Numerical Analysis of Flood Invasion Path and Mass Flow Rate in Subway Stations under Heavy Rainfall Conditions

Abstract

The occurrence of extreme weather, such as heavy rainfall and sudden increases in precipitation, has led to a notable rise in the frequency of flooding in subway stations. By conducting numerical simulations of flood disasters in subway stations under heavy rainfall conditions and gaining insights into the patterns of flood invasion inside the stations, it is possible to develop practical and feasible drainage designs for the stations. This paper employs the computational fluid dynamics (CFD) method, utilising the volume of fluid function (VOF) method and the renormalization k-ε group model within the vortex viscosity model. The complete process of flood invasion into subway stations with varying water levels (1500 mm, 2000 mm, and 2450 mm) is modelled, and the distribution of floods at different times under varying operational conditions is analysed to identify the evolutionary patterns of station flood history. The simulation calculations yielded the mass flow rate time history curve at the tunnel entrance and exit, which was then subjected to an analysis of its development trend over time. The total accumulated water in the subway station is calculated by integrating the difference in mass flow rate between the entrance and the tunnel exit, using the mass flow rate curve. In conclusion, the paper proposes drainage measures that provide valuable insights into pumping strategies when floodwaters infiltrate subway stations. The results indicate that the speed of flood spreading in subway stations increases with higher groundwater levels, and that the mass flow rate of floodwater entering the tunnels increases over time, eventually reaching a stable state. It was observed that, at certain times, the mass flow rate of floodwater into the tunnels exhibited a linear relationship with time.

1. Introduction

Subways serve as a vital instrument for advancing economic and social growth, functioning as a significant conduit for enhancing the quality of life of urban dwellers [1,2]. In recent years, global temperatures have continued to rise at an abnormal rate, leading to the frequent occurrence of extreme weather events such as heavy and very heavy rainfall worldwide [3,4,5]. On 20 July 2021, Zhengzhou, China [6], was subjected to exceptionally heavy precipitation. A considerable number of underground railway lines, including stations on Lines 1 and 2, were inundated. A considerable volume of water accumulated in the Wulongkou car park and the surrounding areas of Line 5, resulting in a breach of the retaining wall and the inundation of the main section of the subway, which ultimately led to casualties. On 25 July 2021, South London was subjected to a precipitation event that resulted in the inundation of numerous underground railway stations. On 1 September 2021, New York, United States, was struck by Hurricane Ida, resulting in a sudden rainstorm and flooding of multiple subway stations. The resilience of underground spaces is limited [7]. Flood disasters present a range of challenges, including rapid infiltration but slow drainage, difficulties in evacuation and rescue, diverse flood invasion paths, and significant damage and loss [8]. Floods can infiltrate subway stations through various pathways, including entrances, exits, elevator shafts, ventilation shafts, and tunnels [9,10]. This poses a significant risk to both the internal space and the people within the station.

