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Stairs in subway stations are vulnerable to floods when rainstorm disasters occur in cities. The stairs, as a critical way for human evacuation, can affect the safe evacuation of people on flood-prone stairs. To evaluate the risk of people evacuating through different slopes and forms of stairs when floods invade subway stations, a numerical model for the water flow on stairs based on the volume of fluid model and the realizable k-ε model was established. The water flow patterns on stairs at the subway station entrance under different slope conditions and with/without rest platforms were simulated. The real-time water flow process on stairs at different inlet depths was obtained, and the escape control index F was used to evaluate the risk of people evacuating through stairs at different slopes and water depths. The results indicate that the presence of a rest platform can cause an increase in water velocity and depth on pedestrian stairs, and people should choose stairs without a rest platform for evacuation during the evacuation process. The research results hope to provide a reference for the people evacuation on stairs, and further improve the theory of safe evacuation of personnel on flood-prone stairs.

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  • A numerical simulation model for the water flow on a stair in subway stations was built based on the realizable k–ε model and VOF model.

  • The escape control index F was used to evaluate the risk of people evacuating through stairs at different slopes and water depths.

  • The water flow numerical simulation model can be applied to simulate the water flow characteristics on stairs in other similar subway stations.

evacuation, flood invasion, subway stair, VOF model, water flow process
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With the acceleration of global urbanization, cities throughout the world are facing increasingly significant challenges (Forero Ortiz & Martínez Gomariz 2020). Rapid urbanization and climate change have resulted in severe flooding disasters in several places worldwide (Chen et al. 2020). Underground spaces, such as shopping malls, tunnels, parking lots, and subway stations) are often vulnerable to urban flooding (Lyu et al. 2019; Valdenebro et al. 2019). Especially floods invade subway systems in large cities, which can result in massive loss of life and economic damages (Cui & Nelson 2019; Shadmehri Toosi et al. 2019; Chen et al. 2021). In 2020, a rainstorm occurred in Huangpu and Zengcheng of Guangzhou, the Guangzhou Metro Line 13 was flooded, resulting in the whole line being shut down. In 2021, an extremely heavy rainstorm occurred in Zhengzhou, causing serious urban waterlogging. The flood destroyed the flood retaining wall and flooded into the subway tunnel, leading to the complete shutdown of the subway line and causing huge losses of life (Xu & Zhou 2022). It can be seen that urban underground space floods have become a very prominent problem in urban public safety in China under the background of rapid development of urbanization (Hou et al. 2022). When the underground space of the city floods, the flood usually flows into the underground space through the underground space staircase. The staircase serves as an essential route for the evacuation of people. Excessive water accumulation and rapid water flow on the stairs may make it difficult for people to escape and increase the difficulty of urban flood risk management. Therefore, it is crucial to analyze flood flow patterns on underground space staircases to minimize the risks of pedestrian evacuation.

With the frequent occurrence of urban floods, the evacuation process of personnel in underground spaces has received considerable attention (Li et al. 2019; Yamada 2020). Physical experiments and numerical simulations are commonly used for studying urban underground space floods. In terms of physical experiments, Toda et al. (2002, 2004) established a 3D urban complex flood testing model and analyzed the flood propagation process of surface floods invading underground spaces from multiple entrances. Ishigaki et al. (2003) used the 3D urban flood model for flood testing, and the test results showed that more than half of the surface flood flowed into the underground space, causing severe problems. In terms of numerical simulation, Yoneyama et al. (2009) utilized the volume of fluid (VOF) approach to simulate the flood on a vertical staircase in an underground location and obtained the water characteristics of the stairs. Mo (2010) simulated the flood intrusion at the subway station, the flow time history of the flood intrusion was obtained, and the impact of existing flood control measures on personnel evacuation was analyzed. Kim et al. (2018) proposed an adaptive transmission method to simulate underground flooding better when two levels are connected, to reproduce multiple horizontal layers connected to stairs or elevators, and to avoid mesh size changes caused by local details in the model. According to the findings, combining physical and numerical models is beneficial to improve the understanding of flood invasion processes and people evacuation on stairs, as well as improving the accuracy of numerical simulations.

The stairs connecting the ground and underground spaces are the primary route for pedestrian escape when floods occur (Liang et al. 2024). Physical experiments and numerical simulations were used to research the safe evacuation of people on stairs. The escape control index F(v, y) was established by Toda et al. (2002) and Ishigaki et al. (2006) to represent the possibility of people going through flood stairs, where v is the water velocity and y is the water depth on the steps. Toda et al. (2002) proposed an F(v, y) of 1.5 m3/s2 for safe evacuation by evaluating the stability of people walking on a 1:3 scale staircase model, and Ishigaki et al. (2006) proposed an F(v, y) of 1.2 m3/s2 for safe evacuation by testing the stability of people walking on a full-size staircase model. Shao et al. (2014) established a free-falling jet downstream of the rest platform in a 1:2 scale physical model experiment of a vertical ladder, which might affect the walking stability of people on the steps. Jiang et al. (2014) investigated the jet force on a cylinder downstream of a rest platform and discovered that the presence of a rest platform in a straight staircase significantly alters hydrodynamic forces, potentially increasing the risk of evacuating personnel downstream of the rest platform. Gotoh et al. (2010) utilized a realistic approach to quantify the hydrodynamic forces acting on the legs of a model put on stairs to assess the impact force of water flow on people on stairs. Liu et al. (2009) used an agent-based personal system model to simulate the evacuation of personnel under the threat of floods to human life, Mori et al. (2009) used a real-sized staircase model to determine the most effective gait evaluation for walking speed and preventing falls when rescue personnel descended and optimized the gait of personnel descending to cope with flooding. Yoneyama et al. (2009) utilized the VOF method to simulate the flow on a staircase model, and the findings revealed that the estimated velocity values were lower than the experimental values due to the coarse mesh of each staircase. Shao et al. (2015) examined flood flow characteristics on stairs with various inclination degrees and shapes based on the VOF model and the realizable k–ε model, as well as comparing the impact of rest platforms on flood flow and personnel evacuation. Hou et al. (2022) developed numerical models with varying slope conditions for simulation, utilizing the escape control index F to evaluate the danger of pedestrians escaping using stairs on different slopes. They suggested that people should avoid steep slopes and instead choose mild slope steps when evacuating. Previous research has focused on studying the flow patterns on stairs in urban underground spaces and constructed in laboratories. Although these studies can obtain the flow characteristics of water on stairs, the limitations of the research subjects prevent them from reflecting the flow characteristics of water on pedestrian steps and escalators in subway stations, as well as assessing the evacuation risk of people on stairs inside the station. And, little study has been conducted on pedestrian steps and escalators in urban subway stations. As a result, it is required to investigate the flow process of water on stairs at stations during a flood and evaluate personnel evacuation.

