# Stratification Failure Mechanism of Coal Pillar Floor Strata with Different Strength in Short Distance Coal Seams

Authors: Fulian He; Qingtao Kang; Shuaifeng Yin; Yuli Liu; Zhishuai Wang; Linsheng Gao
Journal: Geofluids
 (2022)

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## Abstract

The failure of strata with different strength under coal pillar in close distance coal seams has its particularity. Theoretical analysis, numerical simulation, and similar test were used to obtain the failure mechanism of the soft and hard stratification of floor strata under the boundary of wide coal pillar and make out the influence of the strata failure on roadway layout. It shows that the failure of the soft and hard stratification is not synchronous and with different failure forms. The deformation and plastic failure of the soft strata occurs at first; then the fracture of the main bearing hard stratum occurs. Based on the main bearing stratum unbalanced forces acted by upper and lower strata, the initial fracture position and broken blocks span were calculated by bending fracture mechanics model of ultimate span beam. The coal pillar side of the roadway under coal pillar forms “column-beam-column” superimposed structure. The roadway layout under coal pillar and under coal pillar boundary with close distance has large influence on the plastic extension of the “column-beam-column” superimposed structure and the broken of main bearing stratum. The influence of roadway arrangement in floor strata outside coal pillar is smaller than those under coal pillar. It is difficult to control the deformation of roadway surrounding rock if the roadway locates beneath the broken blocks of the main bearing stratum.


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## Body

## 1. Introduction

The stress in floor strata of mined-out area boundary changes rapidly after coal mining, which make the floor damaged in a certain range [1, 2]. If there is a coal pillar in the mined-out area in the close distance coal seams, the coal pillar has two sides at mined-out area boundary, the vertical stress is concentrated in coal pillar’s floor strata, the damage degree of upper coal pillar boundary floor is large, and the damage range is affected largely by coal pillar in close upper coal seam. The damage zone and forms are the main research object when the roadway is arranged in the lower coal seam near the upper coal pillar boundary [3–9]. Many scholars have studied the stress distribution and the damage zone to a certain extent [4, 10–17]. For example, there is a “stress bubble theory” [6, 14, 18] based on semi-infinite elastomers, which is used to study the floor strata stress transfer formula of uniform load or triangular load caused by coal pillar. According to the stress bubble theory, the stress isocline distribution is similar to “bubble” and the stress environment of coal pillar floor strata is analyzed. It can provide theoretical basis for stress environment analysis of roadway surrounding rock in close coal seam under coal pillar. For another example, the “slip line and field theory” [6, 11, 12] was proposed. According to the theory, the boundary line of plastic failure zone produced in the floor strata at the coal pillar boundary is similar to the radial slip line starting from the coal wall. The damaged strata movement within the slip line can be divided into active zone, transition zone, and passive zone, and the problems of floor heave at coal pillar boundary, failure depth of plastic zone, and water inrush mechanism of floor can be analyzed.Through further study on the failure of coal pillar floor strata at the goaf boundary, the authors found that the failure of coal or rock strata with different strength at coal pillar boundary appeared different characteristics when arranging roadway in coal pillar’s floor strata. The upper coal pillar, the intermediate rock strata, and the lower coal pillar are interdependent in close distance coal seams. The hard rock strata in the middle are mainly fractured, while the soft strata are mainly plastic failure. The failure of the lower soft strata leads to the destruction of the bottom support foundation of the upper strata, so that the plastic zones of the upper rock strata and the coal pillar expand, and the concentrated stress changes. Finally, the superimposed coal pillar structure reaches a new equilibrium state.The research on asynchronous deformation and failure mechanism of layered soft and hard strata at coal pillar boundary was conducted on the basis of abutment pressure distribution law of coal pillar in close distance coal seams. The failure limit span of main bearing stratum was calculated by formula. Then, the stability of the overall structure of superimposed coal pillar was determined, and the reasonable layout position of floor roadway was obtained. The research results provide a new aspect for the location selection of roadway in the near coal seam under the coal pillar and have theoretical significance for further research on the damage mode and the extension range of plastic zone of floor strata at the boundary of coal pillar and coal seam goaf.


## 2. Stress Distribution and Failure Mechanism of Coal Pillar Floor Strata in Close Distance Coal Seams

### 2.1. Stress Distribution State of Strata under Coal Pillar

After coal mining, the roof pressure distribution from the coal wall to inner direction of the coal seam is stress reduction area, stress increase area, and original rock stress area. The coal pillar is a kind of special coal seam with small width and goaf on both sides, so that the two sides’ abutment stress can be superimposed on each other. Because of the different width of coal pillars, the superposition degree of abutment pressure on both sides of coal pillars is different, and there are three kinds of roof stress distribution states. The three stress states are the stress peak position in the center of coal pillar (Figure1(a)), the superposition position of high stress in the center of coal pillar (Figure 1(b)), and the raw rock stress area in the center of coal pillar (Figure 1(c)). In every state, there is a high stress area near the coal wall which is higher than the original rock stress. Besides, the stress state of the coal pillar near the coal wall changes from three-way stress state to two-way stress state, or the stress in the direction of mined-out area decreases obviously so that the strength of coal wall near the coal pillar boundary is greatly reduced. Therefore, it tends to be damaged of the coal seam near the coal pillar wall. From the coal wall to the center of the coal pillar, the crushing zone (I), the plastic zone (II), and the elastic zone (III) appear successively.Figure 1
Abutment pressure distribution of coal pillars with different widths.
(a)
Stress peak position in the center(b)
Stress superposition position in the center(c)
Raw rock stress area in the centerAccording to the elastic core theory of coal pillar stability [14], the stability of coal pillar can only be ensured by a certain width of elastic zone in the middle of coal pillar. If the roadway is arranged in the close distance coal seam under the coal pillar, the coal pillar of upper coal seam, the coal pillar beside roadway of lower coal seam, and the intermediate rock strata form the “column-beam-column” superimposed coal pillar structure (Figure 2). The failure of the intermediate strata and the lower coal pillar is affected by the concentrated stress of the upper coal pillar, and their failure type and failure scope are different from the upper coal pillar. The overall stability of superimposed coal pillar structure is affected by the asynchronous failure of different coal and rock strata.Figure 2
“Column-beam-column” superimposed coal pillar structure.The hard layer of the middle strata between the close distance coal seams is taken as the main bearing stratum, as shown in Figure3. If there are soft strata above the main bearing stratum, the soft strata are regarded as the stress transfer cushion between the coal pillar and the main bearing stratum and bear the coal pillar pressure together with the main bearing stratum. The soft rock strata and coal seam beneath the main bearing stratum are regarded as the soft cushion of the main bearing stratum, providing the reaction force and deformation space.Figure 3
The layered coal pillar floor and their stress distribution.The mechanical actions of large width coal pillar (Figures1(b) and 1(c)) on the main bearing floor stratum are showed in Figure 3, which are analyzed by the stress propagation attenuation law of concentrated force in semi-infinite body [18], and the stress distribution characteristics of numerical simulation (Figure 4). Shown as curve 1 in Figure 3, the force of coal pillar on the contact surface of floor is consistent with the pressure of coal pillar. The pressure of main bearing hard stratum at a certain depth in the floor is shown as curve 2 of Figure 3. Compared with the abutment pressure of upper coal pillar, the main bearing stratum pressure decreases and the stress peak shifts inward, and the distribution pattern of pressure curve remains unchanged.Figure 4
Stress distribution and damage location of strata under coal pillar.
(a)
Stress distribution of main bearing stratum at the initial state(b)
Damage location distribution of coal pillar’s floor strata


### 2.2. Deformation and Failure Mechanism of Floor Strata at Coal Pillar Boundary

#### 2.2.1. Asynchronous Failure Mechanism of Floor Strata with Different Strength

The uniaxial compression stress-strain curves of samples from different strength strata in actual mine are shown in Figure5. The soft sample is from no. 5 coal seam under the coal pillar in no. 4 coal seam, while the hard one is from the sandstone stratum between no. 4 coal seam and no. 5 coal seam. The strength of soft sample is obviously weaker than that of hard sample, and the deformation of soft sample is much larger than that of hard sample under the same stress condition. With the increase of stress, the soft sample first reaches the stress intensity peak and then enters the postpeak failure stage. In the postpeak failure stage, the sample’s compressive capacity decreases rapidly and large deformation occurs. The hard sample produces full-section fracture surfaces, while the soft sample produces many vertical fractures and forms debris and powder. It means that the strata with different strength may be destroyed with different forms at different times.Figure 5
Mechanical test and stress-strain curves of samples with different strength.Affected by concentrated stress of coal pillar, the stress of the rock and coal seam closed to coal pillar increases significantly. Moreover, the lateral bound stress of floor strata at coal pillar boundary decreases. Therefore, the coal or rock strata under coal pillar boundary is easy to be destroyed. The floor strata under coal pillar have different strength and stiffness. If floor strata differ to each other greatly, the soft floor strata first produces plastic failure and large deformation, the same as soft sample’s failure. After the failure of the inferior soft strata, the main bearing hard stratum is broken with the deformation of the underlying soft strata.


