Numerical assessment of the water-flow hazard to workers in the water disaster of underground mine

Water disaster is one of the most severe disasters in underground engineering, occurring frequently both in the mining industry and civil construction (Li et al. 2013b; Jiang et al. 2017; Cui et al. 2018). Water inrush accidents greatly endanger workers' lives in underground mines. For example, serious underground water inrush disasters include the Daxing coal mine incident in China, August 7, 2005, which killed at least 121 workers (Cui et al. 2018); the Yesanguan tunnel of Yichang-Wanzhou Railway incident, August 5, 2007, where water inrush occurred in the DK124 + 602 karst tunnels, causing the death of 10 workers (Jiang et al. 2017).

Workers' safety is always the key concern in a disaster, which has always drawn, therefore, the attention of researchers working in the field of safety (Verma & Gupta 2013). Evacuating workers to the surface safely and quickly is the ultimate goal in an emergency escape from water disasters in underground mines, and during such disasters, the existence of good escape routes is critical. Essentially, most current research focuses on finding escape routes (Jalali & Noroozi 2009; Zhao et al. 2019), mainly represented by the shortest-route model and its improvement model, which are based on the theory of the Dijkstra algorithm, Floyd algorithm, or the Ant algorithm. Although much has been achieved from these studies, there is a lack of consideration of the water-disaster environment, especially regarding the water flow in roadways and the worker's own situation. Most evacuation routes are the shortest available, but are not optimal, because they lack quantitative quantification of the specific environment after a water disaster and its impact on workers (Wang 2017; Wu et al. 2020). That is why it is difficult for current emergency plans to include intelligent and dynamic avoidance measures for different types of workers and different types of disaster situations (Wu et al. 2020; Onifade 2021).

Due to the severity of disasters, most mines in China have adopted active emergency plans, but the hazard to workers and the evaluation of evacuation routes are generally not well covered. In fact, it is not easy for workers to remain safe on roadways, especially when they are wading (walking and running) during a water disaster. Workers are often unaware of the power of water flow and are sometimes unaware of the dangers inherent to emergency escape; workers can also take unacceptable risks in the presence of hazards, all increasing the potential for casualties. If workers are in danger, the escape plan may be useless. A full consideration of existing risk is a key issue to reduce the possibility of potential risk (Levens 1998; Kowalski-Trakofler et al. 2010; Verma & Gupta 2013). Eiser et al. (2012) emphasized that disaster hazards always involve interactions between natural and human factors. Understanding worker's flood-related risk-taking behaviors may help develop more effective strategies to prevent and mitigate the impact of floods (Garrido et al. 2012; Hamilton et al. 2020). It is only by considering the hazard posed by water flow to a worker in a water disaster that a clear analysis of worker's safety may be arrived at and a scientific and reasonable evacuation plan provided.

How the professional community should respond to water disasters in underground mines should be based on sound scientific evidence. Therefore, greater attention should be paid to safety work in disaster-risk management, especially concerning the types of danger faced by workers, and numerical assessment should be used to provide an effective management plan for water disasters. However, there is no existing scientific, systematic, or quantitative evaluation framework to address the hazards to workers during underground water disasters.

Fortunately, hazard assessment is currently being developed and improved in the floodwater field, e.g., for flash floods and urban floods. People's stability in floodwaters has seen many advances in the continuous acquisition of stability simulations and real test data in flood (Keller & Mitsch 1993; Endoh & Takahashi 1994; Lind et al. 2004; Jonkman & Penning-Rowsell 2008; Xia et al. 2014; Milanesi et al. 2015; Martínez-Gomariz et al. 2016). Three types of instability experienced by humans in floodwater were considered: friction instability (sliding), moment instability (toppling), and floating instability.

is the critical velocity of toppling instability and is the critical velocity of sliding instability.

Regrettably, due to the complex characteristics of water disasters in underground mines, these evaluation methods cannot be fully adapted. First, an underground mine is different from free space, especially with regard to limitations on entrance and evacuation. There are various types of underground roadways, such as the vertical shaft and the stepped roadway, in which the rising rate of water flow is faster, and space will be flooded (or even submerged).

