Evaluation of Water Inrush Risk in the Fault Zone of the Coal Seam Floor in Madaotou Coal Mine, Shanxi Province, China

Abstract

As coal seams are mined at greater depths, the threat of high water pressure from the confined aquifer in the floor that mining operations face has become increasingly prominent. Taking the Madaotou mine field in the Datong Coalfield as the research object, in the context of mining under pressure, for the main coal seams in the mining area, first of all, an improved evaluation method for the vulnerability of floor water inrush is adopted for hazard prediction. Secondly, numerical simulation is used to conduct a simulation analysis on the fault zones in high-risk areas. By using the fuzzy C-means clustering method (FCCM) to improve the classification method for the normalized indicators in the original variable-weight vulnerability evaluation, the risk zoning for water inrush from the coal seam floor is determined. Then, through the numerical simulation method, a simulation analysis is carried out on high-risk areas to simulate the disturbance changes of different mining methods on the fault zones so as to put forward reasonable mining methods. The results show that the classification of the variable-weight intervals of water inrush from the coal seam floor is more suitable to be classified by using fuzzy clustering, thus improving the prediction accuracy. Based on the time effect of the delayed water inrush of faults, different mining methods determine the duration of the disturbance on the fault zones. Therefore, by reducing the disturbance time on the fault zones, the risk of karst water inrush from the floor of the fault zones can be reduced. Through prediction evaluation and simulation analysis, the evaluation of the risk of water inrush in coal mines has been greatly improved, which is of great significance for ensuring the safe and efficient mining of mines.

1. Introduction

Research on the mechanism of water inrush from the floor has always been a research hotspot in mine water disasters. Especially as the resources of the upper coal seams have been almost exhausted, many mining areas have begun to mine the lower coal seams. The mining of the lower coal seams not only faces water disaster problems such as water accumulation in the goaf of the roof but also needs to deal with the threat of high-pressure Ordovician limestone karst water in the deep floor [1]. In the early 20th century, the major coal-mining countries in the world had already discovered the key role of the floor aquiclude in the prevention and control of floor water disasters and carried out a series of studies on rock mass structures and failure characteristics to reveal the significance of the thickness of the floor aquiclude [2]. With the continuous improvement of many related theories such as geology and mechanics, the inherent relationship between water pressure and the thickness of the aquiclude has been explored. Some scholars have studied the anti-water inrush ability of the aquiclude in the coal seam floor from the perspective of statics and deduced the relevant safe water pressure values [3]. There are also studies on the failure mechanism of the floor by improving the rock mass strength theory of Hoek–Brown [4]. Later, starting from the “key stratum” theory of the overlying strata, Qian Minggao et al. put forward the key stratum theory of the floor to study the failure mechanism of the floor aquiclude and the mechanism of water inrush from the floor [5]. For the intact rock section, the mechanism of water inrush from the floor is actually a “sandwich” structure. The “lower three zones” theory elaborates three important component structures for the formation of the water-conducting channel in the floor: the floor failure zone, the water-resisting zone, and the water-conducting rising zone [6]. Theories such as the “progressive water-conducting rising” theory and the “strong seepage channel” theory have studied the formation mechanism of the water-conducting rising zone of the confined water in the aquiclude floor and systematically carried out research on the mechanism of water inrush from the coal seam floor. Zhang Baoliang et al. analyzed the law of water-conducting rising of the confined water in the coal seam floor and used two-dimensional similar-material simulation tests to show the formation process of the water inrush channel when the confined water in the coal seam floor rises [7]. Bian Kai et al. used numerical simulation means and studied the law of water-conducting rising of the confined water in the coal seam floor based on the fluid–solid coupling theory and simulated the extension mechanism between the original water-conducting rising height and the re-water-conducting rising height under various mining conditions [8].

However, in actual engineering cases, water inrush disasters in coalfields are all related to geological structures, especially faults. Structures play an important role in mine water inrushes [9]. On the one hand, structures change the integrity of strata. For faults, they sometimes make the minable coal seams connect with aquifers, increasing the risk of water inrush. Moreover, faults also play a connecting role and are potential water inrush channels. On the other hand, structures have the function of storing water. When mining, if certain water-storing structures are encountered, there may be risks of increased water inflow or water inrush. In China, the proportion of water disasters caused by faults in coal mine floor water inrush accidents is relatively large. Yin Huiyong et al. have summarized and prospected the issues regarding the setting of water-proof coal (rock) pillars for mine faults in China. Among them, relevant studies from theoretical calculations to numerical simulations for different fault conditions have been continuously carried out, pointing out the existing problems and development prospects [10]. Zhang Qingyan et al. have developed a large indoor water inrush and mud inrush test system that takes into account mass transfer and the in situ stress state, which is used to study the mechanism of water inrush and mud inrush in tunnels in water-rich fault fracture zones [11]. Lu Tong adopted a combination of theoretical analysis and numerical simulation to study the water inrush mechanism of fault activation from the basic characteristics of faults to the influence of mining and excavation, with fault activation and water inrush channels as the research objectives [12].

In the phenomenon of water inrush caused by geological structures, there is also the situation of delayed water inrush of faults. The situation of delayed water inrush of faults is relatively common in the actual coal mining process. For example, there are concealed faults in the working face, and the nature of the faults is that of water-resisting faults. Under the influence of mining activities, they slowly become activated and cause water inrush [13]. Chen Kunfu et al. applied the stress–permeability coupling model in the process of surrounding rock deformation and the failure to analyze water inflow and stability and studied the mechanism of delayed water inrush in the fault fracture zone [14]. Liu Weitao et al., aiming at the characteristics of the Ordovician limestone aquifer in the Carboniferous-Permian coalfields in North China, carried out a fluid–solid coupling simulation and seepage creep calculation on the fault zone by using numerical simulation software on the basis of obtaining the required mechanical parameters of fault materials [15]. Wu Qiang et al., based on on-site measurements and laboratory tests, carried out three-dimensional elastoplastic numerical simulation, revealed the weakening mechanism and main controlling factors of the fault zone, and put forward the role of the time weakening effect in water inrush from the fault structure of the coal seam floor [16]. Judging from the current research results, more scholars tend to use numerical software to conduct relevant research on the mechanism of delayed water inrush of the fault zone. If one wants to know the lagging characteristics of the fault zone in terms of the time effect, the superiority of numerical simulation can be well exerted and reflected. It can not only simulate the seepage change process brought about by the time difference but also simulate the different water inrush characteristics brought about by the stress–strain changes in the fault zone under different geological conditions [17].

