# Research of Rock Burst Risk Induced by Mining and Field Case in Anticlinal Control Area

Authors: Shitan Gu; Zhimin Xiao; Bangyou Jiang; Ruifeng Huang; Peng Shan
Journal: Advances in Civil Engineering
 (2018)

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## Abstract

Stress concentration caused by tectonic stress and mining disturbance in coal mines induces a unique type of rock burst. No. 3201 working face controlled by an anticline structure in the Shandong mining area is used as the research background. The formation mechanism for anticlines is analyzed. Theoretical research shows that the bigger the tectonic couple is, the smaller the foundation stiffness, and the greater the bending degree and elastic strain energy of the coal will be. The distribution characteristics of abutment pressure and maximum principle stress in anticlinal control areas are analyzed using UDEC numerical software. The results show that rock bursts result from interactions between abutment pressure and residual tectonic stress. The “connection-overlay-separation” phenomenon of abutment pressure presents with working face advancement. Furthermore, the energy criterion for rock burst initiation is established based on the energy principle. Residual energy “E0−EC” and rock burst danger characteristics during mining are discussed. Based on the simulation results, microseismic monitoring data for No. 3201 working face are analyzed, and the law of microseismic energy is consistent with the variation law for the residual energy “E0−EC” at the peak of the simulated abutment pressure. The microseismic energy and frequency are higher during mining, increasing the risk of rock burst events. It can provide scientific basis for prevention and control of rock burst.


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## Body

## 1. Introduction

Rock bursts are common dynamic disasters in coal mining. The elastic energy of coal and rock is released in the form of a sudden, sharp, and violent burst, with instantaneous destruction and rock expulsion. The intensity of a rock burst and the resulting damage are more prominent in abnormal stress areas of anticline structures. Since the first report of a British rock burst in 1738, the disaster has spread all over the world and presents a serious threat to safe mining [1–4]. Coal and rock geological history in anticline structures highlights the transformation and presents the geological structure characteristics of rock burst events. Complex tectonic stress fields and mining stress fields overlap in these structures, which increases the complexity of rock bursts and the difficulty of controlling them. Therefore, research on the mechanism of rock burst prevention has become one of the key scientific and technical problems in the field of rock mechanics [5, 6].Many scholars at home and abroad have carried out thorough research on the mechanism and prevention of rock bursts, with remarkable results. A series of theories, such as energy theory, stiffness theory, strength theory, and impact tendency theory, have been proposed [7–10]. At present, research on the theory of rock burst events is mainly focused on the crack propagation law, energy damage, and the stability of the local area on the basis of fracture mechanics, damage theory, and catastrophe theory. Dyskin et al. [11, 12] reported that roadways surrounding rock are affected by the concentrated compressive stress, which leads to the further growth and coalescence of cracks, finally causing the cracked surface to separate, and inducing rock burst by the buckling failure induces the impact. Based on the Griffith energy theory and the associated criterion, crack propagation is coupled with material damage, and the critical stress R value of a rock burst can be determined [13]. Some scholars [14–17] established a catastrophe structure instability model for coal and rock masses and analyzed the stress and stiffness of the surrounding rock as well as the expansion energy of coal and rock masses.The fold rock burst is a special type of rock burst that occurs in coal and rock masses. Because of the special environment of coal and rock masses and the stress environment, the cause of rock bursts in this area is complex. Wrinkles are usually the result of slow deformation of rock strata under the influence of horizontal pressure in the region; that is, a fold is formed under longitudinal bending [18]. Near the fold structure, the tectonic stress field is dominated by horizontal stress, and the mining stress fields are superimposed on each other. This produces more intense stress differentiation, resulting in high energy accumulation and leading to crack propagation, coalescence, and an irreversible process of nonlinear dynamics. Mining in the fold area can easily cause the release of stress-induced rock bursts, which often occurs in the axis of the fold [19–21]. According to the statistics released by the Tianchi Coal Mine and Mentougou Mine, rock bursts occurred 78 times in the geological structure area and 31 times in the anticlinal belt, accounting for 40% of rock burst events. The research indicates that the axis of the anticline, which has a wing angle greater than 45 degrees, and the turning position form tectonic stress concentration and accumulate a great deal of elastic energy. The rock burst induced by mining occurs in these areas [22–24]. To address the problems such as the lack of early warning methods and prevention technology for rock bursts, many scholars have conducted thorough research. As a result, rock bursts can be effectively controlled to a certain extent [25–29].At present, the mechanism of fault rock bursts has received the most attention. However, there are few studies on evolution laws for tectonic stress, mining stress, and energy evolution and the control mechanism for tectonic rock bursts. No. 3201 working face controlled by an anticline structure is used as the research background in this paper. The mechanical model for the anticline is constructed, and a theoretical solution for deflection and the elastic strain energy of the rock beam are deduced. The internal factors that affect the formation of the anticline and its impact are then discussed. A numerical model of the anticline is also established using UDEC software, and abutment pressure and the maximum principal stress distribution characteristics of the anticline under working faces with different mining distances are simulated and analyzed. Then, based on the energy principle, the criterion for rock burst initiation is established, and rock burst danger before the working face in the anticline-controlled area is studied. In addition, a microseismic monitoring system is used to monitor the microseismic events during the mining process of No. 3201 working face, as well as when the working face is close to and far from the axis of the anticline. The characteristics of microseismic events and the rock burst risk are discussed.


