Stability control of goaf‐driven roadway surrounding rock under interchange remaining coal pillar in close distance coal seams

The roadway surrounding rock stability under the influence of interchange remaining coal pillar in close distance coal seams is one of the key factors affecting the coal mines safe and efficient mining. To reduce the roadway deformation, theoretical analysis, numerical simulation, and on‐site verification were used to study the influence of geological, mining, and support factors on the stability of the floor roadway surrounding rock. A design method for strengthening the roadway surrounding rock support was proposed. The results showed that the coal seam depth, the distribution characteristics of the remaining coal pillar load, the starting point position of stress recovery in the upper coal seam goaf and the lower coal seam goaf lateral load had a significant influence on the lower coal seam stress. The peak stress in the lower coal seam increased linearly with the increase of the coal seam depth, the remaining coal pillar, and the lower coal seam goaf lateral peak stress. The remaining coal pillar influence area width increased linearly and exponentially with the increase of the remaining coal pillar width and the distance between the starting point of stress recovery in goaf and the coal pillar edge, respectively. The peak stress and shear strength of the narrow coal pillar decreased exponentially with the increase of the spacing between bolts or cables. The roadway surrounding rock deformation decreased exponentially with the increase of the distance between the strengthening support area and the remaining coal pillar edge. For the Baigou coalmine, a design scheme for bolt strengthening support parameters has been proposed. The roadway surrounding rock deformation tended to stabilize after 21 days, with deformation values of 264 and 488 mm for the roof and floor, and two sides, respectively.


| INTRODUCTION
Coal is the main energy source and chemical raw material in China. 1 Close distance coal seams exist in some mines.Due to technical reasons, the upper coal seam is usually mined first, and then the lower coal seam.The mining of the overlying coal seam causes damage to the floor (roof of the lower coal seam), [2][3][4][5] and the remaining coal pillars cause stress concentration in the underlying coal rock layer, 6 both of which have adverse effects on the stability of the surrounding rock of the lower coal seam roadway.One of the keys to ensuring safe and efficient coal mining is to take rational measures to control the large deformation of the lower coal seam roadway surrounding rock.A large amount of research has been conducted on the stability control of the lower coal seam roadway surrounding rock under the influence of the remaining coal pillars.For example, the rational layout of the lower coal seam roadway, 7 support methods, 8 and methods for destroying the remaining coal pillars. 60][11] In addition, He et al. 12 analyzed the fracture of hard strata between two coal seams and concluded that there is a risk of roof tension fracture when the lower coal seam roadway is arranged under the remaining coal pillar.By determining the stability of the overall structure of the superimposed coal pillar, the rational layout of the lower coal seam roadway is obtained.Liu et al. 13 determined the rational layout of the lower coal seam roadway by analyzing the accumulation and release of energy in the roadway surrounding rock under the remaining coal pillar.However, previous studies have mainly considered the parallel layout of the lower coal seam roadway and the remaining coal pillar, with less consideration given to the interchange layout of them.Shen et al. 14 proposed a control method for the goaf retaining roadway surrounding rock based on determining the evolutionary law of roof displacement and surrounding rock stress of the roadway under the interchange remaining coal pillar.Chen et al. 15 proposed a partition differentiation combination control technology for the roadway based on determining the stress and plastic zone of the roadway surrounding rock under the interchange remaining coal pillar.
Production practice shows that, the excessive size of the coal pillar reduces the coal seam recovery rate.To improve the coal seam recovery rate, the narrow coal pillar technology has been continuously promoted. 16,17However, it is very difficult to control the narrow coal pillar stability under high-stress conditions when drilling along the goaf. 18o improve the narrow coal pillar stability, control technologies such as rational coal pillar width, 19 roof cutting pressure relief, [20][21][22][23][24] and strengthened support 25 have been proposed.7][28] In addition, Chen et al. 29 proposed filling the goaf to improve the narrow coal pillars stability.
Previously, narrow coal pillar was used for drilling along the goaf in a single coal seam.For close distance coal seams, the influence of the remaining coal pillar on the lower coal seam mining increases with the coal seam distance decrease.Especially when the remaining coal pillar intersects with the lower coal seam roadway, the mining superimposed stress field is very complex which further increases the difficulty of controlling the narrow coal pillar stability.Therefore, the stress distribution law in the lower coal seam and a design method for strengthening the narrow coal pillar roadway surrounding rock support were studied based on the engineering background of the interchange of the remaining coal pillar and the lower coal seam roadway.