In the research on floor water inrush, the multidisciplinary and cross-disciplinary applications centered around many basic theories have also achieved a lot of progress. For example, the applications of ArcGIS, artificial neural networks, the analytic hierarchy process, and fractal theory have further strengthened the research on the mechanism of floor water inrush [18,19,20]. Wu Qiang et al., on the basis of summarizing the main controlling factors of coal seam floor water inrush, utilized the ArcGIS multi-source information composite overlay technology combined with the analytic hierarchy process, entropy weight and variable weight, etc., to evaluate the risk of floor water inrush through the vulnerability index method [21,22,23,24]. Jin Dewu et al. applied the artificial neural network method to the prediction and forecast of floor water inrush, which fully demonstrated the applicability of the learning process of artificial neural networks in the problem of water inrush forecasting [25]. Shi Longqing et al., through the method of coupled weighting, combined the analytic hierarchy process and the entropy weight method from the perspectives of subjective and objective weighting and established a multi-source information fusion evaluation model on the basis of selecting eight main controlling factors for analysis [26]. Currently, in the evaluation of the risk of floor water inrush, the water inrush coefficient method and the floor water inrush vulnerability index method are widely used. From past research, we found that the water inrush coefficient method belongs to an empirical formula and only considers two influencing factors. In comparison, the vulnerability index method, under the comprehensive action of considering multiple factors, not only has a complete index system but also has a more perfect evaluation method [27,28]. By comparing the two evaluation results, it can be found that the prediction accuracy of the water inrush coefficient method is poor, and there is no transition area from the safe area to the vulnerable area, which obviously does not conform to the actual geological situation. Meanwhile, in the practical application of the vulnerability index method, we found that the algorithm for dividing the index intervals needs to be improved and optimized. In many application scenarios, we often need to classify certain specific things according to certain standards [29]. For example, the recognition of pictures, the classification of animals, the comparison and selection of fingerprints, the sorting in logistics, and even the classification of engineering scales in engineering and the classification of soils and rocks in geology, etc. [30,31,32]. In mathematics, the method of classifying objective things through certain definitions and calculations is called cluster analysis, which is a classification method in multivariate statistics. However, in the classification process, the basis and standards for classification are difficult to determine and divide in certain scenarios and applications. For example, there is no clear dividing basis for defining good and bad in some things, and the dividing boundaries of some qualitative indicators are difficult to quantify. For the classification of such things, the fuzzy mathematics method is often used for cluster analysis in many current practical applications [33]. There are many qualitative and quantitative indicators in the evaluation of coal seam floor water inrush, and the classification relationship among the indicators is fuzzy. Therefore, fuzzy cluster analysis is more applicable to the division of variable-weight intervals and the zoning of vulnerability indexes for coal seam floor water inrush. Fuzzy cluster analysis can be divided into four types according to the implementation methods. Among them, relational clustering, hierarchical clustering, and graph theory clustering are limited by the size of the data volume and are not suitable for the evaluation of coal seam floor water inrush. Therefore, the fourth type of clustering method based on the objective function has more universal applicability in classifying the variable-weight intervals and grading the vulnerability indexes in the evaluation of coal seam floor water inrush in terms of certain application practicality [34].

Taking the Madaotou minefield threatened by the karst water of the Ordovician limestone in the floor as the research object, this paper uses the variable-weight vulnerability index method based on the FCCM to evaluate the risk of the main mining coal seams. Since there are qualitative and quantitative differences among the main controlling factors of water inrush from the coal seam floor, the classification relationship among the indicators is fuzzy. Therefore, the clustering effect of FCCM is better than that of the commonly used K-means clustering in the past. The FCCM can transform the clustering of data into a nonlinear optimization problem according to a certain discriminant criterion and solve it through iteration. Based on the time effect of delayed water inrush of faults, different mining methods determine the duration of disturbance to the fault zone. Therefore, the risk of karst water inrush from the floor of the fault zone can be reduced by reducing the disturbance time to the fault zone. When mining the strata in this area in the future, it is necessary to conduct surveys on the height of the confined water rising zone to prevent floor water inrush accidents caused by the reduction in the thickness of the effective aquifuge layer of the floor.

2. Materials and Methods

2.1. Study Area

The Madaotou minefield is located in the southwest of the Datong Coalfield, within the territory of Zuoyun County, Datong City. It is about 45 km away from the urban area of Datong in the northeast direction and about 15 km away from Zuoyun County in the northwest direction. The minefield is about 20.087 km long from east to west and about 12.575 km wide from north to south. The designed production capacity of the mine is 10.00 Mt/a. The strata exposed by boreholes in the minefield, from old to new, include the Cambrian System, Ordovician System, Carboniferous System, Permian System, Jurassic System, Cretaceous System, and Quaternary System. The main mining coal seams are those of the Taiyuan Formation in the Carboniferous System. From the perspective of geological structure, this area is generally cut into two parts by the F99 and F98 fault groups, and at the same time, a typical graben area is formed. Under normal conditions, the hydraulic connection between the karst groundwater in the limestone and surface water is relatively poor. However, in the areas where fault structures are developed, the hydraulic connection among various aquifers mainly depends on fault channels. Based on the data of previous exploration hydrological boreholes, the natural flow field of the Ordovician karst fissure water has been drawn. The drainage conditions of the karst fissure water are relatively complex. As shown in Figure 1, the runoff direction is from west to east, and it is locally affected by the graben.

