Instability prediction model of remaining coal pillars under remining disturbance

To address the instability timing problem of residual coal pillars under mining disturbance, their stress migration law and instability mechanism were studied via numerical simulation, physical simulation, and engineering tests considering residual coal remining in the 3101 working face of the Shenghua Coal Industry. The results show that as the mining progresses, the stress concentrates on both sides of the remaining coal pillar and empty roadway. When the first coal pillar in front of the working face loses its bearing capacity, the stress is transmitted forward, resulting in the advanced collapse of the empty roadway roof and an excessive load on the second coal pillar in front of the working face. Additionally, the critical value prediction model of the coal pillar stability safety factor fs ${f}_{{\rm{s}}}$ was constructed. If fs ${f}_{{\rm{s}}}$ is less than the critical value during the repeated mining period, the remaining coal pillar must be reinforced. A hollow grouting crossed anchor is selected for coal pillar reinforcement; thus, realizing the safe mining of the remaining coal pillars. Our research results provide theoretical support for the safe secondary mining of coal in China and similar coal mines worldwide.


| INTRODUCTION
As China's main energy source, coal has long played the role of ballast and stabilizer for energy security in support of China's steady and rapid socioeconomic development. [1][2][3][4][5] Furthermore, it is expected to continue playing an indispensable role in the long-term future, particularly during China's energy transformation and development. [6][7][8] However, from 1931 to 2008, affected by outdated coal mining methods, the coal recovery rate was only 10%-25%, [9][10][11][12] and the remaining high-quality resources in the mine destruction area reached 77.3 billion tons, which were not effectively recovered. Substantial amounts of precious anthracite, 13 coking coal, and other scarce coal were wasted. Efficient residual coal recovery is conducive to the full utilization of scarce resources and the sustainable development of the coal industry. It is among the most important development directions for coal resource development. [14][15][16][17][18] According to previous research on traditional pillar goaf, the roof between the remaining coal pillars has been found to be suspended for a long time. In engineering practice, the local or total instability of the coal pillar group under disturbance has occurred many times, which leads to large-scale roof collapse, [19][20][21][22][23][24] in turn resulting in a sharp increase in the working resistance of the support and support crushing accidents. 25,26 This is completely different from solid coal mining. Traditional mine pressure and strata control theory cannot quantitatively explain the instability timing of the remaining coal pillars under mining disturbance.
Domestic and foreign scholars have carried out a lot of research on the instability of coal column groups. 27, 28 Hashiba and Fukui 29 and other researchers indicated that the failure of a single coal pillar causes the load to be transferred to an adjacent coal pillar and causes overload. This gradual overload process leads to group failure that results in a sudden collapse of the roof of the working face. Zhang et al. 30 studied the coordinated deformation model and stability of the thick rock-coal pillar system. Zhang et al. 31 constructed a fluid-solid coupling numerical model of a mine underground reservoir under the coupling effect of mining water immersion and defined the calculation method of coal pillar damage degree to quantify the damage degree of coal pillars. Wu et al. 32 proposed a coal pillar failure criterion and instability mechanism by analyzing the relationship between the surrounding rock stability and the size and stress distribution of the coal pillar. Liu et al. 33 produced the theory that the "basic measurement scale-borehole comprehensive parameter method," which can realize the evaluation of a complex fracture network proposed. The evaluation results indicate that the coal pillar failure exhibits obvious zonal characteristics and the damaged coal pillar can be divided into the stripping area, the yield area and the load-bearing area. Bertuzzi et al. 34 Come to the conclusion that the extended DISL multicurve envelope provides a very good predictor for the rock mass strength of coal pillars. Zhu et al. 35 found that the coal column failure in the chamber will lead to the sudden fracture of the key formation so that the working face support is squeezed by strong dynamic loads. Previous research results have been obtained through in-depth investigations on the instability law of coal pillar groups; however, there is a lack of in-depth research on the instability prediction model of coal pillar groups under disturbance conditions. Accordingly, in this study, a prediction model of coal pillar group instability under disturbance conditions is constructed via numerical and physical simulations and engineering testing to predict remaining coal pillar instability during the mining process. Our research results could provide theoretical support for the safe secondary mining of coal-scarce resources in China.

