Study on the law of stress distribution in the presence of remaining coal pillar in a close-distance coal seam and the reasonable location of the roadway

Abstract

In order to reveal the impact of remaining coal pillar on roadway layout of the lower seam after the upper part of the close coal seam is reversely mined, theoretical analysis and numerical simulation are conducted in this paper. With the roadway to be excavated in a mine located in Shanxi as the research object, theoretical analysis and numerical simulation are performed to explore the evolution of stress field in the lower coal seam under the influence of the leftover coal pillar. Also, an analysis is conducted on the mechanism of deformation and destruction occurring to the roadway in the lower coal seam, so as to determine the rational layout of roadway in the lower coal seam and the optimal parameters related to roadway support. The research results are as follows. (1) The mining operations conducted in the upper coal seam affect the magnitude of the principal stress, the principal stress ratio and the principal stress deflection angle of the lower coal seam, causing different patterns of deflective stress in the lower coal seam. (2) With the center line of coal pillar as the axis of symmetry, the influencing factors for the lower coal seam are symmetrically distributed. The larger the distance from the centerline, the larger the deflected plastic zone of the roadway surrounding rock. (3) In order to determine the rational layout of the roadway, the study area is divided into two zones by considering the main influencing factors. Allowing for the mode of mining and to ensure safety, it is recommended that the roadway should be positioned at the edge of the H-II area, such as at the location that is 15–20 m or 40–45 m away from the study area. Taking into account these influencing factors, the original tunnel support parameters are optimized. According to the data collected through on-site mining pressure observation, the support optimization scheme achieves satisfactory results.

Introduction

Close-distance coal seams are common in China^1,2,3,4,5. In the practice of close-distance coal mining⁶, downstream mining is predominant, which leads to stress perturbation in the rock layer of the lower coal seams after repeated mining in the upper coal seams^7,8,9,10,11. This results in the broken and unstable top plate of the roadway. Therefore, it is crucial to explore the reasonable arrangement of the roadway and the perimeter rock support technology suitable for the close-distance lower coal seam.

At present, there have been plenty of research conducted on the arrangement of roadway in the lower part of close-distance coal seams^{12,13,14,15,16,17,18,19,20}. Huang et al.²¹ investigated the reasonable coal pillar misalignment distance (CPMD) through the coupling control of stress field, displacement field and fracture field (three fields) in shallow buried closely spaced multi-seam (SBCSM-S) mining. By means of similar simulation and theoretical analysis, coupling control was achieved on the downhole centralized stress and the fracture of the ground. Zhang et al.²² conducted physical similarity simulation experiments to determined the characteristics of fracture evolution and the fracture-bearing structure on both sides of the coal pillar. In addition, there are many studies conducted to deduce the analytical solution for the plastic zone of the rocks surrounding the roadway^23,24,25,26. By applying the elastic-plasticity theory, Zhao et al.^27,28 deduced the eight implicit equations of the plastic zone for the damage caused to the rocks surrounding the roadway in the non-uniform stress field. This provides theoretical guidance for the analysis on stability of the surrounding rock, the design of the support, and the dynamic prevention and control of disasters for the roadway. Given the mode of roadway support in close-distance coal seams, Zhou, Wang et al.^29,30 proposed the effective roadway perimeter rock regulation mechanism and support mode for the pattern of stress distribution on the bottom plate in the close-distance coal seam, which ensures the safety of coal mining.

It can be seen from above that various methods have been adopted by scholars to study the pattern of stress evolution, roadway location selection, the law of roadway plastic zone evolution and the control of surrounding rocks in the lower coal seam after the mining operations conducted in the upper coal seam. This is of great significance to the safety in mining operations conducted in the close-distance coal seam. In this paper, a reasonable layout of roadway is determined for the lower coal seam after mining in the upper coal seam according to the pattern of stress evolution in the lower coal seam and the morphology of the plastic zone in the roadway, along with a variety of influencing factors. Thus, the efficiency and safety of coal mining can be improved.

Project overview

For a specific mine located in Shanxi, China, the recoverable coal seams are coal seams 11 and 13, with an average distance of about 10 m in between, both of which are suitable for close-distance mining. At present, coal seam 11 has been reversely mined to the full, with coal seam 13 as the main area of mining operations. This coal seam has a depth of about 300 m, an average thickness of 13 m. According to the geological conditions on the working face, the integrated histogram of its top and bottom plates was drawn, as shown in Fig. 1a. The average inclination angle of the coal seam is 6°, for which it belongs to horizontal close-distance coal seam. In this paper, the roadway under study is the working face of Shanxi coal mine 13,402, which is to be dugged back to the wind lane. In the north of the working face is the preparation lane of coal seam 13; in the south of the working face is the west wing of the preparation lane of coal seam 13; in the west and east are the non-mined working faces 13,402 and 13,403, respectively. The working face is covered by the hollow area of working faces 11,202 and 11,203, with a 25 m coal pillar present between the two working faces. Figure 1b illustrates the three-dimensional distribution of coal seams.

Fig. 1

Mining relationship and rock layer histograms.

