Gray Evaluation of Water Inrush Risk in Deep Mining Floor.

With the increase of the mining intensity of coal resources in China, the geological conditions of minefields have become more and more complex. The mining conditions of high pressure and high stress bring great challenges to the safe mining of coal resources. To accurately evaluate the risk of water inrush from the broken floor under high pressure and high stress, a gray evaluation model coupling the work breakdown structure (WBS), the risk-based supervision (RBS) theory, ordered binary comparison quantization method, and the center-point triangular whitenization weight function was proposed in this paper. Taking the No. 21 coal seam of Shanxi Formation in Guhanshan minefield as an example, studying the distribution characteristics of high pressure and high stress and the water inrush mechanism from the broken floor during No. 21 coal seam mining and analyzing the hydrochemical characteristics of the main water inrush aquifers below the No. 21 coal seam floor, this paper determined five main factors, including fault fractal dimensions, aquifer pressure, water-richness, destroyed floor depth, and effective aquiclude thickness. First, the work breakdown structure (WBS), the risk-based supervision (RBS) theory, and the ordered binary comparison quantization method were used to calculate the weight vectors of each index. Then, the center-point triangular whitenization weight function based on the work breakdown structure (WBS), the risk-based supervision (RBS) theory, and the ordered binary comparison quantization method were constructed to evaluate the water inrush risk from the broken floor under high pressure and high stress. Finally, the risk of water inrush from the broken floor during No. 21 coal seam mining in Guhanshan minefield was predicted using the gray evolution trend, which effectively reflects the risk characteristics of water inrush from the coal seam floor under high pressure and high stress. The results show that the evaluation and prediction results are consistent with the actual situation in Guhanshan minefield, which indicates that the model is suitable for evaluating and predicting the risk of water inrush from the broken floor under high pressure and high stress.

Introduction

Although areas of karst strata account for one quarter of the world’s continental areas, due to the differences of geological conditions and coal seam occurrence, there are no problems of floor water inrush in the process of coal seam mining in some countries, such as the United States, Canada, Australia, Germany, and the U.K. Only Hungary, Poland, Yugoslavia, and Spain are affected by the karst water in different degrees in the process of coal seam mining. In foreign countries, coal seams have been mined for more than 100 years; therefore, they are also the first to study the water inrush from the coal seam floor. In China, the research on floor water inrush started in the 1960s.[1]

China is a country with coal as its main energy source, and coal resource will still be the main energy source in China for a long time.[2,3] In recent years, with the increase of coal mining depth in China, the mine geological conditions have become more and more complex and changeable.[4,5] The problems of high pressure and high stress have become one of the major challenges restricting safe production of coal mines. For example, the 2131 working face of Hanwang Mine in the Jiaozuo mining area has developed minor structures and broken rock strata. After mining, the roof pressure destroys the strength of the floor aquiclude, and the floor water inrush occurs under the action of water pressure. The water bursting discharge reaches 900 m3/h, causing the working face to be flooded. The aquiclude below the 1441 working face of Wangfeng Mine in the Jiaozuo mining area is thin and the water pressure is high. In addition, the concentration of mine pressure at the initial stage of mining has damaged the compressive strength of the aquiclude. At the same time, the water pressure of L8 limestone has not decreased significantly, resulting in many water inrush accidents in the mining face, with the water yield varying from 126 to 1680 m3/h.[6] Therefore, it is of great theoretical significance and practical value to evaluate and predict the risk of water inrush from the broken floor under high pressure and high stress as accurately as possible for safe and efficient production of minefields.

In recent years, with the continuous development of science and technology, many scholars have studied the risk of water inrush from limestone karst aquifers during coal seam mining.[7−10] For example, Shi[11] used probability indexes to assess the risk of water inrush from the coal seam floor by quantitative main controlling factors. Wu[12] put forward the construction of an evaluation index system and used the vulnerability index method[13] to assess the risk of water inrush from the coal seam floor. Qiu[14] used the fuzzy analytic hierarchy process (FAHP) and the gray correlation analysis to assess the risk of water inrush from limestone karst aquifers. The risk index model allowed for subdivision of the coal seam 13 floor area into two zones and four subzones, providing a more detailed scientific basis for safe production and control of water inrush. Based on GIS multisource information fusion technology, Zhu[15] constructed a dimensionless model for water inrush risk assessment. Using the Fisher discriminant model, Zhang[16] evaluated and predicted the water inrush risk from the coal seam floor. The above theories promote the rapid development of prevention and control technology of mine water disasters in China. However, due to the continuous increase of coal seam mining depth, a series of new changes have appeared in water inrush from the broken floor under the conditions of high pressure and high stress, and the prevention and control of water inrush have become more difficult. It is necessary to have a further understanding of the risk assessment, prediction, and prevention of water inrush from the coal seam floor. Guhanshan coal mine is located between the earthquake zone of North China Plain and the Fen-Wei earthquake zone and is greatly affected by the seismic activities of the two earthquake zones. The rock mass below the No. 21 coal seam is subjected to abnormal high stress in the horizontal direction. The sealing effect of karst cavities, the release pressure of the working face floor, and high stress acting on the coal seam floor lead to a higher water pressure of floor aquifers. As a result, in the joint and fault areas, the floor is broken extensively. Therefore, analyzing the law of water inrush from the No. 21 coal seam floor in Guhanshan minefield, this paper expounded the distribution characteristics of high pressure and high stress and the mechanism of water inrush from the broken floor. Combined with the hydrochemical characteristics of the main water inrush aquifers below the No. 21 coal seam floor, five main controlling factors, including fault fractal dimensions, aquifer pressure, water-richness, destroyed floor depth, and effective aquiclude thickness, were selected. The WBS-RBS evaluation index system was established, and the weight vectors of each index were calculated using the work breakdown structure, RBS theory, and the ordered binary comparison quantization method. Then, the center-point triangular whitenization weight function based on the work breakdown structure, RBS theory, and the ordered binary comparison quantization method was constructed to evaluate the water inrush risk from the broken floor under high pressure and high stress, and the risk of water inrush from the broken floor during No. 21 coal seam mining in Guhanshan minefield was predicted by the gray evolution trend.