| ENGINEERING GEOLOGICAL CONDITION
In this study, the 3101 working face of the Shenghua Coal Industry, which is a typical residual coal mining working face after traditional pillar mining, is taken as the study object. According to survey statistics, the thickness of No. 3 coal seam is 6.5 m, the average buried depth is 300 m, the remaining coal pillar widths are 4-6, 9-10, 15-16, 19-21, and 24-27 m, and the remaining gob width is approximately 4-6 m. When the coal pillar width is large, due to the stability of the surrounding rock of the roadway, the width of the old roadway formed by the expansion can reach 9-12 m. To grasp the rock mechanical properties of the No. 3 coal seam roof in the Shenghua Coal Industry, two boreholes are arranged in the No. 3 coal seam roof. In addition, two boreholes are arranged on the solid coal roof to detect the mechanical properties of the roof rock and compare them with the remaining coal to determine the changes in the mechanical properties of the remaining coal roof and pillars.
After sorting the experimental data, the rock mechanical parameters are obtained, as detailed in Tables 1 and 2. Based on the change in the mechanical properties of the roof, as summarized in Table 3 Table 1. After the initial stress is balanced, the working face is mined along the X-direction with an excavation step of 2.5 m. A measuring point is set every 3 m in the coal seam (7 m from the model bottom boundary) to form a measuring line to monitor the vertical stress, as shown in Figure 1.

| Numerical simulation scheme
In this study, a total of 12 models were established to change the size and number of empty lanes and coal pillars. The empty lane sizes used were 5 and 10 m, the coal pillar sizes were 5, 10, 15, 20, and 25 m, the number of empty lanes was 2 and 3, and the number of coal pillars was 1 and 2. The specific numerical simulation test schemes are shown in Table 4. Data are recorded every 2.5 m of mining during face stopping: (1) Extract the stress value of each measuring point on the measuring line and draw the stress curve of each measuring line. (2) Record the yield state of the remaining coal pillar.

| Numerical simulation results and analysis
3.3.1 | Stress field and failure unit distribution of the roadway surrounding rock under mining disturbance Scheme 12 is similar to the 3101 working face of the Shenghua Coal Industry; thus, the stress migration law of scheme 12 is analyzed here. As shown in Figures 2 and 3, after the initial balance of the Scheme 12 remining model is achieved until the excavation is completed, the stress distribution cloud map of the roadway and surrounding rock and the distribution map of the failure unit are shown. The remaining coal pillars and empty lanes are numbered from left to right. The remaining coal pillar 1, remaining coal pillar 2, empty lane 1, empty lane 2, and empty lane 3 are, respectively, numbered from left to right. Owing to a large number of excavation steps, four representative stages are selected for analysis.
From Figures 2 and 3, it can be seen that when the remaining coal pillar model is balanced, the stress concentration area appears at the initial stage of excavation on both sides of the remaining coal pillar and the empty roadway. The stress at the remaining coal pillar 1 is 20-23 MPa, while that at the remaining coal pillar 2 is 16-18 MPa. In the mining process, the stress is redistributed. When the mining distance reaches 32.5 m, the stress is more concentrated on both sides of the remaining coal pillar and the empty roadway, and that at remaining coal pillar 1 reaches 22-26 MPa. At this time, the remaining coal pillar 1 plastic zone penetrates and the bearing capacity decreases, and the stress is passed forward, causing stress concentration at the remaining coal pillar 2. The stress increased by a large margin (to 20 MPa) and the roof above empty roadway 2 exhibited a large advanced caving area. When the mining distance reaches 62.5 m, the stress at remaining coal pillar 2 reaches 22 MPa, the plastic zone runs through it, and the bearing capacity decreases; the roof above empty roadway 3 collapses in advance. It can also be seen that as the remining progresses, the stress will concentrate to the remaining coal column and both sides of the empty lane, and a stress increase zone is formed inside the coal column. It is worth noting that the stress concentration degree is related to the coal column distance; the closer to the coal column, the higher the degree of stress concentration, basically in the shape of a "bubble." Meanwhile, the stress spreads horizontally towards the empty alley roof slate layer at the coal column boundary. The larger the size of the empty alley, the greater the influence of the roadway roof via the supporting pressure transmitted by the coal column. As stress concentrates on both sides of the remaining coal column and empty alley, the edge of the coal column first begins to yield, the effective bearing area gradually decreases, and the degree of stress concentration increases accordingly. The increase in stress will further expand the width of the coal column yield zone and reduce the width of the elastic core area of the coal column. The gradual submission or collapse of the edge of the coal column will lead to the gradual destruction of the coal column from the outside to the inside, and instability damage will occur when the effective support area of the coal column is reduced to a certain extent. When residual coal column 1 loses its bearing capacity, the stress here will be transmitted forward, resulting in the collapse of the empty alley roof and the stress at remaining coal column 2 will increase significantly. This may lead to sudden instability failure caused by excessive load on coal column 2 and cause sudden instability of large-scale coal column groups, inducing the "domino effect," leading to mining disasters.