Floodwater characteristics and population behavior determine the likelihood of a death of a disaster victim (Di Mauro et al. 2012). Hamilton et al. (2020) stressed that further exploration of methods to increase the likelihood of evacuation and reduce ‘risky’ behavior during a disaster is needed. Therefore, the great value lies in the development of a scientific and quantitative evaluation model for water-flow hazard (WH) in water disasters in underground mines.

In this paper, a new model for evaluating the hazard posed by water flow to workers in water disasters in underground mines is created. According to mine and water-disaster characteristics, creating a hazard assessment for workers is achieved by using existing stability analysis. In other words, this can assess the hazards posed by different water-flow conditions at different locations to the worker with different physical characteristics. Moreover, the dynamic visualization of WH in water disasters is realized in time and space, providing an example of water-resource management (Roushangar & Alizadeh 2019) and the mitigation of water related-risks, discussed in the hydrology editorial of Montanari et al. (2013).

The underlying mechanisms in the creation of casualties by water disasters in underground mines are complex. Based on the previous work on the stability of people in floodwater and workers' safety in water disasters of underground mines, we conclude that there are five recurring factors in the hazards that affect workers:

1. Roadway factors: such as roadway type, road slope, friction coefficient, traffic equipment, or auxiliary equipment for workers, handrail, and obstacles.

2. Hydrologic factors: such as the type of water disaster (surface flooding, water inrush), water inflow, and inrush point.

3. Hydraulic factors: such as water depth, flow velocity, water density, water-rise rate, water temperature, the degree of turbidity, and items floating in the flow.

4. Worker factors: such as body height, body weight, clothes, physical and psychological health, escape direction, walking way, and familiarity with the roadway.

5. Other physical factors: such as oxygen concentration, harmful gas density, light levels on the roadway, wind speed, refuge chamber, and the prewarning time.

Not all factors directly affect the safety of workers facing a disaster because of the particularity of underground mine water disaster. The factors can be divided into direct impact factors (such as water depth and flow velocity) and indirect impact factors (such as hydrologic factors). Indirect impact factors show their hazard effects by influencing direct factors, such as water inrush hydrologic factors, which are reflected by the spread of water flow. The method in this paper considers the WH to workers, mainly analyzing the influencing factors related to roadway and water flow; at the same time, quantitative generalization is a necessary condition.

Based on the roadway gradient, pedestrian roads in underground mines are generally divided into five categories: horizontal roadway, sloped roadway, stepped roadway, inclined shaft, and vertical shaft. In horizontal, sloped, and stepped roadways, workers can walk through; in vertical and inclined shafts, traffic equipment or auxiliary equipment is needed for workers; for example, cages are often used in coal mine shafts for the vertical transport of workers.

Regarding water disasters in underground mines, three points should be considered for hazard analysis. The first is whether workers can walk through flooded roadways (horizontal roadway and sloped roadway). The second is whether workers can go up by flooded stepped roadway. And the third is whether workers can be raised by auxiliary equipment in a shaft (vertical and inclined shafts), such as by using mine cages in the vertical shaft of an underground coal mine. This paper presents a numerical assessment model for WH to workers in water disasters in underground mines that: (1) takes the disaster environment and workers' physical parameters into account; (2) incorporates increased available information of physical mechanisms from previous studies; (3) facilitates the understanding by workers, intuitively and easily, of the potential hazards they face, via dynamic visualization of WH in time. Based on the pedestrian-roadway type and water-disaster characteristics of an underground mine, we believe that there are seven hazards for workers: floating, slipping, toppling, drowning, sweeping, equipment hazard, and secondary hazard. The framework, shown in Figure 1, shows a model of water flow to a worker in water disasters of underground mines.

Based on previous stability analysis, workers are challenged by their degrees of three types of instability in the horizontal and sloped roadway during water disasters: floating instability, slipping instability, and toppling instability. Combined with the characteristics of the rapid rise of water flow in underground mines, this paper has taken into account the hazard of drowning.