Materials and Methods

Study Area

The Guhanshan coal mine is located in the center of the Jiaozuo coalfield, about 25 km from Jiaozuo city, Henan province, in eastern China. The mine is irregularly developed, covering an area of around 17.00 km2. It is located in the Cathaysian tectonic belts. The minefield has a monoclinic structure, with faults as the main structural form, as shown in Figure . According to the borehole data, the stratum in Guhanshan minefield consists of Ordovician (O), Carboniferous (C), Permian (P), Jurassic (J), Paleogene (E), and Quaternary (Q). Shanxi Formation and Taiyuan Formation of the Carboniferous-Permian are the main coal-bearing strata, and they include two minable coal seams. There are five coal seams in Shanxi Formation, only the No. 21 coal seam can be mined, and 11 coal seams in Taiyuan Formation, and only the No. 12 coal seam can be mined. Coal seam No. 21 is currently being mined.

Figure 1

(A) Location map of Henan Province. (B) Location map of the Jiaozuo Mining Area in Henan Province. (C) Fault distribution in Guhanshan minefield.

The target coal seam for the risk assessment of floor water inrush is the No.21 coal seam. The No.21 coal seam is mineable throughout the field, with a thickness ranging from 3.15 to 6.27 m, with an average of 4.65 m. The aquifers in Guhanshan minefield mainly include the porous aquifer of Quaternary, the fissured aquifer of the Permian System, L8 limestone aquifer, L2 limestone aquifer, and the Ordovician limestone aquifer. Among them, the average distance between the No. 21 coal seam and the Quaternary strata is 290.93 m, and the Quaternary aquifer basically does not affect the minefield. The conditions of water recharging and runoff of the fissured aquifer of the Permian System above the No. 21 coal seam are poorer, and the water-richness is weaker. It is easy to be drained and generally does not cause mine water inrush. The thickness of the L8 limestone aquifer (below the No. 21 coal seam) ranges from 5.07 to 10.07 m, with an average thickness of 8.30 m. Karst fractures are developed in different sizes, with uneven water-richness. It is a direct water-filling aquifer for mining the No. 21 coal seam of Shanxi Formation. The thickness of the L2 limestone aquifer (below the L8 limestone aquifer) ranges from 5.90 to 21.62 m, with an average thickness of 12.57 m. Karst fractures are developed in different sizes, with uneven water-richness. It is an indirect water-filling aquifer for mining the No. 21 coal seam of Shanxi Formation. Karst fractures in Ordovician limestone (below the L2 limestone aquifer) are developed, and the water-richness is better. It is an indirect water-filling aquifer for mining the No. 21 coal seam of Shanxi Formation. However, with the changes of mining depth and mine pressure and structure, high pressure and high stress appear in the mining area, and the L2 limestone and Ordovician limestone aquifers also become the main prevention and control objects of mine water inrush.

Distribution Characteristics of High Stress

The stress of roof and floor is redistributed as the coal seam is mined, resulting in displacement, deformation, and even damage of rock mass. Under the action of mine pressure, the vertical abutment pressure is produced along the edge of the goaf and the high-stress concentration is large, as shown in Figure .[17] The rear abutment pressure acts on the goaf, and the side abutment pressure acts on both sides of the coal wall. The front abutment pressure acts on the front of the working face, and the pressure spike appears around the corner of the working face.

Figure 2

Distribution of abutment pressure.