## 2. Formation Mechanism of Anticline Structure

### 2.1. Theoretical Solution for Anticline Formation

In a deep stratum environment, tectonic stress is the maximum principal stress, and the direction is generally at a certain angle to the horizontal with the tendency of the coal seam. Fold formation is closely related to tectonic stress. References [30–32] studied the causes of the Yanshan structure in the Hubei province in China, the Wuxu mine field in the Guangxi province in China, and the Taiyuan tilting structure in the Shanxi province in China. The results show that tectonic coupling is the source of fold formation. Therefore, the coal seam is equivalent to the Winker elastic support and the uniform load of infinite beams, and tectonic coupling is simplified to a single couple. The fold mechanical model is shown in Figure 1. The left side of the w-axis can forms a syncline structure, and the right side can form an anticline structure. The arbitrary microsection dx in the anticlinal model is intercepted, and the width of the microsection is 1 so that we can analyze the model stress, as shown in Figure 2.Figure 1
Mechanical model of a fold.Figure 2
Stress analysis diagram of the anticlinal microsectiondx.Based on the force balance of the microsectiondx,(1)∑Fw=0⇒Fs+dFs−Fs+kwdx−γhdx=0,∑M=0⇒M−M−dM+Fs+dFsdx+kwdx22−γhdx22=0,where Fs is the shear force; γ is the rock density; h is the depth of the rock stratum; M is the rock moment of the couple; k is the foundation stiffness; and w is the deflection.Simplification of Formula (1):(2)dFsdx=γh−kw,dMdx=Fs.From the mechanics of materials, we obtain(3)EId2wdx2=M,where E is the modulus of elasticity and I is the moment of inertia.By means of Formulas (2) and (3), a deflection equation for dx supported by the Winker elastic foundation is obtained:(4)EId4wdx4+kw=γh.From natural boundary conditions and continuous conditions for the beam, the solution for Formula (4) and dx strain energy can be expressed as(5)w=M0k/4EIke−k4EI4xsink4EI4x+γhk,(6)dVε=M2xdx2EI,where dVε is the strain energy of the rock beam macrosection dx.By means of Formulas (3), (5), and (6), anticlinal strain energy can be defined as follows:(7)V=∫0xdVε=∫0xM02e−2αtcos2αt8EIdt=M0264EIα3−e−2αx−e−2αxcos2αx,where α is the characteristic coefficient, α=k/4EI4 and t only represents integral variable in the article.In summary, the deflection of rock and the strain energy of microsectiondx are closely related to the bending moment and location. If the tectonic force is greater and the bending stiffness is smaller, the rock beam deflection and strain energy will increase. When mining disturbance occurs at the location, a great deal of energy stored in the coal and rock will be released instantaneously, which will easily induce rock burst.


### 2.2. Variation of Anticlinal Elastic Strain Energy under Different Factors

According to the geological data for No. 3 coal seam and No. 3201 working face in Shandong Mine, China, the mining area is affected by anticline structures. The relevant parameters for the calculation are as follows. The average depth of coal ish = 800 m. The mean thickness of the coal seam is 6 m. The elastic modulus E = 2.8 GPa of coal is measured using the TAW-2000 electrohydraulic servo testing machine, and flexural rigidity is EI = 5.04 × 1010 N·m2. The volumetric weight is γ = 25 kN/m3. For the foundation stiffness, k = 10 GPa, 15 GPa, and 20 GPa are used. Based on the measured results for in situ stress using the stress-relieving method, the ratio of the maximum horizontal stress to the vertical stress is 1.3–3.2. The tectonic stress concentration factor is taken as 1, 2, and 4, while the corresponding structural couple is M0 = 2.0 × 109 N·m, 4.0 × 109 N·m, and 8 × 109 N·m. In order to facilitate the analysis using the control variable method, anticline formation and energy accumulation are researched with variations in tectonic stress and foundation stiffness.


