Design of Adits for People Passing Spacing in High Altitude Highway Tunnels in Cold Regions

Abstract

Existing research into this topic primarily focuses on low-altitude areas, neglecting the impact of extreme environmental conditions such as low temperature, low oxygen level, and low pressure in high-altitude regions. Based on the smoke diffusion theory, a series of CFD numerical simulations were conducted in order to investigate the characteristics of smoke diffusion in the highway tunnel at high altitude. The results indicated that the increase in altitude would enhance the longitudinal propagation velocity of smoke, leading to a more pronounced impact on temperature, CO concentration, and visibility at characteristic heights. Meanwhile, the altitude intensifies the inhibitory impact of longitudinal ventilation on smoke diffusion upwind of the fire source and augments the acceleration effect on smoke diffusion downwind, thereby impeding personnel evacuation on the downwind side. By taking the hazardous range at a characteristic height under the impact of wind velocity and the deceleration of evacuation velocity due to altitude into consideration, a new recommended reduction factor was deduced to design adits for people passing spacing in highway tunnels at high altitude. The findings can serve as a valuable reference for the personal evacuation in high-altitude highway tunnel fires and the design of spacing between adits for people passing within such tunnels.

1. Introduction

The key characteristics of high-altitude areas are low temperature, low pressure, and low oxygen levels [1]. The unique and challenging natural environment in these regions further complicates personnel evacuation in high-altitude highway tunnels during fire accidents [2]. These are mainly manifested as an increase in smoke diffusion length and smoke diffusion velocity under the same fire scale.

Chen et al. explored the distribution characteristics of temperature and smoke and personal evacuation in the Hsuehshan southbound highway tunnel [3]. Hu et al. conducted full-scale fire tests to study the impact of longitudinal wind velocity on longitudinal distribution of smoke temperature and maximum ceiling temperature [4,5]. Carvel et al. explored the relationship between the heat release rate (HRR) and the width of the tunnel and the ventilation wind velocity during the tunnel fire, and found that fires in narrow tunnels have a higher heat release rate than in wide tunnels [6]. Blanchard et al. proved the reliability of the numerical simulation by comparing the results of FDS numerical simulation with results from experiment in a 1/3 scale tunnel under the condition of lower and higher than critical wind velocity [7]. Gao et al. pointed out that the longitudinal slope can have an obvious impact on the smoke diffusion by conducting a numerical investigation to analyze the thermal smoke behavior and the distribution of the ceiling temperature in a sloping tunnel with the slope varying from 0% to 15% [8]. Xia et al. researched the temperature and CO concentration regulation under the impact of longitudinal ventilation velocity, and found that personal evacuation downstream of a fire is only advantageous when the longitudinal ventilation velocity surpasses the critical ventilation velocity [9,10]. Nilsson et al. studied the behavior and reaction of people in a tunnel fire and pointed out that social influence, etc., is crucial to the decision to leave the vehicle and the choice of exit [11]. In 2013, Caliendo et al. explored the theory that the evacuation time primarily relies on the promptness of evacuation actions, while being minimally influenced by the lead time for evacuation [12]. And an appropriate Computational Fluid Dynamics model was developed to evaluate the exposure to risk of tunnel users during their evacuation process in a fire in 2020 [13].

However, most research on fire smoke diffusion and personnel evacuation in highway tunnels mainly focuses on low-altitude tunnels with a normal temperature, regular ambient atmospheric pressure and normal oxygen levels. The temperature, pressure, and oxygen levels in many of the tunnels in western China are below the normal value.

Yan et al. conducted investigated heat release rate, temperature distribution and smoke diffusion characteristics in a high-altitude tunnel by conducting six full-scale fire tests at an altitude of 4100 m. The impact of altitude on personnel evacuation behavior was also investigated through onsite random evacuation tests [14,15]. Zhang et al. analyzed temperature and concentration distribution characteristics of fire smoke in high-altitude tunnel by conducting model tests in the Guanjiao tunnel [16,17,18]. Wang et al. conducted tunnel fire tests at various altitudes that revealed the impact of altitude on the heat release rate, smoke temperature distribution, smoke diffusion, and toxicity distribution in ultra-high-altitude tunnels [19,20,21,22]. Yan et al. revealed that the maximum temperature beneath the tunnel ceiling and the longitudinal temperature distribution increase as the ambient pressure decreases; this was mainly affected by reduced heat loss due to reduced air density [23]. Aleksander et al. conducted multivariant analyses of different fire development scenarios and evacuation in a highway tunnel based on sound assumptions [24]. Guo et al. investigated the effect of a reduced evacuation velocity at high altitudes and environmental visibility in tunnels on decision-making and movement time during evacuations [25].

As presented above, high altitude has a great impact on smoke diffusion characteristics and personnel evacuation. However, current research has not been able to comprehensively analyze these two effects. Therefore, this paper uses numerical simulations to study the temperature distribution and smoke distribution characteristics at the characteristic height at different altitudes. In addition, a comprehensive analysis was conducted on personnel evacuation in high-altitude highway tunnels by taking the impact of high altitude on personnel evacuation into account. Based on the results, a new recommended reduction factor was deduced to design the spacing of adits for people passing in highway tunnels at high altitude. We hope our study can provide a valuable insight for engineering in high-altitude areas.