Theoretical analysis

In Literature³¹, the most used Moore-Cullen criterion is adopted to assess the damage of rock under a certain level of stress. By substituting the stress formula at any point around the circular roadway under non-isobaric conditions into the criterion, the implicit equation is obtained as follows for the 8th power of the boundary of the damage zone in the peripheral rock of the circular roadway in the non-uniform stress field, established a tunnel stress model, as shown in Fig. 2:

$$\begin{gathered} 9\left( {1 - \eta } \right)^{2} \left( {\frac{a}{r}} \right)^{8} + \left[ { - 12\left( {1 - \eta } \right)^{2} + 6\left( {1 - \eta ^{2} } \right)\cos 2\left| {\theta - \alpha } \right|} \right]\left( {\frac{a}{r}} \right)^{6} \hfill \\ + \left[ {10\left( {1 - \eta } \right)^{2} \cos ^{2} 2\left| {\theta - \alpha } \right| - 4\left( {1 - \eta } \right)^{2} \sin ^{2} \varphi \cos ^{2} 2\left| {\theta - \alpha } \right| - 2\left( {1 - \eta } \right)^{2} \sin ^{2} 2\left| {\theta - \alpha } \right| - 4\left( {1 - \eta ^{2} } \right)\cos 2\left| {\theta - \alpha } \right| + \left( {1 + \eta } \right)^{2} } \right]\left( {\frac{a}{r}} \right)^{4} \hfill \\ + \left[ { - 4\left( {1 - \eta } \right)^{2} \cos 4\left| {\theta - \alpha } \right| + 2\left( {1 - \eta ^{2} } \right)\cos 2\left| {\theta - \alpha } \right| - 4\left( {1 - \eta ^{2} } \right)\sin ^{2} \varphi \cos 2\left| {\theta - \alpha } \right| - \frac{{4C\left( {1 - \eta } \right)\sin 2\varphi \cos 2\left| {\theta - \alpha } \right|}}{{P_{3} }}} \right]\left( {\frac{a}{r}} \right)^{2} \hfill \\ + \left[ {\left( {1 - \eta } \right)^{2} - \sin ^{2} \varphi \left( {1 + \eta + \frac{{2C\cos \varphi }}{{P_{3} \sin \varphi }}} \right)^{2} } \right] = 0 \hfill \\ \end{gathered}$$

(1)

Fig. 2

Stress model of the roadway rock surrounded by non-uniform stress field. P₁/MPa-Maximum principal stress, P₃/MPa-Minimum principal stress, R-Radius of damage zone, a-Roadway radius, r and θ-Polar coordinates of any point in the damage zone.

From Eq. (1), it can be seen that there are more factors affecting the plastic zone of the roadway. In this paper, the geological conditions of a coal mine located in Shanxi are considered to analyze the mining stress field around the rock seam under the remaining coal pillar, from various perspectives including the magnitude of stress, principal stress ratio, principal stress deflection angle, and deflective stress invariant (J₂, J₃), etc. Thus, the reasonable layout of the roadway is determined.

Influence law of principal stress ratio on the damage of the roadway

According to the butterfly damage theory, the principal stress ratio plays an important role in the formation of the plastic zone. Figure 3 illustrates different morphologies exhibited by the plastic zone at different principal stress ratios.

Fig. 3

Morphology of plastic zones in the roadway with different principal stress ratios.

As shown in Fig. 3, the plastic zone of the roadway varies in morphology given different principal stress ratios. For example, when the principal stress ratio (η = P₁/P₃) is 1, the tunnel plastic zone is round under two-way equal pressure; when the principal stress ratio is 1.5, the tunnel plastic zone expands from sphere to ellipse. As the principal stress ratio further rises to 2.5, the tunnel plastic zone further expands, exhibiting the morphology of butterfly-shaped damage. When the principal stress ratio reaches 3, the plastic zone is destructed rapidly, and the range of butterfly leaf expands quickly.

Pattern of impact caused by the magnitude of main stress on the damage of the roadway

According to the butterfly damage theory, if the principal stress ratio is constant, the magnitude of principal stress affects the pattern of plastic damage caused to the roadway, as shown in Fig. 4.

Fig. 4

Diagram of RPP surface and butterfly risk.

As can be seen from Fig. 4, the plastic zone of the roadway is free from damage when the principal stresses P₁ and P₃ are low. As the main stress continues to increase, the roadway plastic zone shifts from the no-damage zone to the no-butterfly stabilization zone. In this circumstance, the damage zone of the rocks surrounding the roadway is shaped like sphere and ellipse. With the further increase in main stress, the roadway plastic zone expands to resemble butterfly. In the mean time, there is a linear relationship between the maximum radius of the plastic zone, denoted as Rmax, and the magnitude of main stress.

Pattern of impact caused by the deflection angle of main stress on the damage of the roadway

Coal mining causes the rocks surrounding the roadway to develop deflection stress field, which leads to the deflection of principal stress. According to Eq. (1), the angle of principal stress deflection is an important factor affecting the morphology of the plastic zone. As can be seen from Fig. 5, there is directionality in the butterfly leaf in the plastic zone of the rocks surrounding the roadway; the butterfly leaf is consistently close to the angular equilibrium between the angle of the largest principal stress and the smallest principal stress clip angle, basically ranging from 38° to 45°; when the principal stress deflection occurs, the butterfly leaf will also be corresponding deflection. When the deflection of principal stress occurs, the butterfly leaf is deflected accordingly.

