## 4 Analysis of Results
### Effect of \(L_{w}\) on the Stability of the Ventilation Network  
Based on the above analysis, it can be seen that the cross-section size of the cross passage affects the air flow direction of the double-hole tunnel in the range of 80 m \(<\)\(L_{\rm t}\), \(L_{\rm p}\)\(<\) 180 m. However, when \(L_{\rm t}\) and \(L_{\rm p}\) = 80 m, the \(K\) is less than 1; the air flows from the advance side tunnel to the undercut side tunnel regardless of \(Q_{\rm a}\)\(>\)\(Q_{\rm u}\) or \(Q_{\rm u}\)\(>\)\(Q_{\rm a}\). In order to explore the influence of \(L_{\rm w}\) on the air flow direction of the double-hole tunnel, \(Q_{\rm a}\)\(>\)\(Q_{\rm u}\) and \(L_{\rm t}\) = 80 m were kept unchanged, only the \(L_{\rm w}\) (10, 20, 30, 40, 50 m) were changed, and the flow and resistance of each branch section were shown in Figures 15 and 16. In Figure 15, when \(L_{\rm w}\) = 10 m, \(Q_{1}\) = 27.5 m\({}^{3}\)/s, after the air flowed through the cross passage, \(Q_{3}\) = 35.8 m\({}^{3}\)/s, the cross-section flow of the advance side tunnel increased by 8.3 m\({}^{3}\)/s (\(Q_{3}\)-\(Q_{1}\)), and the cross-section flow of the undercut side tunnel decreased by 8.2 m\({}^{3}\)/s (\(Q_{2}\)-\(Q_{4}\)). When \(L_{\rm w}\) = 20, 30, 40, and 50 m, \(Q_{1}\) = 28.2, 26.5, 30.9, and 27.7 m\({}^{3}\)/s, the cross-section flow of the advance side tunnel decreased by 4.6, 1.2, 3.3, and 4.4 m\({}^{3}\)/s, respectively, and the cross-section flow of the undercut side tunnel increased by 4.6, 1.6, 2.2, and 4.2 m\({}^{3}\)/s, respectively. In Figure 16, the resistance \(h_{\rm m}\) of each branch was non-uniform. Figure 14: Comparison of the resistance of each branch under different \(H_{\rm t}\) conditions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Difference in the Air Flow Demand of Two** & \(L_{\rm w}\)**/(m)** & \(R_{\rm 1}\) **(N-s\({}^{2}\)/m\({}^{8}\))** & \(R_{\rm 2}\) **(N-s\({}^{2}\)/m\({}^{8}\))** & \(R_{\rm 3}\) **(N-s\({}^{2}\)/m\({}^{8}\))** & \(R_{\rm 4}\) **(N-s\({}^{2}\)/m\({}^{8}\))** & \(K\)** \\ \hline \(Q_{\rm a}\) & 2.5 & \(5.4\times 10^{-4}\) & \(6.8\times 10^{-3}\) & \(2.3\times 10^{-4
It can be seen from Table 6 that when \(L_{\rm w}\) = 10 m, \(K\) = 4.499 \(>\) 1, the air flowed from the undercut side tunnel to the advance side tunnel. When \(L_{\rm w}\) = 20, 30, 40, and 50 m, the \(K\) are all less than 1, and the air flowed from the advance side tunnel to the undercut side tunnel. According to _The technical code for highway tunnel construction_ (JTG F60-2009), the safe layout distance of the co-excavation working face for the excavation of two parallel tunnels should be determined according to the distance between the two tunnels and the surrounding rock, and should not be less than 2 times the diameter of the tunnel [25]. \(L_{\rm w}\) = 30, 40, and 50 m meet the above requirements, but the \(K\) are all less than 1, indicating that within the allowable range of the regulations, changing \(L_{\rm w}\) does not affect the air flow direction of the double-hole tunnel. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Difference in the Air Flow Demand of Two Holes** & \(L_{\rm w}\)**/(m)** & \(R_{1}\) & \(R_{2}\) & \(R_{3}\) & \(R_{4}\) & \(K\) \\ \hline \multirow{4}{*}{\(Q_{\rm a}\)} & \(1.6\times 10^{-3}\) & \(1.5\times 10^{-3}\) & \(5.1\times 10^{-4}\) & \(2.1\times 10^{-3}\) & 4.499 & \(1.6\times 10^{-3}\) \\  & \(5.5\times 10^{-3}\) & \(7.8\times 10^{-3}\) & \(2.1\times 10^{-3}\) & \(2.0\times 10^{-3}\) & 0.652 & \(5.5\times 10^{-3}\) \\ \(>\) & \(3.0\times 10^{-3}\) & \(5.4\times 10^{-3}\) & \(6.9\times 10^{-5}\) & \(5.5\times 10^{-5}\) & 0.687 & \(3.0\times 10^{-3}\) \\ \(Q_{\rm u}\) & \(1.2\times 10^{-3}\) & \(5.6\times 10^{-3}\) & \(5.3\times 10^{-5}\) & \(2.1\times 10^{-4}\) & 0.851 & \(1.2\times 10^{-3}\) \\  & \(1.6\times 10^{-4}\) & \(4.6\times 10^{-3}\) & \(9.4\times 10^{-5}\) & \(6.8\times 10^{-4}\) & 0.253 & \(1.6\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table}