Study on the Natural Smoke Exhaust Performance of Board-Coupled Vertical Shaft in High-Altitude Tunnel Fires

: Vertical shaft natural ventilation is a common smoke exhaust method in highway tunnel fires. This study investigated the vertical shaft natural smoke exhaust work in highway tunnel fires with the effect of multiple factors through numerical simulation. Using the analysis of the flow field of smoke in nearby areas of the vertical shaft and the quantitative calculation of the gas exhausted through the vertical shaft, considering the impact of shaft division and board height, an optimal vertical shaft arrangement was proposed, and the working conditions of this arrangement in low-pressure environments were discussed. The results show that dividing a single large vertical shaft into multiple small vertical shafts and appropriately adjusting the board height can reduce the incidence of vertical shaft plug holes and significantly enhance the vertical shaft smoke exhaust performance. Meanwhile, the board-coupled shaft (BCS) has excellent working ability in low-pressure environments, and when pressure drops, smoke exhaust efficiency will improve. This research offers a foundation and reference value for improving the vertical shaft smoke exhaust system in highway tunnels.


Introduction
Tunnel building has advanced quickly in recent years as urbanization has increased, providing convenience and opportunity for people to travel and for economic growth.Meanwhile, it has also presented new issues and difficulties in the prevention and management of tunnel fires [1].Considering the tunnel's elongated and narrow structure, extremely high-temperature hazardous smoke produced by a fire may easily accumulate inside the tunnel and rapidly sink with longitudinal propagation (as seen in Figure 1), which can cause large casualties and significant economic losses [2,3].For example, the Saint Gotha tunnel fire (Switzerland, 2001, 20 deaths), the Xinqidaolang tunnel fire (China, 2011, 4 deaths) [4], the Yanhou tunnel fire (China, 2014, 40 deaths) [5], and the Maoliling tunnel fire (China, 2019, 5 deaths) [6].Therefore, it is crucial to discharge harmful smoke quickly and efficiently when tunnel fire occurs.Currently, the mechanical and natural ventilation systems are the two major types of ventilation utilized within tunnels.Among them, vertical shaft natural ventilation is commonly employed in tunnels for its advantages of cheap cost, minimal air pollution, and simple construction, such as the Nanjing Tongjimen Road Tunnel and the Chengdu Hongxing Road Underground Tunnel.
Several scholars have conducted extensive studies on the longitudinal smoke flow and the smoke exhaust effect below the vertical shaft in tunnel fires.With the utilization of a scaled subway tunnel model, Yao et al. [7] confirmed that compared with tunnels without shafts, tunnel shafts could control the length of smoke backflow within a very small range.Wang et al. [8] combined theoretical analysis and experiments to investigate the impact of varying the quantity, dimensions, and arrangement of vertical shafts on smoke exhaust in tunnel fires.Zhao et al. [9] proposed using plug hole height to describe the degree of vertical shaft blockage and analyzed the effect of the shaft's shape on smoke exhaust efficiency through numerical simulation.They discovered that as the shaft's length and height grow, the overall mass flow rate through the vertical shaft increases, which is more sensitive to the shaft's length.The impact of varying the vertical shaft-fire source distance in highway tunnels was examined by Zhang et al. [10]; they discovered that wider tunnels and bigger shaft areas are more likely to result in vertical shaft plug holes.Gao et al. [11,12] introduced a novel method (Richard number) for identifying the vertical shaft plug hole.Additionally, they utilized numerical modeling to study the effect of variations in environmental pressure on the natural smoke exhaust capability of tunnel vertical shafts.Sun et al. [13] established a segmented predictive model for the smoke back layer length and used numerical simulation to investigate the impact of vertical shafts on induced velocity in slope tunnels.Using a small-scale model, Liang et al. [14] investigated the natural smoke exhaust characteristics of vertical shafts in slope tunnel fires and discovered that the fire plume's deflection angle is only correlated with the tunnel's slope and has little correlation with the vertical shaft's size.Several scholars have conducted extensive studies on the longitudinal smoke and the smoke exhaust effect below the vertical shaft in tunnel fires.With the utiliz of a scaled subway tunnel model, Yao et al. [7] confirmed that compared with tun without shafts, tunnel shafts could control the length of smoke backflow within a small range.Wang et al. [8] combined theoretical analysis and experiments to invest the impact of varying the quantity, dimensions, and arrangement of vertical shaf smoke exhaust in tunnel fires.Zhao et al. [9] proposed using plug hole height to des the degree of vertical shaft blockage and analyzed the effect of the shaft's shape on sm exhaust efficiency through numerical simulation.They discovered that as the sh length and height grow, the overall mass flow rate through the vertical shaft incre which is more sensitive to the shaft's length.The impact of varying the vertical shaf source distance in highway tunnels was examined by Zhang et al. [10]; they discov that wider tunnels and bigger shaft areas are more likely to result in vertical shaft holes.Gao et al. [11,12] introduced a novel method (Richard number) for identifyin vertical shaft plug hole.Additionally, they utilized numerical modeling to study the e of variations in environmental pressure on the natural smoke exhaust capability of tu vertical shafts.Sun et al. [13] established a segmented predictive model for the smoke layer length and used numerical simulation to investigate the impact of vertical shaf induced velocity in slope tunnels.Using a small-scale model, Liang et al. [14] investig the natural smoke exhaust characteristics of vertical shafts in slope tunnel fires and covered that the fire plume's deflection angle is only correlated with the tunnel's s and has little correlation with the vertical shaft's size.It is evident that the vertical shaft plug hole and smoke layer separation can damage the vertical shafts' smoke exhaust condition [15].Hence, it is equally essential and beneficial to discover new approaches for improving the vertical shaft natural smoke exhaust efficiency.Utilizing slightly slanted vertical shafts during tunnel fires has been demonstrated to greatly increase natural smoke exhaust capacity [16].Zhang et al. [17] investigated the impact of the shaft-smoke curtain distance on the smoke exhaust in tunnel fires and proposed the optimal distance between the vertical shaft and the smoke curtain.A board-coupled shaft (BCS) optimization approach was presented by Cong et al. [18][19][20], and they also discussed the effect of the board height and fire source on the tunnel smoke flow field and smoke exhaust efficiency.Shao et al. [21] demonstrated that a board-coupled shaft was also applicable in deeply buried tunnels through numerical simulation and forecasted the relationship between shaft height and gas flow velocity.
In practical engineering, there are inevitably multiple factors that jointly affect the shaft natural smoke exhaust in tunnel fires.Therefore, the goal of this research is to consider the comprehensive effects of different factors, including the vertical shaft division, board height, and environmental pressure.A typical natural smoke exhaust highway tunnel was used as the primary research subject.Using the analysis of the smoke flow field near the vertical shaft and the quantitative calculation of the gas exhausted through the vertical shaft, the working condition and overall smoke exhaust performance of the vertical shaft were evaluated.This study could offer a certain reference basis for designing natural smoke exhaust systems in highway tunnels and provide recommendations for improving smoke exhaust performance.

