Distribution and Variation of Mining-Induced Stress in the Reverse Fault-Affected Coal Body

China Coal Technology Engineering Group Shenyang Research Institute, Fushun 113122, China State Key Laboratory of Coal Mine Safety Technology, Fushun 113122, China Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110819, China State Key Laboratory of Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China


Introduction
Reverse faults are common geological structures widely distributed in China's coal-producing areas [1][2][3], especially those in the southwest of the country, such as Guizhou, Yunnan, and Sichuan. Underground coal mine projects in these areas often take place across or close to these reverse faults [4][5][6]. In fact, the coal bodies often lose their stability when the mining face gets too close to the reverse fault [7][8][9][10][11]. Also, reverse faults have sealing properties, so mining stress will also have an impact on gas bearing and its migration. erefore, the mining activities in the reverse fault area inflict massive challenges to the site construction and maintenance [12][13][14]. To ensure safety and improve mining productivity around the coal seam in the reverse fault area, it is necessary to study the stress variation trend of reverse fault-affected mined coal bodies. At present, significant achievements have been made in the analysis of mined coal body stress in reverse fault regions. However, due to high susceptibility to rockbursts caused by the mining conditions-incurred reverse fault instability, plenty of research efforts have been focused on fields related to the prevention of rockbursts, such as stress variation, the stability of reverse fault zone, and the slip of reverse fault zone. To clarify the stress variation characteristics of reverse fault-affected mined coal bodies and explore the stress distribution characteristics of the mined coal bodies under various working faces, reverse fault distances, reverse fault dip angles, and fault throws, the actual working conditions of a typical working face in Guizhou mining area, were taken as the reference for the research herein.

eoretical Model.
To study the stress distribution characteristics of the reverse fault-affected mined coal body, we established a geomechanical analysis model for coal rocks, measuring H and L along the X and Y axes respectively, as shown in Figure 1. A reverse fault was designed in front of the mining face, and O marks the intersection point of the reverse fault and the roof of the coal seam. It is vertically subject to the stress of the overburden above the roof of the coal seam and horizontally to the horizontal stress. Under normal circumstances, the horizontal and vertical stresses are approximately equal, but due to the existence of a reverse fault, the horizontal compression should become obvious in actuality, so the horizontal stress is set herein as 1.5 times the vertical stress [4]. With the advancement of the mining face, the upper roof becomes an area subject to abutment stresses of various magnitudes and the front side of the working face and the rear side of the goaf become areas subject to increasing levels of abutment stress, whereas the goaf turns into an area subject to decreasing levels of abutment stress. With the advancement of the working face, the scope of the abutment stress also changes. Since hanging walls serve as the active plates in reverse faults, the effects of all mechanical stresses will also become more obvious. For this reason, the mining activities on the hanging wall of the reverse fault are taken as the object of mechanical analysis herein [15].
According to the distribution law of mine pressure [16], the vertical stress of roof can be divided into eight areas, the maximum stress value of AB and BC is K 1 · q x , the maximum stress value of FG and GH is K 3 · q x , the maximum stress value of CD and DF is K 2 · q x , and the stress value of OA and HJ is q x . e stress in the horizontal direction is q y , according to the boundary conditions of the mechanical analysis model of reverse fault, the horizontal stress is 1.5q x [4,12]. In order to quantitatively calculate the law of coal stress variation, the vertical stress variation curve of roof stress support area is simplified as linear variation.
In the analysis process, it is assumed that the coal geological body is homogeneous and isotropic. According to rock mechanics [16], the concentrated force P acting on the plane will affect any point M (x, y) below the plane, and its vertical stress value can be expressed as erefore, under the combined action of horizontal stress and vertical stress in the reverse fault-affected area, the vertical stress of M (x, y) can be expressed as