| Yield failure analysis of the residual coal pillar under mining disturbance
In the mining process of Schemes 1-12, the remaining coal pillars are in a state of yield failure and are prone to instability and collapse. The stress of the roof and coal pillars at this time is shown in Figure 4A-M.
It can be seen from Figure 4 that when the mining distance of Scheme 1 reaches 35 m, the remaining coal pillar completely yields and fails. At this time, the width of the remaining coal pillar is 5 m, and the average stress is 10 MPa. From Schemes 2 to 5, when the mining distance reaches 45, 47.5, 50, and 52.5 m, respectively, the remaining coal pillars are completely yielded and destroyed, and the remaining coal pillar width is 10 m  It can be known from Figure 4A,C-E that with the advancement of the mining face in Schemes 1-10, the stress of the remaining coal pillars is redistributed due to mining. The shape of the gravitational curve of the unmined coal seam and the remaining coal pillar is basically the same, and the stress distribution curve of the empty roadway and the coal pillar is presented as a whole: from the linear rapid increase of the empty roadway to the peak, after the peak, the gravitational force falls back to zero (at the empty roadway), and then increases rapidly again and then slowly decreases and gradually stabilizes; according to Figure 4F-L, the shape and change of the stress curve of the first remaining coal pillar in Schemes 11-14 are similar to those in Schemes 1-10. The upper stress of the second remaining coal pillar is much smaller than that of the first remaining coal pillar before the first remaining coal pillar is mined. When the first remaining coal pillar is mined out, the stress of the second remaining coal pillar increases rapidly, but its maximum value is still smaller than that of the first remaining coal pillar.

| Coal pillar failure analysis
In engineering practice, it is relatively difficult to conduct research on the yield failure mechanical behavior of a "legacy coal pillar group" bearing system. The reasons for this are mainly manifested in the following aspects: (1) multiple influencing factors; (2) relatively long data monitoring cycles; and (3) difficult visualization of the destruction process. This seriously restricts the continuous advancement of related research, affecting the construction of coal pillar group instability prediction models under disturbance conditions. Therefore, it is proposed to construct a simplified structural model of the "remaining coal pillar group" bearing system in a composite residual mining area to provide guidance for coal pillar group instability analysis under disturbance conditions. Specifically, the structural model of the remining stope system of the remaining coal pillar group is simplified, and the yield failure characteristics of the remaining coal pillar structure with different height ratios are analyzed through laboratory experiments. Then, the coal pillar group instability prediction model under disturbance conditions is constructed.
Coal pillar stability in mining refers to stress redistribution on coal pillars after coal seam excavation. The maximum principal stress after redistribution does not exceed the elastic limit of the coal body; that is, coal pillars are in a stable state of elastic equilibrium. When the stress exceeds the elastic limit of the coal pillar, plastic deformation or shear dislocation occurs, resulting in coal pillar instability. At present, the main coal pillar stability evaluation methods are the ultimate strength theory and progressive failure theory. 36 The finite element strength reduction method is based on the progressive failure theory. By continuously reducing the strength parameters, the value of the strength parameters at the time of failure is obtained. Finally, the coal pillar stability is characterized by the safety factor f s .
(1) Coal pillar ultimate strength: The coal pillar stability has an important relationship with the strength of coal itself. The coal pillar ultimate strength is generally obtained using the Bieniawski formula as follows [36][37][38] : where σ p is the coal pillar ultimate strength, MPa; σ m is the coal pillar uniaxial compressive strength, MPa; w is the coal pillar width, m; and h is the coal pillar height, m; when w/h > 5, n = 1.4; when w/h < 5, n = 1. The coal pillar width height ratio is generally less than 5; therefore, n = 1. (2) Safety coefficient of coal pillar stability.
The ratio of coal pillar ultimate strength to its stress is called the coal pillar stability safety factor ( f s ); therefore, where σ s is the average coal pillar stress (as shown in Figure 4); the other parameters are the same as above.
When f s ＞1.5, the coal pillar maximum stress is mainly concentrated in the core area of the coal pillar, the entire coal pillar plays a bearing role, and finally, the coal pillar can remain stable. As f s gradually decreases, the maximum stress on the coal pillar gradually concentrates to the core area of the coal pillar, the plastic zone gradually increases, and the coal pillar is destroyed from the outside to the inside, eventually leading to the overall instability of the coal pillar.

