Ensuring the safe evacuation of pedestrians has become a key factor in the healthy development of urban rail transit in each country. Currently, the crowding phenomenon is extremely common in subway stations during the morning and evening peak hours, especially in the hub stations such as the Beijing Xuanwumen subway station where the inbound and outbound pedestrians and transfer pedestrians all move within this limited and closed space. Generally, the high density and great psychological pressure of the crowd can easily cause congestion, stranded or even disorder for the complex internal structure of the station. At this time, once emergencies such as fire, gas leak or explosion occur, it is often difficult to get timely and effective evacuation of pedestrians, which can easily result in casualties and property losses. In order to improve the safety factors at subway stations when an emergency occurs, it is necessary to do some preventive work such as controlling the inflows to keep the pedestrian density not very high.

In recent years, various pedestrian dynamics models have been developed to better imitate and understand the behaviors of pedestrian flows. Generally, these methods are divided into two categories: macroscopic models and microscopic models. A macroscopic pedestrian model such as the fluid dynamics model^[1] pays more attention on the overall movement dynamics of the crowd, where pedestrian flows are described by average speed, density, and location, etc. Compared with the macroscopic pedestrian model, the emerging microscopic pedestrian model focuses more on the detailed behaviors of each pedestrian. Some representative microscopic models are the cellular automata model,^[2] the social force model (SFM),^[3] and the agent-based model.^[4] These pedestrian models have already been used to study evacuation dynamics in various scenarios such as dormitory^[5] and stadium^[6] after emergencies.

According to Guoet al.,^[7] fire is the main cause of emergencies. They developed an extended heterogenous lattice gas pedestrian model combined with the Fire Dynamics Simulator (FDS),^[8] which can provide a spread of information of the fire to simulate pedestrian evacuation in a terrace classroom under fire emergency. Shi et al.^[9] proposed an agent-based evacuation model for large public buildings under the fire condition, and the famous FDS was also used to give the realtime fire conditions such as smoke density, temperature and toxic gas density. FDS uses a computational fluid dynamics model to describe the fire-driven fluid flow.^[8] The group at VTT Technical Research Center of Finland further developed the software FDS + Evac^[10] to simulate pedestrian evacuations under fire, and FDS + Evac is fully embedded in FDS. In FDS + Evac, not only the pedestrian evacuation process under fire but also the human egress process without any fire effect can be simulated.^[10] Lei et al.^[5] investigated the evacuation process of students from a dormitory by using FDS + Evac without any fire, and compared the simulation results with the experimental results.

According to the code for the design of the metro in China,^[11] subway stations should have disaster prevention facilities to prevent fire which should be mainly focused on flood, storm, snow, earthquake, lightning, and parking accidents. By the comprehensive analysis of the causes of accidents in subway stations around the world for the last 150 years, fire accident is the highest frequency disaster which can cause huge losses. Because of the complex structure of the subway station, fire accompanied by the diffuseness of toxic gases is extremely easy to spread. Compared with the conventional indoor fire, the fire accident in subway stations can cause more serious damage to property and casualties. In this paper, we mainly focus on pedestrian evacuation in subway stations under the fire conditions based on FDS + Evac. As far as we know, there is not much research on this topic. Lei et al.^[12] studied crowds’ evacuation in a huge terminal subway station using FDS + Evac, however, the fire condition which is a very important factor to affect an evacuation is not considered. The effect of the platform screen door system of the underground railway station on an emergency evacuation under the fire conditions is studied in Ref. [13]. Some detailed problems about pedestrian dynamics under fire in the subway stations need further investigations in this paper.

This paper takes the platform of line 4 in the Beijing Xuanwumen subway station as an example, and the basic attributes of pedestrians at the platform are obtained by the statistical analysis of our survey data. In addition, these basic attributes are as the basic data in the simulation to investigate pedestrian evacuation under the fire. One contribution in this paper is to find the maximum density threshold in the platform which can provide theoretical guidance for the control of inflow in the subway station. Another contribution of this paper is to obtain the realtime effect of fire on the air temperature and pedestrians’ visibility, which can further help us to understand effects of the location of the fire source and the size of the heat release rate (HRR) of the fire on pedestrians’ behavioral characteristics and psychological activities.

