A Numerical Simulation Study on the Spread of Mine Water Inrush in Complex Roadways

Abstract

Emergency water release from underground reservoirs is characterized by its suddenness and significant harm. The quantitative prediction of water spreading processes in mine tunnels is crucial for enhancing underground safety. The study focuses on an underground roadway in a coal mine, constructing a three-dimensional physical model of the complex tunnel network to explore the spatiotemporal characteristics of water flow spreading after water release in coal mine tunnels. The Volume of Fluid (VOF) model of the Eulerian multiphase flow was adopted to simulate the flow state of water in the roadway. The results indicate that after water release from the reservoir, water flows along the tunnel network towards locations with relatively lower altitude terrain. During the initial stage of water release, sloping tunnels act as barriers to water spreading. The water level height at each point in the tunnel network generally experiences three developmental stages: rapid rise, slow increase, and stable equilibrium. The water level height in the tunnel area near the water release outlet rises sharply within a time range of 550 s; tunnels farther from the water release outlet experience a rapid rise in water level height only after 13,200 s. The final stable equilibrium water level in the tunnel depends on the location of the water release outlet and the relative height of the terrain, with a water level height ranging from 0.3 to 3.3 m. The maximum safe evacuation time for personnel within a radius of 300 m from the drainage outlet is only 1 h. In contrast, areas farther away from the drainage location benefit from the water storage capacity of the complex tunnel network and have significantly extended evacuation opportunities.

1. Introduction

Mine water disasters pose a significant threat to the safe production of mines. These disasters easily damage underground equipment and hinder normal mining operations [1], often requiring costly repairs and causing prolonged production delays [2]. In severe cases, uncontrolled water influx may directly lead to the abandonment of the mining area, while posing life-threatening risks to workers through sudden flooding or destabilized workings [3,4]. In recent years, numerical simulation has made remarkable progress in the field of mine safety and planning. Regarding the sudden water inrush caused by emergency water drainage in underground coal mines, researchers have deeply explored key issues such as the mechanism of sudden water inrush, the evolution process of disasters, and emergency response strategies through numerical simulation methods, which have greatly promoted the development of mine safety prevention and control technologies.

Water inrush in underground roadways is extremely hazardous, posing significant threats to miners’ lives, causing substantial damage to mining equipment and disrupting production activities. Researchers have conducted extensive studies on the mechanisms of water inrush. Li et al. [5] conducted a study on the mechanism of water inrush from the floor in deep coal mine exploitation, using Fast Lagrangian Analysis of Continua (FLAC 3D) to simulate the activation and development process of floor fractures under the dynamic load of roof collapse. The large number of numerical simulations have been used to reconstruct the dynamic process of the inrush. A comprehensive investigation was performed to examine the interactive progression among stress distribution [6], deformation patterns, and fluid migration dynamics within geological formations [7,8], while critical early warning indicators were systematically identified and characterized [9,10].

In exploring the spatiotemporal evolution law of water flow spreading in roadways, researchers have carried out a great deal of work. Wu Qiang et al. [11,12] established the concept of proof and model technology of water flow spreading in roadways during mine water inrush, which can simulate and obtain the evolution of water flow in underground roadways, thereby assisting in the scientific implementation of emergency rescue for water disasters. Wang et al. [13] employed the computational fluid dynamics (CFD) software CFX to simulate the propagation dynamics of water inrush within bifurcated roadway sections. By analyzing computational data of water level, flow rate, and pressure, the study systematically examined the influence of roadway slope gradient and inflow discharge magnitude of hydrodynamic spreading patterns. Pathfinding algorithms represent a prevalent computational approach for simulating water inrush propagation, primarily incorporating mine structural configurations, graph theory principles, and the characteristic downward-to-upward propagation dynamics of water inrush events. These algorithms enable semi-quantitative computational frameworks to identify water spread pathways within specified timeframes. Li et al. [14] implemented graph-theoretic algorithms to identify water inrush propagation pathways, subsequently applying the Chézy formula to determine propagation velocities and temporal progression. Wu et al. [15] established a roadway model with adjustable gradients and carried out tests on personnel stability and the walking speed of people wading through water under various water flow conditions in roadways with different gradients.