Research Methodology
In the subject of fire safety engineering, numerical simulation has been extensively utilized and demonstrated to be an effective method for overcoming the constraints of realistic experimental settings [22,23].Software called Fire Dynamics Simulator (FDS) simulates fluid transport in flames through computational fluid dynamics.With an emphasis on computing the heat transfer process and smoke flow in tunnel fires, it resolved the NS formula for low Mach number flow driven by fire buoyancy [24].In this work, tunnel fire scenarios were simulated using FDS version 6.7.6, with an emphasis on estimating the process of heat transfer and smoke flow in tunnel fire incidents.
The simulation employs a highway tunnel model that was 10 m wide × 5 m high, which was consistent with the common one-way dual-lane highway tunnel (10-11.5 m wide and 4.5-5 m high).Meanwhile, in order to save computing resources, the tunnel model length in the study was selected as 100 m [25].Referring to previous experience [26], the vertical shaft area was located downstream of the tunnel, maintaining sufficient distance from the fire source (as seen in Figure 2a).The height of the vertical shaft was uniformly set to 5 m.When there are multiple vertical shafts, the spacing between vertical shafts is 1 m (see Figure 2d).For the board-coupled shaft, the board's size was 13.6 m long × 4.6 m wide, symmetrically arranged below the vertical shaft, maintaining a certain height (see Figure 2e).The tunnel's two ends were configured as "OPEN".Based on the real circumstances, "CONCRETE" with specific heat, density, and conductivity of 1.04 kJ/(kg•K), 2280 kg/m 3 , and 1.8 W/(m•K) was selected for the tunnel's ceiling and side walls.Extending the computational region beyond the tunnel model is important to account for the interaction between gas input and outflow [27].Therefore, an extended domain of 2 m was set at the tunnel's open end.The fire source employed was n-heptane, which has the chemical formula C 7 H 16 and a combustion heat of 44.6 MJ/kg.Considering the impact of supplementary air at the tunnel end [28], the fire source was placed 25 m away from the tunnel's left end, with a size of 2 m × 2 m (as seen in Figure 2b,c).The heat release rate (HRR) of fire source was selected as 10 mw, which is similar to the situation of general vehicle fires in highway tunnels [3].The integrated sub-combustion model FDS automatically calculates smoke and dust generation based on the mixing percentage of Large Eddy Simulation (LES).The smoke and CO yield of n-heptane were set to 0.037 and 0.01, respectively [29].
The layout of relevant measurement points inside the tunnel is shown in Figure 2b,c.Temperature and velocity slices were set along the tunnel's longitudinal centerline.The measuring points for vertical temperature, CO volume fraction, and smoke layer thickness were located 15 m to the right of the fire source, and smoke mass flow rate slices were set along the cross-section of the tunnel.Additionally, smoke mass flow rate slices and CO measuring slices (volume fraction slice and mass fraction slice) were set at the exit position of the vertical shaft.
During the simulation, the environment temperature was set to 20 • C without mechanical ventilation.Considering the highest highway tunnel in China-the Mira Mountain Tunnel, 4752 m above sea level and an environmental pressure of 55.8 kPa-the minimum environmental pressure was selected as 50 kPa [30].This article calculated 16 working conditions, with a simulation time of 200 s, and 150 s-200 s were selected as the stable segment.Table 1 displays the precise operating conditions.Temperature and velocity slices were set along the tunnel's longitudinal centerline.The measuring points for vertical temperature, CO volume fraction, and smoke layer thickness were located 15 m to the right of the fire source, and smoke mass flow rate slices were set along the cross-section of the tunnel.Additionally, smoke mass flow rate slices and CO measuring slices (volume fraction slice and mass fraction slice) were set at the exit position of the vertical shaft.During the simulation, the environment temperature was set to 20 °C without mechanical ventilation.Considering the highest highway tunnel in China-the Mira Mountain Tunnel, 4752 m above sea level and an environmental pressure of 55.8 kPa-the minimum environmental pressure was selected as 50 kPa [30].This article calculated 16 working conditions, with a simulation time of 200 s, and 150 s-200 s were selected as the stable segment.Table 1 displays the precise operating conditions.In numerical simulations of buoyancy plumes, grid size is crucial and significantly affects the accuracy of simulation results.Higher computation accuracy is associated with smaller grid size; nevertheless, the consequence may be longer calculation times [31].In previous studies, the resolution of the grid could be assessed using the dimensionless formula D * /δ x [24].δ x means the mesh size, and D * means the fire characteristic diameter, which can be calculated by .
Q means the fire HRR, c p means the specific heat of air, ρ ∞ means the environmental air density, T ∞ means the temperature of environment, and g means the acceleration of gravity.
Based on the FDS User Guide, the range of D * /δ x should be 4-16.In this work, HRR was selected as 10 MW, so the calculated grid size (δ x ) range ought to be 0.150 m to 0.600 m.Hence, six grid sizes of 0.500, 0.333, 0.250, 0.200, 0.167, and 0.125 m were examined in this article, corresponding to 2, 3, 4, 5, 6, and 8 grids per unit length, respectively.Figure 3 illustrates the vertical temperature distribution and longitudinal mass flow rate variation with varying grid sizes (working conditions: environmental pressure = 100 kPa, vertical shaft division: 1, 4 m length × 4 m width, HRR = 10 MW, no board).Vertical thermocouples were installed 15 m downstream of the fire source, and gas mass flow slices were arranged every 5 m along the tunnel's longitudinal direction to measure the positive gas flow through the tunnel's cross-section (as seen in Figure 2a).The findings show that the distribution of vertical temperature and longitudinal mass flow rate gradually converges as the grid size lowers, indicating that the simulation results are becoming more accurate.Furthermore, the difference might be almost negligible since the size of grid is smaller than 0.167 m, indicating that further reducing grid size will not significantly increase the accuracy of simulation.Finally, after considering the accuracy of simulation and computational speed, 0.167 m (6 grids/m) was determined to be the most appropriate grid size.In addition, the model size of this study is consistent with the FDS model size of Gao et al. [11,12].Hence, we directly utilized the previous model validation results to demonstrate the effectiveness of the FDS model simulation results.