This paper continues with the description of FDS + Evac in Section 2. Section 3 gives the framework of the simulated platform and also the composition of pedestrian flow coming from the collected data of the platform. Section 4 studies the effects of fire dynamics, different initial densities of the crowd, and different fire positions on evacuation.

In this paper, FDS + Evac is chosen to simulate the evacuation of pedestrians in the subway station. FDS + Evac, allowing to simulate both pedestrian dynamics and fire dynamics, treats each pedestrian as a separate agent who has his or her own properties. The SFM of Helbing et al.^[14] is used as the starting point of the movements of pedestrians in FDS + Evac. Besides, the modification of SFM developed by Langston et al.^[15] is also adopted to describe the movement of pedestrians from the one-circle representation to a three-circle one.^[10] Pedestrians are driven not only by physical forces but also by desired forces and psychological forces.

In the SFM, pedestrian i is driven by the desired force, ; the interaction force between pedestrians i and j, f_{i j}; and the interaction force between pedestrian i and walls w, f_iw:

The desired force reflects pedestrians’ willingness to achieve the desired velocity:

The interaction force f_{i j} describes the pedestrian’s psychological tendency to steer away from others, and the physical force which occurs only when the distance between two pedestrian centers d_{i j} is less than the sum of the radii of these two pedestrians r_{i j} = r_i+r _j:

The interaction force between pedestrian i and walls w, f_iw, is described analogously:

Here, , , and are respectively the torques of the contact force, social force, and motive force. is the radial vector pointing from the center of pedestrian i to the point of contact, and points from the center of pedestrian i to the fictitious contact point of the social force. denotes the target angle, w⁰ denotes the maximum target angular velocity of a turning agent, and w_i(t) is the angular velocity of pedestrian i. For more details, we refer readers to Ref. [10].

The interactions between the fire and pedestrians are also considered in FDS + Evac. The conditions of fires such as air temperature, air density, smoke, and radiation levels can cause pedestrians to be incapable. The fire condition may also be influenced by opening the windows or doors. In FDS + Evac, pedestrians’ desired walking speed reduces with increasing smoke concentration according to Frantzich and Nilsson.^[16] It is expressed by

Unknown or unfamiliar routes usually have additional threats to the safe evacuation of pedestrians. Because of this reason, few people choose the emergency exit in the case of fire or other emergencies.^[10] The familiarity of the exit route and the herding behavior are two very important factors to affect pedestrians’ route selection.^[17] The exit selection algorithm embedded in FDS + Evac is based on game theory. According to FDS + Evac Technical Reference and User’s Guide,^[10] pedestrians choose a route through which the evacuation is estimated to be the fastest. The estimated evacuation time of pedestrians is based on the distance to the exit and the congestion degree in front of the exit. Besides, the estimated evacuation time is not the only factor in the choice of exit, the embedded algorithm in FDS + Evac also takes the familiar degree of pedestrians to different exits, the visibility near the exit and the fire condition near the exit into consideration. For more details, readers can refer to Ref. [10].

According to FDS User’s Guide,^[18] FDS can imitate the spread of smoke and heat from fire by solving a plurality of Navier–Stokes equations, especially the k–ɛ turbulence model.^[19] Multiple meshes which are uniformly spaced three-dimensional grids are adopted in FDS to compute the mass and species transport in fire.^[20] This paper only gives the description of the computing methods of temperature and visibility in FDS due to the limited space of the paper. We refer readers to Ref. [18] and Ref. [20] for more details of FDS.

FDS Technical Reference Guide^[20] gives the detailed computing method of temperature T in each mesh which is obtained from density and species mass fractions:

FDS User’s Guide^[18] gives the detailed computing method of pedestrian’s visibility which has a close relationship with the smoke of a fire. The expression for the estimated visibility of pedestrians is

The parameters mentioned in this paper are specified in Table 1.

Table 1.

Table 1.