Fig. 5

Relationship between the main stress direction and butterfly leaf rotation angle.

Pattern of impact caused by bias stress invariant on the damage of the roadway

The damage of deformation to the medium relates mainly to the bias tensor, which reflects the stress in the deformed rocks. The second and third invariants, which are related to the bias tensor, are the parameters used to characterize shear stress, distortion energy and strain (tensile strain, compressive strain, plane strain), respectively.

By analyzing the characteristics of bias stress distribution, the accumulation of aberration energy and strain type in the roadway surrounding rock can be determined, which is conducive to analyzing the characteristics of damage caused to coal rocks. Bias stress invariant analysis overcomes the dificiencies in evaluating the stability of roadway surrounding rock against a single vertical or horizontal stress-strain and other independent indicators. For this purpose, the eight implicit equations of the second invariant of bias stress J₂ related to the radius at any point of the roadway surrounding rock are obtained³².

$$\begin{gathered} {J_2}=\frac{{9{B^2}}}{4}{\left( {\frac{a}{r}} \right)^8} - \left[ {3{B^2}+\frac{3}{2}AB\cos 2\theta } \right]{\left( {\frac{a}{r}} \right)^6}+\left[ {\frac{5}{2}+\frac{1}{3}{{(2\mu - 1)}^2}{B^2}{{\cos }^2}2\theta +\frac{1}{4}{A^2}+AB\cos 2\theta - \frac{1}{2}{B^2}{{\sin }^2}2\theta } \right]{\left( {\frac{a}{r}} \right)^4} \hfill \\ +\left[ {{B^2}({{\sin }^2}2\theta - {{\cos }^2}2\theta )+AB\left( {\frac{2}{3}\mu - \frac{5}{6}} \right)cos2\theta - \frac{2}{3}{p_y}B(2\mu - 1)cos2\theta } \right]{\left( {\frac{a}{r}} \right)^2}+\left[ {\frac{{{B^2}}}{4}+\frac{{{A^2}}}{{12}} - \frac{1}{3}(A - {p_y})} \right] \hfill \\ \end{gathered}$$

(2)

To explore the directionality in the second invariant J₂ of the bias stress tensor, the deflection angle α is substituted into Eq. (2), which leads to another equation below that describes J₂ in the presence of deflection angle α:

$$\begin{aligned} {J_2}= & \frac{{9{B^2}}}{4}{\left( {\frac{a}{r}} \right)^8} - \left[ {3{B^2}+\frac{3}{2}AB\cos 2\theta \left( {\theta - \alpha } \right)} \right]{\left( {\frac{a}{r}} \right)^6}+\left[ {_{{\frac{1}{4}{A^2}+AB\cos 2\left( {\theta - \alpha } \right) - \frac{1}{2}{B^2}{{\sin }^2}2\left( {\theta - \alpha } \right)}}^{{\frac{5}{2}+\frac{1}{3}{{(2\mu - 1)}^2}{B^2}{{\cos }^2}2\left( {\theta - \alpha } \right)+}}} \right]{\left( {\frac{a}{r}} \right)^4} \\ & +\left[ {_{{AB(\frac{2}{3}\mu - \frac{5}{6})cos2\left( {\theta - \alpha } \right) - \frac{2}{3}{p_y}B(2\mu - 1)cos2\left( {\theta - \alpha } \right)}}^{{{B^2}({{\sin }^2}2\left( {\theta - \alpha } \right) - {{\cos }^2}2\left( {\theta - \alpha } \right))+}}} \right]{\left( {\frac{a}{r}} \right)^2}+\left[ {\frac{{{B^2}}}{4}+\frac{{{A^2}}}{{12}} - \frac{1}{3}(A - {p_y})} \right] \\ \end{aligned}$$

(3)

Numerical simulation

Numerical modeling and calibration of the model of the mining zone

In this paper, with a coal mine located in Shanxi to be dug back to the wind tunnel as the research object, the data on its geological conditions are used to establish a large-scale three-dimensional numerical simulation model, as shown in Fig. 6. The X direction of the model represents the direction of the working face, whose length is 500 m; the Y direction represents the tendency, whose ength is 250 m; the Z direction represents the direction of the overburden, whose length is 82 m. Coal seam 13 has a thickness of 13.4 m, for which it belongs to the extra-thick coal seam. Given a boundary effect caused by FLAC^3D, which needs to be eliminated, the quarry was surrounded by coal pillars as a means to protect it. The use of boundary coal pillars proves reasonable as they develops original rock stress at the edge when the working face is advancing. In order to improve the accuracy of research results, the coal body in the researched roadway and roadway boundary was subject to mesh densification. With displacement constraints imposed at the upper, lower, left, right and lower boundaries of the model, stress boundary conditions are applied at the upper boundary of the model. Given the actual burial depth of the roadway, a vertical stress of 7.5 MPa was applied at the top of the model, and the gradual horizontal stress was applied around the model, which is 1.3 times the vertical gravity. The commonly used M-C intrinsic model was used to evaluate the damage caused to the rock. Its mechanical parameters are shown in Table 1.

Fig. 6

Numerical simulation model.