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In numerical simulations of buoyancy plumes, grid size is crucial and significantly affects the accuracy of simulation results.Higher computation accuracy is associated with smaller grid size; nevertheless, the consequence may be longer calculation times [31].In previous studies, the resolution of the grid could be assessed using the dimensionless formula  * / [24]. means the mesh size, and  * means the fire characteristic diameter, which can be calculated by means the fire HRR,  means the specific heat of air,  means the environmental air density,  means the temperature of environment, and g means the acceleration of gravity.Based on the FDS User Guide, the range of  * / should be 4-16.In this work, HRR was selected as 10 MW, so the calculated grid size ( ) range ought to be 0.150 m to 0.600 m.Hence, six grid sizes of 0.500, 0.333, 0.250, 0.200, 0.167, and 0.125 m were examined in this article, corresponding to 2, 3, 4, 5, 6, and 8 grids per unit length, respectively.Figure 3 illustrates the vertical temperature distribution and longitudinal mass flow rate variation with varying grid sizes (working conditions: environmental pressure = 100 kPa, vertical shaft division: 1, 4 m length × 4 m width, HRR = 10 MW, no board).Vertical thermocouples were installed 15 m downstream of the fire source, and gas mass flow slices were arranged every 5 m along the tunnelʹs longitudinal direction to measure the positive gas flow through the tunnel's cross-section (as seen in Figure 2a).The findings show that the distribution of vertical temperature and longitudinal mass flow rate gradually converges as the grid size lowers, indicating that the simulation results are becoming more accurate.Furthermore, the difference might be almost negligible since the size of grid is smaller than 0.167 m, indicating that further reducing grid size will not significantly increase the accuracy of simulation.Finally, after considering the accuracy of simulation and computational speed, 0.167 m (6 grids/m) was determined to be the most appropriate grid size.In addition, the model size of this study is consistent with the FDS model size of Gao et al. [11,12].Hence, we directly utilized the previous model validation results to demonstrate the effectiveness of the FDS model simulation results. (a)