Table 1. Parameters in FDS + Evac. . Symbol Meaning Value m default male mass 80 kg Ai strength of social repulsive force (pedestrian-pedestrian) 2000 N Bi characteristic distance of social repulsive force (pedestrian-pedestrian) 0.04 m Aw strength of social repulsive force (pedestrian-wall) 2000 N Bw characteristic distance of social repulsive force (pedestrian-wall) 0.08 m λi anisotropic parameter 0.5 κ coefficient of sliding friction 4×104 kg·m−1·s−1 k body compression coefficient 1.2×105 kg·s−2 cd damping parameter 500 kg·s−1 the moment of inertia 4.0 kg·m2 angular relaxation time 0.2 s ω0 angular velocity parameter 4π s−1 the random torque 0.4 kg·m2·s−2 C light-reflecting sign 3 light-reflecting sign 8

Table 1. Parameters in FDS + Evac. .

The simplified two-dimensional (2D) top view chart of the platform of line 4 at Xuanwumen subway station is shown in Fig. 1. The effective area of the platform for pedestrians is 1200 m².

Fig. 1.

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	Fig. 1. The simplified 2D top view chart of the platform of line 4 at Xuanwumen subway station.

There are stairs and escalators on both sides of the platform, and the lifts near the middle as shown in Fig. 1. When fire occurs, both the lifts and the escalators stop running. The escalators, however, can still be used as static stairs to evacuate pedestrians from an emergency. According to the requirement of the code for design of the metro in China,^[11] pedestrians should realize the safety evacuation within 6 minutes. In our study, we also take 6 minutes as the critical evacuation time to simulate. Furthermore, when fire occurs, pedestrians on the platform are considered to be safe once they arrive at the upper floor.

Pedestrian evacuation at the investigated platform in this paper is different from that in the traditional double exit room. One difference is that the evacuation channels on both sides of the platform are relatively narrow and relatively long because of the special and complex structure of the subway station, so the difficulty of the safety evacuation of pedestrians is relatively large. Besides, the platform surrounded by soil and rock is mostly under the ground, and there are no windows on the platform. The degree of psychological panic of pedestrians often increases in this relatively confined space after a fire has started, thus the evacuation disorder is more serious, so the probability of a stampede accident on the platform is much higher than that in a conventional double exit room. Furthermore, due to the relatively closed space of the platform, heat and smoke can accumulate quickly and cannot dissipate after the fire. Therefore, the air temperature on the platform increases faster and the visual field of pedestrians also decreases faster compared with those in the traditional room.

In this paper, we choose P₁ in Fig. 1 as the observation place to obtain the statistical data of pedestrians’ basic attributes. The data mainly contains the distribution of men and women, luggage statistics, and age structure, and the corresponding results are shown in Figs. 2, 3, 4, and Table 2. It is worth noting that the statistical data are collected for a whole week from 8:30 am to 11:00 am. From the statistical results, we can obtain that the gender difference is not significant, and the ratio of male to female is 1 to 1 basically. Most pedestrians have no luggage or carry small pieces of luggage, which cannot affect the efficiency of travel. The proportion of pedestrians carrying large pieces of luggage is close to 5%. Generally, most pedestrians who carry large pieces of luggage transfer to the Beijing South Railway Station, so whether pedestrians carry large pieces of luggage or not is related to their travel purposes. In addition, we can find that adults occupy the main position, followed by the elderly. In general, because of the existence of stairs/escalators at the subway station, it is very dangerous for children to take the subway for travel, so the proportion of children is smallest.

Fig. 2.

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	Fig. 2. Distribution of male and female at the platform of line 4 at Xuanwumen subway station.

Fig. 3.

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	Fig. 3. Luggage statistics at the platform of line 4 at Xuanwumen subway station.

Fig. 4.

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	Fig. 4. Age structure at the platform of line 4 at Xuanwumen subway station.

Table 2.

Table 2.

Table 2. The composition of pedestrian flow. . Adult Elderly Child Proportion 96% 3% 1%

Table 2. The composition of pedestrian flow. .

For different types of pedestrians, they have their unique body sizes and velocities in FDS + Evac, we apply the composition of pedestrian flow in Table 2 for all simulations in this paper. According to FDS + Evac Technical Reference and User’s Guide,^[10] pedestrian radius, unimpeded walking velocities, and reaction time are chosen from uniform distributions whose ranges are also listed in Table 3.

Table 3.

Table 3.