#### 2.2.2. Deformation and Movement Analysis of Soft Stratum as a Cushion in Coal Pillar’s Floor Strata

Affected by mining, the stress and boundary conditions of the floor strata are changed at coal pillar boundary. According to the slip line and field theory, the coal and rock within the floor slip line at coal pillar boundary have displacement upward toward the goaf (Figure6). Therefore, it provides deformation space for coal and rock mass outside the slip line.Figure 6
Displacement field of coal and rock mass in slip field of coal pillar floor.The bending failure or shear failure of the main bearing hard stratum under coal pillar is generated on the basis of deformable space provided by the soft mat strata below. The lateral bound stress of soft mat strata decreases due to the lateral rock movement which indicates that the horizontal stressσx decreases. Affected by the concentrated stress of coal pillar, the vertical stress σy increases compared with the in situ stress at the coal pillar boundary. Because the concentrated vertical stress under coal pillar, the maximum principal stress σ1 and minimum principal stress σ3 of coal pillar boundary floor strata are the σyandσx, respectively. According to Mohr-Coulomb strength theory [19] (acted in Figure 7), both the increase of the maximum principal stress and the decrease of the minimum principal stress will increase the radius of the molar stress circle, thus making it easier to reach the failure condition. The strength of soft mat stratum is small so that it occurs plastic failure and large deformation at first under the condition of reduced lateral binding, and then the main bearing stratum breaks with the deformation of the underlying soft strata.Figure 7
Analysis of Mohr-Coulomb strength curve of rock failure.If the roadway is arranged in the lower soft mat strata, especially under the coal pillar, the plastic failure range of soft mat strata is large, and the deformation of roadway roof and two sides is large, which provides more deformation space for main bearing stratum, so far as to the point of separating the hard layer from the weak layer of roadway roof strata. Therefore, large deformation conditions exist in the soft mat strata at the coal pillar boundary floor, which can provide vertical deformation and movement space for the main bearing stratum.


### 2.3. Fracture of the Main Bearing Stratum and Its Influence on the Lower Roadway and the Upper Coal Pillar

#### 2.3.1. The Broken Span and Position of the Main Bearing Stratum at Coal Pillar Boundary

Take the main bearing stratum as a research object. Assuming that the initial deformation of the main bearing stratum has not occurred, the stress in the soft mat strata beneath the main bearing stratum is the original rock stress, and the acting force of the soft mat strata on the main bearing stratum is assumed to be the uniform distributed forcek0γh without the influence of roadway in the lower weak strata. According to the distribution pattern of abutment pressure of the main bearing stratum, the stress curve of the main bearing stratum is arranged as a multisegment straight line distribution, with the initial pressure value k1γh, the peak pressure value k2γh, and the pressure value k3γh in the stable zone of stress superposition affected by the coal pillar boundary. Assuming that the main bearing stratum is a fixed beam at both ends, the mechanical model is established, as shown in Figure 8(a). The reaction force of strata beneath the main bearing stratum can offset part of the roof pressure of the main bearing stratum, so the model is further simplified and shown in Figure 8(b).Figure 8
Stress model of main bearing stratum under coal pillar.
(a)
Load diagram of main bearing stratum(b)
Simplified load diagram of main bearing stratumThe letterq is used to replace the stress value at the inflection points of the stress curve: q1=k1−k0γh, q2=k2−k0γh, and q3=k3−k0γh.The spacing between stress curves inflection points isl1,l2,l3. The shear force at the endpoints of AandB is RAandRB, and the bending moment is MAandMB, respectively.The calculation process of the bending moment of the main bearing layer is as follows:(i)
AC section:0≦x≦l1(1)Mx=−q2−q16l1x3−q12x2+RAx+MA.(ii)
CD section:l1≦x≦l1+l2(2)Mx=q2−q36l2x3+q3−q2l12l2−q22x2+q2−q1l12+q2−q3l122l2+RAx+q1−q2l126−q2−q3l136l2.(iii)
DB section:l1+l2≦x≦l1+l2+l3(3)Mx=−q32x2+2q3−q1−q2l12+q2+q3l22+RAx+2q2−q1−3q3l126−5q2+q3l226−q2+q3l1l22+MA.The deflection and rotation angle of the fixed endpoint A of the fixed beam are both 0, and the following equation can be obtained by using Castigliano’s second theorem.(4)ωA=∂VE∂RA=1EI∫0l1Mx1∂Mx1∂RAdx+1EI∫l1l1+l2Mx2∂Mx2∂RAdx+1EI∫l1+l2l1+l2+l3Mx3∂Mx3∂RAdx=0,(5)θA=∂VE∂MA=1EI∫0l1Mx1∂Mx1∂MAdx+1EI∫l1l1+l2Mx2∂Mx2∂MAdx+1EI∫l1+l2l1+l2+l3Mx3∂Mx3∂MAdx=0.By substituting equations (1), (2), and (3) into equations (4) and (5), respectively, and using software-assisted calculation, the formulas of MAandRA can be obtained (see Supplementary Materials), and then, the bending moment formulas of the main bearing beam at different positions can be obtained.Stress and stress inflection point in floor strata under coal pillar could be obtained by in situ stress measurement or simulation test. According to the numerical simulation results in Section3, the following parameters are obtained: q1=0,q2=20.5MPa,q3=10.7MPa,l1=6.1m,andl2=5m.The overburden pressure of the main bearing stratum under the coal pillar boundary gradually decreases to the value lower than the original rock stress in the direction of goaf. When the overburden pressure is lower than the stress of the original rock, the main bearing beam will not bend downward, and the fixed end of the main bearing beam needs strong clamping action of the upper and lower rock strata, so the position where the overburden pressure is equal to the original rock stress is regarded as the pointA of the fixed end of the main bearing beam under the coal pillar boundary. The fixed end B on the other side of the main bearing beam gradually extends to the center of the coal pillar; that is, the span of the beam keeps increasing until the main bearing beam reaches the maximum bending moment and breaks. Under the condition of numerical simulation, the overburden pressure of the main bearing beam is large. Firstly, the bending moment value of fixed point B in AC section in Figure 8 is calculated. Set the span between the fixed ends of the main bearing beam as r, and the calculation formulas of MAandRA are obtained according to formulas (4) and (5).
(6)MA=q1−q2r330l1−q1r212,RA=3q2−q120l1r2+q1r2.The formula of bending moment can be obtained by substituting formulas ofMAandRA into formula (1).
(7)Mx=−0.56x3+0.5r2x−0.11r3.The ultimate span of the main bearing stratum beam is calculated according to the ultimate tensile stress that the beam can bear. The calculation formula is as follows [19]:
(8)σ=MmaxymaxJ=12Mmaxymaxh3=6Mmaxh2,(9)Mmax=σh26.In the formulas,h is the thickness of main bearing stratum, J is the end face moment of main bearing stratum (J=h3/12), ymax is the distance between the end face of the stratum and the center of gravity (ymax=h/2), and Mmax is the maximum bending moment of the main bearing stratum.According to the numerical simulation conditions and formula (9), the tensile strength σmax of the main bearing strata is 3.83 MPa, and the corresponding ultimate bending moment Mmax is 6540 kN·m. By calculation, the extreme moment Mmax was obtained at the position “x=0.548r,” and the ultimate span r of the main bearing beam was 4.5 m. The calculated results are the failure position and span under the initial action of coal pillar’s abutment pressure on the main bearing beam. The main bearing stratum is further deformed and destroyed under the abutment pressure, resulting in stress transfer, and the reaction force of the soft strata under the main bearing stratum will gradually increase. The main bearing beam outside the initial fracture span forms a structure similar to cantilever beam, and further breaks occurs possibly, while the soft strata plastic zone beneath the main bearing beam develops further to both sides until a new equilibrium state (Figure 4(b)).