The safe evacuation of personnel during water inrush incidents in underground mines has attracted scholarly attention [16]. The dynamic routing algorithm was developed to identify time-critical evacuation routes in temporal networks, specifically addressing emergency scenarios induced by underground mine water influx [17,18]. Ma et al. [19] established an evacuation time matrix within graph theory constructs, subsequently deriving a tactical navigation system that dynamically adjusts escape routes during mining hydraulic emergencies. Researchers have explored algorithmic approaches to optimize evacuation path planning in mining flood disasters. The researchers proposed to improve the Dijkstra algorithm, which enhances the practicality and effectiveness of the algorithm in complex scenarios. As a result, it becomes possible to calculate the optimal water-evading path when water inrush occurs underground [20,21]. There are also scholars who have combined the Dijkstra algorithm with the breadth-first search algorithm and conducted simulations in the water inrush scenarios of a three-dimensional virtual space [22,23]. Yang et al. [24] constructed a virtual simulation scene with 3D roadway and personnel models based on OpenGL, conducted a visual simulation of emergency evacuation, and evaluated and analyzed the simulation results. They subsequently developed a reference technical framework for the emergency evacuation of underground space workers. A human–environment–computer interaction system was developed, which combines the A*-3D Time algorithm with mixed reality (MR) technology [25]. Ji et al. [26] established a visualization model for the evacuation of personnel in underground mines and simulated the evacuation process of personnel in underground mines. Through the simulation, information such as evacuation time, exit flow rate, and evacuation routes was obtained. However, the influence of dynamic fluctuations in underground tunnel water levels on personnel evacuation duration remains critically understudied.

Based on the above analysis, scholars have carried out extensive research in the field of mine water disasters, mainly focusing on aspects such as the mechanism of water inrush, the spatiotemporal evolution of water flow propagation, and the safety evacuation of personnel. Currently, the research methods mainly involve the use of numerical simulation software such as FLAC 3D and Storm Water Management Model (SWMM) [27], and the research objects are concentrated on water inrush of different scales, bifurcated roadways, and “H”-shaped roadway structures. However, due to the complexity of the underground roadway network, the research on the law of water flow propagation within the complex underground roadway network during water inrush accidents is very limited. In order to systematically understand the law of water flow spreading in the complex underground network and deepen the understanding of the fluid transport mechanism in the mining space, this study selects a roadway network with a complex underground structure as the research object. The RNG k-ε turbulence model and the Eulerian multiphase flow model (VOF) are adopted to simulate the flow state of water in the roadway. At the same time, in order to ensure the accuracy of the simulation, the volume fraction, momentum equation, and turbulence equation are all discretized using the second-order upwind scheme. This study systematically explores the spatiotemporal evolution law of water flow propagation in a complex roadway network. Taking the spatiotemporal changes in the water level elevation in the roadway as the key criterion, it provides a theoretical basis for the safe evacuation of underground personnel.

