Introduction
The stability of the surrounding rock mass of the roadway is not only related to the spatial position and its layout but is also affected by excavation dynamic disturbance [1–3], including the disturbing load such as rock burst. In the process of coal mining, the coal or rock mass accumulates a large amount of elastic energy under a state of high stress and is suddenly broken or thrown out with obvious dynamic effects, such as sound, vibration, or gas wave. According to the characteristics of rock deformation and the problems of earthquakes and rock bursts, scholars began to do some research work on rock bursts in coal mines in the late 1860s. Their research also gradually revealed that the rock burst is an instability phenomenon caused by crack propagation and deformation localization. This phenomenon is closely related to the mechanical properties of anisotropic rock mass with original cracks and also associated with the evolution of the stress-strain field in surrounding rock mass under external loadings. The changing of the stability of surrounding rock mass affects the occurrence of rock burst to a certain extent. For the rock medium, when the stress exceeds its peak strength, the rock mass begins to fail and its bearing capacity decreases with the increasing deformation, which is called material softening. Therefore, the instability and failure is essentially a physical instability for the structure of rock mass. Many scholars have carried out extensive research on excavation disturbance. Kan proposed that the deeply buried roadway will still be affected by the disturbance even if the distance is 5 times greater than the tunnel diameter according to the mining pressure observation method [4]. Zhou et al. studied the evolution characteristics of the excavation-disturbed region in the roadway and pointed out that the evolution characteristics of the excavation-disturbed region and the characteristics of the disturbing stress field have a certain degree of similarity [5]. Leng studied the relationship between the excavation rate and excavation disturbance and suggested that the reduction effect of excavation disturbance can be achieved by accelerating the excavation rate [6]. Zuo et al. studied the failure mechanism of deep rock roadway under dynamic disturbance and highlighted that a small disturbance can lead to large-scale instantaneous dynamic propagation of cracks when the depth of the roadway is significantly large [7]. Song studied different horizontal spacing, vertical distance, and excavation sequences of roadways and proposed influential factors for excavation disturbance in the roadway [8–12]. The current research mostly reveals the law of the surrounding rock stress and deformation from the perspective of the mechanism of rock damage and failure by disturbance. Li et al. explored the formation mechanism of the rock disintegration phenomenon of surrounding rock in deep rock mass tunnels from the perspective of stress wave propagation [13]. Wen et al. studied the dynamic response characteristics of rock under low-frequency perturbation loads and high-stress conditions for the stability of interlayer rock in the goaf during upward mining [14]. Mutaz prepared a physical model of 50 mm sandstone cubes, tested it under different loading conditions and proposed the crack mode-changing stress (CMCS) concept [15]. However, these tests and findings were obtained under the condition of static stress. The occurrence of disturbing load not only causes heavy casualties and huge economic losses but also causes surface collapse and local earthquakes.
This paper will establish the controlling equations for the dynamic stability analysis of the laminar split structure of the coal wall of the roadway theoretically from the perspective of disturbing load on the surrounding rock mass of the roadway. Additionally, it will discuss the influence of disturbing load on the stability of the surrounding rock mass of the roadway. The stability of the surrounding rock mass of the roadway in a rock burst accident will also be analyzed, which can provide a basis and reference for the risk analysis of rock burst under similar conditions.
Analysis on the Stability of the Laminar Split Structure of the Coal Wall of the Roadway With Disturbing Load
The Controlling Equations for Dynamic Stability Analysis
To explore the vibration problem of a general rectangular plate under longitudinal loading, such as the deflection , this paper assumes that the problem corresponds to plane stress in elastic theory according to the theory of dynamic stability of elastic system [16], and the corresponding longitudinal loading can be expressed as follows.
The vibration differential equation can be expressed as follows.
The deflection function can be expressed in series form as follows.
Substituting Equation (3) into Equation (1), the differential equations for the coefficient of deflection function in the series form are obtained as follows:
To analyze the disturbance effect of dynamic loading on the rectangular plate, the internal forces within the plate can be expressed by the proposed static stresses in the plane problem, regardless of the longitudinal inertia force. The expressions of loading are as follows.
The coefficient of deflection function in series form can be expressed as follows.