#### 2.3.2. The Influence of Main Bearing Stratum Fracture on the Lower Roadway and Upper Coal Pillar

The broken blocks occlude to each other, so they form a “masonry beam” structure, which is similar to the broken roof in goaf, as shown in Figure9. The broken blocks are subjected to the joint action of the reaction force R at the two support positions, the horizontal extrusion force T between the broken blocks, and the reaction force r of the soft strata beneath the broken blocks, so as to resist the roof load q. When the broken blocks cannot resist the load pressure q, it will produce slip dislocation at the articulated position of the blocks and break away from the in situ stratum.Figure 9
Mechanical action of fracture blocks.If the roadway is arranged under the broken blocks, the reaction forcer of the lower strata on the broken block is reduced, and the displacement space is provided for the further deformation of the broken blocks. As a result, it is difficult to control surrounding rock of roadway within the scope of broken blocks and the lower plastic failure zone so that the roadway in the lower strata should avoid the action range of the broken block. The deformation of the broken blocks and the inferior soft stratum increases, resulting in the increase of the roadway side plastic zone and the decrease of the supporting capacity of the upper coal pillar, and the plastic zone of the upper coal pillar increases. Therefore, the plastic zone and stability of upper coal pillar should be reevaluated.


## 2.1. Stress Distribution State of Strata under Coal Pillar

After coal mining, the roof pressure distribution from the coal wall to inner direction of the coal seam is stress reduction area, stress increase area, and original rock stress area. The coal pillar is a kind of special coal seam with small width and goaf on both sides, so that the two sides’ abutment stress can be superimposed on each other. Because of the different width of coal pillars, the superposition degree of abutment pressure on both sides of coal pillars is different, and there are three kinds of roof stress distribution states. The three stress states are the stress peak position in the center of coal pillar (Figure1(a)), the superposition position of high stress in the center of coal pillar (Figure 1(b)), and the raw rock stress area in the center of coal pillar (Figure 1(c)). In every state, there is a high stress area near the coal wall which is higher than the original rock stress. Besides, the stress state of the coal pillar near the coal wall changes from three-way stress state to two-way stress state, or the stress in the direction of mined-out area decreases obviously so that the strength of coal wall near the coal pillar boundary is greatly reduced. Therefore, it tends to be damaged of the coal seam near the coal pillar wall. From the coal wall to the center of the coal pillar, the crushing zone (I), the plastic zone (II), and the elastic zone (III) appear successively.Figure 1
Abutment pressure distribution of coal pillars with different widths.
(a)
Stress peak position in the center(b)
Stress superposition position in the center(c)
Raw rock stress area in the centerAccording to the elastic core theory of coal pillar stability [14], the stability of coal pillar can only be ensured by a certain width of elastic zone in the middle of coal pillar. If the roadway is arranged in the close distance coal seam under the coal pillar, the coal pillar of upper coal seam, the coal pillar beside roadway of lower coal seam, and the intermediate rock strata form the “column-beam-column” superimposed coal pillar structure (Figure 2). The failure of the intermediate strata and the lower coal pillar is affected by the concentrated stress of the upper coal pillar, and their failure type and failure scope are different from the upper coal pillar. The overall stability of superimposed coal pillar structure is affected by the asynchronous failure of different coal and rock strata.Figure 2
“Column-beam-column” superimposed coal pillar structure.The hard layer of the middle strata between the close distance coal seams is taken as the main bearing stratum, as shown in Figure3. If there are soft strata above the main bearing stratum, the soft strata are regarded as the stress transfer cushion between the coal pillar and the main bearing stratum and bear the coal pillar pressure together with the main bearing stratum. The soft rock strata and coal seam beneath the main bearing stratum are regarded as the soft cushion of the main bearing stratum, providing the reaction force and deformation space.Figure 3
The layered coal pillar floor and their stress distribution.The mechanical actions of large width coal pillar (Figures1(b) and 1(c)) on the main bearing floor stratum are showed in Figure 3, which are analyzed by the stress propagation attenuation law of concentrated force in semi-infinite body [18], and the stress distribution characteristics of numerical simulation (Figure 4). Shown as curve 1 in Figure 3, the force of coal pillar on the contact surface of floor is consistent with the pressure of coal pillar. The pressure of main bearing hard stratum at a certain depth in the floor is shown as curve 2 of Figure 3. Compared with the abutment pressure of upper coal pillar, the main bearing stratum pressure decreases and the stress peak shifts inward, and the distribution pattern of pressure curve remains unchanged.Figure 4
Stress distribution and damage location of strata under coal pillar.
(a)
Stress distribution of main bearing stratum at the initial state(b)
Damage location distribution of coal pillar’s floor strata


## 2.2. Deformation and Failure Mechanism of Floor Strata at Coal Pillar Boundary

### 2.2.1. Asynchronous Failure Mechanism of Floor Strata with Different Strength

The uniaxial compression stress-strain curves of samples from different strength strata in actual mine are shown in Figure5. The soft sample is from no. 5 coal seam under the coal pillar in no. 4 coal seam, while the hard one is from the sandstone stratum between no. 4 coal seam and no. 5 coal seam. The strength of soft sample is obviously weaker than that of hard sample, and the deformation of soft sample is much larger than that of hard sample under the same stress condition. With the increase of stress, the soft sample first reaches the stress intensity peak and then enters the postpeak failure stage. In the postpeak failure stage, the sample’s compressive capacity decreases rapidly and large deformation occurs. The hard sample produces full-section fracture surfaces, while the soft sample produces many vertical fractures and forms debris and powder. It means that the strata with different strength may be destroyed with different forms at different times.Figure 5
Mechanical test and stress-strain curves of samples with different strength.Affected by concentrated stress of coal pillar, the stress of the rock and coal seam closed to coal pillar increases significantly. Moreover, the lateral bound stress of floor strata at coal pillar boundary decreases. Therefore, the coal or rock strata under coal pillar boundary is easy to be destroyed. The floor strata under coal pillar have different strength and stiffness. If floor strata differ to each other greatly, the soft floor strata first produces plastic failure and large deformation, the same as soft sample’s failure. After the failure of the inferior soft strata, the main bearing hard stratum is broken with the deformation of the underlying soft strata.


### 2.2.2. Deformation and Movement Analysis of Soft Stratum as a Cushion in Coal Pillar’s Floor Strata

Affected by mining, the stress and boundary conditions of the floor strata are changed at coal pillar boundary. According to the slip line and field theory, the coal and rock within the floor slip line at coal pillar boundary have displacement upward toward the goaf (Figure6). Therefore, it provides deformation space for coal and rock mass outside the slip line.Figure 6
Displacement field of coal and rock mass in slip field of coal pillar floor.The bending failure or shear failure of the main bearing hard stratum under coal pillar is generated on the basis of deformable space provided by the soft mat strata below. The lateral bound stress of soft mat strata decreases due to the lateral rock movement which indicates that the horizontal stressσx decreases. Affected by the concentrated stress of coal pillar, the vertical stress σy increases compared with the in situ stress at the coal pillar boundary. Because the concentrated vertical stress under coal pillar, the maximum principal stress σ1 and minimum principal stress σ3 of coal pillar boundary floor strata are the σyandσx, respectively. According to Mohr-Coulomb strength theory [19] (acted in Figure 7), both the increase of the maximum principal stress and the decrease of the minimum principal stress will increase the radius of the molar stress circle, thus making it easier to reach the failure condition. The strength of soft mat stratum is small so that it occurs plastic failure and large deformation at first under the condition of reduced lateral binding, and then the main bearing stratum breaks with the deformation of the underlying soft strata.Figure 7
Analysis of Mohr-Coulomb strength curve of rock failure.If the roadway is arranged in the lower soft mat strata, especially under the coal pillar, the plastic failure range of soft mat strata is large, and the deformation of roadway roof and two sides is large, which provides more deformation space for main bearing stratum, so far as to the point of separating the hard layer from the weak layer of roadway roof strata. Therefore, large deformation conditions exist in the soft mat strata at the coal pillar boundary floor, which can provide vertical deformation and movement space for the main bearing stratum.


## 2.2.1. Asynchronous Failure Mechanism of Floor Strata with Different Strength

The uniaxial compression stress-strain curves of samples from different strength strata in actual mine are shown in Figure5. The soft sample is from no. 5 coal seam under the coal pillar in no. 4 coal seam, while the hard one is from the sandstone stratum between no. 4 coal seam and no. 5 coal seam. The strength of soft sample is obviously weaker than that of hard sample, and the deformation of soft sample is much larger than that of hard sample under the same stress condition. With the increase of stress, the soft sample first reaches the stress intensity peak and then enters the postpeak failure stage. In the postpeak failure stage, the sample’s compressive capacity decreases rapidly and large deformation occurs. The hard sample produces full-section fracture surfaces, while the soft sample produces many vertical fractures and forms debris and powder. It means that the strata with different strength may be destroyed with different forms at different times.Figure 5
Mechanical test and stress-strain curves of samples with different strength.Affected by concentrated stress of coal pillar, the stress of the rock and coal seam closed to coal pillar increases significantly. Moreover, the lateral bound stress of floor strata at coal pillar boundary decreases. Therefore, the coal or rock strata under coal pillar boundary is easy to be destroyed. The floor strata under coal pillar have different strength and stiffness. If floor strata differ to each other greatly, the soft floor strata first produces plastic failure and large deformation, the same as soft sample’s failure. After the failure of the inferior soft strata, the main bearing hard stratum is broken with the deformation of the underlying soft strata.


