# Field Measurement and Mechanical Analysis of Height of the Water Flowing Fracture Zone in Short-Wall Block Backfill Mining beneath the Aquifer: A Case Study in China

Authors: Yun Zhang; Shenggen Cao; Tong Wan; Jijun Wang
Journal: Geofluids
 (2018)

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## Abstract

Short-wall block filling mining (SBBM) technology has become an effective way to recover coal resources beneath the aquifer, which are unsuitable, or cannot be used by long-wall mining, such as corner coal pillars, industrial square pillars, and irregular coal blocks as well as the coal beneath buildings, railways, and water bodies. The SBBM method can not only enhance the recovery ratio but also provide a solution for the environment problems associated with gangues on the surface. However, whether the height of water flowing fractures will reach to the aquifer to cause water loss during SBBM has always been a key problem. Therefore, based on the theory of elastic foundation beam and SBBM characteristics, a mechanical model for calculating the height of a water flowing fracture zone in the overlying strata of SBBM was established, and this model calculated that the height of the water flowing fracture zone was 27.0 m in the experimental working face, and the height of the water flowing fracture zone was measured as 26.8 m according to washing fluid loss in the hole, core damage analysis, and drilling TV imaging detection. The comparison results demonstrated that the calculated value almost fit well with the field-measured data, validating the accuracy of the proposed mechanical model, while the predicted value (48.7 m) in theRegulations of coal mining under building, railways and water-bodies deviates greatly from the measured results. This reveals that the prediction formula in Regulations is not effective in predicting the height of the water flowing fracture zone in SBBM. The present research results are of great significance to further enhancing the recovery ratio of coal resources and improving the water-preserved mining theory.


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## Body

## 1. Introduction

During the coal mining process, overlying strata experience significant mining-induced movements and deformation, inevitably causing the collapse and fracturing of strata and forming a lot of fractures [1–3]. Many water flowing channels, also referred to as water flowing fracture zone, are formed once these fractures are interconnected. As shown in Figure 1, when this water flowing fracture zone develops towards the aquifer or water-rich regions on the surface, serious water loss can be triggered, thereby leading to the deficiency of water resources and further inducing a series of environmental problems such as land desertification, sparse ground vegetation, and dry-up of streams [4–6]. Meanwhile, because of large-scale mining for a long time and some deployment patterns during mining in long-wall faces, massive gangues are discharged and heaped up after the mining [7–10] (Figure 1), bringing severe challenges on the mine’s ecological environment and results in the waste of vast residue coal resources such as a lot of corner coal pillars and irregular blocks [11, 12]. Destruction of the environment and waste of coal resources are facing serious problems that threaten the government’s strategy of sustainable development. To address these problems, an effective environmentally friendly mining method, namely, short-wall block backfill mining (SBBM) method, was proposed in this study. This strategy not only enhanced the recovery ratio of coal mines and reduced gangue discharge but also avoided further mining-induced water loss.Figure 1
Coal-mining-induced severe environmental problems. (a) Land desertification; (b) dry-up of streams; (c) sparse ground vegetation; (d) development of fractures towards the ground; (e) stacking of gangues.
(a)
(b)
(c)
(d)
(e)Currently, a great deal of research has been carried out on the protection of underground and ground water resource. Sun and Miao [13] and Miao et al. [14] put forward the concept and the principle of water-resisting key strata and systemically analyzed the basic mechanical properties of water-resisting key strata and the distribution of interconnected fractures. Xu et al. [15–17] investigated the effect of key strata on the development height of the water flowing fracture zone in depth and proposed a new method for predicting the height of the water flowing fracture zone based on the position of key strata. Some scholars also extensively examined the block caving mining method. Based on the research results of the roof movement, Zhou [18, 19] systematically analyzed the strata behavior regularity in block caving mining. Cao et al. [20] examined the mechanism of the instability of protective coal pillars in the block caving mining process based on the theory of cusp catastrophe. However, related theories regarding the development rules of the water flowing fracture zone during SBBM have been poorly investigated to date and need further exploration. At present, the height of the water flowing fracture zone in the mining process is also calculated according to the empirical formula in Regulations of coal mining under building, railways and water-bodies [21] (hereinafter referred to as the Regulations). In consideration of the particularity of the arrangement of working faces in the SBBM and the filling of gangue in the gob, whether the empirical formula in the Regulations is still valid in SBBM process needs further investigation.Based on the SBBM technological characteristics, a new mechanical analysis method was established for calculating the height of the water flowing fracture zone in the overlying strata during the SBBM process, and the related mechanical properties of the development rules of the water flowing fracture zone were analyzed. Furthermore, the applicability of theRegulations was further judged. The present research results are of important significance to enhancing the recovery ratio of coal resources and protecting ecological environment.


## 2. Engineering Geological Conditions and Field Measurement Results

### 2.1. Engineering Geological Conditions

The Shaanbei coal mine is located in Yulin City, Shaanxi Province, China. The area of the mine field is 1.52 km2, and the recoverable coal reserve is 4.98 million tons. The surface of the mine field is covered by driftsands. The region of the mine belongs to arid and semi-arid areas with deficient water resource, sparse vegetation, and serious water loss, featured by typical semi-acrid and semi-desert continental climate. Moreover, the burial depth of coal seams is generally within 112.8–184.5 m, which belongs to the shallow buried coal seam. The geological structure is simple and the coal quality is good, and long-wall mining is the main practiced method in the mine. The SBBM experimental region was to the north of the no. 10304 long-wall working face, with a mining length of about 150 m and a total experimental area of 19,500 m2. It is estimated that about 13,000 tons of coal in total can be recovered. The coal seam exhibits simple storage structures with slightly varying thicknesses and can be regarded as a nearly flat coal seam. The average thickness and burial depth of the coal seam are 5 m and 145 m, respectively. A layer of the aquifer can be observed on the mining coal seam, with an average distance of 105 m away from the coal seam. This aquifer serves as the main potentially protected water resource for the mine. The top of the coal seam mainly consists of mudstone, fine sandstone, siltstone, sandy mudstone, fine sandstone, medium sandstone, siltstone, red clay, and driftsand from the bottom up. The aquifer is above the red clay layer. Figure 2 displays the detailed columnar illustration as well as physical and mechanical parameters of the coal seam.Figure 2
Columnar illustration and physical/mechanical properties of the coal seam.In combination with the occurrence of corner coal pillars, the experimented region can be divided into two blocks for mining. The advancing length of each block was 72.5 m, with a mining height of 5 m; in addition, the protective coal pillar between the blocks was about 5 m in length, and the backfilling ratio of gangues in the gob was about 80%. Figure3 shows the geographic position of the mine and the related detailed arrangement in the SBMM working face.Figure 3
Geographic position of the mine and the detailed arrangement in the SBMM working face. (a) Geographical position of the mine; (b) detailed arrangement in the SBMM working face.