2. Materials and Methods

2.1. Fire Dynamics Simulator

The fire dynamics simulator (FDS) [26,27] is a code developed by the US National Institute of Standards and Technology. It has been applied to study the temperature and velocity fields in fires by many researchers; this is mainly due to the development of the computing ability of computers and the maturation of computational fluid dynamics (CFDs) [28]. The FDS is designed for large-eddy simulation (LES) of low-velocity and thermal-driven flows. Many advances were developed in version 6, such as hydrodynamics, turbulence models, and scalar transport schemes. Thus, this study was conducted by the FDS (Version 6.8) with an LES model. Additional information on the FDS can be referred to in McGrattan et al. [29]. Many previous studies [30,31] proved the reliability of FDSs applied to simulate the behavior of tunnel fires.

2.2. Fire Scenarios Analysis

As shown in Figure 1, a tunnel model based on an actual highway tunnel is employed in this study. The tunnel spans 800 m with a horseshoe-shaped cross-section and a total width of 10.75 m. The maximum height is 7.3 m. The materials of “concrete” as a conventional material used for highway tunnels is set to the floor, sidewalls, and ceiling. An air “supply” vent is set in the left entrance of the tunnel to provide longitudinal ventilations, and “open” is set in the other portal. The “simple chemistry” combustion model is used with heptane fuel [32]. The yield of CO and soot is 0.01 g/g and 0.037 g/g, respectively. Based on the Guidelines for Design of Ventilation of Highway Tunnels [33], the HRR of the worst-case scenario is chosen as 30 MW. Referring to the heat release rate of different types and numbers of vehicles published by the highway tunnels manual [34], the fire scale of 30 MW is caused by full truck fires, which were chosen as the fire source. The height of the fire source is 2.6 m, the same as the height of a truck. As the altitude increases, the ambient pressure varies from 101.325 kPa to 54.048 kPa and the ambient temperature varies from 26 °C to 15 °C due to the effect of altitude [35]. The gravity is considered to be 9.81 m/s² as the effect of altitude on gravity is slight. The quality of the fuel is not considered, which means the maximum heat release rate of the fire source can also be achieved under a low temperature, low oxygen, and low pressure environment, at high altitude [36]. Referring to previous studies, the simulation time is set as 600 s.

2.3. Critical Velocity

In order to further investigate the characteristics of smoke movement and the spacing of adits for people passing, it is crucial to consider the longitudinal wind velocity. In practical engineering, the longitudinal wind velocity has a significant impact on the fire smoke diffusion. Furthermore, natural wind within tunnels fluctuates frequently due to the constantly changing wind direction and velocity. Furthermore, high-altitude areas experience more severe wind conditions compared to low-altitude regions. Notably, this calculation does not account for mechanical ventilation measures implemented within the tunnel.

Equations (1) and (2) are chosen to calculate the critical velocity based on previous research [37].

When $\dot{Q}/{\rho }_a{C}_p{T}_a\sqrt{g}{H}^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\le 0.15{\left(H/W\right)}^{\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$,

$$u/\sqrt{gH}=0.81{\left(\dot{Q}/{\rho }_a{C}_p{T}_a\sqrt{g}{H}^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{\left(H/W\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$12$}\right.}{e}^{\raisebox{1ex}{$-L_b$}\!\left/ \!\raisebox{-1ex}{$18.5H$}\right.}$$

(1)

When $\dot{Q}/{\rho }_a{C}_p{T}_a\sqrt{g}{H}^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}>0.15{\left(H/W\right)}^{\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$,

$$u/\sqrt{gH}=0.43e^{-\raisebox{1ex}{$L_b$}\!\left/ \!\raisebox{-1ex}{$18.5H$}\right.}$$

(2)

where ${\rho }_a$ is the ambient density, $C_p$ is the heat capacity, $g$ is the gravitational acceleration, $H$ is the tunnel height, $L_b$ is the back-layering length, where $L_b=0$ defines the critical velocity, $T_{\mathsf{\alpha }}$ is the ambient gas temperature, $u$ is the longitudinal velocity, and W is the tunnel width. As shown in Equation (1), ambient density, ambient gas temperature, and heat capacity change as the altitude increases. As a result, the maximum critical velocity of 3.56 m/s is chosen to design simulations.

According to the data on the tunnel operating period [38,39], the control wind velocity of tunnel longitudinal ventilation varies from 2.0 m/s (maximum natural longitudinal ventilation velocity) to 8.0 m/s (maximum control longitudinal ventilation velocity). The wind velocity in the tunnel should be accelerated to a figure greater than the critical velocity after the fire was observed. Thus, to study the characteristics of smoke diffusion under natural longitudinal ventilation velocity and control longitudinal ventilation velocity in a tunnel fire, the general velocity group (the longitudinal ventilation velocity is 2 m/s, test 2, 5, 8, 11, 14, 17) and critical velocity group (the longitudinal ventilation velocity is 4 m/s, test 3, 6, 9, 12, 15, 18) are set. Meanwhile, a 0 velocity group (the longitudinal ventilation velocity is 0 m/s, test 1, 4, 7, 10, 13, 16) is set for comparative analysis. The simulation did not take any additional mechanical ventilation measures within the tunnel into account, except for longitudinal ventilation.