2.2. Methods

Vulnerability refers to the ability to resist corresponding disasters reflected by the inherent attributes before the occurrence of disasters themselves. The evaluation of floor water inrush vulnerability means the ability of the floor aquiclude to resist water inrush during the coal mining process. In this evaluation, the variable-weight interval classification method for vulnerability is improved by using the fuzzy C-means clustering method, and this classification method is applied to conduct the vulnerability evaluation zoning, realizing the evaluation of karst water inrush vulnerability of the coal seam floor based on the fuzzy C-means clustering. Based on the analysis of the geological conditions of the mining area and the vulnerability evaluation, the process of the disturbance change in the fault zone caused by coal mining under the influence of the graben structure is constructed by using numerical simulation software (Itasca International Inc., Itasca, IL, USA). The disturbance characteristics of the fault zone caused by coal mining under different mining methods are revealed, so as to comprehensively evaluate the risk of water inrush in the floor fault zone. The detailed flow chart of the methods used in this study is shown in Figure 2.

2.2.1. Vulnerability Assessment

• (1). Vulnerability Index

The vulnerability model of water inrush from the coal seam floor is based on the analysis of geological conditions, the analysis of water inrush factors, and the contribution mechanism of each factor to water inrush [35]. The results are reflected in the vulnerability index (VI), and its calculation formula can be expressed as follows:

(1)$VI=\sum _{k=1}^n{W}_k{f}_k(x,y)$

where $W_k$ is the weight of the influencing factor; $f(x,y)$ is the single-factor influence value function; $n$ is the number of influencing factors. $f_k\left(x,y\right)$ is the normalized value of the quantized value of the k-th master control factor.

First, the state vector function needs to be constructed. Second, the parameter values in the vector function that meet the expected weights need to be inversely calculated. Therefore, this paper adopts the state–variable-weight vector mathematical function (Formula (2)), which conforms to the water inrush decision-making law in previous studies. The state–variable-weight vector function can satisfy the adjustment of the coal seam floor fragility evaluation for the corresponding change in the index. The amplitude change in the weight adjustment is shown in Figure 3, based on which the demand for weight change can be achieved [36].

(2)$S_j\left(x\right)=\left\{\begin{array}{c}{e}^{a_1(d_{j1}-x)}+c-1, x\in \left[0,d_{j1})\right.\\ c, x\in \left[d_{j1},d_{j2})\right.\\ e^{a_2(x-d_{j2})}+c-1, x\in \left[d_{j2},d_{j3})\right.\\ e^{a_3(x-d_{j3})}+e^{a_2(d_{j3}-d_{j2})}+c-2, x\in \left[d_{j3},1\right]\end{array}\right.$

where $d_{j1}, d_{j2} \mathrm{a}\mathrm{n}\mathrm{d} d_{j3}$ are the j-th factor variable-weight interval thresholds; $c, a_1, a_2 \mathrm{a}\mathrm{n}\mathrm{d} a_3$ are the adjustment parameters.

Combining the determined state–variable-weight vector with the vulnerability index method, a variable-weight calculation model for the evaluation of the vulnerability to water inrush from the coal seam floor can be obtained, as shown in Formula (3).

(3)$W\left(X\right)={\displaystyle \frac{W_{0}S\left(X\right)}{\sum _{j=1}^n{w}_j^{\left(0\right)}{S}_i\left(X\right)}}=\left({\displaystyle \frac{w_1^{\left(0\right)}{S}_1\left(X\right)}{\sum _{j=1}^m{w}_j^{\left(0\right)}{S}_i\left(X\right)}},{\displaystyle \frac{w_2^{\left(0\right)}{S}_2\left(X\right)}{\sum _{j=1}^m{w}_j^{\left(0\right)}{S}_i\left(X\right)}},\dots ,{\displaystyle \frac{w_n^{\left(0\right)}{S}_n\left(X\right)}{\sum _{j=1}^m{w}_j^{\left(0\right)}{S}_i\left(X\right)}}\right)$

The evaluation index system for karst groundwater inrush from the coal seam floor of the Madatou Mine constructed here takes into account three aspects: hydrogeological conditions, aquiclude conditions, and geological structures. There are a total of seven indicators as follows: distribution of structures; distribution of intersection and end points of faults; fault scale index; water pressure of the aquifer; water abundance of the aquifer; equivalent thickness of the effective aquiclude; thickness of the brittle rock on the floor. The vulnerability index method is adopted for the preliminary data processing.

• (2). Fuzzy C-means clustering method

Based on the water inrush vulnerability evaluation method of the floor and the variable-weight theory, aiming at the mining situation with pressure in the main coal seam in the mining area, by improving the classification method in the vulnerability evaluation of the original variable weight, FCCM is employed to change the weight of the main control factor index and divide the interval and the evaluation interval [37]. Fuzzy C-means clustering is the process of dividing data into n vectors $x_i(i=1,2,\cdots ,n)$ to form c fuzzy groups. By minimizing the value function of non-similarity indicators, the clustering centers of each group are calculated. The algorithm is based on the idea of fuzzy mathematics, so the degree of belonging to each group is determined by the membership relationship between (0,1) for each given data point [38]. Adapted to the introduction of fuzzy partition, the membership matrix U allows elements with values between (0,1). According to the normalization principle, the sum of the membership degrees of a dataset is always equal to 1, which can be expressed by the following formula [39]:

(4)$\sum _{i=1}^c{u}_{ij}^k,\forall j=1,2\cdots ,n$

Then, the objective function (or value function) of fuzzy C-means clustering is as follows:

(5)$J\left(U,c_1,\cdots ,c_c\right)=\sum _{i=1}^c{J}_i=\sum _{i=1}^c\sum _j^n{u}_{ij}^m{d}_{ij}^2$

In the formula, U_i,j is between 0 and 1; C_i is the cluster center of fuzzy group i, $d_{ij}=‖c_i-x_j‖$ is the Euclidean distance between the i-th cluster center and the j-th data point; and $m\in \left[1,\infty )\right.$ is a weighted index, which is the key to distinguishing hard clustering from fuzzy clustering.

