## 1 Introduction  
In recent years, China has implemented the Western Development Policy, the construction of transportation infrastructure has shifted westward, and the scale and structure of the road network in the western region have been continuously improved. Due to the dense mountains and ravines in the western region, tunnel engineering is developing in the direction of \"deep burial, long distance, and large cross-section\" [1; 2; 3]. The complex construction technology and harsh conditions of the long highway tunnel have brought new challenges to the tunnel ventilation. If the ventilation is not smooth, pollutants such as CO and dust cannot be removed from the tunnel effectively. This situation may cause dyspnea for construction workers and lead to death by suffocation in severe cases [4; 5; 6]. In the selection of ventilation methods for long highway tunnels, full diameter air flow ducts are mostly used to match high-power forced ventilations in foreign countries [7], while in China, inclined shafts, parallel pilot tunnels, and shafts are usually built and a combination of forced and roadway ventilation methods are adopted [8; 9]. Through numerical simulation and on-site monitoring, scholars discussed the above ventilation measures and ventilation effects, and summarized the air flow and pollutant migration laws in the tunnel under the forced ventilation method [4; 10; 11]. At the same time, the correction coefficients of key parameters such as air flow demand, fan efficiency, air flow duct leakage rate, and air flow duct resistance during tunnel construction ventilation are also studied, which provides theoretical guidance for tunnel construction [12; 13; 14; 15; 16]. However, most of the above-mentioned studies focus on single-hole tunnels, and few scholars focus on the construction and ventilation of double-hole tunnels. In contrast, the double-hole tunnel has the following advantages: (1) During the construction period, the construction difficulty is small, and the probability of collapse is small [17]; (2) During operation, the piston air flow can be fully utilized to achieve the complementarity of the two holes [18]; (3) In terms of disaster prevention and rescue, when a major accident occurs in one tunnel, the other tunnel can operate normally and can be used for rescue and evacuation [19]. Based on the above advantages, the construction of a double-hole tunnel has shown a new trend. A double-hole tunnel includes an advance side tunnel, undercut side tunnel, pedestrian crossings, and traffic crossings [20; 21]. When ventilating the tunnel, the maximum air flow demand of tunnels should be determined by a number of factors; for example, the smoke discharged from the working face of the double tunnel, the maximum number of workers, the minimum allowable air flow velocity, the degree of dilution of exhaust gases from internal combustion engines. Then fresh air flow should be directed to the working face through forced air flow ducts to meet the ventilation demand [22; 23; 24]. After fresh air flows back twice, air flow resistance \(R_{\rm m}\) of each branch of the double-hole tunnel must be overcome before it can be discharged into the atmosphere. At present, the influence of factors such as the difference in the air flow demand of the two holes, the distance from the cross passage to the working face, and the safe layout distance between the double-hole working faces caused by the asynchronous construction period on the stability of \(R_{\rm m}\) and ventilation network is not clear.