Table 1. Summary of all tests.

Test No.	Altitude, m	Ambient Pressure, kPa	Ambient Temperature, °C	Longitudinal Ventilation Velocity, m/s
1–3	0	101.325	26.0	0, 2, 4
4–6	1000	89.876	24.7	0, 2, 4
7–9	2000	79.501	22.2	0, 2, 4
10–12	3000	70.121	18.3	0, 2, 4
13–15	4000	61.66	16.8	0, 2, 4
16–18	5000	54.048	15.0	0, 2, 4

shows the summary of all fire tests.

2.4. Grid Size

Previous research indicates that the accuracy of the simulation results is greatly affected by the size of the grid. And the mesh size is closely related to the fire characteristic diameter $D^{*}$. When the fire characteristic diameter $D^{*}$ is between 4 and 16 times the grid size, the simulation results can reflect the real situation more accurately [27]. Equation (3) is used to calculate $D^{*}$:

$$D^{*}={\left(\dot{Q}/{\rho }_{\mathrm{\infty }}{c}_p{T}_{\mathrm{\infty }}\sqrt{g}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.},$$

(3)

where $D^{*}$ is the fire characteristic diameter, $\dot{Q}$ is the HRR, ${\rho }_{\mathrm{\infty }}$ is the air density, $c_p$ is the specific heat capacity of air, $T_{\mathrm{\infty }}$ is the ambient temperature, and $g$ is the gravity acceleration.

The calculation results indicate that the suitable grid size for the 30 MW fire varies between 0.233 m and 0.94 m. Figure 2 shows the comparison of simulation results with grid sizes of 0.25 m, 0.3 m, 0.5 m, 0.75 m, and 0.9 m for the case of a 0 m altitude and without ventilation at 300 s. It can be seen from Figure 2 that with the decrease in the grid size, the discrepancy in temperature at different vertical heights with different grid sizes becomes negligible except for the grid size of 0.9 m. This means that when the grid size is no greater than 0.75 m, further refining the grid size cannot significantly improve the simulation accuracy, and more simulation time is required. Thus, the final determined grid size is 0.5 m. Considering the more complex flow fields near the fire source, the grid size in the zone X = 200–600 m, Y = −7–7 m, and Z = −1–7 m was refined as 0.25 m.

2.5. Verification of Numerical Simulation Reliability

We attempted to compare the simulation results with the experimental results in order to ascertain the reliability of the simulation results. Yan et al. [14] conducted six full-scale tunnel fire experiments in a tunnel at a high altitude of 4100 m. The smoke-spreading characteristics, maximum temperature, and longitudinal temperature distribution were studied. In this research, at an altitude of 4100 m, the ambient pressure is 62.63 kPa, the ambient temperature is 9–11 °C, and the ambient air density is 0.84 kg/m³. The longitudinal ventilation velocity of Test 6 varies from 0 to 1 m/s. The fire area is 2.0 m² and the fire scale is 1.55 MW. A special test was conducted to compare with the experiment results based on the above environmental conditions. The comparison results shown in Figure 3 show that the FDS predictions are in good agreement with the experimental results.

Slight discrepancies are observed near the fire source, with slightly higher temperatures in the experimental results compared to the FDS results. However, these discrepancies become negligible away from the fire source due to complex turbulent and heat transfer phenomena that occur in close proximity to fire sources. Additionally, a constant longitudinal wind velocity was set in the FDS model, which continuously varied during Yan’s experiment. Overall, the results of the comparison prove the reliability of the FDS simulation.

2.6. Personal Evacuation Scenarios Analysis

Based on the same tunnel model shown in Figure 1, an evacuation model was created in Pathfinder. The width of adits for people passing is 2 m [40]. Considering the worst-case scenario, the number of vehicles and personnel load should be determined by the tunnel traffic jam situation. Based on the literature [41,42,43], the number of vehicles and personal load under the traffic jam situation in the tunnel model is determined, as shown in

Table 2. Number of vehicles and personal load.

Vehicle Type	Proportional Coefficient	Passenger Capacity	Body Length	Vehicle Distance	Total Quantity	Personal Load
Mini Bus	80.70%	5	6.0 m	1.5 m	184	920
Medium Bus	1.75%	11	7.2 m	1.5 m	4	44
Large Bus	1.75%	45	13.7 m	2.0 m	4	180
Mini Van	10.96%	2	6.0 m	1.5 m	25	50
Medium Truck	3.07%	2	7.2 m	1.5 m	7	14
Large Truck	1.32%	2	13.7 m	2.0 m	3	6
Articulated Truck	0.43%	2	18.0 m	2.0 m	1	2

.

