## 5 Conclusions  
Based on the difference in the air flow demand between two working faces in a double-hole tunnel, this paper simulated the influence of structural parameters such as \(L_{\rm t}\) (distance from the traffic cross passage to the working face), \(L_{\rm p}\) (distance from the pedestrian cross passage to the working face), \(H_{\rm t}\) (height of the upper step), and \(L_{\rm w}\) (safe step distance of the working face of the double tunnel) on the structural stability of the ventilation network of the double-hole tunnel, and draws the following conclusions:  
1. If there is a difference in the volume flow of the double-hole tunnel, the \(R_{\rm m}\) of each branch in the ventilation network structure changes non-uniformly due to the influence of \(L_{\rm t}\), \(L_{\rm p}\), \(L_{\rm w}\), and \(H_{\rm t}\), resulting in significant differences in the \(K\) and the air flow direction of the tunnel under different working conditions.
2. When \(L_{\rm t}\) and \(L_{\rm p}=80\) 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 low air flow demand to the tunnel with large air flow demand. When \(L_{\rm t}\) and \(L_{\rm p}=130\) m, there is a difference in the air flow direction between the two. The results show that the size of the cross passage affects the stability of the ventilation network in the range of \(80\) m < \(L_{\rm t}\), \(L_{\rm p}\) < \(180\) m.
3. In the construction regulations [25], the stability of the ventilation network has nothing to do with \(L_{\rm w}\). When \(3\) m < \(H_{\rm t}\) < \(3.5\) m, there is an \(H_{\rm t}\) that makes K = 1, and the ventilation network of the double-hole tunnel tends to be stable and the flow field does not interfere with each other.  
The above studies prove the possibility of complementary construction ventilation of the two tunnels, which is conducive to replenishing the surplus air flow from the side with small air flow demand to the tunnel with large air flow demand. In the follow-up work, the curves of \(L_{\rm t}\) and \(L_{\rm p}\) and \(K\) values should be fitted to judge the application range of double-hole complementary ventilation.  
All authors contributed to the writing of the paper and provided critical input that helped shape the research, analysis, and paper. H.D.: Conceptualization, formal analysis, writing original draft, study conception and design, analysis and interpretation of results, draft manuscript preparation. S.C.: designed the research, supervised the work. Y.R.: carried out the research. All authors have read and agreed to the published version of the manuscript.  
This study was supported by the National Natural Science Foundation of China (No. 42202321), by the Key Science and Technology Projects in Transportation Industry Funded by Ministry of Transport, China (2021-MS5-126), by the list of Key Science and Technology Projects in Guangxi's Transportation Industry (No. 18).  
Not applicable for studies not involving humans or animals.  
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The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.