Advances in Civil Engineering
where q x is the vertical stress, MPa; q y is the horizontal stress, MPa; A, B, C, D, F, G, H, and J are Y-axis lengths, and K 1 , K 2 , and K 3 are stress concentration factors. When the coal load exceeds its strength, the coal body will undergo plastic deformation and fails, which leads to a reduction in stress. In view of this, the Mohr-Coulomb strength criterion was applied to analyze the stability of the coal body and determine whether failure occurs (see Equation (3)), before analyzing its stress characteristics. σ 1 − σ 3 σ 1 + σ 3 + 2 cot ϕ < sin ϕ, stability, where σ 1 is the first principal stress, MPa; σ 3 is the third principal stress, MPa; φ is the friction angle in coal body. While mining the working face, shear stresses on mined coal bodies are relatively negligible in magnitude compared with the vertical and horizontal stresses, which makes it reasonable to omit their contributions in calculations. In fact, vertical stress of the coal body is generally taken as the first principal stress and the horizontal stress of working face inclination as the third principal stress [17]. With the decrease of the distance between working face and reverse fault, the stress concentration magnitude of coal body in front of working face and σ 1 increase gradually. σ 3 is influenced by the mining roadway on both sides of the working face, so stress will not be concentrated during mining activities. Moreover, when the position of coal body in front of the working face and the working face is the same, the difference in σ 3 is not large and hence can be simplified as equal. As such, Equation (3) (σ 1 − sσ 3 )/(σ 1 + σ 3 + 2 cot φ) can be converted into 1 − ((2σ 3 + 2 cot φ)/(σ 1 +σ 3 + 2 cot φ)), whose value increases gradually with the increase of σ 1 .
is implies that (σ 1 − σ 3 )/(σ 1 + σ 3 + 2 cot φ) also increases gradually, which in turn indicates that, as the mining activity on the working face proceeds, the stability of mining-induced coal decreases gradually; when the coalbearing capacity exceeds its strength, the coal will undergo plastic deformation and fails, resulting in the reduction of coal stress. e same can be inferred that, as the mining activity proceeds along the direction of the working face to the reverse fault, if the coal-bearing capacity does not exceed its strength, the coal body stress in front of the working face will increase, and the stress concentration coefficient will gradually increase; if the bearing capacity of the coal body exceeds its strength, the coal pillar between the working face and the reverse fault will fail, and the coal body will effectively lose the capacity to bear the load inflicted on it, hence lowering the stress concentration coefficient of the coal body in front of the working face.

Mechanical Calculations Associated with the Reverse
Fault-Affected Mined Coal Body. Xinchun Coal Mine is located in the west of Tongzi County, Guizhou Province, with a designed production capacity of 900,000 t/a and service life of 62a. e 1503 working face is located in the southeast of the mine. e C5 coal seam has been mined to a depth of 300-420 m using the strike longwall mining method. In the mining area of the 1503 working face, there lies the F4 reverse fault, which has a fault dip angle of 60°, length of 195 m, fault spacing of 0-6 m, and average length of 4 m.
ere is no other structure in the mining area of the 1503 working face; the working face layout is as illustrated in Figure 2.
To get a clearer understanding of the mechanical distribution characteristics of the reverse fault-affected mined coal body, the required calculation parameters were selected from the field geological conditions of Xinchun Coal Mine: Advances in Civil Engineering vertical stress q x � 9.0 MPa, horizontal stress q y � 13.5 MPa, the distance between the coal seam and the roof � 9 m, and the mining height of the coal seam � 2.0 m. Relevant principles of mining science were consulted to determine the selection range of each stress zone, while a field investigation was conducted to determine specific parameters. Starting from a working face position separated by 70 m from the reverse fault, the distance parameter OA is 57 m, AB is 28 m, BC is 2 m, CD is 4 m, DF is 100 m, FG is 2 m, Hg is 28 m, K 1 is 2.3, K 2 is 0.8, and K 3 is 2.0. Substituting relevant parameters into (2), the vertical stress distribution curve of the mined coal body is calculated at various working face positions from the reverse fault, as shown in Figure 3.
When the distance between the working face and the reverse fault is 70 m, 40 m, and 10 m, respectively, there is a stress concentration area in front of the working face, and the coal body stress rises, and the vertical stress of the coal body reaches the maximum at 5 m in front of the working face. After that, the coal body stress begins to decline and gradually returns to the original stress state after exceeding the influence range of the stress increase area. By calculation, the maximum vertical stress of coal body in front of working face is 15.82 MPa and the stress concentration coefficient is 1.58 when the distance from the reverse fault is 70 m; when the distance from the reverse fault is 40 m, the maximum vertical stress of the coal body is 16.43 MPa, and the stress concentration coefficient is 1.64; when the distance from the reverse fault is 10 m, the maximum vertical stress of the coal body is 18.52 MPa, and the stress concentration coefficient is 1.85. It is found that with the decrease of the distance between the working face and the reverse fault, the stress concentration degree of the coal body in front of the working face increases, and the maximum value of the vertical stress increases.
When the distance between the working face and the reverse fault is 70 m, 40 m, and 10 m, respectively, stress concentration areas are formed in front of the respective working faces. In these areas, the coal body stress rises and the vertical stress of the coal body reaches its maximum at 5 m in front of the working face. After that, the coal body stress begins to decline and gradually returns to the original stress state after exceeding the influence range of the stress increase area. According to the calculation, the maximum vertical stress of the coal body in front of the working face is 15.82 MPa and the stress concentration coefficient is 1.58 when the distance from the reverse fault is 70 m. When the distance from the reverse fault is 40 m, the maximum vertical stress of the coal body is 16.43 MPa, and the stress concentration coefficient is 1.64; when the distance from the reverse fault is 10 m, the maximum vertical stress of the coal body is 18.52 MPa, and the stress concentration coefficient is 1.85. It was also found that, with the decrease of the distance between the working face and the reverse fault, the stress concentration magnitude of the coal body in front of the working face increases, and the maximum value of the vertical stress increases.