2. Numerical Method

2.1. Physical Model

The geometrically constrained physical roadway model in this study was computationally reconstructed using photogrammetric survey data from operational mining panels at Shigetai Mine. Shigetai Coal Mine is located in the northern part of the Shenmu North Mining Area of the Northern Shaanxi Jurassic Coalfield. It has experienced a marine–continental evolutionary process from the Paleozoic to the present. During the Late Paleozoic, coastal plain-type Carboniferous–Permian strata were deposited. In the Mesozoic, coal-bearing formations of the inland lake system and red rock series were deposited. In the Cenozoic, influenced by inland uplift and subsidence and arid climate, reddish-brown and yellowish-brown sub-clay, sub-sand, and sand layers were formed. The coal-bearing strata belong to the Early–Middle Jurassic Yan’an Formation, and the Triassic strata serve as the sedimentary basement of the coal-measure strata. The coal mine storage water goaf of Shigetai Mine was completed in 2016. The goaf as a whole is higher in the east and lower in the west, with a length of about 2170 m and a width of about 1865 m. The maximum water storage area of the underground reservoir is 1.36 million square meters, and the maximum water storage capacity is about 1.714 million cubic meters. The elevation of the goaf floor is 1078–1107 m. Based on the occurrence conditions and hydraulic characteristics of groundwater, the aquifers in the mining area are divided into pore phreatic water in the Cenozoic loose layers, fissure phreatic water and confined water in the Mesozoic clastic rocks, as well as fissure and karst phreatic water in the burnt-altered rocks. The process of water inrush spreading and its inundation scope directly determine the severity of the underground disaster situation. Based on the principle of hydrodynamics, the main driving forces of water flow movement are gravity (i.e., elevation difference) and pressure (i.e., water pressure difference). Among them, the mine structure determines the elevation variations at each location and is a crucial factor influencing water flow movement; the inflow conditions, including the inlet position, water inrush volume, and duration, constitute the specific driving source of water flow movement. The mine structure, the position of the water inrush inlet, the volume of water inrush and its duration, etc., jointly determine the spreading process of water inrush and the inundation degree of the mine. In this study, a physically representative model featuring a complex tunnel network was adopted. This model incorporates variations in elevation across different sections of the tunnels, reflecting the true underground environment more accurately.

The physical model can be seen from Figure 1. It adopts full-scale modeling, with a tunnel width of 5 m and a height of 3.4 m. The total length of the roadway is approximately 2170 m, and the roadway structure is relatively complex. As can be seen from Figure 2, the roadway network presents a pattern of multiple roadways in parallel. The types of each branch roadway include long roadways, bifurcated roadways, T-shaped roadways, etc., and some roadways have a circular structure. During grid division, the impact of grid size in the VOF model on the capture accuracy of gas–liquid interfaces was considered. In total, 15 and 10 grids were used to fill the tunnel width and height, respectively. The grid division adopted a poly-hexcore method, which uses polyhedral grids at the tunnel walls to ensure a good fit, and hexahedral grids inside the tunnel to ensure accurate capture of gas–liquid interfaces. The total number of grids in the tunnel is 3.17 million. The height of the underground water level is 15 m, and the size of the dam’s water inlet is 1 m × 0.5 m. After the dam bursts, water flows into the tunnel in this area, flowing along the tunnel terrain at different heights. In terms of boundary condition settings, an inlet was set at the front end of the tunnel near the water-accumulated area, with an inlet water flow rate of 0.90 m³/s. The outlet was set as a free-flow outlet to simulate water flowing out of the tunnel under natural conditions. In the simulation, kinetic energy loss of water flowing on a rough wall was considered, with a roughness coefficient of 0.5 and a roughness height of 0.01 m.

2.2. Governing Equation

Mine water inrush exhibits flow characteristics such as high inertial force, unsteadiness, non-uniformity, transition between rapid and slow flow, and coexistence and alternation of open and full flow. Based on the flow state of water within the tunnel, the calculation model employs the Eulerian multiphase flow model (VOF) based on the liquid surface tracking method to simulate the flow state of water in the tunnel. Due to the slow exchange of velocity, temperature, and pressure between water and air, which has no significant impact on their densities, the simulation process is treated as incompressible flow. Furthermore, the flow of water and air is time-dependent, and its momentum equation is as follows:

$${\displaystyle \frac{\partial \left(\rho \overrightarrow{v}\right)}{\partial t}}+\nabla ·\left(\rho \overrightarrow{v}\times \overrightarrow{v}\right)=-\nabla P+\nabla ·\left[\mu \left(\nabla \overrightarrow{v}+\nabla {\overrightarrow{v}}^T\right)\right]+\rho \overrightarrow{g}+\overrightarrow{F}$$

(1)