Equation (7) can be expressed in matrix form.
The intrinsic vibration frequency for the laminar split plate can be expressed by the following.
Equation (7) can be expressed as follows and is called the differential-integral Mathieu's equation.
(1) The case of simple support constraint at both ends
It is assumed that the laminar split rock (coal) is only subjected to a longitudinal dynamic loading σ = Nx(t), regardless of the influence of the inner loading Ny and Nxy on the laminar split plate. The longitudinal loading Nx(t) is simplified as the sum of the static pressure loading and the periodic loading , where is the amplitude of the periodic loading and is the frequency of the periodic loading.
Assuming that the deflection of the laminar split plate is , the dynamic equation can be expressed as follows according to the Kirchhoff theory of thin plates.
The intrinsic vibration equation of the laminar split plate can be expressed as follows.
Based on the principle that the static stability and intrinsic vibration need to be consistent, the deflection function is expressed as follows.
It satisfies the boundary condition of static stability as well as the boundary displacement condition of vibration.
The figure function of intrinsic vibration can be expressed as follows.
Substituting Equation (16) into Equation (14).
The frequency of intrinsic vibration can be expressed as follows.
Substituting Equation (18) into Equation (11), the dynamic stability equation for the laminar split plate with simple support constraint can be expressed as follows.
(2) The case of fixed constraint at both ends
The dynamic equation for the fixed constraint model can be expressed as follows.
The deflection function of the laminar split plate can be expressed as follows.
The figure function of intrinsic vibration can be expressed as follows.
The intrinsic frequency is calculated by the energy method, and the maximum deformation potential energy and the maximum kinetic energy of the computation model are required as follows.
The lowest intrinsic frequency of the laminar split plate is obtained by assuming m = 1.
The dynamic stability equation of the laminated plate with the fixed constraint model can be expressed as follows.
The Influence of Disturbing Load on Dynamic Stability
The boundary of the coal wall of the underground roadway is considered as a simple support constraint at both ends, where the height a is 3 m, and the thickness h is 0.1 m. The elastic modulus E of coal mass is 5 GPa, the Poisson's ratio μ is 0.3, the density is 1500 kg/m3, and the loads on the laminar split plate are N0 = 0.5Nc and Nt = μNc. The amplitude of the periodic load is between 0 and 0.4.
The boundary expression of the main dynamic instability region of the laminar split structure can be expressed as follows.
The value of parameter ω can be obtained by the value of other parameters.
The boundary of the main dynamic instability region reaches the maximum value when the value of amplitude is equal to 0.4, and the corresponding term is as follows.
The frequency of the main dynamic instability region in the coal wall varies from 33.3 to 100.13 Hz, and the dominant frequency of the blasting seismic wave is within this range. Due to the influence of drilling blasting disturbance, parametric resonance will occur in the laminar split plate and lead to dynamic instability.
When the laminar split plate is subjected to a longitudinal dynamic disturbing load, a continuous dynamic unstable region will probably emerge. If the frequency of disturbing load falls within the dynamic unstable region, the structure experiences parametric resonance and leads to dynamic instability. The boundary of the main dynamic instability region of the laminar split plate expands with the increasing amplitude of the cyclic disturbing load, and the larger the range of the instability region the greater the risk of structural instability. Attention should be paid to the influence of the disturbing load on the stability while maintaining the stability of the laminar split structure. By controlling the range of frequency of dynamic disturbing load and reducing the intensity of disturbing load, the amplitude of periodic disturbing load will be weakened, and parametric resonance will be prevented, which can maintain the dynamic stability of the laminar split structure.
The Influence of Disturbing Load on the Instability of Surrounding Rock Mass
After the stress reaches the ultimate strength, the surrounding rock mass may not immediately be destroyed and may maintain an unstable state of equilibrium. However, the surrounding rock mass will suddenly fall into instability while some triggering factors appear in the surrounding rock mass, such as the dynamic disturbing load caused by excavation blasting, roof breaking pressure, mechanical vibration, and so on. This paper takes the surrounding rock mass of the intersecting roadway as the research object and analyzes the stability of the surrounding rock mass of the roadway under the condition of disturbing load.
