Case Study regarding the Stress Distribution and Microseismic Laws of Coal and Rock Underlying the Residual Coal Pillar

The stress distribution characteristics, stress gradient evolution, and focal mechanism of microseism (MS) events during mining of working face 103_ (lower) 07 under an overlying residual coal pillar were investigated. Numerical simulations and MS observations were utilized. The coupling relationship between the stress gradient and MS activity was also analysed, which indicated the correlation between the fracture of coal/rock and stress gradient. In addition, the secondary disturbance of the coal mining underlying a fractured hard-thick roof is discussed. The following four points were addressed: (1) the high stress initially concentrated under the edge of the overlying residual coal pillar, and its contribution to both the local coal and rock fracture and the signi ﬁ cant change in the stress gradient; (2) the deformation and fracture ﬁ rst occurred in coal and rock underlying the edge of the residual pillar. The stress concentration gradually transferred to the interior of the pillars and was accompanied by the failure of coal and rock; (3) a high correlation between the deformation and fracture of coal/rock and the stress gradient was observed. The fractures under the pillars principally appeared in the high-stress gradient area; (4) the disturbance caused by mining of the underlying working face may cause instability of the high-level fractured roof, accompanied by high-energy MS.


Introduction
Affected by the formation period and environment, coal resources generally exist in the form of multiple seams. Coal mining is gradually transferred to the lower coal seams, with gradual depletion of the upper coal seams. An advantage of multiseam coal mining is that the mining of the overlying coal seam can change the stress distribution overall, release the pressure and energy of the lower seams, and provide pressure-relief protection. The latter may reduce the occurrence of dynamic disasters, such as rock bursts and coal and gas outbursts [1][2][3][4][5]. However, for closely spaced coal seams (such as the bifurcation of coal), the stope stress distribution and rock stratum movement law may become more complex under the mutual disturbance of multiseam coal mining [6][7][8][9][10][11][12][13]. In addition, unreasonable mining layouts, such as residual coal pillars in goaf, are frequently more likely to cause local stress concentration and induce coal and rock dynamic disasters [14][15][16].
The stress field of the surrounding rock will be modified as a result of mining. The stress is redistributed [17,18], which in addition to changing the stress state of the mining coal seam, may also affect the stress structure for a certain distance above and below the coal seam [3,[19][20][21]. Macroscopically, the overlying coal seam can destroy the stratum structure and release the original elastic energy of the surrounding coal and rock, thus providing pressure-relief protection for the underlying coal seam [22,23]. Nevertheless, the stress can be transferred but cannot disappear, and the stress relief effect is limited to the pressure-relief area below the goaf. This is accompanied by stress concentration in the residual pillars, including corner and irregular pillars at the edge [4]. Under the action of excavation and unloading, the overburden will result in stress concentration at the edge of the goaf, and then, the concentrated stress is transmitted to the floor, which may cause the formation of the initial stress area, stress concentration area, and stress release area in the underlying coal and rock. The stress concentration area is roughly U-shaped [24][25][26]. The range of the stress concentration area in the underlying coal seam is directly related to the spacing between it and the overlying goaf [27,28]. Therefore, there are two different stress distribution areas in the underlying coal seam in a large-area goaf, including the stress concentration area under the residual pillars and the stress release area under the goaf, and a certain diffusion angle in the stress concentration area [29][30][31][32][33]. It is interesting that the disturbance of multiple seam mining may be principally manifested in the vertical stress, whereas the influence on the horizontal stress is unclear [34].
For the failure and instability of coal and rock caused by mining, microseism (MS) monitoring is more capable of reflecting the stress, deformation, and failure characteristics [35][36][37], compared to numerical, similar material simulations, and on-site observations [38][39][40]. Therefore, for the disturbance of multiseam mining, the stress concentration caused by the overlying residual pillars and the secondary deformation and fracture law of the overlying strata caused by the underlying working face can be understood using MS data. MS velocity inversion has been continuously developed and has become mature since the application of seismic wave tomography technology to the field of geophysics [41]. In addition, the coupling relationship between wave velocity, stress, and fracture has also been confirmed [42][43][44][45]. The focal mechanism analysis based on waveform is also widely used in underground engineering to determine the fracture characteristics of coal and rock [46][47][48][49].
Overall, much research on the change of stope stress distribution caused by overlying residual pillar and the corresponding MS effects have been carried out, and some progress has also been made. However, there are obvious differences in the stress distribution at different positions of the pillar, and there is also a certain time-space relationship between the fracture of coal/rock and stress distribution. Additionally, some researchers have noted that the failure and instability of coal and rock are closely related to the stress gradient [36,50].
Herein, based on numerical simulation and MS analysis, the stress distribution characteristics, stress gradient evolution, and focal mechanism of MS during mining under overlying residual coal pillars were investigated, and the coupling relationship between stress gradient and MS was also analysed. A correlation between the fracture of coal/rock and stress gradient was found. Moreover, the secondary disturbance of the underlying mining on the overlying high-level fractured roof is discussed.  (BCM), which was the last working face in this area. The southwest of the working face was the goaf of the 4304 working face, and the north was the goaf of the 103_ (lower) 06 working face. In addition, the goafs of 103_ (upper) 07 and 103_ (upper) 08 working face were located above the 103_ (lower) 07 working face. The thickness of the mining seam (i.e., #3_ (lower) coal) was 3.0-3.47 m with a dip angle of 5-28°, and the spacing between coal seams #3_ (lower) and #3_ (upper) was 9.34-11.14 m. The strike and dip lengths for the 103_ (lower) 07 working face were 635-992 m and 136-238 m, respectively, and the maximum mining depth was 477.36 m. The immediate roof was mainly siltstone and locally mudstone, with a thickness of 0-5.35 m. The primary roof was interbedded with medium-fine sandstone or siltstone, and the thickness was 3.54-12.50 m. The immediate floor was principally siltstone and locally mudstone, with a thickness of 0-3.18 m. The primary floor was interbedded with siltstone, fine sandstone, or fine sandstone, with a thickness of 8.56-18.77 m. The 103_ (lower) 07 working face was covered with Jurassic strata, with a thickness of 214-292.64 m, which was mainly composed of interbedded medium sandstone, fine sandstone, and siltstone. The spacing between the #3_ (lower) coal seam and the Jurassic strata was approximately 15.92-92.15 m. The geological structure of the working face was relatively simple, and there were two faults, x-f46 and x-f29, in the mining range. The working face was advanced from 4 August 2019 to 1 December 2020, and an overview of the 103_ (lower) 07 working face is shown in Figure 1.