$\overrightarrow{v}=\left(x,y,z\right)$ represents the fluid velocity; ρ and μ represent the density and dynamic viscosity coefficient of the fluid, respectively; $\overrightarrow{g}$ is the acceleration of gravity; and $\overrightarrow{F}$ is the additional source term force at the interface. When studying the relationship between the gas–liquid interface and time, the explicit interface tracking method is commonly used in the VOF model. The volume fraction equation of the q-phase is discretized according to the following formula:

$${\displaystyle \frac{{\alpha }_q^{n+1}{\rho }_q^{n+1}-{\alpha }_q^n{\rho }_q^n}{\Delta t}}V+{\sum }_f\left({\rho }_q^{n+1}{U}_f^{n+1}{\alpha }_{q,f}^{n+1}\right)=\left[S_{{\alpha }_q}+{\sum }_{P=1}^n\left({\dot{m}}_{pq}-{\dot{m}}_{qp}\right)\right]V$$

(2)

The volume fraction of the main phase is constrained and calculated using the following equation:

$${\sum }_{q=1}^n{\alpha }_q=1$$

(3)

n+1 represents the index of the current time step; n is the index of the previous time step; ${\alpha }_q^{n+1}$ represents the volume fraction of the grid at time step n + 1; ${\alpha }_q^n$ represents the volume fraction of the grid at time step n; ${\alpha }_{q,f}^{n+1}$ represents the q phase volume fraction of the grid at time step n + 1; $U_f^{n+1}$ represents the volumetric flux passing through the grid surface at time step n + 1; and V represents the grid volume. ${\dot{m}}_{qp}$ represents the mass transfer from phase q to phase p; ${\dot{m}}_{pq}$ represents the mass transfer from phase p to q; and the source term S_α equals zero.

The flow state of water in the tunnel belongs to turbulence, and the RNG k-ε turbulence model is commonly used in complex open full-flow problems. This model can handle complex water flow problems such as large curvature, strong pressure gradient, and swirling flow. The governing equation is

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

(4)

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

(5)

G_K represents the turbulent kinetic energy generation term due to the average velocity gradient; and G_b represents the turbulent kinetic energy generation term caused by buoyancy. Y_M represents the contribution of pulsating expansion in compressible turbulence to the total dissipation rate. α_k and α_ε are the reciprocal of the effective Prandtl numbers of k and ε, respectively. S_k and S_ε are user-defined source terms.

2.3. Distribution of Water Level Height Measuring Points

In order to comprehensively analyze the variation law of the height of the water level at each position of the roadway with the flow time, 34 monitoring points were set up along the distance between the roadway and taking into account the characteristics of the intersection, slope, bifurcation, and other road sections. As evident from the layout of water level monitoring points in Figure 2, the roadway exhibits characteristics such as slope, intersection, bifurcation, and corners. As can be seen from Figure 2, the lowest point of the roadway is designated as the reference point for zero height, and the corresponding relative terrain height of each water level monitoring point is indicated.

Figure 2 shows the inlet of the tunnel model, with a height of 15 m. Additionally, the zero reference plane and outlet are marked in the figure. As can be seen from Figure 2, the tunnel network has a significant slope, with an elevation difference ranging from 2.4 to 11.4 m.

2.4. Research Methodology

In this study, the flow state of the water in the roadway is turbulent, and the RNG k-ε turbulence model was adopted. This model is most commonly applied in complex free-surface and full-flow problems and can handle complex water flow issues such as large curvature, strong pressure gradients, and swirling flows. The Eulerian multiphase flow model (VOF) based on the liquid surface tracking method was selected to simulate the flow state of water in the roadway. The influence of the grid size in the VOF model on the accuracy of capturing the gas–liquid interface was considered. In total, 15 and 10 grids, respectively, are used to fill the width and height of the roadway. The grid is divided using the poly-hexcore method; that is, polyhedral grids are used at the roadway wall surface to ensure a good fit to the roadway wall, while hexahedral grids are used inside the roadway to ensure the accuracy of capturing the gas–liquid interface. The inlet condition of the model is set to 0.90 m³/s, and the outlet is a free-flow outlet to simulate the situation where water flows out of the roadway under natural conditions. In the simulation, the kinetic energy loss of the water flow on the rough wall surface is considered, with a roughness coefficient of 0.5 and a roughness height of 0.01 m.