In fact, when we analyze slipping and toppling instability, floating instability has been analyzed. If the worker experiences floating instability, slipping and toppling will not exist; therefore, the WH of floating instability is defined as 1. If no floating instability occurs, then slipping and toppling stability are analyzed.

It is interesting to note that Milanesi et al. (2015) developed a new conclusion on instability analysis and took the destabilizing effect of local slope and fluid density into account, expanding the application's scope. Milanesi et al. (2015) described the legs as paired cylinders of diameter d (m), spaced d/2, and schematized the torso with a single cylinder of diameter D = 2d. Then, the critical condition for slipping instability is that the sum of the drag force of the water flow and the projection of weight parallel to the slope is greater than the friction force. The toppling instability occurs if the buckling moment due to the components of hydrodynamics (drag and lift), buoyancy, and weight exceeds the moment calculated at the pivot point relative to the normal component of the weight. The limiting critical depths are regarded as a function of the flow velocity, which is the slipping (⁠⁠) and toppling (⁠⁠) (Milanesi et al. 2015). The validity of its critical condition has verified by comparing with the existing experimental data in Milanesi et al. (2015).

As the area of the underground mine is limited, the water flow during a disaster rises rapidly. On June 2, 1984, a water inrush occurred in Fangezhuang Mine, Kailuan, Hebei Province, and water filled the whole coal mine. On August 23, 2010, a drowning accident occurred in Dongjiagou Coal Mine, Liulin County, Shanxi Province, which resulted in five deaths. Therefore, we believe that evaluating WH in water disasters in underground mines must include the hazard of drowning, which is independent of flow velocity.

A depth constraint of drowning was suggested by Cox et al. (2010) who proposed a maximum admissible water depth of 1.2 (m) for adults. Milanesi et al. (2015) introduced a maximum admissible water depth (m) as a function of the height of the neck. The depth limits can be set as functions of the size of the body (H), so that the head is completely above the water surface. In particular, the head can be considered 1/8 H (Drillis et al. 1964); in order to keep a freeboard, the head height was assumed to be 3/16 H by Milanesi et al. (2015). Therefore, is assumed to be 13/16 H in this study.

For water-flow conditions judged to be greater than critical instability, once wading is a more dangerous action, so it is more dangerous if the corresponding water-flow conditions increase further. In order to ensure the safety and security of miners escaping from disasters, we do not recommend miners to choose this type of roadway by risky actions, so its hazard can still be called 1. If the purpose of the demand is only to obtain a purer hazard-evaluation value, removing the minimum value function that takes 1.0 in Equation (5) is sufficient.

In actual disaster situations, the initial value of HR_VIS is set to 0. Once the interactive information alerts the relevant equipment to abnormalities, it is set to 1. When it can be restored to normal use after repair, it is then set to 0.

In addition, dangerous debris and other (even heavy) objects may be transported by the water flow in the water disaster. Mine roadways such as driving faces cannot be hardened immediately due to production reasons, and there will be coal blocks of varying sizes in the unhardened sections. Therefore, in the course of a water disaster, the water flow can not only directly act on the workers, but also impact the transport of coal, making it float or roll. Moving coal may strike a worker's body, causing injury or death, thereby causing secondary hazards (WH₂) to escaped workers. The impact of debris factor in floods was quantified based on empirical methods by Ramsbottom et al. (2003, 2006) and Kvočka et al. (2018). In the mine water disaster, this hazard depends mainly on the type of water disaster, the location of inrush point, the characteristics of the water flow, and the size of the block. If the block particles are too small or remain stationary under the action of water flow, then define its hazard as 0. If the block floats and moves in the tunnel and its particle size will have an impact on miner safety, then define its hazard as 1. The underground space of the coal mine is complex, and it is difficult to obtain data on the movement of coal in the water flow in the post-disaster environment. At present, it is mainly based on the discovery of underground mine workers during escape and evacuation and reporting to the ground for interactive acquisition. For the roadway sections that may have problems with predictive analysis, video surveillance should be strengthened. With the continuous construction and development of smart mines, rich dynamic data can be obtained through video, mobile robots, and other methods in the later period.