Given that existing research cannot precisely reflect the water flow patterns on stairs in subway stations and related works on the water intrusion process on pedestrian stairs and escalators in subway stations are rare this paper established a numerical model of water flow on escalators and pedestrian stairs. The flow patterns on pedestrian stairs at the entrance of the station under different slopes and with/without rest platforms were investigated. The real-time flow process of water flow on stairs at different entrance depths was obtained. The risk of pedestrians evacuating through pedestrian stairs and escalators at various slopes and entry depths was evaluated. It hopes to provide a reference for personnel evacuation on stairs, and further improve understanding of water flow patterns on subway station stairs for urban flood risk management and the safety of subway passengers.

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The VOF model is commonly used for numerical modeling of free surface tracking. This method simulates the movement of two or more fluids by solving a set of momentum and continuity equations while monitoring the volume occupied by each fluid to calculate the free surface (Lin et al. 2022). When the fluid is filled into the calculation unit: α = 1, no fluid in the calculation unit: α = 0. In this model, the free surface of the two-phase flow is determined by the volume ratio function of the fluid mesh within each mesh unit. The continuity equation for volume fraction in the VOF model can be expressed as follows:
(1)
where α is the fluid volume fraction in the control volume; t is the time; and V is the fluid velocity.
The Navier–Stokes equation is the fundamental governing equation in fluid computing (Hou et al. 2022). The continuity and momentum equation of the fluid can be expressed as:
(2)
(3)
where ρ is the volume fraction average density; ui and uj are the velocities in the xi and xj directions; xi and xj are Cartesian coordinates; P is the pressure; μ is the dynamic viscosity; and μt is the turbulent viscosity coefficient.
The renormalization group (RNG) k–ε model adopts the RNG method, considering the rotation and swirl in the flow, which can better handle swirling flow. The expression can be expressed as follows:
(4)
(5)
where k is the turbulent kinetic energy; ε is the turbulent dissipation rate; Gk is the turbulent kinetic energy caused by the average velocity gradient; u is the velocity, i, j = 1, 2, 3. For the constants, default values were chosen: C1ε = 1.44, C2ε = 1.44, αk = αε = 1.39; μeff is the hydrodynamic viscosity under turbulent conditions μeff = μ + μt.
The realizable k–ε model, which takes into account the detailed physical processes of the fluid, is better than the standard k–ε model and the RNG k–ε model in simulating the complex fluid (Kositgittiwong et al. 2013). This model presents a more reasonable turbulence viscosity equation, which adopts a new energy dissipation rate transfer equation derived from an accurate vortex transfer equation. The k–ε turbulence model equation can be expressed as:
(6)
(7)
where G is the turbulent kinetic energy caused by the average velocity gradient; δk = 1.0, and δε = 1.0.

The RNG k–ε model exhibits higher accuracy in predicting vortex flow and high-speed flow. The realizable k–ε model can provide more accurate prediction results in strong reverse pressure gradient and flow separation due to the separation phenomenon of water flow on the stairs. Therefore, this study used the VOF model and the realizable k–ε model to predict the flow pattern of floods at the station. In the VOF model, the surface tension coefficient was used to simulate the interaction between water and air. Select standard wall functions for near-wall surfaces. Pressure and velocity were coupled through the pressure implicit and splitting operator method. In addition, the control equation was discretized using the finite volume technique, and the momentum equation, volume fraction, and turbulent kinetic energy were solved using the QUICK algorithm. Pressure interpolation was performed using the PRESTO technique, and the transient formula is of the second-order implicit format.

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Geometric modeling

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Two physical models were created to investigate the characteristics of water flow on stairs, namely the escalator and pedestrian staircase in Exit B1 of Shakou Road Station, as shown in Figure 1. There is no rest platform on the escalator in Figure 1(a), which has a step height of 0.1 m and a width of 0.2 m. The pedestrian staircase in Figure 1(b) has three rest platforms, each with a step height of 0.08 m and a width of 0.16 m. The two staircase models in Exit B1 of Shakou Station were utilized for numerical simulation calculations in this research, and the staircase water flow test model supplied in reference (Shao et al. 2015) (shown in Section 3.2) was used to validate the correctness of the numerical simulation approach.
Figure 1
Staircase model at B1 exit of Shakou Road station. (a) Escalator step model. (b) Pedestrian staircase model.
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Staircase model at B1 exit of Shakou Road station. (a) Escalator step model. (b) Pedestrian staircase model.

Figure 1
Staircase model at B1 exit of Shakou Road station. (a) Escalator step model. (b) Pedestrian staircase model.
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Staircase model at B1 exit of Shakou Road station. (a) Escalator step model. (b) Pedestrian staircase model.

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Computational domain and boundary conditions

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The boundary condition for the numerical model of the escalator and pedestrian stairs is shown in Figure 2. The uniform flow was applied at the lower part of the inlet boundary. A pressure inlet boundary with atmospheric pressure was set at the upper part of the inlet and the top of the model. A stepped pressure inlet boundary is considered at the top of the model to ensure stable atmospheric pressure (Shao et al. 2014). The side wall, step surface, and platform surface of the stairs were all equipped with nonslip wall boundary conditions.
Figure 2
Computational domain and boundary. (a) Boundary conditions for escalator. (b) Boundary conditions for pedestrian stair.
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Computational domain and boundary. (a) Boundary conditions for escalator. (b) Boundary conditions for pedestrian stair.

Figure 2
Computational domain and boundary. (a) Boundary conditions for escalator. (b) Boundary conditions for pedestrian stair.
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Computational domain and boundary. (a) Boundary conditions for escalator. (b) Boundary conditions for pedestrian stair.

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The numerical model calculation region of the step model in reference (Shao et al. 2015) is shown in Figure 3. The upstream boundary of the model is set at 2.5 m upstream of the x-direction staircase entrance, while the downstream boundary is set at the staircase exit. The uniform flow with velocity was applied at the lower part of the inlet. A pressure inlet boundary with atmospheric pressure is set at the upper part of the inlet and the upper opening of the model. The top of the model was considered a stepped pressure inlet boundary. The pressure outlet boundary was applied at the outlet, and the side walls, step surfaces, and platform surfaces of stairs were all equipped with nonslip wall boundary conditions (Hou et al. 2022).
Figure 3
Stair model calculation region (Shao et al. 2015).
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Stair model calculation region (Shao et al. 2015).

Figure 3
Stair model calculation region (Shao et al. 2015).
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Stair model calculation region (Shao et al. 2015).

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Mesh independence

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This study selected the step model provided in reference (Shao et al. 2015) and established three different mesh sizes to evaluate the impact of mesh sensitivity on the accuracy of the numerical model. The selected mesh density sizes are shown in Table 1.

