# Establishment and Application of Bed-Separation Water Inrush Coefficient Method Considering Water Resistance of Fractured Rock Mass

Authors: Jianghui He; Wenping Li; Wei Qiao; Qiqing Wang; Zhi Yang; Liangning Li
Journal: Geofluids
 (2022)

---

## Abstract

Deep mining in Ordos Basin faces the threat of bed-separation water inrush (BWI), so it is necessary to carry out BWI risk assessment before mining. However, the existing BWI risk assessment methods fail to provide a universal risk classification standard. In this paper, taking three coal mines in Ordos Basin as research cases, the water resistance of fractured rock mass was analyzed, and a BWI coefficient (BWIC) method for BWI risk assessment was established. Firstly, by comparing the weight of each BWI-related factor, the formula for calculating the thickness of equivalent water-resisting layer of fractured rock mass was derived. The weight of each BWI-related factor was obtained by entropy weight method. Secondly, based on the stress arch theory, the overall BWIC in bed separation zone corresponding to different excavation lengths was obtained. BWIC was expressed by the ratio of the Cretaceous water pressure to the total thickness of the unbroken water-resisting layer and the equivalent water-resisting layer of the fractured rock mass. Finally, by comparing the value range of the overall BWIC in the bed separation zone corresponding to the excavation length with and without BWI, the standard of BWI risk classification was determined. The application results verified the scientificity of BWIC method and the universality of the BWI risk classification standard proposed in this paper.


---

## Body

## 1. Introduction

Bed separation is a layered cavity formed between adjacent strata due to uneven settlement of strata in overburden during underground coal mining [1–5]. When the water in the surrounding aquifer accumulates into the bed separation, bed-separation water is formed. Once the bed-separation water breaks through the water-resisting layer below it and flows into the mining site, it will cause bed-separation water inrush (BWI) [6]. BWI has the characteristics of large instantaneous water volume and strong destructiveness. Coal is still the most important fossil energy in China, and Ordos Basin has become China’s main coal producing area [7, 8]. In underground coal mining, because China has the most complex geological conditions and the largest coal mining scale in the world, almost all accidents caused by BWI occur in China. For example, in 2016, a BWI occurred at Zhaojin coal mine in China, resulting in 11 deaths. Therefore, for those coal mines facing BWI threat in Ordos Basin, BWI risk assessment has important reference value for the formulation of safe mining scheme.At present, mine engineers still have different views on the formation mechanism of BWI. Some views are that the power to induce BWI comes from the impact of the fracture of the rock stratum constituting the bed separation on the bed-separation water [9–11], while some views are that the bed-separation water pressure is the power to drive the bed-separation water to break through the aquiclude [12, 13]. In fact, in the overburden, the inrush of bed-separation water in the fracture zone should be caused by the fracture of rock stratum, but the inrush of bed-separation water above the fracture zone should be driven by bed-separation water pressure. Although BWI is not a new type of roof water hazards in coal mining in recent years, but due to the lack of attention, there are few research results on risk assessment of BWI. Multifactor-weighted superposition method is a mature risk assessment method, and it is often used in mine roof/floor water inrush risk assessment [14, 15]. However, in the multifactor-weighted superposition method, the result of data standardization processing will be affected by the value range of the data set, which will lead to the BWI risk may be wrongly evaluated and the boundary values between different risk levels changing with the change of evaluation area, for example, assuming that the values of one of the BWI-related factors in mining areas A and B are data set A=a1,a2,⋯,ai,⋯,am and data set B=b1,b2,⋯,bj,⋯,bn, respectively. The maximum and minimum values in data set A are amax and amin, respectively, and the maximum and minimum values in data set B are bmax and bmin, respectively. The value of the BWI-related factor at coordinate point X in mining area A is ax, and the value of the BWI-related factor at coordinate point Y in mining area B is by, and ax=by. If amax=bmax and amin=bmin cannot exist at the same time, the standardized values of ax and by will not be equal, and the BWI risk at coordinate point X and coordinate point Y will be evaluated as unequal, which is not in line with the reality. The water inrush coefficient method, which was improved from the empirical formula suitable for floor water inrush risk assessment and suitable for roof water inrush risk assessment, has been used in BWI risk assessment [16]. However, the evaluation results were not convincing because the water-resisting capacity of the fractured Jurassic strata in Ordos Basin due to the fracture self-healing effect was not considered.The above analysis shows that there is still a lack of practical methods suitable for BWI risk assessment in Ordos Basin. Moreover, the BWI risk corresponding to different excavation lengths cannot be obtained by using the existing BWI risk assessment methods, which is not conducive to guiding relevant disaster prevention and control. Therefore, the purpose of this paper is to analyze the role of BWI-related factors in BWI and establish a BWI risk assessment method that can provide water inrush risk corresponding to different excavation lengths and universal risk classification standard.


## 2. Engineering Geological Background of Coal Mining in Ordos Basin

Ordos Basin is the main coal producing area in China, and Jurassic coal seams are the main excavation objects. In the middle of the basin, a thick layer of Cretaceous strata is deposited above the Jurassic Anding Formation (Figure1). The Cretaceous strata are mainly composed of thick sandstone with a small amount of sandy mudstone intercalation, which has good integrity (Figures 2 and 3(a)) and is not easy to deform, while the Jurassic Anding Formation is mainly composed of mudstone and sandy mudstone and has weathering zone inside, which is easy to deform (Figures 3(b) and 4). In the subsidence caused by underground mining, due to the asynchronous deformation between sandstone and sandy mudstone in Cretaceous and between Cretaceous and Jurassic Anding Formation, layered cavities (i.e., bed separations) appear in Cretaceous and the interface between Cretaceous and Jurassic Anding Formation (Figure 5). When the water in the aquifer around a bed separation converges into the bed separation, bed-separation water is formed, which can lead to the decline of the water level in the surrounding aquifer (Figure 6). When the bed-separation water suddenly burst into the mining area, BWI is formed. Due to the deformation of sandy mudstone intercalation in Cretaceous is clamped by its adjacent thick sandstone layers, bed separations in Cretaceous have smaller scale. On the contrary, because the overall antideformation ability of Cretaceous is greater than that of Jurassic Anding Formation, the deformation difference between Cretaceous and Jurassic Anding Formation is larger; bed separations at the interface of Cretaceous and Jurassic Anding Formation have larger scale. Therefore, the bed-separation water at the interface between Cretaceous and Jurassic Anding Formation is the focus of this study.Figure 1
Engineering geological background in the study area.Figure 2
Outcrop of Cretaceous strata (December 2018, Jingbian, China).Figure 3
Rock cores drilled in the Yingpanhao mine of (a) Cretaceous strata and (b) the Jurassic Anding Formation.
(a)(b)Figure 4
Outcrop of the interface between Cretaceous strata and the Jurassic Anding Formation in the Ordos Basin (October 2019, Jingbian, China).Figure 5
Schematic diagram of Cretaceous bed-separation water formation and mining disturbed overburden zoning during Jurassic coal seam mining:Ti: total thickness of all strata between the ith layer and the coal seam.Figure 6
Changes of Cretaceous water level during the formation of a Cretaceous BWI in Cuimu coal mine. ①: natural recovery period of water level; ②: filling period of water in Cretaceous aquifer into bed separation; ③: bed-separation water inrush period; ④: water level recovery period after water inrush channel closure.