#### 2.2.1. Different Tectonic Couple

(1) Analysis of anticlinal deflection. When the foundation stiffness is k = 10 GPa, the tectonic couple is taken as M0 = 2.0 × 109 N·m, 4.0 × 109 N·m, and 8.0 × 109 N·m. The corresponding anticlinal deflection curve is shown as Figure 3.Figure 3
Distribution curves of anticlinal deflection with different tectonic couple.It can be seen from Figure3 that the uplift degree of the anticline is increased with the increase of tectonic coupling when foundation stiffness is constant. The deflection peak is located 2 m from the center of the w-axis. As the distance from the center of the w-axis increases, the deflection value of anticlinal with different couple decreases and gradually becomes consistent. However, a certain deflection value remains. The greater the anticline uplift is, the greater the dip angle of the working face will be.(2) Analysis of anticlinal elastic strain energy. When the foundation stiffness is k = 10 GPa, the tectonic couple is taken as M0 = 2.0 × 109 N·m, 4.0 × 109 N·m, and 8.0 × 109 N·m. The corresponding anticlinal elastic strain energy curve is shown in Figure 4.Figure 4
Distribution curves of anticlinal elastic strain energy with different tectonic couple.It can be seem from Figure4 that the anticlinal elastic strain energy increases with the increase of the tectonic coupling when the foundation stiffness is constant. With the increase of distance from the center of the w-axis, elastic strain energy presents a “logarithmic curve” change trend; that is, it appears to increase first and then gradually becomes gentle. Since there is still a certain amount of uplift deformation away from the center of the w-axis, a large amount of elastic energy is stored. When mining activity occurs at the anticline control area, the superimposition of the deformation energy caused by mining stress and the residual elastic energy increases. A small amount of energy is released in the form of surface energy, and the rest of the energy is the source of energy for the occurrence of a rock burst. At this time, if the released energy is greater than the energy consumed by the damage, it will easily lead to shock under mining disturbance (such as roof fracture movement, coal blasting, and mechanical vibrations).


#### 2.2.2. Different Foundation Stiffness

(1) Analysis of anticlinal deflection. When the tectonic couple is M0 = 4.0 × 109 N·m, the foundation stiffness is taken as k = 10 GPa, 15 GPa, and 20 GPa. The corresponding anticlinal deflection curve is shown in Figure 5.Figure 5
Distribution curves of anticlinal deflection with different foundation stiffness.It can be seen from Figure5 that the anticline deflection decreases with increased foundation stiffness when the tectonic couple is constant. The deflection peak is located 2 m from the center of the w-axis. As the distance from the center of the w-axis increases, the deflection value decreases. If key stratum exists in the coal strata, and the stiffness of the key layer is greater, the anticline structure is more difficult to form. However, the greater the stiffness of the key layer stored a large amount of energy, the greater the possibility of rock burst becomes.(2) Analysis of anticlinal elastic strain energy. When the tectonic couple is M0 = 4.0 × 109 N·m, the foundation stiffness is taken as k = 10 GPa, 15 GPa, and 20 GPa. The corresponding anticlinal elastic strain energy curve is shown in Figure 6.Figure 6
Distribution curves of anticlinal elastic strain energy with different foundation stiffness.It can be seem from Figure6 that the anticlinal elastic strain energy decreases with the increase of foundation stiffness when the tectonic coupling is constant. A large amount of elastic strain energy is stored in the anticlinal wing. When the mining face is pushed into the area, surrounding rock stress increases significantly with the influence of mining, and the stored elastic strain energy is likely to be released suddenly, increasing risk of rock burst.


## 2.1. Theoretical Solution for Anticline Formation

In a deep stratum environment, tectonic stress is the maximum principal stress, and the direction is generally at a certain angle to the horizontal with the tendency of the coal seam. Fold formation is closely related to tectonic stress. References [30–32] studied the causes of the Yanshan structure in the Hubei province in China, the Wuxu mine field in the Guangxi province in China, and the Taiyuan tilting structure in the Shanxi province in China. The results show that tectonic coupling is the source of fold formation. Therefore, the coal seam is equivalent to the Winker elastic support and the uniform load of infinite beams, and tectonic coupling is simplified to a single couple. The fold mechanical model is shown in Figure 1. The left side of the w-axis can forms a syncline structure, and the right side can form an anticline structure. The arbitrary microsection dx in the anticlinal model is intercepted, and the width of the microsection is 1 so that we can analyze the model stress, as shown in Figure 2.Figure 1
Mechanical model of a fold.Figure 2
Stress analysis diagram of the anticlinal microsectiondx.Based on the force balance of the microsectiondx,(1)∑Fw=0⇒Fs+dFs−Fs+kwdx−γhdx=0,∑M=0⇒M−M−dM+Fs+dFsdx+kwdx22−γhdx22=0,where Fs is the shear force; γ is the rock density; h is the depth of the rock stratum; M is the rock moment of the couple; k is the foundation stiffness; and w is the deflection.Simplification of Formula (1):(2)dFsdx=γh−kw,dMdx=Fs.From the mechanics of materials, we obtain(3)EId2wdx2=M,where E is the modulus of elasticity and I is the moment of inertia.By means of Formulas (2) and (3), a deflection equation for dx supported by the Winker elastic foundation is obtained:(4)EId4wdx4+kw=γh.From natural boundary conditions and continuous conditions for the beam, the solution for Formula (4) and dx strain energy can be expressed as(5)w=M0k/4EIke−k4EI4xsink4EI4x+γhk,(6)dVε=M2xdx2EI,where dVε is the strain energy of the rock beam macrosection dx.By means of Formulas (3), (5), and (6), anticlinal strain energy can be defined as follows:(7)V=∫0xdVε=∫0xM02e−2αtcos2αt8EIdt=M0264EIα3−e−2αx−e−2αxcos2αx,where α is the characteristic coefficient, α=k/4EI4 and t only represents integral variable in the article.In summary, the deflection of rock and the strain energy of microsectiondx are closely related to the bending moment and location. If the tectonic force is greater and the bending stiffness is smaller, the rock beam deflection and strain energy will increase. When mining disturbance occurs at the location, a great deal of energy stored in the coal and rock will be released instantaneously, which will easily induce rock burst.