Therefore, the WH for different workers at any point of the mine can be evaluated by the WH model dynamically at any time during the disaster process or in the post-disaster environment.

The Beiyangzhuang Coal Mine is located in Yuxian County, Hebei province, Northern China. The total mining area is about 52 km², its north-south length is about 10 km, and its east-west width is between 5 and 8 km. The method of minefield development is vertical shaft development, with three vertical shafts designed: main shaft, auxiliary shaft, and air shaft. Figure 2 shows the structure of the mine roadway and the distribution of the working face.

As of September 2019, there have been three water-burst accidents in the mine, occurring in March 2012, May 2012, and September 2014. Based on an analysis of the mine's history, it can be concluded that under the influence of karst Ordovician limestone water, the mine has experienced the hazard of floor water inrush, and the water-rich is strong in this area.

The roadway is modeled as a topological structure consisting of 8,761 points and 8,850 segments. The paragraphs of 6,134, 8,600, and 8,840, as well as the water inrush point, are clearly marked on the 2D map of the mine roadway. The 3D display of a mine roadway is shown in Figure 3, and the water inrush point is assumed to be at driving face No. 1. Wu et al. (2016) had assessed the risk of water inrush at the Yuzhou mining area using the vulnerability index method, which is extracted from the Beiyangzhuang coal mine. The driving face No.1 is located in a strong vulnerable zone and contains faults, so it is very likely to burst water. The basic law of curves of inrush flux at the bottom of this mine was outlined and designed by Zhao et al. (2020). The water inrush from Ordovician limestone was simulated in this study, and the curve of which is shown in Figure 4. The water inrush was simulated for 28 h, in order to make the case can fully analyze and demonstrate the depth, speed, and WH value characteristics of each water flow in the early, middle, and late stages after the occurrence of water disaster. The diffusion process of mine water can be simulated as one-dimensional, unsteady, and non-uniform open channel flow (Zhao et al. 2020). The de Saint-Venant system of equations is established, according to the law of conservation of mass and the law of conservation of momentum. The corresponding water spreading processes can be simulated by the Storm Water Management Model (SWMM) (Zhao et al. 2020) to obtain the water depth and flow velocity of inrush water along the mine roadways. In the future, these data could also be monitored by sensors during a mine water disaster, even identified and predicted by numerical models using artificial intelligence technologies (Alizadeh et al. 2020; Zhao et al. 2020).

Most mine water in China contains suspended solids (He et al. 2002), consisting of materials such as silt or small coal particles; thus, the density of mine water is usually greater than normal water. It can be supposed that the density of mine water (⁠⁠) is in this simulation. The value of the drag coefficient depends on the shape of the exposed object (Jonkman 2007). Among the studies on the human body, a value of ranging from 1.1 to 2.0 was adopted by Keller & Mitsch (1993), Lind et al. (2004), and Jonkman & Penning-Rowsell (2008). To take into account the roughness that would characterize a clothed human body, a value of was adopted by Milanesi et al. (2015). Accordingly, it is also assumed to be 1 in this study.

Karvonen et al. (2000) have conducted experiments on human stability in water flow, with the body heights ranging from 1.60 to 1.95 m, and the body weights vary from 48 to 100 kg. According to the ‘Report on Nutrition and Chronic Diseases in China (2015)’ released by the National Health and Family Planning Commission of China, the average height of adult men in China is 1.671 m and the average weight is 66.2 kg. Underground miners in China are basically all adult males with their own physical parameters. The physical parameters assumed for the model of underground workers are shown in Table 2.

Xia et al. (2014) revealed that the selection of needs to be estimated using the ground surface roughness and the characteristics of shoe soles. A friction coefficient of 0.3–1.0 was used in the human-stability analyses conducted by Keller & Mitsch (1993) and Jonkman & Penning-Rowsell (2008). For the study of human stability in the breakwater, Endoh & Takahashi (1994) conducted a series of tests on the friction coefficient for a range of leather and rubber-soled shoes on various ground surfaces as shown in Table 3.