Arrangement of MS
Geophones. An MS monitoring system was equipped with 24 geophones in the BCM, of which nine geophones were distributed near the 103_ (lower) 07 working face (in Table 1). Geophones 1#, 2#, 3#, 6#, and 7# were located close to the working face. The MS signal was recorded in real time during mining of the working face.

Stress Evolution Law and MS Characteristics in Coal
Pillar Areas. The irregular goaf of working face 103_ (upper) 08 was above working face 103_ (lower) 07, which resulted in the 103_ (lower) 07 working face advanced through the goaf boundary twice (defined as the first and second boundaries) during mining and approached the residual triangular pillar of the goaf at the completion of mining. Therefore, the effect of the residual corner and triangular pillars on the 103_ (lower) 07 working face was very evident. The stress evolution law and MS characteristics during mining of the working face under the overlying residual pillars remain to be analysed. This analysis would indicate the effect of the residual pillar on the underlying working face, especially under the corner pillar at the second boundary and the triangular pillar near the stopping line. were used to monitor the stress-ZZ of the area under the residual corner pillar, and the points along LX 2 and LY 2 were used to monitor the stress-ZZ of the area under the residual triangular pillar, as shown in Figure 1. The horizontal and vertical displacements were constrained at the bottom boundary of the model (the displacements along X, Y, and Z were 0), and the horizontal displacement was limited at the side boundary (i.e., the displacements along X and Y were 0), while the top boundary was parameterized as a free boundary. An equivalent vertical stress of 8.125 MPa was applied on the top boundary, and the horizontal stress was applied around the model according to 1.25 times of the vertical stress. The model adopted the Mohr-Coulomb strength criterion, and the mechanics of each stratum are shown in Figure 1(b). The surrounding mined working face was excavated to form goafs. After initial equilibrium, the 103_ (lower) 07 working face was excavated stepwise, utilizing 10 m steps. The stress parameters were recorded at the same time.