## 3. Methods and Materials

### 3.1. BWI-Related Factors and Their Quantification

As shown in Figure5, BWI is caused by the breakthrough of the Jurassic protective layer by the Cretaceous bed-separation water above it. Therefore, the research objects directly involved in BWI process include the Cretaceous bed-separation water and the Jurassic protective layer. In the Jurassic protective layer, the upper part is the unbroken Jurassic strata (UJS), and the lower part is the fractured Jurassic strata (FJS). The water-resisting capacity of FJS is due to the closure of fractures in FJS under the action of water flow. Furthermore, the strata in FJS can be divided into fractured mudstone and fractured sandstone. The role and quantification of each BWI-related factor in BWI are described below.
(1)
Bed-separation water pressure (Pb)The bed-separation water pressure (Pb) provides the inducing power for the occurrence of BWI. Since the bed-separation water comes from the aquifer around the bed separation, when the bed separation is filled with water, Pb will gradually increase to be consistent with the water pressure in the aquifer around the bed separation. Since the bed separations at the interface between Cretaceous and Jurassic strata are the focus of this study, in this study, the Cretaceous Pb can be expressed by the water pressure in the aquifer at the bottom of Cretaceous.
(2)
UJS thickness (TU)UJS is the key factor affecting BWI because it can prevent the release of bed-separation water. Because the integrity of UJS is not damaged, it has greater strength and better water-resisting capacity than FJS. The greater the thickness of UJS (TU) is, the stronger its water-resisting capacity is. TU can be calculated as follows:
(1)TU=TJ−TF,(2)TF=M∗RFM,where TJ is the thickness of Jurassic strata between coal seam and Cretaceous (that is, the thickness of Jurassic protective layer); TF is the thickness of FJS; M is the mining thickness; and RFM is the ratio of TF and M, which can be obtained through field monitoring.
(3)
Closure potential of mudstone fractures in FJS (Cm)Due to the low strength (with an average saturated uniaxial compressive strength of 4.75 MPa) and low softening coefficient (with an average softening coefficient of 0.34), the Jurassic mudstone can be easily argillated and deformed after encountering water (Figure7), resulting in the self-healing effect of fractures in Jurassic mudstone under the action of water flow.Figure 7
Argillization of Jurassic mudstone core after encountering water.In FJS, the better the closure effect of mudstone fractures, the stronger the water-resisting capacity of mudstone, and the smaller the probability of BWI. Here, the closure potential of mudstone fractures in FJS (Cm) was used to evaluate the closure effect of mudstone fractures. Because Cm is positively correlated with the volume of mudstone and the volume of mudstone is positively correlated with the mudstone thickness, Cm is positively correlated with the mudstone thickness. On the contrary, because Cm is negatively correlated with the opening degree of mudstone fractures, and the opening degree of mudstone fractures is positively correlated with the height of available subsidence space of mudstone before mudstone fracture, Cm is negatively correlated with the height of available subsidence space of mudstone before mudstone fracture. Therefore, Cm can be quantified by the following formula:
(3)Cm=∑i=1ncmi,(4)cmi=tmiΨmi=tmiM−Tmi∗η−1.where cmi, tmi, and Ψmi refer to the closure potential, thickness, and height of available settlement space of the ith mudstone layer in FJS, respectively; η refers to the average expansion coefficient of the fractured rock mass, which can be obtained through field monitoring; and Tmi refers to the total thickness of all strata between the ith mudstone layer in FJS and the coal seam.
(4)
Closure potential of sandstone fractures in FJS (Cs)Due to the low cementation degree, the Jurassic sandstone is easy to disintegrate after encountering water (Figure8), and the fractures in the Jurassic sandstone are easy to be filled and closed by the disintegrated rock debris.Figure 8
Disintegration of Jurassic sandstone core after encountering water.In FJS, the better the closure effect of sandstone fractures, the stronger the water-resisting capacity of sandstone, and the smaller the probability of BWI. Here, the closure potential of sandstone fractures in FJS (Cs) was used to evaluate the closure effect of sandstone fractures. Because Cs is positively correlated with the sandstone fracture length and the sandstone fracture length is positively correlated with the sandstone thickness, Cs is positively correlated with the sandstone thickness. On the contrary, because Cs is negatively correlated with the opening degree of sandstone fractures, and the opening degree of sandstone fractures is positively correlated with the height of available subsidence space of sandstone before sandstone fracture, Cs is negatively correlated with the height of available subsidence space of sandstone before sandstone fracture. Therefore, Cs can be quantified by the following formula:
(5)Cs=∑i=1ncsi,(6)csi=tsiΨsi=tsiM−Tsi∗η−1.where csi, tsi, and Ψsi refer to the closure potential, thickness, and height of available settlement space of the ith sandstone layer in FJS, respectively; and Tsi refers to the total thickness of all strata between the ith sandstone layer in FJS and the coal seam.


### 3.2. Bed-Separation Water Inrush Coefficient (BWIC) Method

#### 3.2.1. Obtaining the BWI-Related Factors at Each Coordinate Point

According to the strata information revealed by each borehole, the values of BWI-related factors in each borehole are calculated. Then, through interpolation calculation, the values of each BWI-related factor at any coordinate point in the area to be evaluated can be obtained. Interpolation calculation can be realized by using a drawing software named Surfer.


#### 3.2.2. Identifying the Weight of Each BWI-Related Factor

UJS with a certain thickness and the same water-resisting capacity as FJS was called the equivalent strata of FJS (E-FJS). In order to calculate the thickness of E-FJS, it is necessary to determine the weight of each BWI-related factor in BWI.In this paper, the mining areas 106A and 108 in Shilawusu coal mine are taken as examples to explain how to obtain the weight of each BWI-related factor. Mining in mining area 106A has been completed, mining in mining area 108 is still in progress, and 1000 m has been excavated. When the excavation length was 554 m, a BWI occurred in mining area 106A, but no BWI occurred in mining area 108 during mining. Because the total amount of water in a bed separation is limited, the water inflow in a BWI has the characteristics of rapid increase and rapid decrease (Figure9). However, the instantaneous water inflow of BWI is very large, so BWI is very destructive.Figure 9
Comparison of water inflow in mining areas 106A and 108 in the Shilawusu coal mine.Even though mining areas 106A and 108 have the same mining width, similar mining depth, and similar mining thickness, there are differences in BWI-related factors between the two mining areas, which eventually lead to differences in BWI risk between the two mining areas. Therefore, by comparing the differences of BWI-related factors between mining area 106A and mining area 108, the weight of each BWI-related factor in the formation of BWI can be obtained under the premise of excluding the influence of mining width, mining depth, and mining thickness on BWI. The principle of obtaining the weight of each BWI-related factor is consistent with the basic principle of entropy weight method. Therefore, in this paper, entropy weight method was used to obtain the weight of each BWI-related factor.The data used for weight calculation obtained fromm sampling points and n BWI-related factors is written as:
(7)X=xijm×n=x11⋯x1n⋮⋱⋮xm1⋯xmn.After standardization, the following results can be obtained:(8)R=rijm×n=r11⋯r1n⋮⋱⋮rm1⋯rmn, where rij is the standardization value of the ith sampling point for the jth BWI-related factor. For the BWI-related factors positively correlated with BWI, rij is calculated as follows:
(9)rij=xij−minjxijmaxjxij−minjxij, whereas for the BWI-related factors negatively correlated with BWI, rij is calculated as follows:
(10)rij=maxjxij−xijmaxjxij−minjxij.The information entropy of thejth BWI-related factor (ej) is defined as:
(11)ej=−1lnm∑i=1mpij∗lnpij, where pij is calculated as follows:
(12)pij=rij∑i=1mrij.Because whenpij infinitely approaches 0, pij∗lnpij approaches 0; here, when pij=0, the value of pij∗lnpij was set to 0. The entropy weight of the jth BWI-related factor (wj) can be calculated by the following formula:
(13)wj=1−ejn−∑j=1nej.In this paper, there are four BWI-related factors, son=4, and w1, w2, w3, and w4 refer to the weight of Pb, TU, Cm, and Cs, respectively.


#### 3.2.3. Calculating the E-FJS Thickness (TE−FJS)

After calculating the weight of each BWI-related factor in BWI, the water-resisting capacity index (Vi) of Jurassic protective layer at the ith sampling point can be calculated by the following formula:
(14)Vi=TUi∑i=1mTUiw2+Cmi∑i=1mCmiw3+Csi∑i=1mCsiw4.Equation (14) can be transformed into:
(15)Vi=TUi∗k1+Cmi∗k2+Csi∗k3,where k1, k2, and k3 are constants.Assuming that the values ofTU, Cm, and Cs at the coordinate point A are TUA, CmA, and CsA, respectively, and the values of TU, Cm, and Cs at the coordinate point B are TUB, CmB, and CsB, respectively, then according to Equation (15), the water-resisting capacity index of Jurassic protective layer at the coordinate points A and B can be shown as follows:
(16)VA=TUA∗k1+CmA∗k2+CsA∗k3,(17)VB=TUB∗k1+CmB∗k2+CsB∗k3,where VA and VB are the water-resisting capacity index of Jurassic protective layer at the coordinate points A and B, respectively. Then, the restriction conditions (18) and (19) were set as follows:
(18)VA=VB;CsA=CsB,TUA≠0;TUB=0,CmA=0;CmB≠0,(19)VA=VB;CmA=CmB,TUA≠0;TUB=0,CsA=0;CsB≠0.By synthesizing Equations (16) and (17) and restriction condition (18), the following equation can be obtained:
(20)TUA∗k1=k2k1∗CmB∗k1=km∗CmB∗k1, where km is a constant and its value is the ratio of k2 to k1. From Equation (20), it can be concluded that:
(21)TUA=km∗CmB.The physical meaning of Equation (21) can be expressed as when Cm is dimensionless and the unit of TU is m, the water-resisting capacity of UJS with TU=kmm is equal to that of one unit of Cm. UJS with a certain thickness and the same water-resisting capacity as mudstone in FJS was called equivalent strata of mudstone in FJS (E-M-FJS). Therefore, the E-M-FJS thickness (TE−M−FJS) can be obtained as:
(22)TE−M−FJS=km∗Cm.By synthesizing Equations (16) and (17) and restriction condition (19), the following equation can be obtained:
(23)TUA∗k1=k3k1∗CsB∗k1=ks∗CsB∗k1, where ks is a constant and its value is the ratio of k3 to k1. From equation (23), it can be concluded that:
(24)TUA=ks∗CsB.The physical meaning of Equation (24) can be expressed as when Cs is dimensionless and the unit of TU is m, the water-resisting capacity of UJS with TU=ksm is equal to that of one unit of Cs. UJS with a certain thickness and the same water-resisting capacity as sandstone in FJS was called equivalent strata of sandstone in FJS (E-S-FJS). Therefore, the E-S-FJS thickness (TE−S−FJS) can be obtained as:
(25)TE−S−FJS=ks∗Cs.The relationship amongTE−FJS, TE−M−FJS, and TE−S−FJS satisfies the following equation:
(26)TE−FJS=TE−M−FJS+TE−S−FJS.According to Equations (22), (25), and (26), the formula for calculating TE−FJS can be obtained as follows:
(27)TE−FJS=km∗Cm+ks∗Cs.