2.2.2. Numerical Simulation

• (1). Conceptual model of engineering geology

Taking the 8201 working face of the Madatou Coal Mine as an example, according to the distribution map of the working faces in the mining area, the distribution of geological structures, and the drilling data near the working face, two faults have formed a graben structure. The dip angle of the faults is 70°. Due to the large extension of the fault strike in the graben area in the middle and south of the entire mining area, there are certain differences in the dip angles of faults in different parts, and, meanwhile, the throw range is 30–230 m. In order to make the local model more in line with the actual geological conditions, this paper selects the drilling data of three boreholes on the typical profile line as the basis for modeling. The three boreholes are located at the left end of the graben, inside the graben, and at the right end of the graben, respectively. An engineering geological physical conceptual model shown in Figure 4 has been established.

Boundary conditions of the established numerical model: The displacements in the horizontal and vertical directions are zero, and the displacement of the lower boundary of the model is also zero. The top of the model is a free boundary. The simulated working face for coal seam mining is located at the footwall of Fault F98 on the left end of the model. The burial depth of the coal seam is about 340 m. The size of the working face is 220 m. The average thickness of Coal No. 3–5 is 14 m. The water pressure of the Ordovician limestone at the bottom is about 3.4 Mpa. The overall size of the model is 500 m in width, 600 m in height, and 1500 m in length. The model is divided into 1,042,214 units in total. The generalization of the model from the top to the bottom includes the sandstones of the Upper and Lower Shihezi Formations, the sandstones of the Shanxi Formation, the sandstones of the Taiyuan Formation, Coal No. 3–5, the mudstones of the Benxi Formation, and the Ordovician limestones, in sequence. For the convenience of calculation, the model has been simplified to a certain extent (Figure 5).

• (2). Simulation scheme design

The purpose of numerical simulation is to explore the water inrush mechanism of the karst aquifer along the fault zone under the influence of the graben structure. The simulated mined coal seam is Coal No. 3–5. The simulation is divided into two different mining directions, that is, starting mining close to the fault zone and starting mining away from the fault zone. It aims to simulate the disturbance impact of mining on faults and the evolution law of seepage under different mining methods. According to the “Detailed Rules for Prevention and Control of Water in Coal Mines”, the calculated design for retaining the water-proof and water-blocking coal pillar in the fault zone during this simulation is 100 m. The excavation steps start from one side of the fault. The cut hole is opened at the location where the water-proof and water-blocking coal pillar of the fault is reserved, and the mining starts from right to left. It is divided into 14 steps in total, with 20 m mined in each step.

3. Results

3.1. Vulnerability Assessment Results

According to Formula (1), the mathematical model of the variable-weight coal seam floor water inrush vulnerability evaluation based on fuzzy C-means clustering in the Madaotou mine is expressed as follows:

(6)$\begin{array}{cc}\hfill VWVI=& {\displaystyle \sum _{i=1}^m}{\displaystyle \frac{w_i^{\left(0\right)}{S}_i\left(X\right)}{\sum _{j=1}^m{w}_j^{\left(0\right)}{S}_i\left(X\right)}}{f}_i\left(x,y\right)\hfill \\ & \hspace{1em}\hspace{1em}\hspace{1em}={\displaystyle \frac{w_1^{\left(0\right)}{S}_1\left(X\right)}{\sum _{j=1}^7{w}_j^{\left(0\right)}{S}_i\left(X\right)}}{f}_1\left(x,y\right)+{\displaystyle \frac{w_2^{\left(0\right)}{S}_2\left(X\right)}{\sum _{j=1}^7{w}_j^{\left(0\right)}{S}_i\left(X\right)}}{f}_2\left(x,y\right)+{\displaystyle \frac{w_3^{\left(0\right)}{S}_3\left(X\right)}{\sum _{j=1}^7{w}_j^{\left(0\right)}{S}_i\left(X\right)}}{f}_3\left(x,y\right)\hfill \\ & \hspace{1em}\hspace{1em}\hspace{1em}+{\displaystyle \frac{w_4^{\left(0\right)}{S}_4\left(X\right)}{\sum _{j=1}^7{w}_j^{\left(0\right)}{S}_i\left(X\right)}}{f}_4\left(x,y\right)+{\displaystyle \frac{w_5^{\left(0\right)}{S}_5\left(X\right)}{\sum _{j=1}^7{w}_j^{\left(0\right)}{S}_i\left(X\right)}}{f}_5\left(x,y\right)+{\displaystyle \frac{w_6^{\left(0\right)}{S}_6\left(X\right)}{\sum _{j=1}^7{w}_j^{\left(0\right)}{S}_i\left(X\right)}}{f}_6\left(x,y\right)\hfill \\ & \hspace{1em}\hspace{1em}\hspace{1em}+{\displaystyle \frac{w_7^{\left(0\right)}{S}_7\left(X\right)}{\sum _{j=1}^7{w}_j^{\left(0\right)}{S}_i\left(X\right)}}{f}_7\left(x,y\right)\hfill \end{array}$

In the formula, VWVI represents the variable-weight vulnerability index; W_i represents the variable-weight vector of influencing factors; f_i(x,y) represents the single-factor influence value function; w⁽⁰⁾ represents the constant weight vector; S(X) represents the -dimensional partitioned state–variable-weight vector; m represents the number of indicators; and $i=1, 2,\dots , 7$.

Based on the variable-weight values of each evaluation unit factor in the obtained evaluation area, the calculation is performed by ArcGIS (Environmental Systems Research Institute, Redlands, CA, USA) according to Formula (6). When dealing with the vulnerability evaluation zoning, the FCCM is used to grade the variable-weight vulnerability index values. The final evaluation result is shown in Figure 5. Since only Coal No. 3–5 will be mined in the five-year work plan at the current stage, the distribution positions of the planned working faces during the planning period are added to Figure 6. At present, the mining area is mainly divided into four areas for mining, namely, the No. 1 mining area, the No. 2 mining area, the No. 3 mining area, and the No. 4 mining area.