Numerical Model and Calculation Scheme
Numerical Model
Considering the requirements of the software of FLAC3D for dynamic analysis, the boundary where the disturbing load is set as a non-reflective boundary to eliminate the influence on the incidence of disturbing load, and the other boundaries are set as infinite boundaries. The disturbing load is applied to the left boundary of the numerical model within a certain range of the same height as the coal seam, which can simulate the disturbing load caused by blasting or excavation in nearby mining areas. The position of the disturbing load is shown in Figure 1, and the value of the disturbing load with respect to time is shown in Figure 2, in which the maximum value pmax is called the intensity of the disturbing load.
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Numeric Calculation Scheme
According to the relevant regulations on blasting in the operation guidelines in the mining excavation, the intensity of disturbing load pmax of the blasting loading can be determined by Equation (29), which changes within the range of 5–30 MPa.
Considering the characteristics of the disturbing load, let us assume the depth of the roadway H equals 700 m, the elastic modulus of the roof or floor of the roadway Ed equals 20 GPa, and the elastic modulus of the coal seam Em equals 6 GPa. The intensity of disturbing load pmax equals 5, 10, 15, 20, 25, and 30 MPa, respectively, according to the actual disturbance intensity.
This paper focuses on analyzing the coal seam in Zone A because it is closer to the disturbance source than other zones and experiences the greatest influence. Within the observation plane at the middle and bottom of the coal seam, a measuring point is arranged at a distance of 3.5 m from the boundary on both sides of the roadway. The time-domain changes of relevant characteristic quantities including stress and energy density are recorded during the disturbance process. Simultaneously, measuring points are arranged at the midpoint of the roadway to record the relative horizontal displacement between the two sides of the roadway and the relative vertical displacement between the roof and floor of the roadway.
Stress Distribution Characteristics in the Surrounding Rock Mass of the Roadway
Equivalent Stress Changing Over Time
Figure 3 shows the time history of equivalent stress σeqv at the measurement point in the surrounding rock mass of the roadway with time changing between 0 and 16 ms. Figure 4 shows the contours of equivalent stress in surrounding rock mass on the middle of the roadway with the intensity of disturbing load being 10 MPa and the time being 0, 2.4, 3.6, and 16 ms, respectively. It can be shown that the equivalent stress fluctuates over time under the condition of the disturbing load. The value of equivalent stress rapidly increases after 2 ms and reaches its maximum value at around 3.6 ms, which is about three times higher than the stress value before disturbance. The degree of stress concentration increases in a short time and the risk of dynamic instability in the surrounding rock mass consistently increases. The surrounding rock mass will undergo instantaneous instability when the bearing loading reaches the critical value of instability. At the same time, when the released energy induced by instability is enough, the broken rock blocks will flow into the space of the roadway at a certain rate and the accident of rock burst will happen in the roadway. Due to the damping effect of surrounding rock mass, the amplitude of equivalent stress gradually decreases and tends to the stable state before disturbance over time.
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Equivalent Stress Changing With the Intensity of the Disturbing Load
Figure 5 shows the contours of equivalent stress in surrounding rock mass on the middle of the roadway with the time being 3.6 ms and the intensity of the disturbing load being 5, 10, 15, 20, 25, and 30 MPa, respectively. Figure 6 shows the changing curve of the maximum value (σeqv)max of equivalent stress with the intensity of the disturbing load pmax. It can be concluded that the equivalent stress in the surrounding rock mass of the roadway increases with the increasing intensity of the disturbing load. For example, the maximum equivalent stress increases from 21.94 to 49.06 Mpa when the intensity of the disturbing load changes from 5 to 30 MPa. Owing to the increasing risk of instability caused by the increasing bearing loading, the surrounding rock mass tends to break and become unstable when the bearing load reaches the critical value of instability.