Analysis of Vertical Shaft Smoke Exhaust Process
The combined action of the vertical and horizontal inertial forces mostly affects the smoke flow in the vertical shaft natural smoke exhaust [32].The smoke rate generated by the fire source primarily determines the horizontal inertial force, while the density difference between the higher and lower portions of the vertical shaft causes the chimney effect to create the vertical force.The chimney effect forces the smoke to be released through the shaft as it spreads below the vertical shaft.If the vertical inertia force caused by the chimney effect is significant, a low-temperature zone will develop below the shaft, and the fresh air at the bottom will also be released.This indicates that the vertical shaft plug hole phenomenon is occurring.
In this study, considering the inevitable heat transfer, 25 °C was defined as the criterion for distinguishing between flue gas and air.The exhaust gas from the vertical shaft contains pure smoke and air, and the CO content is mainly created by pure smoke.To a certain extent, the CO exhaust rate can be regarded as the exhaust rate of pure smoke.The specific calculation formula is as follows [11]: In the formula,  means the CO mass flow rate (mg/s),  means the CO mass fraction (mg/kg), and  means the total gas mass flow rate through the vertical shaft (kg/s).In addition, the mass flow rate of pure smoke ( ) and air ( ) passing through the vertical shaft can be calculated using the following formulas [11,12]:

Analysis of Vertical Shaft Smoke Exhaust Process
The combined action of the vertical and horizontal inertial forces mostly affects the smoke flow in the vertical shaft natural smoke exhaust [32].The smoke rate generated by the fire source primarily determines the horizontal inertial force, while the density difference between the higher and lower portions of the vertical shaft causes the chimney effect to create the vertical force.The chimney effect forces the smoke to be released through the shaft as it spreads below the vertical shaft.If the vertical inertia force caused by the chimney effect is significant, a low-temperature zone will develop below the shaft, and the fresh air at the bottom will also be released.This indicates that the vertical shaft plug hole phenomenon is occurring.
In this study, considering the inevitable heat transfer, 25 • C was defined as the criterion for distinguishing between flue gas and air.The exhaust gas from the vertical shaft contains pure smoke and air, and the CO content is mainly created by pure smoke.To a certain extent, the CO exhaust rate can be regarded as the exhaust rate of pure smoke.The specific calculation formula is as follows [11]: In the formula, m CO means the CO mass flow rate (mg/s), M CO means the CO mass fraction (mg/kg), and m total means the total gas mass flow rate through the vertical shaft (kg/s).In addition, the mass flow rate of pure smoke (m smoke ) and air (m air ) passing through the vertical shaft can be calculated using the following formulas [11,12]: where η means the vertical shaft smoke exhaust efficiency, CO sha f t means the CO volume fraction at the vertical shaft outlet (ppm), CO tunnel means the CO volume fraction 10 m upstream of the vertical shaft (ppm), m smoke means the mass flow rate of pure smoke exhausted from the vertical shaft (kg/s), m total means the total gas mass flow rate exhausted from the vertical shaft (kg/s), and m air means the air mass flow rate through the vertical shaft (kg/s).Among them, according to the tunnel's stable stage flue gas layer's thickness, CO tunnel is obtained by the CO average volume fraction inside the smoke layer.Similarly, CO sha f t is obtained by the CO average volume fraction at the outlet of the vertical shaft, while m total is directly obtained by measuring the outlet mass flow rate of the vertical shaft.

The Influence of the Vertical Shaft Division on the Vertical Shaft Natural Smoke Exhaust
Figure 4 displays the temperature field near the vertical shaft with different vertical shaft divisions.When the vertical shaft's total cross-sectional area remains constant, as shown in Figure 4a-c, the degree of the vertical shaft plug hole is greatly decreased, and the low-temperature region within the shaft is significantly reduced with an increase in vertical shaft number.As the shaft's overall temperature grows, the effective smoke exhaust area and smoke exhaust capacity both increase.Meanwhile, when multiple vertical shafts are arranged, the increase in shaft length helps alleviate the phenomenon of vertical shaft plug holes, as shown in Figure 2c,d.
where η means the vertical shaft smoke exhaust efficiency,  means the CO volume fraction at the vertical shaft outlet (ppm),  means the CO volume fraction 10 m upstream of the vertical shaft (ppm),  means the mass flow rate of pure smoke exhausted from the vertical shaft (kg/s),  means the total gas mass flow rate exhausted from the vertical shaft (kg/s), and  means the air mass flow rate through the vertical shaft (kg/s).Among them, according to the tunnel's stable stage flue gas layer's thickness,  is obtained by the CO average volume fraction inside the smoke layer.Similarly,  is obtained by the CO average volume fraction at the outlet of the vertical shaft, while  is directly obtained by measuring the outlet mass flow rate of the vertical shaft.