Table 1

Mesh schemes for the simulation model

MeshNodesElementsMesh size on the staircase area (mm)
1 19,779 19,085 12 
2 28,553 27,716 10 
3 44,367 43,346 8 
MeshNodesElementsMesh size on the staircase area (mm)
1 19,779 19,085 12 
2 28,553 27,716 10 
3 44,367 43,346 8 
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The water velocity on the middle position of the stair under mesh schemes 1, 2, and 3 is shown in Figure 4. It can be seen that the speed of grid schemes 1, 2, and 3 does not change much. The mesh number increases significantly from mesh scheme 2 to mesh scheme 3, but the results do not change much. Mesh scheme 2 was employed in this investigation due to its computational efficiency. The grid for the steps model consists of 28,553 nodes with a maximum mesh size of 10 mm and a total of 27,716 elements. The calculation region of the model is separated into the structural mesh, and the selected numerical model calculation mesh is depicted in Figure 5.
Figure 4
Water velocity on the stair.
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Water velocity on the stair.

Figure 4
Water velocity on the stair.
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Water velocity on the stair.

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Figure 5
Stair model calculation mesh.
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Stair model calculation mesh.

Figure 5
Stair model calculation mesh.
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Stair model calculation mesh.

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The two staircase models at the B1 entrance also belong to the staircase model and can be carried out using the grid size in mesh 2 to the mesh division. The mesh in the escalator model consists of 62,183 nodes, with a maximum grid size of 10 mm and a total of 60,378 elements. The mesh in the pedestrian staircase model consists of 74,734 nodes, with a maximum mesh size of 10 mm and a total of 72,763 elements. The selected numerical model calculation grids are shown in Figures 6 and 7, respectively.
Figure 6
Calculation mesh of the escalator model.
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Calculation mesh of the escalator model.

Figure 6
Calculation mesh of the escalator model.
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Calculation mesh of the escalator model.

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Figure 7
Calculation mesh of the pedestrian stair model.
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Calculation mesh of the pedestrian stair model.

Figure 7
Calculation mesh of the pedestrian stair model.
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Calculation mesh of the pedestrian stair model.

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Model validation

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A comparative analysis was conducted between the numerical simulation and the experimental results (Shao et al. 2015) to validate the accuracy of the numerical simulation. This experiment takes the entrance staircase of a specific subway station as a prototype to establish the physical model. The model mainly includes an inlet pool, a staircase, and a tailrace channel, with a model size of approximately 20 m × 1.2 m × 3.5 m (as shown in Figure 8). The step can be divided into two sections, each of which contains 13 steps that are 14 mm wide and 8 mm high. The middle part is connected by a rest platform (S14), and each step can be numbered from S1 to S28.
Figure 8
Step model diagram (Shao et al. 2015).
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Step model diagram (Shao et al. 2015).

A jet flow occurred below the first resting platform of the step in the water flow test, and due to the height of the step decreasing, an air cavity was formed below the jet (Zhang et al. 2023). However, the airflow below the resting platform adheres to the vertical plane of the steps in numerical simulations. If there is no air cavity below the jet, no jet will be formed (Figure 9(a)). As a result, a ventilation gap was opened at the vertical plane of the 15th step (downstream first step of the first rest platform) (Figure 9(a)), and an atmospheric pressure inlet boundary was applied. The numerical simulation flow pattern along the stepped chute with an open ventilation gap and h = 15 cm is shown in Figure 9(b). The jet and the air cavity under the jet tongue are identical to those described by Shao et al. (2015).
Figure 9
Simulated flow pattern along the staircase. (a) No ventilation gap. (b) Ventilation gap.
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Simulated flow pattern along the staircase. (a) No ventilation gap. (b) Ventilation gap.

Figure 9
Simulated flow pattern along the staircase. (a) No ventilation gap. (b) Ventilation gap.
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Simulated flow pattern along the staircase. (a) No ventilation gap. (b) Ventilation gap.

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A water depth of 0.15 m was selected for this simulation validation to demonstrate the reliable accuracy of the model under different simulation scenarios, and the RNG k–ε model and the realizable k–ε model were selected for numerical simulation during the simulation process. The computational cost of the two models is shown in Table 2. All calculations in this study are performed in a personal computer with 8 Intel(R) Core(TM) i7-7700 K CPUs @ 4.20 GHz, 32 GB of RAM, and 1 NVIDIA GeForce GT 730 GPU card. During the calculation process, there is not much difference in the computational costs required between the RNG k–ε model and the realizable k–ε model. The comparison between the numerical simulation and measured water surface elevation is shown in Figure 10. The results indicate that the RNG k–ε model cannot simulate the jet well behind the rest platform, and the realizable k–ε model can more accurately simulate the water flow field, which is consistent with the conclusion in reference (Shao et al. 2015). Therefore, this study adopted the VOF model and the realizable k–ε model is more accurate in simulating the flood flow pattern on stairs.
Table 2

Comparison of computational cost

Inlet water depthElementsModelNumber of time stepsTime step sizeMax iterationsNumber of processorsCalculation time
0.15 m 27,716 RNG k–ε model 1,000 0.005 s 20 1 1.93 h 
0.15 m 27,716 Realizable k–ε model 1,000 0.005 s 20 1 1.87 h 
Inlet water depthElementsModelNumber of time stepsTime step sizeMax iterationsNumber of processorsCalculation time
0.15 m 27,716 RNG k–ε model 1,000 0.005 s 20 1 1.93 h 
0.15 m 27,716 Realizable k–ε model 1,000 0.005 s 20 1 1.87 h 
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Figure 10
Comparison between simulated and test results of water depth on the stairs.
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Comparison between simulated and test results of water depth on the stairs.

Figure 10
Comparison between simulated and test results of water depth on the stairs.
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Comparison between simulated and test results of water depth on the stairs.

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Numerical simulation results

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A numerical simulation of water flow characteristics was conducted on the pedestrian stairs and escalators at the B1 entrance of the Shakou Road subway station on Line 5 of Zhengzhou urban rail transit under flood invasion (Figure 11). The slope of the pedestrian stairs was 26.6° (with a step height of 0.08 m and a step width of 0.16 m), the slope of the escalators was 26.6° (with a step height of 0.1 m and a step width of 0.2 m), and the water depth at the entrance of both stairs was 0.15 m.
Figure 11
Staircase at B1 entrance of the Shakou Road subway station.
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Staircase at B1 entrance of the Shakou Road subway station.

Figure 11
Staircase at B1 entrance of the Shakou Road subway station.
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Staircase at B1 entrance of the Shakou Road subway station.