3. Results and Discussion

3.1. Analysis of Water Spreading Process in Tunnel

To comprehensively understand the dynamic distribution pattern of water spread in the adjacent tunnel network after underground water discharge, Figure 3 illustrates the dynamic distribution of water spread in the tunnels at different times. After underground water discharge occurs, water begins to enter the tunnel entrances near the water-accumulating areas, as shown in Figure 3a. At 400 s, water enters from the tunnel entrances. Since measuring points 1, 2, and 17 (as shown in Figure 2) are closest to the water inlet, water first accumulates in these areas and then spreads to other areas of the tunnel. As shown in Figure 3b, within 1200 s after water discharge occurs, water in the water-accumulating area still converges at the areas where measuring points 1, 2, and 17 are located, and the water level gradually rises. As shown in Figure 3c, at 3200 s, it is evident that water flows along the tunnel network towards areas with relatively lower terrain. The figure clearly demonstrates that the relative elevation of the terrain determines the direction of water flow. For example, in the areas adjacent to measuring points 18, 29, and 30 shown in Figure 2, there is no water flow, because these three measuring points have relatively high elevations of 8.7 m, 11.4 m, and 10.4 m, respectively. Areas with high relative elevation act as barriers to the spread of water. As shown in Figure 3d, at 7200 s, underground water discharge further spreads along the tunnel network, and the water level in the tunnels gradually rises. The highest water level in the flooded area reaches 1.5 m. As the time of water spread increases, the water level gradually increases in the tunnels. When the water level is higher than the slope of the tunnel, water will bypass the sloping tunnel and quickly spread towards lower water level areas. It can be seen from Figure 3e that at 11,200 s, underground water discharge bypasses the sloping tunnel where measuring point 18 is located and spreads towards areas such as measuring points 19 to 21. As illustrated in Figure 3e, the continuous propagation of water inrush demonstrates sustained fluid migration and convergence toward lower elevation zones with reduced hydraulic head. When the temporal duration reaches 19,460 s, the area spanning monitoring points 7 to 15 becomes entirely submerged by the advancing water front. Furthermore, the water depth within this inundated region exhibits a progressive increase correlated with temporal evolution. As further evidenced in the figure, despite prolonged temporal propagation of the water inrush, the roadway sector encompassing monitoring points 26 to 34 maintains persistent dryness. This phenomenon primarily arises from the region’s relative elevation of 11.4 m, which exceeds the discharge outlet’s elevation threshold. Consequently, hydraulic connectivity remains obstructed, preventing water ingress into this zone. However, numerical simulation indicates that through the mechanism of continuous fluid transportation over a long period of time, areas at higher altitudes than the drainage outlet will also be completely submerged. From the above analysis, it can be seen that water enters the areas where measuring points are located through the tunnel network. Due to the significant slope variations in the tunnels, the final water level in the tunnel areas is related to their relative elevation. The final equilibrium water level distribution ranges from 0.3 to 3.3 m.

3.2. The Variation in Water Level Height in the Tunnel

To quantitatively analyze the pattern of water level height variation with flow time at various locations in the tunnel, monitoring points were set up at sections with multiple confluences, steep slopes, and bifurcations. Once the underground water-logged area is drained, the accumulated water will flow into nearby tunnels through the drainage outlet. The tunnel inlet mentioned in this article is shown in Figure 1. After the water flows into the nearby tunnels, it spreads rapidly through the tunnels, and the variation in water level height with time is shown in Figure 4.