| Project characteristics
To improve the coal seam recovery rate, a 5 m wide narrow coal pillar was remined between the 100,204 tailentry and the 100,202 goaf.The remaining coal pillar in No. 9 coal seam is diagonally intersected with the 100,204 tailentry.The width and height of the 100,204 tailentry are 4.8 and 3.1 m respectively.Under such conditions, the stress concentration of the remaining coal pillar and the adjacent goaf jointly affect the narrow coal pillar stability, which may lead to the narrow coal pillar instability and the 100,204 tailentry large deformation.

| Mechanical model establishment
After mining on both sides of the remaining coal pillar, due to the movement of the roof, stress concentration occurred inside the coal pillar.The load distribution on the coal pillar with different widths is inconsistent, as shown in Figure 3.In Figure 3, K 1 and K 2 are stress concentration coefficients; γ is the volume force of the rock mass, N/m 3 ; H is the coal seam depth, m.Moreover, Figure 3A,C can be regarded as special forms of Figure 3B.
Based on the linear elasticity theory, the floor is simplified as a semi-infinite body.To facilitate the solution, the nonlinear load in Figure 3B is simplified as a linear load.According to Figure 3B, a mechanical model to analyze the influence of remaining coal pillar on the lower coal seam stress distribution characteristics is established, as shown in Figure 4.In Figure 4, ξ is the distance from the load unit to the origin, m; l 1 -l 5 represent the area of linear load actions, m.
In the coordinate system shown in Figure 4, the function expression of the load q i for each segment is as follows: where, 5 .As shown in Figure 4, taking any microelement dξ, the small concentrated force F at that microelement causes the vertical stress dσ z at point A in the floor to be 1 : where, q is the linear load, MPa.By integrating Equation ( 2), it can be obtained that the vertical stress at point A under any load is: Assuming that the peak stress around the goaf after the mining of No. 10 coal seam is K 3 γH.According to the superposition principle, the vertical stress at point A is: According to the production practice experience of Baigou coalmine, the widths l 1 , l 2 , l 3 , l 4 , and l 5 of each load acting area are 0, 11, 6, 20, and 8 m.The stress concentration coefficients K 1 , K 2 , and K 3 are 3, 2.1, and 2.3.The average volume force of the overlying rock mass is 26,000 N/m 3 .According to Equation (12), Matlab is used for visual analysis of stress, as shown in Figure 5.

| The influence of remaining coal pillar on the floor stress distribution
The area between the minimum vertical stresses is considered as the remaining coal pillar influence area.The stress distribution characteristics of the lower coal seam are characterized by the maximum vertical stress σ zmax and the remaining coal pillar influence area width x a , as shown in Figure 6.
According to Equation ( 12), it can be found that the factors affecting the floor stress distribution characteristics include the coal seam depth H, the stress concentration coefficients K 1 , K 2 , and K 3 , the widths l 1 , l 2 , l 3 , l 4 , and l 5 of each load acting area.
To explore the influence of various factors on the lower coal seam vertical stress distribution under the remaining coal pillar, the control variable method is used to calculate the changes of the vertical stress distribution characteristics under the influence of a single factor, as shown in Figures 7-9.][32][33] In single factor analysis, except for the factors that need to be analyzed, the values of each factor are taken as the median.In addition, considering the actual,K 2 is not greater than K 1 , then K 2 is taken as 1.
Equations ( 3) to (12) all have a linear growth function relationship with the coal seam depth.When the burial depth of the coal seam increases from 300 to 1500 m, the maximum vertical stress increases from 28.1 to 140.7 MPa.The remaining coal pillar influence area width remains unchanged at 138.6 m.
Figure 7A shows that the maximum vertical stress and the remaining coal pillar influence area width increase linearly and logically with the increase of stress concentration coefficient K 1 , respectively.Figure 7B,C shows that the maximum vertical stress increase exponentially and linearly with the increase of stress concentration coefficient K 2 and K 3 , respectively.The remaining coal pillar influence area width does not change with the increase of stress concentration coefficient K 2 and K 3 .As the stress concentration coefficient K 1 and K 2 increase, the load of the remaining coal pillar on the floor increases.And with K 1 increases, the diffusion range  of the load in the lower coal seam increases.Therefore, the maximum vertical stress and the remaining coal pillar influence area width increase.However, compared to K 1 , the influence of K 2 on the floor stress distribution range is negligible, so the remaining coal pillar influence area width does not change with the change of K 2 .With the increase of stress concentration coefficient K 3 , the goaf lateral vertical stress in the lower coal seam increases, but the remaining coal pillar load diffusion range in the floor does not change, so the maximum vertical stress increases, and the remaining coal pillar influence area width remains unchanged.
Figure 8 shows that the maximum vertical stress increases logarithmically with the increase of x 2 and x 3 , but it does not change with the increase of x 1 , x 4 , and x 5 .The remaining coal pillar influence area width increases linearly with the increase of x 1 , x 2 , and x 3 , it increases exponentially with the increase of x 4 , and it increases logarithmically with the increase of x 5 .With the increase of x 1 , the load influence area on the floor increases, but the influence on the floor stress directly below the remaining coal pillar is small.Therefore, the maximum vertical stress in the lower coal seam remains unchanged, and the remaining coal pillar influence area width increases.With the increase of x 2 and x 3 , the load influence area on the floor increases.According to the principle of stress superposition, the floor stress directly below the remaining coal pillar increases, so the maximum vertical stress and the remaining coal pillar influence area width increase.With the increase of x 4 and x 5 , the goaf load influence on the floor vertical stress directly below the remaining coal pillar becomes less and less, the influence of remaining coal pillar load on floor stress is becoming increasingly significant, resulting in the increase of the remaining coal pillar influence area width.
The range method is used to analyze the degree of influence of various factors on the lower coal seam vertical stress distribution characteristics, as shown in Table 1.
From Table 1, it can be seen that the influence of coal seam depth H, stress concentration coefficients K 1 and K 3 on the maximum vertical stress is relatively significant.The degree of influence is ranked in descending order as H, K 3 , and K 1 .The influence of the load zone x 1 , x 2 , x 3 , and x 4 on the remaining coal pillar influence area width is relatively significant.The degree of influence is ranked in descending order as x 1 , x 2 , x 4 , and x 3 .