### 2.2. Field Measurement

#### 2.2.1. Test Method

During the field of the SBBM process, the height of the water flowing fracture zone was comprehensively determined by observation of washing fluid loss in the hole, core damage degree analysis, and drilling TV imaging detection. After mining and backfilling in the working face, an observation hole, denoted as hole F, was arranged on top of the working face to measure the height of the water flowing fracture zone. The detailed arrangement of the hole is shown in Figures3 and 4. Hole F was located at the center of the upper part of the mining region, 75 m away from the starting cut and 145 m in depth. The final level of the hole was in direct touch with the immediate roof. During the drilling process, the loss of the washing fluid, the core damage degree, and the development of fractures in the strata were used to comprehensively predict the height of the water flowing fracture zone.Figure 4
Illustration of the positions of the aquifer and the observation hole.


#### 2.2.2. Test Results

Figure5 shows the variation in the loss of washing fluid in hole F, and Figure 6 displays the distribution of fractures in the strata in accordance with the drilling TV imaging results. At a drilling depth of 118.2 m, the loss of washing fluid increased slightly from 0.28 m3/h to 2.12 m3/h; meanwhile, the development width of fractures in the drilling was small, and no obvious cracks were observed, suggesting a complete lithology. Figure 6(a) shows the drilling TV image of the hole at a depth of 113.0 m, indicating that the strata exhibited morphological integrity and no fractures. With increasing drilling depth, the loss of the washing fluid increased rapidly to 5.47 m3/h; i.e., the loss of washing fluid varied significantly. According to the core observation results, the recovery ratio of core was <50%, and a lot of narrow fractures with different directions were developed in the core. Figure 6(b) shows the boundary at the top of the water flowing fracture zone. It can be observed that a vertical fracture began to appear at a depth of 118.2 m. With increasing drilling depth, the loss of washing fluid in the hole varied slightly. Meanwhile, as shown in Figure 6(c), both the density of the vertical fractures and the damage range increased with increasing drilling depth. Therefore, it can be concluded that the development peak of the water flowing fracture zone was located at a depth of about 118.2 m, and the height of the water flowing fracture zone was 26.8 m.Figure 5
Relationship between the loss of washing fluid in the hole and the drilling depth.Figure 6
Drilling TV imaging detection results of the distribution of fractures in the strata. (a) No fracture; (b) first vertical fracture; (c) fractured zone.
(a)
(b)
(c)


## 2.1. Engineering Geological Conditions

The Shaanbei coal mine is located in Yulin City, Shaanxi Province, China. The area of the mine field is 1.52 km2, and the recoverable coal reserve is 4.98 million tons. The surface of the mine field is covered by driftsands. The region of the mine belongs to arid and semi-arid areas with deficient water resource, sparse vegetation, and serious water loss, featured by typical semi-acrid and semi-desert continental climate. Moreover, the burial depth of coal seams is generally within 112.8–184.5 m, which belongs to the shallow buried coal seam. The geological structure is simple and the coal quality is good, and long-wall mining is the main practiced method in the mine. The SBBM experimental region was to the north of the no. 10304 long-wall working face, with a mining length of about 150 m and a total experimental area of 19,500 m2. It is estimated that about 13,000 tons of coal in total can be recovered. The coal seam exhibits simple storage structures with slightly varying thicknesses and can be regarded as a nearly flat coal seam. The average thickness and burial depth of the coal seam are 5 m and 145 m, respectively. A layer of the aquifer can be observed on the mining coal seam, with an average distance of 105 m away from the coal seam. This aquifer serves as the main potentially protected water resource for the mine. The top of the coal seam mainly consists of mudstone, fine sandstone, siltstone, sandy mudstone, fine sandstone, medium sandstone, siltstone, red clay, and driftsand from the bottom up. The aquifer is above the red clay layer. Figure 2 displays the detailed columnar illustration as well as physical and mechanical parameters of the coal seam.Figure 2
Columnar illustration and physical/mechanical properties of the coal seam.In combination with the occurrence of corner coal pillars, the experimented region can be divided into two blocks for mining. The advancing length of each block was 72.5 m, with a mining height of 5 m; in addition, the protective coal pillar between the blocks was about 5 m in length, and the backfilling ratio of gangues in the gob was about 80%. Figure3 shows the geographic position of the mine and the related detailed arrangement in the SBMM working face.Figure 3
Geographic position of the mine and the detailed arrangement in the SBMM working face. (a) Geographical position of the mine; (b) detailed arrangement in the SBMM working face.


## 2.2. Field Measurement

### 2.2.1. Test Method

During the field of the SBBM process, the height of the water flowing fracture zone was comprehensively determined by observation of washing fluid loss in the hole, core damage degree analysis, and drilling TV imaging detection. After mining and backfilling in the working face, an observation hole, denoted as hole F, was arranged on top of the working face to measure the height of the water flowing fracture zone. The detailed arrangement of the hole is shown in Figures3 and 4. Hole F was located at the center of the upper part of the mining region, 75 m away from the starting cut and 145 m in depth. The final level of the hole was in direct touch with the immediate roof. During the drilling process, the loss of the washing fluid, the core damage degree, and the development of fractures in the strata were used to comprehensively predict the height of the water flowing fracture zone.Figure 4
Illustration of the positions of the aquifer and the observation hole.