As can be seen from Figure 4a, water level measurement points 1 to 7 are the areas closest to the tunnel inlet. After the start of drainage, the water level at measurement point 1 begins to rise rapidly at 550 s, reaching a height of 1.5 m around 3400 s, and then stabilizing at 1.6 m at 15,400 s. The flow velocity of water in the roadway mainly depends on the relative height of the roadway, which is consistent with the analysis results in the literature [11]. The variation pattern of water level height at measurement point 2 is similar to that at measurement point 1, i.e., the water level begins to rise rapidly at 1100 s and reaches a height of 1.1 m around 3400 s. Meanwhile, due to the influence of water level height, drainage rapidly spreads to other areas of the tunnel. The water level height at measurement points 3 to 4 begins to rise at 1600 s, reaching 0.5 m at 3400 s, and then slowly rising to 0.6 m. This is mainly because the areas where measurement points 3 and 4 are located are 1 m higher in elevation compared to measurement points 1 and 2. Subsequently, as the terrain height decreases, the water level height at measurement points 5 to 8 begins to rise rapidly at 3300 s, reaching a height of 1.3 m around 5300 s, and then stabilizing at 1.8 m at 15,400 s. The delay in the start of water level rise in this area is mainly due to the elevated positions of measurement points 3 and 4, which serve to delay the flow of water to some extent. From the above analysis, it can be seen that the water level rise pattern near the tunnel inlet is similar in the adjacent areas. The water level heights at the measurement points all undergo three states: rapid rise, slow rise, and stable equilibrium. The speed of drainage spread and the final height of water level at each measurement point are closely related to the terrain height of the area. As can be seen from Figure 2, the water level measurement points 9 and 10 of the tunnel are located in the area after the tunnel bifurcation. The so-called tunnel bifurcation means that the tunnel where measuring points 9 and 10 are located and the tunnel where measuring points 11 and 12 are located are two roadways that branch out after the bifurcation point. Compared to the height of the zero reference point, they are 6.1 m and 2.4 m, respectively. The relative height of the overall area is lower than that of the area containing measurement points 1–8. Therefore, as can be seen from Figure 4b, the water level at measurement point 10 begins to rise rapidly at 5300 s and stabilizes at 3.3 m at 13,200 s. Since measurement point 9 is located on the slope of the tunnel, under the influence of the terrain elevation difference, the water flow in the tunnel enters the area of measurement point 10 through the gap on the slope side. Therefore, when the water level at measurement point 10 is higher than that at measurement point 9, the water begins to flow into the area of measurement point 9 after 13,200 s, causing the water level at this location to rise rapidly. At around 22,000 s, the water level reaches 3 m. Figure 4c shows the variation curve of water level height over time from measuring point 11 to measuring point 16. From the change in water level height at the measuring point, it can be seen that once the water in the flooded area flows through the measuring point position, the water level height at that position will rapidly rise. Measuring point 12 is located at a relatively low height of 2.4 m, similar to the water level change pattern at measuring point 10. The water level starts to rise rapidly at 6000 s and stabilizes at 3.3 m at 16,500 s. When the water level at measuring point 12 exceeds that at measuring point 11, the water flow begins to flow into the area of measuring point 11 after 17,600 s, causing the water level at that location to rapidly rise. The water level from measuring point 13 to measuring point 16 gradually increases after 13,200 s, and finally stabilizes within the range of 2.8–3.5 m. Figure 4d shows the variation curve of water level height over time from measuring point 17 to measuring point 21. It can be seen from Figure 2 that the roadway water level measuring points 17 to 21 are located near the roadway inlet area, and the relative height of measuring point 17 is 7.4 m compared with the zero reference point, and the relative height of other measuring points is 8.4 m. Therefore, it can be seen from Figure 4d that the water level of measuring point 17 rises rapidly almost at the initial time of water discharge, reaching 1.3 m near 3300 s, and then stabilized at 1.6 m with the growth of water spreading time. Since the relative height from measuring point 18 to measuring point 21 is higher than that of measuring point 17, there is no water flow in the area for a long time after the discharge of water in the ponding area. When the height of water level measuring point 17 reaches 1.4 m, the water flow gradually flows to the area from measuring point 18 to measuring point 21. Since then, the water level in the area has not been set at 0.2 m. In addition, it can be seen from Figure 2 that the relative height of the area from measuring point 22 to measuring point 34 reaches 11.4 m. Due to its high terrain, the water flow still does not pass through the area within 22,000 s (about 6.1 h) after the emergency discharge in the ponding area. From the perspective of emergency, the area is in a relatively safe state, and subsequent analysis is not required.