| Physical simulation experiment
(1) A large coal-rock combined body is selected in No. 3 coal seam of the 3301 working face of the Shenghua Coal Industry and processed into a simplified structural model of the residual coal pillar bearing system with different height ratios. In the numerical simulation of the yield failure state of the remaining coal pillar, the size of the specimen is set to φ50 × 65 (diameter × height), φ50 × 33, and φ50 × 26 mm, and the remaining coal pillar diameter is 5, 10, and 12.5 m, respectively, as shown in Figure 5. (2) The stress-strain curve of the simplified structural model was obtained by loading the electrohydraulic servo rock mechanics test machine, and its uniaxial compressive strength was obtained accordingly. The main physical and mechanical parameters of the specimen are shown in Table 5.

| Coal pillar stability analysis
The uniaxial compressive strength of each simplified coal pillar in Table 4 and the ultimate pressure data of the remaining coal pillars in Figure 4 are substituted into Equations (1) and (2). After performing the calculation, the coal pillar stability safety factor when the coal pillar yields and collapses is shown in Table 6. Schemes 11 and 12 are numbered from left to right as coal pillars 1 and 2, respectively. In solid coal mining, when f s is less than 1.5, the coal pillar does not remain stable for a long time. However, it can be seen from Table 5 that during the re-existence of the remaining coal, the roof between the remaining coal pillars is suspended for a long time. In field engineering practice, the bearing capacity of the remaining coal pillars decreases due to the mining disturbance. When f s is greater than 1.5, the phenomenon of coal pillar yield and collapse also occurs. It can be concluded that (1) the larger the size of the empty roadway, the larger the critical value of f s when the remaining coal pillar collapses. (2) When mining the residual coal, the size of the remaining coal pillar is the same; however, the larger the size of the residual coal pillar, the easier it is for the coal pillar to lose stability, and the corresponding f s critical value is larger.
During the mining process, when the value f s is less than the critical value, the coal pillar enters the plastic failure stage and the strength of the coal pillar decreases. After the coal pillar enters the plastic failure stage, it is unstable under the action of overlying rock. The mechanical model of the roof of the working face can be simplified into a cantilever beam structure. The length of the cantilever beam is the sum of the width of the old roadway, the width of the coal pillar, the distance between the remining face, and the periodic fracture line. With the advancement of the working face, after the first weighting of the main roof, the structure formed by the fractured rock layer will undergo periodic weighting of the working face roof. If the length of the cantilever beam is greater than the periodic weighting step, the main roof will break in advance.

| Coal pillar instability prediction model
The coal pillar mining distance in Table 5 is x, and f s is y for the construction of the curve diagram of the remaining coal pillar mining distance and f s , as shown in Figure 6.
The correlation curve between the coal pillar width and the coal pillar stability safety factor is shown in Figure 6. When the empty roadway size is 5 m and the mining coal pillar size is 0, 2.5, 7.5, and 12.
where x is the remaining coal pillar mining width (m) and y is the coal pillar stability safety factor f s . The prediction model can predict the coal pillar stability safety factor f s critical value during the mining of the remaining coal pillars, with a calculation fitting data error of less than 5%. If f s is greater than the critical value during the residual coal remining period, the residual coal pillar can be safely mined; if f s is less than the critical value during this period, the residual coal pillar needs to be reinforced before mining. Applicable conditions: empty lane width: 5 and 10 m; roof and floor rock physical properties similar to the engineering background.  Figure 7, where σ m is an uniaxial compressive strength of 19 MPa. The calculation results are shown in Table 7.
It can be seen from Table 7 that the No. 2 coal pillar is most likely to yield and collapse; thus, the coal pillar stress gauge is installed on the No. 2 remaining coal pillar to record the coal pillar stress change. The coal pillar and surrounding empty roadway widths are approximately 20 and 4.5 m, respectively. A working face measurement schematic is shown in Figure 7. The uniaxial compressive strength of the left coal pillar specimen was obtained via sampling and testing. The real-time coal pillar stress was 20.49 MPa, as measured by the field coal pillar stress meter. According to the prediction model calculation, when the mining distance reaches 24 m, the remaining No. 2 coal pillar is approximately 10 m. At this time, f s is 1.62, which is less than the critical coal pillar stability safety factor value ( f s = 1.65). It can also be seen that the coal pillar yields and collapses at this moment, thus losing its bearing capacity, leading to the instability of the adjacent coal pillar due to excessive bearing capacity. This in turn results in a "domino" effect, causing largescale collapse and endangering a safe mining operation. Therefore, hollow grouting with a breaking force of 420 kN and a diameter of 22 mm is used to reinforce the F I G U R E 7 3101 working face support load measuring points and empty roadway residual coal pillar distribution map. A support pressure recorder is arranged along the inclination of the 3101 working face, and its measuring holes are, respectively, connected with the lower chamber of the front and rear columns of the support. The entire working face has five pressure support column monitoring pressure recorders (respectively, installed in the No. 4,No. 14,No. 26,No. 36,and No. 48 supports), whose positions are shown in Figure 7.
By monitoring the hydraulic support load, the change in roof pressure as the working face advances can be determined. We can also assess whether the prediction model is consistent with the industrial test.