The model simulation program is to conduct excavation according to the practicalities. It began with the simulation of reverse mining on two working faces: 11,202 and 11,203. The mining of upper seam was followed by the wind tunnel digging on the working face 13,402. By simulating upper seam mining, its impact on roadway excavation in the mined area was simulated. During mining operations, the free fall method was used for top plate management, with the falling coal rocks gradually compacted over time to form a load-bearing structure that withstands the pressure of overlying rocks. This directly affects the pattern of stress distribution around the mined area. Therefore, the double yield intrinsic model is adopted in this study to simulate the state of gangue heavy compaction under the condition of free fall of the roof plate in the mined area.

Table 1 Mechanical parameters of the model rock mass.

The built-in Double-yield model of FLAC^3D is applicable to describe the gradual recovery of rock stress in the mined area more accurately. For this purpose, a model sized 1 m×1 m×1 m was built in FLAC^3D for calibration, with restriction imposed on the bottom and surrounding displacements of the model. Also, a vertical load of 10^− 5/step was applied at the top. The trial-and-error method was used to continuously correct the model parameters³³. The stress-strain curve of the corrected numerical model was found consistent with the results of theoretical calculation, as shown in Fig. 7. The finalized mechanical parameters of the rocks in the mined area are shown in Table 2.

Fig. 7

Calibration of the dual-zone service model for the extraction zone.

Table 2 Mechanical parameters of goaf.

The main stress distribution law of 13# coal seam

After the completion of reverse mining in coal seam 11, the remaining coal pillar and the mined area have some impact on coal seam 13 and the surrounding rocks. This paper focuses mainly on the reasonable layout of roadway in coal seam 13, with reference made to the layout of reverse mining roadway in coal seam 11 back for excavation along the bottom plate of the coal seam. In the established numerical model along the y-axis direction, the stress slices of 40 m, 110 m, 200 m are cut at three different positions, as shown in Fig. 8. By comparing the pattern of changes in stress at different positions in the presence of remaining coal pillar, a further theoretical reference is provided for the reasonable layout of the roadway.

Fig. 8

Stress cloud of the lower coal seam.

As shown in Fig. 9, the three patterns of stress distribution are basically identical without considering the impact of the boundary. Besides, the vertical stress, maximum principal stress and minimum principal stress are all concentrated in close proximity to the remaining coal pillar. Due to no difference in the influencing factors, such as the range at both sides of the mined area, the stresses are symmetrically distributed at both sides, with the centerline of the coal pillar as the axis. At 40 m of the slice, all three stresses are concentrated on both sides of the pillar, with the vertical stress at the top and bottom of the pillar being about 4 times the original rock stress. The maximum principal stress is distributed in a similar way to the vertical stress, with the stress at the top and bottom of the pillar reaching about 5.6 times the original rock stress. The minimum principal stress appears to be concentrated at the top and bottom of the coal column, with the stress reaching about 2 times the original rock stress. As the position of the slice becomes further along the y-axis, the range of stress concentration in the middle of the model expands compared with the boundary, which is due to the boundary effect. Also, there is a rise in the stress in the middle of the model. Meanwhile, the stress concentration coefficient of the vertical stress in the middle of the model increases from 3.87 to 5.87. When the distance along the y-axis increases to the 200 m position of the slice, the stress concentration coefficient of the vertical stress decreases from 5.87 to 4.53. At this time, the maximum principal stress concentration coefficient and the minimum principal stress concentration coefficient reach about 5.6 times the original rock stress. Likewise, the same trend is exhibited by the maximum principal stress concentration coefficient and the minimum principal stress concentration coefficient.

Fig. 9

Layout of Monitoring Lines and Slice position.

This paper revolves aound the stress distribution in coal seam 13 and the reasonable layout of the roadway, for which coal seam 13 is the focus of research. As analyzed above, the stress in the middle of the model is higher. Therefore, there are three stress lines extracted from the top and bottom plates in coal seam 13 at 110 m of the slices and the top plate of the roadway to be dug in the established numerical model, as shown in Fig. 8. The stress distribution patterns of the three measurement lines are shown in Fig. 10.

Fig. 10

Pattern of stress distribution in the lower coal seam. (a) Maximum principal stress. (b) Minimum principal stress. (c) Vertical stress.