## 2.2.2. Deformation and Movement Analysis of Soft Stratum as a Cushion in Coal Pillar’s Floor Strata

Affected by mining, the stress and boundary conditions of the floor strata are changed at coal pillar boundary. According to the slip line and field theory, the coal and rock within the floor slip line at coal pillar boundary have displacement upward toward the goaf (Figure6). Therefore, it provides deformation space for coal and rock mass outside the slip line.Figure 6
Displacement field of coal and rock mass in slip field of coal pillar floor.The bending failure or shear failure of the main bearing hard stratum under coal pillar is generated on the basis of deformable space provided by the soft mat strata below. The lateral bound stress of soft mat strata decreases due to the lateral rock movement which indicates that the horizontal stressσx decreases. Affected by the concentrated stress of coal pillar, the vertical stress σy increases compared with the in situ stress at the coal pillar boundary. Because the concentrated vertical stress under coal pillar, the maximum principal stress σ1 and minimum principal stress σ3 of coal pillar boundary floor strata are the σyandσx, respectively. According to Mohr-Coulomb strength theory [19] (acted in Figure 7), both the increase of the maximum principal stress and the decrease of the minimum principal stress will increase the radius of the molar stress circle, thus making it easier to reach the failure condition. The strength of soft mat stratum is small so that it occurs plastic failure and large deformation at first under the condition of reduced lateral binding, and then the main bearing stratum breaks with the deformation of the underlying soft strata.Figure 7
Analysis of Mohr-Coulomb strength curve of rock failure.If the roadway is arranged in the lower soft mat strata, especially under the coal pillar, the plastic failure range of soft mat strata is large, and the deformation of roadway roof and two sides is large, which provides more deformation space for main bearing stratum, so far as to the point of separating the hard layer from the weak layer of roadway roof strata. Therefore, large deformation conditions exist in the soft mat strata at the coal pillar boundary floor, which can provide vertical deformation and movement space for the main bearing stratum.


## 2.3. Fracture of the Main Bearing Stratum and Its Influence on the Lower Roadway and the Upper Coal Pillar

### 2.3.1. The Broken Span and Position of the Main Bearing Stratum at Coal Pillar Boundary

Take the main bearing stratum as a research object. Assuming that the initial deformation of the main bearing stratum has not occurred, the stress in the soft mat strata beneath the main bearing stratum is the original rock stress, and the acting force of the soft mat strata on the main bearing stratum is assumed to be the uniform distributed forcek0γh without the influence of roadway in the lower weak strata. According to the distribution pattern of abutment pressure of the main bearing stratum, the stress curve of the main bearing stratum is arranged as a multisegment straight line distribution, with the initial pressure value k1γh, the peak pressure value k2γh, and the pressure value k3γh in the stable zone of stress superposition affected by the coal pillar boundary. Assuming that the main bearing stratum is a fixed beam at both ends, the mechanical model is established, as shown in Figure 8(a). The reaction force of strata beneath the main bearing stratum can offset part of the roof pressure of the main bearing stratum, so the model is further simplified and shown in Figure 8(b).Figure 8
Stress model of main bearing stratum under coal pillar.
(a)
Load diagram of main bearing stratum(b)
Simplified load diagram of main bearing stratumThe letterq is used to replace the stress value at the inflection points of the stress curve: q1=k1−k0γh, q2=k2−k0γh, and q3=k3−k0γh.The spacing between stress curves inflection points isl1,l2,l3. The shear force at the endpoints of AandB is RAandRB, and the bending moment is MAandMB, respectively.The calculation process of the bending moment of the main bearing layer is as follows:(i)
AC section:0≦x≦l1(1)Mx=−q2−q16l1x3−q12x2+RAx+MA.(ii)
CD section:l1≦x≦l1+l2(2)Mx=q2−q36l2x3+q3−q2l12l2−q22x2+q2−q1l12+q2−q3l122l2+RAx+q1−q2l126−q2−q3l136l2.(iii)
DB section:l1+l2≦x≦l1+l2+l3(3)Mx=−q32x2+2q3−q1−q2l12+q2+q3l22+RAx+2q2−q1−3q3l126−5q2+q3l226−q2+q3l1l22+MA.The deflection and rotation angle of the fixed endpoint A of the fixed beam are both 0, and the following equation can be obtained by using Castigliano’s second theorem.(4)ωA=∂VE∂RA=1EI∫0l1Mx1∂Mx1∂RAdx+1EI∫l1l1+l2Mx2∂Mx2∂RAdx+1EI∫l1+l2l1+l2+l3Mx3∂Mx3∂RAdx=0,(5)θA=∂VE∂MA=1EI∫0l1Mx1∂Mx1∂MAdx+1EI∫l1l1+l2Mx2∂Mx2∂MAdx+1EI∫l1+l2l1+l2+l3Mx3∂Mx3∂MAdx=0.By substituting equations (1), (2), and (3) into equations (4) and (5), respectively, and using software-assisted calculation, the formulas of MAandRA can be obtained (see Supplementary Materials), and then, the bending moment formulas of the main bearing beam at different positions can be obtained.Stress and stress inflection point in floor strata under coal pillar could be obtained by in situ stress measurement or simulation test. According to the numerical simulation results in Section3, the following parameters are obtained: q1=0,q2=20.5MPa,q3=10.7MPa,l1=6.1m,andl2=5m.The overburden pressure of the main bearing stratum under the coal pillar boundary gradually decreases to the value lower than the original rock stress in the direction of goaf. When the overburden pressure is lower than the stress of the original rock, the main bearing beam will not bend downward, and the fixed end of the main bearing beam needs strong clamping action of the upper and lower rock strata, so the position where the overburden pressure is equal to the original rock stress is regarded as the pointA of the fixed end of the main bearing beam under the coal pillar boundary. The fixed end B on the other side of the main bearing beam gradually extends to the center of the coal pillar; that is, the span of the beam keeps increasing until the main bearing beam reaches the maximum bending moment and breaks. Under the condition of numerical simulation, the overburden pressure of the main bearing beam is large. Firstly, the bending moment value of fixed point B in AC section in Figure 8 is calculated. Set the span between the fixed ends of the main bearing beam as r, and the calculation formulas of MAandRA are obtained according to formulas (4) and (5).
(6)MA=q1−q2r330l1−q1r212,RA=3q2−q120l1r2+q1r2.The formula of bending moment can be obtained by substituting formulas ofMAandRA into formula (1).
(7)Mx=−0.56x3+0.5r2x−0.11r3.The ultimate span of the main bearing stratum beam is calculated according to the ultimate tensile stress that the beam can bear. The calculation formula is as follows [19]:
(8)σ=MmaxymaxJ=12Mmaxymaxh3=6Mmaxh2,(9)Mmax=σh26.In the formulas,h is the thickness of main bearing stratum, J is the end face moment of main bearing stratum (J=h3/12), ymax is the distance between the end face of the stratum and the center of gravity (ymax=h/2), and Mmax is the maximum bending moment of the main bearing stratum.According to the numerical simulation conditions and formula (9), the tensile strength σmax of the main bearing strata is 3.83 MPa, and the corresponding ultimate bending moment Mmax is 6540 kN·m. By calculation, the extreme moment Mmax was obtained at the position “x=0.548r,” and the ultimate span r of the main bearing beam was 4.5 m. The calculated results are the failure position and span under the initial action of coal pillar’s abutment pressure on the main bearing beam. The main bearing stratum is further deformed and destroyed under the abutment pressure, resulting in stress transfer, and the reaction force of the soft strata under the main bearing stratum will gradually increase. The main bearing beam outside the initial fracture span forms a structure similar to cantilever beam, and further breaks occurs possibly, while the soft strata plastic zone beneath the main bearing beam develops further to both sides until a new equilibrium state (Figure 4(b)).