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Water flow pattern on the pedestrian stair

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Figures 12 and 13 depict the water velocity and depth on the pedestrian stairs, respectively. The conversion of gravitational potential energy to kinetic energy during the water flow process causes the water velocity to rise, as shown in Figure 12. The water velocities on the 2nd and 76th steps are 0.82 and 2.82 m/s, respectively. The water velocity increased 2 m/s from the upper to the lower part of the stairs. The water velocities at the 22nd, 42nd, and 58th steps are 1.95, 2.2, and 2.06 m/s, respectively. The water velocities after the 22nd, 42nd, and 58th steps are 2.52, 3.20, and 2.95 m/s, respectively. Therefore, the water velocities have increased by 0.57, 1.0, and 0.89 m/s, respectively, due to the presence of a resting platform. The water velocities are 0.82 and 2.82 m/s on the 2nd and 76th steps, respectively, rising by 2 m/s from the top of the steps to the bottom. Water velocities are 1.95, 2.20, and 2.06 m/s at the 22nd, 42nd, and 58th steps, and water velocities are 2.52, 3.20, and 2.95 m/s after the 22nd, 42nd, and 58th steps, respectively. As a result, the water velocities have increased by 0.57, 1.0, and 0.89 m/s, respectively. This is due to the existence of a resting platform in the center of the steps causing water disorder, resulting in a rapid rise in water velocity behind the platform. As illustrated in Figure 13, the presence of a resting platform might result in an increase in water depth of up to 0.04 m.
Figure 12
Water velocity on the stair.
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Water velocity on the stair.

Figure 12
Water velocity on the stair.
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Water velocity on the stair.

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Figure 13
Water depth on the stair.
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Water depth on the stair.

Figure 13
Water depth on the stair.
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Water depth on the stair.

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The variation of the escape control index F for stairs at different slopes is shown in Figure 14. The evolution of the escape control index F is related to the water velocity and depth and increases with the increase in water velocity and depth. Ishigaki et al. (2006) proposed that when the escape control index is less than 1.2 m3/s2, the evacuation of people on stairs is safe. The escape control index on the 48th step is 1.19 m3/s2, which is close to the limit value, indicating that the presence of a rest platform causes an increase in the velocity and depth of water on the stairs behind the platform, increasing the risk of safe evacuation of people. As a result, when a subway station floods, it is suggested that people use stairs without rest platforms to evacuate.
Figure 14
Changes in the escape control index F on the stair.
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Changes in the escape control index F on the stair.

Figure 14
Changes in the escape control index F on the stair.
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Changes in the escape control index F on the stair.

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Water flow process on the pedestrian stair

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The water flow process of the staircase at an inlet water depth of 0.15 m is shown in Figure 15. The flood had not reached the first resting platform on the steps when it invaded for about 2 s (Figure 15(a)) and the water proceeded to spread downstream. It had traversed the first resting platform in 4 s (Figure 15(b)), reached three resting platforms in 8 s (Figure 15(d)), and was nearing the bottom of the stairs in 10 s (Figure 15(e)). However, the depth of the water on and below the steps at this time was not great. As the water continues to flow, the gravitational potential energy of the water is transformed into kinetic energy, and the water velocity and depth progressively tend to stabilize at 20 s (Figure 15(g)). The existence of the rest platform causes the water velocity to accelerate and increases the water depth on the steps behind the rest platform, which is consistent with the previous conclusion. It is recommended that people avoid using stairs with rest platforms when evacuating.
Figure 15
Water flow process on the pedestrian stair. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 10 s. (f) Contour of water volume fraction at 14 s. (g) Contour of water volume fraction at 20 s.
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Water flow process on the pedestrian stair. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 10 s. (f) Contour of water volume fraction at 14 s. (g) Contour of water volume fraction at 20 s.

Figure 15
Water flow process on the pedestrian stair. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 10 s. (f) Contour of water volume fraction at 14 s. (g) Contour of water volume fraction at 20 s.
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Water flow process on the pedestrian stair. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 10 s. (f) Contour of water volume fraction at 14 s. (g) Contour of water volume fraction at 20 s.

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Water flow pattern on the escalator

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Figures 16 and 17 show the water velocity and depth on the escalator, respectively. It can be seen in Figure 16 that as the water gradually spreads on the escalator, the water velocity gradually increases. The water velocity on the escalator gradually stabilizes when it rises to around 2.46 m/s because there is no resting platform on the escalator. The water depth on the escalator is stable throughout the entire escalator and has been maintained at around 0.128 m, as shown in Figure 17.
Figure 16
Water velocity on the escalator.
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Water velocity on the escalator.

Figure 16
Water velocity on the escalator.
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Water velocity on the escalator.

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Figure 17
Water depth on the escalator.
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Water depth on the escalator.

Figure 17
Water depth on the escalator.
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Water depth on the escalator.

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The variation of the escape control index F on the escalator is shown in Figure 18. The overall trend of the escape control index on the escalator is consistent with the trend of the water velocity on the escalator because the water depth tends to be a constant value. The escape control index is less than the crucial number, suggesting that the escalator evacuation is safe. As a result, during the evacuation process, people should try to choose stairs without rest platforms. For the selection of escalators, it is necessary to consider whether their power has been turned off and whether they have sufficient safety and stability to avoid electric shock and falls during evacuation.
Figure 18
Evolution of the escape control index F on the escalator.
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Evolution of the escape control index F on the escalator.

Figure 18
Evolution of the escape control index F on the escalator.
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Evolution of the escape control index F on the escalator.

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Effect of inlet water depth and slope

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This study established three physical models of stair slopes that are suitable for pedestrian walking to simulate based on the subway design code (Code for design of metro (GB 50157-2013)). The slope of the staircase is 29.7° (with a step height of 0.08 m and a step width of 0.14 m), 28.1° (with a step height of 0.08 m and a step wide of 0.15 m), and 26.6° (with a step height of 0.08 m and a step width of 0.16 m), respectively. The escalator has a slope of 26.6 ° (with a step height of 0.1 m and a step width of 0.2 m). Four simulated situations with different inlet water depths were used, namely 0.09, 0.12, 0.15, and 0.18 m. The 16 distinct calculation circumstances were investigated illustrated in Table 3.