Figure 4 shows the escape options for the worst-case scenario. When the fire source located at the entrance of an adit for people passing in the middle of the tunnel, this adit is not available for personal evacuation. In this situation, an adjacent adit would bear the personnel load within 1.5 times of the spacing. As set out above, the large truck as a fire source is located at the entrance of adit C. All passengers within adit B and adit C and half the passengers within adit A and adit C are going to evacuate from adit B.

The calculation method of the personnel evacuation speed is shown as follows [44]:

$$V={\alpha }_1{\alpha }_{2}V\left(k_s\right)$$

(4)

where: ${\alpha }_1$ is the altitude reduction factor of the evacuation speed; ${\alpha }_2$ is the panic reduction factor of the evacuation speed, which is 1.346; $V\left(k_s\right)$ is the speed of people’s evacuation in smoke on the plain. In an environment with no smoke, the speed of children’s evacuation is 0.8 m/s, the speed of adult men’s evacuation is 1.2 m/s, the speed of adult women’s evacuation is 1.0 m/s, and the evacuation speed of the elderly is 0.72 m/s [45].

The altitude correction coefficient of the evacuation speed is mainly determined by the maximum oxygen uptake demand.

Table 3. The altitude reduction factor and evacuation speed under the comprehensive influence.

Altitude, km	Altitude Reduction Factor				Evacuation Speed, m/s
	Child	Adult Man	Adult Woman	The Elderly	Child	Adult Man	Adult Woman	The Elderly
0	1	1	1	1	1.04	1.56	1.30	0.94
1	1	1	1	1	1.04	1.56	1.30	0.94
2	0.955	0.961	0.959	0.961	1.00	1.50	1.25	0.90
3	0.872	0.889	0.883	0.881	0.91	1.39	1.15	0.83
4	0.749	0.783	0.772	0.772	0.78	1.22	1.00	0.72
5	0.584	0.641	0.620	0.617	0.61	1.00	0.81	0.58

shows the altitude correction coefficient of the evacuation speed [46] and the evacuation speed in a fire scenario under the comprehensive influence of panic psychology and altitude effect.

The proportion of different types of people and their characteristic parameters in the tunnel is shown in

Table 4. Proportion of evacuees and characteristic parameters.

Personal Type	Children	Adult Man	Adult Woman	The Elderly
Diameter, cm	30	40	35	35
Proportion, %	15	40	35	10

[47]. As the evacuation speed at an altitude of 1 km is the same as at an altitude of 0 km, 25 tests consisting of five spacings of adits for personal evacuation (50 m, 100 m, 150 m, 200 m, and 250 m) and five altitudes (1 km, 2 km, 3 km, 4 km, and 5 km) under the traffic jam situation are established to simulate the RSET at different altitudes. Figure 5 shows the first simulation of a 50 m spacing of adits for personal evacuation at an altitude of 1 km.

3. Results

3.1. Safe Standard

This study focuses on the one-dimensional diffusion of smoke at the characteristic height of human eyes along the tunnel centerline to investigate the distribution characteristics of fire smoke and its impact on personnel evacuation. According to national regulations [48], 60 °C is chosen as the safety standard for the smoke temperature. Similarly, 10 m is chosen as the safety standard for visibility and 400 ppm is chosen for the CO concentration. The characteristic height is set as 2 m. In order to enhance the presentation of the results, the analysis was carried out within 100 m upstream to 400 m downstream of the fire source. For unillustrated segments, indicators in the 0 wind velocity group exhibited symmetrical distribution relative to the position of the fire source both upstream and downstream. In contrast, indicators for the general wind velocity group and critical wind velocity group remained unaffected.

3.1.1. Temperature

Figure 6 presents the variation in longitudinal temperature at a characteristic height at 300 s. As the altitude increases, the area near the fire source area in a high-altitude tunnel experiences strong thermal radiation due to factors such as the environmental temperature, pressure, and air-specific heat. The characteristic height exhibits higher temperatures compared to lower altitudes. Specifically, the increase in altitude leads to an increase in temperature near the fire source area. However, beyond a certain distance from the fire source, there remains a more rapid replenishment of air in the high-altitude tunnel leading to a faster reduction in the smoke temperature along its path. Therefore, when considering temperature as a hazardous factor, a greater danger exists near the fire source area in a high-altitude tunnel, whereas a greater danger exists far from the fire source area in a low-altitude tunnel.

When the longitudinal ventilation wind velocity of the tunnel reaches 2 m/s, the temperature distribution at the characteristic height in the tunnel clearly changes. Under the current conditions, the longitudinal airflow of the tunnel is not enough to make the high-temperature smoke flow along the airflow, resulting in the phenomenon of smoke back-layering. The temperature of the upwind area of the fire location where the phenomenon of smoke back-layering occurs is slightly lower than that of the no wind velocity group, and is within the safe temperature range in the whole simulation process. With the increase in the ventilation wind velocity, the temperature near the fire source area decreases, but increases along the way. At a 2 m/s wind velocity, the smoke downwind of the fire reaches a hazardous temperature earlier than the no wind velocity group.