As can be seen from Fig. 10, when the impact of boundary coal pillar is ignored, the three patterns of stress changes show a similar trend of “first decreasing, then increasing, and finally decreasing”, with the two decreasing trends falling into the range of impact caused by the mined area at both sides of the coal pillar. Also, the stress is relatively low, with the increasing trend falling into the range of impact caused by the coal pillar. The stress is concentrated in the remaining coal pillar and transferred to the lower rock layer, which increases the stress in this area. Different layers are affected by the concentrated stress of the coal pillar to varying extents, which is reflected in the distribution of the maximum principal stress in coal seam 13. As shown in Fig. 10a, the further the lower coal seam is from the position of the coal pillar, the smaller the maximum principal stress. Also, the maximum stress at the top plate of the coal seam is 21.19 MPa. The maximum principal stress at the top plate of the roadway to be dug and the bottom plate of the coal seam declines in sequence, and the difference is 2.68 MPa between the maximum and the maximum at the top plate of the coal seam. According to the distribution of minimum principal stress in coal seam 13, as shown in Fig. 10b, the minimum principal stress in the area affected by the remaining coal pillar differs to some extent from the former. Specifically, the minimum principal stress at the top plate of the roadway to be excavated is the largest, followed by that at the bottom plate of the coal seam and that at the top plate of the coal seam in descending order. By comparing the distribution of the minimum principal stress at 110 m of the slice in Fig. 9, it can be found out that the distribution of principal stress is highly consistent between the survey line and the cloud map, with the minimum principal stress concentrated above coal seam 13. Besides, the degree of stress concentration is reduced at the top plate of coal seam 13. As the distance to the coal pillar increases, the minimum principal stress develops an area of stress concentration within coal seam 13. Also, the degree of stress concentration is reduced again at the bottom plate of the coal seam. Finally, the minimum principal stress is distributed in descemding order as follows: “the top plate of the roadway to be excavated > the bottom plate of the coal seam > the top plate of the coal seam”. From Fig. 10c that shows the vertical stress distribution in coal seam 13, it can be seen that the distribution of vertical stress in the area affected by coal pillar is identical to the maximum principal stress.

In summary, the remaining coal pillar in the upper coal seam is the main influencing factor for stress elevation in the lower rock layer; the stress in the area affected by the coal pillar varies significantly; the stability of roadway surrounding rock in this area can be affected to a significant extent.

Pattern of principal stress ratio distribution in coal seam 13

According to the analysis described in Section “The main stress distribution law of 13# coal seam”, the stress in the lower stratum varies significantly in the area affected by the coal pillar in the presence of the remaining coal pillar, which causes the principal stress ratio η to change as well. The principal stress ratio η refers to the ratio of the maximum principal stress to the minimum principal stress. According to the theory of butterfly damage of roadway, the principal stress ratio η is one of the important influencing factors, and the change of η affects the morphology of plastic zone in the roadway surrounding rock. In this subsection, the principal stress ratio η in different layers and at different locations is also studied in the presence of the remaining coal pillar, with the slices of principal stress ratio at 40 m, 110 m and 200 m cut along the y-axis direction, as described in Section “The main stress distribution law of 13# coal seam”. Figure 11 shows the cloud diagrams of the principal stress ratio.

Fig. 11

Cloud view of principal stress ratio in the lower coal seam.

As indicated by the principal stress ratio cloud diagram presented in Fig. 11, the principal stress ratio changes more significantly above the mined area and near the remaining coal pillar. According to the cloud diagrams, principal stress ratio varies evidently at different positions along the y-axis. From the above analysis, it can be seen that this ratio is affected by the boundary of the model, and it is higher in the middle of the model and wider in range compared to the boundary of the model. Therefore, with the cloud map of principal stress ratio for the slice at 110 m as reference, the cloud map of the area near the coal pillar was locally enlarged, as shown in Fig. 12. Thus, a better understanding is gained as to the impact of remaining coal pillar on the principal stress ratio of roadway surrounding rock and the underlying rock layer.

Fig. 12

Cloud view of principal stress ratios in the region of the coal pillar.

As shown in Fig. 12, the principal stress ratio is distributed symmetrically with the coal pillar as the center, with higher ratios concentrated in the mined area near the top of the coal pillar and in the upper parts on both sides of the coal pillar. The maximum principal stress ratio is 4.17. As the coal pillar is 25 m in width, the stress in the middle of the coal pillar is lower, as is the stress ratio in this area.

In order to further this study, it was established through the above analysis that the principal stress ratio is larger in the middle of the model. Therefore, three lines of main stress ratio measurement were extracted respectively from the slices at 110 m of the top and bottom plates of coal seam 13 and from the top plate of the roadway to be excavated in the established numerical model, as shown in Fig. 13.

Fig. 13

Pattern of distribution of principal stress ratio in the lower coal seam.

As shown in Fig. 13, when the impact of the boundary coal pillar is ignored, there is a similar trend shown by the changes of principal stress ratio at the three different positions as mentioned above in the horizontal direction. Also, U-shaped distribution is exhibited by the principal stress ratio at both sides of the mined area. In the area affected by the coal pillar, the principal stress ratio conforms to M-shaped distribution at the top plate of the coal seam. In the area affected by the coal pillar, the principal stress ratio conforms to M-shaped distribution as well at the top plate of the coal seam. Differently, the principal stress ratio exhibits V-shaped distribution at the top plate of the coal seam and the top plate of the roadway to be excavated. The main reason for these findings lies in the depressurized surrounding rock near the mined area, which causes the low degree of stress concentration and the accordingly low principal stress ratio. At both sides of the coal pillar is the main stress concentration area, which means the principal stress ratio increases on both sides of the coal pillar but decreases in the middle of the pillar. In the vertical direction, there is no obvious difference observed in principal stress ratio between the three positions at both sides of the mined area. In the area affected by the coal pillar, the principal stress ratio at the top plate of the coal seam is significantly higher than at the other two locations, with the maximum difference reaching 0.85. Nevertheless, there is no obvious difference found in principal stress ratio between the bottom plate of the coal seam and the top plate of the roadway to be excavated in several affected areas.