| Support method and strength
Pre-tensioned anchoring support is one of the main methods for supporting roadways. 34The development of coal pillar cracks along the goaf leads to poor integrity and low support strength. 35Improving the bearing capacity of coal pillar can effectively control roof deformation. 36Therefore, improving the narrow coal pillar stability is one of the keys to controlling the roadway surrounding rock stability.Under high stress, coal pillar generally exhibits shear failure, so it is necessary to improve the coal pillar shear strength.
According to the Mohr Coulomb strength criterion, cohesion and internal friction angle are indicators that characterize the shear strength of rock mass shear strength.Under the anchoring influence, the equivalent cohesion c' is 37 : the equivalent internal friction angle φ' is 37 : where, c is the coal mass cohesion; φ is the coal mass internal friction angle, °; r b is the bolt or cable radius, m; σ t is the bolt or cable tensile strength, MPa; s l and s c are the axial and circumferential spacing of bolt or cable along the roadway, m; α is the bolt or cable density factor: where, R is the roadway width, m; and η is the friction coefficient between bolt(cable) and rock mass.When the threaded bolts are adopted, η = tanφ; otherwise, η = tan(φ/2).
The interaction relationship between the bolt(cable) and the surrounding rock is shown in Figure 9.In Figure 9, L is the anchoring section length, m; Z is the free section length, m; R b is the drilling radius, m; p(z)is the bolt or cable axial force, kN.
After applying the pretension, assuming that the rock mass and bolt(cable) are well combined and there is no interface slip, the axial displacement of the bolt(cable) is expressed as 38 : ( ) where, u is the bolt(cable) axial displacement, m; k is the shear stiffness between bolt(cable) and rock mass, GPa/ m.The axial force and displacement of the bolt(cable) have the following relationship: ( ) Assuming the pretension is P.There are boundary conditions p(z = Z) = P and p(z = Z + L) = 0. Solving Equation ( 16) and Equation ( 17), there is: where, ( ) The effect of anchor pretension on the equivalent cohesion of coal mass is shown in Equation ( 19) 38 : By combining Equation ( 18) and integrating Equation ( 19), the equivalent cohesion of coal mass under pre tension is obtained as Equation ( 20): From the above analysis, it can be seen that the cohesive force of the anchored rock mass is: The narrow coal pillar undergoes plastic yielding under high stress, so the coal mass cohesion at this location is residual cohesion, which is approximately 30% of the coal mass cohesion. 39Similarly, the residual internal friction angle is approximately 60% of the coal mass internal friction angle. 40,41he vertical stress in the narrow coal pillar is related to the cohesion and internal friction angle as follows: where, f is the friction coefficient of coal seam roof and floor; m is the roadway height, m.The rational anchoring parameters can be determined by obtaining the required stress of the coal pillar through Equation ( 22).
In the Baigou coalmine, the coal mass cohesion is 0.24 MPa, the coal mass internal friction angle is 39°.
The radius of the bolt and cable is 0.011 m, the tensile strength of the bolt and cable is 500 and 1350 MPa respectively, the elastic moduli of bolt and cable are 210 and 190 GPa, respectively.The shear stiffness between bolt (cable) and rock mass is 4.6 GPa/m.The pretension of the bolt and cable are 22 and 180 kN, respectively.The friction coefficient of coal seam roof and floor is 0.2.The maximum vertical stress, equivalent cohesion and internal friction angle variation curves of the narrow coal pillar with different bolt and cable spacing are shown in Figures 10 and 11.
Figures 10 and 11 show that the maximum vertical stress, equivalent cohesion, and equivalent internal friction angle decrease exponentially with increase of bolt and cable spacing.The influence of cables on equivalent cohesion is relatively significant.The effect of bolts on the equivalent internal friction angle is relatively significant.
According to Equation ( 22) and the initial roadway support parameters below the No. 9 coal seam goaf, considering the stability and economic benefits of the coal pillar, the strengthening support plan is shown in Figure 12.The maximum vertical stress in the narrow coal pillar is 3.7 MPa, which meets the requirements.
Based on the mining and geological conditions of the No.After reaching the initial equilibrium of the model, the No. 9 coal seam is first excavated for 10 m each time.After excavation, the goaf is filled to simulate stress recovery in the goaf.After the No. 9 coal seam goaf stabilizes, excavate the 100,202 working face for 10 m each time, and fill the goaf after excavation.Finally, drilling 100,204 tailentry along the goaf.In the model, the Strain-softening model is used for the coal seam, mudstone layer, and sandy mudstone layer.The Mohrcoulomb model is used for the limestone layer.The double yield model is used for the goaf gangue.The physical and mechanical parameters of the rockiness are shown in Table 2.The cap pressure of goaf gangue is shown in Table 3.
The comparison of the calculation results between the numerical model and the theoretical model is shown in Figure 14. Figure 14 shows that the numerical model has good consistency with the theoretical model, therefore the numerical model is reliable.
Figure 14 shows that the influenced area of the lower coal seam roadway exceeds the remaining coal pillar edge.Set up the strengthening support area that exceeds the remaining coal pillar edge by 0, 8, 16, 24, 32, and 40 m, and analyze the influence of the strengthening support area on the roadway surrounding rock deformation.The displacement of the roadway surrounding rock is shown in Figure 15.The variation of the convergence of the roof and floor, two sides of the roadway with the distance between the strengthening support area and the remaining coal pillar edge is shown in Figure 16.In Figure 16, the symbol con represents the roadway surrounding rock convergence, and the symbol l d represents the distance between the strengthening support area and the remaining coal pillar edge.
Figures 15 and 16 show that the convergence of the roof and floor, the convergence of the two sides decrease exponentially with the distance between the strengthening support area and the remaining coal pillar edge.When the distance between the strengthening support area and the remaining coal pillar edge exceeds 16 m, the deformation of the roadway surrounding rock is basically no difference.
Based on Figures 14 and 16, it can be seen that the minimum vertical stress point is 13 m away from the remaining coal pillar edge, which is not significantly different from 16 m.Therefore, it can be determined that the strengthening support area is the remaining coal pillar influence area.