| Mine pressure characteristics analysis
(1) Stress curve analysis of the No. 2 coal pillar.
The coal mining machine records the data every cycle until the No. 2 coal pillar is mined out. The stress curve of the No. 2 coal pillar is shown in Figure 8.
It can be seen from Figure 8 that before the mining distance reaches 15 m, the stress of the No. 2 coal pillar is approximately 9 MPa and increases slowly. After the mining distance reaches 15 m, the No. 2 coal pillar is mined; therefore, the coal pillar stress increase accelerates. After the mining distance reaches 24 m, the predicted position is reached, and the remaining No. 2 coal pillar is approximately 10 m. At this time, the stress of the No. 2 coal pillar reaches its peak at 20.53 MPa and f s is 1.88, which is greater than its critical value ( f s = 1.65). When the distance reaches 24-35 m, the stress of the No. 2 coal pillar decreases rapidly. When its mining distance reaches 35 m, the coal pillar is mined completely.
(2) Support working resistance distribution analysis. Figure 9 shows the average working resistance distribution of the front and rear columns of the bracket. According to the diagram, the average working resistance of the front column is distributed between 424 and 517.1 kN, accounting for 47%-57% of the rated working resistance. The average working resistance of the rear column is between 82.2 and 156.5 kN, accounting for 9%-17% of the rated working resistance. The working resistance of the front column is significantly greater than that of the rear column, and the rear column features low-resistance working characteristics. It can be seen that the ZF3800/15/23 four-column low-level caving hydraulic support exhibits low-resistance working characteristics after using a hollow grouting crossed anchor to reinforce the remaining coal pillars, which enables the smooth mining of the remaining coal pillars.

| Industrial test disscusion
(1) The prediction model reveals that the No. 2 coal pillar will yield and fail during the mining process. A hollow grouting crossed anchor with a breaking force of 420 kN and a diameter of 22 mm is selected to reinforce the remaining coal pillars. A ZF3800/15/23 four-pillar low-position top-coal hydraulic support is used to realize the safe mining of the remaining coal pillars, which verifies the effectiveness of the prediction model. (2) The industrial test results are consistent with the prediction model calculation results. Furthermore, a safety production is guaranteed by verifying the soundness and effectiveness of the prediction modeling method via field detection. The prediction model can provide a reference for the safe production of residual coal mining under similar engineering conditions.

| CONCLUSIONS
(1) As the mining process progresses, the stress concentrates on both sides of the remaining coal pillar and empty roadway. When the coal pillar in front of the working face loses its bearing capacity, the stress is transmitted forward, which leads to the advanced collapse of the empty roadway roof and an increase in stress at the coal pillar in front of the working face, potentially causing damage to the coal pillar due to excessive load. (2) The prediction model can predict the critical value of the coal pillar stability safety factor f s during the mining the remaining coal pillar group, with a fitting data error of less than 5%. If f s is less than the critical value during the remaining coal remining period, it is necessary to reinforce the remaining coal pillars before mining. (3) The prediction model results reveal that the No. 2 coal pillar will yield and fail during the mining process. A hollow grouting crossed anchor with a breaking force of 420 kN and a diameter of 22 mm is selected to reinforce the remaining coal pillar group. Furthermore, a ZF3800/15/23 four-pillar, lowposition, top-coal hydraulic support is used to realize the safe mining of the remaining coal pillar group, which verifies the prediction model effectiveness.