## 2.2. Variation of Anticlinal Elastic Strain Energy under Different Factors

According to the geological data for No. 3 coal seam and No. 3201 working face in Shandong Mine, China, the mining area is affected by anticline structures. The relevant parameters for the calculation are as follows. The average depth of coal ish = 800 m. The mean thickness of the coal seam is 6 m. The elastic modulus E = 2.8 GPa of coal is measured using the TAW-2000 electrohydraulic servo testing machine, and flexural rigidity is EI = 5.04 × 1010 N·m2. The volumetric weight is γ = 25 kN/m3. For the foundation stiffness, k = 10 GPa, 15 GPa, and 20 GPa are used. Based on the measured results for in situ stress using the stress-relieving method, the ratio of the maximum horizontal stress to the vertical stress is 1.3–3.2. The tectonic stress concentration factor is taken as 1, 2, and 4, while the corresponding structural couple is M0 = 2.0 × 109 N·m, 4.0 × 109 N·m, and 8 × 109 N·m. In order to facilitate the analysis using the control variable method, anticline formation and energy accumulation are researched with variations in tectonic stress and foundation stiffness.


### 2.2.1. Different Tectonic Couple

(1) Analysis of anticlinal deflection. When the foundation stiffness is k = 10 GPa, the tectonic couple is taken as M0 = 2.0 × 109 N·m, 4.0 × 109 N·m, and 8.0 × 109 N·m. The corresponding anticlinal deflection curve is shown as Figure 3.Figure 3
Distribution curves of anticlinal deflection with different tectonic couple.It can be seen from Figure3 that the uplift degree of the anticline is increased with the increase of tectonic coupling when foundation stiffness is constant. The deflection peak is located 2 m from the center of the w-axis. As the distance from the center of the w-axis increases, the deflection value of anticlinal with different couple decreases and gradually becomes consistent. However, a certain deflection value remains. The greater the anticline uplift is, the greater the dip angle of the working face will be.(2) Analysis of anticlinal elastic strain energy. When the foundation stiffness is k = 10 GPa, the tectonic couple is taken as M0 = 2.0 × 109 N·m, 4.0 × 109 N·m, and 8.0 × 109 N·m. The corresponding anticlinal elastic strain energy curve is shown in Figure 4.Figure 4
Distribution curves of anticlinal elastic strain energy with different tectonic couple.It can be seem from Figure4 that the anticlinal elastic strain energy increases with the increase of the tectonic coupling when the foundation stiffness is constant. With the increase of distance from the center of the w-axis, elastic strain energy presents a “logarithmic curve” change trend; that is, it appears to increase first and then gradually becomes gentle. Since there is still a certain amount of uplift deformation away from the center of the w-axis, a large amount of elastic energy is stored. When mining activity occurs at the anticline control area, the superimposition of the deformation energy caused by mining stress and the residual elastic energy increases. A small amount of energy is released in the form of surface energy, and the rest of the energy is the source of energy for the occurrence of a rock burst. At this time, if the released energy is greater than the energy consumed by the damage, it will easily lead to shock under mining disturbance (such as roof fracture movement, coal blasting, and mechanical vibrations).


### 2.2.2. Different Foundation Stiffness

(1) Analysis of anticlinal deflection. When the tectonic couple is M0 = 4.0 × 109 N·m, the foundation stiffness is taken as k = 10 GPa, 15 GPa, and 20 GPa. The corresponding anticlinal deflection curve is shown in Figure 5.Figure 5
Distribution curves of anticlinal deflection with different foundation stiffness.It can be seen from Figure5 that the anticline deflection decreases with increased foundation stiffness when the tectonic couple is constant. The deflection peak is located 2 m from the center of the w-axis. As the distance from the center of the w-axis increases, the deflection value decreases. If key stratum exists in the coal strata, and the stiffness of the key layer is greater, the anticline structure is more difficult to form. However, the greater the stiffness of the key layer stored a large amount of energy, the greater the possibility of rock burst becomes.(2) Analysis of anticlinal elastic strain energy. When the tectonic couple is M0 = 4.0 × 109 N·m, the foundation stiffness is taken as k = 10 GPa, 15 GPa, and 20 GPa. The corresponding anticlinal elastic strain energy curve is shown in Figure 6.Figure 6
Distribution curves of anticlinal elastic strain energy with different foundation stiffness.It can be seem from Figure6 that the anticlinal elastic strain energy decreases with the increase of foundation stiffness when the tectonic coupling is constant. A large amount of elastic strain energy is stored in the anticlinal wing. When the mining face is pushed into the area, surrounding rock stress increases significantly with the influence of mining, and the stored elastic strain energy is likely to be released suddenly, increasing risk of rock burst.