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Deformation Characteristics in the Surrounding Rock Mass of the Roadway
The Relative Horizontal Displacement Between the Two Sides of the Roadway
(1) The relative horizontal displacement changing over time
Figure 7 shows the contours of horizontal displacement between the two sides of the roadway on the intersection position with the intensity of the disturbing load being 10 MPa and the time being 0, 2.4, 4.5, and 16 ms, respectively. Figure 8 shows the curve of relative horizontal displacement Ub between the two sides of the roadway with time changing over 0–16 ms. According to Figures 7 and 8, it can be concluded that the relative horizontal displacement between the two sides of the roadway fluctuates over time under the condition of the disturbing load. In the early stage of disturbance, the relative horizontal displacement rapidly increases and reaches its maximum value at around 4.5 ms, which increases by around 45.58 mm compared with the value before the disturbance. At this particular moment, the deformation in the surrounding rock mass toward the space of the roadway reaches the largest and the greatest possibility of instability of surrounding rock mass may happen. As time goes by, the amplitude of the fluctuation of relative horizontal displacement decreases, and the relative horizontal displacement gradually decreases with some fluctuations and ultimately returns to the value before the disturbance.
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(2) The relative horizontal displacement changing with the intensity of the disturbing load
Figure 9 shows the contours of horizontal displacement between the two sides of the roadway on the intersection position with the time being 4.5 ms and the intensity of the disturbing load being 5, 10, 15, 20, 25, and 30 MPa, respectively. Figure 10 shows the curve of relative horizontal displacement Ub changing with the intensity of the disturbing load. It can be concluded that the relative horizontal displacement between the two sides of the roadway increases with the increasing intensity of the disturbing load. For example, the value of relative horizontal displacement increases from 199.78 to 251.21 mm when the intensity of the disturbing load changes from 5 to 30 MPa, resulting in an increment of about 25.74%. The deformation in the surrounding rock mass on the left side of the roadway is relatively large due to its proximity to the disturbance load. The lateral deformation of the coal and rock mass toward the interior of the roadway is more significant on this side, leading to a higher possibility of instability. If a rock burst occurs, the coal and rock mass on the side closer to the disturbance source will likely be the first to fail and flow into the roadway space.
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The Relative Vertical Displacement Between the Roof and Floor of Roadway
(1) The relative vertical displacement changing over time
Figure 11 shows the contours of vertical displacement between the roof and floor of the roadway on the intersection position with the intensity of the disturbing load being 10 MPa and the time being 0, 3.6, 7.5, and 16 ms, respectively. Figure 12 shows the curve of relative vertical displacement Uv between the roof and floor of the roadway with time changing over 0–16 ms. According to Figures 11 and 12, the results can be concluded as follows.
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① Affected by the disturbing load, the relative vertical displacement between the roof and floor of the roadway fluctuates over time. In the early stage of disturbance, the relative vertical displacement between the roof and floor of the roadway increases rapidly and reaches its maximum value at around 3.6 ms with a 36.14 mm increment in vertical displacement caused by the disturbing load compared with before the disturbance. At this particular moment, the clamping effect of the roof and floor on the surrounding rock mass is enhanced and the stress concentration is intensified. The instability of the surrounding rock mass may happen when the bearing loading reaches the strength limit of the rock mass, and there may be a rock burst when the accumulated energy inside the surrounding rock mass is large enough.
② The relative vertical displacement between the roof and floor of the roadway gradually decreases with some fluctuations and it reaches the minimum value at around 7.5 ms. The relative vertical displacement decreases by about 15.97 mm, which weakens the clamping effect between the roof and floor of the roadway and the friction force inside the coal seam. The surrounding rock mass is likely to suddenly lose stability because of the decrease of the clamping effect. The amplitude of the fluctuation of relative vertical displacement between the roof and floor of the roadway gradually decreases and returns to the state before the disturbance.
(2) The relative vertical displacement changing with the intensity of the disturbing load
Figure 13 shows the contours of vertical displacement between the roof and floor of the roadway on the intersection position with the time being 3.6 ms and the intensity of the disturbing load being 5, 10, 15, 20, 25, and 30 MPa, respectively. Figure 14 shows the curve of relative vertical displacement Uv changing with the intensity of the disturbing load. It can be concluded that the relative vertical displacement between the roof and floor of the roadway increases with the increasing intensity of the disturbing load. For example, the value of relative vertical displacement increases from 124.96 to 193.42 mm when the intensity of the disturbing load changes from 5 to 30 MPa, resulting in an increment of about 54.78%. The relative vertical displacement between the roof and floor of the roadway fluctuates over time, and the amplitude of fluctuation increases with the increasing intensity of the disturbing load. The surrounding rock mass will undergo instantaneous instability and break during one or multiple disturbances, which will lead to the accumulated energy release. There will be a rock burst accident if the accumulated energy is large enough.