### 2.2.2. Test Results

Figure5 shows the variation in the loss of washing fluid in hole F, and Figure 6 displays the distribution of fractures in the strata in accordance with the drilling TV imaging results. At a drilling depth of 118.2 m, the loss of washing fluid increased slightly from 0.28 m3/h to 2.12 m3/h; meanwhile, the development width of fractures in the drilling was small, and no obvious cracks were observed, suggesting a complete lithology. Figure 6(a) shows the drilling TV image of the hole at a depth of 113.0 m, indicating that the strata exhibited morphological integrity and no fractures. With increasing drilling depth, the loss of the washing fluid increased rapidly to 5.47 m3/h; i.e., the loss of washing fluid varied significantly. According to the core observation results, the recovery ratio of core was <50%, and a lot of narrow fractures with different directions were developed in the core. Figure 6(b) shows the boundary at the top of the water flowing fracture zone. It can be observed that a vertical fracture began to appear at a depth of 118.2 m. With increasing drilling depth, the loss of washing fluid in the hole varied slightly. Meanwhile, as shown in Figure 6(c), both the density of the vertical fractures and the damage range increased with increasing drilling depth. Therefore, it can be concluded that the development peak of the water flowing fracture zone was located at a depth of about 118.2 m, and the height of the water flowing fracture zone was 26.8 m.Figure 5
Relationship between the loss of washing fluid in the hole and the drilling depth.Figure 6
Drilling TV imaging detection results of the distribution of fractures in the strata. (a) No fracture; (b) first vertical fracture; (c) fractured zone.
(a)
(b)
(c)


## 2.2.1. Test Method

During the field of the SBBM process, the height of the water flowing fracture zone was comprehensively determined by observation of washing fluid loss in the hole, core damage degree analysis, and drilling TV imaging detection. After mining and backfilling in the working face, an observation hole, denoted as hole F, was arranged on top of the working face to measure the height of the water flowing fracture zone. The detailed arrangement of the hole is shown in Figures3 and 4. Hole F was located at the center of the upper part of the mining region, 75 m away from the starting cut and 145 m in depth. The final level of the hole was in direct touch with the immediate roof. During the drilling process, the loss of the washing fluid, the core damage degree, and the development of fractures in the strata were used to comprehensively predict the height of the water flowing fracture zone.Figure 4
Illustration of the positions of the aquifer and the observation hole.


## 2.2.2. Test Results

Figure5 shows the variation in the loss of washing fluid in hole F, and Figure 6 displays the distribution of fractures in the strata in accordance with the drilling TV imaging results. At a drilling depth of 118.2 m, the loss of washing fluid increased slightly from 0.28 m3/h to 2.12 m3/h; meanwhile, the development width of fractures in the drilling was small, and no obvious cracks were observed, suggesting a complete lithology. Figure 6(a) shows the drilling TV image of the hole at a depth of 113.0 m, indicating that the strata exhibited morphological integrity and no fractures. With increasing drilling depth, the loss of the washing fluid increased rapidly to 5.47 m3/h; i.e., the loss of washing fluid varied significantly. According to the core observation results, the recovery ratio of core was <50%, and a lot of narrow fractures with different directions were developed in the core. Figure 6(b) shows the boundary at the top of the water flowing fracture zone. It can be observed that a vertical fracture began to appear at a depth of 118.2 m. With increasing drilling depth, the loss of washing fluid in the hole varied slightly. Meanwhile, as shown in Figure 6(c), both the density of the vertical fractures and the damage range increased with increasing drilling depth. Therefore, it can be concluded that the development peak of the water flowing fracture zone was located at a depth of about 118.2 m, and the height of the water flowing fracture zone was 26.8 m.Figure 5
Relationship between the loss of washing fluid in the hole and the drilling depth.Figure 6
Drilling TV imaging detection results of the distribution of fractures in the strata. (a) No fracture; (b) first vertical fracture; (c) fractured zone.
(a)
(b)
(c)


## 3. Short-Wall Block Backfill Mining (SBBM) Technique

### 3.1. Coal Mining Method

The SBBM technique is mainly used for recycling corner coal pillars, industrial square pillars, and irregular coal blocks as well as the coal beneath buildings, railways, and water bodies, all of which are unsuitable or cannot be exploited by long-wall mining. The SBBM technique also exhibits a lot of advantages such as less investment, short operating period, and quick returns. Particularly, a set of short-wall mining equipment is only 20% of a set of long-wall mining fully mechanized mining equipment in terms of cost. To be specific, based on the block caving mining technology, the gangues are filled in the gob as the backfill body after the mining of a block, and the next block is simultaneously mined. Accordingly, both the temporal continuity and spatial independence of mining and backfilling during the whole operating process can be ensured; i.e., SBBM can be regarded as a high-efficiency backfilling mining method characterized by mining/backfilling concurrence. The SBBM technique can greatly enhance the recovery ratio of the mine and prolong the mine’s service life. Meanwhile, the filling of gangues that are piled up on the surface in the gob can reduce the damages to the environment and the enterprise’s investment in environmental protection.Figure7 displays the structure of a typical SBBM system. Apparently, the system mainly consists of two subsystems, namely, gangue transportation system and coal transportation system. In the former transportation system, the transportation route of gangues is from the vertical feeding system, storage silo, main track roadway, auxiliary transportation roadway of SBBM, to the SBBM working face; in the latter transportation system, the coal in the working face is first transported to the haulage roadway of SBBM, then to the main haulage roadway and the main shaft, and finally to the ground surface.Figure 7
Illustration of the short-wall block backfill mining (SBBM) system.


