Spatiotemporal modeling of water inrush spreading in mine roadway networks Open Access

Water inrush is a major hazard for underground mines and can occur during mining and tunnel construction. Water-inrush disaster threatens mine-worker safety, and modifies the groundwater flow field. For example, 181 miners died in a water-inrush accident at Huayuan coal mine in Shandong province, China, on August 17, 2007. Earlier, on June 2, 1984, two mines were submerged due to a water-inrush accident at Fangezhuang coal mine in Hebei Province. To prevent water inrush, significant research has been devoted to examining its mechanisms (Sammarco 1986; Shi et al. 2017; Li et al. 2018), water sources (Guo et al. 2015; Jiang et al. 2019; Wu et al. 2019; Zhang et al. 2020), and how to predict it (Meng et al. 2012; Hao et al. 2017; Wu et al. 2021). However, water inrush accidents are still frequent and difficult to accurately predict because of increasingly complex hydrogeologic conditions that occur with increasing mining depth. Designing a rescue plan and a water-inrush-control plan is also difficult because the process of water-inrush spreading is not clear. Therefore, a technique must be developed to quantitatively predict the spreading of water inrush to prevent mines from being submerged.

The water-inrush process is highly nonlinear (Ma et al. 2016), and the structure of a mine roadway network is complex and large scale. Thus, a major challenge for predicting water-inrush spreading is to establish a complex roadway network system and a water-inrush flow model. Although numerical groundwater modeling has become an essential tool for investigating water resources in porous media aquifers, numerical modeling has been less successful in mine roadway networks. Li et al. (2013) established a one-dimensional (1D) roadway model and water-inrush spreading path by searching for the local minimum in roadway elevation. Qin et al. (2011) calculated the water-inrush spreading in local bifurcated roadways by using a numerical simulation based on computational fluid dynamics. Although these studies have helped to understand the spreading characteristics of water inrush in mine roadway networks or in bifurcated roadways, the complete hydrodynamic process in mine roadway networks and water-inrush-control equipment has not been considered. Conversely, pipe-flow models consider the complete hydrodynamic process and have been successfully applied to storm sewer systems and karst aquifer systems (Chen & Goldscheider 2014; Yu et al. 2014). However, pipe-flow theory has yet to be applied to mine roadway networks.

The applicability of pipe-flow theory to water inrush needs to be verified. Currently, there is a lack of public data to test the validity of pipe-flow theory for water inrush events. The hydraulic model experiment can monitor the flow process under different inflow conditions to verify the numerical results, which has been widely used in urban flooding (Jeong & Jeong 2021). Moreover, calibration and validation are indispensable for model simulation (Xu et al. 2019) based on experimental data. Sensitivity analysis can quantitatively evaluate the influence of each parameter on the simulation results to improve the efficiency of model parameter identification. In previous studies, sensitivity analysis was applied to karst conduits (Peterson & Wicks 2006) and drainage pipes (Peng et al. 2020) to evaluate the sensitivity of the conduit geometric or hydraulic parameters. However, little research has been conducted to analyze the sensitivity of roadway geometry and hydraulic parameters in mine water inrush events.

Given this situation, we propose herein a spatiotemporal modeling approach based on pipe-flow theory to simulate the spreading of water inrush in mine roadway networks. This approach considers the energy-loss term for the improvement of simulation capability, and the effect of pump and water-blocking equipment for simulating the real flow process of water inrush. Next, a typical mine roadway system was established for the experimental research. Then, the simulation results are verified by comparison with experimental cases. A sensitivity analysis is also done to assess the importance of roadway geometry and hydraulic parameters in controlling water-inrush spread in mine roadway networks. Finally, the applicability of this approach in mine roadways is confirmed by applying it to a real water-inrush event in the Beiyangzhuang coal mine. And, the effect of water-inrush control measures is evaluated for this water-inrush event.

The flow of water inrush in mine roadway networks is unsteady and nonuniform and involves two processes: free-surface flow and pressurized flow. In addition, the spread of water inrush is affected by pumps and water-blocking equipment in the mine roadway. Figure 1 shows the procedure for constructing the spatiotemporal model of water-inrush spreading. First, the basis of the model is the generation of a mine roadway network system. Second, the equations governing the spatiotemporal variation of water head and discharge are derived from the law of conservation of mass and momentum. Next, the boundary conditions are set according to the water inrush conditions. Finally, the spatiotemporal spreading of water inrush in the mine roadway is obtained by solving the control equations with the given boundary conditions.

