Coal and Gas Outburst Affected by Law of Small Fault Instability during Working Face Advance

To analyze the effect of small faults in the working face on coal and gas outbursts, the coal and gas outburst accident in the 21431 working face was studied with the 3DEC numerical simulation method, and the main research contents were the change laws of both stresses at the small fault and the overburden strata movement rate in the small fault zone of which the drop height and the strike were designed into different groups. The results show that the risk of small fault slip increases with the advancing working face. In addition, there is a positive correlation between the risk and the small fault throw. The movement rate of overburden strata in the small fault zone increases along with the rising of the small fault throw, which increases the energy transferred to the coal seam from the surrounding rock under the effect of the small fault. Hence, the effect of small faults on the working face on coal and gas outbursts was positively correlated with the small fault throw. Under the influence of a small fault strike, the closer it is to the small fault along the dip distance at the same working face, the greater the risk will be of a coal and gas outburst. And the bigger the small fault strike is, the greater is the stress concentration degree in front of the working face and the more the elastic energy is stored and the greater is the possibility of an outburst. The paper analyzes the influence of small faults on coal and gas outbursts in the working face, which has reference significance for the prediction and prevention of coal and gas outburst disaster in the working face.


Introduction
In the production process of coal mines, the small fault is one of the major geological problems that have troubled mine production for a very long time. Due to the small fault structure of the mining face, even under low gas condition, coal and gas outbursts in the mining face are still frequent. By a statistic of the distribution rule of gas disasters in mining areas, it is found that the fault structure is closely related to the occurrence of the outburst [1][2][3][4]. According to relevant statistics, nearly 80% of coal and gas outburst accidents are caused by small faults [5,6], and these outburst accidents mostly occurred at coal roadway heading faces, followed by open-off cut, raise and dip, uncovering coal seam in the crosscut, mining face, and rock roadway heading face [7,8].
Coal and gas outbursts have been a major geological hazard to underground coal mining for over 150 years and continue to cause serious problems all over the world [9][10][11][12]. Coal and gas outbursts are extremely violent dynamic disasters [13]. The research from Guo et al. [14] believed that the prominent influencing factors changed from three to four, that is, the tectonic stress field, the physical and mechanical properties of tectonic coal, coal seam gas, and structural combination characteristics. The influence of tectonic, geostatic, and mining stresses on coal and gas outbursts (CGO) becomes more obvious with increasing mining depth [15][16][17][18]. Liu et al. [19] established a mechanical analysis model of the expansion and evolution of the plastic zone in front of the driving face by numerical simulation method, analyzed the characteristics of the expansion and evolution of the plastic zone in front of the driving face, and discussed the physical and mechanical process and basic conditions of the development of coal and gas explosion caused by the evolution of the plastic zone. Zhang and Lowndes [20] used fault tree coupling analysis (FTA) and an artificial neural network (ANN) model to predict the potential risk of a coal and gas outburst during underground mining of thick and deep coal seams in China. Zhai et al. [21] and Gong and Guo [22] statistically analyzed the 153 outburst accidents in the Pingdingshan mining region. The results indicate that the outburst accidents in this mining region were primarily influenced by the following factors: geological structure, mining depth, and the lithology of the roof and floor. In particular, gas outburst accidents of the highest frequency and intensity were reported in regions where geological structures were developed. Through the analysis of gas occurrence in the Pingdingshan mining area, Wang et al. [23] found that the in situ stress plays a leading role in the no. 8, 10, and 12 coal and gas outbursts and the outburst risk is the greatest. Chen et al. [24] took the Zhaozhuang coal mine as the research object and found through statistics that the control range of the fault with a drop of less than 5 m is about 30 m away from the pinch-out end of the fault. Guo et al. [25] analyzed the structural coal in nearly 60 coal and gas outburst cases in the Jiulishan mine of a coking coal group and found that structural coal accounted for 82.7%, indicating that the existence of structural coal has great risk of causing coal and gas outbursts. Shu et al. [26,27] studied the 3rd coal seam of the Shitai coal mine in the Huaibei mining area and found that fault structure plays an obvious role in controlling gas content.
Cui and Yao [28] found that the fault has a controlling effect on the nonuniformity of gas occurrence and nonequilibrium of gas drainage in the coal seam on the working face, and there is a large gas pressure gradient between the two coal seams on the fault, leading to coal and gas outbursts. Zuo et al. [29,30] according to the phenomena of coal and gas outburst induced by fault activation under dynamic disturbance. Based on the theory of fold mutation, the mechanical model of fault and surrounding rock mechanics was established, and the influencing factors of coal and gas outbursts were analyzed by introducing a dynamic disturbance factor. Zhao and Lei [31] think that in coal and gas explosions, the penetration of the plastic zone caused by high pressure gas storage and excavation disturbance is a necessary condition, and the mutation of the velocity field, displacement field, and stress field in the plastic zone is a sufficient condition. Zhao et al. [32] concluded that tectonic soft coal is mainly formed on the fault top wall under the effect of the fault structure. He and Chen [33] and Wei and Yao [34] discovered that the compressoshear fault formed because of large compressive stresses has a good effect on sealing the gas and is most beneficial to the occurrence of coal and gas outbursts. On the contrary, the extensional fault is conducive to releasing coal seam gas and not conducive to the occurrence of protrusion. The research of Jia et al. [35] found that as the angle between the fault strike and the direction of the stope main stress increases, the prominent hazard range also increases. With the heading of the working face toward the fault, the tectonic stress and the stope stress near the fault both form a relatively high concentrated stress, which is conducive to the formation of large protrusions [36,37]. Wang [38] found that coal and gas outbursts are more likely to happen when the working face moves from the top wall to the footwall.
However, considering the difficulty in accurately identifying small faults [39,40] (faults with a drop less than 5 meters) and the low gas content of coal seams in the mining area after gas drainage, it is difficult to let the coal and gas outburst accidents happen in the mining face [41]. Currently, for small faults, there are few studies on the control action of the minor faults' drop and trend on the coal and gas outburst in the mining face.
In the study of scholars like Huang et al. [42] and Wang and Lv [43], a fault with a drop of less than 5 meters was selected for study. However, the existing technology is not mature enough and the interference of different geological conditions makes it difficult to identify small faults with a fault spacing of about 3-5 m. Therefore, this paper selects the fault with a drop of less than 5 m (or even slightly more than 5 m) as a small fault to study the influence of small faults on coal and gas outbursts in the process of working face mining.
In this paper, the coal and gas outburst of the 2143 1 mining face of a mine are taken as the research object. The 3DEC three-dimensional discrete element numerical simulation method is used to analyze the control effect of different drops and different trends on the coal and gas outburst in the mining face during the coal seam mining process, in order to improve the effectiveness and pertinence of the mining face antiburst measures under the influence of small faults.