### 3.2. Arrangement in the Working Face and Key Equipment

In the SBBM working face, four branch roadways were arranged for constituting a mining block, and the protective pillar was set between the two blocks. In each block, the pillars were extracted in retreat from top to bottom. During the recovery of coal pillars, the temporal coal pillar, with a width in the range 0.5–1.5 m, was arranged between the wings. The length of the wing was no greater than 11 m, and the width was about 3 m. The intersection angle between the wing and the branch roadway was about 45°. After the recovery of a block, the gangues were filled into the wing, the branch roadway, and the joint roadway from top to bottom. The temporal coal pillars and the fire dams can act as a barrier to ensure that the filling ratio satisfies the design requirements.SBBM technology mainly includes mining and backfilling. With regard to the mining technology, four track walking hydraulic supports were used and cooperated with the coal cutter for ensuring the safety in the coal cutting and loading. In more detail, four track walking hydraulic supports were divided into two sets: one set (the first two supports) was arranged in the branch roadway, and the other set (the latter two supports) was arranged in the joint roadway between the two adjacent branch roadways. Both the branch roadway and the joint roadway were about 5 m in width. With regard to the backfilling technology, two track walking hydraulic supports were arranged in the branch roadway; in cooperation with the waste throwing machine and the pushdozer, the gangues were filled in the gob and were in full contact with the roof. Accordingly, the gangues can serve as the permanent carrier and cooperated with the protective coal pillars between the blocks for supporting the overlying strata. Figure8 displays the detailed arrangement of the SBBM working face.Figure 8
Arrangement in the SBBM working face and key equipment.


## 3.1. Coal Mining Method

The SBBM technique is mainly used for recycling corner coal pillars, industrial square pillars, and irregular coal blocks as well as the coal beneath buildings, railways, and water bodies, all of which are unsuitable or cannot be exploited by long-wall mining. The SBBM technique also exhibits a lot of advantages such as less investment, short operating period, and quick returns. Particularly, a set of short-wall mining equipment is only 20% of a set of long-wall mining fully mechanized mining equipment in terms of cost. To be specific, based on the block caving mining technology, the gangues are filled in the gob as the backfill body after the mining of a block, and the next block is simultaneously mined. Accordingly, both the temporal continuity and spatial independence of mining and backfilling during the whole operating process can be ensured; i.e., SBBM can be regarded as a high-efficiency backfilling mining method characterized by mining/backfilling concurrence. The SBBM technique can greatly enhance the recovery ratio of the mine and prolong the mine’s service life. Meanwhile, the filling of gangues that are piled up on the surface in the gob can reduce the damages to the environment and the enterprise’s investment in environmental protection.Figure7 displays the structure of a typical SBBM system. Apparently, the system mainly consists of two subsystems, namely, gangue transportation system and coal transportation system. In the former transportation system, the transportation route of gangues is from the vertical feeding system, storage silo, main track roadway, auxiliary transportation roadway of SBBM, to the SBBM working face; in the latter transportation system, the coal in the working face is first transported to the haulage roadway of SBBM, then to the main haulage roadway and the main shaft, and finally to the ground surface.Figure 7
Illustration of the short-wall block backfill mining (SBBM) system.


## 3.2. Arrangement in the Working Face and Key Equipment

In the SBBM working face, four branch roadways were arranged for constituting a mining block, and the protective pillar was set between the two blocks. In each block, the pillars were extracted in retreat from top to bottom. During the recovery of coal pillars, the temporal coal pillar, with a width in the range 0.5–1.5 m, was arranged between the wings. The length of the wing was no greater than 11 m, and the width was about 3 m. The intersection angle between the wing and the branch roadway was about 45°. After the recovery of a block, the gangues were filled into the wing, the branch roadway, and the joint roadway from top to bottom. The temporal coal pillars and the fire dams can act as a barrier to ensure that the filling ratio satisfies the design requirements.SBBM technology mainly includes mining and backfilling. With regard to the mining technology, four track walking hydraulic supports were used and cooperated with the coal cutter for ensuring the safety in the coal cutting and loading. In more detail, four track walking hydraulic supports were divided into two sets: one set (the first two supports) was arranged in the branch roadway, and the other set (the latter two supports) was arranged in the joint roadway between the two adjacent branch roadways. Both the branch roadway and the joint roadway were about 5 m in width. With regard to the backfilling technology, two track walking hydraulic supports were arranged in the branch roadway; in cooperation with the waste throwing machine and the pushdozer, the gangues were filled in the gob and were in full contact with the roof. Accordingly, the gangues can serve as the permanent carrier and cooperated with the protective coal pillars between the blocks for supporting the overlying strata. Figure8 displays the detailed arrangement of the SBBM working face.Figure 8
Arrangement in the SBBM working face and key equipment.


## 4. Mechanical Analysis of the Height of the Water Flowing Fracture Zone in SBBM

According to SBBM technological characteristics, this study calculated the damage height of the overlying strata in the working face after mining and backfilling to determine the height of the water flowing fracture zone in the final overlying strata formed in the SBBM. As shown in Figure9, a stratum above the coal seam (i.e., the mth stratum) was used as the object, and the overlying strata was simplified as the uniformly distributed load qm; meanwhile, in the lower strata that supported the rock beam, coal bodies (including both protective coal pillars and entity coal) and the backfill body were simplified as the Winkler elastic foundation. This study also assumed that la denotes the length of each block (i.e., the length of the gob), lb denotes the width of the protective coal pillar between the blocks, hk denotes the mining height of the coal seam, h1,h2,h3,…, hj denote the thicknesses of various strata above the coal seam (total thickness of m layers of strata above the coal rock and thus can be written as Hm=∑hmm=1,2,3,…,j), ka denotes the coal’s elastic foundation coefficient, kb denotes the backfill body’s elastic foundation coefficient, and k1,k2,… km−1 denote the elastic foundation coefficients of various strata beneath the mth stratum. Accordingly, the mechanical model of the overlying strata in the SBBM process based on elastic foundation beam was established.Figure 9
Basic environment state for mechanical analysis of SBBM stope.The elastic foundation coefficients of the backfill body, the coal seam, andm−1 strata above the bedrock can be written as
(1)1kam=1ka+1k1+1k2⋯+1km−2+1km−1,Thecombinationofcoalandstrata1kbm=1kb+1k1+1k2⋯+1km−2+1km−1,Thecombinationofbackfillingbodiesandstrata.As shown in Figure9, the model under that state exhibits a positively symmetrical structure. Therefore, to simplify the calculation, half of the model was selected for further analysis. Because of the difference in the number of blocks (denoted as n), the calculations were performed in the following two cases: (1) n is an even number and (2) n is an odd number.