The Influence of the Vertical Shaft Division on the Vertical Shaft Natural Smoke Exhaust
Figure 4 displays the temperature field near the vertical shaft with different vertical shaft divisions.When the vertical shaft's total cross-sectional area remains constant, as shown in Figure 4a-c, the degree of the vertical shaft plug hole is greatly decreased, and the low-temperature region within the shaft is significantly reduced with an increase in vertical shaft number.As the shaft's overall temperature grows, the effective smoke exhaust area and smoke exhaust capacity both increase.Meanwhile, when multiple vertical shafts are arranged, the increase in shaft length helps alleviate the phenomenon of vertical shaft plug holes, as shown in Figure 2c,d.Figure 5 shows the gas mass flow rate through the vertical shaft with different vertical shaft divisions.When the vertical shaft is divided into 2 m length × 2 m width, the total gas mass flow rate through the vertical shaft is highest.Furthermore, regardless of how the vertical shaft is divided, it is always the first vertical shaft that exhausts the largest gas mass flow rate.Therefore, the following section of this article mainly focuses on the basic setting conditions of 4 vertical shafts with a size of 2 m length × 2 m width, which is also the optimal vertical shaft division method obtained in this section.Figure 5 shows the gas mass flow rate through the vertical shaft with different vertical shaft divisions.When the vertical shaft is divided into 2 m length × 2 m width, the total gas mass flow rate through the vertical shaft is highest.Furthermore, regardless of how the vertical shaft is divided, it is always the first vertical shaft that exhausts the largest gas mass flow rate.Therefore, the following section of this article mainly focuses on the basic setting conditions of 4 vertical shafts with a size of 2 m length × 2 m width, which is also the optimal vertical shaft division method obtained in this section.

Smoke Flow Situation near Vertical Shafts with Different Board Heights
The temperature and velocity distribution variations of traditional vertical shaft and board-coupled shaft (BCS) (board height = 3.8 m) in highway tunnel fires are shown in Figure 6a,e.It is evident that the board's presence primarily influences the air flow both upstream and downstream of vertical shafts, and it also significantly eliminates the occurrence of a vertical shaft plug hole.In tunnel fires, the smoke generated by combustion and the air replenished at both ends of the tunnel coexist in a relatively stable vertical layering relationship.Smoke moves along the tunnel's ceiling and is exhausted from vertical shafts through the chimney effect while also carrying some downstream air.The presence of the board forcibly stratifies the smoke and air under vertical shafts, making it easier for the upper smoke layer to be exhausted through vertical shafts.Only a small amount of smoke escapes downstream, significantly reducing the smoke layer's thickness.In addition, it is more difficult for the lower air layer to enter vertical shafts, thus reducing the occurrence of the vertical shaft plug hole.
Figure 6b-h show the temperature and velocity distribution variations near vertical shafts with different board heights.As the board height increases, the phenomenon of the vertical shaft plug hole is significantly weakened or even disappears, and a noticeable vortex is generated below the board and gradually expands from upstream to downstream along the board.The increase in the board height gradually enhances the limiting effect on the upper smoke and lower air, increasing the difficulty of the lower air's entry into vertical shafts.Meanwhile, if the board height becomes too high, the smoke layer upstream of vertical shafts is destroyed.Although the smoke above the board is easier to exhaust from vertical shafts, the smoke below the board is more severely confined and can only flow downstream along the board.This inevitably leads to collisions between upstream smoke and downstream air moving along the board, resulting in vortices.As the board height continues to increase, more upstream smoke is layered below the board, causing the vortex range to further expand, impacting the stability of the smoke layer underneath the board as well as the vertical shaft's smoke exhaust effect.
Obviously, the optimal board height should be used to avoid the occurrence of the vertical shaft plug hole while limiting the degree of upstream smoke diversion as much  The temperature and velocity distribution variations of traditional vertical shaft and board-coupled shaft (BCS) (board height = 3.8 m) in highway tunnel fires are shown in Figure 6a,e.It is evident that the board's presence primarily influences the air flow both upstream and downstream of vertical shafts, and it also significantly eliminates the occurrence of a vertical shaft plug hole.In tunnel fires, the smoke generated by combustion and the air replenished at both ends of the tunnel coexist in a relatively stable vertical layering relationship.Smoke moves along the tunnel's ceiling and is exhausted from vertical shafts through the chimney effect while also carrying some downstream air.The presence of the board forcibly stratifies the smoke and air under vertical shafts, making it easier for the upper smoke layer to be exhausted through vertical shafts.Only a small amount of smoke escapes downstream, significantly reducing the smoke layer's thickness.In addition, it is more difficult for the lower air layer to enter vertical shafts, thus reducing the occurrence of the vertical shaft plug hole.
Figure 6b-h show the temperature and velocity distribution variations near vertical shafts with different board heights.As the board height increases, the phenomenon of the vertical shaft plug hole is significantly weakened or even disappears, and a noticeable vortex is generated below the board and gradually expands from upstream to downstream along the board.The increase in the board height gradually enhances the limiting effect on the upper smoke and lower air, increasing the difficulty of the lower air's entry into vertical shafts.Meanwhile, if the board height becomes too high, the smoke layer upstream of vertical shafts is destroyed.Although the smoke above the board is easier to exhaust from vertical shafts, the smoke below the board is more severely confined and can only flow downstream along the board.This inevitably leads to collisions between upstream smoke and downstream air moving along the board, resulting in vortices.As the board height continues to increase, more upstream smoke is layered below the board, causing the vortex range to further expand, impacting the stability of the smoke layer underneath the board as well as the vertical shaft's smoke exhaust effect.
Obviously, the optimal board height should be used to avoid the occurrence of the vertical shaft plug hole while limiting the degree of upstream smoke diversion as much as feasible, which depends on the upstream specific smoke layer thickness of vertical shafts.