Mechanical Analysis of Fault Plane
The force model of a fault plane is established in a threedimensional Cartesian coordinate system, as shown in Figure 1. The plane ABCD is the simplification of the fault plane, and the X, Y, and Z axes are, respectively, parallel to the maximum horizontal principal stress σ 2 , the minimum horizontal principal stress σ 3 , and the vertical principal stress σ 1 . The line segment OE is the line connecting the intersection point E of the outer normal line of the plane ABCD with the fault plane and the origin O, and the angles with the X, Y, and Z coordinate axes are α, β, and γ, respectively.
For the stress analysis of the fault plane, the normal stress σ n and the shear stress τ on the fault plane are the resultant force of the vertical principal stress σ 1 , the maximum horizontal principal stress σ 2 , and the minimum horizontal principal stress σ 3 in the normal direction of the fault plane and the resultant force of the components on the fault plane.
According to the principle of force synthesis, the resultant normal stress σ n of the vertical principal stress σ 1 and the maximum horizontal principal stress σ 2 and the minimum horizontal principal stress σ 3 on the fault plane are σ n = σ 1 ′ + σ 2 ′ + σ 3 ′ = σ 1 × cos 2 γ + σ 2 × cos 2 α + σ 3 × cos 2 β: Because of the different directions of shear stress components, the results of force synthesis are as follows: Among them, the vertical principal stress σ 1 mainly depends on the burial depth. Then, where ρ is the average density of the overlying strata, kg/m 3 ; H is the burial depth, m; and g is the gravitational acceleration, 9.8 m/s 2 .
Because of the existence of pores in the rock mass, gas exists in the pores of the rock mass, which produces pressure on the pores. Considering the existence of gas, pore pressure (P) is introduced here, and the horizontal principal stress includes the axial horizontal tectonic stress (σ x and σ y ), the horizontal stress component(σ h ) of vertical stress (σ 1 ), and formation pore pressures (P); the maximum horizontal principal stress and the minimum horizontal principal stress σ 2 and σ 3 , respectively, can be expressed as where σ h is the horizontal component of the vertical stress σ 1 , MPa; σ x is the component of the tectonic stress along the X axis direction, MPa; σ y is the component of the tectonic stress along the Y axis direction, MPa; μ is Poisson's ratio of the rock material; δ is the Biot coefficient; and the horizontal stress component (σ h ) of the vertical stress (σ 1 ) is where n is the ratio of p to σ n , which is a constant. Substituting equations (3)-(5) into equations (1) and (2), the normal stress and shear stress formulas on the fault plane can be obtained: If there is no fluid flow system (no gas flow), then the maximum horizontal principal stress and the minimum horizontal principal stress σ 2 and σ 3 , respectively, can be expressed as (7) is changed to In addition, the relationship between the dip angle φ of the fault plane, the cross-section of the section, and the sharp angle ω of the maximum horizontal principal stress can also be obtained from Figure 1:

