Study of the influence of coal column width on the stress-fracture-displacement evolution law in sequential coal seam mining

Abstract

The connectivity of the fissures in the adjacent air section represents a crucial foundation for the deployment of surface gas extraction drill holes in abandoned mines. To elucidate the impact of coal column width on overlying rock movement and fissure development in adjacent mine openings, a theoretical derivation and discrete element simulation approach was employed, utilizing the 8# coal seam in Baode Mine as a case study. The results demonstrate that, as a consequence of mining activities, the stress within the overlying rock layer of the mining area exhibits a distinctive pattern, comprising four distinct phases: concentration-unloading(yielding)-recovery-unloading-concentration. This pattern is observed to intensify with increasing coal column width. The elastic region in the center of the segmental coal column begins to appear as the width of the coal column increases. In addition, the vertical stress curve undergoes a transition from a single-peaked to a double-peaked configuration. Furthermore, the peak of the stress value demonstrates a decline in both velocity and magnitude. The peak stress value demonstrates a decelerating and decreasing trend. The coal column in the section transitions from a completely unstable state to a stable state in a gradual manner. The connectivity between the adjacent mining areas shifts from a completely through state to a gradually closed state. The sinking amount of the coal column in the section decreases from 2.56 m in the unstable state to 0.49 m in the 30 m width and exhibits a tendency towards stability. The findings of the theoretical derivation and simulation analysis suggest that the optimal width for coal columns in the section is approximately 20–25 m.

Introduction

Coal as an important energy source in China will always occupy the main position of China’s energy system long into the future^1,2, in the context of China’s high demand for coal resources, with the high-intensity, high-efficiency mining of coal, left more and more of the air mining area, the air mining area is facing the stability of the coal column in the long term is poor, gas along the fractures gushed to the bottom and other difficulties come one after another^3,4,5. However, the complex gas storage and transportation space is formed by the interconnection of section coal columns and interlayer mining fractures, and the accurate assessment of the interconnection characteristics between mining areas is an important basis for analyzing the gas accumulation and transportation in mining areas, and maintaining the stability of coal columns in mining areas^6,7. Therefore, by analyzing the load-bearing capacity, the structure of the overburden and the movement law of the coal column between adjacent faces under the conditions of different widths of the coal column sections, and then optimizing the reserved size of the coal column sections and clarifying the connection characteristics between the airspace zones, We can not only ensure the stability of the airspace zones by supporting the overburden pressure, but also block the diffusion of gas in the airspace zones and reduce the influence of the gas from the adjacent airspace zones on the gas of the face, to ensure the safety and high efficiency of mining. Safe and efficient mining of the working face.

In view of the diversity and complexity of the causes of coal column destabilization, the fissure patterns caused by mining activities in different geological environments show differences. Many scholars have carried out extensive and in-depth research on the destabilization mechanism of coal pillars, the stability evaluation, and the characteristics of the movement and destruction of the rock strata above the mining area, and have achieved remarkable research results. Han et al.⁸, Zheng and Liu⁹ established the formula for calculating the width of the plastic zone in coal seams around the mining cavity, the evolution law of different areas of the coal column and the surrounding stress field, and the development of the plastic zone. Liu et al.¹⁰, Wu et al.¹¹ established a non-uniform superimposed stress model of coal column and a model of intersegmental peripheral rock instability based on the mechanism of peripheral rock destabilization, which revealed the destabilizing situation and the nature of deformation of coal column and peripheral rock in the segment. Chen et al.¹² revealed the coupling characteristics of internal stress field, plastic zone and seepage zone of zonal coal column under different influences by establishing a numerical model of waterproof coal column flow-solid coupling.

Qin and Xu¹³, Ju and Xu¹⁴ studied the fracture development characteristics of the overlying rocks and analyzed the breakage mechanism of the top rock layer. Yi et al.¹⁵, Tan et al.¹⁶ analyzed the stability conditions for the formation of a “masonry beam” structure and proposed a method for calculating the height of the hydraulic fracture zone from the critical fracture of a rock formation. Yu et al.¹⁷ pointed out that the overburden fissure development after coal seam mining was distributed in a U shape, and the height of fissure development near the coal wall was obviously larger than that in the center of the mining area. Li et al.¹⁸ established a surface subsidence trajectory model for working face back mining. Lin et al.¹⁹, Ding et al.²⁰ analyzed the fissure evolution law of overburden under different mining heights, advancing speeds, and inclination angles of coal seams, and accurately identified the overburden unloading gas transport storage area along open-cut mining. Wang et al.²¹, Ju et al.²² analyzed the effect of cleavage on the strength and engineering stability of the rock mass and the stress change and compressive deformation of the top and bottom rock layers.