## 2.2.1. Different Tectonic Couple

(1) Analysis of anticlinal deflection. When the foundation stiffness is k = 10 GPa, the tectonic couple is taken as M0 = 2.0 × 109 N·m, 4.0 × 109 N·m, and 8.0 × 109 N·m. The corresponding anticlinal deflection curve is shown as Figure 3.Figure 3
Distribution curves of anticlinal deflection with different tectonic couple.It can be seen from Figure3 that the uplift degree of the anticline is increased with the increase of tectonic coupling when foundation stiffness is constant. The deflection peak is located 2 m from the center of the w-axis. As the distance from the center of the w-axis increases, the deflection value of anticlinal with different couple decreases and gradually becomes consistent. However, a certain deflection value remains. The greater the anticline uplift is, the greater the dip angle of the working face will be.(2) Analysis of anticlinal elastic strain energy. When the foundation stiffness is k = 10 GPa, the tectonic couple is taken as M0 = 2.0 × 109 N·m, 4.0 × 109 N·m, and 8.0 × 109 N·m. The corresponding anticlinal elastic strain energy curve is shown in Figure 4.Figure 4
Distribution curves of anticlinal elastic strain energy with different tectonic couple.It can be seem from Figure4 that the anticlinal elastic strain energy increases with the increase of the tectonic coupling when the foundation stiffness is constant. With the increase of distance from the center of the w-axis, elastic strain energy presents a “logarithmic curve” change trend; that is, it appears to increase first and then gradually becomes gentle. Since there is still a certain amount of uplift deformation away from the center of the w-axis, a large amount of elastic energy is stored. When mining activity occurs at the anticline control area, the superimposition of the deformation energy caused by mining stress and the residual elastic energy increases. A small amount of energy is released in the form of surface energy, and the rest of the energy is the source of energy for the occurrence of a rock burst. At this time, if the released energy is greater than the energy consumed by the damage, it will easily lead to shock under mining disturbance (such as roof fracture movement, coal blasting, and mechanical vibrations).


## 2.2.2. Different Foundation Stiffness

(1) Analysis of anticlinal deflection. When the tectonic couple is M0 = 4.0 × 109 N·m, the foundation stiffness is taken as k = 10 GPa, 15 GPa, and 20 GPa. The corresponding anticlinal deflection curve is shown in Figure 5.Figure 5
Distribution curves of anticlinal deflection with different foundation stiffness.It can be seen from Figure5 that the anticline deflection decreases with increased foundation stiffness when the tectonic couple is constant. The deflection peak is located 2 m from the center of the w-axis. As the distance from the center of the w-axis increases, the deflection value decreases. If key stratum exists in the coal strata, and the stiffness of the key layer is greater, the anticline structure is more difficult to form. However, the greater the stiffness of the key layer stored a large amount of energy, the greater the possibility of rock burst becomes.(2) Analysis of anticlinal elastic strain energy. When the tectonic couple is M0 = 4.0 × 109 N·m, the foundation stiffness is taken as k = 10 GPa, 15 GPa, and 20 GPa. The corresponding anticlinal elastic strain energy curve is shown in Figure 6.Figure 6
Distribution curves of anticlinal elastic strain energy with different foundation stiffness.It can be seem from Figure6 that the anticlinal elastic strain energy decreases with the increase of foundation stiffness when the tectonic coupling is constant. A large amount of elastic strain energy is stored in the anticlinal wing. When the mining face is pushed into the area, surrounding rock stress increases significantly with the influence of mining, and the stored elastic strain energy is likely to be released suddenly, increasing risk of rock burst.


## 3. Stress Evolution Law of Anticline Axis with Mining

### 3.1. Establishment of Numerical Model

Based on the characteristics of anticline structures and rock bursts, the mechanical response of an anticline structure is simulated using UDEC numerical software. Considering the large scope of anticline geological structures, the numerical model is not based on the actual site modeling. The model only studies the response laws for mining coal stress under the influence of anticline tectonic structures. The design size of the model is 300 m × 180 m in the horizontal and vertical directions. Coal seam thickness is 6 m. Horizontal constraints are applied to the left and right boundaries of the model. The vertical constraint is applied to the bottom boundary. The vertical equivalent loadp (p=γH) is applied to the top of the model, for simulating the overburdened stratum. Volumetric weight γ is taken 25 kN/m3. Buried depth of coal seam H is taken 800 m. So, the vertical equivalent load p=γH=25kN/m3×800m=20MPa. The maximum horizontal principal stress is 3–5 times greater than the vertical stress [3]. Therefore, an initial horizontal stress of 60 MPa is applied to simulate the concentrated structure stress in the anticlinal axis. The Mohr–Coulomb model is used to calculate the numerical model. The simplified model is shown in Figure 7.Figure 7
Simplified graphic numerical model.