#### 3.2.4. Calculating theBWIC at Each Coordinate Point

The formula for calculating theBWIC at each coordinate point xi,yi can be obtained as follows:
(28)BWICxi,yi=Pbxi,yiTUxi,yi+TE−FJSxi,yi, where BWICxi,yi, Pbxi,yi,TUxi,yi, and TE−FJSxi,yi, respectively, refer to the BWIC, Pb, TU, and TE−FJS at the coordinate point xi,yi. According to Equation (27), Equation (28) can be transformed into:
(29)BWICxi,yi=Pbxi,yiTUxi,yi+km∗Cmxi,yi+ks∗Csxi,yi, where Cmxi,yi and Csxi,yi, respectively, refer to the Cm and Cs at the coordinate point xi,yi.


#### 3.2.5. Obtaining the OverallBWIC Corresponding to Different Excavation Lengths

Since any excavation length corresponds to a stress balance arch (Figure10), the average BWIC in the bed separation zone in the stress balance arch corresponding to each excavation length was used as the overall BWIC corresponding to each excavation length. Therefore, the overall BWI risk when the excavation length is lx can be expressed by the following formula:
(30)BWIClx=1z∑i=1zBWICxi,yi, where BWIClx and z, respectively, refer to the overall BWIC and the number of selected coordinate points within the distribution range of bed separation zone when the excavation length is lx. In this paper, for the convenience of calculation, z refers to the number of grid points after each bed separation zone distribution range was divided into squares with side length of 10 m.Figure 10
Schematic diagram of stress balance arches and bed separations in mining disturbed overburden.With the increase of the excavation length, the size of the stress balance arch expands continuously. When the excavation length reaches a specific value, the size of the stress balance arch develops to the maximum, which is called the limit arch. The maximum height of limit arch is about 0.7 times of mining depth. Then, as the excavation continues, the stress balance arch exists in the form of moving arch, which has the same size as the limit arch [17, 18]. In order to observe the shape of the stress balance arch, some mining cases in Cuimu coal mine, Buerdong coal mine, and Daliuta coal mine in Ordos Basin were studied. The mining process of mining area 21301 in Cuimu coal mine was simulated by using the discrete element software UDEC. The results show that the deformed and broken rock strata are located in a triangular area as a whole, the two sides of the triangle are rock fracture lines, and the bottom of the triangle is the distribution range of goaf. In the triangular area, the deformation and fracture degree of the rock stratum below the bed separation is large, while the deformation of the rock stratum above the bed separation is small (Figure 11(a)). Similar material physical simulation experiments of mining cases in Buerdong coal mine and Daliuta coal mine also show that the rock strata that can deform and fracture are located in the triangular area surrounded by the two rock fracture lines and the distribution area of goaf (Figures 11(b) and 11(c)). Because the deformation and failure of overburden occur in the stress balance arch, the area surrounded by the triangle composed of rock fracture lines and goaf can be equivalent to the area in the stress balance arch, that is, the stress balance arch can be simplified into a triangle with a base angle of about 60° [19, 20].Figure 11
Stress balance arch and its simplification based on some coal seam mining experiments. (a) Numerical simulation experiment of coal seam mining in Cuimu coal mine; (b) similar material simulation experiment of coal seam mining in Buerdong coal mine; (c) similar material simulation experiment of coal seam mining in Daliuta coal mine.
(a)(b)(c)


#### 3.2.6. Grading BWI Risk

In actual mining, the excavation length with or without BWIs is called danger excavation length (ld) and safety excavation length (ls), respectively. The BWIClx corresponding to ld and ls are BWICld and BWICls, respectively. BWIClx greater than BWICld indicates a high risk of BWI, while BWIClx smaller than BWICls indicates a low risk of BWI. Therefore, the risk level with BWIClx greater than BWICld was identified as danger, the risk level with BWIClx smaller than BWICls was identified as safety, and the risk level with BWIClx greater than BWICls less than BWICld was identified as transition. Further division of the transition can be achieved by means of the average value of BWICld and BWICls. Here, the average value of BWICld and BWICls was marked as BWIClt. The risk level with BWIClx greater than BWICls less than BWIClt was identified as relatively safe, and risk level with BWIClx greater than BWIClt less than BWICld was identified as relatively dangerous. In addition, when the excavation length is less than la, the BWI risk was determined as safe because the stress balance arch has not expanded to the Cretaceous bed separation zone (Figure 10). The principle of BWI risk classification is shown in Figure 12.Figure 12
Principle of BWI risk classification based onBWIC method.


## 3.1. BWI-Related Factors and Their Quantification

As shown in Figure5, BWI is caused by the breakthrough of the Jurassic protective layer by the Cretaceous bed-separation water above it. Therefore, the research objects directly involved in BWI process include the Cretaceous bed-separation water and the Jurassic protective layer. In the Jurassic protective layer, the upper part is the unbroken Jurassic strata (UJS), and the lower part is the fractured Jurassic strata (FJS). The water-resisting capacity of FJS is due to the closure of fractures in FJS under the action of water flow. Furthermore, the strata in FJS can be divided into fractured mudstone and fractured sandstone. The role and quantification of each BWI-related factor in BWI are described below.
(1)
Bed-separation water pressure (Pb)The bed-separation water pressure (Pb) provides the inducing power for the occurrence of BWI. Since the bed-separation water comes from the aquifer around the bed separation, when the bed separation is filled with water, Pb will gradually increase to be consistent with the water pressure in the aquifer around the bed separation. Since the bed separations at the interface between Cretaceous and Jurassic strata are the focus of this study, in this study, the Cretaceous Pb can be expressed by the water pressure in the aquifer at the bottom of Cretaceous.
(2)
UJS thickness (TU)UJS is the key factor affecting BWI because it can prevent the release of bed-separation water. Because the integrity of UJS is not damaged, it has greater strength and better water-resisting capacity than FJS. The greater the thickness of UJS (TU) is, the stronger its water-resisting capacity is. TU can be calculated as follows:
(1)TU=TJ−TF,(2)TF=M∗RFM,where TJ is the thickness of Jurassic strata between coal seam and Cretaceous (that is, the thickness of Jurassic protective layer); TF is the thickness of FJS; M is the mining thickness; and RFM is the ratio of TF and M, which can be obtained through field monitoring.
(3)
Closure potential of mudstone fractures in FJS (Cm)Due to the low strength (with an average saturated uniaxial compressive strength of 4.75 MPa) and low softening coefficient (with an average softening coefficient of 0.34), the Jurassic mudstone can be easily argillated and deformed after encountering water (Figure7), resulting in the self-healing effect of fractures in Jurassic mudstone under the action of water flow.Figure 7
Argillization of Jurassic mudstone core after encountering water.In FJS, the better the closure effect of mudstone fractures, the stronger the water-resisting capacity of mudstone, and the smaller the probability of BWI. Here, the closure potential of mudstone fractures in FJS (Cm) was used to evaluate the closure effect of mudstone fractures. Because Cm is positively correlated with the volume of mudstone and the volume of mudstone is positively correlated with the mudstone thickness, Cm is positively correlated with the mudstone thickness. On the contrary, because Cm is negatively correlated with the opening degree of mudstone fractures, and the opening degree of mudstone fractures is positively correlated with the height of available subsidence space of mudstone before mudstone fracture, Cm is negatively correlated with the height of available subsidence space of mudstone before mudstone fracture. Therefore, Cm can be quantified by the following formula:
(3)Cm=∑i=1ncmi,(4)cmi=tmiΨmi=tmiM−Tmi∗η−1.where cmi, tmi, and Ψmi refer to the closure potential, thickness, and height of available settlement space of the ith mudstone layer in FJS, respectively; η refers to the average expansion coefficient of the fractured rock mass, which can be obtained through field monitoring; and Tmi refers to the total thickness of all strata between the ith mudstone layer in FJS and the coal seam.
(4)
Closure potential of sandstone fractures in FJS (Cs)Due to the low cementation degree, the Jurassic sandstone is easy to disintegrate after encountering water (Figure8), and the fractures in the Jurassic sandstone are easy to be filled and closed by the disintegrated rock debris.Figure 8
Disintegration of Jurassic sandstone core after encountering water.In FJS, the better the closure effect of sandstone fractures, the stronger the water-resisting capacity of sandstone, and the smaller the probability of BWI. Here, the closure potential of sandstone fractures in FJS (Cs) was used to evaluate the closure effect of sandstone fractures. Because Cs is positively correlated with the sandstone fracture length and the sandstone fracture length is positively correlated with the sandstone thickness, Cs is positively correlated with the sandstone thickness. On the contrary, because Cs is negatively correlated with the opening degree of sandstone fractures, and the opening degree of sandstone fractures is positively correlated with the height of available subsidence space of sandstone before sandstone fracture, Cs is negatively correlated with the height of available subsidence space of sandstone before sandstone fracture. Therefore, Cs can be quantified by the following formula:
(5)Cs=∑i=1ncsi,(6)csi=tsiΨsi=tsiM−Tsi∗η−1.where csi, tsi, and Ψsi refer to the closure potential, thickness, and height of available settlement space of the ith sandstone layer in FJS, respectively; and Tsi refers to the total thickness of all strata between the ith sandstone layer in FJS and the coal seam.