Analysis of the Vertical Shaft Smoke Exhaust Efficiency with Different Board Heights
Figure 7 shows the gas mass flow rate through vertical shafts with different board heights.A traditional vertical shaft tunnel without a board is set as a control group.The gas mass flow rate through vertical shafts gradually rises with increasing board height before abruptly decreasing, particularly at heights above 4.0 m.

Analysis of the Vertical Shaft Smoke Exhaust Efficiency with Different Board Heights
Figure 7 shows the gas mass flow rate through vertical shafts with different board heights.A traditional vertical shaft tunnel without a board is set as a control group.The gas mass flow rate through vertical shafts gradually rises with increasing board height before abruptly decreasing, particularly at heights above 4.0 m.Considering the two functions of the board underneath vertical shafts, one being the diversion effect on upstream smoke (adverse effect) and the other being the blocking effect on downstream air (beneficial effect), the smoke exhaust efficiency cannot be simply determined by the mass flow rate ratio between pure smoke the total gas exhausted from vertical shafts.At this time, the absolute amount of pure smoke discharged through vertical shafts needs to be taken into account.As a result, the mass flow rate of CO exhausted from vertical shafts is employed as the reference amount, as was previously specified.Furthermore, to compare the smoke exhaust situation with different board heights, the mass flow rate ratio of CO (ηco) is used to represent the degree of improvement in vertical shaftsʹ smoke exhaust efficiency (as seen in Figure 8).
Figure 8 illustrates the mass flow rate of pure smoke and air through vertical shafts with different board heights.Within a certain range (3.2-4.0 m), increasing the height of the baffle is beneficial for exhausting more pure smoke from the vertical shaft.When the board height exceeds the critical value (4 m), continuing to raise the board height can lead to a decrease in pure smoke exhausted from the vertical shaft.Furthermore, when the board height reaches 4.0 m, as seen in Figure 8, the degree of smoke exhaust improvement, ηco, similarly achieves its maximum value.Considering the two functions of the board underneath vertical shafts, one being the diversion effect on upstream smoke (adverse effect) and the other being the blocking effect on downstream air (beneficial effect), the smoke exhaust efficiency cannot be simply determined by the mass flow rate ratio between pure smoke the total gas exhausted from vertical shafts.At this time, the absolute amount of pure smoke discharged through vertical shafts needs to be taken into account.As a result, the mass flow rate of CO exhausted from vertical shafts is employed as the reference amount, as was previously specified.Furthermore, to compare the smoke exhaust situation with different board heights, the mass flow rate ratio of CO (η co ) is used to represent the degree of improvement in vertical shafts' smoke exhaust efficiency (as seen in Figure 8).

Smoke Flow Situation near Vertical Shafts with Different Environmental Pressures
The preceding paragraph states that changing the division of vertical shafts and adjusting the board height appropriately can help improve the vertical shaft smoke exhaust capacity.Therefore, this specific working condition (vertical shaft division: 4, 2 m long × 2 m wide, board height = 4.0 m) was selected to study the impacts of changing environ- Figure 8 illustrates the mass flow rate of pure smoke and air through vertical shafts with different board heights.Within a certain range (3.2-4.0 m), increasing the height of the baffle is beneficial for exhausting more pure smoke from the vertical shaft.When the board height exceeds the critical value (4 m), continuing to raise the board height can lead to a decrease in pure smoke exhausted from the vertical shaft.Furthermore, when the board height reaches 4.0 m, as seen in Figure 8, the degree of smoke exhaust improvement, η co , similarly achieves its maximum value.The preceding paragraph states that changing the division of vertical shafts and adjusting the board height appropriately can help improve the vertical shaft smoke exhaust capacity.Therefore, this specific working condition (vertical shaft division: 4, 2 m long × 2 m wide, board height = 4.0 m) was selected to study the impacts of changing environment pressure on vertical shaft natural smoke exhaust in tunnel fires.Figure 9 shows the temperature and velocity distribution near vertical shafts with different environmental pressures.As the tunnel pressure decreases, the heat dissipation of each vertical shaft becomes more uniform, and more vertical shafts are utilized.However, the smoke layer height underneath the vertical shaft remains relatively unchanged.Low environmental pressure causes the vertical shaft's smoke exhaust capacity to drop and the air entrainment capacity to deteriorate.The board height should be appropriately lowered to transfer more smoke through the vertical shaft.The preceding paragraph states that changing the division of vertical shafts and adjusting the board height appropriately can help improve the vertical shaft smoke exhaust capacity.Therefore, this specific working condition (vertical shaft division: 4, 2 m long × 2 m wide, board height = 4.0 m) was selected to study the impacts of changing environment pressure on vertical shaft natural smoke exhaust in tunnel fires.Figure 9 shows the temperature and velocity distribution near vertical shafts with different environmental pressures.As the tunnel pressure decreases, the heat dissipation of each vertical shaft becomes more uniform, and more vertical shafts are utilized.However, the smoke layer height underneath the vertical shaft remains relatively unchanged.Low environmental pressure causes the vertical shaft's smoke exhaust capacity to drop and the air entrainment capacity to deteriorate.The board height should be appropriately lowered to transfer more smoke through the vertical shaft.

