## 5 Evacuation Modeling
### Evaluation of RSET and ASET  
The evacuation process is generally investigated by comparing the Available Safe Egress Time (ASET) and the Required Safe Egress Time (RSET). In particular, ASET represents the time required to exceed the tenability criteria after the fire has occurred, whereas RSET is the time within which each occupant reaches a safe place. Thanks to the combination of the FDS and its evacuation module (Evac), the ASETs of each user within the tunnel and the RSETs can be determined. ASET can be estimated using the aforementioned FED. In this respect, both the toxic effects of gaseous fire products (FED\({}_{\text{toxic gases}}\)) and the exposure of people to heat and radiant heat flux (FED\({}_{\text{heat}}\)) should be taken into account. According to the FED concept, a user is considered to be incapacitated when at least one of FED\({}_{\text{toxic gases}}\) and FED\({}_{\text{heat}}\) exceeds unity [35]. The FED\({}_{\text{toxic gases}}\) value for each escaping user is automatically \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Fire Location**} & \multicolumn{2}{c}{**Number of People Escaping from:**} \\ \cline{2-3}  & **Portal A** & **Emergency Exit** \\ \hline
145 m & 68 & - \\
280 m & 139 & - \\
420 m & 211 & - \\
570 m & 168 & 123 \\
710 m & 168 & 199 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Number of people escaping from portal A and emergency exit. Figure 2: Schematic layout of queued vehicles upstream of the fire source. calculated by the FDS model as a combination of different toxic gas concentrations as follows [17]:  
\[\text{FED}_{\text{toxic gases}}\;=\;(\text{FED}_{\text{CO}}\;+\;\text{FED}_{ \text{CN}}\;+\;\text{FED}_{\text{NOx}}\;+\;\text{FLD}_{\text{irr}})\cdot\text{HV}_{ \text{CO}_{2}}\;+\;\text{FED}_{\text{O}_{2}}, \tag{2}\]  
where \(\text{FED}_{\text{CO}}\) is the fraction of an incapacitating dose of CO, \(\text{FED}_{\text{CN}}\) is the fraction of an incapacitating dose of NOx, \(\text{FLD}_{\text{irr}}\) is the fraction lethal dose of irritants, \(\text{HV}_{\text{CO}_{2}}\) is the hyperventilation factor induced by carbon dioxide, and \(\text{FED}_{\text{O}_{2}}\) is the fraction of an incapacitating dose of low O2 hypoxia. Each \(\text{FED}_{\text{toxic gases}}\) value is computed as the integral from zero to the time (t\({}_{\text{i}}\)) needed by the user to reach a safe place. The \(\text{FED}_{\text{heat}}\) value due to both the heat and radiant heat flux exposure has been calculated as follows [35]:  
\[\text{FED}_{\text{heat}}\;=\;\sum_{\text{t}_{\text{i}}}^{\text{t}_{\text{2}}} \biggl{(}\frac{1}{\text{t}_{\text{frac}}}\;+\;\frac{1}{\text{t}_{\text{conv}}} \biggr{)}\Delta\text{t} \tag{3}\]  
where \(\text{t}_{\text{frac}}=16.67/q^{1.33}\) is the time in minutes to incapacitation due to a radiant heat flux \(q\) in kW/m\({}^{2}\), and \(\text{t}_{\text{conv}}=5\cdot 10^{7}\cdot T^{-3.4}\) is the time in minutes to incapacitation due to a temperature T in \({}^{\circ}\)C. An automatic procedure, based on Visual Basic for Applications (VBA) code, was developed in this paper for estimating the \(\text{FED}_{\text{heat}}\) every time step of the simulation, which was set equal to 2 s. Both temperature and radiant heat flux were measured at 2 m above the road pavement along the escape routes (sidewalks) upstream of the burning vehicle. RSET includes three-time components: (i) vehicle queuing time; (ii) the detection and reaction time (i.e., the pre-movement time); (iii) the user movement time. The pre-movement time was assumed to be 90 s in the event of 8, 50, and 100 MW fire; while it increased by 60 s (for a total of 150 s) for the 30 MW fire to take into account the time needed for all occupants to leave the bus [36]. Although the vehicles into the tunnel are assumed to be stationary when the fire started, the arrival time of every vehicle was taken into account by assigning an extra pre-movement time to each user. The user movement time depends in particular on the user walking speed [5].