With the advancement of the working face, the rock mass near the open-off cut maintains the pressure relief state, and the load is redistributed in the goaf, giving rise to the floor rock mass in the expansion state (pressure relief-expansion stage). As the working face continues to advance, due to the reduction of the mine pressure intensity, the rock mass above the goaf gradually falls, and the rock mass below the coal seam is gradually recompacted, returning to a new equilibrium condition (compression-stability stage). Therefore, the rock mass below the coal seam repeatedly changes in three stages, compression, expansion, and recovery, as shown in Figure . At the boundary of the compression and expansion zones, the floor rock mass is prone to shearing failure. Bed-separated fissures and vertical fractures usually exist in the floor rock mass in the expansion state. Therefore, the floor rock mass around the marginal zone of the coal pillar is easy to be damaged due to its developed fractures. Besides, under the action of horizontal and vertical stresses, there is often a heaving floor in the middle of the expansion zone, and the strike of the heaving floor is consistent with that of the working face, which indicates that a damaged floor is caused by horizontal abnormal tectonic stress.

Figure 3

Temporal-spatial relation model between the floor rock mass and stope.

According to the theory of mine pressure, there may be three types of pressure acting on coal seams, including both existing internal and external stress fields, existing plastic zone, and single elastic distribution. If the distribution of abutment pressure is approximately simplified as uniform load (Figure ), the abutment stress at any point of the rock mass below the coal seam can be calculated according to the elasticity theory. Taking the plastic distribution as an example, the sum of the stresses acting at any point of the rock mass below the coal seam is calculated.

Figure 4

Simplified model of the abutment pressure.

According to the elasticity theory, assuming that the floor rock mass is elastic stratum and the abutment pressure acting on the floor rock mass is regarded as the plane load, the sum of the stresses produced by the distributed loads on any point M(x, z) (Figure ) under the floor is the stress (σ, σ, τ) acting at point M(x, z); therefore, the principal stress acting at point M(x, z) is σ1 and σ3

Distribution Characteristics of High Pressure

When the coal seam is not mined, the water pressure of the L8 limestone, L2 limestone, and Ordovician limestone aquifers generally depends on their water head height. Taking the shallow aquifer as an example, its hydraulic gradient value is relatively small, which causes its water pressure to be low. But with the increase of the buried depth of the aquifer, the water pressure also increases. However, as the coal seam is mined, the stress of the roof is redistributed, and its own weight is transferred to the coal pillar, forming abutment stress higher than the original stress (Figure ). When the increased abutment stress is transmitted to the karst water cavity, the karst water cavity is compressed, resulting in a smaller groundwater storage space and an obvious increase of the water pressure. At the same time, if the water inlet and the water outlet of the karst water cavity are also blocked by sediment particles brought by a current, a closed water-filled cave is formed, leading to a sharp increase of water pressure. Because of the incompressibility of water, it can transmit all of the pressure acting on itself in all directions according to the original size. As a result, the rock mass below the coal seam is compressed by the abutment pressure, similar to the principle of “hydraulic press”. The water pressure can reach the maximum of abutment pressure, that is, KmaxγH, where Kmax is the concentration index of the abutment pressure, γ is the average bulk density of strata, and H is the mining depth. The diagrammatic sketch of the abnormally high pressure during No. 21 coal seam mining is shown in Figure .

Figure 5

Abnormal high pressure affected by mining.

Mechanism of Water Inrush from the Broken Floor under High Pressure and High Stress

Guhanshan minefield is located between the earthquake zone of the North China Plain and the Fen-Wei seismic belt, with active tectonic movement. The geological structure of the mining area is obviously controlled by the principal stress in the NEE-SWW direction, and it is obtained from the stress analysis of the goaf floor, as shown in Figure . When the roof does not collapse, in the vertical direction, the pressure of the roof does not act on the goaf floor, and the floor is in a state of pressure relief. As a result, the goaf floor is mainly affected by the tectonic stress in the NEE-SWW direction, namely, horizontal stress, high pressure of the L8 limestone aquifer, and the expansion force of floor strata. Therefore, during the mining of No. 21 coal seam of Shanxi Formation in Guhanshan minefield, the concentrated high stress acting on the coal seam floor in the horizontal direction caused the development of small-sized faults and joints in the rock mass below the coal seam floor. As mining of the No. 21 coal seam is continued, the rock mass below the coal seam is compressed by abutment pressure, and the water pressure can reach the maximum of abutment pressure. Under the condition of abnormally high pressure, the maximum horizontal principal stress acting on the coal seam floor is greater than its uniaxial compressive strength, easily resulting in the damage failure of the rock mass below the coal seam floor and then causing water inrush accidents.[18] The water inrush mode is shown in Figures and 8.

Figure 6

Stress analysis of the goaf floor.

Figure 7

Water inrush model of fault activation.

Figure 8

Water inrush model of fracture coalescence.