Table 3

Numerical simulation conditions

ConditionStep slopeRest platformSimulated inlet depth (m)
1 29.7° Yes 0.09 
2 29.7° Yes 0.12 
3 29.7° Yes 0.15 
4 29.7° Yes 0.18 
5 28.1° Yes 0.09 
6 28.1° Yes 0.12 
7 28.1° Yes 0.15 
8 28.1° Yes 0.18 
9 26.6° Yes 0.09 
10 26.6° Yes 0.12 
11 26.6° Yes 0.15 
12 26.6° Yes 0.18 
13 26.6° No 0.09 
14 26.6° No 0.12 
15 26.6° No 0.15 
16 26.6° No 0.18 
ConditionStep slopeRest platformSimulated inlet depth (m)
1 29.7° Yes 0.09 
2 29.7° Yes 0.12 
3 29.7° Yes 0.15 
4 29.7° Yes 0.18 
5 28.1° Yes 0.09 
6 28.1° Yes 0.12 
7 28.1° Yes 0.15 
8 28.1° Yes 0.18 
9 26.6° Yes 0.09 
10 26.6° Yes 0.12 
11 26.6° Yes 0.15 
12 26.6° Yes 0.18 
13 26.6° No 0.09 
14 26.6° No 0.12 
15 26.6° No 0.15 
16 26.6° No 0.18 
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Effect of inlet water depth on water flow pattern and safe evacuation

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Figure 19 depicts the water velocity and depth on the staircase slope of 26.6°. The water velocity and depth on the stairs rise as the water depth increases. As shown in Figure 19(a), under the inlet water depths of 0.09, 0.12, 0.15, and 0.18, the water velocity range on the staircase is 0.58–2.02, 0.63–2.61, 0.82–3.17, and 1.00 − 3.40 m/s, respectively. At this time, the maximum velocities occur at the 62nd, 64th, 48th, and 52nd steps, and the difference between the maximum and minimum velocities is 1.44, 1.98, 2.35, and 2.40 m/s, respectively. The difference in water velocity between the maximum inlet water depth of 0.18 m and the minimum inlet water depth of 0.09 m is 0.42–1.38 m/s. As shown in Figure 19(b), the water depth at the 22nd, 40th, and 58th steps has changed due to the presence of a resting platform. Under the inlet water depth conditions of 0.09, 0.12, 0.15, and 0.18 m, the maximum water depth at the 22nd, 40th, and 58th steps is 0.13, 0.15, 0.18, and 0.21 m, respectively. The maximum water depth under the inlet water depth of 0.18 m is 0.08 m higher than the inlet water depth of 0.09 m.
Figure 19
Staircase slope: 26.6°. (a) Water velocity on the stair. (b) Water depth on the stair.
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Staircase slope: 26.6°. (a) Water velocity on the stair. (b) Water depth on the stair.

Figure 19
Staircase slope: 26.6°. (a) Water velocity on the stair. (b) Water depth on the stair.
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Staircase slope: 26.6°. (a) Water velocity on the stair. (b) Water depth on the stair.

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The water velocity and depth on the staircase slope of 28.1° is depicted in Figure 20. As shown in Figure 20(a), under the inlet water depths of 0.09, 0.12, 0.15, and 0.18 m, the water velocity range on the staircase is 0.60–2.23, 0.78–2.68, 0.85–2.87, and 0.98–3.32 m/s, respectively. The difference between the maximum and minimum velocities is 1.63, 1.90, 2.02, and 2.34 m/s, and the maximum velocities occur at the 64th, 64th, 50th, and 36th steps, respectively. The difference in water velocity between the maximum inlet water depth of 0.18 m and the minimum inlet water depth of 0.09 m is between 0.38 and 1.09 m/s. As shown in Figure 20(b), the water depth at the 22nd, 40th, and 58th steps has changed due to the presence of a resting platform. Under the inlet water depth conditions of 0.09, 0.12, 0.15, and 0.18 m, the maximum water depth at the 22nd, 40th, and 58th steps is 0.14, 0.16, 0.18, and 0.2 m, respectively. The maximum water depth under the inlet water depth of 0.18 m is 0.07 m higher than the inlet water depth of 0.06 m.
Figure 20
Staircase slope: 28.1°. (a) Water velocity on the stair. (b) Water depth on the stair.
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Staircase slope: 28.1°. (a) Water velocity on the stair. (b) Water depth on the stair.

Figure 20
Staircase slope: 28.1°. (a) Water velocity on the stair. (b) Water depth on the stair.
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Staircase slope: 28.1°. (a) Water velocity on the stair. (b) Water depth on the stair.

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Figure 21 depicts the water velocity and depth on the staircase slope of 29.7°. As shown in Figure 21(a), under the inlet water depths of 0.09, 0.12, 0.15, and 0.18 m, the velocity range of the water on the staircase is 0.58–2.36, 0.69–2.64, 0.80–3.18, and 1.06–3.42 m/s, respectively. The maximum velocities at this time occur at the 46th, 46th, 76th, and 32nd steps, and the difference between the maximum and minimum velocities is 1.78, 1.95, 2.38, and 2.36 m/s, respectively. The difference in water velocity between the maximum inlet water depth of 0.18 m and the minimum inlet depth of 0.09 m is between 0.48 and 1.06 m/s. As shown in Figure 21(b), the water depth at the 22nd, 40th, and 58th steps has changed due to the presence of a resting platform. Under the inlet water depth conditions of 0.09, 0.12, 0.15, and 0.18 m, the maximum water depth on the 22nd, 40th, and 58th steps is 0.14, 0.16, 0.19, and 0.20 m, respectively. The maximum water depth under the inlet water depth of 0.18 m is 0.06 m higher than the inlet water depth of 0.09 m.
Figure 21
Staircase slope: 29.7°. (a) Water velocity on the stair. (b) Water depth on the stair.
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Staircase slope: 29.7°. (a) Water velocity on the stair. (b) Water depth on the stair.

Figure 21
Staircase slope: 29.7°. (a) Water velocity on the stair. (b) Water depth on the stair.
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Staircase slope: 29.7°. (a) Water velocity on the stair. (b) Water depth on the stair.

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Effect of staircase slope on water flow pattern and safe evacuation

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Figure 22 depicts the effect of the staircase slope on the water velocity and depth on the stairs at different inlet water depths. The water velocity increases with the inlet water depth increases. The water velocity on stairs does not vary significantly under three stair slopes suitable for people walking. This is due to the small range of stair slope variation and the relatively similar water flow pattern on stairs.
Figure 22
Water velocity under different inlet water depths. (a) Inlet water depth: 0.09 m. (b) Inlet water depth: 0.12 m. (c) Inlet water depth: 0.15 m. (d) Inlet water depth: 0.18 m.
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Water velocity under different inlet water depths. (a) Inlet water depth: 0.09 m. (b) Inlet water depth: 0.12 m. (c) Inlet water depth: 0.15 m. (d) Inlet water depth: 0.18 m.

Figure 22
Water velocity under different inlet water depths. (a) Inlet water depth: 0.09 m. (b) Inlet water depth: 0.12 m. (c) Inlet water depth: 0.15 m. (d) Inlet water depth: 0.18 m.
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Water velocity under different inlet water depths. (a) Inlet water depth: 0.09 m. (b) Inlet water depth: 0.12 m. (c) Inlet water depth: 0.15 m. (d) Inlet water depth: 0.18 m.

