## 3 Results
### Impact on Personal Evacuation
#### 3.4.3 Position of the Adit for People Passing  
The existing investigations and analyses suggest that the response to a fire can generally be categorized into three primary stages as follows: fire detection, confirmation of fire occurrence, and evacuation actions [38]. To ensure the safe evacuation of all persons, particularly in hazardous situations, it is imperative to establish adequate spacing of adits for people passing so that individuals can safely move from upstream and downstream areas of the fire source. The maximum permissible distance should be defined as the distance that people can safely evacuate within the required safe egress time (RSET). The RSET is  
\[REST=T_{d}+T_{pre}+T_{t}, \tag{3}\]  
where \(T_{d}\) is the alarm time; \(T_{pre}\) is the pre-moving time for personal evacuation; and \(T_{t}\) is the personal evacuation time. The smoke detectors used in actual engineering can detect fires of 100 kW. The fire alarm start time is calculated based on the \(t^{2}\) fire model in this research. Typically, the development law of fires in the initial stage is as follows:  
\[Q_{f}=\alpha t^{2} \tag{4}\]  
Figure 11: ASET of tunnels with different curvature radii at different distances from the fire source. where t is the time of fire occurrence; \(Q_{f}\) is HRR, which is set as 100 kW in the calculation of alarm time; and \(\alpha\) is the fire growth coefficient, which is set as 0.187 kW/s\({}^{2}\) in this study. Therefore, the alarm time of the fire detection system can be determined as follows:  
\[T_{d}=sqrt\left(Q_{f}/\alpha\right)=sqrt(100/0.187)\approx 23.1\;\text{s} \tag{5}\]  
The time interval between the receipt of the fire alarm and the initiation of evacuation measures, known as the pre-action time or personal evacuation response time, is crucial in fire emergencies. Determining the pre-action time primarily depends on factors such as building type and characteristics associated with occupant safety. The existing research data [39; 40; 41; 42] show that the pre-moving time for personal evacuation ranges from 30 s to 210 s. In this study, a pre-action time of 90 s was observed. Currently, no study has indicated any influence of the curvature radius on personal evacuation speed or their choices in a curved tunnel. Therefore, the personal evacuation time \(T_{t}\) is assumed to be consistent between curved and straight tunnels. This issue is not further discussed in this paper. Figure 12 shows the temperature distribution in the tunnel with a curvature radius of 400 m within 200 m from the fire source. From left to right, the temperature distributions are at 83.1 s, 113.1 s, 143.1 s, and 173.1 s. Based on the set alarm time of 23.1 s and the pre-moving time for a personal evacuation of 90 s, people will start to evacuate at 113.1 s, and the temperature distribution in the tunnel at this time is shown in Figure 12b. At this time, as discussed before, the high-temperature smoke hits the outer wall of the tunnel for the first time, which leads to the green area on the outer side. The green area means that the temperature within this area approaches 60 \({}^{\circ}\)C, which is not suitable for people to pass through. In general, during evacuation procedures, individuals should disperse along the pedestrian lane on both sides of the traffic lanes. However, the hazardous zone formed in the outer side of the tunnel, which means people should evacuate along the inner side of the tunnel. As shown in Figure 12c, the second hit of the high-temperature smoke appeared at 143.1 s. The presence of a second high-temperature zone within the tunnel renders the inner side unsuitable for evacuation, necessitating the evacuation route to be redirected along the outer side of the tunnel. However, the feasibility of such back-and-forth movement between the inner and outer sides of the tunnel is compromised for individuals trapped in a fire.