Stress Distribution under the Residual Pillars.
The stress distribution along the monitoring lines under the residual pillars during different advancing stages was calculated. The vertical stress distribution along the X and Y directions under the pillars is shown in Figure 2. The stress distribution is shown when the working face was advancing near the pillars (the position-X of the working face was 1052 m and 612 m, respectively).
According to Figure 2, the high stress was principally concentrated in the areas under the pillar edge and was affected by the bearing pressure of the goaf. The overall stress level of each point along the Y direction was greater than that along the X direction, which was related to the different degree of fracture of the overlying roof. There was a peak of vertical stress at the area under the pillar edge, and the vertical stress at each point near this area fluctuated significantly. In particular, for the points arranged along the X direction, the stress value fluctuated greatly. Combined with the plastic failure characteristics under the pillars indicated by simulations, it can be concluded that the stress concentration caused local failure of coal/rock under the pillar edge, accompanied by a significant change in the vertical stress gradient. According to the comparison of stress along the monitoring lines, all the maximum stress differences between adjacent points occurred in the areas under the coal pillar edge. Among these differences, the maximum occurred under the corner pillar (42.78 MPa and 53.49 MPa along the X and Y directions, respectively). These differences were significantly greater than those under the triangular pillar (37.22 MPa and 28.19 MPa along the X and Y directions, respectively). Additionally, the overall stress level under the corner pillar was also greater than that under the triangular pillar, and it was found that the mining of the working face had a significant disturbance effect on stress concentration, deformation, and failure of the nearby coal pillars.

Variation Characteristics of Stress Gradient and MS
under Residual Pillars. Coal and rock fracture occurs not only in the high-stress area but also in the high-stress gradient area as a consequence of the small binding force. Combined with the analysis of Figure 2, the stress difference between the adjacent points under the pillar edge was significant, and there was a substantial difference between areas experiencing the maximum stress (points X 1 and X 2 along the X direction and points Y 1 and Y 2 along the Y direction). Thus, based on the calculated stress at points X 1 , X 2 , Y 1 , and Y 2 , the coupling relationship between the stress gradient and MS during mining near the pillars is shown in Figure 3.
According to the evolution characteristics of MS during work face advancement (Figure 3), it was found that the count and maximum energy of MS increased significantly when advancing under the residual pillars. This indicated deformation and fracture of coal and rock under the superposition of the stress concentration under the coal pillars and the mining-induced disturbance stress. Interestingly, there was a high coupling between the stress gradient and MS. For example, the count and maximum energy of the MS events increased significantly when advancing to 66 m before the second boundary of the goaf, and the stress gradi-ent under the corner pillar edge also began to increase simultaneously. Subsequently, both the MS and stress gradient decreased synchronously to relatively small values at the edge area of the corner pillar. Similarly, the stress gradient and MS changed at the same time when advancing to the area under the triangular pillar, and the variation in the stress gradient corresponded to the change in the MS. Thus, it can be indicated that there was a high correlation between the deformation and fracture of coal/rock and the stress gradient.
Both the stress gradient and MS gradually increase when approaching the residual pillars, while it starts to decrease when deviating from the influencing area of the coal pillars. This indicates that the disturbance of mining on the stress distribution and failure of the area under the residual pillar was mainly affected by the advanced abutment pressure of the working face. In addition, the stress gradient and MS decreased when approaching the junction of the horizontal boundary extension line of the residual triangular pillar and tail entry of the working face, followed by a high value of MS energy (7:88 × 10 5 J), indicating that the elastic energy in the coal and rock under the residual pillar accumulated rapidly after local deformation and failure. This was influenced by the superposition of advanced abutment stress of the working face and lateral abutment stress of the goaf. Subsequently, macroscopic fracture occurred and was accompanied by high energy release.
In addition, the MS increased when advancing to 600 m under the middle position of the overlying goaf. High energy values appeared intermittently, indicating that the mining disturbance caused the reactivity and migration of the high-level fractured roof and generated high-energy tremors.