Close modal
The variation of the escape control index F for stairs at different slopes is shown in Figure 23. The evolution of the escape control index F is related to water velocity and depth. As shown in Figure 23, with the gradual increase in water depth, the escape control index increases. Moreover, under three different slopes, the escape control index under the inlet water depth of 0.18 m is greater than the limit value of 1.2 m3/s2 after the 22nd step (i.e., the mutation caused by the first rest platform). This indicates that when the inlet water depth is greater than 0.18 m, the water velocity and depth on the stairs are larger, which will have an impact on the evacuation of personnel on the stairs. The water velocity and depth on the stairs at the entrance of a subway station increase with the increase in the inlet water depth, and the F near the rest platform can reach 1.63 m3/s2, which exceeds the critical safety value of 1.2 m3/s2, increasing the risk of personnel safe evacuation. Therefore, in the design process of subway stations, water blocking and drainage facilities need to be provided at the entrance to avoid water flowing onto the stairs and affecting the safety of people.
Figure 23
Impact of stair slope on the change of the escape control index F. (a) Staircase slope: 26.6°. (b) Staircase slope: 28.1°. (c) Staircase slope: 29.7°.
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Impact of stair slope on the change of the escape control index F. (a) Staircase slope: 26.6°. (b) Staircase slope: 28.1°. (c) Staircase slope: 29.7°.

Figure 23
Impact of stair slope on the change of the escape control index F. (a) Staircase slope: 26.6°. (b) Staircase slope: 28.1°. (c) Staircase slope: 29.7°.
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Impact of stair slope on the change of the escape control index F. (a) Staircase slope: 26.6°. (b) Staircase slope: 28.1°. (c) Staircase slope: 29.7°.

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Effect of inlet water depth on the water intrusion process

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Figure 24 depicts the water flow process of the Shakou Road subway station B1 staircase under the inlet water depth of 0.09 m. The flood had not yet reached the first rest platform on the stairs when it invaded for about 4 s (Figure 24(b)), and the water continued to spread downstream. It had already passed the first rest platform after 6 s (Figure 24(c)). As previously stated, the presence of the rest platform would cause the water velocity to accelerate; however, due to the shallow depth of the inlet water, the third resting platform only reached 14 s (Figure 24(e)). As the water continues, it reaches the bottom of the staircase about 18 s (Figure 24(f)), but there is not much water below the staircase at this time, and it has not entirely spread to the end. As the water continues to flow, it reaches the bottom of the staircase fully at approximately 24 s (Figure 24(g)) and progressively achieves a stable velocity and depth condition at about 30 s (Figure 24(h)).
Figure 24
Water flow process on the staircase under the inlet water depth of 0.09 m. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 14 s. (f) Contour of water volume fraction at 18 s. (g) Contour of water volume fraction at 24 s. (h) Contour of water volume fraction at 30 s.
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Water flow process on the staircase under the inlet water depth of 0.09 m. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 14 s. (f) Contour of water volume fraction at 18 s. (g) Contour of water volume fraction at 24 s. (h) Contour of water volume fraction at 30 s.

Figure 24
Water flow process on the staircase under the inlet water depth of 0.09 m. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 14 s. (f) Contour of water volume fraction at 18 s. (g) Contour of water volume fraction at 24 s. (h) Contour of water volume fraction at 30 s.
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Water flow process on the staircase under the inlet water depth of 0.09 m. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 14 s. (f) Contour of water volume fraction at 18 s. (g) Contour of water volume fraction at 24 s. (h) Contour of water volume fraction at 30 s.

Close modal
The water flow process of the staircase under the inlet water depth of 0.12 m is shown in Figure 25. The water had not yet reached the first resting platform on the stairs when it invaded for about 2 s (Figure 25(a)), and the water continued to spread downstream. It had already passed the first resting platform at 4 s (Figure 25(b)). The water completely crossed three rest platforms at 10 s (Figure 25(e)) but did not reach the bottom near the bottom of the steps at roughly 12 s (Figure 25(f)). As the water continues to flow, it reaches the bottom of the steps at 16 s and continues to flow (Figure 25(g)). The water velocity and depth start to stabilize at 26 s (Figure 25(h)).
Figure 25
Water flow process on the staircase under the inlet water depth of 0.12 m. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 10 s. (f) Contour of water volume fraction at 12 s. (g) Contour of water volume fraction at 16 s. (h) Contour of water volume fraction at 26 s.
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Water flow process on the staircase under the inlet water depth of 0.12 m. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 10 s. (f) Contour of water volume fraction at 12 s. (g) Contour of water volume fraction at 16 s. (h) Contour of water volume fraction at 26 s.

Figure 25
Water flow process on the staircase under the inlet water depth of 0.12 m. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 10 s. (f) Contour of water volume fraction at 12 s. (g) Contour of water volume fraction at 16 s. (h) Contour of water volume fraction at 26 s.
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Water flow process on the staircase under the inlet water depth of 0.12 m. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 10 s. (f) Contour of water volume fraction at 12 s. (g) Contour of water volume fraction at 16 s. (h) Contour of water volume fraction at 26 s.

Close modal
Figure 26 depicts the water flow process of the staircase at the entrance with a water depth of 0.18 m. The water had already reached the first rest platform on the stairs when it invaded for about 2 s (Figure 26(a)), and the water proceeded to spread downstream. It had already reached the second rest platform at 4 s (Figure 26(b)). At about 6 s, the water had already arrived at the third rest platform (Figure 26(c)). It reaches the bottom of the staircase in about 8 s (Figure 26(d)). However, the water depth on and below the stairs has become small. As the water continues to flow, the water velocity and depth condition tend to stabilize (Figure 26(h)).
Figure 26
Water flow process on the staircase under the inlet water depth of 0.18 m. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 10 s. (f) Contour of water volume fraction at 12 s. (g) Contour of water volume fraction at 14 s. (h) Contour of water volume fraction at 16 s.
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Water flow process on the staircase under the inlet water depth of 0.18 m. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 10 s. (f) Contour of water volume fraction at 12 s. (g) Contour of water volume fraction at 14 s. (h) Contour of water volume fraction at 16 s.

Figure 26
Water flow process on the staircase under the inlet water depth of 0.18 m. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 10 s. (f) Contour of water volume fraction at 12 s. (g) Contour of water volume fraction at 14 s. (h) Contour of water volume fraction at 16 s.
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Water flow process on the staircase under the inlet water depth of 0.18 m. (a) Contour of water volume fraction at 2 s. (b) Contour of water volume fraction at 4 s. (c) Contour of water volume fraction at 6 s. (d) Contour of water volume fraction at 8 s. (e) Contour of water volume fraction at 10 s. (f) Contour of water volume fraction at 12 s. (g) Contour of water volume fraction at 14 s. (h) Contour of water volume fraction at 16 s.

