approximately 32.0% because, as the angle of internal friction increases, so does the shear strength of the tunnel's surrounding rock and the tunnel's capacity for self-stabilization, which are conducive to maintaining stability. Comparing Figure 5a,b, it can be seen that \(f_{s}\) decreases slightly with increasing depth of overburden when \(L/D\) is a constant because the greater that the burial depth is, the greater that the overburden pressure is, and consequently, the greater that the potential for it to destabilize is. Based on the numerical calculations and the strength reduction technique, [PERSON] et al. (2016) proposed a simple analytical equation to calculate the safety factor for open face tunneling as follows  
\[f_{s}=\frac{0.9\tan\varphi^{\prime}+18(c^{\prime}/\gamma D)}{2+3(d/D)^{6\tan \varphi^{\prime}/F_{s}}}, \tag{25}\]  
where \(c^{\prime}\), \(\varphi^{\prime}\), and \(\gamma\) are the soil cohesion, friction angle, and soil unit weight, respectively; and \(d\) is the unlined distance behind the tunnel face and is taken as 0 in this paper. Using \(D\) as the equivalent diameter of a noncircular section, this article calculates the height of the pipe-jacking machine. This section compares the current solution with [PERSON]'s solutions and [PERSON]'s equation for verification. In the theoretical model of [PERSON] (2016), \(\theta\) obtained under the same conditions is brought into the procedure to calculate the safety factor for the model and to use it to check against the solution in this paper. The variation of \(f_{s}\) with \(L/D\) for the case of \(\varphi^{\prime}=40^{\circ}\) is given in Figure 6. It is easy to see that both [PERSON]'s solution and the model solution of this paper have a safety factor \(f_{s}\) that decreases with increasing \(L/D\), also verifying the accuracy of Figure 5. The safety factor obtained from [PERSON]'s solution is greater than that of the model solution of this paper in all operating conditions, indicating that the solution of this paper provides a safer solution and is more conducive to providing suggestions for engineering.