Hydrochemical Characteristics of the L8 Limestone Aquifer

As shown in Figure , the distribution of L8 limestone water samples is relatively discrete in the square projection area, mainly distributed in the zones of No. 1, No. 3, and No. 5. The content of the alkaline-earth metal is higher than that of the alkali metal, and the content of weak acid is higher than that of strong acid, with the hardness of carbonic acid being higher than 50%. The hydrochemistry types include HCO3-Ca, HCO3-K + Na, HCO3-Ca·Mg, SO4-Mg·K + Na, HCO3-Mg, HCO3-Ca·K + Na, and HCO3-K + Na·Mg. Among them, 25 water samples are HCO3-Ca and 18 water samples are HCO3-K + Na. Both are the main hydrochemistry types of the L8 limestone aquifer, accounting for 74% of the total number. The pH ranges from 7 to 8, with weak alkalinity. TDS of most water samples is about 500 mg/L, and a few samples are more than 1000 mg/L, which implies that the water quality is good.

Figure 9

Durov diagram of the hydrochemical characteristics of L8 limestone, L2 limestone, and Ordovician limestone in Guhanshan minefield.

Hydrochemical Characteristics of the L2 Limestone Aquifer

As shown in Figure , the L2 limestone water samples are concentrated in the square projection area, all of which are distributed in the zones of No. 1, No. 3, and No. 5. The content of the alkaline-earth metal is higher than that of the alkali metal, and the content of weak acid is higher than that of strong acid, with the hardness of carbonic acid being higher than 50%. The hydrochemistry types of all water samples are HCO3-Ca, which is the main hydrochemistry type of the L2 limestone aquifer. The pH ranges from 7.1 to 8.4, with weak alkalinity. The content of TDS is relatively stable, mainly about 350 mg/L, and a few samples are less than 300 mg/L, which implies that the water quality is good.

Hydrochemical Characteristics of the Ordovician Limestone Aquifer

As shown in Figure , the Ordovician limestone water samples are concentrated in the square projection area, all of which are distributed in the zones of No. 1, No. 3, and No. 5. The content of the alkaline-earth metal is higher than that of the alkali metal, and the content of weak acid is higher than that of strong acid, with the hardness of the carbonic acid being higher than 50%. The hydrochemistry types of all water samples are HCO3-Ca, which is the main hydrochemistry type of the Ordovician limestone aquifer. The pH ranges from 7.6 to 8.4, with weak alkalinity. The content of TDS is relatively stable, mainly about 300 mg/L, and a few samples are more than 400 mg/L, which implies that the water quality is good.

Through the above analysis, it can be seen that the water quality of L2 limestone water samples is similar to that of Ordovician limestone water samples, and their hydrochemistry types are both HCO3-Ca, while there are some differences between L8 limestone water samples, L2 limestone water samples, and Ordovician limestone water samples. Therefore, we regard the L8 limestone aquifer as a relatively independent aquifer system and believe that there is a close hydraulic connection between the L2 limestone aquifer and the Ordovician limestone aquifer, that is to say, it is regarded as a water-bearing rock series with a unified hydraulic connection.

Results

Main Controlling Factors

The risk assessment of water inrush from the broken floor under high pressure and high stress is no longer a simple assessment by the water inrush coefficient. Based on the distribution characteristics of high pressure and high stress and analyzing the mechanism of water inrush from the broken floor under high pressure and high stress during No. 21 coal seam mining, this paper selected five main factors, including fault fractal dimensions, aquifer pressure, water-richness, destroyed floor depth, and effective aquiclude thickness, for the assessment of water inrush from the broken floor under high pressure and high stress during No. 21 coal seam mining. According to the results of the above hydrochemical analysis between different aquifers, the L8 limestone aquifer is regarded as a relatively independent aquifer system, and we believe that there is a close hydraulic connection between the L2 limestone aquifer and the Ordovician limestone aquifer; that is to say, it is regarded as a water-bearing rock series with a unified hydraulic connection.

Fault Fractal Dimensions

The structural feature of Guhanshan minefield is mainly fault, which is the external display of high stress in Guhanshan minefield. The more complex the fault is, the more broken the floor rock mass is, which implies higher stress. The fault fractal dimension is based on the faults below the coal seam floor, using the fractal geometry method and selecting the information dimension of the fault area to carry out fractal quantitative research on the fault system, which can better reflect the complexity of the faults and be used as an important index for the risk assessment of water inrush from the broken floor under high pressure and high stress.[19,20]

In this paper, taking the faults below the No. 21 coal seam of Shanxi Formation as the research object, the affected area of faults exposed when mining the No. 21 coal seam is divided into several square areas by using square grids (200 × 200), and the fault fractal dimension is carried out for each square area, obtaining a contour map of fault fractal dimension (Figure ). The thresholds are 0.7, 1.1, and 1.5, which implies that the fault fractal dimension is large near the fault zone.

Figure 10

Contour map of the fault fractal dimension.