A substantial body of scholarship has been devoted to the phenomenon of flooding in subways, with notable advances having been made in this field of inquiry. The extant literature can be classified into two principal categories. The initial category of research comprises physical experimental simulation studies on the phenomenon of flood invasion. Keiichi, Kensaku [11] were the first to establish a three-dimensional urban complex block flood test model. The process and flow characteristics of surface floods invading underground spaces from multiple entrances and flowing along stairs were subjected to analysis. Taisuke, Keiichi [12] conducted simulation experiments on the evacuation of personnel from underground streets and subway station stairs during water ingress using a 1:1 scale model. Additionally, they conducted experiments to test the hypothesis that opening basement doors would facilitate escape to the ground. Shao, Jiang [13] employed a 1:2 scale physical model to investigate the characteristics of flood flow on staircases with intermediate resting platforms. Baba and Ishigaki [14] investigated the difficulties associated with the evacuation of underground spaces through the utilisation of three physical models: doors, stairs, and cars. The limitations of safe evacuation were also explored. Ishigaki, Asai [15] conducted an investigation into the efficacy of a safety evaluation method for the elderly, using both experimental results and numerical simulations of underground space flooding. The second category of research employs numerical simulation through the use of computer-assisted fluid dynamics. Toda, Kawaike [16] employed a horizontal two-dimensional submerged flow model based on unstructured grids, an underground submerged flow model based on pond models, and a runoff model based on motion wave models to predict underground submergence. Ishigaki, Kawanaka [17] employed numerical methods to investigate the susceptibility of subterranean areas to extreme flood intrusion and the challenges associated with evacuation during such events. Li, Xia [18] employed the LES model in conjunction with the VOF method to investigate the flow characteristics and fluid–human interactions occurring on stairs. A risk assessment was conducted based on fluid dynamics modelling and mechanical instability analysis. Hitoshi, Hiroyuki [19] employed the particle method to calculate the hydrodynamic forces acting on model legs positioned on stairs. Kim, Rhee [20] put forth an adaptive transmission method to more accurately simulate underground flooding during two-layer connections, while circumventing alterations in grid size due to local model details.

A variety of techniques have been utilised by scholars to simulate the process of flood inundation into subway stations, as previously investigated in the literature [21,22,23,24,25]. In their study, Chen, Dai [24] employed a combination of the VOF and k-ε models to simulate turbulent flows, resulting in precise simulations of the free surface, velocity, and pressure on complex step spillways. The simulation outcomes were found to be in close alignment with the measured data, thereby substantiating the efficacy of turbulent numerical simulation for overflow scenarios in intricate step spillways. Cheng, Chen [21] integrated the renormalization group (RNG) k-ε model with VOF, demonstrating superior simulation capabilities in comparison to the standard k-ε model in capturing the flow dynamics of stepped spillways. Qian et al. [23] employed the VOF model in conjunction with the realizable k-ε, shear stress transport k-ω, v²-f, and large eddy simulation (LES) turbulence models, and concluded that the realizable k-ε model is the most effective method for simulating the flow of stepped spillways. Kositgittiwong, Chinnarasri [22] conducted an analysis of the flow velocity profile of a stepped spillway using a range of turbulence models, including the standard k-ε, realizable k-ε, RNG k-ε, standard k-ω, and shear stress transport k-ω models. The results of this analysis demonstrated that all of the aforementioned models yielded satisfactory simulation results. Several studies [21,22,23,25] have highlighted the efficacy of the RNG k-ε model in accurately simulating turbulence in flood scenarios within subway stations.

The studies referenced above have demonstrated that numerical simulation has facilitated a deeper comprehension of the flood intrusion process in subterranean environments. The research primarily concentrates on the flooding trend in each subway, the various means of egress for individuals within each subway station, and the limitations of the designated evacuation level. Nevertheless, the current body of research still exhibits certain limitations and gives insufficient consideration to the following areas. (1) The path of floodwater ingress into subway stations; (2) the total volume of water accumulating within stations; and (3) the variation in floodwater flow rates into tunnels. This article presents a case study of Xinxiu Park Station in Nanning City, China. The VOF gas–liquid two-phase flow method was employed in conjunction with the k-ε model to simulate the spatial distribution of floods at varying time intervals within the subway station. Subsequently, the total accumulated water volume within the station was quantified under simulated operational conditions. Furthermore, we analysed the temporal changes in floodwater mass flow rates entering the tunnel and proposed appropriate drainage measures.