Based on the above analysis, this study conducts a large number of experiments on different rock bodies based on field research, theoretically analyzes the destabilization mechanism of the coal pillar in the section according to the experimental parameters, and constructs a three-dimensional physical model in combination with the actual geological conditions, analyzes the force characteristics and damage evolution rules of the coal column and the overlying rock of the mining area under the width of the coal pillars in different sections, and then optimizes the coal column dimensions in the section, which is an important theoretical guide for the working face where the geological conditions are similar. This research result provides important theoretical guidance for mine coal safely and efficiently.

Engineering background

This study takes 81308 working face and 81309 working face in 8# coal seam of Baode Mine as the background. Both workings are located in the three-pan area of Baode Mine. The 81308 tunnel is north of the No. 2 main auxiliary roadway, south of the well field boundary, and east and west are 81307 tunnel and 81309 tunnel, respectively. The width of 81308 and 81309 adits is 200 m, and the advance lengths are 2489.5 m and 2552 m, respectively. The coal and rock seams are generally oriented nearly north–south, with an average thickness of 6.02 m. The structure is simple and stable, with a single type of coal. The average coal seam thickness is 6.02 m and the coal type is single, simple and stable. The average thickness is 6.02 m, and the structure is simple and stable. The comprehensive histogram of coal seams is shown in Fig. 1.

Fig. 1

Comprehensive histogram of coal seams.

Theoretical analysis and computational derivation

Mechanical analysis of coal column stability in sections

In the process of coal seam face mining, the sectional coal column will successively pass through the process of pre-mining, one-sided face mining and two-sided face mining, and in the different stages of coal seam face mining, the sectional coal pillar has different stress distribution characteristics. However, the stress distribution characteristics of the coal column are also affected by reserving different widths. When the working face at either side of the coal column is mined out, the fissure morphology characteristics after the collapse and stabilization of the overlying rock strata in the mining cavity are shown in Fig. 2, and this paper analyzes the stress state suffered by the sectional coal pillar under different widths.

Fig. 2

Schematic diagram of the collapse of the overburden structure of the mining area on both sides of the coal column in the section.

The stress on the coal pillar in the cross section is caused by the gravitational transfer of the overburden structure load and the gravitational transfer of the rock load directly above the coal body. It is generally believed that a coal pillar can be stabilized as long as the supporting stresses to which it is subjected remain below its ultimate load-carrying capacity. As shown in Fig. 3, the elastic–plastic deformation region and stress distribution characteristics of coal pillar with large width, medium width and small width of coal pillar are shown, in which the original rock stress of the coal pillar is γH, the peak vertical stress is KγH, H is the depth of the buried coal seam, K is the stress concentration coefficient above the coal pillar, it is the average capacity of the rock layer overlying the coal pillar.

Fig. 3

Schematic diagram of elastic–plastic region and stress distribution for different coal column widths. (a) In the case of a large width of the coal column. (b) In the case of a medium width of the coal. (c) In the case of a smaller width of the coal column.

As the width of the reserved section coal column increases, the phenomenon of stress concentration occurs on both sides of the coal column. The supporting stress curve assumes a hump shape, and the two ends of the coal column are damaged by the effect of stress concentration. This results in the formation of a further rupture zone and plastic zone. The stable area situated between the stress peaks on either side is designated as the elastic area, wherein the stress on the coal column gradually returns to the original rock stress.

When the width of the coal column is moderate, the peak stress curves on both sides of the column are bimodal, and the stresses in the center of the column are close to the original rock stresses or slightly larger than the original rock stresses due to the phenomenon of stress superposition. As the width of the coal column is gradually reduced, the elastic region in the center of the coal column is correspondingly reduced.

When the width of the coal column is small, the stress distribution curve shows a “saddle” shape. Stress superposition occurs in the center of the column due to the stress concentration in the overburden, and the stress value increases sharply. Concurrently, the stress concentration peaks on both sides of the coal column also increase, causing the elastic region to shrink. As the width of the coal column continues to decrease, the elastic region in the center of the coal column may disappear completely. Once the supporting stress of the coal column exceeds its ultimate load-bearing capacity, the phenomenon of destabilization damage will occur.

Theoretical derivation of coal column width in sections

Matsuoka and Nakai proposed the SMP damage criterion in 1974 based on the theory of space sliding surfaces, which overcomes the singularity of the Mohr–Coulomb yield criterion in the deviatoric plane and the equivalence of the compressive strength of the Drucker-Prager criterion, and also takes into account the effect of the mean principal stresses^23,24. Matsuoka In order to make the SMP criterion applicable in materials with cohesion, the cohesive stress is added to the standard equation to form the extended SMP criterion as shown in Eqs. (1) to (3):

$$\begin{aligned} & \frac{{\sigma_{1} + \sigma_{0} }}{{\sigma_{3} + \sigma_{0} }} = \frac{1}{4}\left( {\sqrt K + \sqrt {K - 3 - 2\sqrt K } - 1} \right)^{2} \\ & K = 8\tan^{2} \varphi + 9 \\ & \sigma_{0} = c\cot \varphi \\ \end{aligned}$$

(1)

where $\sigma_{1}$ and $\sigma_{3}$ are the maximum and minimum principal stresses within the coal column cell, $\sigma_{0}$ is bonding stress, $\varphi$ is angle of internal friction, $c$ is cohesive force of the material.