Aquifer Pressure

Generally, the deeper the coal seam is buried, the larger is the aquifer pressure acting on the coal seam floor. Under the joint action of hydrostatic pressure and hydrodynamic pressure, the aquifer pressure causes deformation and failure of the rock mass below the coal seam floor, which further widens the original structural cracks or produces new structural cracks. This action enhances the water transmissibility of the water inrush passageway and weakens the strength of the confining beds located in the coal seam floor. The water-resisting ability of the floor confining beds decreases, which causes the occurrence of water inrush from a coal seam floor. Therefore, the aquifer pressure as a main controlling factor for the risk assessment of water inrush from the broken floor under high pressure and high stress is of great significance.[21,22] According to the borehole data of the research area, it can be found that the pressure of the aquifer below the coal seam floor is more than 6 MPa in the whole minefield. The contour maps of the L8 limestone aquifer pressure and the L2 limestone–Ordovician limestone aquifer pressure are shown in Figure .

Figure 11

Contour maps of the pressure of main water-filling aquifers below the No. 21 coal seam.

Aquifer Water-Richness

Under the mining conditions of high pressure and high stress, the water-richness of the aquifers below the coal seam floor is directly related to the water bursting discharge. Therefore, it is very important to zone the water-richness of the water-bearing rock series with high pressure below the coal seam floor for risk assessment and prediction of water inrush from the broken floor. In this paper, an information fusion model for the water-richness assessment of the L8 limestone aquifer and the L2 limestone–Ordovician limestone aquifer was constructed based on four main factors, namely, water inflow of drilling, the aquifer thickness, core rate of drilling, and the fault influencing factor. The comprehensive zone maps of water-richness for the L8 limestone aquifer and the L2 limestone–Ordovician limestone aquifer were drawn, as shown in Figure . It can be seen from Figure that the distribution law of water-richness for the L8 limestone aquifer is uneven, but on the whole, it is inclined to medium water-richness or strong water-richness. The water-richness of the L2 limestone–Ordovician limestone aquifer is better, which belongs to the strong water-richness area in general, and easy to induce accidents of water inrush from the coal seam floor under the action of high pressure and high stress.

Figure 12

Comprehensive zone maps of the water-richness of main water-filling aquifers below the No. 21 coal seam.

Destroyed Floor Depth

Owing to high pressure and high stress, there are many joints and fractures in the rock mass below the coal seam floor, and the heaving floor is a serious problem. According to the theory of “Down Four Zones” (Figure ), the rock mass within the range from the coal seam floor to the aquifer roof is divided into four parts: the broken zone caused by underground pressure (I), a new damaged zone (II), the original damaged zone (III), and the original water flowing crevice zone (IV).[23,24] Due to the influence of mining pressure, the original water flowing crevice zone may be expanded again, but the increased height is lower. Although the original damaged zone is affected by the mine pressure, it still maintains the same continuity as the coal seam is not mined, and its water-resistance performance remains unchanged. The broken zone is continuously destroyed by the mine pressure, forming obvious water flowing channels.[25] In this paper, a three-dimensional finite difference program in Flac3D is used to simulate the destroyed floor depth during No. 21 coal seam mining under high pressure and high stress, and the model size is 400 × 216 × 600. First, the self-weight stress of the rock mass is calculated to obtain the primary stress field, and all nodal displacements are assigned to zero and the stress field is retained. Taking 20 meters as a step to push forward in the x-axis direction, the destroyed floor depth is simulated. The initial stress equilibrium state of the model is shown in Figure a, and the simulation results are shown in Figure b.

Figure 13

Division model of the floor failure characteristics during No. 21 coal seam mining.

Figure 14

Numerical simulation.

It can be seen from Figure that the maximum destroyed floor depth is 7.2 m in the early mining period (20 m). The maximum destroyed floor depth gradually increases to 12.6 m with continuous mining. As the No. 21 coal seam is mined continuously to the 120 m level, the plastic zone occurred in the floor, and the maximum destroyed floor depth was stable up to 18.76 m until the mining depth was up to 400 m. The contour map of the destroyed floor depth is shown in Figure .

Figure 15

Contour map of the destroyed floor depth.

Effective Aquiclude Thickness

The effective aquiclude is the protective rock mass below the broken zone and above the original water flowing crevice zone. The effective thickness of the aquiclude is the difference between the thickness of the aquiclude and the thickness of the broken zone and the original water flowing crevice zone (Figure ).[26] Under mining conditions of high pressure and high stress, the effective aquiclude is the main factor for resisting water inrush from the karst aquifer, and it is an important index to assess the risk of water inrush from the broken floor.

Figure 16

Sketch map of effective aquiclude.

Figure shows the contour map of the effective thickness of aquiclude below the No. 21 coal seam in Guhanshan minefield. In the mining area, taking the effective thickness of aquiclude within the range from the No. 21 coal seam floor to the L8 limestone aquifer roof and the effective thickness of aquiclude within the range from the L8 limestone aquifer floor to the L2 limestone–Ordovician limestone aquifer roof as an example, both gradually become thinner from west to east, but there are also several areas with the local thickness increasing suddenly. As a result, under similar conditions of water pressure and complexity of geological structures and other factors, the thinning of effective aquiclude leads to an increased risk of water inrush from the broken floor.

Figure 17

Contour map of the effective thickness of aquiclude below the No. 21 coal seam floor.