To determine the coefficient of friction provided by each of the different shoe types, an experiment was developed by Martínez-Gomariz et al. (2016) who showed that the friction coefficients for a waterproof boot and wet surface are 0.58. Therefore, based on the result of Martínez-Gomariz et al. (2016) and Table 3, it can be assumed that the value of for a mine roadway is 0.60 in this simulation.

Through the WH model, we can evaluate the hazard posed by mine water flow to a worker at every position during the disaster process. Furthermore, the changing process of WH in a certain period deserves attention, and the overall status of a hazard at a certain time is critical.

To better understand the dangers of disaster to workers, the temporal variations of water depth, flow velocity, and WH for worker-1 (m = 72 kg, H = 1.72 m) at different sites are shown in Figure 5, which gives a clear picture of the water-flow information and the WH to a worker for the whole time of the disaster. From the data in Figure 5, it is apparent that the depth of the water increases continuously, and the trend of flow velocity is complex, with its variation greatly fluctuating as the water-disaster unfolds. Based on the comparison of water depth, flow velocity, and WH break-line changes in Figure 5, we believe that the characteristics of mine water flow are fully taken into account in the quantification process of WH. In Figure 5, there is a clear upward trend in WH to worker-1 with increasing water depth at the site. Finally, when the comprehensive hazard-effect of the water flow is inevitably going to cause danger to workers, the hazard-evaluation value is still considered as 1, even if the depth and velocity of the flow are changing slightly. This is to ensure the safety of workers, and water-flow conditions are considered dangerous whenever they exceed critical conditions. The risky actions are not recommended in the disaster escape.

To eliminate the influence of data with different dimensions on the analysis results and to facilitate further comparative analysis between different variables and WH, it is necessary to normalize the data set. The data of water depth and flow velocity are normalized to be dimensionless quantities, which is implemented through the function method of min-max scaling. Furthermore, the dynamic visualization of normalized water depth, flow velocity, and WH also can understand how these change over time in the whole roadway, which are shown in Figure 6. For an emergency to be declared, it is critical to recognize, in detail, the degree of hazards facing workers. Obviously, it is not reasonable to evaluate the hazards of water flow to workers according to only water depth or flow velocity. As can be seen from Figure 6, the dynamic visualization of WH combines the dynamic changes of water depth and flow velocity. Compared with the spread of normalized water depth and flow velocity, the area of WH is larger because it not only includes water depth and velocity, but also quantifies the type and gradient of the roadway, water density, worker physical characteristics of body weight and height, and applies the physical mechanism of stability. For example, when T = 5 h, the practical guiding significance of WH is stronger than that of water depth and flow velocity through visualization. It can be seen from the WH diagrams of T = 2, 5, 11, 19, and 27 h in Figure 6 that the scope of the hazards of water flow to underground workers at different times is very different. That is to say, the latest escape time for workers at different locations during the flooding process is different. In fact, the WH information of this model can be displayed at any time through dynamic visualization. Therefore, the WH can help workers make decisions about the time to escape.

Comparing the distribution of water depth and flow velocity at the same time, we can conclude that the change in water depth is more prominent in Figures 5 and 6. This is also why the traditional methods of assessing workers' hazards directly use water depth. However, it is not enough to just use the water depth and ignore the flow velocity. The comparative analysis of the normalized water depth, flow velocity, and WH diagrams of T = 5, 11, and 27 h in Figure 6 confirms this point.

Due to differences in the human body, the impacts of water disasters on the hazards to different workers are different, even under the same water-flow conditions at the same location. Figure 7 provides the WH for three workers (worker-1, worker-2 (m = 95 kg, H = 1.82 m), and worker-3 (m = 60 kg, H = 1.62 m)) under the same flow conditions. Overall, the trends of WH for different workers are consistent with the change in disaster. Microscopically, worker-3 is more dangerous than or equal to worker-1, and worker-1 is more dangerous than or equal to worker-2. In other words, workers who are taller and heavier in an underground water disaster are more conducive to safety.