Numerical Simulation of the Stress in the Reverse Fault-Affected Coal Body
To verify the calculation accuracy of the mechanical model with respect to the coal body stress and explore the mechanisms of how the stress concentration coefficient of the mined coal body would both increase and decrease under the influence of the reverse fault, the FLAC 3D numerical simulation module was used to analyze the stress variation trend of reverse fault-affected mined coal body, using which the influences on the mined coal body stress exerted by mining the hanging wall versus the footwall, as well as by reverse fault dip angle, fault throw, etc., were discussed.

Numerical Model.
is study constructed the 3D numerical simulation model based on the 1503 mining face of Xinchun Coal Mine and declared the X-axis along the In the calculation, the mining process was simulated by excavation step by step, and the working face excavation was simulated by empty element. e reverse fault is simulated by adding 2 m-long weak bands in the middle of the upper and lower walls of the model. In the simulation, the coal-rock body model was regarded as an elastoplastic body and the Mohr-Coulomb model was selected. e mechanical parameters of coal and rock mass in 1503 working face used in the simulation process are selected according to references [18,19], and the mechanical parameters of coal and rock mass are as shown in Table 1. Vertical movements were limited by the X and Y directions of the model and the Z-direction of the bottom plane. e upper part is a free surface, on which a vertical load is to be applied to simulate the dead weight of the overlying strata. e vertical stress is 9.0 MPa, and stress with 1.5 times of that magnitude will be applied along the horizontal direction.

Variation of Hanging-Wall Mining-Inflicted Stress on
the Coal Body. When the working face was 70 m, 40 m, and 10 m away from the reverse fault, the vertical stress distribution of coal body is shown in Figure 4.
When the working face is 70 m away from the reverse fault, under the shearing action of the reverse fault, the roof of the coal seam becomes wedged, the vertical stress concentration of surrounding rock is relatively low, and the maximum vertical stress of the coal body in front of the working face is 18.2 MPa. When the working face is 40 m away from the reverse fault, the vertical stress concentration magnitude of the coal body in front of the working face increases, and the maximum vertical stress increases to 19.2 MPa. Lastly, when the working face is 10 m away from the reverse fault, the vertical stress concentration of the coal body in front of the working face further increases, and the maximum vertical stress rises to 19.8 MPa. From the statistics above, it can be concluded that, when the working face is mined toward the direction of the reverse fault, as the distance from the reverse fault decreases, the stress concentration magnitude of the coal body in front of the working face gradually increases, and the maximum of the advanced stress gradually increases.
Stress monitoring points were arranged at 65 m, 35 m, and 5 m away from the reverse fault, and the variation curve of the vertical stresses at the monitoring points was obtained as the mining activity on the working face proceeds, as shown in Figure 5.
With the advancement of the working face, the vertical stresses of the coal body at the monitoring points significantly increase. When the mining face is 110 m away from the reverse fault, the stresses captured by the three monitoring points show little difference. e monitoring point at the 65 m point is closer to the working face at this instance; hence, the greater influence from the mining activities and the highest vertical stress were recorded. e 5 m monitoring point is farthest from the working face; thus, the influence of mining activities is relatively small and the vertical stress is the least. At 70 m away from the reverse fault, the maximum vertical stress read by the monitoring point at the 65 m point Compared with the results of mechanical calculation, the numerical simulation results are identical to the conclusion of mechanical analysis. e stress concentration magnitude of the coal body in front of the working face is gradually increasing, and the maximum stress value is constantly increasing. Moreover, the stress concentration magnitude of theoretical calculation is basically consistent with the results in Figure 5, which again confirms the accuracy of theoretical analysis.