Table 3. Pedestrian parameters for different body types. . Body type Pedestrian radius r/m Unimpeded walking speed/(m/s) Reaction time τ/s Adult 0.255±0.035 1.25±0.30 1±0.2 Elderly 0.250±0.020 0.80±0.30 1±0.2 Child 0.210±0.015 0.90±0.30 1±0.2

Table 3. Pedestrian parameters for different body types. .

Based on FDS + Evac, this section first studies the effect of fire dynamics which can result in increasing the air temperature and reducing the pedestrian visibility. Then, the influence of different pedestrian densities on evacuation under fire is investigated to provide the feasible suggestions to the subway operator of line 4. Following it, the comparison of the effects of different fire positions on evacuation is focused on.

4.1. Effect of fire dynamics

In the simulation, it is assumed that fire occurs in the center of the platform as shown in Fig. 5, and HRR is set to be 1 kW.

Fig. 5.

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	Fig. 5. The simplified three-dimensional (3D) top view chart of the platform of line 4 at Xuanwumen subway station.

After fire occurs, the air temperature, the smoke density or other factors may be changed with time, which can result in the change of pedestrians’ visibility, velocity or other properties. By using FDS + Evac, the snapshots of temperature and pedestrians’ visibility at different time instants are obtained in Figs. 6 and 7. It is worth noting that both the air temperature and pedestrians’ visibility are derived in the height of z = 1.6 m in this paper. When fire occurs, smoke, and heat usually spread upwards quickly, and this is one reason why we need to crawl in the fire. In addition, smoke and heat not only spread upwards but also spread to both ends of the platform. Once they arrive at both ends of the platform, they will accumulate and produce a return flow. The temperature, therefore, is relatively high around the fire source and both ends of the platform at the beginning time in the plane z = 1.6 m shown in Figs. 6(a) and 6(b). The temperature between the position of the fire source and the end of the platform, however, is relatively low in the plane z = 1.6 m also as figures 6(a) and 6(b) show. The reason is that the transferred heat and smoke from the fire source may concentrate in its upper layer of air, and the temperature above the plane z = 1.6 m may have a certain increase. With the increase of time, smoke and heat on both ends of the platform in the plane z = 1.6 m begin to return to a relatively low z plane. The temperature, therefore, begins to decrease continually as shown in Figs. 6(b) and 6(c). There is a similar reason for the change of the radius of pedestrians’ visibility in Figs. 7(a)–7(c).

Fig. 6.

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	Fig. 6. Snapshots of temperature at different time instants.

Fig. 7.

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	Fig. 7. Snapshots of pedestrians’ visibility at different time instants.

The decrease of the radius of pedestrians’ visibility can directly result in the decrease of pedestrians’ velocity in a certain degree. Note that the default radius of visibility is 30 m for all pedestrians in FDS + Evac. Figure 8 shows the mean temperature and visibility change in the time period from 300 s to 360 s, from which the varying degrees are further seen clearly.

Fig. 8.

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	Fig. 8. Mean temperature and radius of visibility from 300 s to 360 s. (a) Mean air temperature and (b) mean radius of visibility.

The real time fire conditions directly affect the pedestrians’ movement, and the snapshots of the pedestrian evacuation at different time instants are also collected as shown in Fig. 9. From this figure, we can see that the pedestrians begin to escape from the platform, and they try their best to find the nearest stairs/escalators as soon as possible. Note that the initial density at the platform is set to be 0.2 p/m₂, and the proportion of the pedestrians knowing the stairs/escalators is listed in the following Table 4 according to the estimation of our survey data.

Fig. 9.

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	Fig. 9. Snapshots of pedestrian evacuation at different time instants: (a) t = 2 s, (b) t = 18 s, (c) t = 36 s, and (d) t = 250 s.

Table 4.

Table 4.

Table 4. The composition of pedestrians knowing the corresponding stairs/escalators. . Stairs/escalators Left Right Both Neither Proportion 40% 40% 18% 2%

Table 4. The composition of pedestrians knowing the corresponding stairs/escalators. .

4.2. Effect of pedestrian density

In order to achieve safe evacuation from the platform of line 4 within the required time of 6 minutes after the fire, we specially set different initial densities of pedestrians at the platform to imitate the crowd evacuation.