2. Construction of Numerical Calculation Model

2.1. Turbulence Mathematical Model and VOF Model

The principal turbulence models are the Spalart model, the k-ε model, the Reynolds stress model, and the large eddy simulation (LES) model, among others. The Spalart model is primarily employed in the field of aeronautics for the simulation of wall-confined flows. The Reynolds stress model does not necessarily yield superior results to the k-ε model for general reflux flow. However, it is a computationally demanding approach that necessitates a high level of computational resources. The LES model is only applicable to three-dimensional problems, yet it is a highly computationally intensive model. In conclusion, the k-ε model has been selected for inclusion in this article. The aforementioned models comprise the standard k-ε model, the RNG k-ε model, and the realizable k-ε model. The RNG k-ε model and the realizable k-ε model demonstrate superior accuracy in comparison to the standard model. Given the complex layout of the subway station under study, comprising numerous columns, the RNG k-ε model was selected as the turbulence model for this research. In order to reduce the complexity of the model and the computational workload, the components of the subway station were simplified during the modelling process. For example, stairs were represented as sloping surfaces, as the primary focus of the article is not the flow of floodwater over stairs, and this simplification has a minimal impact. The transport equations for the RNG k-ε model are as follows:

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho k\right)+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho k{u}_i\right)={\displaystyle \frac{\partial }{\partial x_j}}\left({\alpha }_k{\mu }_{eff}{\displaystyle \frac{\partial k}{\partial x_j}}\right)+G_k+G_b-\rho \epsilon -Y_M+S_k$$

(1)

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho \epsilon \right)+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho \epsilon u_i\right)={\displaystyle \frac{\partial }{\partial x_j}}\left({\alpha }_{\epsilon }{\mu }_{eff}{\displaystyle \frac{\partial \epsilon }{\partial x_j}}\right)+C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}\left(G_k+C_{3\epsilon }{G}_b\right)-C_{2\epsilon }\rho {\displaystyle \frac{{\epsilon }^2}{k}}-R_{\epsilon }+S_{\epsilon }$$

(2)

where G_k denotes the turbulent kinetic energy generation term due to the mean velocity gradient; G_b is the buoyancy-induced turbulent kinetic energy generation term; Y_M represents the contribution of the pulsating expansion to the total dissipation rate in compressible turbulence; α_k and α_ε are the inverse of the effective Prandtl number for k and ε, respectively; and S_k and S_ε are user-defined source terms.

A further objective of this article is to provide an accurate representation of the position of the flood liquid level, which is a fundamental aspect in determining the volume occupied by the flood. The volume of fluid (VOF) method is typically employed and is widely recognised for delineating interfaces between two or more immiscible fluids [26,27,28]. In the VOF model, the sum of the volume fractions for all fluids is equal to one. It thus follows that if the volume fraction of each fluid (phase) is denoted as α_q, it holds that ${\displaystyle \sum }{\alpha }_q=1$. In this study, the model treats the fluids as two distinct phases, air and water, which are immiscible, constituting a gas–liquid two-phase flow. The VOF model provides an accurate determination of the liquid level position, expressed as ${\alpha }_w+{\alpha }_a=1$.

2.2. Construction of Numerical Models for Subway Stations

This article employs Xinxiu Park Station in Nanning City, China as the exemplar for this simulation, as illustrated in Figure 1. The models were constructed using CAD drawings. The station features an island platform with two levels: the hall and the platform. The effective length of the station is 120 m, with both the platform and station hall measuring 20.3 m in width. The internal configuration of the station exhibits a uniform distribution between the hall and platform. These are connected by means of stairs, escalators, and elevators. Three passages are identified as S1, S2, and S3 (Figure 2). The S1 and S3 passages are flanked by escalators, with stairs situated in the centre. The staircase designated as S2 is a split staircase. The central section of the primary structure incorporates three apertures aligned with the tunnel axis, which are utilized in the construction of the aforementioned stairways. The station has three entrances and exits, designated A, B, and C. Entrance/exit A is relatively uncomplicated, featuring only stairs with minimal distance from the stairs to the platform floor. The configuration of Entrance/Exit B and C is analogous, with a comparatively greater distance from the entrance stairs to the station hall floor. Both B and C comprise a combination of straight-running stairs, dual parallel stairs, and elevators. The elevators are situated in close proximity to the staircase, while the dual parallel stairs are located at a midway point between the entrance stairs and the station hall floor. The station hall floor is situated at an elevation of 4.3 m above ground level, with a height of 10.7 m. The platform floor is situated at an elevation of 4.05 m from ground level, with a height of 14.75 m. The tunnel section is rectangular in shape and measures 5400 mm in length by 4050 mm in width. In order to conduct simulations of flooding, the entrances and exits of the subway station are designated as inlets, while the tunnels in which vehicles are operated serve as the outlets for flooding, as illustrated in Figure 3.