The WH at the early stages of a water disaster (e.g. T = 2 h) and the WH at the late stages (e.g. T = 11, 19, and 27 h) are obviously different in Figure 6. This difference indicates that the escape routes should be different at different times, and reasonable routes should be planned according to the WH in the water disaster. Furthermore, for different workers, due to different physical qualities, the ability to cope with water disasters is also different, as shown in Figure 7. Therefore, it is necessary to develop corresponding dangerous dynamic visualizations for workers with different physical conditions.

For a simple mine water disaster, such as a small water inrush with slow inflow speed, the shortest escape route can be effective. But for a complex disaster, the shortest route is difficult to guide workers through in an emergency, if the water flow can lead to the direct death of workers in the dangerous location of the escape route, such as in the roadway of WH = 1 in the WH of Figure 6. To draw up a safe and reliable evacuation plan, evaluating the safety of escape routes is essential. In other words, it is necessary to assess the hazards to workers in evacuating routes; this is the value of the hazard assessment in this study.

The numerical setting of some parameters of the simulation analysis in this paper is based on literature references and actual assumptions. In fact, the simulation results of the WH model can not only serve the work of escape and evacuation, but also adapt to emergency training, drill operations, and even design for part of the roadway. Therefore, the various possible parameters need to be analyzed in future work. The hazard value calculated by the WH model can not only display visualization to help escape and rescue work but also has a negative correlation with the safe wading speed of workers in mine water disaster. In the next work, the safety wading speed model is mainly established, and the WH hazard value is used to directly plan the escape and evacuation route under the condition of enough to ensure the safety of workers.

Water accidents are one of the major accidents in underground mines, which greatly endanger workers' lives. This study was aimed at establishing a systematic and quantitative evaluation model for numerical assessment of the WH to workers in the water disaster of an underground mine, which is from multiple influencing factors to quantitative comprehensive quantification. Nine factors, namely roadway type, road slope, friction coefficient, traffic equipment or auxiliary equipment, water depth, flow velocity, water density, body height, and body weight, were directly utilized in a WH model. At the same time, hydrologic factors (like the type of water disaster, water inflow, and inrush point) were indirectly reflected in the evaluation model by affecting the water spreading process.

The methodology described in this paper provided a solution to characterizing WH and worker safety in underground mines by understanding the details of danger in water disasters while using human-stability analysis in water flows and real features of water disasters in underground mines. A case study of a coal mine in China has also proved the efficiency of this WH model. The results illustrate that this WH model can assess the hazards of different WH conditions to workers with different physical characteristics at different locations. Therefore, the WH model overcomes the shortcomings of current approaches to model escape routes, which cannot quantitatively describe disasters and individual physical differences, and is an expression of a more detailed categorical evaluation of the hazard to workers from various water-flow conditions. Under different water-flow conditions, the magnitude of the hazard to each miner affected by the water flow can be clearly and unambiguously recognized. Thus, it also meets the urgent demands of water-disaster management for underground mines.

This study also gave a new approach to mine disaster emergency responses by dynamically visualizing the hazard of workers. Mapping hazards is an important step towards disaster-risk management. The dynamic visualization of WH in water disasters is realized in time and space to help workers to understand the degree of WH in real time, intuitively, and easily. Finally, the WH model can serve not only the workers in an underground mine but also rescuers. It is a significant measure for rescuers' safety to choose a suitable time to rescue, avoid dangerous roads, and have a better judgment on the locations of hazards based on the dynamic visualization of WH.

This research was financially supported by the China National Natural Science Foundation (41877186, 42027801), the Inner Mongolia Science and Technology Major Project (2020ZD0021), Fundamental Research Funds for the Central Universities (2010YD02), and State Key Laboratory of Coal Resources and Safe Mining. Lastly, the authors would like to thank the editor and the reviewers for their constructive suggestions.

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