## 4 Analysis of Results
### Effect of \(L_{\text{p}}\) on the Stability of Ventilation Network  
Furthermore, in order to study the influence of different \(L_{\text{p}}\) on the air flow direction of the tunnel, the multi-section flow \(Q_{\text{m}}\) and resistance \(h_{\text{m}}\) of the tunnel were extracted,  
Figure 10: Comparison of the resistance of each branch of the tunnel under different Lt conditions.  
Figure 9: Comparison of the flow rate of each section of the tunnel under different \(L_{\text{t}}\) conditions.  
as shown in Figures 11 and 12. If \(Q_{\rm a}>Q_{\rm u}\), when \(L_{\rm p}=80\) m, the cross-sectional flow rate of the advance side tunnel decreases by \(2.2\) m\({}^{3}\)/s (\(Q_{\rm 1}-Q_{\rm 3}\)), and the cross-sectional flow rate of the undercut side tunnel increases by \(1.5\) m\({}^{3}\)/s (\(Q_{\rm 4}-Q_{\rm 2}\)); when \(L_{\rm p}=130\) m, the cross-sectional flow rate of the advance side tunnel increases by \(0.11\) m\({}^{3}\)/s, and the cross-sectional flow rate of the undercut side tunnel decreases by \(0.11\) m\({}^{3}\)/s; when \(L_{\rm p}=180\) m, the cross-sectional flow rate of the advance side tunnel increases by \(0.04\) m\({}^{3}\)/s, and the cross-sectional flow of the undercut side tunnel decreases by \(0.04\) m\({}^{3}\)/s. If \(Q_{\rm a}<Q_{\rm u}\), when \(L_{\rm p}\) is \(80\) m, \(130\) m, and \(180\) m, the cross-sectional flow rate of the advance side tunnel decreases by \(3.4\), \(0.5\), and \(0.04\) m\({}^{3}\)/s, respectively, and the cross-sectional flow rate of the undercut side tunnel increases by \(3.2\), \(0.5\), and \(0.07\) m\({}^{3}\)/s, respectively.  
In Figure 12, with the increase of \(L_{\rm p}\), the resistance \(h_{\rm m}\) of each branch also decreases, but the trend of \(h_{\rm m}\) is different from that in Figure 10. Combined with the data in Figures 11 and 12, the \(R_{\rm m}\) and \(K\) under different \(L_{\rm p}\) conditions are calculated and summarized in Table 4. When \(L_{\rm p}=80\) m, \(Q_{\rm a}>Q_{\rm u}\), \(K=0.45<1\); \(Q_{\rm a}<Q_{\rm u}\), \(K=0.036<1\)  
Figure 11: Comparison of the flow rate of each section of the tunnel under different \(L_{\rm p}\) conditions.  
Figure 12: Comparison of the resistance of each branch of the tunnel under different \(L_{\rm p}\) conditions.  
indicating that the air flows from the advance side tunnel to the undercut side tunnel. When \(L_{\rm p}\) = 130 m, \(Q_{\rm a}>Q_{\rm u}\), \(K\) = 3.003 \(>\) 1, the air flows from the undercut side tunnel to the advance side tunnel, \(Q_{\rm a}<Q_{\rm u}\), \(K\) = 0.551 \(<\) 1, and the air flows from the advance side tunnel to the undercut side tunnel. When \(L_{\rm p}\) = 180 m, if \(Q_{\rm a}>Q_{\rm u}\), \(K\) = 2.257 \(>\) 1, the air flows from the undercut side tunnel to the advance side tunnel, if \(Q_{\rm a}<Q_{\rm u}\), \(K\) = 0.35 \(<\) 1, the air flows from the precedent tunnel to the undercut side tunnel.  
In summary, when \(L_{\rm t}\), \(L_{\rm p}\) = 80 and 180 m, the air flow direction of the tunnel is not restricted by the cross-section size of the cross passage: when \(L_{\rm t}\), \(L_{\rm p}\) = 80 m, the air flows from the advance side tunnel to the undercut side tunnel; when \(L_{\rm t}\) and \(L_{\rm p}\) = 180 m, the air flows from the tunnel with small air flow demand to the tunnel with large air flow demand. When \(L_{\rm t}\) = 130 m, the air flows from the undercut side hole to the advance side hole. However, when \(L_{\rm p}\) = 130 m, the air flows from the tunnel with small air flow demand to the tunnel with large air flow demand, which indicates that the size of the cross passage affects the air flow direction of the double-hole tunnel.