Close modal

When the inlet water depth is 0.09 m, the water can flow from above the stair to below after 18 s, and the flow pattern tends to stabilize after about 30 s. When the inlet water depth is 0.12 m, the water can flow from above the stair to below after 16 s, and the flow pattern tends to stabilize after about 26 s. When the inlet water depth is 0.15 m, the water can flow from above the stair to below after 10 s, and the flow pattern tends to stabilize after about 20 s. When the inlet water depth is 0.18 m, the water can flow from above the stair to below after 8 s, and the flow pattern tends to stabilize after about 16 s. As the depth of the inlet water increases, the water above the staircase can reach the lower part faster and gradually stabilize. Therefore, to reduce the risk of people evacuating on stairs, it is recommended that water-blocking facilities be installed at the entrance of subway stations to reduce water flow onto the stairs.

Water flow pattern and safety evacuation assessment on the escalator

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The different water depths at the entrance have an impact on the water flow pattern and safe evacuation on the escalator. Figure 27 shows the water velocity and depth on the escalator when the slope of the staircase is 26.6°. As the depth of water at the entrance increases, the water velocity and depth on the staircase gradually increase and tend to stabilize. Because there is no resting platform on the escalator, the water cannot be accelerated. As shown in Figure 27(a), the velocity range of the water on the staircase is 0.63–1.73, 0.87–2.37, 1.06–2.50, and 1.25–2.65 m/s under the condition of water depth of 0.09, 0.12, 0.15, and 0.18 m. The difference between the maximum and minimum velocities is 1.10, 1.50, 1.44, and 1.40 m/s, respectively. The difference in water velocity between the maximum inlet water depth of 0.18 m and the minimum inlet water depth of 0.09 m is within the range of 0.62–0.92 m/s. The water depth on the steps was stabilized, as indicated in Figure 27(b). The water depth on the steps remains roughly 0.11, 0.12, 0.13, and 0.14 m under the water depth of 0.09, 0.12, 0.15, and 0.18 m, respectively. The water depth difference between the maximum inlet water depth of 0.18 m and the lowest inlet water depth of 0.09 m is 0.03 m.
Figure 27
Water flow pattern at different inlet depths. (a) Water velocity on the escalator. (b) Water depth on escalator.
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Water flow pattern at different inlet depths. (a) Water velocity on the escalator. (b) Water depth on escalator.

Figure 27
Water flow pattern at different inlet depths. (a) Water velocity on the escalator. (b) Water depth on escalator.
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Water flow pattern at different inlet depths. (a) Water velocity on the escalator. (b) Water depth on escalator.

Close modal
Figure 28 depicts the escape control index F in different inlet water depths on the escalator, and the general pattern is comparable to the water velocity in Figure 28(a). As the depth of the entering water grows, the escape control index F steadily rises and tends to stabilize. The escape control index F of the escalator is 0.07–0.19, 0.10–0.28, 0.14–0.32, and 0.17–0.37 m3/s2, respectively, under the inlet water depths of 0.09, 0.12, 0.15, and 0.18 m. The escape control index is less than the pedestrian staircase escape control index and does not exceed the allowed value of 1.2 m3/s2. This is because the energy consumption effect of the escalator is greater than that of the pedestrian staircase due to its unique structural design, and the water velocity and depth of the escalator are mostly constant compared to those on the pedestrian staircase. The presence of rest platforms may cause mutations. Therefore, choosing an escalator for evacuation is relatively safe. However, it is necessary to consider the safety and stability of escalators to avoid electric shock and falls during evacuation.
Figure 28
Effect of inlet water depth on the escalator escape control index.
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Effect of inlet water depth on the escalator escape control index.

Figure 28
Effect of inlet water depth on the escalator escape control index.
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Effect of inlet water depth on the escalator escape control index.

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This study developed a numerical simulation model for the water flow on stairs based on the realizable k–ε model and the VOF model, which can be applied to simulate the water flow characteristics on stairs in subway stations. Take the most widely used island-style station, Shakou Road subway station, as the case study. The water flow characteristics on the step at the B1 entrance on the Shakou Road subway station were investigated under the different slopes, with/without a rest platform, and different inlet water depths. The risk of personnel safety evacuation on the stairs was evaluated, and the real-time water flow process on the stairs at different inlet water depths was simulated. The suggestions for people evacuation and subway design were presented and can provide references for other similar subway stations. The following are the main conclusions:

  • (1) The presence of rest platforms causes water velocity and depth increase in the stairs, with velocity and depth increasing from 1 and 0.12 m to 3.4 and 0.21 m, respectively. The sudden increase in water depth and velocity caused the escape index near the rest platform to exceed the critical safety value of 1.2 m3/s2, which increases the evacuation risk for people. However, the staircase slope that is suitable for walking has a relatively minor effect on the water depth and velocity of the staircase, which has little impact on the safe evacuation of people.

  • (2) The water velocity and depth on the escalator are relatively stable, and the escape index on the escalator does not exceed the limit value of 1.2 m3/s2, which is lower than the pedestrian staircase. This phenomenon is caused by the lack of rest platforms on escalators. As a result, it is suggested that people choose stairs without rest platforms for evacuation. Moreover, it is important to ensure that the escalator has sufficient safety and stability to avoid electric shock and falls during evacuation in designing subway stations.

  • (3) The water above the staircase can reach the lower part faster as the depth of the inlet water increases. When the inlet water depth is 0.09, 0.12, 0.15, and 0.18 m, the water can flow from above the staircase to below after passing through 18, 16, 10, and 8 s, respectively. Therefore, to reduce the risk of people evacuating on stairs, it is recommended that water blocking and drainage facilities be provided at the entrance to avoid water flowing onto the stairs and affecting the safety of people in the design process of subway stations.

Overall, this study developed a numerical simulation model for the water flow on stairs based on the realizable k–ε model and the VOF model. It may be applied to simulate the water flow characteristics on stairs in subway stations. A study was conducted on the water flow patterns on the pedestrian stairs and escalators at the B1 entrance of the Shakou Road subway station, which is the most widely used island-style station. The results are expected to facilitate the flood control design of subway stations and the risk assessment of personnel evacuation. However, this study did not investigate the flow pattern of water on stairs during people evacuation or its effect on personnel evacuation. Since the high density of people evacuating on stairs, future studies are suggested to the changes in water flow patterns during evacuation on pedestrian stairs and escalators, as well as the safety and stability performance of escalators under human evacuation and flood impact. The evolution of water flow patterns on stairs during people evacuation is crucial for assessing the safe evacuation of people within subway stations.

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This work was supported by the Key Research and Development Project of Henan Province (grant number: 241111322600), Open Foundation of National Engineering Research Center of High-speed Railway Construction Technology (grant number: HSR202304), Science and Technology Research Project of Henan Province (grant number: 242102241012) and the Program for High Level Talents Fund Project of Henan University of Technology (grant number: 2023BS060).

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All relevant data are included in the paper or its Supplementary Information.

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The authors declare there is no conflict.