The generation of a mine roadway network is the prerequisite for calculating water inrush spreading and involves two steps:

• (1)

  Construct a topologically connected mine roadway network. The mine roadway is generalized as a 1D network composed of nodes and segments. Table 1 lists the representative objects making up the nodes and segments. The key position, where water movement varies considerably, is abstracted as nodes that include the position of branches, variations in slope, inflections, and ends. The segments consist of three parts: a net roadway between two adjacent nodes (roadway segment), a roadway with a pump (pump segment), and a roadway with watergates or retaining wall (water-blocking segment). Then, the relationship between nodes and segments is established to form the mine roadway network.

• (2)

  Add attribute data to each node and segment. Mine roadway attribute data includes node coordinates, geometric parameters of roadway segments, pumping yield, and the opening size of the water-blocking segment (Table 1). The geometric parameters are the important parameters for calculating the water inrush spread and have large uncertainties.

In summary, Equations (1)–(10) constitute the spatiotemporal model for water-inrush spreading in a mine roadway network. Various types of water-inrush sources, such as floor water, roof water, or water inrush from old goaf, can be simulated by changing the inflow boundary.

In this paper, experiments were carried out to verify the accuracy of the simulation results of the spatiotemporal model. First, a typical mine roadway system was established as a prototype to test the model, including main roadways, connection roadways, pump, water sump, and shaft. Figure 2(a) and 2(b) show the 1D and three-dimensional roadway network system diagrams, respectively. The cross-section of most roadways is rectangular, and the size is shown in Figure 2(c). The circular cross-section of the shaft has a diameter of 6 m. Next, considering the requirements of experiment accuracy and site conditions, the prototype roadway system is designed as an undistorted model with a similarity ratio of 1:10 according to the gravity similarity criterion. Thus the length scale λ_L is 10, the time scale λ_t is 3.162 (λ_t = λ_L^0.5) and the flow scale λ_Q is 316.228 (λ_Q = λ_L^2.5). Figure 3 shows the mine roadway network used in the experiments studied herein.

In addition, two variables need to be monitored in the experiments: inflow and water head. The inflow of water inrush is regulated by an automatic valve and monitored by a flowmeter to 0.05% accuracy. Eighteen water head monitoring points monitored by piezometric tubes are used in the experiment [Figure 2(a)] to determine the spreading of water inrush in the roadway network.

The flow of water inrush is highly nonlinear and difficult to predict in a water-inrush accident. Two types of water-inrush flow curves are common: approximately constant flow and unsteady flow. When the water-inrush source is sufficient and the water-inrush channel is fully developed, the water-inrush flow curve is nearly constant. In contrast, the flow curve of water inrush increases first and then decreases. This study investigates four experiment cases to study the spreading of water inrush for different water-inrush flow curves. Point p₀ with the highest elevation of the roadway system is the water-inrush location (Figure 2(a)). The following water-inrush flow curves for the four experiment cases are shown in Figure 4:

Case 1: The water-inrush flow curve is approximately constant. The average water-inrush flow is 10.4 m³/h, and the experiment lasts about 15 min.

Case 2: The water-inrush flow curve is approximately constant. The average water-inrush flow is 20.8 m³/h, and the experiment lasts about 15 min.

Case 3: The water-inrush flow curve is unsteady, and first increases and then decreases. The peak flow is 20.1 m³/h, and the experiment lasts 53 min.

Case 4: The water-inrush flow curve is unsteady, and first increases and then decreases. The peak flow is 25.3 m³/h, and the experiment lasts 53 min.

In the four experiment cases, the monitoring interval is 30 s. The water head and discharge in the prototype can be obtained by using the length scale and flow scale, respectively.