2.3. Model Meshing and Boundary Condition Setting

The grid division area is the space within the subway station where fluid can exist (Figure 3). The blue arrow indicates the entrance of the model, while the red arrow indicates the exit of the model. The mesh is divided using poly-hexcore, which is less numerous and faster to compute than other mesh types. The article presents three distinct working conditions. In order to verify the independence of the meshes, calculations are carried out with the boundary conditions of Case 3 in order to test the results. In the verification process, a variety of cell numbers and grid shapes are employed for analysis. The flow rate at the tunnel exit was calculated when the floodwater invaded the subway station at t = 1 s, as illustrated in

Table 1. Tests for grid independence.

Test Number	Number of Grid Cells (×106)	Mass Flow Rate at Tunnel Exit (kg/s)
1	0.2	98.26
2	0.4	65.32
3	0.9	60.13
4	1.4	59.01
5	1.7	57.99
6	2.4	57.35
7	2.8	56.30
8	3.3	56.37

and Figure 4. At this juncture, the fluid at the tunnel exit is air. As the number of grids increases, the results in the table demonstrate a progressive convergence towards a specific value. As the number of grids increases, the calculation becomes more accurate. Nevertheless, when the number of grids is excessive, the computational burden increases significantly, while the accuracy improvement is relatively modest. At this juncture, the mesh is exhibiting boundary effects. Accordingly, a grid of test 4 was selected for analysis in the article.

The article employs the VOF method to determine the location of the flood level by the finite element method. Also, a surface tension model is used, and the surface tension coefficient of water is set constant at 0.071 N/m. Turbulence simulation is carried out using the RNG k-ε model. The mathematical model is solved by the SIMPLE method.

In the context of boundary conditions, the specification of water level heights at inlets is categorised into three distinct types: water inlet, air inlet, and fluid outlet. A velocity inlet is specified on the input surface with a mean velocity for the water inlet, whereas other inlets and outlets are designated as pressure inlets and pressure outlets. As the inlet and outlet are directly connected to the external environment, the pressure inlet and pressure outlet are both at atmospheric pressure. The text makes the assumption that air is incompressible. If air were compressible, the cumulative volume of air within a subway station would increase, thereby raising the air pressure inside. Such a change would consequently impact the pressure level at the pressure inlet and, in turn, the velocity magnitude at the water inlet. Nevertheless, this is at odds with the simulation setup, which assumes air to be incompressible throughout. In flood simulations, an initial velocity is assumed to be present when water enters subway stations. The classification of water flow and air at the entrance results in a fluid volume fraction of 1 at the water inlet. While water inlets are used to specify flood heights, it is important to note that, in reality, flood heights rarely remain constant; they fluctuate. This discrepancy has an impact on the realism of the water levels. In order to ascertain the flow velocity of floods at the entrance, Jiang [29] constructed a 1:2 physical model of a subway station entrance staircase for experimental purposes. The relationship between the single-width flow rate of floodwater intrusion into the underground space and the water depth of groundwater accumulation is obtained, as illustrated by the following Equation (3):

$$q=1.417H^{1.5}$$

(3)

where, q is the unit width flow rate, in m²/s; and H is the surface water depth, in m.

3. Simulation of Water Intrusion into Subway Station Operating Conditions

The simulated subway station is situated in an area where the highest recorded water level with a 100-year return period is 2900 mm.

Table 2. Maximum water level at subway station.