3.2. Comparison of the Results of the Traditional Water Inrush Coefficient Method

The water inrush coefficient is defined as the water pressure borne by the unit thickness of the aquiclude on the coal seam floor, and it is a quantitative index for measuring the risk degree of water inrush from the coal seam floor under the condition of mining under pressure. It has been revised several times during the application process. Its calculation formula in the “Detailed Rules for Prevention and Control of Water in Coal Mines” is as follows:

(7)$T={\displaystyle \frac{P}{M}}$

where T is the water inrush coefficient, MPa/m; P is the water pressure to which the aquifer base plate is subjected, MPa; and M is the thickness of the base plate water barrier, m.

According to Formula (7), by counting the data on water pressure and the thickness of the floor aquiclude for each Ordovician limestone borehole, the corresponding water inrush coefficient is calculated. According to the “Detailed Rules for Prevention and Control of Water in Coal Mines”, in areas with developed geological structures, the critical water inrush coefficient is generally not greater than 0.06 MPa/m, and in normal areas, the critical water inrush coefficient is not greater than 0.1 MPa/m. Since the geological structures in the research area are relatively developed, for safety reasons, a critical water inrush coefficient of 0.06 MPa/m is adopted to conduct the zoning for the evaluation of the water inrush risk for Coal No. 3–5 in the Madatou Mine, respectively (Figure 7).

3.3. Comparative Analysis

It can be seen from Figure 6 that the overall water inrush coefficient of Coal No. 3–5 during the mining in the Madatou Coal Mine is not large, and only some local areas show dangerous areas (areas where collapse columns appear). From the calculation formula, we can know that the water inrush coefficient method belongs to an empirical formula and only considers two influencing factors. In comparison, the vulnerability index method, under the comprehensive effect of considering multiple factors, not only has a complete index system but also has a more perfect evaluation method. By comparing the two evaluation results, it can be found that the prediction accuracy of the water inrush coefficient method is relatively poor, and there is no transition area from the safe area to the vulnerable area, which obviously does not conform to the actual geological situation.

As shown in Figure 7, it is found that the traditional water inrush coefficient method predicts almost the entire mining area as a safe area, with only a few local areas being identified as dangerous areas. On the one hand, in terms of the pressure-bearing situation of the floor of Coal No. 3–5, almost the entire mining area is a pressure-bearing area, with the maximum water pressure reaching 3.7 MPa. However, relatively speaking, the thickness of the aquiclude on the floor of Coal No. 3–5 is relatively thick (the maximum thickness is 117 m). According to the water inrush coefficient method, the conclusion that the whole area is safe is drawn. It can be found from the vulnerability evaluation method (Figure 5) that most areas of the evaluation area for Coal No. 3–5 are relatively safe areas and moderately safe areas. However, due to the influence of faults and collapse columns in the areas where geological structures are distributed, these areas are mostly relatively vulnerable areas and vulnerable areas. In the northern part of the mining area, the water pressure of the Ordovician limestone is high. In the northeastern part, due to the relatively reduced thickness of the aquiclude, there are local vulnerable areas and most of the areas are transition areas. By comparing the evaluation zoning maps of the two methods for the karst water inrush from the coal seam floor of the Madatou Mine, it can be found that the water inrush coefficient method ignores many key factors, such as the water abundance of the aquifer. It is rather unreasonable to give the result that the whole area is dangerous only based on the thickness of the effective aquiclude and the water pressure borne by the aquiclude. In addition, the water inrush coefficient method does not take geological structure factors into account, while these factors have a very important influence in the process of water inrush from the coal seam floor. In the vulnerability index method, the above problems ignored by the water inrush coefficient method are comprehensively considered, and the influence of various water inrush factors on the actual situation is analyzed in an all-round way, resulting in a more detailed vulnerability zoning, which has greater guiding significance for production.

4. Discussion

4.1. Analysis of the Initial Equilibrium State

As shown in Figure 8 of the model, due to the influence of geological processes, the strength of the fault zone is lower than that of the surrounding rock, and a low-stress area is formed within the fault zone where the stress is relatively lower compared to that in the normal strata. Affected by the upper load, the fault zone is mainly under compressive stress, and a stress concentration area is formed at the bottom of the graben. Since the fault is not disturbed under the natural state, from the perspective of geophysical exploration results, when it is close to the Ordovician limestone aquifer, the fault zone exhibits water-conducting characteristics. However, as the distance from the Ordovician limestone increases and the overlying strata are composed of alternating layers of sandstone and mudstone, the fault zone shows water-blocking characteristics. Therefore, in order to be more in line with the actual situation, when assigning parameters during modeling, the initial water pressure state as shown in the figure is generalized by taking various factors into comprehensive consideration.

After the initial equilibrium of the model, there is a relatively small seepage phenomenon from the top of the Ordovician limestone to the Benxi Formation. This indicates that in the absence of mining, the karst water in the Ordovician limestone will have a certain upward migration phenomenon. However, due to the relatively large thickness and small permeability coefficient of the mudstone in the Benxi Formation and the presence of an ancient, weathered crust developed at the top of the Middle Ordovician System, there is a certain hindering effect on the upward migration of confined water under the natural state.

4.2. Disturbance Characteristics of Forward Mining

4.2.1. Development Law of the Plastic Zone

The identification of the simulation results is determined by the failure modes in the model. Plastic failure can be divided into two types: tensile failure (tension-n; tension-p) and shear failure (shear-n; shear-p). “n” stands for “new”, indicating newly emerged plastic failure; “p” stands for “past”, indicating that the yield state has occurred before.