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The Distribution Characteristic of the Plastic Zone in the Surrounding Rock Mass of the Roadway
The Plastic Zone Distribution Changing Over Time
Figure 15 shows the distribution of the plastic zone on the middle plane in the surrounding rock mass of the roadway with the intensity of the disturbing load being 10 MPa and the time being 0, 2.4, 3.6, and 16 ms, respectively. Figure 16 shows the curve of the depth of the plastic zone changing over time. Under the effect of the disturbing load, the depth of the plastic zone in the surrounding rock mass of the roadway changes over time. The degree of stress concentration reaches its maximum at around 3.6 ms. Compared to the initial state, the depth of the plastic zone H at the roadway intersection increases from 1.5 to 1.75 m, an increase of 16.67%. The surrounding rock mass at the roadway edge closer to the disturbance source is greatly affected, with the depth of the plastic zone increasing by 0.5 m, indicating an expansion in the potential damage range in the event of a rock burst.
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There will be a range of broken zones in the plastic zone around the surrounding rock mass and shear damage may occur in the broken zone. The surrounding rock mass at the edge of the roadway, which is closer to the disturbing load, is greatly affected and the depth of the plastic zone increases by 0.5 m. The increasing depth of the plastic zone indicates an expansion in the damage range of rock bursts.
The Plastic Zone Distribution Changing With the Intensity of the Disturbing Load
Figure 17 shows the distribution of plastic zone on the middle plane in the surrounding rock mass of the roadway with the time being 3.6 ms and the intensity of the disturbing load being 5, 10, 15, 20, 25, and 30 MPa, respectively. Figure 18 shows the curve of the depth of the plastic zone changing with the intensity of the disturbing load. As shown in Figures 17 and 18, the range of the plastic zone in the surrounding rock mass of the roadway increases with the increasing intensity of the disturbing load.
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The depth of the plastic zone in the surrounding rock mass of the roadway increases by 0.5 m when the intensity of the disturbing load changes from 5 to 30 MPa, resulting in an increment of about 33.33%. The surrounding rock mass at the edge of the roadway, which is closer to the disturbing load, is greatly affected and its depth of plastic zone increases by 0.25 m. The range of the plastic zone in the surrounding rock mass of the roadway shows an expanding trend with the increasing intensity of the disturbing load. It indicates that both the amount of rock (coal) thrown into the space of the roadway and the damage range of the surrounding rock mass will increase if there is a rock burst in the roadway.
The Characteristic of Energy Accumulation in the Surrounding Rock Mass of the Roadway
The Energy Accumulation Changing Over Time
Figure 19 shows the contours of the energy density Ud at the bottom in the surrounding rock mass of the roadway with the intensity of the disturbing load being 10 MPa and the time being 0, 2.4, 3.6, and 16 ms, respectively. Figure 20 shows the time history of the energy density Ud recorded at the observation point over 0~16 ms. According to Figures 19 and 20, the results can be concluded as follows.
- 1
Under the effect of the disturbing load, the energy density in the surrounding rock mass of the roadway fluctuates over time. The energy density rapidly increases after approximately 2 ms of the disturbing load and reaches its maximum value at around 3.6 ms. At this particular moment, the position of energy accumulation approaches the edge of the roadway, which moves closer to the edge by 20% compared with the distance before the disturbance. The stress concentration and deformation in the surrounding rock mass are also larger than the values before the disturbance, and the risk of rock burst is relatively stronger than the state before the disturbance.
- 2
The value of energy density at the observation point in the surrounding rock mass of the roadway increases by 209.66 kJ·m−3 during the disturbance process, which is about a 50.77% increment compared with the value before the disturbance. However, the amplitude of the fluctuation of energy density rapidly decays and returns to the state before disturbance.
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Figure 21 shows the spatial characteristics of the energy accumulation zone in the surrounding rock mass for each model roadway. Figures 22–24 present the variation of the total energy , average energy density , and the factor of average energy density in the energy accumulation zone with time t. From these, it can be concluded that:
- 1.