When the longitudinal wind velocity of the tunnel exceeds the critical wind velocity, the longitudinal temperature distribution in the tunnel changes significantly. The longitudinal wind pressure of the tunnel under this condition is stronger than the thermal effect of the fire, the smoke back-layering phenomenon is inhibited, and the temperature of the upstream area of the fire basically experiences no temperature rise. Due to the rapid flow of fresh air diluting the high-temperature smoke, the maximum temperature of each position in the tunnel under the critical wind velocity is less than that of the general wind velocity group.

Compared to a different wind velocity at the same altitude, in a no slope tunnel, smoke diffusion is symmetrical along the fire source when there is no wind velocity. As the wind velocity increases, the smoke diffusion velocity on the upwind side of the fire source is significantly impeded. The velocity and distance of the smoke diffusion decrease with the increasing wind velocity. When longitudinal ventilation reaches a critical velocity, the smoke back-layering is completely controlled. However, on the downwind side of the fire source, ventilation brings fresh cold air and replenishes oxygen at the fire source. With the increasing wind velocity, the maximum temperature gradually rises at a characteristic height while smoke diffusion accelerates due to the increased airflow. Nevertheless, cold air limits the hazardous range affected by ultra-high temperatures caused by fire. With the increasing altitude, the air buoyancy gradually decreases, leading to an increase in the longitudinal smoke diffusion distance and an acceleration in the diffusion velocity.

3.1.2. Visibility

Figure 7 presents the variation in longitudinal visibility at a characteristic height for 300 s. In the initial stage of the fire, due to the thermal updraft generated by the fire source, smoke primarily accumulates in the tunnel vault. This has a minimal impact on visibility at a characteristic height and there remains no significant change in the temperature rise or smoke concentration. As the fire progresses, smoke continues to vertically disperse throughout the tunnel, resulting in a continuous decline in visibility at a characteristic height away from the fire source. However, as distance increases, human eye visibility gradually improves. For instance, visibility at a distance of 300 m from the fire source in working conditions 1, 4, 7, 11, 14 and 17 remains within the safe range at 300 s. However, the visibility within the area 400 m away from the fire source is lower than 5 m at 360 s.

No matter what the longitudinal wind velocity is, visibility becomes a disaster factor when a tunnel fire occurs, but its influence range and action time differ. Under the conditions of no longitudinal wind in the tunnel, the visibility at the characteristic height of the tunnel is greater than 10 m within 240 s, which is conducive to personnel evacuation. Affected by the low buoyancy at a high altitude, the visibility at a characteristic height is partly less than 10 m at an altitude of 4000 m and 5000 m (test 13 and test 16). However, with the further accumulation of smoke, the visibility at the characteristic height of the tunnel is gradually affected and has become a key disaster factor at 300 s. The visibility near the fire source is always in the safe range, mainly due to the effect of the fire plume generated by the heated air continuously rising under the action of buoyancy. However, the key disaster factor in this area is temperature. When considering the longitudinal wind velocity, during the initial stage of fire development, the presence of longitudinal wind exerts a certain inhibitory effect on smoke diffusion at the characteristic height of the tunnel. The higher the wind velocity is, the smaller the overall reduction in visibility and the shorter the affected length will be. Simultaneously, the introduction of cold air by longitudinal wind partially dilutes smoke concentration and improves visibility. However, an increase in longitudinal wind velocity also accelerates smoke spread along its direction. As the fire progresses, downwind areas gradually become affected and this is directly proportional to the longitudinal wind velocity. The higher the longitudinal wind velocity is, the faster the same position enters hazardous visibility, and the longer the affected area of visibility danger persists. When comparing tunnels at different altitudes under identical longitudinal ventilation wind velocities, we see that higher altitudes have a greater impact on visibility. Hazardous visibility is reached earlier from the fire source at the same position, and the duration of visibility danger is prolonged. The visibility from the same position of the fire source reaches the hazardous standard earlier, and the length of the hazardous range is longer. Considering that air density and oxygen content decrease with altitude, both the flame height and smoke elevation are reduced. Consequently, buoyancy for high-temperature smoke under the influence of longitudinal wind spreading along the tunnel gradually diminishes. In most cases, compared to longitudinal temperature changes at a characteristic height, smoke-induced visibility decline serves as a key disaster factor in fires and should be considered as a main element in escape design. It should be noted that, at 360 s, human visibility within 20–80 m upstream of the fire source of test 11, 14, and 17 (altitude of 3000 m, 4000 m, and 5000 m) is affected by back-layering due to the low air buoyancy at a high altitude when the vertical ventilation velocity is 2 m/s. The occurrence of this phenomenon was not observed in test 2, 5, and 8 (altitudes of 0 m, 1000 m, and 2000 m).

3.1.3. CO Concentration

Figure 8 presents the variation in longitudinal CO concentration at a characteristic height for 300 s. Long tunnels in high-altitude areas are influenced by factors such as tunnel structure, altitude effect, geographical location, and other variables. In comparison to low-altitude areas, the incomplete combustion of combustible materials intensifies during a fire incident. The fire smoke often contains various toxic gases primarily composed of CO, which poses a risk to personnel evacuation. Incomplete combustion occurs at all stages of a fire. However, it takes some time for the CO concentration to reach a certain level. Based on this premise, an analysis is conducted on the CO concentration at the characteristic height of 300 s.