Following a water inrush event in underground mines, the tunnel network gradually becomes inundated as water propagation advances over time, with rising water levels across different zones significantly hindering safe personnel evacuation. Empirical evidence indicates that evacuation difficulty increases with proximity to the discharge outlet.

Table 1. Table of water spread influence range in roadways.

Measurement Points	Distance from Water Source (m)	Time to Reach Water Level at 0.5 m (s)
1	50	950
2	100	1555
3	175	3413
4	236	3586
5	296	3758
6	319	3672
7	330	3715
8	400	3586
9	387	14,213
10	463	5875
11	405	17,496
12	493	6005
13	567	17,885
14	750	13,651
15	844	13,478
16	913	16,200

quantifies safe evacuation times for monitoring points within 1000 m of the water release location, revealing critical spatiotemporal patterns: Water depth exceeds 0.5 m within 100 m of the outlet 1555 s post-inrush, while warning-level inundation occurs at 3700 s in the 200–300 m and 200–400 m zones, 6000 s in the 400–500 m range, and 17,885 s in the 500–1000 m area. Notably, regions beyond 500 m exhibit extended evacuation windows due to the combined effects of complex tunnel geometry, elevation variations, and the formation of large water retention basins. Therefore, when setting up locations for the safe evacuation of personnel underground, factors such as accident-prone areas and evacuation routes should be comprehensively considered, and it is advisable to keep as far away from the accident area as possible [23]. An exception occurs at monitoring points 9 and 11 near the outlet, where protruding obstacles create hydrodynamic diversion pathways, allowing water to bypass these zones through adjacent tunnels and maintain lower water levels over extended durations. This spatial–temporal progression underscores the critical relationship between infrastructure topology, hydraulic behavior, and evacuation feasibility during mine flooding emergencies.

4. Conclusions

In order to understand in detail the dynamic law of the spread of water flow in the roadway network after the water discharge in the ponding area of the coal mine, this paper selects the typical full-scale complex roadway network as the research object, selects the Euler multiphase flow model (VOF) to simulate the flow state of water in the roadway, and explores the law of roadway water spread in the process of emergency water discharge in the coal mine with the characteristics of water spread distribution and the change in water level height at each point of the roadway. The specific research results are as follows:

When the underground water discharge occurs, the water flows along the roadway network to the location with relatively low terrain. Water begins to enter the tunnel entrances near the water-accumulating areas. Due to the different relative altitudes of each roadway in the underground roadway network, the slope roadway plays a role in preventing the spread of water at the initial stage of water discharge. The equilibrium water level height of the roadway area is related to its relative height, and the stable equilibrium water level height is distributed in the range of 0.3–3.3 m.

The idea of water level rise at each point of the roadway network is similar; that is, it generally has three development states of rapid rise, slow rise, and stable balance. Once the discharge occurs, the water level in the roadway area near the discharge outlet rises sharply within 550 s; the slope roadway can slow down the speed of water spread and water level rise to a certain extent; and the water level in the roadway far from the discharge outlet begins to rise rapidly after 13,200 s. In addition, due to its high terrain, there are still some areas where the water flow still does not pass through within 22,000 s after the underground emergency discharge, and this area is an evacuable area.

Following a water inrush event, safe evacuation becomes increasingly challenging for personnel in areas closer to the discharge outlet. Those within a 300 m radius of the outlet face a maximum safe evacuation window of merely 1 h. In contrast, regions farther from the discharge location benefit from significantly extended evacuation opportunities due to the water retention capacity of complex tunnel networks, which function similarly to reservoir systems, effectively delaying water level rise and creating critical time buffers for escape. This spatial pattern highlights the inverse relationship between the proximity to the hazard source and available evacuation time during underground flooding emergencies.