According to the above analysis, the principal stress ratio η is the inevitable result of the non-isobaric stress field, playing a more important role in the damage of roadway surrounding rock. The principal stress ratio η shows significant fluctuations in the area affected by the coal pillar, which requires attention paid to the stability of the roadway in this arrangement. However, the minimum principal stress ratio η is reached here, and roadway damage can be reduced through rational layout.

Pattern of principal stress deflection angle in coal seam 13

To calculate the angle of maximum principal stress deflection, it is necessary to determine the three positive stress values at the same point³⁴. Thus, Eq. (4) can be used to calculate the maximum principal stress deflection angle θ at this point.

$${\text{cos}}\left( {2\theta } \right)=\left( {{\sigma _1} - {\sigma _2}} \right)/\left( {{\sigma _1}+{\sigma _2}} \right)$$

(4)

where $\:{\sigma\:}_{1}$ and $\:{\sigma\:}_{2}$ are the two positive stress values at the point and $\:{\sigma\:}_{1}$ > $\:{\sigma\:}_{2}$, respectively.

Through the values of $\:{\sigma\:}_{1}$ and $\:{\sigma\:}_{2}$ as obtained from the above analysis, the deflection angles on the three survey lines can be calculated, as shown in Fig. 14.

Fig. 14

Pattern of minimum principal stress distribution in the lower coal seam.

As shown in Fig. 14, without considering the impact of boundary coal pillar, the deflection angles on the three different measurement lines show a similar trend of change, and the distribution of deflection angle follows the opposite pattern to that of principal stress ratio. In the area affected by the coal pillar, the principal stress ratio conforms to inverted, M-shaped distribution at the top plate of coal seam, while it conforms to inverted, V-shaped distribution at the top plate of coal seam and the top plate of the roadway to be excavated. The minimum deflection angle is reached at the coal seam roof, which is 30.51°. The maximum deflection angle of 40.95° is reached at the bottom plate of the coal seam and the bottom plate of the roadway to be excavated.

From above, it can be found out that the deflection angle reached under the maximum principal stress varies significantly in the area affected by the coal pillar, and there is an increased likelihood of roofing when the roadway is located here. However, the maximum principal stress deflection angle also reaches the lowest level here. Through a reasonable layout of the roadway, the risk of roofing can be prevented.

Pattern of distribution of bias stress invariant in coal seam 13

The built-in FISH language in FLAC^3D can be used to extract the bias stress invariant from the model. In order to explore the impact of remaining coal pillar on the bias stress invariant of coal seam 11, three different locations in coal seam 11 were treated as the measurement lines. Figures 15 and 16 shows the pattern of distribution followed by the bias stress second invariants J₂ and J₃ of the three lines, respectively.

Fig. 15

Pattern of second invariant (J₂) distribution pattern of bias stress in the lower coal seam.

Fig. 16

Pattern of distribution of the third invariant (J₃) of bias stress in the lower coal seam.

As shown in Fig. 15, when the impact of the boundary is ignored, the second invariant (J₂) of the bias stress on the three measurement lines follows a similar pattern of distribution to the principal stress ratio. In the area affected on both sides of the mined area, J₂ shows a U-shaped distribution. In the area affected by the coal pillar, J₂ shows an M-shaped distribution at the top plate of the coal seam, while it shows a V-shaped distribution at the top plate of the coal seam and the top plate of the roadway to be excavated. The maximum of J₂ is reached on the line of the coal seam roof, and it reaches the minimum on the line of the coal seam bottom plate and at the top plate of the roadway to be excavated.

As can be seen from Fig. 16, without considering the impact of the boundary, the third invariant of bias stress (J₃) on the three measurement lines follows a different pattern of distribution from J₂ at the top plate of the coal seam. Also, and the pattern of distribution is consistent between J₃ and J₂ on the two remaining measurement lines. In the area affected on both sides of the mined area, J₃ exhibits a U-shaped distribution. In the area affected by the coal pillar, the J₃ at the top plate of the coal seam suddenly decreases in the middle of the coal pillar. It ends up showing a M-shaped distribution, which is short on two sides but long in the middle. In comparison, J₃ shows a V-shaped distribution at the top plate of the coal seam and the top plate of the roadway to be excavated. The maximum of J₃ is reached on the line of the coal seam roof, as is its minimum.

From above, it can be seen that J₂ can be used to determine the severity of deformation caused to the surrounding rock, and that J₃ can be used to determine the type of strain in the rock layer. J₂ and J₃ vary significantly in the area affected by the coal pillar. As shown in Figs. 17 and 18, the cloud diagram of distribution for J₂ and J₃ near the roadway surrounding rock was extracted by establishing the model at different locations where the roadway is arranged.

Figure 17shows the evolution of the second invariant (J₂) of the bias stress at different locations of the roadway. Obviously, J₂ is symmetrically distributed on both sides with the centerline located at 30 m. With a considerable distance at both sides to the centerline, the area of J₂ concentration is deflected. It is deflected clockwise on the left and counterclockwise on the right. Finally, J₂ is concentrated at the top and bottom of the roadway on both sides. The further J₂ is away from the centerline, the larger the value of it.

Fig. 17

Evolutionary pattern of J₂ at different locations of the roadway.