Risk Assessment

Evaluation Index System with the Work Breakdown Structure and the Risk-Based Supervision Theory (WBS-RBS Theory)

According to the analysis of main controlling factors of water inrush from the No. 21 coal seam floor under the mining conditions of high pressure and high stress in Guhanshan minefield, the WBS-RBS evaluation index system for the risk assessment of water inrush from the broken floor was constructed, as shown in Figure .

Figure 18

WBS-RBS evaluation index system.

Index Weight Calculation Based on WBS-RBSWBS-RBS-Ordered Binary Comparison Quantization Method

First, two decision-making experts were invited to make pairwise comparisons among five main controlling factors, and the comparison matrix R, which is based on the relative importance, was obtained. The results are shown in Table .where and when r = 1/2, it implies that the indicator u is of the same importance as itself.

Table 1

Relative Importance of Evaluation Indicators

	evaluation indicators
	R1	R2 (MPa)	R3	R4 (m)	R5 (m)
R1	0.5	1	1	1	1
R2 (MPa)	0	0.5	1	1	1
R3	0	0	0.5	0	1
R4 (m)	0	0	1	0.5	1
R5 (m)	0	0	0	0	0.5

According to the comparison matrix R, the importance ranking index z of each evaluation indicator was solved.

The judgment matrix P was constructed based on the importance ranking index z, as shown in Table .where . Assuming Q = lg P = [lg(p)], we calculated the antisymmetric matrix Q, as shown in Table , and assuming , we also calculated the matrix G, as shown in Table .

Table 2

Judgment Matrix

P	p1	p2	p3	p4	p5
p1	1	1/2	1/6	1/4	1/8
p2	2	1	1/4	1/2	1/6
p3	6	4	1	2	1/2
p4	4	2	1/2	1	1/4
p5	8	6	2	4	1

Table 3

Antisymmetric Matrix

Q	q1	q2	q3	q4	q5
q1	0	–0.301	–0.778	–0.602	–0.903
q2	0.301	0	–0.602	–0.301	–0.778
q3	0.778	0.602	0	0.301	–0.301
q4	0.602	0.301	–0.301	0	–0.602
q5	0.903	0.778	0.301	0.602	0

Table 4

Matrix G

G	g1	g2	g3	g4	g5
g1	1	0.574	0.161	0.304	0.093
g2	1.741	1	0.280	0.530	0.161
g3	6.207	3.565	1	1.888	0.574
g4	3.288	1.888	0.530	1	0.304
g5	10.808	6.207	1.741	3.288	1

The weight vectors of evaluation indicators are shown in Tables and6.

Table 5

Weights of Evaluation Indicators Calculated by the Sum-Product Method

evaluation indicators	R1	R2 (MPa)	R3	R4 (m)	R5 (m)
weights (Wa)	0.250	0.224	0.174	0.197	0.155

Table 6

Weights of Evaluation Indicators Calculated by the Square Root Method

evaluation indicators	R1	R2 (MPa)	R3	R4 (m)	R5 (m)
weights (Wb)	0.469	0.269	0.076	0.143	0.043

Sum-product method:

Square root method:

Series binary comparison method

The importance ranking index set R′ = {R1R2R4R3R5} was solved based on the ranking index z. Taking R1 as a criterion, we compared the relative importance between R1 and R2, R2 and R4, R4 and R3, and R3 and R5, using the series binary comparison method. The fuzzy tone operators were judged to be obviously, slightly, slightly, and slightly, respectively. Based on the relation between the tone operators and relative weights (Table ), the weight vector W was calculated using the formula (ϕ = ϕ · ϕ)

Table 7

Relation between the Tone Operators and Relative Weights

tone operators	same		a little		slightly		obviously		more obviously		prominently
relative weights	1.0	0.905	0.818	0.739	0.667	0.60	0.538	0.481	0.429	0.379	0.333

After normalization, the weight vector of evaluation indicators was obtained by the series binary comparison method as follows

Weight decision-making was conducted (as shown below) by the geometric averaging operator.

The decision weight vector of evaluation indicators is as follows:

Pairwise comparison matrices R* based on the relative importance of five evaluation indicators for the L8 limestone aquifer and the L2 limestone–Ordovician limestone aquifer were calculated as follows

Judgment matrices P* based on the importance ranking index were calculated as follows

Antisymmetric matrices Q* based on the importance ranking index were calculated as follows

Quasi-optimal transfer matrices G* based on the importance ranking index were calculated as follows

The weight vector of the L8 limestone aquifer and the L2 limestone–Ordovician limestone aquifer was calculated by the sum-product method as follows

The weight vector of the L8 limestone aquifer and the L2 limestone–Ordovician limestone aquifer was calculated by the square root method as follows

The weight vector of the L8 limestone aquifer and the L2 limestone–Ordovician limestone aquifer was calculated by the series binary comparison method as follows

Weight decision-making was conducted (as shown below) by the geometric averaging operator.

The ordered binary comparison quantization method was coupled with the work breakdown structure and the RBS theory to determine the weight matrix of indicators, as shown in Table .