The horizontal stress and vertical support pressure can be both uniformly distributed, the coal seam mining height is M, in the section of the coal column arbitrarily take the width of the unit, the unit limit equilibrium force characteristics as shown in Fig. 4.

Fig. 4

Schematic diagram of limit equilibrium force analysis of coal column unit body.

When the coal pillar unit reaches limit equilibrium conditions $\sum {F_{x} } = 0$, Simplification yields Eq. (4):

$$2\left( {\sigma_{y} f + c} \right) - M\frac{{d\sigma_{x} }}{dx} = 0$$

(2)

where $\sigma_{x}$ is vertical support pressure, $\sigma_{y}$ is horizontal stress, $f$ is coefficient of internal friction.

As the plastic zone area to obtain the section of coal columns follow the SMP yield criterion, according to the Eq. (1) can be organized to obtain the Eq. (5)

$$\begin{aligned} & In\left( {\sigma_{y} f + c} \right) = \frac{2Af}{M}x + E \\ & A = \frac{1}{4}\left( {\sqrt K + \sqrt {K - 3 - 2\sqrt K } - 1} \right)^{2} \\ \end{aligned}$$

(3)

where E is a constant.

When the limit equilibrium boundary condition x = 0, the gangue constraint stress on the coal column $P_{a} = \sigma_{x}$, brought into the above equation to obtain Eq. (4):

$$\sigma_{y} = e^{{\frac{2Af}{M}x}} \left( \begin{gathered} \frac{c}{f} + A\sigma_{0} + AP_{a} \hfill \\ - \sigma_{0} \hfill \\ \end{gathered} \right) - \frac{c}{f}$$

(4)

When the support pressure reaches the maximum value $\sigma_{y} = K^{\prime } \gamma H$, x = X₀ is the width of the rupture zone and plastic zone on one side of the coal column, which is brought into Eq. (4) to get Eq. (5).

$$X_{0} = \frac{M}{2Af}In\frac{{c + fK^{\prime } \gamma H}}{{c + f\left( {A\sigma_{0} + AP_{a} - \sigma_{0} } \right)}}$$

(5)

Considering the almost symmetrical distribution of the support stress in the elastic region of the coal column in the section, in order to simplify the research process, half of the elastic region of the coal column in the section is selected as the object of analysis, and its mechanical model is shown in Fig. 5. $\sigma_{y}$ is support pressure. The supporting pressure is assumed to be uniformly distributed along the thickness of the coal seam, and the supporting pressure distribution curve is approximated as a quadratic curve in the form of Eq. (6):

$$\sigma_{y} = Ax^{2} + Bx + C$$

(6)

Fig. 5

Schematic stress distribution in the elastic region of the middle part of the coal pillar.

The maximum and minimum stresses in the original rock are known from the bearing pressure distribution curve. When $x = 0$, $\sigma_{y} = K^{\prime } \gamma H$, the original rock stress curve is the minimum. When $x = L$, $\sigma_{y} = - \gamma H$, the original rock stress curve is the maximum. Derivation of x in equation and final collation gives Eq. (7).

$$\begin{aligned} A & = \frac{{\left( {1 - K^{\prime } } \right)\gamma H}}{{L^{2} }} \\ B & = 2\frac{{\left( {K^{\prime } - 1} \right)\gamma H}}{L} \\ C & = - K^{\prime } \gamma H \\ \end{aligned}$$

(7)

According to the elasto-mechanical functional relationship, and the complex dual harmonic function whose fourth-order mixed partial derivatives are zero, assuming that Eq. (8) holds.

$$\begin{aligned} \Phi & = \frac{1}{12}Ax^{4} + \frac{1}{6}Bx^{3} + \frac{1}{2}Cx^{2} \\ & \quad + x\left( {Dy^{3} + Ey^{2} + Fy + G} \right) + Qy^{4} \\ & \quad + Ry^{3} + Iy^{2} + Jy + N \\ \end{aligned}$$

(8)

A partial derivation of Eq. (8) yields the stress component as Eq. (9).

$$\begin{aligned} \sigma_{x} & = \frac{{\partial^{2} \Phi }}{{\partial y^{2} }} = 6Dxy + 2Ex + 12Qy^{2} + 6Ry + 2I \\ \sigma_{y} & = \frac{{\partial^{2} \Phi }}{{\partial x^{2} }} = Ax^{2} + Bx + C \\ \sigma_{{{\text{x}}y}} & = - \frac{{\partial^{2} \Phi }}{\partial x\partial y} = - \left( {3Dy^{2} + 2Ey + F} \right) \\ \end{aligned}$$