Chen
B.
,
Gong
H.
,
Chen
Y.
,
Li
X.
 &
Zhao
X.
 (
2020
)
Land subsidence and its relation with groundwater aquifers in Beijing Plain of China
,
Sci. Total Environ.
,
735
,
139111
.
Google Scholar
Crossref
Search ADS
PubMed
 
Cui
J.
 &
Nelson
J.
 (
2019
)
Underground transport: An overview
,
Tunn. Undergr. Space Technol.
,
87
,
122
–
126
.
Google Scholar
Crossref
Search ADS
 
Forero Ortiz
E.
 &
Martínez Gomariz
E.
 (
2020
)
Hazards threatening underground transport systems
,
Nat. Hazard.
,
100
,
1243
–
1261
.
Google Scholar
Crossref
Search ADS
 
Gotoh
H.
,
Ikari
H.
,
Sakai
T.
 &
Tanioka
H.
 (
2010
)
Computational mechanics of a force on a human leg in flow over a underground staircase in urban flood
,
Doboku Gakkai Ronbunshuu B
,
50
,
865
–
870
.
Google Scholar
 
Hou
J.
,
Chen
G.
,
Zhang
Y.
,
Li
B.
,
Yang
S.
,
Tong
Y.
,
Zhang
D.
 &
Fu
D.
 (
2022
)
A simulation study on risks of pedestrian evacuation from flooded staircases of different slopes in the underground space
,
Nat. Hazards.
,
110
,
519
–
543
.
Google Scholar
Crossref
Search ADS
 
Ishigaki
T.
,
Keiichi
T.
 &
Kazuya
I.
 (
2003
)
Hydraulic model tests of inundation in urban area with underground space
,
IAHR Congress, Disaster Prevention Research Institute, Kyoto University, Japan
.
Google Scholar
 
Ishigaki
T.
,
Toda
K.
,
Baba
Y.
,
Inoue
K.
 &
Nakagawa
H.
 (
2006
)
Experimental study on evacuation from underground space by using real size models
,
Annu. Disaster Prev. Res. Inst.
,
50
,
583
–
588
.
Google Scholar
 
Jiang
L.
,
Shao
W.
,
Zhu
D.
 &
Sun
Z.
 (
2014
)
Forces on surface-piercing vertical circular cylinder groups on flooding staircase
,
J. Fluid Struct.
,
46
,
17
–
28
.
Google Scholar
Crossref
Search ADS
 
Kositgittiwong
D.
,
Chinnarasri
C.
 &
Julien
P.
 (
2013
)
Numerical simulation of flow velocity profiles along a stepped spillway
,
Proc. Inst. Mech. Eng., Part E: J. Process Mech. Eng.
,
227
,
327
–
335
.
Google Scholar
Crossref
Search ADS
 
Liang
C.
,
Guo
K.
 &
Guan
M. F.
 (
2024
)
Computational hydraulics and hazard assessment of flooding on underground staircases
,
Tunn. Undergr. Sp. Tech.
,
144
,
105511
.
Google Scholar
Crossref
Search ADS
 
Liu
Y.
,
Okada
N.
,
Shen
D.
 &
Li
S.
 (
2009
)
Agent-based flood evacuation simulation of life-threatening conditions using vitae system model
,
Jpn Soc. Nat. Disaster Sci.
,
31
,
69
–
77
.
Google Scholar
Crossref
Search ADS
 
Lyu
H.
,
Shen
S.
,
Zhou
A.
 &
Yang
J.
 (
2019
)
Perspectives for flood risk assessment and management for mega-city metro system
,
Tunn. Undergr. Space Technol.
,
84
,
31
–
44
.
Google Scholar
Crossref
Search ADS
 
Mo
W.
 (
2010
)
Numerical Simulation of Water Intrusion Process in Subway Stations and Research on Disaster Prevention Strategies
.
Hangzhou
:
ZheJiang University
.
Google Scholar
 
Mori
T.
,
Kotani
K.
,
Asao
T.
,
Horii
K.
,
Ishigaki
T.
,
Baba
Y.
 &
Toda
K.
 (
2009
)
Identification of the optimum gait pattern for descending stairs in a flooded condition: An electromyographic study
,
Proc. Annu. Meet. Jpn Ergon. Soc.
,
4
,
456
–
457
.
Google Scholar
 
Shadmehri Toosi
A.
,
Calbimonte
G.
,
Nouri
H.
 &
Alaghmand
S.
 (
2019
)
River basin-scale flood hazard assessment using a modified multi-criteria decision analysis approach: A case study
,
J. Hydrol.
,
574
,
660
–
671
.
Google Scholar
Crossref
Search ADS
 
Shao
W.
,
Jiang
L.
,
Zhang
Y.
,
Zhu
D.
 &
Sun
Z.
 (
2014
)
Hydraulic features of air-water mixture flow on a staircase with rest platforms
,
J. Hydraul. Eng.
,
140
,
4010
–
4016
.
Google Scholar
Crossref
Search ADS
 
Shao
W.
,
Jiang
L.
,
Fang
L.
,
Zhu
D.
 &
Sun
Z.
 (
2015
)
Assessment of the safe evacuation of people walking through flooding staircases based on numerical simulation
,
J. Zhejiang Univ. Sci. A
,
16
,
117
–
130
.
Google Scholar
Crossref
Search ADS
 
Toda
K.
,
Oyagi
R.
,
Inoue
K.
 &
Aihata
S.
 (
2002
)
On the inundation process in the underground space
,
Annu. Rep. Inst. Disaster Pre, Kyoto Univ.
,
42
,
293
–
302
.
Google Scholar
 
Toda
K.
,
Kuriyama
K.
,
Oyagi
R.
 &
Inoue
K.
 (
2004
)
Inundation analysis of complicated underground space
,
Proc. Hydral. Eng.
,
47
,
877
–
882
.
Google Scholar
Crossref
Search ADS
 
Valdenebro
J.
,
Gimena
F.
 &
Javier
L.
 (
2019
)
Construction process for the implementation of urban utility tunnels in historic centres
,
Tunn. Undergr. Space Technol.
,
89
,
38
–
49
.
Google Scholar
Crossref
Search ADS
 
Xu
S.
 &
Zhou
Z.
 (
2022
)
Study on 7·20 extreme rainstorm and metro line flood control in Zhengzhou
,
Water Res. Hydro. Eng.
,
53
,
41
–
54
.
Google Scholar
 
Yoneyama
N.
,
Toda
K.
,
Aihata
S.
,
Yamamoto
D.
, (
2009
)
Numerical analysis for evacuation possibility from small underground space in urban flood
. In:
Zhang
C.
 &
Tang
H.
 (eds.)
Advances in Water Resources and Hydraulic Engineering
,
Berlin
:
Springer
, pp.
107
–
112
.
Google Scholar
Crossref
Search ADS
 
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