Model Validation

Since it is difficult to find experimental works with a similar fire scale and similar tunnel structure to this work, to verify the reliabilities of the simulation software and the grid calculation method in this study, using the same method of modeling, boundary condition setting, and grid calculating, to simulate a 0.75 MW combustion experiment in an 88 m-long channel carried out by Hu et al. [43]. The full-scale FDS model included the same tunnel structure, fire location, HRR, and the same sensor placements. The purpose of this section is to prove the feasibility of the software and modeling methods used, rather than to completely replicate the experiment, so the byproduct parameters related to the fuel type are ignored, and only the ceiling temperature data from the simulation and the experiment were compared. The ceiling temperature can comprehensively reflect the smoke diffusion and heat transfer process, and it can be regarded as a characteristic parameter for evaluating similar combustions. The ceiling temperature distributions within 80 m of the fire source were compared, as shown in Figure 5. The simulated data by FDS are represented by the red line, and the experimental data from Hu et al. are shown as black cubes.

**Figure 5.** Comparison of temperature distributions between simulation and experiment. **Figure 5.** Comparison of temperature distributions between simulation and experiment.

It could be found that the distribution data simulated by FDS were highly coincident with the experimental measurement data, with the 2.5% mean absolute percentage error (MAPE), proving that the grid calculation methods and the FDS simulation used above It could be found that the distribution data simulated by FDS were highly coincident with the experimental measurement data, with the 2.5% mean absolute percentage error (MAPE), proving that the grid calculation methods and the FDS simulation used above are reliable. The reliability of the model mentioned in Section 3.1 was demonstrated.

smoke diffusion and heat transfer process, and it can be regarded as a characteristic parameter for evaluating similar combustions. The ceiling temperature distributions within 80 m of the fire source were compared, as shown in Figure 5. The simulated data by FDS are represented by the red line, and the experimental data from Hu et al. are shown as

### are reliable. The reliability of the model mentioned in Section 3.1 was demonstrated. **3. Result and Discussion**

black cubes.

*3.1. Longitudinal Ventilation Velocity vs. Available Safe Escape Time*

**3. Result and Discussion**  *3.1. Longitudinal Ventilation Velocity vs. Available Safe Escape Time*  The influence of longitudinal ventilation velocity on ASET was discussed in this sec-The influence of longitudinal ventilation velocity on ASET was discussed in this section. Distributions of ASET and back-layering length (BLL) at different longitudinal ventilation velocities of 0 m/s, 1.0 m/s, 2.0 m/s, 4.5 m/s, and 6.0 m/s are shown in Figure 6. The following results were obtained:

	- velocity is 0 m/s, the ASET values in the area of 250 m upstream and downstream of the fire source will be substantially lower than that at the velocity of 1.0 m/s. This (3) Higher ventilation velocities increased the evacuation risk compared with the lowvelocity mode of 1.0 m/s. Although the BBL of 1.0 m/s velocity was the longest, it

might be because the high concentration of smoke accumulated near the fire source, resulting in a rapid decline of visibility, due to the lack of airflow control, which ham-