Highest Water Level Information	Water Level/Elevation (m)
The most unfavourable water level within the station section with a 100-year return period	76.40
Station entrance ground elevation	73.50
Highest water level	2.90

indicates that, with a height of 450 mm for the three steps at the station entrance and exit, the highest water level on the station steps is 2450 mm. In simulating this station, the primary consideration is the analysis of flood flow and distribution under varying water levels at different times.

Table 3. Working condition simulation settings.

Condition Number	Depth of Water
Condition 1	1500 mm
Condition 2	2000 mm
Condition 3	2450 mm

outlines the assumed operational conditions based on different water level heights.

3.1. Analysis of Flood Invasion Situation

In accordance with the aforementioned operational conditions, the flood-spreading area continues to expand over time until it encompasses the entirety of the subway station and subsequently flows into the tunnel. The progression is illustrated in Figure 5a–g and Figure 6a–g, which depict the distribution of the flood at various time intervals when the flood height outside the station is 1500 mm, referred to as Condition 1 in Table 3. At the 10 s mark, the floodwaters had all passed through the stairwells at the entrances (Figure 5a). The phenomenon of rapid air movement above the water current was observed at all entrances (Figure 6a). This was due to the fact that when the velocity of the water flow was higher, the pressure above it was lower, which resulted in an acceleration of the flow of air. As the floodwater reached the bottom of the stairs, its velocity increased. The lowest point of the staircase in Entrance B was situated in close proximity to the elevator wall. As the floodwater approached the wall, it was observed to move at a relatively high velocity. Concurrently, the floodwaters descended the elevator shaft at high velocity (Figure 6b). The floodwater proceeded to flow towards the wall at each corner of the double-run staircase at a high velocity (Figure 6c). At time point t = 20 s, the floodwater entered the platform level at A, while the floodwater at the other entrances had not yet reached platform level (Figure 5b). At t = 30 s, the floodwater from all entrances reached the platform level (Figure 5c). Some floodwater gained access to the station floor via S1 and S2. As the staircase proceeded in a downward direction, the velocity of the water flow increased (Figure 6d,e). At t = 60 s, the entire station level was inundated (Figure 5d). The floodwater gained access to the station floor via three distinct routes. A vortex was observed to form at passage S2 and subsequently flowed in a downward direction (Figure 6g). Analysing the 90 s, 150 s, and 480 s cloud diagrams, it was found that the height of the flood in the subway station gradually increased with time after the flood had completely inundated the subway station (Figure 5e–g). The mass flow rate of the floodwater at the tunnel outlet at 480 s of floodwater intrusion was determined to be 41,728 m³. The mass flow rate at the entrance was consistently recorded at 43,303 m³. At this juncture, the discrepancy between the two values is 1575 m³, which represents 3.64% of the mass flow rate at the entrance. The percentage is relatively insignificant, and it can be posited that the total volume of floodwater within the station remains largely unaltered following 480 s of floodwater intrusion. The intrusion process thus reached a conclusion. The station is comprised of a straightforward configuration, with a discernible trajectory of floodwater intrusion. The floodwater flows from a higher elevation to a lower elevation, gradually covering the entire subway station. Upon entering the subway station, the flood flows into the station hall floor, subsequently traversing the staircase openings situated in the centre of the station hall floor, and finally, into the platform floor. Ultimately, the floodwater enters the tunnel and flows out of the subway station. This conclusion is consistent with Lin’s assertion that both flows originate from the platform level and subsequently enter the station level before exiting via the tunnel. The overall time required for floods to invade subway stations is relatively brief, leaving a limited window of opportunity for individuals within the station to evacuate. It is therefore recommended that people be evacuated as soon as possible before the floodwater enters the subway station to avoid being trapped.