Figure 18 shows the evolution of the third invariant (J₃) of bias stress at different locations of the roadway. Evidently, the distribution of J₃ is consistent with that of J₂, which is also symmetrically distributed with the centerline at 30 m. As both sides are far away from the centerline, the top and bottom of the coal pillar are under tensile strain. When the position on both sides moves away from the center line, J₃ induces not only tensile strain on the top and bottom plates of the roadway, but also compressive strain in the coal pillar. The farther the position, the more significant the strain. In the ranges of 0–5 m and 55–65 m, compressive strain increases sharply, especially in the two gangs of the roadway.

Fig. 18

Evolutionary pattern of alley J₃ at different locations.

From above, it can be inferred that the deviatoric stress invariant varies with the location on the roadway. The farther it is away from the centerline (30 m location), the larger the deviatoric stress invariant. In order to protect the roadway surrounding rock against severe damage and large strain, the roadway is positioned near the centerline as much as possible.

Reasonable location of the roadway

Evolution law of the plastic zone in surrounding rock at different locations of the roadway

By establishing the FLAC^3D numerical model of different locations on the roadway in the presence of remaining coal pillar, the evolution law of the plastic zone on the roadway at different locations was determined, as shown in Fig. 19. According to the development of the plastic zone on the roadway, the reasonable arrangement of the roadway was determined.

Figure 19 shows the evolution law of the plastic zone at different locations of the roadway. Obviously, with the center of the coal pillar as the origin, symmetrical distribution is exhibited by the pattern of damage caused to the peripheral rock plastic zone of the roadway on both sides of the coal pillar. Also, there are different patterns shown by the distribution of the peripheral rock plastic zone at different locations on either side. At the center (30 m) of the coal pillar, the roadway is located right below the coal pillar. The plastic zone of roadway surrounding rock is symmetrically distributed with the axis of center line of the roadway. The damage caused to the bottom plate of the roadway is insignificant, but that caused to the top plate of the roadway and the two gangs is serious. When the roadway is arranged on both sides of the center of the coal pillar, the pattern of damage caused to plastic zone changes differently on both sides.

Fig. 19

Evolution pattern of the plastic zone at different locations of the roadway.

In the range of 0–30 m, i.e., when the roadway is arranged on the left of the remaining coal pillar, the plastic zone of the roadway surrounding rock is gradually deflected toward the top plate and bottom plate of the roadway from the position of 30 m. There is a gradual increase in the depth and range of destruction caused to the top plate and bottom plate of the roadway. Differently, the severity of destruction caused to both gangs is gradually reduced, but the depth of destruction caused to the left gang is smaller than the right gang. In the range of 30–65 m, i.e., when the roadway is arranged on the right of the remaining coal pillar, the plastic zone of the roadway surrounding rock changes in the same way as on the left. The plastic zone of the roadway surrounding rock is also deflected toward the top plate and the bottom plate of the roadway, but the plastic zone differs between the two gangs. The gang on the right of the roadway is destructed to a lesser extent than the gang on the left.

From above, it can be seen that J₂ is closely associated with the plastic zone. Since J₂ is symmetrically distributed along the axis of the coal pillar, it is only necessary to focus analysis on either side of the center line of the coal pillar. The relationship between them is shown in Fig. 20.

Fig. 20

Evolutionary pattern of J2 at different locations of the roadway.

From Fig. 20, it can be seen that the morphology of the plastic zone is highly relevant to J₂. At the position of 0 m, J₂ is mainly concentrated on the top plate and bottom plate of the roadway. Accordingly, the damage caused to the plastic zone is also mainly concentrated on the top plate and bottom plate of the roadway. As this position moves away, the area of J₂ concentration is deflected counterclockwise, gradually shifting toward the two gangs of the roadway. Accordingly, the area of plastic damage is also deflected counterclockwise.

From above, it can be inferred that when the roadway is arranged in the range of 25–35 m, the occurrence of plastic damage is concentrated on the top plate of the roadway and in the two gangs, the impact of the plastic zone is limited, and the roadway is easy to maintain. When the roadway is arranged in the ranges of 15–20 m and 40–45 m, plastic damage is deflected toward the left of the roadway top plate, the right of the bottom plate, and the right gang of the roadway. The plastic zone expands slightly compared with the area right below the coal pillar, where the roadway should be arranged. For the roadway, it is necessary to pay attention to the stability of the gangs of the coal pillar and that of the top plate of the roadway near the working face. When the roadway is arranged in the ranges of 0–10 m and 50–65 m, plastic damage is concentrated on the top plate of the roadway and the gangs of the coal pillar. Also, there is an increase in the depth and range of damage, which is likely to cause roofing and gang slice.

The area for rational arrangement of the roadway

To arrange the roadway at a place that facilitates maintenance and ensures safety, the area with high stability of the roadway perimeter rock is expected according to the distribution law of the mining stress field. Based on the above analysis of multiple factors leading to roadway damage, the combined impact of various factors was analyzed, as shown in Fig. 21.

Fig. 21

Range of reasonable roadway arrangement. (a) Effect of stress and principal stress ratio. (b) Clamping angle effect of the maximum principal stress.