has almost no threat to upstream passengers, which is reflected in the ASET, because the back-layering with low concentrations did not sink into the evacuation space. The higher the ventilation velocity, the lower the distributions of ASET. For the low-, medium-, and high-velocity modes, the average ASET value decreased by 8% to 25% for each 1 m/s increase in ventilation velocity. The ASET value decreased slightly and tended to be constant in the process of velocity increases from 4.5 m/s to 6.0 m/s, which was almost the lowest distribution of ASET. It can be inferred from the above that the lower ASET value at a higher ventilation velocity might be related to the destruction of smoke stratification. To prove this hypothesis, the time of smoke sinking into the evacuation space of 2 m height from the road within 150 m downstream of the fire source at longitudinal ventilation velocities of 0 m/s, 1.0 m/s, and 2.0 m/s is illustrated in Figure 7. The stratification was not affected by ventilation airflow at a velocity of 0 m/s. Although accurately figuring out the duration of stable smoke stratification was difficult, it was straightforward to see the relationship between stratification and velocity. The average times for smoke flow sinking into the evacuation space of 1.0 m/s and 2.0 m/s velocities were 67% and 41% of the average time at the velocity of 0 m/s. With the increase in velocity, the smoke stratification downstream was more unstable due to more airflow disturbances and would sink into the evacuation space earlier. The sinking smoke would bring heat, CO, and low visibility to passengers, and result in low ASET values. which was almost the lowest distribution of ASET. It can be inferred from the above that the lower ASET value at a higher ventilation velocity might be related to the destruction of smoke stratification. To prove this hypothesis, the time of smoke sinking into the evacuation space of 2 m height from the road within 150 m downstream of the fire source at longitudinal ventilation velocities of 0 m/s, 1.0 m/s, and 2.0 m/s is illustrated in Figure 7. The stratification was not affected by ventilation airflow at a velocity of 0 m/s. Although accurately figuring out the duration of stable smoke stratification was difficult, it was straightforward to see the relationship between stratification and velocity. The average times for smoke flow sinking into the evacuation space of 1.0 m/s and 2.0 m/s velocities were 67% and 41% of the average time at the velocity of 0 m/s. With the increase in velocity, the smoke stratification downstream was more unstable due to more airflow disturbances and would sink into the evacuation space earlier. The sinking smoke would bring heat, CO, and low visibility to passengers, and result in low ASET values. (4) The computation of ASET mainly depends on high convective heat and low visibility. In the process of selecting the index that first reached the threshold value to compute

effect of ventilation, airflow may also cause the excessive temperature at the ceiling,

velocity mode of 1.0 m/s. Although the BBL of 1.0 m/s velocity was the longest, it has almost no threat to upstream passengers, which is reflected in the ASET, because the back-layering with low concentrations did not sink into the evacuation space. The higher the ventilation velocity, the lower the distributions of ASET. For the low-, medium-, and high-velocity modes, the average ASET value decreased by 8% to 25% for each 1 m/s increase in ventilation velocity. The ASET value decreased slightly and tended to be constant in the process of velocity increases from 4.5 m/s to 6.0 m/s,

(3) Higher ventilation velocities increased the evacuation risk compared with the low-

(4) The computation of ASET mainly depends on high convective heat and low visibility. In the process of selecting the index that first reached the threshold value to compute the ASET, it was found that the temperature index close to the fire source first reaches its threshold value, and the rapid reduction in visibility is the primary threat faced by passengers in other places, which is also consistent with the conclusion of Gehandler et al. [44]. Take a ventilation velocity of 2 m/s as an example, as shown in Figure 8. In addition, the heat and CO from hot toxic smoke are not the key factors for determining ASET, because they reach the threshold very slowly due to the action of buoyancy and ventilation airflow. the ASET, it was found that the temperature index close to the fire source first reaches its threshold value, and the rapid reduction in visibility is the primary threat faced by passengers in other places, which is also consistent with the conclusion of Gehandler et al. [44]. Take a ventilation velocity of 2 m/s as an example, as shown in Figure 8. In addition, the heat and CO from hot toxic smoke are not the key factors for determining ASET, because they reach the threshold very slowly due to the action of buoyancy and ventilation airflow.

*Fire* **2022**, *5*, x FOR PEER REVIEW 10 of 17

which may damage the tunnel structure.

**Figure 6.** Distribution of ASET and back-layering length (BLL) at different longitudinal ventilation velocity (v). **Figure 6.** Distribution of ASET and back-layering length (BLL) at different longitudinal ventilation velocity (v).

*Fire* **2022**, *5*, x FOR PEER REVIEW 11 of 17

**Figure 7.** Time of downstream smoke sinking into evacuation space (within 2 m height from the road) after ignition. **Figure 7.** Time of downstream smoke sinking into evacuation space (within 2 m height from the road) after ignition. road) after ignition.