Under the effect of the disturbing load, the energy accumulation zone moves toward the edge of the surrounding rock mass of the roadway and the total energy in the energy accumulation zone gradually increases over time, which reaches its maximum value at around 3.6 ms. At this particular moment, the total energy increases by 84.44 MJ. However, the total energy quickly decreases and basically returns to the state before disturbance.
- 2.
The average energy density reaches its maximum value at around 3.6 ms, which increases by 1.53 MJ·m−3 and indicates that the degree of energy accumulation significantly increases compared with the state before disturbance. The factor of average energy density also reaches its maximum value at around 3.6 ms and increases by 1.05 MJ·m−4. These indicate the greatest risk of rock burst.
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Energy Accumulation Changing With the Intensity of the Disturbing Load
Figure 25 shows the contours of energy density Ud at the bottom in the surrounding rock mass of roadway with the time being 3.6 ms and the intensity of the disturbing load being 5, 10, 15, 20, 25, and 30 MPa, respectively. Figures 26 and 27 show the maximum value of energy density (Ud)max and the position of energy accumulation zone d changing with the intensity of the disturbing load, respectively. The results can be concluded as follows.
- 1
The maximum value of energy density in the surrounding rock mass of the roadway increases with the increasing intensity of the disturbing load. It increases from 513.08 kJ·m−3 to 1099.83 kJ·m−3 when the intensity of the disturbing load changes from 5 MPa to 30 MPa, resulting in an increment of about 116%.
- 2
The position of the energy accumulation zone gradually decreases with the increasing intensity of the disturbing load, which indicates that the energy accumulation zone gradually moves closer to the edge of the roadway. For example, the position of the energy accumulation zone decreases from 2.5 to 1.5 m when the intensity of the disturbing load changes from 5 to 30 MPa. It will increase the risk of rock bursts.
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Figures 28–30 show the total energy ΣU, the average energy density , and the factor of average energy density changing with the intensity of the disturbing load, respectively, Figure 31 shows the spatial characteristics of the energy accumulation zone in surrounding rock mass. The results can be concluded as follows.
- 1
With the increasing intensity of the disturbing load, the energy accumulation zone generally expands outward and its range gradually increases, which indicates that the energy accumulation zone gradually moves closer to the edge of the roadway. When the intensity of the disturbing load changes from 5 to 30 MPa, the total energy of the energy accumulation zone increases from 166.16 to 376.46 MJ, resulting in an increment of about 126%.
- 2
With the increasing intensity of the disturbing load, the factor of average energy density in the energy accumulation zone increases from 1.26 to 5.11 MJ·m−4, resulting in an increment of about 304%. The substantial increase in the factor of average energy density will significantly increase the risk of rock bursts in the roadway.
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Analysis of Engineering Example
The Overview of Production and Geology in a Mine
Geological Conditions
The No. 7153 working face is located in the middle of east forth mining area in a mine, where there was a rock burst a few months ago. The fault named F318 is in the west of No.7153 working face and the No. 7153down fully mechanized mining face is in its east. The north of No.7153 working face is the goaf of No.7151 mining face and the south is the goaf of No.7154 working face. The elevation of No.7153 working face is about −559 ~ −585 m and its depth is about 610 m. The direction length of No.7153 working face is about 175 m, and its tendency length is about 54–89 m with an average dip angle of 6°. The length of No.7153 working face is 67 m and its height is 2 m, which is shown in Figure 32.
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The Properties of Surrounding Rock
The immediate roof of the coal seam belongs to mudstone with a height of 1.93 m. The main roof of the coal seam is the hard sandy mudstone with a thick height, which is divided into two layers. The first layer of the main roof is thick dark gray sandy mudstone with a height of 3.96 m and the second layer of the main roof is sandy mudstone with a height of 22.9 m. The floor of the coal seam is siltstone with a thickness of more than 4 m. The hard rocks of the main roof and floor will play a significant clamping effect on the coal seam, which can bear great loading and easily accumulate energy. The properties of the surrounding rock and the coal seam are shown in Table 1.