From Figure 9, the development law of the plastic failure of the coal seam roof and floor strata during the advancement of the working face can be observed. When the working face advances to 20 m, the development degree of the plastic zone around it is relatively small, the influence range of mining is also relatively small, and shear failure is the main form. At this time, no obvious deformation and failure occur in the coal seam floor. Meanwhile, the top of the fault zone is affected by mining and partial shear failure occurs, and extremely small plastic failure appears at the bottom of the model fault, and this failure is based on the past yield state. When the working face advances to 40 m, the development of the plastic zone around it becomes larger, and local tensile failure occurs in the roof and floor, but no new shear failure occurs in the fault. With the continuous advancement of the simulated working face, the plastic failure range of the roof and floor in the coal seam goaf further expands, and the roof mining fissure zone develops most significantly, approximately in a “saddle” shape. When the mining advancement distance reaches 120 m, the No. 2 fault begins to show plastic failure due to the influence of mining. After that, as the working face advances, the influence range of plastic failure continuously increases. When it reaches 200 m, a plastic failure zone appears in the middle of the graben. When the working face advances to 240–280 m, the height of the roof water-conducting fissure zone reaches a maximum of about 194 m, and the average influence range of the floor failure zone is 25 m. At this time, the plastic failure range in the middle of the graben increases and is mainly concentrated at the bottom of the fault, and the plastic zone failure in the fault zone extends upward along the fault zone, and the range gradually becomes larger. However, there is no communication between the failure range of the roof and floor and the fault zone, and this phenomenon is closely related to the dip angle of the fault and the distance of the reserved water-proof coal pillar.

4.2.2. Distribution Law of the Stress Field

Figure 10 presents the dynamic change trend of the stress distribution inside the model during the process of the working face advancing. Since the mining operation of the working face was started, the surrounding rock stress was immediately redistributed, and an elliptical stress arch structure was formed in the roof and floor areas of the working face. When the working face was advanced to the point of 40 m, the rock strata in the roof and floor of the goaf initially showed a tensile stress zone. With the continuous and in-depth progress of the simulation advancing operation, it can be clearly observed that the stress concentration degree at both ends of the working face shows a continuously intensifying trend. Meanwhile, the disturbance effect on the fault zone is also constantly increasing. Especially around the section of the fault zone that is parallel to the working face, the stress concentration phenomenon is particularly remarkable. Through comparative analysis with the development status of the plastic zone, it can be known that the disturbance effect caused by the mining activities continues to spread and expand towards the deep part of the fault, which then leads to the emergence of shear failure at the bottom of the fault zone and gradually develops upward along the fault zone. This dynamic evolution process not only accelerates the activation process of the fault but also speeds up the rising rate of the confined water simultaneously.

4.2.3. Variation Law of the Seepage Field

As illustrated in Figure 11, when the working face had been advanced by 20 m, no conspicuous impact was exerted on the confined water in the coal seam floor. However, within the fault zone, a certain degree of confined water upwelling occurred near the aquifer. Upon advancing to 120 m, an evident seepage phenomenon emerged in the fault zone. The distribution of the floor-confined water manifested as a certain level of water level decline centered around the working face, indicating that due to the upwelling of the confined water along the fault zone and the stress variation, the water pressure of the aquifer also underwent changes. When the working face was further advanced to 160 m, the upwelling of the karst-confined water in the floor within the fault zone became increasingly pronounced. Meanwhile, local seepage also appeared in the right fault zone of the graben area. In contrast to the seepage pattern of the left fault, the right fault not only exhibited a tendency for confined water to upwell along a small section of the fault zone but also presented an obvious seepage phenomenon in the rock strata adjacent to the fault zone. The difference lies in the fact that, as the right fault was relatively farther away from the working face, the perturbation intensity was relatively low. Consequently, the confined water in the floor was unable to upwell along the fault zone, resulting in a wider seepage range in the local water-resisting layer section compared to that of the left fault. Although the right side of the model had not been excavated, it provided valuable reference and guidance for subsequent mining operations. As the working face mining continued and the working face drew nearer to the fault, the upwelling height of the confined water within the fault zone ceased to increase further; nevertheless, the water pressure within the fault zone gradually rose.

Figure 12 depicts the seepage variation diagram of the fault zone in the graben area when the working face has been advanced to 280 m. In Figure 11, the position of F1 is on the left side of the fault. Owing to the presence of a sufficiently safe water-proof and water-isolation coal pillar, on the one hand, the plastic failure zone has not extended to this location. On the other hand, the seepage of the fault zone has only developed 16.5 m in the direction of the working face. Hence, a water inrush channel has not been formed. Although the confined water possesses certain dynamic conditions, due to the hysteresis of the fault zone seepage, the likelihood of posing a water inrush threat to the working face at the current stage is relatively low. The position of F2 in Figure 11 is within the confined water upwelling zone of the water-resisting layer in the coal seam floor (resulting from mining activities). Its development height is evidently relatively high, with an approximate upwelling height of 35 m. It not only diminishes the effective thickness of the water-resisting floor layer but also constitutes a significant potential safety hazard for subsequent coal seam mining. Simultaneously, there is a tendency for the water pressure within the graben area to increase.