### 4.1. Mechanical Model of the SBBM Working Face Whenn Is an Even Number

Whenn is an even number, the center of the protective pillar in the n/2th block was set as the symmetry point, and the origin, denoted as O, was set at the junction between the protective coal pillar and the n/2th block; then, the mechanical coordinate system was established by using the displacement function wmx as the unknown quantity, as shown in Figure 10.Figure 10
Established mechanical model of themth stratum when n is an even number.According to Winkle’s assumption for elastic foundations [22–24], the settlement amount of any point on the foundation surface is proportional to the pressure on the point per unit area. Actually, the foundation is simulated as a series of independent springs on the rigid foundation; next, when the pressure (p) is applied on any point on the foundation surface, only the point sank by wx because of the independence of the springs, while no sedimentation was observed at the other points. The following expression can be derived:
(2)p=kwx,where p denotes the pressure on the foundation per unit area, wx denotes the subsidence of the foundation, and k denotes the elastic foundation coefficient.Based on the elastic foundation beam theory, the deflection of the rock beam, denoted aswx, and the applied load, denoted as q, satisfy the following differential equation of the deflection curve of the foundation beam:
(3)EId4wxdx4+p=q,where EI denotes the flexural rigidity of the cross section of the rock beam.Therefore, by assuming the prearranged protective coal pillars in the SBBM working face, the backfill body and (m−1) bed rock as independent springs, and the entity coal in the right part as semi-infinite elastic foundation, the mth rock beam can be treated as a semi-infinite long beam. By substituting (2) into (3), the deflection curve equations of the mth rock beam above the coal and the backfill body can be written as
(4)d4w1mxdx4+kamw1mxEmIm=qmEmIm,−lb2≤x≤0d4w2mxdx4+kbmw2mxEmIm=qmEmIm,0≤x≤lad4w3mxdx4+kamw3mxEmIm=qmEmIm,la≤x≤la+lb…d4wnmxdx4+kbmwnmxEmIm=qmEmIm,n−22la+n−12lb≤x≤n2la+n−12lbd4wn+1mxdx4+kamwn+1mxEmIm=qmEmIm,x>n2la+n−12lbwhere EmIm denotes the flexural rigidity of the cross section of the mth rock beam.By setting the characteristic coefficientsα=kae/4EmIm4 and β=kbe/4EmIm4 and solving (4), the deflection curve equations of the mth rock beam can be written as
(5)wmx=w1mx=eαxa1cosαx+b1sinαx+e−αxc1cosαx+d1sinαx+qmkam−lb2≤x≤0w2mx=eβxa2cosβx+b2sinβx+e−βxc2cosβx+d2sinβx+qmkbm0≤x≤law3mx=eαxa3cosαx+b3sinαx+e−αxc3cosαx+d3sinαx+qmkamla≤x≤la+lb…wnmx=eβxancosβx+bnsinβx+e−βxcncosβx+dnsinβx+qmkbmn−22la+n−12lb≤x≤n2la+n−12lbwn+1mx=eαxan+1cosαx+bn+1sinαx+e−αxcn+1cosαx+dn+1sinαx+qmkamx>n2la+n−12lb.The rotation angle, bending moment, and shearing force of any cross section in themth rock beam can be written as
(6)θmx=dwmxdxMmx=−EmImdθmxdx=−EId2wmxdx2Qmx=dMmxdx=−EId3wmxdx3.The elastic foundation coefficient of the backfill body and the backfill ratio satisfy the following expression [25]:
(7)kc=σ0hk1−φ,where σ0 and φ denote the stress of the primary rock and the backfill ratio (0<φ<1), respectively.Because of the symmetrical model structure and load, the deflection curve and the bending-moment curve of the rock beam are symmetrical, and the rotation-angle curve and the shearing-force curve are anti-symmetrical; accordingly, the rotation angle and shearing force at the symmetrical point equaled to 0. Furthermore, according to the qualitative analysis results of the semi-infinite long beam as shown in Figure10, when x→+∞, then w→0 and θ→0. Based on the above analysis, the boundary conditions of the beam can be described as
(8)θ1m−lb2=0,Q1m−lb2=0θnm+∞=0,wnm+∞=0.The continuity condition can then be described as follows. The deflection, bending moment, rotation angle, and shearing force at the connection point among the protective coal pillar, the gob, and the entity coal equaled to each other.By substituting the boundary conditions and continuity condition into (5), a1,b1,c1,d1,a2,b2,c2,d2,…,an+1,bn+1,cn+1, and dn+1 can be solved; i.e., with these parameters, the bending subsidence equation and the bending-moment equation of the mth rock beam, denoted as wmx and Mmx, respectively, can be solved.


### 4.2. Mechanical Model of the SBBM Working Face Whenn Is an Odd Number

Figure11 displays the established mechanical model of the mth stratum, when n is an odd number. The center of the n+1/2th block was selected as the symmetry point, and the junction between the n+1/2th block and the protective coal pillar was set as the origin (O). Next, the mechanical calculation model of the mth stratum was established by using the displacement function wmx as the unknown quantity.Figure 11
Established mechanical model of themth stratum when n is an odd number.According to the elastic foundation beam theory, the general formula of the deflection curve of themth stratum in the overlying rock can be written as
(9)wm′x=w1m′x=eβxa1′cosβx+b1′sinβx+e−βxc1′cosβx+d1′sinβx+qmkbm−la2≤x≤0w2m′x=eαxa2′cosαx+b2′sinαx+e−αxc2′cosαx+d2′sinαx+qmkam0≤x≤lbw3m′x=eβxa3′cosβx+b3′sinβx+e−βxc3′cosβx+d4′sinβx+qmkbmlb≤x≤la+lb…wnm′x=eβxan′cosβx+bn′sinβx+e−βxcn′cosβx+dn′sinβx+qmkbmn−22la+n−12lb≤x≤n2la+n−12lbwn+1m′x=eαxan+1′cosαx+bn+1′sinαx+e−αxcn+1′cosαx+dn+1′sinαx+qmkamx>n2la+n−12lb.The boundary conditions of the model can be described as(10)θ1m′−la2=0,Q1m′−la2=0θn+1m′+∞=0,wn+1m′+∞=0.Similarly, the continuity condition can be described as follows. The deflection, bending moment, rotation angle, and shearing force at the connection point among the protective coal pillar, the gob, and the entity coal equaled to each other.Similarly, by substituting the boundary conditions and continuity condition into (9), a1′,b1′,c1′,d1′,a2′,b2′,c2′,d2′,…,an+1′,bn+1′,cn+1′, and dn+1′ can be solved; i.e., the deflection equation and the bending-moment equation of the mth rock beam, denoted as wm′x and Mm′x, respectively, can be solved.


