## 4 Evacuation Modeling
### Queue Formation and People Evacuation  
Several FDS + Evac simulations were performed to assess the exposure to risk of the tunnel users under the different fires investigated, each of which involved a certain \(\text{HRR}_{\text{max}}\) and location of the burning vehicle in the tunnel tube. It is worth mentioning that the vehicles in the queue occupy: (i) both lanes of the north tube upstream of the fire for Scenario 0; (ii) the remaining undisrupted lane (i.e., the left lane) of the north tube upstream of the fire for Scenarios Ia and Ib; (iii) both lanes, including one upstream and one downstream of the fire, of the adjacent tube used for two-way traffic for Scenarios IIa and IIb. The number of queued vehicles was computed by assuming that: (i) vehicles in the queue stop without passing the fire; (ii) vehicles queue up one behind the other maintaining a safety distance of 2 m; (iii) the first queued vehicle stops at 10 m from the burning vehicle. Figure 4 shows a schematic layout of the queued vehicles upstream and/or downstream of the burning vehicle for each scenario examined. It should be noted that each tunnel user, initially positioned next to his/her own vehicle, evacuates towards a safe place (portals or emergency exit) using the nearest sidewalk.  
The number of users potentially at risk in a tube obviously depends on the number of cars, HGVs, and buses present in the queue. The occupancy rates of the cars and vans, HGVs, and buses were assumed to be equal to 1.7 [28], 1, and 30 people, respectively. Given that the percentage of heavy vehicles was equal to 25% of the traffic flow (i.e., 23% of HGVs and 2% of buses), we estimated an average occupancy rate considering all the vehicles in the queue (i.e., cars, vans, buses, and HGVs) equal to 2 for Scenarios 0, Ia, and IIa; while that related to light vehicles only (i.e., cars and vans) was calculated to be 1.7 for Scenarios IIa and IIb. Obviously, by multiplying the number of queuing vehicles by 2 or 1.7, we were able to estimate the corresponding number of users escaping from the fire for the mentioned scenarios.  
It was assumed that, depending on the fire location, the users leave the tunnel by escaping towards the entrance portal (portal A) or the emergency exit (located in the middle of the tunnel length) when the north tube is used for unidirectional traffic (i.e., Scenarios 0, Ia, and Ib); while the users escape from one of the two portals (portals C or D) of the adjacent tube or from the emergency exit when this tunnel tube is employed for two-way traffic (i.e., Scenarios IIa and IIb). With reference to the emergency exit, it should be noted that it was assumed not to be usable by evacuees when the fire source was located in the middle of the tunnel length (i.e., next to the emergency exit).  
Figure 4: Schematic layout of queued vehicles upstream and/or downstream of the burning vehicle for each scenario examined. Scenario 0: ordinary conditions of functionality of the tunnel system (i.e., both lanes of each tube are used for one driving direction) with a fire that occurs in the north tube; Scenario Ia: partial closure of the north tube (i.e., only the right lane is closed due to a traffic accident) with a fire that might occur on the left lane of the north tube; Scenario Ib: similar to Scenario Ia, but with the HGVs traveling towards the north tube diverted to an alternative itinerary; Scenario IIa: complete closure of the north tube (i.e., both lanes are closed due to a traffic accident) with a fire that might occur on the lane of the adjacent tube that is used by traffic traveling towards the north; Scenario IIb: similar to Scenario IIa, but with the HGVs traveling towards the north tube diverted to an alternative itinerary.  
Table 1 shows the number of vehicles in the queue and the number of users escaping from one of the tunnel portals and/or from the emergency exit for each fire location and scenario investigated.