## 3.2. Bed-Separation Water Inrush Coefficient (BWIC) Method

### 3.2.1. Obtaining the BWI-Related Factors at Each Coordinate Point

According to the strata information revealed by each borehole, the values of BWI-related factors in each borehole are calculated. Then, through interpolation calculation, the values of each BWI-related factor at any coordinate point in the area to be evaluated can be obtained. Interpolation calculation can be realized by using a drawing software named Surfer.


### 3.2.2. Identifying the Weight of Each BWI-Related Factor

UJS with a certain thickness and the same water-resisting capacity as FJS was called the equivalent strata of FJS (E-FJS). In order to calculate the thickness of E-FJS, it is necessary to determine the weight of each BWI-related factor in BWI.In this paper, the mining areas 106A and 108 in Shilawusu coal mine are taken as examples to explain how to obtain the weight of each BWI-related factor. Mining in mining area 106A has been completed, mining in mining area 108 is still in progress, and 1000 m has been excavated. When the excavation length was 554 m, a BWI occurred in mining area 106A, but no BWI occurred in mining area 108 during mining. Because the total amount of water in a bed separation is limited, the water inflow in a BWI has the characteristics of rapid increase and rapid decrease (Figure9). However, the instantaneous water inflow of BWI is very large, so BWI is very destructive.Figure 9
Comparison of water inflow in mining areas 106A and 108 in the Shilawusu coal mine.Even though mining areas 106A and 108 have the same mining width, similar mining depth, and similar mining thickness, there are differences in BWI-related factors between the two mining areas, which eventually lead to differences in BWI risk between the two mining areas. Therefore, by comparing the differences of BWI-related factors between mining area 106A and mining area 108, the weight of each BWI-related factor in the formation of BWI can be obtained under the premise of excluding the influence of mining width, mining depth, and mining thickness on BWI. The principle of obtaining the weight of each BWI-related factor is consistent with the basic principle of entropy weight method. Therefore, in this paper, entropy weight method was used to obtain the weight of each BWI-related factor.The data used for weight calculation obtained fromm sampling points and n BWI-related factors is written as:
(7)X=xijm×n=x11⋯x1n⋮⋱⋮xm1⋯xmn.After standardization, the following results can be obtained:(8)R=rijm×n=r11⋯r1n⋮⋱⋮rm1⋯rmn, where rij is the standardization value of the ith sampling point for the jth BWI-related factor. For the BWI-related factors positively correlated with BWI, rij is calculated as follows:
(9)rij=xij−minjxijmaxjxij−minjxij, whereas for the BWI-related factors negatively correlated with BWI, rij is calculated as follows:
(10)rij=maxjxij−xijmaxjxij−minjxij.The information entropy of thejth BWI-related factor (ej) is defined as:
(11)ej=−1lnm∑i=1mpij∗lnpij, where pij is calculated as follows:
(12)pij=rij∑i=1mrij.Because whenpij infinitely approaches 0, pij∗lnpij approaches 0; here, when pij=0, the value of pij∗lnpij was set to 0. The entropy weight of the jth BWI-related factor (wj) can be calculated by the following formula:
(13)wj=1−ejn−∑j=1nej.In this paper, there are four BWI-related factors, son=4, and w1, w2, w3, and w4 refer to the weight of Pb, TU, Cm, and Cs, respectively.


### 3.2.3. Calculating the E-FJS Thickness (TE−FJS)

After calculating the weight of each BWI-related factor in BWI, the water-resisting capacity index (Vi) of Jurassic protective layer at the ith sampling point can be calculated by the following formula:
(14)Vi=TUi∑i=1mTUiw2+Cmi∑i=1mCmiw3+Csi∑i=1mCsiw4.Equation (14) can be transformed into:
(15)Vi=TUi∗k1+Cmi∗k2+Csi∗k3,where k1, k2, and k3 are constants.Assuming that the values ofTU, Cm, and Cs at the coordinate point A are TUA, CmA, and CsA, respectively, and the values of TU, Cm, and Cs at the coordinate point B are TUB, CmB, and CsB, respectively, then according to Equation (15), the water-resisting capacity index of Jurassic protective layer at the coordinate points A and B can be shown as follows:
(16)VA=TUA∗k1+CmA∗k2+CsA∗k3,(17)VB=TUB∗k1+CmB∗k2+CsB∗k3,where VA and VB are the water-resisting capacity index of Jurassic protective layer at the coordinate points A and B, respectively. Then, the restriction conditions (18) and (19) were set as follows:
(18)VA=VB;CsA=CsB,TUA≠0;TUB=0,CmA=0;CmB≠0,(19)VA=VB;CmA=CmB,TUA≠0;TUB=0,CsA=0;CsB≠0.By synthesizing Equations (16) and (17) and restriction condition (18), the following equation can be obtained:
(20)TUA∗k1=k2k1∗CmB∗k1=km∗CmB∗k1, where km is a constant and its value is the ratio of k2 to k1. From Equation (20), it can be concluded that:
(21)TUA=km∗CmB.The physical meaning of Equation (21) can be expressed as when Cm is dimensionless and the unit of TU is m, the water-resisting capacity of UJS with TU=kmm is equal to that of one unit of Cm. UJS with a certain thickness and the same water-resisting capacity as mudstone in FJS was called equivalent strata of mudstone in FJS (E-M-FJS). Therefore, the E-M-FJS thickness (TE−M−FJS) can be obtained as:
(22)TE−M−FJS=km∗Cm.By synthesizing Equations (16) and (17) and restriction condition (19), the following equation can be obtained:
(23)TUA∗k1=k3k1∗CsB∗k1=ks∗CsB∗k1, where ks is a constant and its value is the ratio of k3 to k1. From equation (23), it can be concluded that:
(24)TUA=ks∗CsB.The physical meaning of Equation (24) can be expressed as when Cs is dimensionless and the unit of TU is m, the water-resisting capacity of UJS with TU=ksm is equal to that of one unit of Cs. UJS with a certain thickness and the same water-resisting capacity as sandstone in FJS was called equivalent strata of sandstone in FJS (E-S-FJS). Therefore, the E-S-FJS thickness (TE−S−FJS) can be obtained as:
(25)TE−S−FJS=ks∗Cs.The relationship amongTE−FJS, TE−M−FJS, and TE−S−FJS satisfies the following equation:
(26)TE−FJS=TE−M−FJS+TE−S−FJS.According to Equations (22), (25), and (26), the formula for calculating TE−FJS can be obtained as follows:
(27)TE−FJS=km∗Cm+ks∗Cs.


### 3.2.4. Calculating theBWIC at Each Coordinate Point

The formula for calculating theBWIC at each coordinate point xi,yi can be obtained as follows:
(28)BWICxi,yi=Pbxi,yiTUxi,yi+TE−FJSxi,yi, where BWICxi,yi, Pbxi,yi,TUxi,yi, and TE−FJSxi,yi, respectively, refer to the BWIC, Pb, TU, and TE−FJS at the coordinate point xi,yi. According to Equation (27), Equation (28) can be transformed into:
(29)BWICxi,yi=Pbxi,yiTUxi,yi+km∗Cmxi,yi+ks∗Csxi,yi, where Cmxi,yi and Csxi,yi, respectively, refer to the Cm and Cs at the coordinate point xi,yi.