The distribution of floods across a cloud map varies under different working conditions due to the varying heights of flood invasion at the same time point. Figure 7 illustrates the extent of flood inundation resulting from the inundation of subway stations by 1500 mm, 2000 mm, and 2450 mm floods for a 30 s duration. Upon reaching a height of 1500 mm, the volume fraction of water in the entrance channel and station hall levels was minimal, with the flooded area being constrained and only a limited quantity of floodwater traversing the S1 channel (Figure 7a). Upon reaching a height of 2000 mm, the floodwater began to accumulate in the station hall level, accompanied by a notable increase in the volume of water within the entrance channel. It was observed that floodwater was flowing through both the S1 and S3 channels (Figure 7b). Upon reaching a height of 2450 mm, the area inundated by floodwater in the station hall level exhibited a notable expansion, accompanied by a considerable increase in the volume of water. The floodwater inundated passages S1, S2, and S3 (Figure 7c). A comparison of the velocity vector plots for the three conditions reveals that the velocity distributions are similar for all three conditions (Figure 8). All of the aforementioned scenarios result in the maximum air flow velocity occurring above the flood inlet. Vortices are readily formed at S1, S2 and S3 irrespective of the presence or absence of water. The aforementioned comparison demonstrates that as the height of the floodwater intrusion increases, the intrusion speed also increases. Consequently, the volume of water entering the subway station increases over the same duration, resulting in a wider distribution range of floods and continued accumulation of water. In order to mitigate the aforementioned risks, it is recommended that water barriers or other flood control measures be installed at entrances in order to reduce the height of invading floods, control the spread of floods within subway stations, and prevent flood overflow into tunnels, which could impact other critical sections and stations of the subway system.

3.2. Trend of Mass Flow Rate Changes

In this paper, the mass flow rate at the station entrance and the tunnel exit, and their difference (D-value), are statistically plotted over time when floodwater intrudes into the station, as illustrated in Figure 9a–c. A comparison of the three graphs in Figure 9 reveals that the three working conditions exhibit comparable trends. From the mass flow rate at the tunnel exit, it can be observed that the floodwater commences its flow into the tunnel following an interval of time during which it has been in the station. The initial mass flow rate of the floodwater is relatively low. The mass flow rate into the tunnel demonstrates an increase over time, with a initially rapid growth rate that subsequently decelerates. Concurrently, the central portion of the curve exhibits a linear correlation. The D-value curve persists in its decline with the passage of time, and its overall trajectory is antithetical to that of the mass flow rate curve at the tunnel exit. A comparison of the three operating conditions reveals that, with a constant water inflow, the mass flow rate from the subway station to the tunnel exhibits a steady increase over time, ultimately reaching a fixed value equivalent to the inflow at the station entrance. Therefore, the total accumulated water within the station remains relatively constant. Moreover, it was determined that the lower the flood elevation of the intruding subway station, the longer it takes for the flood volume to stabilise within the station and the more gradual the mass flow rate-time curve.

The results of the simulation were found to be linear. In order to guarantee the accuracy of the aforementioned numerical results, a theoretical derivation was conducted for verification purposes. As previously stated, the relationship between the inflow of water in the subsurface space and the depth of water in front of the surface inlet can be expressed as follows:

$$Q=a{h}_w^b$$

(4)

where, Q is the single width flow rate at the entrance of the underground space (m²/s); h_w is the depth of water on the ground at the entrance of the underground space (m); and a, b are obtained from Equation (3).

Owing to

$$h_w=v_{t}t-h_e$$

(5)

where $v_t$ is the road surface water rising speed (m/s); t is the length of time water has been standing outside the station(s); and $h_e$ is the step height in front of the entrance to the underground space (m), we find that

$$Q=a{\left(v_{t}t-h_e\right)}^b$$

(6)

Integrating the flow rate in Equation (6) over the length of time, the total amount of floodwater inflow to the subsurface space at a given T-second moment is calculated and can be expressed as

$$V_T={\displaystyle \frac{aB}{v_t\left(b+1\right)}}{\left(v_{t}T-h_e\right)}^{b+1}$$