Variation of Footwall Mining-Inflicted Stress on the Coal Body.
In order to analyze the footwall mining-inflicted stress on the coal body, when the working face was 70 m, 40 m, and 10 m away from the reverse fault, the vertical stress distribution of coal body was shown in Figure 6.
During footwall face mining, the coal body stress distribution also shows a variation trend whereby the closer the coal body gets to the reverse fault, the more concentrated the coal stress becomes. When the footwall working face is 70 m away from the reverse fault, the maximum vertical stress in front of the working face is 17.4 MPa; 40 m away, the maximum vertical stress becomes 18.9 MPa; 10 m away, and the maximum vertical stress rises to 19.0 MPa. Comparing the stress distribution in the event of hanging wall mining, it can be concluded that footwall mining incurs weaker stress concentration.
Stress monitoring points were arranged at 65 m, 35 m, and 5 m away from the reverse fault, and the variation curve of the vertical stresses at the monitoring points was obtained as the mining activity on the working face proceeds, as shown in Figure 7.
With the advancement of the working face, the stresses recorded at the monitoring points increase.

Influence of Reverse Fault Dip Angle on Coal Body
Stress. Four reverse fault mining simulation models were established. Adjustments made for the model used throughout this experimental section were as follows. e mechanical properties of the fault plane are the same, the fault throw, the rock physical and mechanical properties are the same, and only the reverse fault dip angle has been changed to 30°, 45°, 60°, and 75°, respectively. e stress distribution characteristics of the mined coal body are as shown in Figures 8-10.
When the working face is 70 m and 40 m away from the reverse fault, the larger is the reverse fault dip angle and the smaller is the maximum advanced stress of the coal body.
is is caused by the varying reverse fault dip angles, which diversify the volume of the resulting trapezoidal coal pillars between the working face and the reverse fault. Analogously, the smaller the dip angle, the larger the coal volume above the coal pillar and the higher the load. Moreover, the presence of a reverse fault structure has also diminished the effectiveness of stress transfer across the mined coal bodies, increasing the gravity load on the coal pillars as well as the stress concentration.
When the working face is 10 m away from the reverse fault, the stress on the coal body in front of the working face reaches its maximum when the dip angle of the reverse fault is 45°. Compared with the stress concentration area in front of the working face in Figure 10, part of the coal body stress concentration area does not reach its maximum at the 30°d ip angle reverse fault, whereas the maximum is reached at other dip angles. is suggests that only part of the coal body can still bear the load effectively in the stress concentration area at the 30°dip angle, whereas the remaining coal body part has failed and completely lost its load-bearing capacity, hence resulting in the reduction in stress concentration Advances in Civil Engineering magnitude. is conclusion further verifies that obtained in the theoretical analysis, which also claims the reduction in stress concentration. Stress monitoring points were arranged at 65 m, 35 m, and 5 m away from the reverse fault, and the variation curve of the vertical stresses at the monitoring points was obtained as the mining activity on the working face proceeds, as shown in Figure 11.
At 45°, 60°, and 75°dip angles, the stress concentration magnitudes of the coal body in front of the working face gradually increase, whereas at 30°dip angle, the stress concentration magnitude of the coal body in front of the working face gradually increases first before decreasing once the distance from the reverse fault reaches 10 m. It is also worthy to note that the change in reverse fault dip angle mainly affects the stress concentration magnitude of the coal body in front of the working face, and not the stress variation trend.
When the working face is far away from the monitoring point, the vertical stress is the initial stress, and when the working face is 35 m away from the monitoring point, the vertical stress begins to rise obviously. By comparing both the two stresses, it can be seen that the value of the stress where the increase is the most significant is 1.02-1.39 times that of the initial stress, as shown in Table 2.