**Figure 8.** The downstream ASET distribution and the time when FEDCO, FEDheat, temperature, and visibility indexes reach the threshold at the velocity of 2.0 m/s. **Figure 8.** The downstream ASET distribution and the time when FEDCO, FEDheat, temperature, and visibility indexes reach the threshold at the velocity of 2.0 m/s.

### **Figure 8.** The downstream ASET distribution and the time when FEDCO, FEDheat, temperature, and visibility indexes reach the threshold at the velocity of 2.0 m/s. *3.2. Evacuation Slides Spacing vs. Required Safe Escape Time*

*3.2. Evacuation Slides Spacing vs. Required Safe Escape Time*  The influence of spacing and number of evacuation slides on RSET in different longitudinal ventilation velocities are discussed in this section. The RSET distributions on both sides of the fire source were similar because slides were symmetrically installed. The RSET distributions under conditions of different slide spacings (D) are shown in Figure 9. The RSET distributions of the downstream tunnel (Y > 500 m) when using different D *3.2. Evacuation Slides Spacing vs. Required Safe Escape Time*  The influence of spacing and number of evacuation slides on RSET in different longitudinal ventilation velocities are discussed in this section. The RSET distributions on both sides of the fire source were similar because slides were symmetrically installed. The RSET distributions under conditions of different slide spacings (D) are shown in Figure 9. The RSET distributions of the downstream tunnel (Y > 500 m) when using different D values from 30 m to 80 m are shown as Curve 1, and the red dots denote the RSET values The influence of spacing and number of evacuation slides on RSET in different longitudinal ventilation velocities are discussed in this section. The RSET distributions on both sides of the fire source were similar because slides were symmetrically installed. The RSET distributions under conditions of different slide spacings (D) are shown in Figure 9. The RSET distributions of the downstream tunnel (Y > 500 m) when using different D values from 30 m to 80 m are shown as Curve 1, and the red dots denote the RSET values near the evacuation slides. The variation in the longest evacuation times for the entire tunnel (the max RSET values in Curve 1 for increasing D) are recorded as Curve 2.

tunnel (the max RSET values in Curve 1 for increasing D) are recorded as Curve 2.

values from 30 m to 80 m are shown as Curve 1, and the red dots denote the RSET values near the evacuation slides. The variation in the longest evacuation times for the entire

near the evacuation slides. The variation in the longest evacuation times for the entire

**Figure 9.** RSET distributions in conditions of different slide spacing (D). **Figure 9.** RSET distributions in conditions of different slide spacing (D).

It could be found that with the decrease in slide spacing D, the downstream RSET showed a nonlinear downward trend, and the inflection point might be at D = 60 m. To be specific, as D reduced from 80 m (total 11 slides) to 60 m (total 15 slides), the max RSET value shortened by 39 s for each additional slide. As D continued reducing from 60 m to 30 m (total 31 slides), the max RSET value shortened 11 s for each additional slide, and the shortened time was only 28% of the former. This indicated that the effect of decreasing RSET by further reducing the evacuation slide spacing (increasing the number of slides) It could be found that with the decrease in slide spacing D, the downstream RSET showed a nonlinear downward trend, and the inflection point might be at D = 60 m. To be specific, as D reduced from 80 m (total 11 slides) to 60 m (total 15 slides), the max RSET value shortened by 39 s for each additional slide. As D continued reducing from 60 m to 30 m (total 31 slides), the max RSET value shortened 11 s for each additional slide, and the shortened time was only 28% of the former. This indicated that the effect of decreasing RSET by further reducing the evacuation slide spacing (increasing the number of slides) is weakened after D is less than 60 m. It could also reflect the fact that the cost-effectiveness of installing slides declines after the slide spacing is less than 60 m.