Distribution of MS Events under Residual Pillars.
According to the distribution of MS events with energy > 10 3 J under the pillar, as shown in Figure 4, the events were concentrated in areas of the corner pillar (area A), fault structure (area B), triangular pillar (area C), and section pillar (area D). Significant deformation and fracture of coal/ rock occurred, especially in the areas under the edge of coal pillars with abnormal stress gradients. In the entire area under the corner pillar, the MS events were mainly distributed along the tail of the 103_ (lower) 07 working face, confirming a significant correlation between the stress gradient and deformation and fracture of coal/rock. Additionally, high-energy MS events scattered throughout the overlying and adjacent goafs, indicating that the mining of the working face may cause further deformation and instability of the overlying fractured roof.
In conclusion, the numerical simulations showed that there were significant stress concentrations in the residual coal pillar areas, and the high stress was first concentrated in the areas under the edge of the pillars, causing local fracture of coal and rock; significant change in stress gradient occurred in those regions. Among these regions, the stress difference in the area under the junction of the pillar and goaf was the largest. Mining had an obvious disturbance effect on the stress distribution, deformation, and fracture of coal and rock under coal pillars, which was principally related to the advanced abutment pressure of the working face. There was a high correlation between the deformation and fracture of coal/rock. The stress gradient, the deformation, and fracture degree under the edge of pillars with abnormal stress gradients were greater than in other areas. Additionally, the mining disturbance of the underlying working face may cause the reactivity and migration of the high-level fractured roof, accompanied by high-energy tremors. 5 Lithosphere under the pillars during mining of the working face, the Pwave velocity and velocity gradient were inversed based on the MS signals.
2.3.1. Distribution of P-Wave Velocity. The inversion was divided into four stages when advancing through the corner and triangular pillars, and the distribution of the P-wave velocity at each stage is shown in Figure 5. The working face advanced through the corner pillar area from 7 January to 5 May 2020 and through the triangular pillar area from 15 October to 1 December 2020.
According to the distribution characteristics of the P-wave velocity under the corner pillar (Figures 5(a)-5(d)), the high P-wave velocity was mainly concentrated near the tail entry under the middle of the coal pillar. There was a significantly low value under the edge of the pillar, indicating that there was an obvious fracture in this area. The high stress was mainly concentrated in the middle of the coal pillar.    Many small-scale fractures near the tailentry caused the transfer of high stress to the front and outside of the working face. Finally, the macrofracture of coal/rock caused a decrease in concentrated stress near the pillar edge, and the high stress transferred was to the exterior of the working face.
According to Figures 5(e) and 5(f), the P-wave velocity under the triangular pillar first increased and then decreased, which was related to the gradual deformation and fracture of coal and rock under the pillar and the transfer of the advanced abutment pressure zone to the exterior of the pillar. The high velocity under the triangular pillar was mainly concentrated around the roadways, indicating that high stress mainly appeared in the small pillars formed by roadway intersections. In addition, the velocity under the edge of the pillar was low, and the high velocity gradually transferred to the area under the interior of the pillar with the advancement of the working face, indicating that the macroscopic fracture first occurred under the edge of the pillar and then gradually developed in the interior of the coal pillar.