### 3.2. Evolution Law of Abutment Pressure

The numerical model is explored step by step in the UDEC numerical software, monitoring the abutment pressure at the range of 60 m in front of the coal wall. With continuous advancement of the working face, the evolution law of abutment pressure in front of the coal wall is obtained as shown in Figure8, in which negative distance between working face and anticlinal axis indicates that the working face has advanced through the anticlinal axis.Figure 8
The distribution curves of abutment pressure in front of the coal wall with different advancing distances. (a), (b), (c), and (d).
(a)
(b)
(c)
(d)The following can be seen from Figure8. (1) In Figures 8(a)–(c), with the advancing of working face, the abutment pressure increases significantly by the influence of tectonic stress. (2) When the distance is 4 m between the working face and anticlinal axis in Figure 8(c), the maximum value of the abutment pressure is 60 MPa. (3) When the working face advances through the anticlinal axis in Figure 8(d), the influence range of the abutment pressure decreases.Through numerical simulation, the “connection-overlay-separation” phenomenon of the abutment pressure is presented between the abutment pressure and the high tectonic stress. It is noted that the abutment pressure in front of the coal wall and high tectonic stress begins to intersect in Figure8(b). The two overlay each other in Figures 8(b)–8(d), and gradually separate in Figure 8(d).


### 3.3. Evolution Law of Maximum Principal Stress with Mining Influence

A vertical monitoring line is set up in the anticlinal axis of the numerical model. In the model, 7 monitoring points are established: 3 points are located on the roof (above the coal seam 0.6 m, 7.8 m, and 18.5 m), 3 points are located in the floor strata (below the coal seam 0.53 m, 7.68 m, and 18.42 m), and 1 point is located in the coal seam (above the floor 3.1 m). Using the UDEC numerical software to simulate the process of working face advancement, the evolution curves for the maximum principal stress in the anticlinal axis are shown in Figure9.Figure 9
Distribution curves of maximum principal stress of anticlinal axis. (a), (b), and (c).
(a)
(b)
(c)The following can be seen from Figure9. (1) When the mining face is greater than 40 m from the anticline axis, the coal seam and floor tectonic stress are not affected by the working face advancement. (2) When the mining face is 20–40 m away from the anticline axis, the stress from the coal seam, roof, and floor increases as the working face continues to advance. Additionally, the closer the floor rock is to the coal, the faster the maximum principal stress value increases. (3) Tectonic stress in the anticlinal axis increases rapidly when the distance between the working face and the anticlinal axis is less than 20 m. When the distance between the working face and anticlinal axis is 4 m, the maximum value for the abutment pressure is reached. (4) The roof and floor have some residual stress when the working face advances through the anticlinal axis.


## 3.1. Establishment of Numerical Model

Based on the characteristics of anticline structures and rock bursts, the mechanical response of an anticline structure is simulated using UDEC numerical software. Considering the large scope of anticline geological structures, the numerical model is not based on the actual site modeling. The model only studies the response laws for mining coal stress under the influence of anticline tectonic structures. The design size of the model is 300 m × 180 m in the horizontal and vertical directions. Coal seam thickness is 6 m. Horizontal constraints are applied to the left and right boundaries of the model. The vertical constraint is applied to the bottom boundary. The vertical equivalent loadp (p=γH) is applied to the top of the model, for simulating the overburdened stratum. Volumetric weight γ is taken 25 kN/m3. Buried depth of coal seam H is taken 800 m. So, the vertical equivalent load p=γH=25kN/m3×800m=20MPa. The maximum horizontal principal stress is 3–5 times greater than the vertical stress [3]. Therefore, an initial horizontal stress of 60 MPa is applied to simulate the concentrated structure stress in the anticlinal axis. The Mohr–Coulomb model is used to calculate the numerical model. The simplified model is shown in Figure 7.Figure 7
Simplified graphic numerical model.


## 3.2. Evolution Law of Abutment Pressure

The numerical model is explored step by step in the UDEC numerical software, monitoring the abutment pressure at the range of 60 m in front of the coal wall. With continuous advancement of the working face, the evolution law of abutment pressure in front of the coal wall is obtained as shown in Figure8, in which negative distance between working face and anticlinal axis indicates that the working face has advanced through the anticlinal axis.Figure 8
The distribution curves of abutment pressure in front of the coal wall with different advancing distances. (a), (b), (c), and (d).
(a)
(b)
(c)
(d)The following can be seen from Figure8. (1) In Figures 8(a)–(c), with the advancing of working face, the abutment pressure increases significantly by the influence of tectonic stress. (2) When the distance is 4 m between the working face and anticlinal axis in Figure 8(c), the maximum value of the abutment pressure is 60 MPa. (3) When the working face advances through the anticlinal axis in Figure 8(d), the influence range of the abutment pressure decreases.Through numerical simulation, the “connection-overlay-separation” phenomenon of the abutment pressure is presented between the abutment pressure and the high tectonic stress. It is noted that the abutment pressure in front of the coal wall and high tectonic stress begins to intersect in Figure8(b). The two overlay each other in Figures 8(b)–8(d), and gradually separate in Figure 8(d).