| VERIFICATION
According to the analysis in Section 4.2, the 100,204 tailentry was ultimately selected the distance between the strengthening support area and the remaining coal pillar edge is 20 m.The support method is a combination  To verify whether the roadway supporting parameters are rational, the cross point method is used to monitor the surface displacement of the roadway during drilling.The monitoring results are shown in Figure 17.
Figure 17 shows that the deformation rate of the surrounding rock within 12 days of the roadway drilling is relatively high, and the deformation tends to ease within 12-21 days.After 21 days, the deformation of the roadway tends to stabilize, with a maximum displacement of 488 mm for two sides and 264 mm for the roof and floor.The convergence of roadway surrounding rock is within the safe range, which means that the strengthening support parameters can meet the needs of surrounding rock control.
The stress equation of the lower coal seam under the remaining coal pillar was derived, and the influencing factors on the stress distribution characteristics of the lower coal seam were obtained.
The influence of coal seam depth, remaining coal pillar peak stress, and the lower coal seam goaf lateral peak stress on the lower coal seam peak stress is relatively significant.As the coal seam depth, the remaining coal pillar peak stress, and the goaf lateral peak stress increase, the lower coal seam peak stress increases linearly.
The influence of the remaining coal pillar width and the distance between the starting point of stress recovery in upper coal seam goaf and the coal pillar edge on the remaining coal pillar influence area width is relatively significant.As the remaining coal pillar width and the distance between the starting point of stress recovery in upper coal seam goaf and the coal pillar edge increase, the remaining coal pillar influence area width increases linearly and exponentially, respectively.
The vertical stress and shear strength of the narrow coal pillar decrease exponentially with the increase of bolt or cable spacing.The convergence of the roadway surrounding rock decreases exponentially with the increase of the distance between the strengthening support area and the remaining coal pillar edge.
The design method of bolt(cable) support parameters based on the remaining coal pillar influence area and the anchored coal mass peak stress is proposed.And conduct verification in Baigou coalmine.On-site monitoring shows that the deformation of the surrounding rock tends to stabilize after 21 days, with the maximum convergence values of 264 mm and 488 mm for the roof and floor, and two sides, respectively.
Baigou coalmine is located in Jinzhong, Shanxi Province, China.The mining coal seams are No. 9 and No. 10 coal seams, with an average thickness of 1.3 and 4.3 m, respectively.The average spacing between the two coal seams is 5.7 m.The lithology of the coal roof and floor is shown in Figure 1.The average inclination of the coal seams is 6°.The 100,204 working face is mining the No. 10 coal seam, with a maximum depth of 423 m.The No. 9 coal seam has been mined out, leaving a 17 m wide coal pillar above the 100,204 working face.The angle between the remaining coal pillar and the 100,204 tailentry is 30°.The schematic diagram of the 100,204 working face neighboring relationship is shown in Figure 2.