Geofluids
Bring it into equation (6) to get The derivative of equation (11) with respect to the fault strike ω: Since σ n is consistent with the trend of the three principal stresses, and σ x > σ y , so ∂σ n /∂ω > 0, that is, the resultant normal stress σ n on the fault plane is positively correlated with the fault strike ω; when ω = 90°, the normal stress σ n is the largest. That is to say, when the angle between the fault strike and the maximum horizontal principal stress of the stope is larger, the fault stress is larger. At the same time, ∂ð τ 2 − σ 2 n Þ/∂ω > 0 can be obtained, which means that as the fault strike increases, the difference between the shear stress and the normal stress increases continuously, and the shear stress on the fault plane provides the power for the unstable sliding of the fault. The normal stress on the fault plane prevents the unstable sliding of the fault, so the risk of an unsteady fault slide is positively correlated with the fault strike. This is consistent with the relationship between outburst frequency and fault strike found by Jia et al. [35] through the collation of outburst accidents in the Hegang mining area. That is, with the increase of the angle between the fault strike and the maximum horizontal principal stress, the number of outbursts begins to increase.

Calculation Model and Scheme
3.1. Project Summary. The coal seam no. 1 of a mine in Henan province is located in the lower part of the lower Shanxi formation of the Permian system, and its roof features are as follows: the pseudoroof is mudstone with an average thickness of 0.3 m. The direct roof is sandy mudstone with an average thickness of 8.6 m. The old roof is largely occupied sandstone with a minimum thickness of 6.6 m, a maximum thickness of 12.7 m, and an average thickness of 11.6 m. The floor of coal seam II 1 is characterized by the following: the direct floor is gray-black sandy mudstone containing plant debris fossils, and the local facies changes into medium-fine-grained sandstone. The minimum thickness is 6.67 m, the maximum thickness is 15.69 m, and the average thickness is 7.8 m. The minimum thickness of the base is 5.5 m, the maximum thickness is 14.7 m, and the average thickness is 9.1 m. The 2143 1 working face of the coal seam is 102 m away from the lower gateway. In the process of advancing, the working face encounters a normal fault. The normal fault strike has an included angle of 42°with the lower gateway, the fault inclination angle is 53°, and the drop is about 4 meters.