is weakened after D is less than 60 m. It could also reflect the fact that the cost-effectiveness of installing slides declines after the slide spacing is less than 60 m. Further, to identify the slow evacuating area and the high-risk area of the tunnel, the tunnel was longitudinally divided into five areas, I, II, III, IV, and V, by the distance from the fire source. Each area had two parts, including a 100 m upstream part and a 100 m downstream part, as shown in Table 9. Taking the low-velocity ventilation mode as an example, the comparison of RSET distributions with the ASET distribution at the velocity of 1.0 m/s is shown in Figure 10. The ASET curve is the actual ASET distribution of the tunnel; the average ASET curve is the average ASET value in each part, which roughly reflects the overall situation in the part. The RSET curve represented the variation of the Further, to identify the slow evacuating area and the high-risk area of the tunnel, the tunnel was longitudinally divided into five areas, I, II, III, IV, and V, by the distance from the fire source. Each area had two parts, including a 100 m upstream part and a 100 m downstream part, as shown in Table 9. Taking the low-velocity ventilation mode as an example, the comparison of RSET distributions with the ASET distribution at the velocity of 1.0 m/s is shown in Figure 10. The ASET curve is the actual ASET distribution of the tunnel; the average ASET curve is the average ASET value in each part, which roughly reflects the overall situation in the part. The RSET curve represented the variation of the maximum RSET values when D increased from 30 m to 80 m in each part, the leftmost point represented the condition of D = 30 m, and each RSET value belonged to the passenger with the longest evacuation time in each part.



III 200 < S ≤ 300 200 ≤ Y < 300 700 < Y ≤ 800 IV 300 < S ≤ 400 100 ≤ Y < 200 800 < Y ≤ 900 V 400 < S ≤ 500 0 ≤ Y < 100 900 < Y ≤ 1000

maximum RSET values when D increased from 30 m to 80 m in each part, the leftmost

m/s.

**Figure 10.** ASET compared with RSET corresponding to different D under the condition of v = 1.0 **Figure 10.** ASET compared with RSET corresponding to different D under the condition of v = 1.0 m/s.

As can be seen in Figure 10, the slow evacuating areas were II and III, independent of the value of D. The slow evacuating areas had a larger overall RSET value than other areas, which was always from 100 m to 300 m from the fire source. It could also be proved by Figure 9 that with the increasing distance from the fire source, the RSET value firstly increased and then decreased, and the extreme point was always in these areas. The main reason for this was that passengers in area I had a shorter RT and the crowd moved earlier As can be seen in Figure 10, the slow evacuating areas were II and III, independent of the value of D. The slow evacuating areas had a larger overall RSET value than other areas, which was always from 100 m to 300 m from the fire source. It could also be proved by Figure 9 that with the increasing distance from the fire source, the RSET value firstly increased and then decreased, and the extreme point was always in these areas. The main reason for this was that passengers in area I had a shorter RT and the crowd moved earlier to both sides of the tunnel after ignition. This increased the evacuation pressure on areas II and III, but this effect gradually reduced in areas IV and V far from the fire source.

to both sides of the tunnel after ignition. This increased the evacuation pressure on areas II and III, but this effect gradually reduced in areas IV and V far from the fire source. The high-risk evacuating areas were the downstream parts of III and IV when D ≥ 70 m. Figure 10 shows that in the downstream parts of 200 m to 400 m from the fire source, the average ASET values were lower than the RSET values under conditions of D = 70 m and D = 80 m. However, with the change in ventilation velocity and ASET distributions, The high-risk evacuating areas were the downstream parts of III and IV when D ≥ 70 m. Figure 10 shows that in the downstream parts of 200 m to 400 m from the fire source, the average ASET values were lower than the RSET values under conditions of D = 70 m and D = 80 m. However, with the change in ventilation velocity and ASET distributions, the high-risk areas expand. It could be stated at least that areas III and IV were always in danger when D ≥ 70 m, regardless of the ventilation velocity because the ASET distributions of other velocities were all lower than that of 1 m/s, as shown in Figure 6.