(9)

Since $\sigma_{x}$ does not vary with the position of $y$, $D = Q = R$, $\sigma_{x} = 2Ex + 2I$.When $x = 0$, $\sigma_{x} = - \lambda K^{\prime } \gamma H,$ when $x = L$, $\sigma_{x} = - \lambda \gamma H$. Due to the symmetry of the shear stresses at the contact surfaces of the top and bottom plates of the coal column, $- \sigma_{xy} = \sigma_{xy}$. The components of E and I can be obtained, and the expressions for A, B, C, D, and E are each substituted into the expression for the stress components to obtain Eq. (10).

$$\begin{aligned} \sigma_{x} & = \frac{{\lambda (K^{\prime } - 1)\gamma H}}{L}x - \lambda K^{\prime } \gamma H \\ \sigma_{y} & = \frac{{(1 - K^{\prime } )\gamma H}}{L}x^{2} + \frac{{2\left( {K^{\prime } - 1} \right)\gamma H}}{L}x - K^{\prime } \gamma H \\ \sigma_{xy} & = \frac{{\lambda \left( {K^{\prime } - 1} \right)\gamma H}}{L}y \\ \lambda & = \tan^{2} \left( {\frac{90 - \phi }{2}} \right) \\ \end{aligned}$$

(10)

where $\lambda$ is the pressure measurement factor.

The component expression is brought into the maximum value formula, and the stress reaches the maximum value when $x = 0$ or $y = M/2$, the length of the elastic region in the middle of the coal column can be obtained by organizing the formula according to the SMP criterion as shown in Eq. (11).

$$L = \frac{{\lambda \left( {K^{\prime } - 1} \right)\gamma HM}}{{2\sqrt {\left( {\frac{A - 1}{{A + 1}}} \right)^{2} \left( {\sigma_{0} - \frac{{(1 + \lambda )K^{\prime } \gamma H}}{2}} \right)^{2} - \left( {\frac{{(1 - \lambda )K^{\prime } \gamma H}}{2}} \right)^{2} } }}$$

(11)

Through the results of the experiments on the physical and mechanical parameters of the 8# coal seam in Baode Mine and the relevant data provided by the mine, as shown in Table 1, the parameters are substituted into the above formula, and the elastic region 2L of the coal column in the section is calculated to be 8.42 m, and the plastic region X₀ on the side of the coal column is calculated to be 5.44 m, in summary, the reasonable width of the coal pillar in the section is 19.3 m. The appropriate width for the coal column in this section is 19.3 m.

Table 1 Physical–mechanical parameters made by the Baode 8# coal seam.

Numerical simulation of structural evolution of overburden

Underlying assumption

In order to simplify the research process and better match the results with the actual situation, the following assumptions must be made^25,26,27: the basic unit of the numerical model of particle flow is the round sphere of the rigid body; the contact area between the particles and the particles is relatively small, and the point contact is the contact mode; the particles will produce a certain degree of overlap after being subjected to the force, and the amount of overlap is very small compared to the diameter of the particles; the bonding model of different shapes is established by the mutual contact of the particles, and the bonding strength of the contact area is not consistent with the other areas. Mutual contact to model the bonding of different shapes, the bond strength of the contact area is not consistent with other areas.

Modeling and parameter selection

The numerical model was established according to the actual geological conditions of Baode coal mine as shown in Fig. 6, the model is 550 m long and 160 m high, the width of the model is set to 20 m for the convenience of calculation, and there are 20 seams from bottom to top, the bottom is the 1st seam and the top is the 20th seam. The No. 8 coal seam is in the 8th seam, and there are two workings, 81308 and 81309. This simulation only simulates the 135.9 m overburden layer above the 8# coal seam, and there is a 195.7 m overburden layer above the model that cannot be simulated. By compensating for the uniform load q instead of the gravity of the overburden rock that is not built out of the model, the calculation shows that a stress load of 3.9984 MPa is applied on top of the model.

$$q = \sum_{i = 1}^{20} {\gamma_{i} H_{i} }$$

(12)

where γ is the average bulk weight of the modeled overburden; H is the thickness of the un-modeled overburden layer, m.

Fig. 6

Numerical simulation model diagram.

When simulating and solving practical engineering problems, selecting the accurate microscopic parameters is essential. In this paper, the macroscopic physico-mechanical parameters of each coal rock layer were obtained through a large number of experiments, and the empirical formula method was used to convert the macroscopic mechanical parameters into the corresponding microscopic parameters. Table 2 presents a summary of the macroscopic and microscopic physico-mechanical parameters observed in coal rock layers.