As shown in Fig. 21, the values of various influencing factors fluctuate significantly in the region affected by the coal pillar, which is an unstable region. However, the minimum values of various influencing factors also exist in this region or at the boundary. Therefore, the study area was divided into two regions, namely H-I and H-II. According to the analysis of three different stresses, the area right below the coal pillar is under the maximum stress. Therefore, the roadway can be arranged in the area H-I or the edge area H-II, where the roadway surrounding rock is under low stress. However, the plastic zone of the roadway is larger, which is adverse to the support provided for the roadway. According to the analysis of principal stress ratio, the closer the area H-II is to the centerline, the smaller η is, the higher the stability of the roadway here, and the less severe the damage caused to the roadway surrounding rock. According to the analysis of maximum principal stress deflection angle, the deflection angle in area H-I is less than 38°, and the roadway is in a healthy state. At 240–265 m, the deflection angle in area H-II ranges from 38 to 41°, and the plastic zone is concentrated at the top of the roadway. This leads to a heightened risk of roadway topping.

Therefore, to better support the roadway surrounding rock, the roadway should be arranged at 15–20 m or 40–45 m according to the above analysis that takes into account various factors. The surrounding rock in this range is under low stress, and the principal stress ratio is about 1.5, and the plastic zone of the roadway has not evolved into the butterfly shape yet. For the surrounding rock in this range, the maximum principal stress deflection angle is less than 38°, and the butterfly lobe has not been deflected toward the top of the roadway. There, there is a low risk of roadway topping.

On-site conditions

According to the theoretical analysis and numerical simulation conducted on the reasonable location of the roadway, and by referring to the previous roadway layout of the mine and the reasonable length of the working face, the roadway was arranged right below the upper roadway, i.e., at 15 m. The layout of this roadway and the site of excavation are shown in Fig. 22.

Fig. 22

Roadway layout and site excavation plan. (a) Relationship of roadway layout. (b) Site of roadway excavation.

According to the above theoretical analysis, the roadway should be arranged in a way that enhances the support provided for the coal pillar gangs and the top plate on the left of the roadway. The roadway surrounding rock shows that the depth of damage caused to the top plate is greater than the coal pillar, with the two gangs exhibiting the signs of serious asymmetric and non-uniform deformation. According to the original scheme, theoretical analysis and field measurement were conducted to devise the proposal of optimization for this roadway, as shown in Fig. 23.

Fig. 23

Results of on-site measurement. (a) Optimization of roadway support scheme. (b) Roadway time-deformation curve. (c) Anchor resistance change curve.

As shown in Fig. 23b, the support force of anchors 1 to 4 cables changes steadily and the support force is basically stabilized at about 230 kN. At the same time, the working condition of the anchor cables in the test area is satisfactory, and the breaking of anchor cables does not occur. Therefore, a sufficiently long anchor cable can give full play to its extension performance, make it adaptive to the deformation of the top plate, and maintain a stronger working resistance. Also, no breakage occurs during the deformation of surrounding rock, which effectively ensures the reliability of the support system.

From Fig. 23c, it can be seen that there are three stages in the convergence of the roadway perimeter rock: intense deformation zone, deformation moderating zone, and deformation stabilizing zone. The deformation of the roadway starts to increase significantly for 0 to 20 days of measurement, with the top plate sinking by 34 mm, the bottom plate rising by 10 mm, and the left and right gangs retracting 17 mm and 16 mm, respectively. Also, there should be a shift in the control of roadway perimeter rock from deformation control to stabilization control, which allows a certain deformation of roadway surrounding rock in the initial stage. During 20 to 60 days of measurement, the deformation of the roadway begins to be moderated, and effective support is provided to ensure the load-bearing capacity. After 60 days of measurement, the deformation of the roadway surrounding rock reaches the maximum level and basically tends to stabilize. Finally, the deformation of the top and bottom plates and two gangs is within 40 mm, which indicates the effective control on the non-uniform deformation of the roadway. Therefore, the proposed scheme of support optimization can ensure the stability of roadway surrounding rock.

Results and discussion

• (1) The change of principal stress, principal stress ratio and stress deflection angle at the location of the bottom roadway caused by the mining of upper coal seam is the main influencing factor for the plastic damage of the roadway surrounding rock. The principal stress size determines the size of plastic zone in the roadway surrounding rock; the principal stress ratio affects the shape of plastic zone in the roadway surrounding rock; the angle of principal stress deflection affects the direction of plastic zone in the roadway surrounding rock.

• (2) With the centerline of the coal pillar as the axis, the influencing factors in the lower seam are symmetrically distributed. The plastic zone of roadway surrounding rock is basically concentrated in the middle and large on both sides, with the impact of the upper mined area becoming more significant as the distance to the center of the coal pillar increases. Also, there is an increase in depth of the plastic zone in the surrounding rock on the top plate of the roadway, and the plastic zone is deflected.

• (3) In order to arrange the roadway in a way that facilitates maintenance and is economical, the impact of major influencing factors are analyzed, and the geological conditions of the mine are taken into account. On this basis, it is determined that the roadway should be arranged in the edge area H-II, i.e., at 15–20 m or 40–45 m in the study area. The optimization of the original tunnel support parameters, combined with the data on field pressure observation, illustrates that the proposed scheme can produce the expected results.