Table 8

Weight Matrix Determined by the Ordered Binary Comparison Quantization Method Coupled with the Work Breakdown Structure and the RBS Theory

	breakdown system of RBS theory
breakdown system of work breakdown structure	R1	R2 (MPa)	R3	R4 (m)	R5 (m)
	0.386	0.233	0.119	0.168	0.094
L8 limestone aquifer	0.618	0.618	0.618	0.618	0.618
L2 limestone–Ordovician limestone aquifer	0.382	0.382	0.382	0.382	0.382

Weights of evaluation indicators for the risk assessment of water inrush from the L8 limestone aquifer and the L2 limestone–Ordovician limestone aquifer during No. 21 coal seam mining in Guhanshan minefield are shown in Tables and 10.

Table 9

Weights of Evaluation Indicators for the Risk Assessment of Water Inrush from the L8 Limestone Aquifer during No. 21 Coal Seam Mining in Guhanshan Minefield

	risk of L8 limestone aquifer for the water inrush during No. 21 coal seam mining W* = 0.618
	R11	R12 (MPa)	R13	R14 (m)	R15 (m)
hierarchy weights	0.386	0.233	0.119	0.168	0.094
combined weights	0.239	0.144	0.074	0.104	0.058

Table 10

Weights of Evaluation Indicators for the Risk Assessment of Water Inrush from the L2 Limestone–Ordovician Limestone Aquifer during No. 21 Coal Seam Mining in Guhanshan Minefield

	Risk of L2 limestone–Ordovician limestone aquifer for the water inrush during No. 21 coal seam mining W* = 0.382
	R21	R22(MPa)	R23	R24 (m)	R25 (m)
hierarchy weights	0.386	0.233	0.119	0.168	0.094
combined weights	0.147	0.089	0.045	0.064	0.035

Gray Assessment of Water Inrush Risk Based on the Center-Point Triangular Whitenization Weight Function

Assuming that the number of gray classifications is s, the number of evaluation indicators is m, and the number of evaluation objects is n, the sample observation of the evaluation object (i) for the evaluation indicator (j) is defined as x (i = 1, 2, L, n; j = 1, 2, ..., m), and the object (i) is evaluated according to the sample observation (x (i = 1, 2, L, n; j = 1, 2, ..., m)) of the evaluation object (i) for the evaluation indicator (j). When the gray classifications are divided, the point with the maximum value, which belongs to a certain gray classification, is called the center point. The concrete steps of the gray assessment model based on the center-point triangular whitenization weight function are as follows.

Step 1: The number of gray classifications is determined, and the center points (λ) of each gray classification are determined.

Step 2: The value range of the evaluation indicator (j) is defined as [a1, as+1], and the whitenization weight function of the gray classification k, whose center point is λ = (a + a)/2, is defined as 1. The gray classifications 0 and s + 1 are added, and their corresponding center points are, respectively, determined as λ0 and λ, obtaining a new sequence of center points (λ0, λ1, λ2, ..., λ). The center-point triangular whitenization weight function (f (·)(j = 1, 2, ..., m; k = 1,2, ..., s)) of the evaluation indicator (j) for the gray classification k is obtained by connecting the center point (λ,1) with the center points of gray classifications k – 1 and k + 1. The sketch map of the center-point triangular whitenization weight function is shown in Figure .

Figure 19

Sketch map of the center-point triangular whitenization weight function.

The sample observation of the evaluation indicator (j) is defined as x, and the membership (f(x)) of the sample observation (x) belonging to gray classification k(k = 1, 2, ..., s) is calculated using the following formula

Step 3: Comprehensive convergence coefficient (σ) of the evaluation object (i) for gray classification k is calculated using the following formulawhere f (x) is the whitenization weight function of the evaluation indicator (j) belonging to gray classification k. η is the weight of the evaluation indicator (j).

Step 4: Based on the formula , the classification the evaluation object (i) belongs to is judged. If several objects belong to the same gray classification, the evaluation objects are ranked according to the comprehensive convergence coefficient.

Determination of Center Points

In this paper, four gray classifications are selected to represent “low risk”, “medium risk”, “high risk”, and “extremely high risk”. Combined with expert opinions, the center points of each gray classification are determined (Table ).

Table 11

Center Points of Each Gray Classification

evaluation criterion	evaluation indicators	low risk	medium risk	high risk	extremely high risk
water inrush risk for the L8 limestone aquifer	R11	0.35	0.9	1.3	1.75
	R12	0.875	1.75	3.375	5.125
	R13	0.125	0.375	0.625	0.875
	R14	2.5	7.5	12.5	17.5
	R15	7.5	22.5	37.5	52.5
water inrush risk for the L2 limestone–Ordovician limestone aquifer	R21	0.35	0.9	1.3	1.75
	R22	1.15	2.45	2.75	3.05
	R23	0.125	0.375	0.625	0.875
	R24	2.5	7.5	12.5	17.5
	R25	46.5	51.5	56.5	61.5

Extension of Evaluation Indicators

Combined with the actual situation of the study area, the evaluation indicators are extended. Table shows the extension values and actual values of each indicator. The 15031 working face is selected as an evaluation objective (Figure ).