When there remains no longitudinal wind, the fire source is influenced by the continuous rise of the fire plume. Despite a significant amount of CO production, it does not have a substantial impact on the characteristic height. Additionally, due to heptane fuel usage, CO production levels are lower than those in an actual fire scenario. Under altitude effects, CO concentration at human observation heights increases with altitude elevation. When tunnel ventilation wind velocity is at a low level, upwind sides experience ventilation influence resulting in overall low CO concentrations. However, fresh air brought into ventilation is blocked by smoke back-layering leading to intensified incomplete combustion at fire sources, which results in a hazardous area. However, when the wind velocity exceeds the critical velocity, the introduction of fresh air through ventilation remains unaffected by no existing smoke back-layering. As the proportion of fresh air increases within the tunnel, a significant portion undergoes complete combustion at the source of the fire, resulting in reduced CO concentrations. Although influenced by altitude, the CO concentration in high-altitude tunnels is higher than those in low-altitude tunnels. However, CO concentration still remains significantly below the hazardous level.

3.2. Comprehensive Analysis

Three key factors that threaten the safety of people in tunnel fires are the increase in temperature in the fire source area, the spread of smoke that leads to reduced visibility, and the diffusion of toxic gases. The hazardous range expands under the combined effect of these three factors. Temperature is the key hazardous factor contributing to disaster in the core area of a tunnel fire as results of comparative analysis, regardless of longitudinal ventilation wind velocity. At approximately 300 s, the temperature enters a hazardous level within this core area no matter what the altitude or wind velocity is. The upstream and downstream regions of the fire source are significantly influenced by the wind velocity. This is primarily manifested in the fact that smoke diffusion and temperature distribution exhibit symmetry along the fire source area when there remains no longitudinal wind. However, as the wind velocity increases, they gradually shift towards the downstream side of the fire source. Moreover, both smoke diffusion velocity and distance on the downstream side also increase. In terms of disaster causation at characteristic tunnel heights under different wind velocities, human eye visibility emerges as a key factor for both upstream and downstream regions of the fire source.

Smoke dispersion in a vertically ventilated tunnel can lead to turbulent smoke flow, which disrupts the downstream smoke layering dynamics. The intensity of this turbulence is directly proportional to the wind velocity. Moreover, the longitudinal slope of the tunnel and vehicular movement can further disturb smoke layering, which were ignored in the study. By controlling the longitudinal ventilation velocity, it is possible to prevent smoke back-layering from endangering vehicles and trapped individuals upstream of the fire incident. This approach also prolongs smoke adherence to the tunnel ceiling, restricting its downstream spread and consequently increasing the evacuation time for passengers.

The impact of altitude on fire smoke distribution primarily manifests itself in the reduction in air buoyancy with the increasing altitude, significantly influencing the overall characteristics. Under identical conditions, tunnels situated at higher altitudes exhibit poorer performance at characteristic heights. For instance, only tunnels located at altitudes of 3000 m, 4000 m, and 5000 m reach the hazardous visibility threshold within a timeframe of 300 s. Consequently, for a fixed location away from the fire source, hazardous visibility conditions occur earlier. The impact of altitude on the concentration of CO in smoke manifests itself as an elevation-dependent increase in CO levels at a characteristic height. However, prior to CO concentration reaching a hazardous level, either the temperature or visibility surpasses a hazardous level, thereby precluding CO concentration from becoming a key factor contributing to disasters.

3.3. Design of Adits for People Passing Spacing

3.3.1. The Influence of Altitude on Personnel Evacuation

Existing studies indicate that responses to fires can be broadly categorized into three primary stages: fire detection, confirmation of fire occurrence, and evacuation actions [44]. Among these stages, changes in the ambient temperature and pressure due to altitude have a minimal impact on fire detection and confirmation. However, they significantly affect the stage of evacuation actions. This is primarily observed as a deceleration in evacuation velocity in high-altitude hypoxic environments and an acceleration caused by fear induced by fires. The reduction factor of evacuation velocity in high-altitude environments has been the subject of several studies. The key findings indicate that both the altitude effect and panic psychology significantly impact evacuation velocity during fire disasters. Moreover, the higher the altitude is, the greater the reduction rate of evacuation velocity will be. Specifically, at altitudes of 3 km, 4 km, and 5 km, there is a respective decrease in evacuation velocity by approximately 12%, 23%, and 38% compared to plain areas [45].

3.3.2. Required Safe Egress Time

Adequate adits for people passing that allows for the secure passage of individuals must be established to facilitate the safe evacuation of all personnel in a hazardous range. The maximum safe egress distance should be determined as the distance that personnel can evacuate within the required safe egress time (RSET). The RSET is

$$REST=T_d+T_{pre}+T_t$$

(5)

where: $T_d$ is the alarm time; $T_{pre}$ is the pre-moving time for personnel evacuation; $T_t$ is the time for personnel evacuation.