Table 2 Macro and fine scale physical and mechanical parameters of coal seams.

Excavation program and monitoring point placement

81308 working face and 81309 working face are set up in 8# coal seam, because the simulation results are affected by the boundary effect of the model, the left and right sides of the model are left with a certain width of coal columns not to be mined back, and the middle 200 m of the working face is used to simulate the excavation process, and different widths of coal columns are left between the two working faces. In order to more accurately analyze the stress distribution, subsidence pattern and fracture development characteristics of the overlying rock layer with different excavation distances, monitoring points are set on the numerical model, the interval of horizontal monitoring points is 10 m and the interval of upper and lower monitoring points is 20 m, and the locations of the monitoring points are shown in Fig. 7.

Fig. 7

Schematic diagram of monitoring points.

Simulation results and analysis

In the process of successive mining of the same coal seam, the width of the reserved coal pillar directly affects the force distribution and structural deformation of the overlying rock layer and the bottom plate in the mining area. The width of the coal pillar is crucial for the stability of safe mining in the working face. Utilizing a theoretical derivation of the results, an analysis is conducted on the movement law and distribution characteristics of the overlying rock layer and the coal pillar of the section by establishing the section coal pillar with lengths of 10, 15, 20, 25 and 30 m. Consequently, the movement and distribution characteristics of the overlying rock layer and section coal pillar are analyzed through the theoretical derivation of the results.

Stress distribution law of overburden rock under different width coal column

As the 81308 working face advances, the original stress equilibrium state of the overlying rock layer exceeds its own load limit for the second stress distribution. Upon stabilization, the stress equilibrium state after the second stress distribution is redistributed to reach a new equilibrium state once more. However, the protective effect of the section coal column between adjacent mining areas is influenced by its width. The stress distribution characteristics of the overlying rock of the mining area are analyzed through different section coal pillars.

Figure 8 shows the stress distribution within the overburden rock as influenced by different widths of coal columns, from which it can be seen that when 15 m, 20 m, 25 m and 30 m widths of coal columns are reserved, the coal columns are subjected to larger stresses under the influence of stress concentration. As the width of coal columns increases, the stress concentration areas at their extremities are successively separated, resulting in a distribution of stress that is minimal in the central region and maximal at the two ends. The stress on the coal column section decreases rapidly when the coal column width is 10 m, which indicates that the stress carried by the coal column of 10 m width has exceeded the ultimate strength of the coal column itself and led to the destabilization phenomenon of destructive deformation, and the coal column section is in the state of complete destruction.

Fig. 8

Stress distribution of overburden rock with different widths of coal columns in reserve. (a) 10 m section coal column. (b) 15 m section coal column. (c) 20 m section coal column. (d) 25 m section coal column. (e) 30 m section coal column.

Quantitative analysis of the vertical stress distribution law of overburden rock under different coal pillar widths is shown in Fig. 9. As illustrated in the figure, the stress concentration phenomenon manifests on both sides following the stabilization of the two adjacent mining voids. However, the stress peaks at the left end of the 81308 mining void and the right end of the 81309 mining void are smaller than the stress. This phenomenon can be attributed to the repeated mining influence on the coal and rock columns between the two mining voids, which serve as a support for the overburden loading of the two mining voids and the load of the rock body directly above them. It is evident that the higher the position of the overburden rock, the lower the stress experienced, and the smaller the concentrated stress observed on both sides. When a 10-m wide section of coal pillar is reserved, the instability of the coal pillar leads to less stress concentration on the pillar and the rock layer above it, and the concentrated stress on the bottom plate of the coal seam is greater than that on the overlying rock above the pillar. As the width of the coal pillar increases to 20 m, the support capacity of the coal pillar increases, and the instability of the coal pillar disappears gradually. As the width of the coal pillar increases further, the stress superposition area of the coal pillar in the section is gradually separated, leading to a reduction in the concentrated stress on the coal pillar. The stress change of the overlying rock layer in the mining hollow area exhibits a trend of stress concentration, stress relief, stress recovery, stress relief, stress concentration. The stress change of the collapsed overlying rock on the upper side lags behind the stress change of the overlying rock on the lower side. Consequently, the stress distribution of the overlying rock layer in the mining zone exhibits discernible stage characteristics, accompanied by temporal differences in the stress change of the overlying rock at varying locations.

Fig. 9

Stress distribution of overburden rock with different widths of coal columns in reserve. (a) 10 m section coal column. (b) 15 m section coal column. (c) 20 m section coal column. (d) 25 m section coal column. (e) 30 m section coal column.