the high-risk areas expand. It could be stated at least that areas III and IV were always in danger when D ≥ 70 m, regardless of the ventilation velocity because the ASET distributions of other velocities were all lower than that of 1 m/s, as shown in Figure 6. To explore the reasonable D in conditions of different ventilation velocities that could possibly occur, the downstream ASET distributions of the low-velocity mode, mediumvelocity mode, and high-velocity mode were compared with the downstream RSET distributions of different evacuation spacing Ds from 30 m to 70 m, as shown in Figure 11. The RSET columns recorded the longest evacuation time of each slide, and the evacuation assessments near the evacuation slides represented the worst situation of the entire tun-To explore the reasonable D in conditions of different ventilation velocities that could possibly occur, the downstream ASET distributions of the low-velocity mode, mediumvelocity mode, and high-velocity mode were compared with the downstream RSET distributions of different evacuation spacing Ds from 30 m to 70 m, as shown in Figure 11. The RSET columns recorded the longest evacuation time of each slide, and the evacuation assessments near the evacuation slides represented the worst situation of the entire tunnel. If the ASET distribution of one velocity mode was always higher than the RSET value of one spacing D at any position, it could be considered that the evacuation process was secure, and the maximum D value satisfying the above requirement was the reasonable evacuation spacing of that velocity mode.

nel. If the ASET distribution of one velocity mode was always higher than the RSET value of one spacing D at any position, it could be considered that the evacuation process was secure, and the maximum D value satisfying the above requirement was the reasonable evacuation spacing of that velocity mode. Further, to quantify the safety of each evacuation schemes, Table 10 counts the number of trapped people (among the total of 1870 passengers involved) corresponding to different evacuation spacings under possible ventilation modes. The trapped passengers are located in the position where ASET is less than RSET, as shown in Figure 11. The relative value of the number of trapped passengers can also be reflected by the difference value of time. In each velocity mode, as the evacuation spacing shortens, the number of trapped passengers gradually decreases. Under the same evacuation spacing scheme, the number

**Evacuation Spacing D (m)** 

40 0 0

50 0 0

of trapped passengers is ranked as: low-velocity mode < medium-velocity mode < highvelocity mode, which can indicate that using the low-velocity mode is beneficial to safe evacuation. Specifically, the reasonable slide spacing should not be larger than 60 m if using the low-velocity ventilation mode of 1.0 m/s, it should not be larger than 50 m if using the medium-velocity mode of 2.0 m/s, and should not be larger than 30 m if using the high-velocity mode above 4.5 m/s. The reasonable spacings recommended above do not represent the accurate value but only acceptable ranges. This is because the difference between the evacuation spacing schemes selected in this study is 10 m, which conforms to the general engineering design accuracy. *Fire* **2022**, *5*, x FOR PEER REVIEW 14 of 17

**Figure 11.** Comparison of RSET of different D with ASET of different velocities in the downstream area of fire source within 500 m. **Figure 11.** Comparison of RSET of different D with ASET of different velocities in the downstream area of fire source within 500 m.


Further, to quantify the safety of each evacuation schemes, Table 10 counts the num-**Table 10.** Number and location of trapped passengers under different evacuation spacings.

60 0 13 220 227

**Low-Velocity Mode Medium-Velocity Mode High-Velocity Mode** 

**Number and Location of Trapped Passengers in Tunnel (among the 1870)** 

79 (19 at 700 m, 18 at 740 m, 10 at 780 m, 12 at 820 m, 14 at 860 m, 6 at 900 m)

174 (46 at 700 m, 41 at 750 m, 30 at 800 m, 32 at 850 m, 22 at 900 m, 3 at 950 m)

94 (19 at 700 m, 20 at 740 m, 14 at 780 m, 14 at 820 m, 17 at 860 m, 10 at 900 m)

181 (46 at 700 m, 41 at 750 m, 31 at 800 m, 34 at 850 m, 26 at 900 m, 3 at 950 m)

**1.0 m/s 2.0 m/s 4.5 m/s 6.0 m/s** 