4.3. Disturbance Characteristics of Retreating Mining

4.3.1. Development Law of the Plastic Zone

As can be observed from Figure 13, there exist differences in the developmental patterns of plastic failure of the coal seam roof and floor strata under the conditions of retreat mining and advancing mining. When the working face advancing distance reaches 20 m, the plastic zone developed around the model working face is relatively small, the mining-induced influence range is limited, and shear failure predominates. Meanwhile, no conspicuous damage has occurred on the floor yet. At this juncture, the top of the fault zone has already begun to be affected by mining activities, with partial shear failure taking place. However, when the working face advances to 40 m, the development scope of the plastic zone surrounding the model working face expands. Obvious local tensile failure emerges on the roof and floor, and the range of the plastic failure zone at the bottom of the fault enlarges as well. This indicates that the mining method in close proximity to the fault zone exerts the earliest perturbation on the fault. With the progression of the working face, the plastic failure range of the roof and floor in the goaf will further expand, among which the development of the roof mining-induced fracture zone is the most prominent. When the working face advances to 80 m, the right fault in the graben structural area gradually begins to be influenced by mining, giving rise to plastic failure. As the working face advances to 120 m, the influence range of plastic failure continuously expands, and a plastic failure zone also begins to emerge in the middle of the graben. When the working face advancing distance ranges from 160 m to 200 m, the perturbation and damage conditions of the fault zone in the graben area are comparable to those when advancing mining reaches 280 m. When the working face is advanced to 280 m, the height of the roof’s water-conducting fracture zone reaches approximately 190 m, and the average depth of the floor failure zone is 25 m. The damage at this moment is identical to that of advancing mining. The overall simulation process demonstrates that different mining directions primarily affect the perturbation time of the fault. The failure range of the floor has not yet interconnected with the fault zone, whereas the roof plastic failure has established a certain degree of local connection with the fault zone.

4.3.2. Distribution Law of the Stress Field

Figure 14 illustrates the variation in stress distribution within the model during the advancement of the working face. It exhibits similarities to the stress distribution pattern depicted in Figure 9. Upon commencement of the working face’s mining operation, the surrounding rock stress undergoes redistribution, and an elliptical stress arch emerges on the roof and floor of the working face. When the simulated working face has advanced a distance of 40 m, tensile stress zones start to appear in the strata of the roof and floor of the goaf. As the working face progresses further, the stress concentration at both ends becomes pronounced and continues to expand, concomitantly increasing the perturbation on the fault zone. Likewise, within the range of the fault zone parallel to the working face, the stress concentration is conspicuous. Meanwhile, under the same advancing distance, the tensile stress in the case of retreat mining is consistently smaller compared to that of advancing mining, whereas the compressive stress in retreat mining is slightly larger than in advancing mining. Consequently, the plastic failure in retreat mining leads to a certain degree of connection between the roof and the fault zone.

4.3.3. Variation Law of the Seepage Field

In contrast to the advancing mining method, under the premise of setting the same water-proof and water-isolation protective coal pillars, the retreat mining approach initiates perturbation on the fault zone right from the start of the mining process (as shown in Figure 15). When the working face has advanced 20 m, no significant impact is exerted on the karst-confined water in the coal seam floor. However, within the fault zone, a certain degree of confined water upwelling phenomena occurs near the aquifer. As the working face continues to advance and reaches 40 m, an evident seepage phenomenon emerges within the fault zone. The distribution of the floor-confined water experiences a certain degree of decline centered around the working face, indicating that due to the upwelling of the confined water along the fault zone and the stress variation, the water pressure of the aquifer also undergoes changes. With the increasing upwelling of the confined water in the fault zone, local seepage also appears in the right fault zone. The seepage phenomena within the fault zone all occur earlier than those in the advancing mining method, with an advancement distance approximately 80 m ahead. Nevertheless, the overall subsequent development and distribution situations are identical to those of the advancing mining method.

Figure 16 presents the seepage variation diagram of the fault zone when the working face has been advanced to 280 m. Similar to the advancing mining approach, due to the presence of a sufficiently safe water-proof and water-isolation coal pillar, the plastic failure zone in the horizontal direction of the working face has not extended to this location. The seepage of the fault zone has only developed 17 m in the direction of the working face (as shown in Figure 15—F1), which is slightly larger than that in the advancing mining. Although there is a relatively small range of communication between the roof water-conducting fracture zone and the fault, the upwelling height of the confined water along the fault zone has not reached the plastic failure range. That is to say, the water inrush channel of the coal seam floor is of the structural conduction type, where the fault zone serves as the water-conducting channel. However, the water inrush intensity is insufficient, and the water inrush danger is relatively low. The position of F2 in Figure 15 is within the confined water upwelling zone of the floor’s water-resisting layer. Its development height is evidently relatively high, with an approximate upwelling height of 36 m, which is also relatively increased. This indicates that if the fault zone is perturbed and damaged in advance, the seepage influence of the fault zone will become larger.

4.4. Disturbances and Changes in Fault Zones

From the perspective of the simulation results, the influencing factors of water inrush in the fault zone are multifaceted. It is related not only to natural geological conditions but also to the mining methods adopted, which is in line with the time effect of the fault zone lagging water inrush mechanism. Under the defined conditions of the simulation, although the coal seam mining is threatened by the Ordovician limestone water in the floor, the current risk of water inrush is relatively low. The reasons are as follows:

Firstly, in normal sections, the mining of Coal Seam 3–5 is supported by a sufficiently thick water-resisting layer in the coal seam floor. The lithology of the floor consists of sandstone and mudstone. The sandstone possesses a certain level of physical and mechanical strength, while the mudstone exhibits excellent water-resisting properties.

Secondly, in the fault zone area, despite the relatively large fault throw, both the left and right faults of the graben structure are normal faults. The middle part of the graben belongs to the hanging wall of the fault and has a limited width, rendering it of limited current mining value. The mining activities on both sides of the graben are carried out on the footwall. The coal seam is connected to the weakly water-rich sandstone of the upper strata, and the width of the connected aquifer is small, resulting in weak water richness.

Thirdly, it can be discerned from the simulation results that the working face mining should not cross the fault. Due to coal seam mining, the activation of the fault will cause the groundwater to upwell along the fault zone. Only by leaving sufficient water-proof and water-isolation coal pillars can the safe mining of the working face be ensured to a certain extent.

Finally, the average thickness of the Benxi Formation mudstone in the coal seam floor’s water-resisting layer is 38.45 m. The mudstone itself has good water-resisting properties, and the Benxi Formation is relatively thick within the mining area, constituting the main water-resisting layer between the coal-bearing strata of the well field and the Ordovician limestone aquifer. Importantly, a certain thickness of palaeo-weathered crust is developed at the top of the Middle Ordovician Xiamajiagou Formation. Therefore, it has a certain blocking or even inhibitory effect on the upwelling of the floor-confined water.