In order to further analyze the force on the coal column in different zones, the force process is shown in Fig. 10. As illustrated in figure, in the case of a 10-m-wide column, the stress on the column first increases to its ultimate strength, which is about 42 MPa. As the simulation progresses, the stress on the column continues to increase until it exceeds its ultimate strength. At this point, the column is completely destroyed and destabilized. After that, the stress on the coal column decreases rapidly and is about 14.3 MPa when the top layer of rock is stabilized. When a 15-m wide section is reserved for the coal column, the ultimate strength of the coal column is about 44.1 MPa, although the stress borne by the coal column exceeds its ultimate strength, the coal column is in a partially destructive state and still has some bearing capacity and protective effect, and the stress value after stabilization is about 35.6 MPa. When a 20 m wide section is reserved for the coal column, the stress carried by the coal column does not exceed its ultimate strength, at this time, the coal column is in a completely destructive state and destabilization occurs. In the case of 25 m and 30 m width of the coal column, the stresses of the coal column are 42.07 MPa and 35.88 MPa, respectively, which shows that the ultimate strength of the coal column is directly proportional to its width. Specifically, when the width of coal column is less than 20 m, the smaller the width of coal column, the lower its ultimate strength, the greater the destruction of coal column and the more serious the instability phenomenon. On the contrary, when the width of the coal column is more than 20 m, the stress on the coal column will be less than its ultimate strength, so no instability will occur.

Fig. 10

Distribution of force processes in coal columns of different widths.

The stress distribution of coal and rock columns at different heights under different widths of coal columns is shown in Fig. 11. When the width of the coal column is 20 m, the stresses on the coal column and overlying rock on the square are greater than the stresses on the coal and rock columns at the same horizontal height of the section under other widths. When the width of the reserved coal column is more than 20 m, the concentrated stress on the coal (rock) column gradually decreases with the increase of the width of the coal column, which indicates that the superposition of stresses on the coal column and the overlying rock on the section gradually decreases with the increase of the width of the coal pillar until it decreases to the state that the concentrated area of stress is completely separated. In the event that the width of the reserved coal column is found to be less than 20 m, it can be deduced that the concentrated stress of the coal (rock) column will gradually increase in proportion to the width of the column, which is due to the fact that the larger the width of the column, the stronger the bearing capacity of the column and the lighter the damaged state of the column.

Fig. 11

Distribution of force processes in coal columns of different widths.

Subsidence displacement law of overburden rock under different widths of coal columns

As a result of coal seam mining, the stress equilibrium of the overlying rock layer in the mining area is disturbed, and the overlying rock will produce various degrees of subsidence displacement due to the location of the rock layer and the influence of its own hardness. In general, it manifests itself in the phenomena of separation, fracture and collapse.

The distribution of overburden subsidence under different coal column widths is shown in Fig. 12. As demonstrated in the figure, when the width of the coal column is 10 m, the fissure on the side of the opening eye of the 81308 mining area extends to the upper right of the model, and the fissure on the side of the stopping line of the 81309 mining area extends to the upper left of the model, and the collapsed rock layers of the two mining areas are synthesized into a large trapezoidal arch structure, and the overburden rock in this area has a large displacement. The overburden in this area is highly displaced, which is due to the fact that the coal column in the 10-m section is not strong enough to withstand the stress from the overburden, and then it is completely destroyed and destabilized, resulting in the overburden above the pillar collapsing to different degrees. As the width of the coal column increases, the load-bearing capacity of the column gradually increases, and the degree of fragmentation gradually decreases, resulting in a gradual decrease in the displacement of the overburden collapse above the pillar. When the reserved width of the coal column is increased to 30 m, the collapse of the overburden in the two adjacent mining areas is in the shape of a trapezoidal arch, and the change of the subsidence displacement of the overburden in the two mining areas is basically the same as that of the single mining area, and the coal column plays a protective role as a supporting structure between the two working faces.

Fig. 12

Distribution of force processes in coal columns of different widths. (a) 10m section coal column. (b) 15 m section coal column. (c) 20 m section coal column. (d) 25 m section coal column. (e) 30 m section coal column.

In order to quantitatively characterize the distribution law of overburden subsidence, the distribution of overburden subsidence at different coal column widths is shown in Fig. 13. The findings indicate that under varying coal pillar widths, the subsidence curves of the overlying rock layers in the adjacent mining area are symmetrically distributed. However, when the coal pillar width is set at 10 m, a notable instability phenomenon emerges, leading to a substantial subsidence of approximately 3.6 m on both sides of the pillar and the overlying rock above it. However, as the width of the coal pillar increases, the instability phenomenon diminishes, leading to a gradual decrease in the subsidence of the coal pillar and the surrounding overburden. Subsequent to the stabilization of the mining area, the displacement curve transitions from “V” to “U” as the elevation of the overlying rock layer increases or decreases. This indicates that the subsidence amount, the range, and the displacement curve are smaller when the overlying rock layer is higher. Conversely, when the overlying rock layer is lower, the subsidence amount, the range, and the displacement curve are larger. The location of the area in question has a direct correlation with the magnitude of subsidence, the extent of the range, and the displacement curve’s transition from a “V” shape to a “U” shape. However, the overall distribution of the data remains concave, with two prominent high ends and a central low point. In the vicinity of the two extremities of the mining area, the rock layer exhibits minimal subsidence; however, the subsidence increases towards the center. The phenomenon of “bottom drum” emerges in the bottom plate of the coal seam, a consequence of pressure stress prior to mining and subsequent pressure relief and expansion following mining.