Table 1 Properties of the surrounding rock and the coal seam, such as lithology, modulus of elasticity, Poisson's ratio, compression strength, thickness, and so on.
| Name | Lithology | E/GPa | /MPa | Thickness/m | Description | |
| Immediate roof | Mudstone | 10 | 0.3 | 10 | 1.93 | Mud cementation |
| Main roof | Sandy mudstone | 30 | 0.23 | 30 | 26.86 | Layer mud cementation |
| Coal seam | 3 | 0.37 | 5 | 2.6~6.42 | ||
| Floor | Siltstone | 10 | 0.3 | 10 | > 4 | Mud cementation |
General Situation of Rock Burst Accident
The width of the coal pillar between the No.7153B working face and the goaf of No.7154 working face is changing from 10 to 22 m, and the width of the coal pillar between the No.7153B working face and the fault named F136 is about 30 m. There is floor heave and serious deformation within a distance of about 70 m in the roadway shown in Figure 32 when the No.7153B working face advances about 63 m and there is blasting in the middle of No.7153B working face. For example, the relative horizontal displacement between the two sides of the roadway decreases by 0.4~0.7 m and the height of floor heave is about 300 mm at the distance of about 15 m in the roadway while the relative horizontal displacement between the two sides of the roadway decreases by 0.4~1.3 m and the height of floor heave is about 200–400 mm within the distance about 50–70 m in the roadway. However, the section of the roadway within a distance of about 15–30 m suffers the most serious damage, such as the bending and breaking at the leg of the steel support, the bloating of the two sides of the coal seam, and the breaking of pillar in the spillplate. The relative horizontal displacement between the two sides of the roadway decreases by 1.0–1.3 m and the height of floor heave is about 600–1000 mm within this distance. Figure 33 shows the situation of steel support in the roadway before and after the rock burst.
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Numerical Analysis
Numerical Model
The numerical domain is selected from the No.7153B working face to the influenced range of rock burst in the roadway and a three-dimensional numerical model is established, as shown in Figure 34. The geometric size of the numerical model is 150 × 150 × 100 m, and the section of roadway in the numerical model is the shape of a straight wall semi-arch with the radius of circular arch R being equal to 2.1 m and the rectangular section being 2.1 × 1.5 m. The value of the disturbing load is the same as the value in part 2.1. The stress distribution, deformation of the roadway, and distribution of the plastic zone can be obtained by using finite difference software. Based on these, the stability of the surrounding rock mass of the roadway and the influence of the disturbing load on the occurrence of rock bursts will be analyzed.
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Stability Analysis of Surrounding Rock Mass
Figure 35 shows the time history of equivalent stress and vertical stress at the measurement point in the surrounding rock mass of the roadway with time changing between 0 and 20 ms. Figures 36–40 show the contours of equivalent stress, the contours of vertical stress, the contours of horizontal displacement, the contours of vertical displacement, and the distribution of plastic zone in the surrounding rock mass with time being 0 and 3.6 ms. The values of equivalent stress, vertical stress, horizontal displacement, vertical displacement, and the depth of the plastic zone are given in Table 2.
- 1.
Due to the influence of the disturbing load, the degree of stress concentration is intensified. For example, the maximum value of the equivalent stress and vertical stress at the corner edge of the roadway with the time being 3.6 ms increases by 55.79% and 70.37%, respectively, compared with the value before the disturbance, which indicates that the bearing loading in surrounding rock mass increases significantly. The relative horizontal displacement between the two sides of the roadway and the relative vertical displacement between the roof and floor of the roadway increase by 218% and 40.52%, respectively, which shows that the deformation of surrounding rock mass increases. The maximum depth of the plastic zone increases from 1.75 to 2.25 m with an increment of about 28.57%. These findings indicate a significant reduction in the stability of the surrounding rock mass, in other words, there is a significant increase in the instability of the surrounding rock mass.
- 2.
The deformation of the two sides of the roadway reaches the maximum value, especially, the deformation of the two sides near the floor of the roadway, where the broken rock will preferentially flow into the space of the roadway if there is instability in the surrounding rock mass. The high concentration of stress in the surrounding rock mass and the significant increase of deformation at the corner of the roadway during the disturbing load are the fundamental causes for the instability of the surrounding rock mass and also the key influencing factors for rock bursts. The shape of the roadway after the disturbing load is similar to the shape of the roadway after rock bursts, which confirms the validity of the numerical simulation results to a certain extent.