### 2.3.2. The Influence of Main Bearing Stratum Fracture on the Lower Roadway and Upper Coal Pillar

The broken blocks occlude to each other, so they form a “masonry beam” structure, which is similar to the broken roof in goaf, as shown in Figure9. The broken blocks are subjected to the joint action of the reaction force R at the two support positions, the horizontal extrusion force T between the broken blocks, and the reaction force r of the soft strata beneath the broken blocks, so as to resist the roof load q. When the broken blocks cannot resist the load pressure q, it will produce slip dislocation at the articulated position of the blocks and break away from the in situ stratum.Figure 9
Mechanical action of fracture blocks.If the roadway is arranged under the broken blocks, the reaction forcer of the lower strata on the broken block is reduced, and the displacement space is provided for the further deformation of the broken blocks. As a result, it is difficult to control surrounding rock of roadway within the scope of broken blocks and the lower plastic failure zone so that the roadway in the lower strata should avoid the action range of the broken block. The deformation of the broken blocks and the inferior soft stratum increases, resulting in the increase of the roadway side plastic zone and the decrease of the supporting capacity of the upper coal pillar, and the plastic zone of the upper coal pillar increases. Therefore, the plastic zone and stability of upper coal pillar should be reevaluated.


## 2.3.1. The Broken Span and Position of the Main Bearing Stratum at Coal Pillar Boundary

Take the main bearing stratum as a research object. Assuming that the initial deformation of the main bearing stratum has not occurred, the stress in the soft mat strata beneath the main bearing stratum is the original rock stress, and the acting force of the soft mat strata on the main bearing stratum is assumed to be the uniform distributed forcek0γh without the influence of roadway in the lower weak strata. According to the distribution pattern of abutment pressure of the main bearing stratum, the stress curve of the main bearing stratum is arranged as a multisegment straight line distribution, with the initial pressure value k1γh, the peak pressure value k2γh, and the pressure value k3γh in the stable zone of stress superposition affected by the coal pillar boundary. Assuming that the main bearing stratum is a fixed beam at both ends, the mechanical model is established, as shown in Figure 8(a). The reaction force of strata beneath the main bearing stratum can offset part of the roof pressure of the main bearing stratum, so the model is further simplified and shown in Figure 8(b).Figure 8
Stress model of main bearing stratum under coal pillar.
(a)
Load diagram of main bearing stratum(b)
Simplified load diagram of main bearing stratumThe letterq is used to replace the stress value at the inflection points of the stress curve: q1=k1−k0γh, q2=k2−k0γh, and q3=k3−k0γh.The spacing between stress curves inflection points isl1,l2,l3. The shear force at the endpoints of AandB is RAandRB, and the bending moment is MAandMB, respectively.The calculation process of the bending moment of the main bearing layer is as follows:(i)
AC section:0≦x≦l1(1)Mx=−q2−q16l1x3−q12x2+RAx+MA.(ii)
CD section:l1≦x≦l1+l2(2)Mx=q2−q36l2x3+q3−q2l12l2−q22x2+q2−q1l12+q2−q3l122l2+RAx+q1−q2l126−q2−q3l136l2.(iii)
DB section:l1+l2≦x≦l1+l2+l3(3)Mx=−q32x2+2q3−q1−q2l12+q2+q3l22+RAx+2q2−q1−3q3l126−5q2+q3l226−q2+q3l1l22+MA.The deflection and rotation angle of the fixed endpoint A of the fixed beam are both 0, and the following equation can be obtained by using Castigliano’s second theorem.(4)ωA=∂VE∂RA=1EI∫0l1Mx1∂Mx1∂RAdx+1EI∫l1l1+l2Mx2∂Mx2∂RAdx+1EI∫l1+l2l1+l2+l3Mx3∂Mx3∂RAdx=0,(5)θA=∂VE∂MA=1EI∫0l1Mx1∂Mx1∂MAdx+1EI∫l1l1+l2Mx2∂Mx2∂MAdx+1EI∫l1+l2l1+l2+l3Mx3∂Mx3∂MAdx=0.By substituting equations (1), (2), and (3) into equations (4) and (5), respectively, and using software-assisted calculation, the formulas of MAandRA can be obtained (see Supplementary Materials), and then, the bending moment formulas of the main bearing beam at different positions can be obtained.Stress and stress inflection point in floor strata under coal pillar could be obtained by in situ stress measurement or simulation test. According to the numerical simulation results in Section3, the following parameters are obtained: q1=0,q2=20.5MPa,q3=10.7MPa,l1=6.1m,andl2=5m.The overburden pressure of the main bearing stratum under the coal pillar boundary gradually decreases to the value lower than the original rock stress in the direction of goaf. When the overburden pressure is lower than the stress of the original rock, the main bearing beam will not bend downward, and the fixed end of the main bearing beam needs strong clamping action of the upper and lower rock strata, so the position where the overburden pressure is equal to the original rock stress is regarded as the pointA of the fixed end of the main bearing beam under the coal pillar boundary. The fixed end B on the other side of the main bearing beam gradually extends to the center of the coal pillar; that is, the span of the beam keeps increasing until the main bearing beam reaches the maximum bending moment and breaks. Under the condition of numerical simulation, the overburden pressure of the main bearing beam is large. Firstly, the bending moment value of fixed point B in AC section in Figure 8 is calculated. Set the span between the fixed ends of the main bearing beam as r, and the calculation formulas of MAandRA are obtained according to formulas (4) and (5).
(6)MA=q1−q2r330l1−q1r212,RA=3q2−q120l1r2+q1r2.The formula of bending moment can be obtained by substituting formulas ofMAandRA into formula (1).
(7)Mx=−0.56x3+0.5r2x−0.11r3.The ultimate span of the main bearing stratum beam is calculated according to the ultimate tensile stress that the beam can bear. The calculation formula is as follows [19]:
(8)σ=MmaxymaxJ=12Mmaxymaxh3=6Mmaxh2,(9)Mmax=σh26.In the formulas,h is the thickness of main bearing stratum, J is the end face moment of main bearing stratum (J=h3/12), ymax is the distance between the end face of the stratum and the center of gravity (ymax=h/2), and Mmax is the maximum bending moment of the main bearing stratum.According to the numerical simulation conditions and formula (9), the tensile strength σmax of the main bearing strata is 3.83 MPa, and the corresponding ultimate bending moment Mmax is 6540 kN·m. By calculation, the extreme moment Mmax was obtained at the position “x=0.548r,” and the ultimate span r of the main bearing beam was 4.5 m. The calculated results are the failure position and span under the initial action of coal pillar’s abutment pressure on the main bearing beam. The main bearing stratum is further deformed and destroyed under the abutment pressure, resulting in stress transfer, and the reaction force of the soft strata under the main bearing stratum will gradually increase. The main bearing beam outside the initial fracture span forms a structure similar to cantilever beam, and further breaks occurs possibly, while the soft strata plastic zone beneath the main bearing beam develops further to both sides until a new equilibrium state (Figure 4(b)).


## 2.3.2. The Influence of Main Bearing Stratum Fracture on the Lower Roadway and Upper Coal Pillar

The broken blocks occlude to each other, so they form a “masonry beam” structure, which is similar to the broken roof in goaf, as shown in Figure9. The broken blocks are subjected to the joint action of the reaction force R at the two support positions, the horizontal extrusion force T between the broken blocks, and the reaction force r of the soft strata beneath the broken blocks, so as to resist the roof load q. When the broken blocks cannot resist the load pressure q, it will produce slip dislocation at the articulated position of the blocks and break away from the in situ stratum.Figure 9
Mechanical action of fracture blocks.If the roadway is arranged under the broken blocks, the reaction forcer of the lower strata on the broken block is reduced, and the displacement space is provided for the further deformation of the broken blocks. As a result, it is difficult to control surrounding rock of roadway within the scope of broken blocks and the lower plastic failure zone so that the roadway in the lower strata should avoid the action range of the broken block. The deformation of the broken blocks and the inferior soft stratum increases, resulting in the increase of the roadway side plastic zone and the decrease of the supporting capacity of the upper coal pillar, and the plastic zone of the upper coal pillar increases. Therefore, the plastic zone and stability of upper coal pillar should be reevaluated.