### 3.2.5. Obtaining the OverallBWIC Corresponding to Different Excavation Lengths

Since any excavation length corresponds to a stress balance arch (Figure10), the average BWIC in the bed separation zone in the stress balance arch corresponding to each excavation length was used as the overall BWIC corresponding to each excavation length. Therefore, the overall BWI risk when the excavation length is lx can be expressed by the following formula:
(30)BWIClx=1z∑i=1zBWICxi,yi, where BWIClx and z, respectively, refer to the overall BWIC and the number of selected coordinate points within the distribution range of bed separation zone when the excavation length is lx. In this paper, for the convenience of calculation, z refers to the number of grid points after each bed separation zone distribution range was divided into squares with side length of 10 m.Figure 10
Schematic diagram of stress balance arches and bed separations in mining disturbed overburden.With the increase of the excavation length, the size of the stress balance arch expands continuously. When the excavation length reaches a specific value, the size of the stress balance arch develops to the maximum, which is called the limit arch. The maximum height of limit arch is about 0.7 times of mining depth. Then, as the excavation continues, the stress balance arch exists in the form of moving arch, which has the same size as the limit arch [17, 18]. In order to observe the shape of the stress balance arch, some mining cases in Cuimu coal mine, Buerdong coal mine, and Daliuta coal mine in Ordos Basin were studied. The mining process of mining area 21301 in Cuimu coal mine was simulated by using the discrete element software UDEC. The results show that the deformed and broken rock strata are located in a triangular area as a whole, the two sides of the triangle are rock fracture lines, and the bottom of the triangle is the distribution range of goaf. In the triangular area, the deformation and fracture degree of the rock stratum below the bed separation is large, while the deformation of the rock stratum above the bed separation is small (Figure 11(a)). Similar material physical simulation experiments of mining cases in Buerdong coal mine and Daliuta coal mine also show that the rock strata that can deform and fracture are located in the triangular area surrounded by the two rock fracture lines and the distribution area of goaf (Figures 11(b) and 11(c)). Because the deformation and failure of overburden occur in the stress balance arch, the area surrounded by the triangle composed of rock fracture lines and goaf can be equivalent to the area in the stress balance arch, that is, the stress balance arch can be simplified into a triangle with a base angle of about 60° [19, 20].Figure 11
Stress balance arch and its simplification based on some coal seam mining experiments. (a) Numerical simulation experiment of coal seam mining in Cuimu coal mine; (b) similar material simulation experiment of coal seam mining in Buerdong coal mine; (c) similar material simulation experiment of coal seam mining in Daliuta coal mine.
(a)(b)(c)


### 3.2.6. Grading BWI Risk

In actual mining, the excavation length with or without BWIs is called danger excavation length (ld) and safety excavation length (ls), respectively. The BWIClx corresponding to ld and ls are BWICld and BWICls, respectively. BWIClx greater than BWICld indicates a high risk of BWI, while BWIClx smaller than BWICls indicates a low risk of BWI. Therefore, the risk level with BWIClx greater than BWICld was identified as danger, the risk level with BWIClx smaller than BWICls was identified as safety, and the risk level with BWIClx greater than BWICls less than BWICld was identified as transition. Further division of the transition can be achieved by means of the average value of BWICld and BWICls. Here, the average value of BWICld and BWICls was marked as BWIClt. The risk level with BWIClx greater than BWICls less than BWIClt was identified as relatively safe, and risk level with BWIClx greater than BWIClt less than BWICld was identified as relatively dangerous. In addition, when the excavation length is less than la, the BWI risk was determined as safe because the stress balance arch has not expanded to the Cretaceous bed separation zone (Figure 10). The principle of BWI risk classification is shown in Figure 12.Figure 12
Principle of BWI risk classification based onBWIC method.


## 3.2.1. Obtaining the BWI-Related Factors at Each Coordinate Point

According to the strata information revealed by each borehole, the values of BWI-related factors in each borehole are calculated. Then, through interpolation calculation, the values of each BWI-related factor at any coordinate point in the area to be evaluated can be obtained. Interpolation calculation can be realized by using a drawing software named Surfer.


## 3.2.2. Identifying the Weight of Each BWI-Related Factor

UJS with a certain thickness and the same water-resisting capacity as FJS was called the equivalent strata of FJS (E-FJS). In order to calculate the thickness of E-FJS, it is necessary to determine the weight of each BWI-related factor in BWI.In this paper, the mining areas 106A and 108 in Shilawusu coal mine are taken as examples to explain how to obtain the weight of each BWI-related factor. Mining in mining area 106A has been completed, mining in mining area 108 is still in progress, and 1000 m has been excavated. When the excavation length was 554 m, a BWI occurred in mining area 106A, but no BWI occurred in mining area 108 during mining. Because the total amount of water in a bed separation is limited, the water inflow in a BWI has the characteristics of rapid increase and rapid decrease (Figure9). However, the instantaneous water inflow of BWI is very large, so BWI is very destructive.Figure 9
Comparison of water inflow in mining areas 106A and 108 in the Shilawusu coal mine.Even though mining areas 106A and 108 have the same mining width, similar mining depth, and similar mining thickness, there are differences in BWI-related factors between the two mining areas, which eventually lead to differences in BWI risk between the two mining areas. Therefore, by comparing the differences of BWI-related factors between mining area 106A and mining area 108, the weight of each BWI-related factor in the formation of BWI can be obtained under the premise of excluding the influence of mining width, mining depth, and mining thickness on BWI. The principle of obtaining the weight of each BWI-related factor is consistent with the basic principle of entropy weight method. Therefore, in this paper, entropy weight method was used to obtain the weight of each BWI-related factor.The data used for weight calculation obtained fromm sampling points and n BWI-related factors is written as:
(7)X=xijm×n=x11⋯x1n⋮⋱⋮xm1⋯xmn.After standardization, the following results can be obtained:(8)R=rijm×n=r11⋯r1n⋮⋱⋮rm1⋯rmn, where rij is the standardization value of the ith sampling point for the jth BWI-related factor. For the BWI-related factors positively correlated with BWI, rij is calculated as follows:
(9)rij=xij−minjxijmaxjxij−minjxij, whereas for the BWI-related factors negatively correlated with BWI, rij is calculated as follows:
(10)rij=maxjxij−xijmaxjxij−minjxij.The information entropy of thejth BWI-related factor (ej) is defined as:
(11)ej=−1lnm∑i=1mpij∗lnpij, where pij is calculated as follows:
(12)pij=rij∑i=1mrij.Because whenpij infinitely approaches 0, pij∗lnpij approaches 0; here, when pij=0, the value of pij∗lnpij was set to 0. The entropy weight of the jth BWI-related factor (wj) can be calculated by the following formula:
(13)wj=1−ejn−∑j=1nej.In this paper, there are four BWI-related factors, son=4, and w1, w2, w3, and w4 refer to the weight of Pb, TU, Cm, and Cs, respectively.


## 3.2.3. Calculating the E-FJS Thickness (TE−FJS)

After calculating the weight of each BWI-related factor in BWI, the water-resisting capacity index (Vi) of Jurassic protective layer at the ith sampling point can be calculated by the following formula:
(14)Vi=TUi∑i=1mTUiw2+Cmi∑i=1mCmiw3+Csi∑i=1mCsiw4.Equation (14) can be transformed into:
(15)Vi=TUi∗k1+Cmi∗k2+Csi∗k3,where k1, k2, and k3 are constants.Assuming that the values ofTU, Cm, and Cs at the coordinate point A are TUA, CmA, and CsA, respectively, and the values of TU, Cm, and Cs at the coordinate point B are TUB, CmB, and CsB, respectively, then according to Equation (15), the water-resisting capacity index of Jurassic protective layer at the coordinate points A and B can be shown as follows:
(16)VA=TUA∗k1+CmA∗k2+CsA∗k3,(17)VB=TUB∗k1+CmB∗k2+CsB∗k3,where VA and VB are the water-resisting capacity index of Jurassic protective layer at the coordinate points A and B, respectively. Then, the restriction conditions (18) and (19) were set as follows:
(18)VA=VB;CsA=CsB,TUA≠0;TUB=0,CmA=0;CmB≠0,(19)VA=VB;CmA=CmB,TUA≠0;TUB=0,CsA=0;CsB≠0.By synthesizing Equations (16) and (17) and restriction condition (18), the following equation can be obtained:
(20)TUA∗k1=k2k1∗CmB∗k1=km∗CmB∗k1, where km is a constant and its value is the ratio of k2 to k1. From Equation (20), it can be concluded that:
(21)TUA=km∗CmB.The physical meaning of Equation (21) can be expressed as when Cm is dimensionless and the unit of TU is m, the water-resisting capacity of UJS with TU=kmm is equal to that of one unit of Cm. UJS with a certain thickness and the same water-resisting capacity as mudstone in FJS was called equivalent strata of mudstone in FJS (E-M-FJS). Therefore, the E-M-FJS thickness (TE−M−FJS) can be obtained as:
(22)TE−M−FJS=km∗Cm.By synthesizing Equations (16) and (17) and restriction condition (19), the following equation can be obtained:
(23)TUA∗k1=k3k1∗CsB∗k1=ks∗CsB∗k1, where ks is a constant and its value is the ratio of k3 to k1. From equation (23), it can be concluded that:
(24)TUA=ks∗CsB.The physical meaning of Equation (24) can be expressed as when Cs is dimensionless and the unit of TU is m, the water-resisting capacity of UJS with TU=ksm is equal to that of one unit of Cs. UJS with a certain thickness and the same water-resisting capacity as sandstone in FJS was called equivalent strata of sandstone in FJS (E-S-FJS). Therefore, the E-S-FJS thickness (TE−S−FJS) can be obtained as:
(25)TE−S−FJS=ks∗Cs.The relationship amongTE−FJS, TE−M−FJS, and TE−S−FJS satisfies the following equation:
(26)TE−FJS=TE−M−FJS+TE−S−FJS.According to Equations (22), (25), and (26), the formula for calculating TE−FJS can be obtained as follows:
(27)TE−FJS=km∗Cm+ks∗Cs.