Numerical Calculation Model.
Based on mechanical analysis of the fault plane, the influence of small faults with different drop heights and different strike mining faces on coal and gas outbursts was studied, taking the 2143 1 mining face as the geological prototype; the small fault with drop heights of 1 m, 4 m, and 7 m; a strike of 90°; and an inclination angle of 53°; as well as with strikes of 42°, 65°, and 90°; an inclination angle of 53°; and a drop height of 4 m; all are selected and used for numerical simulation studies. A three-dimensional calculation model is established as shown in Figure 2 by using 3DEC numerical simulation software; the size of the model is 300 m × 80 m × 100 m.
The model has six free faces, in which the four sides and the bottom boundary of the model are fixed at zero speed by 3DEC_DP 5.00 Step 0 2018/3/18 16 4 Geofluids fetching a thin layer, and the top of the model is a stress boundary. The overburden load in the study area is simulated by loading the vertical stress at the top of the model, meanwhile loading the ground stress along the X axis and Y axis directions to simulate the horizontal principal stress. The numerical study area is a single coal seam mining with a buried depth of 450 m. An equivalent load of 9.68 MPa was loaded on the top boundary of the model. The physical and mechanical parameters of the coal and rock required by digital simulation methods are generally measured from physical experiments. However, most of the original rock masses contain rich joints and weak surfaces, so that the physical and mechanical parameters of the original rock mass are generally smaller than those measured by physical experiments. Therefore, the mechanical parameters of the numerical simulation require weakening of physical experimental data, taking 1/2-1/20 of the measured data in the laboratory. The physical and mechanical parameters of the coal seams required for numerical simulation are shown in Tables 1 and 2. 3.3. Computed Scheme. The working face of the model has a length of 80 m, is arranged parallel to the Y axis direction, and is mined in the positive direction of the X axis. The mining height of the mining face is 4 m. The length of each mining in the calculation process is 5 m with the calculation of 3000 time-stepping per step. In order to reduce the influence of boundary stress, a 20 m protective coal column is left at the opening of the working face.
In order to study the risk of instable slide of small faults with different drops during the advancing process of the mining face, the shear stress and normal stress on the fault surface are monitored. At the same time, by monitoring the movement rate of rock near small faults, the energy transferred from surrounding rock to the coal seam under the influence of small faults is reflected. When studying the influence of small faults with different strikes on coal and gas outbursts, the stress and displacement changes in the same mining face are monitored.
Faults are usually described by propensity, inclination, and drop. The small fault in the coal and gas outburst case selected in this paper can be described as 132°< 53°H = 4 m normal faults by the above three factors. Since the angle between the fault strike and the crossheading is 42°, in this numerical simulation, the direction of the crossheading is parallel with the direction of the maximum horizontal principal stress; therefore, the trend, inclination, and drop are used to describe the small fault studied in this paper. Then,  5 Geofluids the small fault in the coal and gas outburst case selected in this paper can also be described as a normal fault of 42°< 53°H = 4 m.
To discuss the influence of different small faults on coal and gas outbursts in the mining face, this chapter chose small faults with different strikes and drops as objects and studied the influence of different small faults on coal and gas outbursts. The scheme of numerical simulation in this paper is shown in Table 3.

Control Effect of Small Fault Drop on Coal
Mining and Gas Outburst Summarizing the variation of normal stress and shear stress on small fault zones with different drops, it can be found that when the working face was advanced to within 40 m-10 m from the fault, the tectonic stress of the small fault zone is gradually released, but the small fault has not been destabilized. The tendency to slide down the fault surface leads to an increase in the normal stress on the small fault zone. However, when the working surface is pushed within 10 m of the small fault, the normal stress on the fault zone drops rapidly, indicating that the small fault begins to lose its stability and slip.
According to the Mohr-Coulomb failure criterion, the shear strength (τ f ) on the fault plane is   6 Geofluids where C f and θ f are the cohesion and internal friction angles of the fault plane rock mass, respectively.
According to equation (13), the slip motion of the small fault and the ratio of shear stress to compressive stress on the small fault zones are related. In order to consider the risk of small fault slip instability of different faults, the shear stress and normal stress data of small faults is processed to obtain the line diagram of the shear stress and normal stress ratio of small faults with different faults during the advancement of the working face, as shown in Figure 5.
It can be seen from Figure 5 that the ratio of the shear stress to the normal stress of each small fault is generally consistent with the trend of the work surface propulsion, and both tend to increase slowly-slowly decrease-rapidly increase-rapidly decrease. The ratio of shear stress to normal stress decreases slowly between 45 m and 30 m from the small fault. However, in the same range, the normal stress and shear stress of the small fault is increasing, indicating that the increase rate of the normal stress on the small fault zone is greater than the increase rate of the shear stress. When the working face is 30 m-10 m away from the small fault, the ratio of shear stress to normal stress increases rapidly and reaches a maximum when it is about 10 m away from the small fault, indicating that the coal mining face enters the influence range of the small fault zone, the increasing trend of shear stress on the fault zone dominates, and the risk of small fault instability and slip is greatest. For small faults with a drop of 1 m, 4 m, and 7 m, the peak values of the ratio of shear stress to normal stress are 0.64, 0.684, and 0.79, respectively. When the mining face is pushed to within 5 m from the fault, the ratio of shear stress to normal stress decreases rapidly, which is caused by the rapid decrease of shear stress and normal stress on the small fault plane. At this time, the small fault begins to lose stability and slip.