## 3. Numerical Simulation Analysis of Coal Pillar Floor Failure in Close Distance Coal Seams

### 3.1. Establishment of Numerical Simulation Model and Failure Analysis of the Coal Pillar Floor

In order to research the law of coal pillar floor failure by simulation analysis, the UDEC numerical calculation model was established according to actual production mine’s strata relationship, as shown in Figure10. The model is 517m×68m in width and height. In the actual strata relationship, the width of the remaining coal pillar of the no. 4 coal seam is 45.5 m, and the spacing between the coal pillar and the lower no. 5 coal seam is 5-7.5 m. Occurrence relation and simplified modified size of strata are shown in Figure 10 and Table 1. According to geological borehole data, different joint densities of coal and rock strata are allocated, and physical and mechanical parameters of each layer are shown in Table 1. Uniform load (-8.39 MPa) was adopted to replace the force of strata stress above the model according to the buried depth of no. 4 coal seam, and the deformation was restricted at the bottom and two sides. In the model, the deformation and failure criterion of blocks were adopted Mohr-Coulomb criterion.Figure 10
Strata distribution of numerical simulation.Table 1
Mechanical parameters of the strata.
LithologyThickness (m)Bulk modulus (GPa)Shear modulus (GPa)Cohesion (MPa)Friction (°)Tension (MPa)Sandstone3028.512.125234.5Fine sandstone3.479.128.34522.54.6Sandy mudstone4.56.174.0712302.62# coal seam0.81.320.61.215.30.7Sandy mudstone3.26.174.0712302.63# coal seam11.320.61.215.30.7Siltstone3.27.54.515.626.53.8Sandy mudstone4.56.174.0712301.64# coal seam2.11.320.61.215.30.7Siltstone3.27.54.515.626.53.83Mudstone22.51.83.321.52.35# coal seam2.21.320.61.215.30.7Fine sandstone2.879.128.34522.58.26Sandy mudstone4.86.174.0712302.6There are 3.2 m siltstone stratum and 2 m mudstone stratum between no. 4 coal seam and no. 5 coal seam. The siltstone stratum is analyzed as the main bearing hard stratum, while the lower mudstone stratum has low strength, which is used as the soft mat strata together with the no. 5 coal seam. After mining at 216 m working face on both sides of the coal pillar in no. 4 coal seam, the roof stress in goaf was transferred to the coal pillar’s position, resulting in a sudden increase of abutment pressure of coal pillar roof and a concentrated load effect on the floor. A survey line was set at 0.4 m below the coal pillar in order to measure the load stress distribution of the main bearing stratum, which was shown in Figure4(a). The failure location distribution of the strata at coal pillar boundary is shown in Figure 4(a).The load stress distribution of main bearing stratum was analyzed in Figure4(a). At the critical position (x=0) of coal pillar and goaf, the stress is greater than that of raw rock stress. The stress decreases rapidly to zero in the direction of goaf and rises rapidly to peak value in the direction of coal pillar’s center and then decreases gradually to a more stable value as it goes away from the pillar’s boundary. According to the theoretical analysis of the main bearing stratum, it is subjected to the fixed support as both ends of the beam, and the fixed support ends have strong bending moment reaction force. Therefore, it is assumed that the right fixed end of the fixed beam in theoretical calculation is at the point where the stress is equal to the original rock stress, shown in Figure 4(a). The red polyline in Figure 4(a) represents the approximate line of the stress curve. The main bearing stratum deforms under the abutment pressure and gradually generates additional force on the underlying strata. At the initial stage of the deformation process of the main bearing stratum, assuming that the reaction force of the underlying soft rock strata on the main bearing stratum is the original rock stress (γh=9.7 MPa), then the parameters in Figure 8 can be obtained in numerical simulation as follows: q1=k1−k0rh=0MPa,q2=k2−k0rh≈20.5MPa,q3=k2−k0rh=10.7MPa.After the action of coal pillar is stabilized, the failure mode and location of coal pillar’s floor strata are shown in Figure4(b). The main bearing stratum is damaged by tension, and the damage location is mainly concentrated near the stress peak under the coal pillar. The obvious open position of the block in the numerical model is shown in Figure 4(b), which is consistent with the fixed end and extreme position of bending moment of the theoretical analysis beam. The plastic zone of the 4# coal seam pillar extends from the pillar boundary to 6.5 m inside the pillar, and the plastic zone shape of the 5# coal seam is a quadrilateral extending towards to the center of the coal pillar. The horizontal distance between the plastic zone boundary and the pillar boundary is 13.4 m, which is obviously larger than the plastic zone of upper coal pillar. The plastic zone of the direct roof of 5# coal seam is not fully developed, which is a triangle with large bottom and small top, and extends towards to the tensile failure zone of the main bearing stratum.


### 3.2. The Roadway Layout and Failure Analysis of Coal Pillar Floor Strata

The roadways at three positions were arranged in the coal seam under the close distance coal pillar. The roadway width and height dimensions are4.2m×2.8m. The simulation results showed that the damage degree of the coal seams and their intermediate strata under coal pillar increased obviously after the roadway was excavated.In Figure11, the horizontal distance between the right side of roadway and the coal pillar boundary is 6.8 m. The plastic zone of the coal pillar boundary on the left side of roadway have developed to the other side of the coal pillar boundary, and the plastic zone of the coal pillar above the roadway was also divided into left and right parts. The displacement of the roadway surrounding rock is large, with the displacement of the two sides of the roadway approaching 1.2 m, and the displacement of the roof and floor approaching 0.5 m, and even the separation occurred in the roadway roof strata, and the deformation space of the main bearing stratum above the roadway is sufficient. The tensile failure range of the main bearing stratum is large and concentrated towards the plastic zone of the coal pillar boundary. The number of opening positions between the model blocks increased and the rotation form of broken blocks appears obviously, which is shown in Figure 11(b). The distance between the ends of the fracture opening angle on the left and right sides of the fracture block A of the main bearing stratum is 0.1 m, and the fracture position on the right side of the fractured block A of the main bearing stratum is near the boundary of the coal pillar.Figure 11
Failure of roadway surrounding rock under coal pillar.
(a)
Distribution of failure range(b)
Rupture location of the blocksThe second roadway location is shown in Figure12(a). The left side of the roadway and the upper coal pillar boundary are in the same horizontal position. The plastic zone of the left side of the roadway developed to 13.6 m away from the coal pillar boundary. The plastic zone of the mudstone layer under the main control rock is still located below the plastic zone boundary of the coal pillar, but the scope is slightly larger than the condition without roadway. The tensile failure of main bearing stratum range is large and scattered, and the tensile failure location is more than that in the condition without roadway. The plastic zone of coal pillar in 4# coal seam extends from the coal pillar boundary to 6.8 m in the coal pillar, and the width of the plastic zone with whole coal pillar’s high increases little, but the plastic width at the bottom of coal pillar increases greatly, extending from the coal pillar boundary to 12.6 m in the coal pillar. The deformation of the left side and left side roof of the roadway is large, with the offset of the left side being 0.3 m and the subsidence of the left side roof being 0.1 m. Therefore, the layout of roadway under the coal pillar boundary has little influence on the plastic zone range, but the large deformation of roadway surrounding rock provides more deformation space for the subsidence of hard main bearing stratum, and the plastic zone range of coal pillar tends to increase when the support conditions of coal pillar are changed by the roadway.Figure 12
Failure distribution of strata with different roadway locations.
(a)
Roadway under coal pillar boundary(b)
Roadway outside coal pillarIn Figure12(b), the roadway is in the floor strata outside the coal pillar, and the horizontal distance between the left side of the roadway and the upper coal pillar is 5.2 m. The plastic zone is 13.6 m wide from the left wall of the roadway to the coal pillar boundary, and the left wall displacement was 0.1 m. The plastic zone range of soft mat strata under the main bearing stratum was slightly larger than that under the condition without roadway, the tensile failure location of main bearing stratum and the plastic zone range of coal pillar changes little, and a small plastic zone was locally generated at the bottom of coal pillar outside the plastic zone of coal pillar boundary. Therefore, the deformation of roadway surrounding rock is small, which have little influence on the fracture and deformation of main bearing stratum and the expansion of coal pillar plastic zone.Vertical measuring line was set in the strata under the coal pillar to measure the strata subsidence at different depths. The horizontal distance between the measuring line and the coal pillar boundary is 6 m. The floor strata subsidence with different roadway locations is shown in Figure13. Under the condition that there is no roadway in the coal pillar floor strata and roadway is arranged outside coal pillar in the coal pillar floor strata, the floor strata subsidence curves at different depths of measuring line position basically coincide, and the roadway in the coal pillar floor strata with 5.2 m outside coal pillar has little influence on the floor subsidence. The floor strata within the range of 0~3.2 m under coal pillar are the main bearing stratum. The extreme values of the subsidence of the main bearing stratum are 0.141 m, 0.144 m, 0.17 m, and 0.37 m, respectively, under the conditions of no floor roadway under coal pillar (Figure 4(b)), internal staggered roadway (Figure 12(b)), vertical roadway (Figure 12(a)), and external staggered roadway (Figure 11(a)). The subsidence is large, and the main bearing stratum has a large space for bending deformation.Figure 13
Subsidence curve of coal pillar floor strata.In the conclusion of the simulation research results, the failure patterns and locations of soft and hard stratified strata under coal pillar are different. The hard main bearing stratum under coal pillar is mainly tensile failure, and the roadway in the coal seam under coal pillar provides more deformation space for the fracture of the main bearing strata. In particular, with the condition of the roadway under the coal pillar, the main bearing stratum has obvious fracture rotation form. Under the condition of roadway layout under coal pillar and roadway layout under coal pillar boundary, the tensile failure range of main bearing stratum is larger, which makes it difficult to control the deformation of roadway surrounding rock. The soft strata failure forms under the coal pillar are mainly plastic failure. The plastic failure range of the close distance coal seam under the coal pillar is obviously larger than that of the plastic zone of the upper coal pillar. With the arrangement of the roadway in the lower coal seam, the plastic zone of the coal seam under the coal pillar is further expanded, and the plastic zone of the upper coal pillar also has a trend of increasing in different degrees.Compared with the three conditions of roadway location, roadway located under coal pillar is the most adverse to roadway surrounding rock control and has a great influence on the failure of “column-beam-column” superimposed coal pillar structure. The walls of the roadway are the plastic state as a whole, and the roadway located below the broken blocks of the main bearing stratum, which is easy to cause layer separation and large deformation of the roadway roof. Therefore, roadway layout in this position should be avoided as far as possible. The roadway located below the boundary of coal pillar is more adverse than that outside below the pillar, which has a great influence on the stability of “column-beam-column” superimposed coal pillar structure, and the roadway is closed to the fracture position of the main bearing stratum, so the surrounding rock conditions of the roadway are adverse. The roadway outside below the pillar has little influence on the deformation and destruction of the “column-beam-column” superimposed coal pillar structure, so it can have better engineering conditions outside the damage range of coal pillar’s floor strata.