Fig. 13

Distribution of overburden subsidence when different widths of coal columns are reserved. (a) 10 m section coal column. (b) 15 m section coal column. (c) 20 m section coal column. (d) 25 m section coal column. (e) 30 m section coal column.

In order to facilitate the visualization and analysis of the subsidence characteristics of the zone coal column, the distribution curve of the subsidence amount of the zone coal column under different coal column widths is statistically presented in Fig. 14. As illustrated in the figure, it is evident that with an increase in the width of the section coal column, there is a corresponding decrease in the subsidence amount of the coal rock column itself. When the width of the reserved sectional coal face is 10 m, the maximum subsidence at the top of the coal face is 2.56 m, when the width of the reserved sectional coal face is 15 m, the maximum subsidence at the top of the coal face is 0.89 m, and when the width of the reserved sectional coal face is 20, 25, 30 m, the maximum subsidence at the top of the coal face is 0.72, 0.55, 0.49 m, respectively. When the width of the coal column section increased to 25 m and later, the subsidence amplitude of the coal column continuously decreased, and the subsidence amount of the elastic area in the center of the coal column was slightly smaller than that on both sides of the column under the same width of the coal column section. This phenomenon indicates that when the coal column is destabilized, the broken state of the coal column provides a connecting channel between adjacent mining airspace areas. As the width of the coal column increases, the degree of self-occurring destruction of the coal column decreases, which in turn makes the connecting fissure between two adjacent mining airspace areas gradually shrink.

Fig. 14

Distribution of roof subsidence of coal rock columns in the section.

Development pattern of overburden fractures under coal columns of different widths

The mining of coal seams provides disturbed space for the layer of rock above it and generates a large number of fractures, and reserving different widths of coal columns will result in different stress distributions in the overlying rock, which will lead to differences in the fractures generated in the overlying rock. The overburden fractures will go through the evolutionary process of initial formation, gradual development, continuous encryption, expansion and compaction. In the cyclic process of formation, development, expansion and compaction of mining fissures, the overburden will form a complex fissure field, which will become a spatial place for gas accumulation and a fissure channel for flow through different fissure partitions.

The overburden fracture distribution for different coal column widths is illustrated in Fig. 15. The fissures in the overburden rock of the two mining zones have a trapezoidal arch structure as a whole, and the rock layers above the coal pillars between the mining zones have an inverted trapezoidal structure, and the distribution of fissures is predominantly lateral to the overburden rock, with a reduced frequency in the central portion. The fractures between the rock layers and the fractures running through the rock layers together form the space for gas storage and transportation. Combined with Fig. 12a. In the event that the width of the coal column section is set at 10 m, the supporting stress of the coal and rock column exceeds its ultimate strength and destabilization occurs, and at this time, the fissures on the left side of the 81308 air-sealed area and the right side of the 81309 air-sealed area have expanded diagonally upward to form a large trapezoidal arch.

Fig. 15

Distribution of overburden fracture development pattern under different widths of reserved coal columns. (a) 10m section coal column. (b) 15 m section coal column. (c) 20 m section coal column. (d) 25 m section coal column. (e) 30 m section coal column.

After mining back to the working face, the overlying rock layer in the cavity area breaks and collapses, and the size of the degree of fragmentation of the coal and rock body determines the size of the cavity formed, usually using the rock fragmentation coefficient K_p to indicate the degree of fragmentation of the coal and rock layers, the rock fragmentation coefficient expression is shown in Eq. (13):

$$K_{\text{p}} = \frac{{h_{{n^{\prime } }} }}{{h_{n} }} = \frac{{h_{n} - \Delta W_{n} + \Delta W_{n + 1} }}{{h_{n} }} = 1 + \frac{{\Delta W_{n + 1} - \Delta W_{n} }}{{h_{n} }}$$

(13)

where h_n is the vertical distance between the nth monitoring point and the n + 1th monitoring point before overburden deformation, m; h_n' is the vertical distance between the nth monitoring point and the n + 1th monitoring point after overburden deformation, m; ΔW_n is the amount of overburden subsidence at the nth monitoring point, m; ΔW_n+1 is the amount of overburden subsidence at the n + 1th monitoring point, m. ΔW_n+1 is the amount of overburden subsidence of the n + 1th monitoring point, m; ΔWn + 1 is the amount of overburden subsidence of the n + 1th monitoring point, m.