Table 12

Extension Values and Actual Values of Each Indicator

	R11	R12	R13	R14	R15	R21	R22	R23	R24	R25
λij0	0.2	0.4	0.06	1	4	0.2	0.6	0.06	1	23
λij5	2	6	1	20	60	2	4	1	20	65
actual values	0.7	1.2	0.38	16	37	0.7	2.3	0.35	16	50

Figure 20

Sketch map of the evaluation objective.

Whitenization Convergence Coefficients

λ is calculated using the formula , and then λ is substituted into the formula of membership, obtaining the whitenization convergence coefficients of evaluation indicators (Table ).

Table 13

Whitenization Convergence Coefficients

	R11	R12	R13	R14	R15	R21	R22	R23	R24	R25
Rij1	0.364	0.629	0.000	0.000	0.000	0.364	0.115	0.100	0.000	0.300
Rij2	0.636	0.371	0.980	0.000	0.030	0.636	0.885	0.900	0.000	0.700
Rij3	0.000	0.000	0.020	0.300	0.970	0.000	0.000	0.000	0.300	0.000
Rij4	0.000	0.000	0.000	0.700	0.000	0.000	0.000	0.000	0.700	0.000

Discussion and Conclusions

Discussion

The comprehensive convergence coefficients of the risk of water inrush from the L8 limestone aquifer and the L2 limestone–Ordovician limestone aquifer are shown in Table .

Table 14

Comprehensive Convergence Coefficients of the Risk of Water Inrush from the L8 Limestone Aquifer and the L2 Limestone–Ordovician Limestone Aquifer

	σ1	σ2	σ3	σ4
water inrush risk for L8 limestone aquifer	0.287	0.451	0.144	0.118
water inrush risk for L2 limestone–Ordovician limestone aquifer	0.208	0.624	0.050	0.118

It can be seen from Table that under the mining conditions of high pressure and high stress, the risk of water inrush from the broken floor is medium when mining the No. 21 coal seam in the 15031 working face. In terms of the water inrush risk for the L8 limestone aquifer, the 15031 working face poses medium risk as a whole, but the areas of high risk and extremely high risk account for a large section; therefore, there is a trend of transition to high risk and extremely high risk. In terms of the water inrush risk for the L2 limestone–Ordovician limestone aquifer, the 15031 working face also belongs to medium risk, which mainly exists in the areas with serious damage of the floor rock mass and the complex structure.

The above analysis shows that the risk of water inrush from the L8 limestone aquifer is higher when mining the No. 21 coal seam of Shanxi Formation in 15031 working face, which is consistent with the actual mining situation and the serious damage of the floor rock mass and the heaving floor under high pressure and high stress in Guhanshan minefield. It shows that the results of the gray assessment on the risk of water inrush from the broken floor based on the center-point triangular whitenization weight function are better.

Guhanshan minefield is divided into several small units with grids of 100 × 100, and the risk of water inrush from the No. 21 coal seam floor is assessed and predicted. The results are shown in Figures and 22. According to the mine data on water inrush over the years, the water inrush sites basically locate in the areas with medium risk, which can better reflect the rationality of the evaluation results. However, special attention should be paid to the water inrush accidents caused by faults, which connect the L8 limestone aquifer with the L2 limestone–Ordovician limestone aquifer or the water flowing fractured zone.

Figure 21

Gray evaluation of the risk of water inrush from the No. 21 coal seam floor in Guhanshan minefield.

Figure 22

Evolution trend of the risk of water inrush from the No. 21 coal seam floor in Guhanshan minefield.

Conclusions

Taking the mining of the No. 21 coal seam as an example, by studying the distribution characteristics of high pressure and high stress, we expound the mechanism of water inrush from the broken floor. Then, five main factors affecting water inrush from the broken floor are determined, including fault fractal dimensions, aquifer pressure, aquifer water-richness, destroyed floor depth, and effective aquiclude thickness; then, the weight vector of each index is calculated using the ordered binary comparison quantization method coupled with the work breakdown structure and the RBS theory, which ensures the effective evaluation of the relative importance of each index in the dynamic model.

Based on the center-point triangular whitenization weight function, a risk assessment model of water inrush from the broken floor is established, which is in line with the mining conditions of high pressure and high stress. Then, the evolution trend of the risk of water inrush from the L8 limestone aquifer and the L2 limestone–Ordovician limestone aquifer is predicted when the No. 21 coal seam is continuously mined. The results show that the L8 limestone aquifer poses a great threat to the mining of the No. 21 coal seam in Guhanshan minefield, while the threat of the L2 limestone–Ordovician limestone aquifer to the mining of the No. 21 coal seam in Guhanshan minefield is mainly concentrated in areas with the developed fracture structure.