## 3.2.4. Calculating theBWIC at Each Coordinate Point

The formula for calculating theBWIC at each coordinate point xi,yi can be obtained as follows:
(28)BWICxi,yi=Pbxi,yiTUxi,yi+TE−FJSxi,yi, where BWICxi,yi, Pbxi,yi,TUxi,yi, and TE−FJSxi,yi, respectively, refer to the BWIC, Pb, TU, and TE−FJS at the coordinate point xi,yi. According to Equation (27), Equation (28) can be transformed into:
(29)BWICxi,yi=Pbxi,yiTUxi,yi+km∗Cmxi,yi+ks∗Csxi,yi, where Cmxi,yi and Csxi,yi, respectively, refer to the Cm and Cs at the coordinate point xi,yi.


## 3.2.5. Obtaining the OverallBWIC Corresponding to Different Excavation Lengths

Since any excavation length corresponds to a stress balance arch (Figure10), the average BWIC in the bed separation zone in the stress balance arch corresponding to each excavation length was used as the overall BWIC corresponding to each excavation length. Therefore, the overall BWI risk when the excavation length is lx can be expressed by the following formula:
(30)BWIClx=1z∑i=1zBWICxi,yi, where BWIClx and z, respectively, refer to the overall BWIC and the number of selected coordinate points within the distribution range of bed separation zone when the excavation length is lx. In this paper, for the convenience of calculation, z refers to the number of grid points after each bed separation zone distribution range was divided into squares with side length of 10 m.Figure 10
Schematic diagram of stress balance arches and bed separations in mining disturbed overburden.With the increase of the excavation length, the size of the stress balance arch expands continuously. When the excavation length reaches a specific value, the size of the stress balance arch develops to the maximum, which is called the limit arch. The maximum height of limit arch is about 0.7 times of mining depth. Then, as the excavation continues, the stress balance arch exists in the form of moving arch, which has the same size as the limit arch [17, 18]. In order to observe the shape of the stress balance arch, some mining cases in Cuimu coal mine, Buerdong coal mine, and Daliuta coal mine in Ordos Basin were studied. The mining process of mining area 21301 in Cuimu coal mine was simulated by using the discrete element software UDEC. The results show that the deformed and broken rock strata are located in a triangular area as a whole, the two sides of the triangle are rock fracture lines, and the bottom of the triangle is the distribution range of goaf. In the triangular area, the deformation and fracture degree of the rock stratum below the bed separation is large, while the deformation of the rock stratum above the bed separation is small (Figure 11(a)). Similar material physical simulation experiments of mining cases in Buerdong coal mine and Daliuta coal mine also show that the rock strata that can deform and fracture are located in the triangular area surrounded by the two rock fracture lines and the distribution area of goaf (Figures 11(b) and 11(c)). Because the deformation and failure of overburden occur in the stress balance arch, the area surrounded by the triangle composed of rock fracture lines and goaf can be equivalent to the area in the stress balance arch, that is, the stress balance arch can be simplified into a triangle with a base angle of about 60° [19, 20].Figure 11
Stress balance arch and its simplification based on some coal seam mining experiments. (a) Numerical simulation experiment of coal seam mining in Cuimu coal mine; (b) similar material simulation experiment of coal seam mining in Buerdong coal mine; (c) similar material simulation experiment of coal seam mining in Daliuta coal mine.
(a)(b)(c)


## 3.2.6. Grading BWI Risk

In actual mining, the excavation length with or without BWIs is called danger excavation length (ld) and safety excavation length (ls), respectively. The BWIClx corresponding to ld and ls are BWICld and BWICls, respectively. BWIClx greater than BWICld indicates a high risk of BWI, while BWIClx smaller than BWICls indicates a low risk of BWI. Therefore, the risk level with BWIClx greater than BWICld was identified as danger, the risk level with BWIClx smaller than BWICls was identified as safety, and the risk level with BWIClx greater than BWICls less than BWICld was identified as transition. Further division of the transition can be achieved by means of the average value of BWICld and BWICls. Here, the average value of BWICld and BWICls was marked as BWIClt. The risk level with BWIClx greater than BWICls less than BWIClt was identified as relatively safe, and risk level with BWIClx greater than BWIClt less than BWICld was identified as relatively dangerous. In addition, when the excavation length is less than la, the BWI risk was determined as safe because the stress balance arch has not expanded to the Cretaceous bed separation zone (Figure 10). The principle of BWI risk classification is shown in Figure 12.Figure 12
Principle of BWI risk classification based onBWIC method.


## 4. Results and Discussion

Taking mining areas 106A and 108 in Shilawusu coal mine as examples, the establishment process ofBWIC method was introduced.


### 4.1. Obtaining the BWI-Related Factors at Each Coordinate Point

The distribution of related factors in mining areas 106A and 108 in Shilawusu coal mine is shown in Figure13.Figure 13
Distribution of (a)Pb, (b) TU, (c) Cm, and (d) Cs in mining areas 106A and 108 in Shilawusu coal mine.
(a)(b)(c)(d)


### 4.2. Identifying the Weight of Each BWI-Related Factor

According to the analysis in Section3.2, the entropy weight method can be used to determine the weight of BWI-related factors, and the sampling points in mining areas 108 and 106A should be located in the range of the bed separation zone corresponding to the excavation length of 554 m. Based on the triangle stress arch theory, it can be determined that when the excavation length is 554 m, the sampling points in mining area 108 are A1-A9, and the sampling points in mining area 106A are B1-B9 (Figure 13). The values of BWI-related factors at each sampling point are shown in Table 1.Table 1
Values of BWI-related factors at each sampling point.
Sampling pointsPb (MPa)TU (m)CmCsA12.78119.77418.85818.997A22.761121.81819.12818.875A32.746123.42519.37818.767A42.768120.7518.82918.922A52.75122.75919.13518.805A62.737124.30419.41118.699A72.755121.84218.79918.839A82.739123.79119.14618.73A92.726125.24819.4518.628B13.01977.90820.41919.315B22.96382.76320.60718.905B32.89888.44820.7618.539B43.10268.00920.0819.796B53.01475.58320.28519.449B62.92583.20120.3919.213B73.19157.79219.72620.319B83.06568.57119.98320.001B92.9578.29920.07819.832By analyzing the data in Table1 according to Equations (9)–(13), the weight of each BWI-related factor can be obtained (Table 2).Table 2
Index weight of BWI-related factors.
BWI-related factorsPbTUCmCsIndex weight0.3540.3900.1580.098Because bed-separation water pressure is the power source of BWI,Pb has a large weight. As the integrity of UJS was not damaged, UJS plays an important role in preventing water inrush, so the weight of TU should be the largest. Because the integrity of the rock strata in FJS has been destroyed, the water-resisting capacity of FJS is still weaker than that of UJS, so the weight of Cm and Cs is less than that of TU. In addition, because the fracture closure degree of mudstone is relatively better than that of sandstone, the water-resisting capacity of mudstone in FJS is stronger than that of sandstone, so the weight of Cm is greater than that of Cs.The above analysis results are obtained by reasonable inference based on the actual engineering geological conditions, which are consistent with the results in Table2, indicating that the calculation results of the weights of BWI-related factors are in line with the reality.