Influence of Small Fault Drop on Impact Energy of
Overburden. Energy dissipation and energy release are important causes of rock mass failure [44][45][46]. When the small fault is unstable and sliding, the energy released by the small fault and the surrounding rock system consisting of the roof will be quickly transferred to the coal seam; assuming that the mass of the small fault zone and the roof plate system is m, the average velocity is v, and the time of energy release is t, the impact stress (F) and energy (W rock ) can be expressed as Since the impact time (t) is very small, the impact load (F) will be large. The energy released by the unstable coal rock mass contributes to the fracture of the coal body and creates favorable conditions for the occurrence of coal and gas outbursts.
According to equation (14), the energy released by the unit coal mass, i.e., the energy density w rock , is as follows: According to equation (15), the amount of energy released by the unit coal rock mass can be judged by the velocity of the overlying strata near the small fault (v).
The upper parts of small faults are sliced, and the displacement change rate of overlying strata during the advancing process of the mining face is observed to judge the energy transferred to the coal seam when the small faults with different drops are unstable. According to the previous analysis, when the mining face is pushed to 5 m away from the small fault, and the small fault begins to slip, the displacement rate cloud map of overlying strata was analyzed, as shown in Figure 6.
It can be seen from Figure 6 that when the mining face is advanced to 5 m of a small fault, the overlying strata of the high velocity movement on the section are concentrated near the upper end of the fault. In addition, comparing the peaks of the displacement change rate of the overburden strata under the influence of small faults with drops of 1 m, 4 m, and 7 m, it can be found that the peak value of the displacement change rate increases with the increase of the drop. Under the influence of a small fault with a drop of 7 m, the peak value of the overburden movement rate is the largest, and the value reaches 0.689.
In order to more accurately compare the energy transferred from the surrounding rock to the coal seam under the influence of small faults with different drop differences, the roof of the coal seam 5 m away from the small fault is monitored, and a broken line chart of the rate change of  Therefore, during the advancement of the mining face, when the small fault with a drop of 7 m is in the unstable slip, the surrounding rock transfers the most energy to the coal seam, which is most beneficial to the occurrence of coal and gas outbursts. When the drop is 1 m, the surrounding rock transfers the least energy to the coal seam, and the promotion of coal and gas outburst accidents is the weakest.

Controlling Effect of Strike of Small Fault on
Coal and Gas Outburst in Mining Face   8 Geofluids the small fault; when the small fault strikes at 42°, the peak velocity is 1.46, the peak velocity is 1.35 when the small fault strikes at 65°, and the peak velocity is 0.54 when the small fault strikes at 90°. The coal and rock mass in the mining face is decompressed by deformation, so that the supporting stress of the mining face is transferred to the deep coal and rock mass. From the velocity cloud diagram under the influence of small faults with strikes of 42°and 65°, it can be found that the closer to the small fault, the smaller the movement rate of the coal and rock mass; on the contrary, the farther away from the small fault, the higher the movement rate of the coal and rock mass. It can be seen that the small fault destroys the continuity of the roof and hinders the transfer of the supporting stress of the mining face to the deep coal and rock mass, which will result in the smaller the distance from the dip direction of the same mining face to the small fault within the influence of the small fault, the greater the stress concentration of the coal and rock mass and the greater the risk of coal and gas outbursts.
Under the influence of three kinds of small faults with different strikes, when the mining face advances to 0 m of the small fault, the coal and rock mass with a unit cell at the boundary of the XZ plane along the dip direction of the mining face is taken as the monitoring point A, and the stress changes are monitored and compared, as shown in Figure 9. It can be found that under the control of three small faults with different strikes, the original stress of the monitoring point A decreases with the increase of the small fault strike; in addition, the stress peak of the monitoring point A increases with the increase of the small fault strike; when the small fault strikes at 42°, the stress peak is 37.2 MPa;   9 Geofluids when the small fault strikes at 65°, the stress peak is 39.5 MPa; and when the small fault strikes at 90°, the stress peak is 43.8 MPa. Therefore, when the mining face is pushed into the range of influence of small faults, the larger the strike of the small fault, the greater the elastic potential of the coal rock mass stored in front of the face and the greater the possibility of protrusion.

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

Conflicts of Interest
The authors declare that they have no conflict of interest.