Figures 10 and 11 show the proportion of evacuated pedestrians from the platform varying with time and initial densities, respectively. Note that the data in the boxes of Fig. 10 give different initial densities (p/m²). From these two figures, it is very clear to find that when the initial density of the crowd is not higher than 1.0 p/m², the design of the platform can reach the standard. It is better to control the inflows of pedestrians in the normal conditions appropriately once the density at the platform reaches the critical threshold. It is worth noting that there exists a reaction time for all pedestrians when a fire occurs, that is the reason why there is no pedestrian achieving safe evacuation in the first few seconds. Besides, from Fig. 10 we can obtain that the proportion of evacuated pedestrians has an approximate linear relationship with the simulation time for a given initial density before this proportion becomes 1.

Fig. 10.

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	Fig. 10. The proportion of evacuated pedestrians from the platform over time for different initial densities.

Fig. 11.

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	Fig. 11. The proportion of evacuated pedestrians from the platform varying with initial densities.

During the process of simulations, we can find that when the initial density is relatively low such as 0.2 p/m² and 0.4 p/m², pedestrians can walk freely to the stairs/escalators after the fire. Pedestrians, however, find it very hard to move forwards when the initial density is high enough especially around the stairs/escalators a few minutes later, after the fire as figure 12 shows. It is easy to explain this phenomenon. After a fire occurs, pedestrians are anxious to evacuate, meanwhile the stairs/escalators cannot satisfy this demand and accordingly become bottlenecks to impede the evacuation.

Fig. 12.

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	Fig. 12. The crowding phenomenon around stair/escalator.

4.3. Effect of fire position

In this section, in order to investigate the effect of fire position on evacuation, we set 4 different positions of fires shown in Fig. 13: Position A, B, C, and D, respectively. Position A is at the center of the platform, position B is between the central position A and the stair/escalator, position C is between the stair/escalator and the toilet, and position D is in front of the stair/escalator. The initial density of pedestrians on the platform is 0.6 p/m².

Fig. 13.

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	Fig. 13. The candidate positions of fire in the simulation.

The different evacuation effects are shown in Fig. 14. From this figure, we can find that the position of the fire has little to do with the evacuation efficiency even though the fire is at position D which is very close to the stair/escalator as shown in Fig. 15. The reason may be that the fire whose HRR is 1 kW is not very large, it cannot result in deadly strike in the first 6 minutes as shown in Fig. 16. At this time, the effect of fire on route selection plays a relatively minor role based on the embedded exit selection algorithm in FDS + Evac. The majority of pedestrians will not change their ideas, and they will still choose their original routes. Another reason may be the initial density set in the simulation is not very high, which can ensure pedestrians escape freely within the first 6 minutes. When HRR is relatively large, the fire at position D will significantly affect the determination of pedestrians’ route selection according to the embedded exit selection algorithm in FDS + Evac. Figure 16 shows the effect of the size of HRR on pedestrian evacuation when fire occurs at position D. From this figure, we can observe that the number of pedestrians at the platform slightly alters especially when HRR is 100 kW or 1000 kW, which means the fire with large HRR can directly result in the death of pedestrians.

Fig. 14.

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	Fig. 14. The comparison of evacuation effects for different fire positions.

Fig. 15.

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	Fig. 15. The snapshot of evacuation under fire at position D.

Fig. 16.

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	Fig. 16. The number of pedestrians at the platform over time under different HRR of fires at position D.

Based on the software FDS + Evac, in this paper we focused on investigating pedestrian evacuation under fire on the platform of subway line 4 in Beijing Xuanwumen subway station, China. Our simulation results show that the fire increases the air temperature and the smoke density, which can directly result in reducing pedestrians’ visibility and walking velocity. The density of pedestrians on the platform should not be very large, in order to meet the requirement of safe evacuation, there always exists a critical threshold of density, and we found that 1.0 p/m² is this threshold value for the platform studied in this paper. Furthermore, in comparison with the evacuation results under fire at different positions, it can be found that the position of the fire has little impact on the evacuation within the first required 6 minutes if the fire is not very large. However, when the HRR of the fire near the stair/escalator is large enough, the fire disaster can cause serious loss.