Distribution of P-Wave Velocity Gradient.
Consistent with the distribution of P-wave velocity, the velocity gradient during mining through the corner and the triangular pillars was also divided into four stages, as shown in Figure 6.
In Figure 6, the high-velocity gradient was mainly distributed near the tailentry when advancing under the corner pillar and was gradually transferred to the area near the strike edge of the pillar. The high velocity gradient was significantly concentrated near the pillar edge from 15 March 2020 and increased from 0.3 km/s 2 to 1.2 km/s 2 . In addition, two large-energy events (1:06 × 10 5 J and 3:61 × 10 4 J) occurred near the pillar edge, where the macroscopic fracture of coal/rock was highly consistent with the high velocity gradient. Then, the high value was transferred to the exterior of the working face, and the range further increased, resulting in many small-scale fractures in this area (Figure 4). The high velocity gradient was mainly distributed in the roadway intersection area when advancing under the triangular pillar, indicating a high-stress gradient. The velocity gradient under the pillar increased, starting 24 October 2020. The  10 Lithosphere high value was significantly concentrated, which coincided with the large-energy event (7:88 × 10 5 J) that occurred on the 27 October. It was demonstrated that the macrofracture of coal/rock occurred in the high-value area of the velocity gradient.
In summary, the deformation and fracture first appeared in the area under the edge of the pillar. The high-stress concentration gradually transferred to the area under the interior of the coal pillar with macrofracture of the coal/rock. Additionally, there was an obvious stress concentration near the roadway under the pillar owing to the intersection effect, which resulted in a significant high-stress gradient. The deformation and fracture of coal/rock mainly occurred in the high-value area of the velocity gradient, and the macrofracture was very consistent with the high velocity gradient.

Spectrum Distribution.
Based on the distribution of the overlying coal pillars, four MS events located under the corner, and triangular pillars were selected to analyse the spectrum distribution law, as shown in Figure 7.
According to Figure 7, the dominant frequency of the four events was generally less than 4 Hz, with significant low-frequency components, indicating that the high-energy events near the edge of the coal pillars were generated by macrofracture of coal/rock. The dominant frequency of MS events under the residual triangular pillar was slightly less than that under the corner pillar, but its amplitude spectrum was greater than that under the corner pillar, showing that the former fracture scale was larger than the latter. Additionally, there was a high-frequency band of MS events on 19 March 2020, and its amplitude spectrum was significantly less than the others, which indicates that there were smallscale fractures.
To analyse the fracture characteristics of coal/rock before the high-energy event under the residual triangular coal pillar, the dominant frequency and location evolution characteristics of 12 MS events in the nearby area before 27 October 2020 were analysed, as shown in Figure 8.
As shown in Figure 8, all the dominant frequencies of the 12 events were greater than that of the event on 27 October 2020, in which the dominant frequencies of the seven events were greater than 30 Hz, and the maximum was close to 100 Hz, and the dominant frequencies of most events were distributed between 30 Hz and 40 Hz. The evolution trend of the spacing between each event and the high-energy event was roughly consistent with the evolution of the dominant frequency of the events. Interestingly, the development of MS events was roughly consistent with the high value distribution of the stress gradient in this area ( Figure 6). This indicated that the fracture was principally concentrated in the area with a high-stress gradient. In addition, microcracks developed from high-stress to low-stress areas, and the fracture scale increased gradually. Finally, macrofractures were formed.

Focal Mechanism.
Overall, 16 MS events located near the pillars were selected to calculate the focal mechanism solution, as shown in Table 2 12 Lithosphere respectively (Figure 10(a)). Combined with the focal mechanism solution of events 1, 2, 3, 5, and 6, it can be inferred that the stress near events 2 and 3 was high, while it was low in the areas of events 1 and 5, which resulted in obvious stress gradient changes and fractures of the coal and rock. According to Figure 10(b), events 8, 9, 10, and 14 near the triangular coal pillar were normal fault sliding, and events 13 and 15 were reverse fault sliding. It can be inferred that there was a high stress area under the edge of the pillar and a low stress area near the roadway, especially in the distribution area of events 9, 10, 13, and 15, which resulted in the formation of an obvious stress gradient between the area under the pillar edge and the roadway intersection area. In general, the focal mechanism solution of MS events near the overlying residual coal pillars also verified the relationship between the stress gradient and fracture.