Analysis of the Vertical Shaft Smoke Exhaust Efficiency with Different Environmental Pressures
Figure 10 shows the gas mass flow rate through vertical shafts with different environmental pressures.With the drop in environmental pressure, there is a noticeable reduction in the gas mass flow rate.The low air density in a low-pressure environment might result in a decrease in the flue gas mass flow rate overall.Meanwhile, low ambient pressure may also weaken the chimney effect, resulting in a reduction in smoke exhausted from vertical shafts.

Analysis of the Vertical Shaft Smoke Exhaust Efficiency with Different Environmental Pressures
Figure 10 shows the gas mass flow rate through vertical shafts with different environmental pressures.With the drop in environmental pressure, there is a noticeable reduction in the gas mass flow rate.The low air density in a low-pressure environment might result in a decrease in the flue gas mass flow rate overall.Meanwhile, low ambient pressure may also weaken the chimney effect, resulting in a reduction in smoke exhausted from vertical shafts.

Analysis of the Vertical Shaft Smoke Exhaust Efficiency with Different Environmental Pressures
Figure 10 shows the gas mass flow rate through vertical shafts with different environmental pressures.With the drop in environmental pressure, there is a noticeable reduction in the gas mass flow rate.The low air density in a low-pressure environment might result in a decrease in the flue gas mass flow rate overall.Meanwhile, low ambient pressure may also weaken the chimney effect, resulting in a reduction in smoke exhausted from vertical shafts.The overall production of tunnel smoke decreases as a result of the drop in environmental pressure.Therefore, the vertical shaft smoke exhaust is measured by calculating the mass flow ratio (η) between pure smoke and total gas exhausted from shafts with different environmental pressures.Figure 11 displays the mass flow rate of pure smoke and air through the vertical shaft with different environmental pressures.Interestingly, although the drop in environmental pressure results in a decrease in the smoke mass flow rate through vertical shafts, the percentage of pure smoke in total gas passing through the vertical shaft rises.This also indicates that utilizing board-coupled shafts in high-altitude regions enhances the vertical shaft working capacity, providing a certain basis for optimizing the vertical shaft natural smoke exhaust system of high-altitude tunnels.
air through the vertical shaft with different environmental pressures.Interestingly, although the drop in environmental pressure results in a decrease in the smoke mass flow rate through vertical shafts, the percentage of pure smoke in total gas passing through the vertical shaft rises.This also indicates that utilizing board-coupled shafts in high-altitude regions enhances the vertical shaft working capacity, providing a certain basis for optimizing the vertical shaft natural smoke exhaust system of high-altitude tunnels.

Conclusions
This work employed a numerical study on the vertical shaft natural smoke exhaust process in typical highway tunnel fires.Some optimization methods for the vertical shaft natural smoke exhaust are considered, including changing the division of vertical shafts and the height of the board.The influence of environmental pressure is studied.By analyzing the smoke flow near the vertical shaft and quantitatively calculating the gas through the vertical shaft, the highway tunnel's vertical shaft natural smoke exhaust work condition is obtained.The following is a summary of the main conclusions: (1) In contrast to a conventional one-shaft vertical natural smoke exhaust, increasing the vertical shaft number (dividing the large shaft into multiple small shafts) can improve the amount of gas exhausted from vertical shafts and reduce the occurrence of the vertical shaft plug hole, which supports vertical shaft natural smoke exhaust in highway tunnel fires.
(2) In addition, a board-coupled shaft has an improved impact on the smoke exhaust efficiency of a vertical shaft, which can significantly eliminate the shaft plug hole phenomenon.Within a certain range, an increase in board height helps to exhaust more smoke from the vertical shaft.After exceeding this limit, continuing to increase the board height causes a decrease in smoke exhaust capacity.(3) Finally, a board-coupled shaft (BCS) is also applicable in low-pressure environments.
As the environmental pressure decreases, the vertical shaft smoke exhaust efficiency