(7)

where B is the width of the entrance staircase to the underground space (m). Then the depth of water $h_T$ (m) in the underground space at T seconds is

$$h_T={\displaystyle \frac{V_T-h_{T}S}{A_{s1}}}$$

(8)

where $A_{s1}$ is the flooded floor area in the underground space (m²), due to the faster rate of flood water intrusion as well as more subway entrances. Therefore, it can be assumed that the flooded area in the underground space $A_{s1}$ is equal to the area of the underground space $A_s$, and S is the area that the water flowed through per unit of time at the tunnel exit (m), so

$$h_T={\displaystyle \frac{aB{\left(v_{t}T-h_e\right)}^{b+1}}{v_t\left(b+1\right)\left(A_{s1}+S\right)}}$$

(9)

Therefore, the rate of rise of the groundwater level $u_t$ (m/s) is

$$u_t={\displaystyle \frac{aB{\left(v_{t}T-h_e\right)}^b}{\left(A_s+S\right)}}$$

(10)

In the numerical simulation setup, the depth of the water in front of the surface portal is maintained at a constant value. Consequently, when the floodwater inundates the entire underground space, the depth of water in the groundwater will increase steadily at some point between the initial inundation and the subsequent equilibrium state. The unit outflow of floodwater from the tunnel is linear with respect to time, which is consistent with the simulation results.

3.3. Total Water Accumulation and Drainage in Subway Stations

In the event of a simulated high water level intrusion occurring in reality, the subsequent flood drainage at subway stations is of greater consequence than the evacuation of passengers. In order to ascertain the subsequent drainage measures, it is first necessary to determine the quantity of accumulated water in the subway station as a result of flooding. By integrating the time using the “D-value” mass flow rate presented in Figure 9a–c, it is possible to ascertain the total accumulated water volume within the station. The volume of accumulated water in a subway station is determined by the area enclosed by the mass flow rate curve and the time axis, representing the difference between flood inflow and outflow. In the calculation, the composite trapezoidal integral was employed. The cumulative volume of floodwater in the subway station under the three working conditions is calculated to be 9301 m³, 11,779 m³, and 15,239 m³, as illustrated in

Table 4. Flood accumulations within the station for floods of different heights.

Depth of Water/mm	Flood Accumulations Within the Station/m3
1500	9301
2000	11,779
2450	15,239

. The lack of comprehensive data precludes the establishment of a definitive numerical correlation between the accumulated water volume within the subway station and the flood height. Nevertheless, it can be discerned that as the height of the floodwater outside the station rises, the volume of accumulated water inside the station will correspondingly increase. In the event of the station being drained, the ingress of floodwater at the level of the flood invasion presents a significant risk to the safety of the personnel on site. Accordingly, the objective of the drainage design is to prevent flooding of the station, with the accumulated flood inside the station considered a fixed value. It is assumed that the flood will not flow into the tunnel through the station, and that the water in the tunnel will not flow back into the station during the pumping process. The pumping time is typically measured in hours (h), whereas the water flow inside the station changes rapidly, often in seconds (s). In the absence of new inflow, the accumulated water in the station hall level will inevitably flow into the platform level over time. If the space occupied by the stairs is not taken into account, the space available for fluid flow on the platform floor is approximately 17,610 m³, which is sufficient to accommodate all accumulated flooding within the subway station. Industrial water pumps can be classified into the following categories according to their intended function: clean water pumps, hot water pumps, corrosion-resistant pumps, oil pumps, sewage pumps, impurity slurry pumps, submersible pumps, vacuum pumps, and specialised pumps. In light of the heterogeneous nature of the flooding within a station, comprising a mixture of water and sedimentary materials, it is evident that the most appropriate pumping apparatus would be a sewage pump, given that its primary function is to remove water from a given environment.