The smoke detectors used in the project can detect a fire over 100 kW. The fire alarm duration, as determined by the preset fire detectors in this research, is calculated based on the $t^2$ fire model. Equation (5) is used to calculate the time:

$$Q_f=\alpha t^2$$

(6)

where: t is the time of the fire occurrence; $Q_f$ is HRR, which is set as 100 kW in the calculation of the alarm time; $\alpha$ is the fire growth coefficient, which is set as 0.187 $\mathrm{k}\mathrm{W}/{\mathrm{s}}^2$ in this study.

Therefore, the alarm time of the fire detectors can be calculated as follow:

$$T_d=sqrt\left(Q_f/\alpha \right)=sqrt\left(100/0.187\right)\approx 23.1 \mathrm{s}$$

(7)

The pre-action time is the time interval between the receipt of the fire alarm and the initiation of evacuation measures, which is significant in fire emergencies. The pre-action time primarily mainly depends on building types and characteristics associated with occupant safety. Previous studies [45,49,50,51] show that the pre-moving time for personnel evacuation varies from 30 s to 210 s. The pre-action time was chosen as 60 s in this study.

Figure 9 shows the RSET in tunnels at different altitudes with different spacing of adits for personal evacuation in a traffic jam situation based on the simulation results of Pathfinder models. It should be noted that when there are disabled people in the fire scenario, their evacuation needs to be specially designed. Therefore, this case is not considered in the article.

The RSET at an altitude of 0 m is the same as the RSET at an altitude of 1 km. As the figure shows, the difference in RSET at different altitudes is small when the spacing of adits for personnel evacuation is small. However, when the pacing of adits for personnel evacuation comes to 150 m, the difference in the RSET between a high-altitude tunnel and a low-altitude tunnel becomes obvious. For example, the difference in the RSET between a tunnel at an altitude of 5 km and a tunnel at an altitude of 1 km is 167% greater when the spacing is 250 m compared to when it is 50 m.

3.3.3. Available Safe Egress Time

Based on the distribution of temperature, visibility, and CO concentration, the available safe egress time (ASET) is determined when any factor reaches a hazardous standard. In a tunnel fire, the safety of personnel is primarily threatened by three factors: the temperature rise in the fire source area, the decrease in visibility due to smoke diffusion, and the dispersion of toxic gases. The result of comparative analysis shows that temperature is the key hazardous factor in the core area of a tunnel fire. At approximately 300 s, temperatures enter a hazardous level within. When fires occur in a highway tunnel, the longitudinal wind velocity should be accelerated over the critical velocity [33]. In terms of disaster causation at characteristic tunnel heights, human eye visibility emerges as a key factor. Additionally, higher altitude results in reduced air buoyancy, which further impacts visibility at characteristic heights. Consequently, for a fixed location away from the fire source, hazardous visibility conditions occur earlier. The impact of altitude on the concentration of CO in smoke manifests itself as an altitude-dependent increase in CO levels at a characteristic height. However, prior to the CO concentration reaching a hazardous level, either temperature or visibility surpasses a hazardous level, thereby precluding CO concentration from becoming a key factor contributing to disasters.

The variation curve of the ASET with a longitudinal distance at different altitudes is shown in Figure 10. Due to the longitudinal ventilation, the ASET decreases first and then increases gradually with the increase in longitudinal distance. At the same time, as the altitude increases, the available safe evacuation time decreases significantly. The main difference in the tunnel at an altitude of 1 km and 2 km is that the temperature at a location of 25 m reached a hazardous level at 272 s and 297 s rather than the visibility at other locations.

3.3.4. Determination of Maximum Spacing

Figure 11 shows the comparison between the RSET and ASET at different altitudes. As shown in the figure, when the ASET is greater than the RSET, the longitudinal distance is a safe escape area for personnel; otherwise, it is a dangerous escape area for personnel. Therefore, the intersection points between the RSET and the ASET are the maximum pedestrian crossing distance.

Based on the analysis above, the recommended values of the reduction factors of the adits for people passing spacing in highway tunnels at different altitudes are given, mainly based on safety factors, as shown in

Table 5. Maximum spacing of adits for people passing and reduction factor.

Altitude, m	Maximum Adits for People Passing Spacing, m	Reduction Factor
0	250	0
1000	250	0
2000	223	0.89
3000	137	0.55
4000	107	0.43
5000	67	0.27

. When the altitude is 2 km, 3 km, 4 km, and 5 km, the spacing of crosswalks should not be greater than 223 m, 137 m, 107 m, and 67 m.

4. Discussion

This research into smoke diffusion in highway tunnel fires revealed peculiar patterns of fire characteristics at different altitudes. The increase in altitude may exert a substantial influence on the environment in a tunnel fire, such as reduced air buoyancy, diminished oxygen content, and decreased air density, which have a significant impact on the smoke distribution characteristics. In a tunnel fire, the three main hazardous factors for individuals are increased temperature, decreased visibility, and increased concentrations of harmful gases. The variation in longitudinal temperature, visibility, and CO concentration at a characteristic height were analyzed under different longitudinal ventilation velocities. And based on the results of numerical simulation under critical wind velocity, the available safe egress time was determined. Additionally, the required safe egress time was ascertained based on the results of the Pathfinder model. Based on this, the minimum spacing of adits for people passing at a different altitude was established by ensuring that the required safe egress time should not exceed the available safe egress time.