## 3.1. Establishment of Numerical Simulation Model and Failure Analysis of the Coal Pillar Floor

In order to research the law of coal pillar floor failure by simulation analysis, the UDEC numerical calculation model was established according to actual production mine’s strata relationship, as shown in Figure10. The model is 517m×68m in width and height. In the actual strata relationship, the width of the remaining coal pillar of the no. 4 coal seam is 45.5 m, and the spacing between the coal pillar and the lower no. 5 coal seam is 5-7.5 m. Occurrence relation and simplified modified size of strata are shown in Figure 10 and Table 1. According to geological borehole data, different joint densities of coal and rock strata are allocated, and physical and mechanical parameters of each layer are shown in Table 1. Uniform load (-8.39 MPa) was adopted to replace the force of strata stress above the model according to the buried depth of no. 4 coal seam, and the deformation was restricted at the bottom and two sides. In the model, the deformation and failure criterion of blocks were adopted Mohr-Coulomb criterion.Figure 10
Strata distribution of numerical simulation.Table 1
Mechanical parameters of the strata.
LithologyThickness (m)Bulk modulus (GPa)Shear modulus (GPa)Cohesion (MPa)Friction (°)Tension (MPa)Sandstone3028.512.125234.5Fine sandstone3.479.128.34522.54.6Sandy mudstone4.56.174.0712302.62# coal seam0.81.320.61.215.30.7Sandy mudstone3.26.174.0712302.63# coal seam11.320.61.215.30.7Siltstone3.27.54.515.626.53.8Sandy mudstone4.56.174.0712301.64# coal seam2.11.320.61.215.30.7Siltstone3.27.54.515.626.53.83Mudstone22.51.83.321.52.35# coal seam2.21.320.61.215.30.7Fine sandstone2.879.128.34522.58.26Sandy mudstone4.86.174.0712302.6There are 3.2 m siltstone stratum and 2 m mudstone stratum between no. 4 coal seam and no. 5 coal seam. The siltstone stratum is analyzed as the main bearing hard stratum, while the lower mudstone stratum has low strength, which is used as the soft mat strata together with the no. 5 coal seam. After mining at 216 m working face on both sides of the coal pillar in no. 4 coal seam, the roof stress in goaf was transferred to the coal pillar’s position, resulting in a sudden increase of abutment pressure of coal pillar roof and a concentrated load effect on the floor. A survey line was set at 0.4 m below the coal pillar in order to measure the load stress distribution of the main bearing stratum, which was shown in Figure4(a). The failure location distribution of the strata at coal pillar boundary is shown in Figure 4(a).The load stress distribution of main bearing stratum was analyzed in Figure4(a). At the critical position (x=0) of coal pillar and goaf, the stress is greater than that of raw rock stress. The stress decreases rapidly to zero in the direction of goaf and rises rapidly to peak value in the direction of coal pillar’s center and then decreases gradually to a more stable value as it goes away from the pillar’s boundary. According to the theoretical analysis of the main bearing stratum, it is subjected to the fixed support as both ends of the beam, and the fixed support ends have strong bending moment reaction force. Therefore, it is assumed that the right fixed end of the fixed beam in theoretical calculation is at the point where the stress is equal to the original rock stress, shown in Figure 4(a). The red polyline in Figure 4(a) represents the approximate line of the stress curve. The main bearing stratum deforms under the abutment pressure and gradually generates additional force on the underlying strata. At the initial stage of the deformation process of the main bearing stratum, assuming that the reaction force of the underlying soft rock strata on the main bearing stratum is the original rock stress (γh=9.7 MPa), then the parameters in Figure 8 can be obtained in numerical simulation as follows: q1=k1−k0rh=0MPa,q2=k2−k0rh≈20.5MPa,q3=k2−k0rh=10.7MPa.After the action of coal pillar is stabilized, the failure mode and location of coal pillar’s floor strata are shown in Figure4(b). The main bearing stratum is damaged by tension, and the damage location is mainly concentrated near the stress peak under the coal pillar. The obvious open position of the block in the numerical model is shown in Figure 4(b), which is consistent with the fixed end and extreme position of bending moment of the theoretical analysis beam. The plastic zone of the 4# coal seam pillar extends from the pillar boundary to 6.5 m inside the pillar, and the plastic zone shape of the 5# coal seam is a quadrilateral extending towards to the center of the coal pillar. The horizontal distance between the plastic zone boundary and the pillar boundary is 13.4 m, which is obviously larger than the plastic zone of upper coal pillar. The plastic zone of the direct roof of 5# coal seam is not fully developed, which is a triangle with large bottom and small top, and extends towards to the tensile failure zone of the main bearing stratum.