The 1D roadway system of the experimental prototype was established and simulated to compare the results of the experiments with those of the simulations. The 1D roadway network system after subdivision contains 180 segments and 177 nodes (Figure 5). The length of the 180 segments ranges from 3 to 5 m, and the roadway slope ranges from 0 to 0.3. The cross-section of the roadway segment is set according to Figure 2(c). The inflow point and the drainage-outlet node are shown in Figure 5. The inflow curves of the experiments are converted to the prototype water-inrush flow used as inflow boundary conditions for the numerical simulation. The simulated parameters for the experimental prototype roadway system are listed in Table 2, which are described as follows:

The roughness coefficient of the segment is 0.015 (Rossman 2010). The water inrush at point p₀ separates along two downstream roadways: AB and AC (Figure 2(a)). The F_r of water inrush on roadway AC is large because of the large slope, so the energy loss on the branch roadway AC cannot be neglected. The energy-loss coefficients α= 0, 3, 5, 7, and 12 were tested on the connecting roadway AC to find the optimal α. Figure 6 compares the simulated water head with that measured at monitoring point h₂ during the experiment. The error between the experiment result and calculation result is the smallest when α is about 7. A larger energy-loss coefficient in the branch roadway corresponds to a smaller distributed discharge. The time step is 0.1 s. The simulation time for each case is the actual time of the experiment multiplied by the time scale 3.162. Finally, the water-inrush scenarios of the four experiments were calculated by using the proposed spatiotemporal model.

The numerical error is evaluated by calculating the percent difference between total inflow, final storage, and total outflow for the entire roadway system. If the numerical error exceeds 10%, then the validity of the analysis results must be questioned (Rossman 2010). The numerical errors of the four experimental cases are 0.55%, 1.65%, 0.45%, and 1.35%, respectively, indicating that the simulation results are numerically stable. In addition, the calculation time of the four experimental cases is 3 s, 4 s, 17 s, and 23 s, respectively. The simulation speed is efficient in terms of calculation time. The larger the water-inrush flow, the longer the calculation time is under the same time step.

Figures 8 and 9 compare the simulated and measured water head at six monitoring points. The simulated water head is consistent with the measured water head at different measuring points, regardless of whether the inflow condition is approximately constant or unsteady.

This study uses a series of perturbation amplitudes (−15, −10, −5, 5, 10, and 15%) to change each parameter while keeping the remaining parameters constant, and the spreading of water inrush is simulated using these parameters. The initial parameter values were based on the calibration Cases 1 and 2. Next, the sensitivity of each of the six parameters was calculated for cases 1 and 2 (see Figure 10). The sensitivity of these parameters may be divided into four ranks according to S value (Xu et al. 2019): the parameter is not sensitive if S < 0.05, the parameter is moderately sensitive if 0.05 ≤ S < 0.2, the parameter is sensitive if 0.2 ≤ S < 1.0, and the parameter is very sensitive if S > 1.0. The results in Figure 10 lead to the following conclusions:

• (1)

  The parameters that most strongly affect the spreading process of water inrush are the roadway length, the cross-sectional width, and the energy-loss coefficient α. Of these, the length of the roadway has the strongest effect on water inrush.

• (2)

  The sensitivity differs when using E_ns and E_rms as objective function, but the sensitivity ranking of the six parameters remains basically the same. The largest calculated sensitivity is for the objective function E_rms.

• (3)

  The water-inrush flow strongly affects the sensitivity of the parameters. Upon increasing the water-inrush flow, the sensitivity of the roadway length, the cross-sectional width, and the energy-loss coefficient α all increase significantly, whereas the sensitivity of dt and n decreases.

The proposed method was applied to the Beiyangzhuang coal mine located in Yuxian County, Hebei Province, northern China (Figure 11) to simulate the spreading of a real water inrush and evaluate the effect of water-inrush control measures. The Beiyangzhuang mining area has an area of 52 km², a length close to 10 km (SN), and a width of 5–8 km (EW). The mine roadway is in the mid-west mining area (Figure 11) and has two mining levels. The ground elevation at the site is about 997 m above sea level (asl). The lowest working level is 560 m at the first mining level and 450 m at the second mining level. The study area forms a synclinal structure with frequent small faults.

The geological and hydrogeological features of the Beiyangzhuang mining area are complex. Borehole data indicate that the main strata include Cambrian–Ordovician carbonates, Jurassic clastic rocks, and Quaternary alluvial deposits. The current working seam is the fifth coal seam in the lower part of the Jurassic strata. The karst aquifer underlying the fifth coal seam is the major water source. The risk of the fifth-floor groundwater bursting in the Beiyangzhuang mining area was evaluated by using the vulnerability index method (Qiang et al. 2016). Figure 11 shows the risk-assessment results superimposed on the mine roadway network. Higher risk means a higher possibility for water inrush. These results show that the eastern roadways of the Beiyangzhuang mine are more dangerous and have a high possibility of water inrush. In 2014, a large coal-floor water-inrush accident occurred when driving the roadway of the second mining level. This water-inrush event is used herein as the research object. The spreading of the water inrush before and after the implementation of water-inrush control measures was simulated using the spatiotemporal model, and the water-inrush control measures were evaluated for this water-inrush event.