Discussion
The #3 coal seam in the BCM was covered with a hard and thick Jurassic stratum, and its deformation and fracture were the main dynamic load sources. According to the analysis previously presented, the mining disturbance of the working face induced the reactivity and migration of the overlying fractured roof. Therefore, the activity law governing the overlying strata during mining of the working face was discussed based on the MS observations. The 103_ (upper) 108 working face was mined from 1 June 2014 to 9 January 2015, and the overlying roof strata remained in a stable state before mining the 103_ (lower) 07 working face. According to the comparison of MS during mining of the two working faces (Figures 3 and 11), the MS event count during mining of working face 103_ 13 Lithosphere (upper) 108 was significantly less than that of working face 103_ (lower) 07, while the former maximum energy was much greater than the latter. During the mining of the 103_ (upper) 108 working face, the maximum energy occurring in 31 days was greater than 10 5 J, of which, the maximum energy during 4 days was greater than 10 6 J and up to 3:16 × 10 6 J. The maximum energy of the MS events in the 103_ (lower) 07 working face was only 7:88 × 10 5 J.
According to the location of the height and energy of MS events in working face 103_ (upper) 108 (Figure 12), it can be inferred that the mining of the working face caused the initial deformation and fracture of the high-level hard and thick roof strata (Jurassic strata). To verify the disturbance effect of the underlying working face on the overlying fractured strata, the height of the MS events at different mining stages and regions of the 103_ (lower) 07 working face was statistically analysed, as shown in Figure 13.
In Figure 13(a), the MS events were principally concentrated near the coal seam. There were few events in the high-level rock strata before advancing to the second boundary of the overlying goaf. The MS events in the high-level roof increased significantly after approaching the second boundary of the goaf. The maximum level of the events was close to -100 m. The energy of some events with high-level distribution was very high and was mainly distributed between -250 m and -150 m, which was consistent with the distribution of the Jurassic strata. According to Figure 13(b), high-level MS events (located at -300 m to -100 m) were mainly concentrated in the goaf along the headentry (area A), the expanding area of the overlying goaf (area B), and the shrinking area of the 103_ (lower) 07 working face (area C). In area C, the distribution level of the events in the residual section coal pillar during the shrinkage stage of the working face was greater than that in the other two areas, and many events were located from -200 m to -100 m. Thus, it can be inferred that the roof stratus in the areas along the headentry and the expanded area of the overlying goaf was not fully fractured. The roof stratus continued to deform and break during mining of the underlying working face. The shrinkage area of the working face was located under the middle area of the 14 Lithosphere overlying goaf, and the deformation and fracture of the high-level strata occurred during mining of the overlying coal seam. The fractured roof strata deformed, fractured, and slipped again once mining disturbance occurred. Additionally, there are obvious high located events in the goaf on both sides of the working face (the areas indicated by the arrows outside areas A and C), which further explained the disturbance effect of mining of the underlying working face on the overlying fractured strata.

Conclusions
(1) The high stress was initially concentrated under the edge area of the residual coal pillar and caused local fracture of coal and rock, as well as a significant change in stress gradient. The stress difference under the junction of the coal pillar and goaf was the greatest (2) The disturbance effect of mining on the nearby coal pillar was principally related to the advanced abutment pressure. Under the superposition of mining disturbance and original stress, the deformation and fracture of coal/rock first occurred under the edge of the residual pillar. The stress concentration was gradually transferred to the pillar interior (3) There was a high correlation between the deformation and fracture of the coal/rock and stress gradient. Fractures under the pillar mainly occurred in the high stress gradient area, accompanied by macroscopic failure (4) Mining disturbance of the underlying working face may cause the reactivity and migration of the highlevel fractured strata, accompanied by high-energy mine tremors

Data Availability
The data used to support the findings of this study are available from authors.

Conflicts of Interest
The authors declare that there is no conflict of interests regarding the publication of this paper.