Influence of Reverse Fault row on Coal Body Stress.
Four reverse fault mining simulation models were established. Adjustments made for the model used throughout this experimental section were as follows. e mechanical properties of the fault plane are the same, the fault dip angle, the rock physical and mechanical properties are the same, and only the reverse fault throw has been changed to 4 m, 10 m, 15 m, and 20 m, respectively. e stress distribution characteristics of the mined coal body are as shown in Figures 12-14.
When the working face is 70 m away from the reverse fault, the maximum stress of the coal body in front of the working face is between 18.2 and 18.5 MPa; at 40 m away, the maximum stress is 19.2-20.4 MPa; at 10 m away, and the maximum stress is 19.8-20.7 MPa. e coal body stress reaches its minimum when the throw is 4 m and is at its maximum when the throw is 20 m. is shows that the coal body stress increases with the fault throw.
Stress monitoring points were arranged at 65 m, 35 m, and 5 m away from the reverse fault, and the variation curves of vertical stresses at the monitoring points were obtained as the mining activity on the working face proceeds, as shown in Figure 15. When the working face is far away from the monitoring point, the vertical stress is the initial stress, and when the working face is 35 m away from the monitoring point, the vertical stress begins to rise obviously. By comparing the two stresses, it can be seen that the value of the stress where the increase is the most significant is 1.04-1.31 times that of the initial stress, as shown in Table 3.

Field Test of the Reverse Fault-Affected Coal Body Stress
To verify the accuracy of the theoretical analysis and numerical simulation, a field test was carried out in the 1503 working face of Xinchun Coal Mine, where intrinsically safe GZY25 borehole stress sensors were used to monitor the coal body stress in front of the working face to analyze the stress variation trend of the mined coal body. GZY 25 borehole stress sensors were mainly used for monitoring the stress change of coal and rock mass, which was composed of sensor, transmitter, and junction box. At 5 m, 35 m, and 65 m from the reverse fault of 1503 transport lane, the layout of measuring points was shown in Figure 2, Φ 42 mm stress test boreholes with 10 m depth were drilled, and the stress sensors were pushed inward using the given conveyor rod accessory. e variation of borehole stress with the advancement of the working face is as shown in Figure 16.
It can be seen that the stress variation trend of the three monitoring points is the same and that the coal stress gradually increases with the decrease of the distance from the working face. When the distance separating the working face and the monitoring point is 35 m, the stress starts to increase obviously. e stress change reaches its maximum when the separation lessens to 5 m. e stress change at the 5 m monitoring point is the largest, while the stress change at the 65 m monitoring point is the smallest, indicating that the closer is the distance to the reverse fault, the higher is the      It can be seen that as the distance from the working face decreases, the stresses at the three monitoring points gradually increase. However, the maximum vertical stress concentration at the monitoring point located 35 m away from the reverse fault is higher than that at the monitoring point located 5 m away, indicating that the coal body at the 5 m monitoring point failed and lost its load-bearing capacity, so the stress concentration magnitude decreases. It has also been verified that the stress concentration magnitude of the coal body decreases. Also, when the working face is 40 m away from the reverse fault, the vertical stress of the 5 m monitoring point increases obviously; when the 35 m monitoring point is 60 m away from the reverse fault, the vertical stress is significantly increased, indicating that when    Advances in Civil Engineering the working face is at a certain distance from the monitoring point, the mining-induced vertical stress on the coal body is significantly increased. is distance is related to several factors, such as mining speed, mining height, and reverse fault parameters.