## 3.3. Evolution Law of Maximum Principal Stress with Mining Influence

A vertical monitoring line is set up in the anticlinal axis of the numerical model. In the model, 7 monitoring points are established: 3 points are located on the roof (above the coal seam 0.6 m, 7.8 m, and 18.5 m), 3 points are located in the floor strata (below the coal seam 0.53 m, 7.68 m, and 18.42 m), and 1 point is located in the coal seam (above the floor 3.1 m). Using the UDEC numerical software to simulate the process of working face advancement, the evolution curves for the maximum principal stress in the anticlinal axis are shown in Figure9.Figure 9
Distribution curves of maximum principal stress of anticlinal axis. (a), (b), and (c).
(a)
(b)
(c)The following can be seen from Figure9. (1) When the mining face is greater than 40 m from the anticline axis, the coal seam and floor tectonic stress are not affected by the working face advancement. (2) When the mining face is 20–40 m away from the anticline axis, the stress from the coal seam, roof, and floor increases as the working face continues to advance. Additionally, the closer the floor rock is to the coal, the faster the maximum principal stress value increases. (3) Tectonic stress in the anticlinal axis increases rapidly when the distance between the working face and the anticlinal axis is less than 20 m. When the distance between the working face and anticlinal axis is 4 m, the maximum value for the abutment pressure is reached. (4) The roof and floor have some residual stress when the working face advances through the anticlinal axis.


## 4. Energy Analysis of Rock Burst Risk

### 4.1. Energy Criterion of Rock Burst

According to the minimum energy principle of rock dynamic failure [33], the failure condition is when the stress exceeds the uniaxial compressive strength, that is σ>σc. Meanwhile, the corresponding energy consumption criterion can be expressed as follows:(8)Ec=σc22E.Research on many rock burst cases has shown that rock bursts often occur in brittle coal and rock. Under the influence of mining disturbance, this energy can easily be released suddenly, accompanied by the occurrence of shock. Based on the generalized Hook’s law, the elastic strain energy of coal in a three-dimensional stress state is calculated as follows:(9)E0=σ12+σ22+σ32−2μσ1σ2+σ1σ3+σ3σ22E,where E is the elastic modulus; μ is Poisson’s ratio; and σ1, σ2, and σ3 stand for the first, second, and third principle stresses.According to the energy theory [34, 35], when the energy released from an unstable coal rock system is greater than the energy consumed, a rock burst will be induced. Therefore, the energy criterion for a rock burst can be established as follows:(10)E0−Ec>0.For specific coal,E and u could be assumed to be constants to a certain extent, in order to theoretically analyze the law of coal seam energy. Therefore, Equations (8), (9), and (10) show that the elastic strain energy depends on the principal stress. When “E0>EC,” a rock burst may be induced in front of the coal wall.


### 4.2. Energy Analysis of Rock Burst Danger

The increased area of abutment pressure in front of a coal wall is a serious risk area. Therefore, the numerical calculation mainly studies the impact risk at the peak of abutment pressure. According to the test results for No. 3 coal mechanics, the coal compressive strength isσc = 18.8 MPa, the elastic modulus is E = 2.8 GPa, Poisson’s ratio is μ = 0.32, and Equation (8) can be solved as EC = 63.11 kJ/m3. The stress state of the abutment pressure peak from numerical simulation is shown in Table 1, in which negative distance between working face and anticlinal axis indicates that the working face has advanced through the anticlinal axis, and the corresponding curve “E0−EC” is shown in Figure 10.Table 1
Value of “E0−EC” at the peak of abutment pressure with different advancement steps.
Distance between face and anticlinal axis (m)
Maximum principal stress,σ1 (MPa)
Intermediate principal stress,σ2 (MPa)
Minimum principal stress,σ3 (MPa)
60
40.75
15.55
10.51
40
41.93
16.51
14.42
20
51.23
18.89
14.29
4
142.6
14.69
39.08
0
40.76
23.64
14.78
−2
44.00
16.30
11.68
−14
38.19
14.26
9.581
−30
32.62
12.70
8.809Figure 10
The “E0−EC” distribution curve of the abutment pressure peak.The following can be seen from Figure10. (1) When the mining face is greater than 40 m from the anticline axis, the residual energy “E0−EC” at the peak of the abutment pressure increases slowly, and the risk of a rock burst is low. (2) In the range of 4–40 m, the residual energy increases rapidly with mining, and the risk of a rock burst begins to increase significantly. (3) When the distance between the working face and anticlinal axis is 4 m, the residual energy “E0−EC” reaches a maximum value of 3066.17 kJ/m3, and the risk of a rock burst is at a maximum. (4) When the working face advances through the anticlinal axis, the value of “E0−EC” decreases, so the risk of a rock burst begins to weaken.


## 4.1. Energy Criterion of Rock Burst

According to the minimum energy principle of rock dynamic failure [33], the failure condition is when the stress exceeds the uniaxial compressive strength, that is σ>σc. Meanwhile, the corresponding energy consumption criterion can be expressed as follows:(8)Ec=σc22E.Research on many rock burst cases has shown that rock bursts often occur in brittle coal and rock. Under the influence of mining disturbance, this energy can easily be released suddenly, accompanied by the occurrence of shock. Based on the generalized Hook’s law, the elastic strain energy of coal in a three-dimensional stress state is calculated as follows:(9)E0=σ12+σ22+σ32−2μσ1σ2+σ1σ3+σ3σ22E,where E is the elastic modulus; μ is Poisson’s ratio; and σ1, σ2, and σ3 stand for the first, second, and third principle stresses.According to the energy theory [34, 35], when the energy released from an unstable coal rock system is greater than the energy consumed, a rock burst will be induced. Therefore, the energy criterion for a rock burst can be established as follows:(10)E0−Ec>0.For specific coal,E and u could be assumed to be constants to a certain extent, in order to theoretically analyze the law of coal seam energy. Therefore, Equations (8), (9), and (10) show that the elastic strain energy depends on the principal stress. When “E0>EC,” a rock burst may be induced in front of the coal wall.