### 4.3. Calculating the E-FJS Thickness (TE−FJS)

According to the weights of BWI-related factors in Table2, Equation (15) can be expressed as:
(31)Vi=2.186×10−4TUi+4.457×10−4Cmi+2.844×10−4Csi.It can be seen from Equation (31) that k1, k2, and k3 are 2.186×10−4, 4.457×10−4, and 2.844×10−4, respectively. Then, km and ks can also be calculated, which are 2.039 and 1.301, respectively, and Equations (22) and (25) can be expressed as follows:
(32)TE−M−FJS=2.039Cm,(33)TE−S−FJS=1.301Cs,Taking mining area 106A in Shilawusu coal mine as an example, whenM, RFM, and η are 10 m, 23, and 1.032, respectively, the TE−M−FJS of mudstone with a thickness of 1 m at different locations in FJS was calculated by using Equations (4) and (32) (Table 3), and the TE−S−FJS of sandstone with a thickness of 1 m at different locations in FJS was calculated by using Equations (6) and (33) (Table 4).Table 3
TE−M−FJS of mudstone at different locations in FJS.
Locationtm (m)Tm (m)cmTE−M−FJS (m)TE−M−FJS/tmTop of FJS12290.3740.76376.3%Bottom of FJS100.10.20420.4%Table 4
TE−S−FJS of sandstone at different locations in FJS.
Locationts (m)Ts (m)csTE−S−FJS (m)TE−S−FJS/tsTop of FJS12290.3740.48748.7%Bottom of FJS100.10.13013.0%Although the rock in FJS still have water-resisting capacity due to the closure of internal fractures, the restored water-resisting capacity is still weaker than that of the unfractured rock because the integrity of the fractured rock has been destroyed. This conclusion can also be obtained by analyzing the data in Table3 and Table 4. It can be seen from Table 3 and Table 4 that the water resistance capacity of mudstone and sandstone in FJS is weaker than that of intact rock. Due to the larger opening and weaker closure of the fractures, the water-resisting capacity of the rock at the bottom of FJS is less than that of the rock at the top of FJS. In addition, in FJS, due to the self-healing effect of fractures in mudstone, the fractures in mudstone are easier to close than those in sandstone, so that the water-resisting capacity of mudstone at the same location is stronger than that of sandstone.The above analysis shows that the method of obtainingTE−FJS determined in this paper is practical, and the formula for calculating TE−FJS is as follows:
(34)TE−FJS=2.039Cm+1.301Cs.


### 4.4. Calculating theBWIC at Each Coordinate Point

Sincekm and ks are 2.039 and 1.301, respectively, Equation (29) can be transformed into:
(35)BWICxi,yi=Pbxi,yiTUxi,yi+2.039Cmxi,yi+1.301Csxi,yi,According to formula (35), the BWIC at each coordinate point in mining areas 108 and 106A can be obtained (Figure 14).Figure 14
Distribution ofBWIC in mining areas 106A and 108 in Shilawusu coal mine.


### 4.5. Obtaining the OverallBWIC Corresponding to Different Excavation Lengths

Based on the triangle stress arch theory, the overallBWIC corresponding to different excavation lengths can be obtained by using Equations (30) and (35) (Figure 15).Figure 15
OverallBWIC corresponding to different excavation lengths in mining areas 106A and 108 in Shilawusu coal mine.


### 4.6. Grading BWI Risk

Because BWI occurred in mining area 106A whenlx=554m, but no BWI occurred in the completed 1000 m mining process in mining area 108, the BWIClx corresponding to the excavation length of 554 m in mining area 106A was regarded as BWICld, and the maximum value of BWIClx in mining area 108 was used as BWICls. According to Figure 15, BWICld=0.024MPa/m, BWICls=0.015MPa/m, so BWIClt=0.020MPa/m. Therefore, Figure 12 can be improved to Figure 16.Figure 16
Discriminant diagram of BWI risk classification based onBWIC method.


## 4.1. Obtaining the BWI-Related Factors at Each Coordinate Point

The distribution of related factors in mining areas 106A and 108 in Shilawusu coal mine is shown in Figure13.Figure 13
Distribution of (a)Pb, (b) TU, (c) Cm, and (d) Cs in mining areas 106A and 108 in Shilawusu coal mine.
(a)(b)(c)(d)


## 4.2. Identifying the Weight of Each BWI-Related Factor

According to the analysis in Section3.2, the entropy weight method can be used to determine the weight of BWI-related factors, and the sampling points in mining areas 108 and 106A should be located in the range of the bed separation zone corresponding to the excavation length of 554 m. Based on the triangle stress arch theory, it can be determined that when the excavation length is 554 m, the sampling points in mining area 108 are A1-A9, and the sampling points in mining area 106A are B1-B9 (Figure 13). The values of BWI-related factors at each sampling point are shown in Table 1.Table 1
Values of BWI-related factors at each sampling point.
Sampling pointsPb (MPa)TU (m)CmCsA12.78119.77418.85818.997A22.761121.81819.12818.875A32.746123.42519.37818.767A42.768120.7518.82918.922A52.75122.75919.13518.805A62.737124.30419.41118.699A72.755121.84218.79918.839A82.739123.79119.14618.73A92.726125.24819.4518.628B13.01977.90820.41919.315B22.96382.76320.60718.905B32.89888.44820.7618.539B43.10268.00920.0819.796B53.01475.58320.28519.449B62.92583.20120.3919.213B73.19157.79219.72620.319B83.06568.57119.98320.001B92.9578.29920.07819.832By analyzing the data in Table1 according to Equations (9)–(13), the weight of each BWI-related factor can be obtained (Table 2).Table 2
Index weight of BWI-related factors.
BWI-related factorsPbTUCmCsIndex weight0.3540.3900.1580.098Because bed-separation water pressure is the power source of BWI,Pb has a large weight. As the integrity of UJS was not damaged, UJS plays an important role in preventing water inrush, so the weight of TU should be the largest. Because the integrity of the rock strata in FJS has been destroyed, the water-resisting capacity of FJS is still weaker than that of UJS, so the weight of Cm and Cs is less than that of TU. In addition, because the fracture closure degree of mudstone is relatively better than that of sandstone, the water-resisting capacity of mudstone in FJS is stronger than that of sandstone, so the weight of Cm is greater than that of Cs.The above analysis results are obtained by reasonable inference based on the actual engineering geological conditions, which are consistent with the results in Table2, indicating that the calculation results of the weights of BWI-related factors are in line with the reality.


## 4.3. Calculating the E-FJS Thickness (TE−FJS)

According to the weights of BWI-related factors in Table2, Equation (15) can be expressed as:
(31)Vi=2.186×10−4TUi+4.457×10−4Cmi+2.844×10−4Csi.It can be seen from Equation (31) that k1, k2, and k3 are 2.186×10−4, 4.457×10−4, and 2.844×10−4, respectively. Then, km and ks can also be calculated, which are 2.039 and 1.301, respectively, and Equations (22) and (25) can be expressed as follows:
(32)TE−M−FJS=2.039Cm,(33)TE−S−FJS=1.301Cs,Taking mining area 106A in Shilawusu coal mine as an example, whenM, RFM, and η are 10 m, 23, and 1.032, respectively, the TE−M−FJS of mudstone with a thickness of 1 m at different locations in FJS was calculated by using Equations (4) and (32) (Table 3), and the TE−S−FJS of sandstone with a thickness of 1 m at different locations in FJS was calculated by using Equations (6) and (33) (Table 4).Table 3
TE−M−FJS of mudstone at different locations in FJS.
Locationtm (m)Tm (m)cmTE−M−FJS (m)TE−M−FJS/tmTop of FJS12290.3740.76376.3%Bottom of FJS100.10.20420.4%Table 4
TE−S−FJS of sandstone at different locations in FJS.
Locationts (m)Ts (m)csTE−S−FJS (m)TE−S−FJS/tsTop of FJS12290.3740.48748.7%Bottom of FJS100.10.13013.0%Although the rock in FJS still have water-resisting capacity due to the closure of internal fractures, the restored water-resisting capacity is still weaker than that of the unfractured rock because the integrity of the fractured rock has been destroyed. This conclusion can also be obtained by analyzing the data in Table3 and Table 4. It can be seen from Table 3 and Table 4 that the water resistance capacity of mudstone and sandstone in FJS is weaker than that of intact rock. Due to the larger opening and weaker closure of the fractures, the water-resisting capacity of the rock at the bottom of FJS is less than that of the rock at the top of FJS. In addition, in FJS, due to the self-healing effect of fractures in mudstone, the fractures in mudstone are easier to close than those in sandstone, so that the water-resisting capacity of mudstone at the same location is stronger than that of sandstone.The above analysis shows that the method of obtainingTE−FJS determined in this paper is practical, and the formula for calculating TE−FJS is as follows:
(34)TE−FJS=2.039Cm+1.301Cs.


## 4.4. Calculating theBWIC at Each Coordinate Point

Sincekm and ks are 2.039 and 1.301, respectively, Equation (29) can be transformed into:
(35)BWICxi,yi=Pbxi,yiTUxi,yi+2.039Cmxi,yi+1.301Csxi,yi,According to formula (35), the BWIC at each coordinate point in mining areas 108 and 106A can be obtained (Figure 14).Figure 14
Distribution ofBWIC in mining areas 106A and 108 in Shilawusu coal mine.


## 4.5. Obtaining the OverallBWIC Corresponding to Different Excavation Lengths

Based on the triangle stress arch theory, the overallBWIC corresponding to different excavation lengths can be obtained by using Equations (30) and (35) (Figure 15).Figure 15
OverallBWIC corresponding to different excavation lengths in mining areas 106A and 108 in Shilawusu coal mine.


## 4.6. Grading BWI Risk

Because BWI occurred in mining area 106A whenlx=554m, but no BWI occurred in the completed 1000 m mining process in mining area 108, the BWIClx corresponding to the excavation length of 554 m in mining area 106A was regarded as BWICld, and the maximum value of BWIClx in mining area 108 was used as BWICls. According to Figure 15, BWICld=0.024MPa/m, BWICls=0.015MPa/m, so BWIClt=0.020MPa/m. Therefore, Figure 12 can be improved to Figure 16.Figure 16
Discriminant diagram of BWI risk classification based onBWIC method.