The QW (WQ) type non-clogging submersible sewage pump exhibits a number of advantageous characteristics, including a compact overall structure, a relatively small volume, low noise levels, a significant energy-saving effect, convenient maintenance, the ability to operate without the necessity of constructing a pump room, and the capacity to function by diving into the water, which greatly reduces engineering costs. In the event of flooding within a subway station, this type of sewage pump can be utilised as a pumping facility. In the process of pumping water, the sewage pump is situated within the tunnel and pumped directly from the tunnel, resulting in an actual head of 14.75 m. When selecting a specific model, it is recommended to choose a submersible sewage pump with a head that is slightly higher than the actual head. Consequently, in light of the considerable accumulation of floods, it is imperative to select submersible sewage pumps with enhanced power and calibre. In consideration of the aforementioned factors, the 250QW600-15-55 submersible sewage pump is selected, exhibiting a rated pumping capacity of 600 m³/h, a power of 55 kW, and an efficiency of 75%. In the event of pumping at an elevation of 14.75 m, the actual pumping capacity is 1027.33 m³/h. Should the pumping capacity exceed the rated pumping capacity to a significant extent, it will inevitably result in damage to the sewage pump. Accordingly, a pumping capacity of 700 m³/h is proposed.

The volume of accumulated water within the station is subject to variation in accordance with the specific operational conditions, and the number of pieces of equipment utilised is also contingent upon these conditions, resulting in a corresponding variation in the required drainage times. The specific circumstances are illustrated in

Table 5. Drainage conditions under different working conditions.

(a) Drainage Situation of 1500 mm Flood Invading Subway Stations
Option	Water Pump/set	Pumping Time/h
Option 1	1	13.3
Option 2	2	6.7
Option 3	3	4.5
Option 4	4	3.4
(b) Drainage Situation of 2000 mm Flood Invading Subway Stations
Option	Water Pump/set	Pumping Time/h
Option 1	1	16.9
Option 2	2	8.5
Option 3	3	5.6
Option 4	4	4.2
(c) Drainage Situation of 2450 mm Flood Invading Subway Stations
Option	Water Pump/set	Pumping Time/h
Option 1	1	14.9
Option 2	2	7.5
Option 3	3	5.0
Option 4	4	3.7

.

It is recommended that drainage facilities, such as pumps, be provided at both the platform level and the station concourse level during the construction of metro stations. In the event of an unforeseen occurrence, such as the intrusion of floodwater into the metro station, a prompt and appropriate response can be initiated.

4. Conclusions

This paper addresses the accumulation of floodwater in the subway station and its subsequent outflow through the tunnel when the water level rises to a level that causes flooding. The objective of the numerical simulation of incoming floods is to develop a contingency plan for future emergencies:

(1)

The manner in which floodwater ingress occurs into subway stations remains consistent regardless of the varying flood heights. In the majority of cases, floodwater enters the subway via the entrance, flows through the station hall level, descends via staircases to the platform level, and eventually reaches the tunnels. Irrespective of the internal configuration of the station, the floodwater is subject to the force of gravity and continues to spread in a downward direction from the entrance of the metro station.

(2)

As flood levels outside the station rise, the speed and extent of floodwater ingress into the subway station increase in parallel. This results in a greater extent of inundation and an increase in the volume of water accumulating within the station. As the height of the floodwater outside the subway station increases, so too does the volume of water accumulating within the station.

(3)

When the flood elevation intruding into a subway station is uniformly constant, the mass flow rate of flood water entering the station varies with time and has the following pattern. It can be demonstrated that for a specific duration, the mass flow rate of floodwater into the tunnel increases in a linear fashion over time. Prior to this, the rate of increase in floodwater mass flow into the tunnel is observed to accelerate. Subsequently, the rate of increase stabilises and becomes constant.

(4)

The present study is limited in several respects, which suggest avenues for future research. The article does not consider the drainage capacity of the station itself. In practice, the station’s infrastructure is capable of accommodating a proportion of the water. Additionally, the actual floodwater levels at the entrance are subject to fluctuations due to external factors such as precipitation and runoff, which were not accounted for in this study. Furthermore, the accumulation of sediment at the flood bottom has the potential to impact the pumping rates, a factor that was not addressed in this study.