## 3.2. The Roadway Layout and Failure Analysis of Coal Pillar Floor Strata

The roadways at three positions were arranged in the coal seam under the close distance coal pillar. The roadway width and height dimensions are4.2m×2.8m. The simulation results showed that the damage degree of the coal seams and their intermediate strata under coal pillar increased obviously after the roadway was excavated.In Figure11, the horizontal distance between the right side of roadway and the coal pillar boundary is 6.8 m. The plastic zone of the coal pillar boundary on the left side of roadway have developed to the other side of the coal pillar boundary, and the plastic zone of the coal pillar above the roadway was also divided into left and right parts. The displacement of the roadway surrounding rock is large, with the displacement of the two sides of the roadway approaching 1.2 m, and the displacement of the roof and floor approaching 0.5 m, and even the separation occurred in the roadway roof strata, and the deformation space of the main bearing stratum above the roadway is sufficient. The tensile failure range of the main bearing stratum is large and concentrated towards the plastic zone of the coal pillar boundary. The number of opening positions between the model blocks increased and the rotation form of broken blocks appears obviously, which is shown in Figure 11(b). The distance between the ends of the fracture opening angle on the left and right sides of the fracture block A of the main bearing stratum is 0.1 m, and the fracture position on the right side of the fractured block A of the main bearing stratum is near the boundary of the coal pillar.Figure 11
Failure of roadway surrounding rock under coal pillar.
(a)
Distribution of failure range(b)
Rupture location of the blocksThe second roadway location is shown in Figure12(a). The left side of the roadway and the upper coal pillar boundary are in the same horizontal position. The plastic zone of the left side of the roadway developed to 13.6 m away from the coal pillar boundary. The plastic zone of the mudstone layer under the main control rock is still located below the plastic zone boundary of the coal pillar, but the scope is slightly larger than the condition without roadway. The tensile failure of main bearing stratum range is large and scattered, and the tensile failure location is more than that in the condition without roadway. The plastic zone of coal pillar in 4# coal seam extends from the coal pillar boundary to 6.8 m in the coal pillar, and the width of the plastic zone with whole coal pillar’s high increases little, but the plastic width at the bottom of coal pillar increases greatly, extending from the coal pillar boundary to 12.6 m in the coal pillar. The deformation of the left side and left side roof of the roadway is large, with the offset of the left side being 0.3 m and the subsidence of the left side roof being 0.1 m. Therefore, the layout of roadway under the coal pillar boundary has little influence on the plastic zone range, but the large deformation of roadway surrounding rock provides more deformation space for the subsidence of hard main bearing stratum, and the plastic zone range of coal pillar tends to increase when the support conditions of coal pillar are changed by the roadway.Figure 12
Failure distribution of strata with different roadway locations.
(a)
Roadway under coal pillar boundary(b)
Roadway outside coal pillarIn Figure12(b), the roadway is in the floor strata outside the coal pillar, and the horizontal distance between the left side of the roadway and the upper coal pillar is 5.2 m. The plastic zone is 13.6 m wide from the left wall of the roadway to the coal pillar boundary, and the left wall displacement was 0.1 m. The plastic zone range of soft mat strata under the main bearing stratum was slightly larger than that under the condition without roadway, the tensile failure location of main bearing stratum and the plastic zone range of coal pillar changes little, and a small plastic zone was locally generated at the bottom of coal pillar outside the plastic zone of coal pillar boundary. Therefore, the deformation of roadway surrounding rock is small, which have little influence on the fracture and deformation of main bearing stratum and the expansion of coal pillar plastic zone.Vertical measuring line was set in the strata under the coal pillar to measure the strata subsidence at different depths. The horizontal distance between the measuring line and the coal pillar boundary is 6 m. The floor strata subsidence with different roadway locations is shown in Figure13. Under the condition that there is no roadway in the coal pillar floor strata and roadway is arranged outside coal pillar in the coal pillar floor strata, the floor strata subsidence curves at different depths of measuring line position basically coincide, and the roadway in the coal pillar floor strata with 5.2 m outside coal pillar has little influence on the floor subsidence. The floor strata within the range of 0~3.2 m under coal pillar are the main bearing stratum. The extreme values of the subsidence of the main bearing stratum are 0.141 m, 0.144 m, 0.17 m, and 0.37 m, respectively, under the conditions of no floor roadway under coal pillar (Figure 4(b)), internal staggered roadway (Figure 12(b)), vertical roadway (Figure 12(a)), and external staggered roadway (Figure 11(a)). The subsidence is large, and the main bearing stratum has a large space for bending deformation.Figure 13
Subsidence curve of coal pillar floor strata.In the conclusion of the simulation research results, the failure patterns and locations of soft and hard stratified strata under coal pillar are different. The hard main bearing stratum under coal pillar is mainly tensile failure, and the roadway in the coal seam under coal pillar provides more deformation space for the fracture of the main bearing strata. In particular, with the condition of the roadway under the coal pillar, the main bearing stratum has obvious fracture rotation form. Under the condition of roadway layout under coal pillar and roadway layout under coal pillar boundary, the tensile failure range of main bearing stratum is larger, which makes it difficult to control the deformation of roadway surrounding rock. The soft strata failure forms under the coal pillar are mainly plastic failure. The plastic failure range of the close distance coal seam under the coal pillar is obviously larger than that of the plastic zone of the upper coal pillar. With the arrangement of the roadway in the lower coal seam, the plastic zone of the coal seam under the coal pillar is further expanded, and the plastic zone of the upper coal pillar also has a trend of increasing in different degrees.Compared with the three conditions of roadway location, roadway located under coal pillar is the most adverse to roadway surrounding rock control and has a great influence on the failure of “column-beam-column” superimposed coal pillar structure. The walls of the roadway are the plastic state as a whole, and the roadway located below the broken blocks of the main bearing stratum, which is easy to cause layer separation and large deformation of the roadway roof. Therefore, roadway layout in this position should be avoided as far as possible. The roadway located below the boundary of coal pillar is more adverse than that outside below the pillar, which has a great influence on the stability of “column-beam-column” superimposed coal pillar structure, and the roadway is closed to the fracture position of the main bearing stratum, so the surrounding rock conditions of the roadway are adverse. The roadway outside below the pillar has little influence on the deformation and destruction of the “column-beam-column” superimposed coal pillar structure, so it can have better engineering conditions outside the damage range of coal pillar’s floor strata.


## 4. Simulation Test Analysis of Strata Failure under Coal Pillar in Close Distance Coal Seams

The physical similarity simulation model was established according to the distribution of the strata in numerical simulation. The similar material ratio was selected according to the mechanical parameters of the strata and experience table of similar material ratio [20], and the distribution and similar material of the strata are shown in Table 2. The geometric similarity ratio of the model is 1 : 50, and the stress similarity ratio is 1 : 67.5. The length, width, and height of the model are 1.6 m, 0.14 m, and 0.8 m, respectively. In the model, 0.9 m coal pillar was left in the no. 4 coal seam, and the roadway of the no. 5 coal seam is 0.16 m away from the coal pillar boundary.Table 2
Similar material ratio of the strata.
LithologyModel thickness (cm)Sand (kg)Cement (kg)Gaco3 (kg)Gypsum (kg)Sandy mudstone935.92.00.02.02# coal seam1.66.20.00.30.6Sandy mudstone727.91.60.01.63# coal seam27.80.00.30.8Siltstone6.425.51.10.01.7Sandy mudstone935.93.20.00.84# coal seam5.220.20.00.92.0Siltstone6.425.51.10.01.7Mudstone4.615.30.01.53.65# coal seam4.417.10.00.71.7Fine sandstone5.622.41.70.00.7Sandy mudstone14.447.90.06.49.6In order to simulate the distribution form of abutment pressure on the coal pillar, according to the law [14] of stress transfer of concentrated load in floor strata, the concentrated load was set above the coal pillar and goaf; that is, a pressure loading device was set above the coal pillar, and 28.5 kg iron was used above the goaf. The concentration degree of concentrated load in the strata gradually decreased, and the abutment pressure on coal pillar below the center of concentrated load reached the maximum and decreased to both sides. The form of abutment pressure curve is shown in Figure 14. With the increase of the concentrated load, the abutment pressure on the coal pillar also increases until the strata under the upper coal pillar are destroyed.Figure 14
Similarity simulation model design.The model strata were damaged after gradually loading from 5 kN to 30 kN through the loading of the upper oil cylinder shown in Figure14. The failure of strata under coal pillar was obviously asynchronous. The coal seam and its direct roof under the coal pillar were first destroyed and swollen due to the small strength, accompanied by the crushed coal powder falling, and then the hard rock stratum under the coal pillar appeared obvious broken blocks. As shown in Figure 15, the right end of the broken block was near the coal pillar boundary, and the initial position of the fracture was 45.5 mm away from the coal pillar boundary, and the fracture was inclined to the direction of the roadway. The upper surface of the broken block had obvious tensile angle; that is, the type of rotary failure had occurred, and the fracture was connected with the plastic failure boundary of the lower soft strata. The left end of the broken block was located below the loading position of the cylinder and 213.5 mm away from the coal pillar boundary. Vertical crack occurred at the left end of the broken block and connected with the plastic failure area below.Figure 15
Failure of strata under coal pillar.


## 5. Conclusions and Prospects

(1)
According to the structure of superimposed coal pillar in close distance coal seams, the stress distribution characteristics of coal pillar’s floor strata under the concentrated stress of upper coal pillar were analyzed, and a new failure mechanism of soft and hard strata under coal pillar has been revealed. The soft strata are destroyed first and produce large deformation, while the hard main bearing stratum is broken at the stress ultimate position with the deformation of lower soft strata(2)
Based on the main bearing stratum unbalanced forces acted by upper and lower strata, the ultimate span and fracture position of the main bearing beam were calculated by the fracture model and mechanical formula. The further deformation and movement mechanism of the floor broken blocks with roadway arranged in the lower coal seam were analyzed, and the difficulty in controlling the roadway surrounding rock under the broken block was revealed as well as the extension mechanism of the plastic zone of upper coal pillar(3)
By analyzing the results of numerical simulation and physical simulation under the real geological conditions, the asynchronous destruction with different forms and positions of the strata under coal pillar are consistent with theoretical analysis. There are risks of tensile fracture of roadway roof and increase of plastic range of superimposed coal pillar structure when roadway arranges under coal pillar and coal pillar boundary. The numerical simulation and physical simulation experiments provided analytical data and examples for theoretical analysis(4)
The fracture position of the main bearing stratum at goaf side appears in the stress reduction area outside the coal pillar boundary. Therefore, the specific position of the fixed ends in the calculation model of the main bearing beam needs to be further studied. In addition, shear failure is also one of the main forms of beam failure, which needs further study



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*Source: 2598738-2022-07-15.xml*