The temperature distribution results are consistent with the findings of previous studies [3,4,5,14,15,16,17,18]. However, it must be pointed out that we further considered one key factor, the longitudinal ventilation velocity. We conducted a comparative analysis of the impact of varying longitudinal ventilation airflow velocities on smoke dispersion within tunnels situated at different elevations. And the design of Adit for People Passing Spacing was based on the critical velocity, which meets the requirements of the national code [33,40]. It is essential to underscore that this aspect has not been considered in previous research [20]. We should acknowledge the limitations of our research. Firstly, it is important to emphasize that enough experiments [4,14,20] ensure the accuracy of our findings on temperature distribution results. The distribution of human visibility has also been confirmed. while the distribution pattern of CO concentration in high-altitude tunnels still requires experimental verification. In the hypothetical case of this paper, the HRR considers the most unfavorable case, which is 30 MW when a fully loaded truck catches fire. But in an actual situation, affected by the oxygen content decline caused by high altitude and other factors, the HRR of a fully loaded truck will also decrease with the increase in altitude. Usually, in an emergency escape, personnel need to bend down and walk, and the characteristic height of the human eye is 1.6 m. Taking into account the safety margin, this study selects 2 m as the characteristic height for analysis. Furthermore, our selection of simulations has limitations. The simulation does not fully capture the incomplete combustion and other real-world fire scenarios, indicating the necessity for further investigation into the distribution of CO concentration. Meanwhile, although the current codes for safe levels of harmful gases are based on concentration values, new models such as a fractional effective dose have been proposed that can further clarify the impact on personnel evacuation. At the same time, only the impact of panic psychology on the speed of personnel evacuation was considered in the simulation of personnel evacuation. The influence of panic psychology on the selection of a personnel evacuation strategy was not taken into account in this study. Panic psychology primarily affects the pre-action time, which was chosen as 60 s in our analysis. Furthermore, the effect of panic psychology on personnel evacuation speed varies at different stages of the fire. However, our simulation in this study utilized a constant speed instead of accounting for variations based on fire development.

Despite its preliminary character, our study clearly indicates the distribution of smoke in tunnels at different altitudes and the spacing of adits for people passing. One important future direction is to explore the more realistic distribution of harmful gases and its impact on personnel evacuation. Another important future direction is the fire source heat release rate under the influence of altitude. Meanwhile, investigating the propagation of combustion among vehicles or the dispersion of smoke in multisource scenarios represents a crucial avenue for future research. Furthermore, evacuation strategies and personal evacuation speed for individuals in more realistic fire scenarios are important in research on the design of adits for people passing spacing.

This work could provide a reference for engineering in high-altitude areas. In the actual project, considering the economic cost comprehensively, the adits for people passing spacing in high-altitude highway tunnels can be slightly larger than the recommended value given in this paper, but should be within a reasonable range. Simultaneously, in the actual project, it is imperative to reduce the spacing of adits for people passings during the design stage and enhance both tunnel management personnel and users’ ability to respond effectively to potential hazards, thereby minimizing the overall response time.

5. Conclusions

A series of numerical simulations were conducted considering altitude and longitudinal ventilation velocity to investigate the characteristics of temperature, CO concentration, and human eye visibility at characteristic heights. Adits for people passing spacing in highway tunnels at high altitude were designed. Following are the major conclusions.

The increase in altitude leads to an acceleration of smoke diffusion. Under the same longitudinal ventilation wind velocity, the upstream smoke diffusion inhibition is minimally affected by altitude. However, the downstream smoke diffusion significantly increases with altitude, including diffusion velocity and diffusion length. The rise in temperature at a characteristic height and the decrease in longitudinal visibility at a characteristic height are attributed to reduced air buoyancy at higher altitudes, resulting in a reduction in available safety egress time.

Longitudinal ventilation in tunnels effectively suppresses upstream smoke diffusion from the fire source and enhances downstream smoke dispersion. At the same altitude, an increase in wind velocity results in elevated rates and an extended hazardous range at a characteristic tunnel height downstream of the fire source.

Comprehensive consideration of the deceleration personnel evacuation velocity under the effects of altitude and panic psychology during fires and the influence of altitude on hazardous range spread as well as a recommended reduction factor are proposed to design adits for people passing spacing in highway tunnels at different altitudes. The adit for people passing spacing should be reduced by 89%, 55%, 43%, and 27% at altitudes of 2 km, 3 km, 4 km, and 5 km, respectively, in comparison to the spacing at sea level (0 m altitude).

The speed and strategies of personnel evacuation under the comprehensive impact of high altitude and panic psychology, as well as the spread of toxic gases at a characteristic height, should be further explored in future works.