The roadway network system of the Beiyangzhuang coal mine is constructed (Figure 12) following the measured elevation, the mining engineering plan, and the cross-sectional size of the roadways. The Beiyangzhuang roadway network system consists of 1606 nodes, of which node 1596 is the inflow node and three shaft exits are the outflow nodes. A total of 1699 segments are used in the simulations. Then, the roadway geometric and the hydraulic parameters are set, as shown in Table 3: There are two cross-section types: rectangular and semicircular arch, the dimensions of which are shown in Figure 13. We use n = 0.015 according to the properties of the wall materials of the roadway, and α = 7 on the branch roadway with large Froude number Fr. Moreover, the inflow curve of the water inrush for this water-inrush accident is set (Figure 14).

To prevent the mine from flooding and avoid casualties, water-inrush control measures have been implemented. Two water-blocking walls and two pumps have been added to the roadway to control the water-inrush spread. The height of the water-blocking segment is 0.71 m. The average displacement of the pump is 483 m³/h. Next, the spreading of the water inrush before and after the implementation of water-inrush control measures was calculated. These two cases were analyzed using a 0.2 s routing step and a 22-day, 19-hour simulation, from 17:00 on September 27 to 12:00 on October 20.

When water inrush occurs at node 1596, the water inrush spreads upward and flows into the roadways of the first mining level. The water head of node 1597 reflects the height of the water inrush spreading upward. Figure 15 compares the simulated water head at node 1597 before and after the water-inrush control measures. The results show that the water head decreases significantly due to the water-inrush control measures. With no water-inrush control measures, the water-inrush rises to about 115 m.

Figure 16 shows the water-inrush spread before and after implementing the water-inrush control measures on October 20. The roadway suffers five levels of submergence according to the water head. The blue line indicates the roadway with no water, and the red line indicates the roadway submerged by a water head of over 3.0 m. Figure 16(a) shows that the water inrush submerges the second mining level roadway and the shaft exits located in the middle of the mine roadway. This situation is dangerous because it would prevent the escape and rescue of mine workers. Conversely, Figure 6(b) shows that the water-inrush control measures are effective because only a few roadways of the second mining area are submerged.

Water-inrush disasters are one of the most pressing problems in the mining industry. To reduce the safety hazard of water-inrush, this paper proposes a novel method to predict water-inrush spreading that uses a spatiotemporal model based on pipe-flow theory to simulate the water-inrush spreading in a mine roadway network. The proposed model considers the energy loss in bifurcated roadways and the role of pumps and water-blocking equipment in controlling the water-inrush spread. The results of experimental studies serve to verify the model calibration and confirm its accuracy. The Nash–Sutcliffe efficiency criterion E_ns for the simulation results is greater than 0.64, which indicates that the model is sufficiently accurate. The importance of the roadway geometry and the hydraulic parameters are studied by using a sensitivity analysis based on the modified Morris screening method. The results indicate that the roadway length, cross-sectional width, and energy-loss coefficient α are the most important parameters affecting the simulation of water-inrush spread. In general, the roadway geometry is more important than the hydraulic parameters. Although the sensitivities differ when using different objective functions or different water-inrush flow curves, the sensitivity ranking of these parameters remains basically the same.

The verified model is then applied to a real water-inrush event in Beiyangzhuang Coal Mine to simulate the water-inrush spreading and evaluate the effect of water-inrush control measures. The simulation results show that the water-inrush spreading decreases significantly upon implementing the inrush control measures. It also demonstrates the effectiveness of the spatiotemporal model for predicting the spreading of water inrush. In general, the approach proposed herein accurately predicts water-inrush spreading and is thus suitable for large-scale mine roadway networks. These results should prove helpful for developing effective water-inrush control measures and assist mining personnel in escaping, thereby ensuring the safety of underground mining.

This research was financially supported by China National Natural Science Foundation (41877186, 42027801), National Key R&D Program of China (2016YFC0801800), Fundamental Research Funds for the Central Universities (2021YQDC08), Innovation Research Team Program of Ministry of Education (IRT1085) and State Key Laboratory of Coal Resources and Safe Mining.

The authors declare that they have no conflict of interest.

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