Conclusions
This work employed a numerical study on the vertical shaft natural smoke exhaust process in typical highway tunnel fires.Some optimization methods for the vertical shaft natural smoke exhaust are considered, including changing the division of vertical shafts and the height of the board.The influence of environmental pressure is studied.By analyzing the smoke flow near the vertical shaft and quantitatively calculating the gas through the vertical shaft, the highway tunnel's vertical shaft natural smoke exhaust work condition is obtained.The following is a summary of the main conclusions: (1) In contrast to a conventional one-shaft vertical natural smoke exhaust, increasing the vertical shaft number (dividing the large shaft into multiple small shafts) can improve the amount of gas exhausted from vertical shafts and reduce the occurrence of the vertical shaft plug hole, which supports vertical shaft natural smoke exhaust in highway tunnel fires.(2) In addition, a board-coupled shaft has an improved impact on the smoke exhaust efficiency of a vertical shaft, which can significantly eliminate the shaft plug hole phenomenon.Within a certain range, an increase in board height helps to exhaust more smoke from the vertical shaft.After exceeding this limit, continuing to increase the board height causes a decrease in smoke exhaust capacity.(3) Finally, a board-coupled shaft (BCS) is also applicable in low-pressure environments.
As the environmental pressure decreases, the vertical shaft smoke exhaust efficiency is improved to a certain extent in highway tunnels.This indicates that the employment of multiple board-coupled vertical shafts in high-altitude highway tunnels has certain rationality and feasibility.

FireFigure 3 .
Figure 3. Vertical temperature distribution and longitudinal mass flow rate variation in tunnel.(a) Vertical temperature distribution 15 m downstream of fire source.(b) Mass flow rate variation through tunnel cross-section.

Figure 3 .
Figure 3. Vertical temperature distribution and longitudinal mass flow rate variation in tunnel.(a) Vertical temperature distribution 15 m downstream of fire source.(b) Mass flow rate variation through tunnel cross-section.

Figure 4 .
Figure 4. Temperature field near the vertical shaft with different vertical shaft divisions (environmental pressure = 100 kPa).

Figure 4 .
Figure 4. Temperature field near the vertical shaft with different vertical shaft divisions (environmental pressure = 100 kPa).

Figure 5 .
Figure 5. Gas mass flow rate through vertical shaft with different vertical shaft divisions.

3. 3 .
The Influence of the Board below the Vertical Shaft on the Vertical Shaft Natural Smoke Exhaust 3.3.1.Smoke Flow Situation near Vertical Shafts with Different Board Heights

FireFire
2024, 7, x FOR PEER REVIEW 9 of 15 as feasible, which depends on the upstream specific smoke layer thickness of vertical shafts.

Figure 6 .
Figure 6.Temperature and velocity distribution near vertical shafts with different board heights.Figure 6. Temperature and velocity distribution near vertical shafts with different board heights.

Figure 6 .
Figure 6.Temperature and velocity distribution near vertical shafts with different board heights.Figure 6. Temperature and velocity distribution near vertical shafts with different board heights.

Figure 7 .
Figure 7. Gas mass flow rate through vertical shaft with different board heights.

Figure 7 .
Figure 7. Gas mass flow rate through vertical shaft with different board heights.

Fire 2024, 7 , 15 Figure 8 .
Figure 8. Mass flow rate of pure smoke and air through vertical shafts with different board heights.

Figure 8 .
Figure 8. Mass flow rate of pure smoke and air through vertical shafts with different board heights.

3. 4 .
The Influence of Environmental Pressure on Natural Smoke Exhaust in BCS Tunnels 3.4.1.Smoke Flow Situation near Vertical Shafts with Different Environmental Pressures

Figure 8 .
Figure 8. Mass flow rate of pure smoke and air through vertical shafts with different board heights.

3. 4 .
The Influence of Environmental Pressure on Natural Smoke Exhaust in BCS Tunnels 3.4.1.Smoke Flow Situation near Vertical Shafts with Different Environmental Pressures

Figure 9 .
Figure 9. Temperature and velocity distribution near vertical shafts with different environmental pressures.

Figure 10 .Figure 9 .
Figure 10.Gas mass flow rate through vertical shaft with different environmental pressures.

Figure 9 .
Figure 9. Temperature and velocity distribution near vertical shafts with different environmental pressures.

Figure 10 .Figure 10 .
Figure 10.Gas mass flow rate through vertical shaft with different environmental pressures.

Figure 11 .
Figure 11.Mass flow rate of pure smoke and air through vertical shafts with different environmental pressures.

Figure 11 .
Figure 11.Mass flow rate of pure smoke and air through vertical shafts with different environmental pressures.

Table 1 .
Tunnel fire conditions of the simulation.

Change in the Environmental Pressure Case Environmental Pressure Board
Height Shaft Size (Number,Figure 2. Arrangement of simulated tunnel measurement points.

Table 1 .
Tunnel fire conditions of the simulation.