In order to more intuitively analyze the development characteristics of the overburden mining fissures and the connectivity between the two mining zones under the width of coal pillars in different sections, the calculated fragmentation coefficients were plotted as contours as shown in Fig. 16. As demonstrated in the figure, when the same width of section coal pillar is reserved, the overburden expansion coefficient of two neighboring mining areas shows symmetrical distribution. Specifically, the coefficient is larger on both sides of a single mining area and smaller in the central area. At the same time, the coefficients of the left side of 81308 mining area and the right side of 81309 mining area are significantly higher than the coefficients of the right side of 81308 mining area and the left side of 81309 mining area. This discrepancy can be attributed primarily to the formation of articulated rock beam structures following the collapse of the overburden rock on both sides of the extraction zone. These structures provide support and protection to the overburden rock, thereby enabling it to maintain its original crushing state. The overburden rock on the right side of the extraction zone 81308 and the left side of the extraction zone 81309 is subjected to the influence of stress concentration, which results in a relatively small coefficient of fragmentation.

Fig. 16

Equivalent values of overburden expansion coefficients for different widths of coal columns in the reserve. (a) 10 m section coal column. (b) 15 m section coal column. (c) 20 m section coal column. (d) 25 m section coal column. (e) 30 m section coal column.

The fracture expansion coefficients of the overburden from the bottom to the top of the coal seam are larger than the fracture expansion coefficients of the overburden in the area of other monitoring lines, which is due to the fact that the overburden in this area is in the collapse zone, and most of the overburden after the collapse is in the fractured state, and the overburden in the central part of the mining area is subjected to the action of the overlying rock layer so as to recover its stress to a certain extent. However, under the influence of the Sub-2 key layer, part of the fractured rock body is not fully compacted and a certain number of voids and fractures still exist.

The coal pillar in the 10-m-wide section is unable to withstand the concentrated stress generated by the overburden rock, resulting in significant damage and destabilization. Consequently, a substantial displacement is observed in the coal pillar within the section and the overburden rock above it. The coal pillar experiences a complete loss of its protective capacity, resulting in a broken state extending approximately 10 m. This fracture enables the connection of the two mining airspace zones, facilitating the transportation of gas between them via the generation of fissures. However, the fracture coefficient of the overburden rock above 10 m of the coal pillar is small, which is due to the fact that the overburden rock will be recompacted by the stress concentration after a large collapse. As the coal pillar width increases to 20 m, the expansion coefficient of the overburden above the right side of the 81308 mining area and the left side of the 81309 mining area begins to rise. Consequently, the degree of damage to the coal pillar in the section gradually decreases, and the connectivity between the two mining areas gradually diminishes. As the width of the coal pillar increases, its crushing coefficient approaches that of the coal pillar on both sides of the single mining area. The concentrated stress on both ends is independent of each other, resulting in the two mining areas becoming almost completely disconnected from each other. This leads to the closure of the fissure channel and the effective blocking of the gas transportation path.

Conclusion

According to the engineering geological conditions of Baode Mine, the reasonable width of 19.3 m for the coal column section can ensure the elastic area in the middle of the coal column within a reasonable range when analyzed by the limit equilibrium condition and the extended SMP damage criterion, so as to ensure the stability between the adjacent mining airspace.

The distribution of overburden stress under varying coal pillar widths exhibits a sequential pattern of concentration-unloading-restoration-unloading-concentration, resulting in a transition from a “U”-type to a “V”-type sinking curve. This transformation is accompanied by the formation of a “bottom drum” at the base of the mining area. In the sub-2 key layer, the collapsed overburden rock exhibits a high coefficient of fragmentation, with a non-uniform degree of compaction in the middle and the presence of articulated rock beams on the two sides, resulting in a broken texture. Above the sub-1 key layer, the middle part experiences gradual compaction, accompanied by wider cracks on both sides.

In the event that the width of the coal column is set at 10 m, the stress that is borne by the coal column surpasses its limit, thereby inducing a state of destabilization, the stress after destabilization is 14.3 MPa, the maximum settlement is 2.56 m, and the coefficient of crushing expansion is 1.13. As the width of the coal column increases, the destabilization phenomenon decreases and the load-bearing capacity increases. When the width of the coal column reaches 20 m, the peak stress reaches 45.43 MPa, and the maximum settlement of the top plate remains at 0.72 m. As the width of the coal column continues to increase, the coal pillar tends to stabilize, the stress superposition phenomenon is separated, the stress is gradually reduced, the amount of subsidence tends to be stable, and the connecting fissure between the two mining areas is gradually closed. When the width of the coal column increases to 30 m, the supporting stress in the middle elastic region decreases to 35.88 MPa, and the maximum settlement amount of the roof plate decreases to 0.49 m. Based on the comprehensive analysis, the reasonable width of the coal column should be between 20 and 25 m.