### 4.3. Calculation of the Height of the Water Flowing Fracture Zone

According to mechanics of materials, the maximum tensile stress of the rock beam can be calculated as(11)σmaxm=6Mmaxmhm2,where σmmax and Mmmax denote the maximum stress of the mth strata in the overlying rock and the maximum bending moment of the mth strata, respectively.According to the first strength theory, the fracturing of the rock beam should satisfy the following expression:(12)σmaxm≥σm,where σm denotes the tensile strength of the mth stratum in the overlying rock.If (12) can be satisfied, the stratum is not destroyed, and the water flowing fracture zone is produced; in contrast, the fractures are formed. First, the 1st stratum above the coal seam is analyzed; if the stratum satisfies (12), the adjacent upper stratum is verified, and the calculation stops until the stratum is not fractured. The height of the water flowing fracture zone equals to the superposition of the thicknesses of various fractured strata:
(13)H=h1+h2+h3+⋯.The detailed engineering parameters and the mechanical parameters of various strata, as displayed in Figures2 and 3, were substituted into the mechanical model of the SBBM working face. Through calculation, the height of the water flowing fracture zone was determined as 27.0 m, and the top of the water flowing fracture zone was about 68.0 m away from the aquifer; i.e., the water flowing fractures did not develop towards the aquifer.


## 4.1. Mechanical Model of the SBBM Working Face Whenn Is an Even Number

Whenn is an even number, the center of the protective pillar in the n/2th block was set as the symmetry point, and the origin, denoted as O, was set at the junction between the protective coal pillar and the n/2th block; then, the mechanical coordinate system was established by using the displacement function wmx as the unknown quantity, as shown in Figure 10.Figure 10
Established mechanical model of themth stratum when n is an even number.According to Winkle’s assumption for elastic foundations [22–24], the settlement amount of any point on the foundation surface is proportional to the pressure on the point per unit area. Actually, the foundation is simulated as a series of independent springs on the rigid foundation; next, when the pressure (p) is applied on any point on the foundation surface, only the point sank by wx because of the independence of the springs, while no sedimentation was observed at the other points. The following expression can be derived:
(2)p=kwx,where p denotes the pressure on the foundation per unit area, wx denotes the subsidence of the foundation, and k denotes the elastic foundation coefficient.Based on the elastic foundation beam theory, the deflection of the rock beam, denoted aswx, and the applied load, denoted as q, satisfy the following differential equation of the deflection curve of the foundation beam:
(3)EId4wxdx4+p=q,where EI denotes the flexural rigidity of the cross section of the rock beam.Therefore, by assuming the prearranged protective coal pillars in the SBBM working face, the backfill body and (m−1) bed rock as independent springs, and the entity coal in the right part as semi-infinite elastic foundation, the mth rock beam can be treated as a semi-infinite long beam. By substituting (2) into (3), the deflection curve equations of the mth rock beam above the coal and the backfill body can be written as
(4)d4w1mxdx4+kamw1mxEmIm=qmEmIm,−lb2≤x≤0d4w2mxdx4+kbmw2mxEmIm=qmEmIm,0≤x≤lad4w3mxdx4+kamw3mxEmIm=qmEmIm,la≤x≤la+lb…d4wnmxdx4+kbmwnmxEmIm=qmEmIm,n−22la+n−12lb≤x≤n2la+n−12lbd4wn+1mxdx4+kamwn+1mxEmIm=qmEmIm,x>n2la+n−12lbwhere EmIm denotes the flexural rigidity of the cross section of the mth rock beam.By setting the characteristic coefficientsα=kae/4EmIm4 and β=kbe/4EmIm4 and solving (4), the deflection curve equations of the mth rock beam can be written as
(5)wmx=w1mx=eαxa1cosαx+b1sinαx+e−αxc1cosαx+d1sinαx+qmkam−lb2≤x≤0w2mx=eβxa2cosβx+b2sinβx+e−βxc2cosβx+d2sinβx+qmkbm0≤x≤law3mx=eαxa3cosαx+b3sinαx+e−αxc3cosαx+d3sinαx+qmkamla≤x≤la+lb…wnmx=eβxancosβx+bnsinβx+e−βxcncosβx+dnsinβx+qmkbmn−22la+n−12lb≤x≤n2la+n−12lbwn+1mx=eαxan+1cosαx+bn+1sinαx+e−αxcn+1cosαx+dn+1sinαx+qmkamx>n2la+n−12lb.The rotation angle, bending moment, and shearing force of any cross section in themth rock beam can be written as
(6)θmx=dwmxdxMmx=−EmImdθmxdx=−EId2wmxdx2Qmx=dMmxdx=−EId3wmxdx3.The elastic foundation coefficient of the backfill body and the backfill ratio satisfy the following expression [25]:
(7)kc=σ0hk1−φ,where σ0 and φ denote the stress of the primary rock and the backfill ratio (0<φ<1), respectively.Because of the symmetrical model structure and load, the deflection curve and the bending-moment curve of the rock beam are symmetrical, and the rotation-angle curve and the shearing-force curve are anti-symmetrical; accordingly, the rotation angle and shearing force at the symmetrical point equaled to 0. Furthermore, according to the qualitative analysis results of the semi-infinite long beam as shown in Figure10, when x→+∞, then w→0 and θ→0. Based on the above analysis, the boundary conditions of the beam can be described as
(8)θ1m−lb2=0,Q1m−lb2=0θnm+∞=0,wnm+∞=0.The continuity condition can then be described as follows. The deflection, bending moment, rotation angle, and shearing force at the connection point among the protective coal pillar, the gob, and the entity coal equaled to each other.By substituting the boundary conditions and continuity condition into (5), a1,b1,c1,d1,a2,b2,c2,d2,…,an+1,bn+1,cn+1, and dn+1 can be solved; i.e., with these parameters, the bending subsidence equation and the bending-moment equation of the mth rock beam, denoted as wmx and Mmx, respectively, can be solved.