F I G U R E 2
The schematic diagram of the 100,204 working face neighboring relationship.F I G U R E 3 The load distribution on coal pillar: (A) Wide coal pillar; (b) medium coal pillar; (c) narrow coal pillar.

F I G U R E 5
The floor vertical stress distribution under the remaining coal pillar.

F I G U R E 6
The lower coal seam stress distribution characteristics.

F I G U R E 7
The variation of lower coal seam vertical stress distribution characteristics with stress concentration coefficients: (A) K 1 ; (B) K 2 ; (C) K 3 .

F I G U R E 8
The variation of lower coal seam vertical stress distribution characteristics with the load acting area: (A) x 1 ; (B) x 2 ; (C) x 3 ; (D) x 4 ; (E) x 5 .

T A B L E 1 F
Range of the maximum vertical stress and the remaining coal pillar influence area width.I G U R E 9 Analytical model of anchoring-grouting rock mass.

F
I G U R E 10 The variation of maximum vertical stress in the narrow coal pillar with support spacing: (A) bolt; (B) cable.

(
9 and No. 10 coal seams in Baigou Coal Mine, a FLAC3D numerical model was established, as shown in Figure 13.The model size is 310 × 399.4 × 89.1 m.Apply simple support constraints around the model, fixed support constraints at the bottom, and pressure of 9.2 MPa at the top.Considering the influence of horizontal in-situ stress on the surrounding rock stability 42 and the influence of burial depth on the ratio λ of horizontal in-situ stress to vertical in situ stress, λ is set to 1.1. 43F I G U R E 11 The variation of equivalent cohesion and internal friction angle of the narrow coal pillar with support spacing: (A) bolt; (B) cable.F I G U R E 12 Cross section diagram of the roadway support: (A) Initial support; (B) strengthening support.F I G U R E 13 Numerical model.

F
I G U R E 14 The comparison of the calculation results between the numerical model and the theoretical model.F I G U R E 15 The displacement of the roadway surrounding rock: (A) 0m; (B) 8m; (C) 16m; (D) 24m; (E) 32m; (F) 40m.F I G U R E 16 The variation of the convergence of the roof and floor, two sides of the roadway with the distance between the strengthening support area and the remaining coal pillar edge. of bolts and cables support.The cross-section diagram of the roadway support is shown in Figure 12B.
Physical and mechanical parameters of the rockiness.Cap pressure of goaf gangue.
T A B L E 2