## 7 Quantitative Risk Analysis
### F-N Curves  
The results of the FDS+Evac in terms of the exposure of evacuating users (downstream of the fire in the direction of portal B) to toxic gases expressed by means of the FED\({}_{\text{toxic gases}}\) as well as the exposure to heat expressed by the FED\({}_{\text{heat}}\) according to [PERSON] et al. (2018), were used for understanding when the tenability limits were exceeded (i.e., FED\({}_{\text{toxic gases}}\)\(\geq\) 1, and/or FED\({}_{\text{heat}}\)\(\geq\) 1 (for a greater in-depth knowledge see [PERSON] et al. (2018))). In this respect, it is to be stressed that the risk analysis was carried out taking into account both the FEDs (i.e., FED\({}_{\text{toxic gases}}\) and FED\({}_{\text{heat}}\)) of all tunnel users and their complete evacuation process (i.e., between t = 0 and t = 10 min after the fire start). This was made for each type of fire (i.e., HRR of 8, 30, 50, and 100 MW) and for the five different positions of fire in the tunnel tube used for bi-directional traffic (i.e., 145, 280, 420, 570, and 710 m from portal A). We found that for some combinations of HRR and positions of fire, the FED\({}_{\text{toxic gases}}\) might be more than 1, while the FED\({}_{\text{heat}}\) was always << 1. As a result, we estimated the number of potential fatalities that might be caused by the exposure to toxic gases for the mentioned combinations of HRR and fire positions. The number of potential fatalities, related to each fire and position, was then associated to the corresponding annual frequency of fire. Subsequently, we calculated the individual cumulative frequency of each fire, and by combining the individual cumulative frequency, we computed the final cumulative frequency F-N with reference to the escaping users downstream of the fire from the tube used for bi-directional traffic. Figure 10 shows, in a bi-logarithmic diagram, the relationship between the final cumulative frequency (F) and the potential number of fatalities (N) of the tube used for bi-directional traffic at both night and day. In this regard, it is to be stressed that overnight the distance (d) between the vehicles in the queue was assumed to be equal both to 10 m and 3 m. In the latter case, as well as during the day, the first vehicle is assumed to stop in front of the burning vehicle after 2.25 s. Figure 10 confirms graphically that the F-N curves with reference to the night cases lies always below that of the day. Table 3 quantifies the reduction of the risk levels by comparing the annual cumulative frequencies for a given number of potential fatalities during the day and the night. In brackets are reported the values of the annual cumulative frequency, as well as the reduction of the risk level, when the distance between the vehicles stopped in the queue is 3 m overnight. In particular, it shows that: (i) the cumulative frequencies of having a certain number of potential fatalities during the night is much lower than the day (e.g., F = 3.86 \(\times\) 10\({}^{-5}\) for N = 1 potential fatality at night (with d = 10 m), or F = 3.86 \(\times\) 10\({}^{-5}\) at night (with d = 3 m), against F = 1.88 \(\times\) 10\({}^{-4}\) associated to the day); (ii) the maximum number of potential fatalities that might be expected during the night due the exposure to toxic gases is also much lower (25 when d = 10 m and 35 when d = 3 m during night-time against 65 during daytime); (iii) the reduction of the risk level (for N \(\leq\) 25 and N \(\leq\) 35 potential fatalities when d = 10 m and 3 m, respectively) is between 80 and 100%. Therefore, significant advantages for escaping users (downstream of the fire in direction of portal B) are expected if the investigated tunnel tube is used for bi-directional traffic during the night rather than the day. It is to be stressed that the results of this paper are related to a distance between the vehicles stopped within the road tunnel tube in event of a fire (during the night) equal both to 3 and 10 m, as well as for the arrival time of the first vehicle downstream of the