## 4.2. Mechanical Model of the SBBM Working Face Whenn Is an Odd Number

Figure11 displays the established mechanical model of the mth stratum, when n is an odd number. The center of the n+1/2th block was selected as the symmetry point, and the junction between the n+1/2th block and the protective coal pillar was set as the origin (O). Next, the mechanical calculation model of the mth stratum was established by using the displacement function wmx as the unknown quantity.Figure 11
Established mechanical model of themth stratum when n is an odd number.According to the elastic foundation beam theory, the general formula of the deflection curve of themth stratum in the overlying rock can be written as
(9)wm′x=w1m′x=eβxa1′cosβx+b1′sinβx+e−βxc1′cosβx+d1′sinβx+qmkbm−la2≤x≤0w2m′x=eαxa2′cosαx+b2′sinαx+e−αxc2′cosαx+d2′sinαx+qmkam0≤x≤lbw3m′x=eβxa3′cosβx+b3′sinβx+e−βxc3′cosβx+d4′sinβx+qmkbmlb≤x≤la+lb…wnm′x=eβxan′cosβx+bn′sinβx+e−βxcn′cosβx+dn′sinβx+qmkbmn−22la+n−12lb≤x≤n2la+n−12lbwn+1m′x=eαxan+1′cosαx+bn+1′sinαx+e−αxcn+1′cosαx+dn+1′sinαx+qmkamx>n2la+n−12lb.The boundary conditions of the model can be described as(10)θ1m′−la2=0,Q1m′−la2=0θn+1m′+∞=0,wn+1m′+∞=0.Similarly, the continuity condition can be described as follows. The deflection, bending moment, rotation angle, and shearing force at the connection point among the protective coal pillar, the gob, and the entity coal equaled to each other.Similarly, by substituting the boundary conditions and continuity condition into (9), a1′,b1′,c1′,d1′,a2′,b2′,c2′,d2′,…,an+1′,bn+1′,cn+1′, and dn+1′ can be solved; i.e., the deflection equation and the bending-moment equation of the mth rock beam, denoted as wm′x and Mm′x, respectively, can be solved.


## 4.3. Calculation of the Height of the Water Flowing Fracture Zone

According to mechanics of materials, the maximum tensile stress of the rock beam can be calculated as(11)σmaxm=6Mmaxmhm2,where σmmax and Mmmax denote the maximum stress of the mth strata in the overlying rock and the maximum bending moment of the mth strata, respectively.According to the first strength theory, the fracturing of the rock beam should satisfy the following expression:(12)σmaxm≥σm,where σm denotes the tensile strength of the mth stratum in the overlying rock.If (12) can be satisfied, the stratum is not destroyed, and the water flowing fracture zone is produced; in contrast, the fractures are formed. First, the 1st stratum above the coal seam is analyzed; if the stratum satisfies (12), the adjacent upper stratum is verified, and the calculation stops until the stratum is not fractured. The height of the water flowing fracture zone equals to the superposition of the thicknesses of various fractured strata:
(13)H=h1+h2+h3+⋯.The detailed engineering parameters and the mechanical parameters of various strata, as displayed in Figures2 and 3, were substituted into the mechanical model of the SBBM working face. Through calculation, the height of the water flowing fracture zone was determined as 27.0 m, and the top of the water flowing fracture zone was about 68.0 m away from the aquifer; i.e., the water flowing fractures did not develop towards the aquifer.


## 5. Discussion

Currently, the height of the water flowing fracture zone was mainly predicted according to the related formula in theRegulations; however, this prediction formula was concluded in the early 1980s through regression statistics based on limited field measurement data of some mines in China [20]. Because of the specificity of arrangement in the SBBM working face and the filling of gangues in the gob, SBBM differs from long-wall mining in roof management, thereby leading to different rules and mechanisms of mine pressure and fracture development. Whether the empirical formula in the Regulation concluded based on the measured data during long-wall mining is applicable for the calculation of the height of the water flowing fracture zone in SBBM still needs further discussion.


### 5.1. Contrastive Analysis of the Height of the Water Flowing Fracture Zone

According to the mechanical parameters of various strata in Figure2, the mean compressive strength of the roof was about 28.4 MPa, suggesting that the strata can be regarded as medium hard strata. In accordance with the prediction formula in Appendix 7 of the Regulations, the height of the water flowing fracture zone can be calculated as
(14)H=100M1.6M+3.6+5.6,where H and M denote the height of the water flowing fracture zone and the mining height, respectively.As listed in Table1, the calculated height of the water flowing fracture zone according to the formula in the Regulations is 48.7 m, and the calculated results based on the established mechanical model is 27.0 m, while the field measured height of the water flowing fracture zone is 26.8 m; i.e., the water flowing fracture zone did not develop towards the aquifer. Apparently, the prediction value according to the formula in the Regulations deviates greatly from the measured results, suggesting that the prediction formula is no longer applicable to the calculation of the height of the water flowing fracture zone in the SBBM; in contrast, the calculated height by the established mechanical model fits well with the measured result, validating high reliability of the proposed calculation model.Table 1
Contrastive analysis of the calculated and measured height of water flowing fracture zone.
Height of the water flowing fracture zone
Measured results of hole F
Prediction results according to the Regulations
Calculation results based on the mechanical model
26.8 m
48.7 m
27.0 m


