## 6 Quantitative Risk Analysis
### F-N Curves  
In this paper, the fractional effective dose (FED) was used to calculate the number of people at risk in the event of a fire in the tunnel tube investigated. Based on the FED concept, an evacuee is considered as a potential victim when the FED corresponding to his/her exposure to temperatures and radiant heat fluxes (FED\({}_{\text{heat}}\)) and/or toxic substances (FED\({}_{\text{toxic gases}}\)) exceeds unity (for more details see [PERSON] et al. [29]). It should be noted that the QRA was performed by considering the FED of all the evacuees and their entire egress process from the tunnel, which occurs using: (i) both the right and left sidewalk upstream of the burning vehicle for Scenario 0 (i.e., users escaping towards portal A); (ii) the left sidewalk upstream of the fire source for Scenarios Ia and Ib (i.e. users escaping towards portal A); (iii) the right sidewalk upstream of the fire for the users escaping towards portal D, and the right sidewalk downstream of the fire for the users escaping towards portal C for Scenarios IIa and IIb. This was carried out for each HRR\({}_{\text{max}}\) (i.e., 8, 15, 30, 50, and 100 MW for Scenarios 0, Ia, and IIa, and 8 and 15 MW for Scenarios Ib and IIb) and location (i.e., 145, 280, 420, 570, and 710 m from portal A of the north tube for Scenarios 0, Ia, and Ib, or portal D of the adjacent tube for Scenarios IIa and IIb) of the fire. For some of the combinations of HRR\({}_{\text{max}}\) and location of the burning vehicle, the FED\({}_{\text{toxic gases}}\) was computed to be greater than 1, while the FED\({}_{\text{heat}}\) was always found to be much less than 1. As a result, the estimated number of people at risk derives only from their exposure to toxic gases. Then, the number of potential victims, referred to each HRR\({}_{\text{max}}\) and location of the fire, was associated with the corresponding annual frequency of fire occurrence in order to compute the individual cumulative frequency of each fire. Subsequently, by combining the individual cumulative frequencies, we calculated the final cumulative frequency with respect to the escaping users from one of the tunnel portals and/or the emergency exit. Figure 11 shows, in a bi-logarithmic diagram, the F-N curves for each scenario investigated, as well as the unacceptable and acceptable limits of the Italian ALARP region. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & \multicolumn{4}{c}{**Annual Frequency of Occurrence of Fire Scenarios [1/Year]**} \\ \cline{2-6}  & **8 MW** & **15 MW** & **30 MW** & **50 MW** & **100 MW** \\ \hline
0 & \(4.46\times 10^{-4}\) & \(2.18\times 10^{-3}\) & \(3.88\times 10^{-4}\) & \(6.68\times 10^{-5}\) & \(4.01\times 10^{-5}\) \\ Ia & \(4.22\times 10^{-4}\) & \(1.68\times 10^{-3}\) & \(2.99\times 10^{-4}\) & \(5.16\times 10^{-5}\) & \(3.10\times 10^{-5}\) \\ Ib & \(4.22\times 10^{-4}\) & \(1.68\times 10^{-3}\) & - & - & - \\ IIa & \(7.96\times 10^{-4}\) & \(3.18\times 10^{-3}\) & \(5.66\times 10^{-4}\) & \(9.75\times 10^{-5}\) & \(5.85\times 10^{-5}\) \\ IIb & \(7.96\times 10^{-4}\) & \(3.18\times 10^{-3}\) & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Annual frequency of occurrence of each scenario reproduced through the FDS + Evac codes.