## 5. Application and Validation

### 5.1. Shilawusu Coal Mine

According to formula (35), the BWIC at each coordinate point in mining areas 201 and 201A in Shilawusu coal mine can be obtained (Figure 17). Based on the triangle stress arch theory, the overall BWIC corresponding to different excavation lengths can be obtained by using Equations (30) and (35) (Figure 18). It can be seen from Figure 18 that the BWI risk in mining areas 201 and 201A during mining belongs to the “safety zone.” In fact, the mining in mining areas 201 and 201A has been completed, and no BWI occurred during mining, which verifies the accuracy of the evaluation results shown in Figure 18.Figure 17
Distribution ofBWIC in mining areas 201A and 201 in Shilawusu coal mine.Figure 18
OverallBWIC corresponding to different excavation lengths in (a) mining area 201 and (b) mining area 201A in Shilawusu coal mine.
(a)(b)


### 5.2. Yingpanhao Coal Mine

According to formula (35), the BWIC at each coordinate point in mining areas 2202 and 2201 in Yingpanhao coal mine can be obtained (Figure 19). Based on the triangle stress arch theory, the overall BWIC corresponding to different excavation lengths can be obtained by using Equations (30) and (35) (Figure 20). It can be seen from Figure 20 that the BWI risk in mining areas 2202 and 2201 during mining belongs to the “relatively safe zone.” In fact, mining has been completed in mining area 2201, and 1000 m excavation has been completed in mining area 2202. No BWI occurred during mining in these two mining areas, which verifies the accuracy of the assessment results shown in Figure 20.Figure 19
Distribution ofBWIC in mining areas 2202 and 2201 in Yingpanhao coal mine.Figure 20
OverallBWIC corresponding to different excavation lengths in (a) mining area 2202 and (b) mining area 2201 in Yingpanhao coal mine.
(a)(b)


### 5.3. Cuimu Coal Mine

According to formula (35), the BWIC at each coordinate point in mining areas 21301 and 21302 in Cuimu coal mine can be obtained (Figure 21). Based on the triangle stress arch theory, the overall BWIC corresponding to different excavation lengths can be obtained by using Equations (30) and (35) (Figure 22). It can be seen from Figure 22 that the BWI risk in mining areas 21301 and 21302 during mining belongs to the “danger zone.” In fact, the mining in mining areas 21301 and 21302 has been completed, and BWIs occurred during mining (Figure 23), which verifies the accuracy of the evaluation results shown in Figure 22.Figure 21
Distribution ofBWIC in mining areas 21301 and 21302 in Cuimu coal mine.Figure 22
OverallBWIC corresponding to different excavation lengths in (a) mining area 21301 and (b) mining area 21302 in Cuimu coal mine.
(a)(b)Figure 23
Water inflow in (a) mining area 21301 and (b) mining area 21302 in Cuimu coal mine.
(a)(b)


## 5.1. Shilawusu Coal Mine

According to formula (35), the BWIC at each coordinate point in mining areas 201 and 201A in Shilawusu coal mine can be obtained (Figure 17). Based on the triangle stress arch theory, the overall BWIC corresponding to different excavation lengths can be obtained by using Equations (30) and (35) (Figure 18). It can be seen from Figure 18 that the BWI risk in mining areas 201 and 201A during mining belongs to the “safety zone.” In fact, the mining in mining areas 201 and 201A has been completed, and no BWI occurred during mining, which verifies the accuracy of the evaluation results shown in Figure 18.Figure 17
Distribution ofBWIC in mining areas 201A and 201 in Shilawusu coal mine.Figure 18
OverallBWIC corresponding to different excavation lengths in (a) mining area 201 and (b) mining area 201A in Shilawusu coal mine.
(a)(b)


## 5.2. Yingpanhao Coal Mine

According to formula (35), the BWIC at each coordinate point in mining areas 2202 and 2201 in Yingpanhao coal mine can be obtained (Figure 19). Based on the triangle stress arch theory, the overall BWIC corresponding to different excavation lengths can be obtained by using Equations (30) and (35) (Figure 20). It can be seen from Figure 20 that the BWI risk in mining areas 2202 and 2201 during mining belongs to the “relatively safe zone.” In fact, mining has been completed in mining area 2201, and 1000 m excavation has been completed in mining area 2202. No BWI occurred during mining in these two mining areas, which verifies the accuracy of the assessment results shown in Figure 20.Figure 19
Distribution ofBWIC in mining areas 2202 and 2201 in Yingpanhao coal mine.Figure 20
OverallBWIC corresponding to different excavation lengths in (a) mining area 2202 and (b) mining area 2201 in Yingpanhao coal mine.
(a)(b)


## 5.3. Cuimu Coal Mine

According to formula (35), the BWIC at each coordinate point in mining areas 21301 and 21302 in Cuimu coal mine can be obtained (Figure 21). Based on the triangle stress arch theory, the overall BWIC corresponding to different excavation lengths can be obtained by using Equations (30) and (35) (Figure 22). It can be seen from Figure 22 that the BWI risk in mining areas 21301 and 21302 during mining belongs to the “danger zone.” In fact, the mining in mining areas 21301 and 21302 has been completed, and BWIs occurred during mining (Figure 23), which verifies the accuracy of the evaluation results shown in Figure 22.Figure 21
Distribution ofBWIC in mining areas 21301 and 21302 in Cuimu coal mine.Figure 22
OverallBWIC corresponding to different excavation lengths in (a) mining area 21301 and (b) mining area 21302 in Cuimu coal mine.
(a)(b)Figure 23
Water inflow in (a) mining area 21301 and (b) mining area 21302 in Cuimu coal mine.
(a)(b)


## 6. Conclusions

The objects directly involved in BWI process include the Cretaceous bed-separation water and the Jurassic protective layer. The bed-separation water pressure (Pb) provides the inducing power for the occurrence of BWI and can be expressed by the water pressure in the aquifer at the bottom of Cretaceous. In the Jurassic protective layer, the upper part is the unbroken Jurassic strata (UJS), and the lower part is the fractured Jurassic strata (FJS). The water-resisting capacity of FJS is due to the closure of fractures in FJS under the action of water flow.The greater the UJS thickness (TU) is, the stronger its water-resisting capacity is. In FJS, the closure potential of mudstone fractures (Cm) was used to evaluate the closure effect of mudstone fractures, and the closure potential of sandstone fractures (Cs) was used to evaluate the closure effect of sandstone fractures. Cm is positively correlated with the mudstone thickness and negatively correlated with the height of available subsidence space of mudstone before mudstone fracture. Cs is positively correlated with the sandstone thickness, and negatively correlated with the height of available subsidence space of sandstone before sandstone fracture. UJS with a certain thickness and the same water-resisting capacity as mudstone in FJS was called equivalent strata of mudstone in FJS (E-M-FJS). UJS with a certain thickness and the same water-resisting capacity as sandstone in FJS was called equivalent strata of sandstone in FJS (E-S-FJS). By comparing the weight of each BWI-related factor, the formulas for calculating the E-M-FJS thickness (TE−M−FJS) and the E-S-FJS thickness (TE−S−FJS) were derived. And the TE−M−FJS corresponding to one unit of Cm is 2.039 m, while the TE−S−FJS corresponding to one unit of Cs is 1.301 m. The weight of each BWI-related factor was obtained by entropy weight method. And the weights of Pb, TU, Cm, and Cs are 0.354, 0.390, 0.158, and 0.098, respectively.In bed-separation water inrush (BWI) risk assessment, the existing multifactor-weighted superposition method cannot provide a universal risk classification standard, and the existing water inrush coefficient method ignores the water separation capacity of FJS, so there is still a lack of scientific BWI risk assessment method. In this paper, three coal mines in Ordos Basin were taken as research cases, and a bed-separation water inrush coefficient (BWIC) method for BWI risk assessment was established. The value of BWIC is the ratio of Pb to the sum of TU, TE−M−FJS and TE−S−FJS. Based on the stress arch theory, the overall BWIC in bed separation zone corresponding to different excavation lengths (BWIClx) was obtained. By comparing the value range of BWIClx with and without BWI, the standard of BWI risk classification was determined. In the BWI risk classification discrimination diagram established based on BWIC method, the area with 0MPa/m<BWIClx≤0.015MPa/m was divided into safety zone, the area with 0.015MPa/m<BWIClx≤0.02MPa/m was divided into relatively safe zone, the area with 0.02MPa/m<BWIClx≤0.024MPa/m was divided into relatively dangerous zone, and the area with BWIClx>0.024MPa/m was divided into danger zone. The application results verified the scientificity of BWIC method and the universality of the BWI risk classification standard proposed in this paper.



---

*Source: 8978653-2022-03-25.xml*