In summary, after the coal seam is mined, a certain plastic zone gradually forms in the fault zone area, and this plastic zone continuously expands as the working face advances. The fault zone mainly undergoes shear failure, and the damage range near the Ordovician limestone aquifer section ascends along the fault zone. Under the combined actions of mining pressure, tectonic stress, and pore water pressure, the karst-confined water in the floor seeps upward along the formed water-conducting channels. Due to the limited influence of the aquifer water pressure and mining activities, the confined water does not continuously upwell but rather seeps in all directions. Over time, this will progressively reduce the water-resisting performance and strength of the surrounding rock mass. From the perspective of different mining methods, by minimizing the perturbation to the fault zone, the intensity of confined water upwelling caused by fault activation can be reduced. This is also one of the reasons for the fault lagging water inrush. The process of fault activation is continuous and relatively long. Given that the graben combination consists of two normal faults, the perturbation and activation phenomena of the fault zone caused by mining activities exhibit distinct characteristics. The fault near the end of the mining working face shows a phenomenon of upwelling and seepage along the fault zone, yet the confined water upwelling zone is relatively small, and the seepage is not pronounced. On the other hand, the fault at the other end of the graben area is less affected by mining. There is no trend of local water pressure increase within the fault zone, but near the fault zone area, the floor seepage phenomenon is obvious, and the upwelling height is relatively large.

5. Conclusions

In this paper, the variable-weight vulnerability index method based on FCCM was used to predict and evaluate the water inrush risk of the floor of the main mining coal seam in the study area. Based on the evaluation results, the high-risk areas of vulnerability were simulated and analyzed by means of numerical simulation to study the water inrush mechanism of the fault zone under the influence of a graben structure. A dual evaluation of the water inrush risk of the coal seam floor combining prediction and evaluation with simulation analysis was formed, and the following main conclusions were generally obtained:

• (1). Compared with the K-means clustering commonly used in the past for variable weights of the floor, in terms of the clustering effect of fuzzy C-means, since there are qualitative and quantitative differences among the main controlling factors of water inrush from the coal seam floor, the classification relationship among the indicators is fuzzy. Therefore, fuzzy clustering analysis is more applicable to the variable-weight zoning and vulnerability index zoning of water inrush from the coal seam floor;

• (2). Based on the time effect of delayed water inrush of faults, different mining methods determine the duration of disturbance to the fault zone. Therefore, the risk of karst water inrush from the floor of the fault zone can be reduced by reducing the disturbance time to the fault zone. When mining the strata in this area in the future, it is necessary to conduct surveys on the height of the confined water rising zone to prevent floor water inrush accidents caused by the reduction in the thickness of the effective aquifuge layer of the floor.

In the future, for mines, not only detection and prediction means can be implemented before the working face is excavated, but also real-time online monitoring and early warning can be established to build a three-dimensional technical method for preventing and controlling Ordovician limestone water inrush from the floor, which is of great significance for improving the technical level of mine water hazard prevention and control and ensuring the safe and efficient mining of mines.

Author Contributions

Data curation, S.Y. and H.D.; Formal analysis, H.D.; Methodology, S.Y.; Software, S.Y. and H.D.; Writing—original draft, S.Y.; Writing—review and editing, M.Y. and M.Z. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

No new data were created or analyzed in this study. Data sharing is not applicable to this article.

Conflicts of Interest

The authors declare no competing interests.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures

Figure 1. The runoff directions from west to east.

Figure 2. Flowchart of the methodology used in this study.

Figure 3. State–variable-weight vector diagram ([36]).

Figure 4. Geological conceptual model of the study area.

Figure 5. Numerical model of fluid–structure interaction.

Figure 6. Fuzzy C-mean variable-weight evaluation division of the No. 3–5 coal seam floor.

Figure 7. Risk assessment zone of the water inrush coefficient of No. 3–5 coal.

Figure 8. Model initial equilibrium state.

Figure 9. Development law of the plastic zone at different advancing distances in the working face. (a) Advance 20 m. (b) Advance 40 m. (c) Advance 80 m. (d) Advance 120 m. (e) Advance 160 m. (f) Advance 200 m. (g) Advance 240 m. (h) Advance 280 m.

Figure 10. Distribution law of stress field at different advancing distances in working face. (a) Advance 20 m. (b) Advance 40 m. (c) Advance 80 m. (d) Advance 120 m. (e) Advance 160 m. (f) Advance 200 m. (g) Advance 240 m. (h) Advance 280 m.

Figure 11. Variation law of the seepage field at different advancing distances in the working face. (a) Advance 20 m. (b) Advance 40 m. (c) Advance 80 m. (d) Advance 120 m. (e) Advance 160 m. (f) Advance 200 m. (g) Advance 240 m. (h) Advance 280 m.

Figure 12. Local seepage diagram of the fault zone during forward mining.

Figure 13. Development law of the plastic zone at different advancing distances in the working face. (a) Advance 20 m. (b) Advance 40 m. (c) Advance 80 m. (d) Advance 120 m. (e) Advance 160 m. (f) Advance 200 m. (g) Advance 240 m. (h) Advance 280 m.

Figure 14. Distribution law of the stress field at different advancing distances in the working face. (a) Advance 20 m. (b) Advance 40 m. (c) Advance 80 m. (d) Advance 120 m. (e) Advance 160 m. (f) Advance 200 m. (g) Advance 240 m. (h) Advance 280 m.

Figure 15. Variation law of the seepage field at different advancing distances in the working face. (a) Advance 20 m. (b) Advance 40 m. (c) Advance 80 m. (d) Advance 120 m. (e) Advance 160 m. (f) Advance 200 m. (g) Advance 240 m. (h) Advance 280 m.

Figure 16. Local seepage diagram of the fault zone during retreat mining.

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