Stress Variation Trend of Reverse Fault-Affected Mined Coal Body
Under the influence of mining, the coal body in the reverse fault region experienced an ongoing increase in vertical stress and an ongoing decrease in horizontal stress, until the coal body reached the point of structural failure. In the initial condition, without the influence of mining, the coal body was in the original rock tectonic stress state. With the approaching of the working face, the vertical stress of the coal body begins to rise and gradually reaches the peak pressure, before entering the pressure relief state when the coal body experiences failure, and the vertical stress decreases to the residual stress. On the other hand, when the horizontal dip stress of the coal body in front of working face is greater than that of original rock, under the influence of the inclined inlet and return air lanes of the working face, the horizontal inclined stress gradually decreases, there is no stress concentration, and the horizontal stress decreases linearly in the mining [20]. Factors such as hanging wall and footwall mining, reverse fault dip angle, and throw mainly affect the stress concentration magnitude of coal body, not the stress variation trend on the coal body. erefore, based on the theoretical analysis, numerical simulation, and field testing, it can be inferred that when the reach of the mining influence coincides with the test point, the vertical stress at the test point will begin to increase, and then with the further decrease in the separation between the working face and the test point, the vertical stress begins to increase significantly. At this point, the vertical stress of the coal body can be generalized as (1.02-1.39)c · H. Finally, once the test point falls on the stress concentration area in front of the working face, the vertical stress will reach its maximum at K · c · H. e horizontal stress then gradually decreases [20], and the variation of coal body stress progresses as shown in Figure 18.
Under the influence of reverse fault, the value of stress concentration coefficient K of the mined coal body is related to the distance L from the test point to the reverse fault, which mainly includes the following two situations: (1) When the working face is mined along the direction facing the reverse fault, with the decrease of the distance L from the reverse fault, if the coal-bearing capacity does not exceed its strength, the coal stress in front of the working face and hence the stress concentration coefficient K will increase gradually.
(2) When the working face is mined along the direction facing the reverse fault, with the decrease of the distance L from the reverse fault, the stress concentration magnitude of the mined coal body increases gradually at first, before decreasing, which occurs when the bearing capacity of the coal body  exceeds its strength, causing the coal body to fail and lose its load-bearing capacity, leading to the decrease in the stress concentration coefficient K.

Conclusions
(1) e mechanical analysis model of reverse fault-affected mined coal body was established, the coal stress characterization equation was derived, the coal stress distribution was calculated, and the Mohr-Coulomb strength criterion was applied to analyze the stability of the coal body. It could be inferred that the closer it gets to the reverse fault, the poorer is the stability of the coal body and that the stress concentration magnitude of the mined coal body is affected by the strength of the coal body. (2) FLAC 3D was used to study the stress variation trend of the mined coal body, and the accuracy of coal body stress calculated by the mechanical model was verified. It is concluded that in case of hanging-wall Advances in Civil Engineering mining, the stress concentration of the mined coal body decreases with the increase of reverse fault dip angle and increases with the increase of reverse fault throw. Also, the stress concentration magnitude in the case of footwall mining is less than that of hanging-wall mining. e choice to mine the hanging wall or footwall and the parameters of reverse fault affect the stress concentration magnitude of the coal body. At the same time, combined with the field monitoring results of the coal body stress measured by intrinsically safe GZY25 borehole stress sensors, it has been verified that the coal body stress concentration magnitude may either increase or decrease, depending on the actual conditions. (3) Based on theoretical analysis, numerical simulation, and field test results, when the mining activity on the working face proceed towards the reverse fault, the vertical stress of the coal body initially demonstrates a significant rise as the distance from the reverse fault lessens. At any point during this stage, the vertical stress can be generalized as (1.02-1.39)c · H. Going into the latter stage, once the test point falls on the stress concentration area in front of the working face, the vertical stress will reach its maximum, which can be acquired by K · c · H. Moreover, the stress concentration coefficient K is related to the distance L from the reverse fault, and two kinds of changes may take place. Firstly, if the coal-bearing capacity does not exceed its strength, the coal stress in front of the working face, and hence the stress concentration coefficient of the mined coal body, will increase gradually. Secondly, the stress concentration magnitude of mining coal body gradually increases first, before decreasing after the coal body bearing capacity exceeds its strength, during which the coal body experiences structural failure and loses its loadbearing capacity, ultimately resulting in the decline of the stress concentration coefficient.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.