### 5.2. Analysis of Mining Upper Limit

For preventing and controlling the loss of water resources after the mining in the working face, theRegulations specifies that for the preset water proof coal pillars in the mining of the coal seam beneath the aquifer, not only should the development height of the water flowing fracture zone be calculated but also the thickness of the protective layer should be considered. Therefore, as shown in Figure 12, the minimum thickness of the water proof coal pillar allowed in mining beneath the aquifer (i.e., the minimum distance between the mining coal seam and the aquifer), denoted as Hf, should be equal to the height of the water flowing fracture zone (H) and the thickness of the protective layer (Hb):
(15)Hf=H+Hb.Figure 12
Relationship between the thickness of the protective layer and the height of the water flowing fracture zone.According to the provisions in theRegulation, the thickness of the protective layer can be determined by considering the structural characteristics and mechanical properties of the coal rock in the SBBM working face:
(16)Hb=3M.By substituting the related data into (15) and (16), in combination with the mechanical theoretical analysis and field measured height of the water flowing fracture zone, the minimum thickness of the waterproof coal pillar allowed on the mining site (Hf) was determined as about 42 m, while the distance between the mining coal seam and the aquifer was 95 m. The thickness of the bed rock far exceeded the allowable minimum thickness of the waterproof coal pillar, indicating that the aquifer was not affected by the mining activities in the SBBM. In addition, the gangues were filled in the gob as the backfill body, which then cooperated with the coal pillar to bear the load of the overlying strata, thereby effectively decreasing the height of the mining-induced water flowing fracture zone. Meanwhile, the mining upper limit of the coal seam and the resulting coal recovery ratio can be enhanced, thus achieving the goal of water-preserved mining beneath the acquirer.


## 5.1. Contrastive Analysis of the Height of the Water Flowing Fracture Zone

According to the mechanical parameters of various strata in Figure2, the mean compressive strength of the roof was about 28.4 MPa, suggesting that the strata can be regarded as medium hard strata. In accordance with the prediction formula in Appendix 7 of the Regulations, the height of the water flowing fracture zone can be calculated as
(14)H=100M1.6M+3.6+5.6,where H and M denote the height of the water flowing fracture zone and the mining height, respectively.As listed in Table1, the calculated height of the water flowing fracture zone according to the formula in the Regulations is 48.7 m, and the calculated results based on the established mechanical model is 27.0 m, while the field measured height of the water flowing fracture zone is 26.8 m; i.e., the water flowing fracture zone did not develop towards the aquifer. Apparently, the prediction value according to the formula in the Regulations deviates greatly from the measured results, suggesting that the prediction formula is no longer applicable to the calculation of the height of the water flowing fracture zone in the SBBM; in contrast, the calculated height by the established mechanical model fits well with the measured result, validating high reliability of the proposed calculation model.Table 1
Contrastive analysis of the calculated and measured height of water flowing fracture zone.
Height of the water flowing fracture zone
Measured results of hole F
Prediction results according to the Regulations
Calculation results based on the mechanical model
26.8 m
48.7 m
27.0 m


## 5.2. Analysis of Mining Upper Limit

For preventing and controlling the loss of water resources after the mining in the working face, theRegulations specifies that for the preset water proof coal pillars in the mining of the coal seam beneath the aquifer, not only should the development height of the water flowing fracture zone be calculated but also the thickness of the protective layer should be considered. Therefore, as shown in Figure 12, the minimum thickness of the water proof coal pillar allowed in mining beneath the aquifer (i.e., the minimum distance between the mining coal seam and the aquifer), denoted as Hf, should be equal to the height of the water flowing fracture zone (H) and the thickness of the protective layer (Hb):
(15)Hf=H+Hb.Figure 12
Relationship between the thickness of the protective layer and the height of the water flowing fracture zone.According to the provisions in theRegulation, the thickness of the protective layer can be determined by considering the structural characteristics and mechanical properties of the coal rock in the SBBM working face:
(16)Hb=3M.By substituting the related data into (15) and (16), in combination with the mechanical theoretical analysis and field measured height of the water flowing fracture zone, the minimum thickness of the waterproof coal pillar allowed on the mining site (Hf) was determined as about 42 m, while the distance between the mining coal seam and the aquifer was 95 m. The thickness of the bed rock far exceeded the allowable minimum thickness of the waterproof coal pillar, indicating that the aquifer was not affected by the mining activities in the SBBM. In addition, the gangues were filled in the gob as the backfill body, which then cooperated with the coal pillar to bear the load of the overlying strata, thereby effectively decreasing the height of the mining-induced water flowing fracture zone. Meanwhile, the mining upper limit of the coal seam and the resulting coal recovery ratio can be enhanced, thus achieving the goal of water-preserved mining beneath the acquirer.


## 6. Conclusions

(1)
This study proposed the SBBM method for the recovery of corner coal pillars, industrial square pillars, and irregular blocks beneath the aquifer and simultaneously addressed the problem of massive stacking of gangues on the earth’s surface. In addition, by measuring the loss of washing fluid, core damage analysis, and drilling TV imaging detection, the height of the water flowing fracture zone in the SBBM working face was determined as 26.8 m.
(2)
Based on the technological characteristics of SBBM and the theory of elastic foundation beam, a mechanical model for the calculation of the height of the water flowing fracture zone in the overlying strata using SBBM was established. The calculated height of the water flowing fracture zone according to the mechanical mode (27.0 m) almost equals to the measured value (26.8 m), thus verifying the accuracy of the proposed mechanical model.
(3)
The distance between the coal seam and the aquifer was 95 m, which far exceeds the allowable minimum thickness of the protective coal pillar (42 m). Therefore, it can be concluded that the aquifer was not affected by mining activities, and simultaneously the mining upper limit of coal seam as well as the recovery ratio of coal can be enhanced in the SBBM.
(4)
The calculated height of the water flowing fracture zone according to the prediction formula in theRegulations (48.7 m) differs greatly from the measured value (26.8 m) and the calculated value according to the established mechanical model (27 m). Furthermore, in contrast with the caving mining method, the SBBM method used the gangues as the backfilling materials and filled them in the gob. The gangues cooperated with the coal pillars for bearing the load of the overlying strata, which can effectively reduce the height of the mining-induced water flowing fracture zone, avoid mining-induced damages on the aquifer, and thus achieve the goal of water-preserved mining beneath the aquifer.



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*Source: 7873682-2018-10-04.xml*