## 4.2. Energy Analysis of Rock Burst Danger

The increased area of abutment pressure in front of a coal wall is a serious risk area. Therefore, the numerical calculation mainly studies the impact risk at the peak of abutment pressure. According to the test results for No. 3 coal mechanics, the coal compressive strength isσc = 18.8 MPa, the elastic modulus is E = 2.8 GPa, Poisson’s ratio is μ = 0.32, and Equation (8) can be solved as EC = 63.11 kJ/m3. The stress state of the abutment pressure peak from numerical simulation is shown in Table 1, in which negative distance between working face and anticlinal axis indicates that the working face has advanced through the anticlinal axis, and the corresponding curve “E0−EC” is shown in Figure 10.Table 1
Value of “E0−EC” at the peak of abutment pressure with different advancement steps.
Distance between face and anticlinal axis (m)
Maximum principal stress,σ1 (MPa)
Intermediate principal stress,σ2 (MPa)
Minimum principal stress,σ3 (MPa)
60
40.75
15.55
10.51
40
41.93
16.51
14.42
20
51.23
18.89
14.29
4
142.6
14.69
39.08
0
40.76
23.64
14.78
−2
44.00
16.30
11.68
−14
38.19
14.26
9.581
−30
32.62
12.70
8.809Figure 10
The “E0−EC” distribution curve of the abutment pressure peak.The following can be seen from Figure10. (1) When the mining face is greater than 40 m from the anticline axis, the residual energy “E0−EC” at the peak of the abutment pressure increases slowly, and the risk of a rock burst is low. (2) In the range of 4–40 m, the residual energy increases rapidly with mining, and the risk of a rock burst begins to increase significantly. (3) When the distance between the working face and anticlinal axis is 4 m, the residual energy “E0−EC” reaches a maximum value of 3066.17 kJ/m3, and the risk of a rock burst is at a maximum. (4) When the working face advances through the anticlinal axis, the value of “E0−EC” decreases, so the risk of a rock burst begins to weaken.


## 5. Field Case

The No. 3201 working face microseismic system detector is arranged as shown in Figure11. The system monitors microseismic events during the mining period for the working face in an anticlinal structure control area. The microseismic monitoring results are selected during the period from July to September 2016. During this period, the working face advances near the anticlinal axis, pushes to the axis, and eventually pushes through the axis. The events are analyzed statistically as shown in Figure 12.Figure 11
The arrangement diagram of No. 3201 working face microseismic system detector.Figure 12
Statistical analysis of No. 3201 working face microseismic events.The following can be seen from Figure12. (1) When the distance between the working face and the anticlinal axis exceeds 168 m, the coal in front of the working face is less affected by the anticlinial structure. Microseismic events and frequency are mainly affected by the mining factor. (2) When the distance between the face and axis is 104–168 m, the microseismic energy and frequency increase gradually with continuous advancement of the working face to the axis. (3) When the distance between the face and the axis is less than 104 m, the superposition of high tectonic stress and mining stress causes the abutment pressure to increase significantly, resulting in higher microseismic energy and frequency. (4) When the face advances through the anticlinal axis, reaching 60 m from the axis, the control of the anticline structure is weakened, and the microseismic energy and frequency are also reduced. From this analysis, it can be seen that the variation law for microseismic energy with the distance between the working face and the axis is consistent with the variation law for the residual energy “E0−EC” at the peak of the simulated abutment pressure.


## 6. Conclusions

(1)
Based on the Winker elastic foundation theory, a mechanical model for an anticline structure is constructed, and theoretical solutions for the deflection and elastic strain energy of a rock beam are deduced. The distribution features of rock beam deflection and elastic strain energy with the change of foundation stiffness and structural coupling are also evaluated using a control variable method, for exploring internal factors of anticline formation and the associated rock burst.
(2)
Affected by high tectonic stress from an anticlinal structure, the “connection-overlay-separation” phenomenon of abutment pressure is presented between the abutment pressure and high tectonic stress with working face advancement. Moreover, the connection area and the overlay area are at serious risk of a rock burst.
(3)
While the working face remains close to the anticline axis, the stress from the roof and floor, and the remaining energy value “E0−EC” of the abutment pressure peak increases continuously. When the working face advances through the anticlinal axis, the principal stress and residual energy begin to decrease. However, there are still residual stresses, which follow certain law distributions with mining.
(4)
The field example shows that the microseismic energy and frequency are affected by high tectonic stress and mining stress, and they increase significantly, which are associated with the possibility of rock bursts.



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*Source: 2632549-2018-10-22.xml*