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Table 2 Equivalent stress, vertical stress, relative horizontal displacement, relative vertical displacement, and the depth of the plastic zone with time being 0 and 3.6 ms, respectively.
| Time/ms | /MPa | /MPa | Ub/mm | Uv/mm | h/m |
| 0 | 7.777 | 11.923 | 156.904 | 408.960 | 1.750 |
| 3.6 | 12.116 | 20.313 | 499.320 | 574.690 | 2.250 |
Conclusions
Based on the analysis of the stability of the surrounding rock mass under the effect of the disturbing load, this paper analyzes the influence of stress and deformation of the surrounding rock mass on the risk of rock bursts by using theoretical analysis and numerical calculation. The main conclusions are shown as follows:
- 1.
The minimum critical loading for the instability of the laminar split structure is obtained for the two cases of simple support constraint and fixed constraint at both ends.
- 2.
The maximum value of equivalent stress increases by 278%, and the maximum value of relative horizontal displacement between the two sides of the roadway increases by 27.6% while the maximum value of relative vertical displacement between the roof and floor of the roadway increases by 38.1%. The degree of stress concentration is intensified and the deformation of the roadway increases, which leads to the increasing possibility of instability of the surrounding rock mass. The depth of the plastic zone in the surrounding rock mass increases by 16.7%, which indicates the increasing range of instability.
- 3.
The maximum value of energy density increases by 55.3%, and the maximum value of total energy increases by 56.3% while the maximum value of average energy density increases by 55.3%. The degree of energy accumulation increases significantly and the value of the factor of average energy density increases by 94.6%, which indicates an increasing risk of rock burst.
- 4.
With the increasing intensity of the disturbing load, the equivalent stress in the surrounding rock mass, the relative horizontal displacement between the two sides of the roadway, the relative vertical displacement between the roof and floor of the roadway, and the depth of the plastic zone show a significant increasing trend, respectively. The maximum value of energy density, the total energy, and the average energy density increases rapidly with the increasing intensity of the disturbing load. These indicate a great risk of rock burst.
- 5.
The stress is highly concentrated in the surrounding rock mass by analyzing contours of equivalent stress in No.7153B working face, and the deformation of the two sides near the floor of the roadway increases significantly by analyzing the contours of horizontal and vertical displacement in the surrounding rock mass. These findings provide great significance for the safe mining of mining engineering.
Author Contributions
Hui Xu: conceptualization, methodology, validation, data curation, writing – original draft preparation, supervision. Wankui Bu: conceptualization, methodology, formal analysis, writing – review and editing, supervision, funding acquisition. Jun Qiu: methodology, validation. Long Ma: investigation, visualization. Hao Qin: conceptualization, methodology, formal analysis, supervision. Yajun Li: theoretical analysis, data curation. Weishe Zhang: theoretical analysis, data curation. Pengxiang Li: theoretical analysis, software, writing – original draft preparation, writing – review and editing. Dong Zhang: software, writing – original draft preparation. Chen Jia: investigation, visualization. All authors have read and agreed to the published version of the manuscript.
Acknowledgments
This research was funded by Shandong Provincial Natural Science Foundation, grant number ZR2020ME100, and Heze University Natural Science Foundation, grant number XY21BS42.
Consent
The authors have nothing to report.
Conflicts of Interest
The authors declare no conflicts of interest.
Data Availability Statement
All relevant data presented in the article are stored according to institutional requirements and, as such, are not available online. However, all data used in this manuscript can be made available upon request to the authors.
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Abstract
ABSTRACT
The rock burst is one of the major dynamic disasters in deep underground engineering, such as coal mining, and has become a significant technical challenge urgently requiring solutions in rock mechanics and engineering. In the related research, there are many reports on the stability analysis of the laminar split structure under static loads and few reports on the stability analysis under dynamic loads. This paper addresses the stability of surrounding rock in deep roadways, focusing on the key factor of disturbed load. First, the paper theoretically establishes the control equation for analyzing the dynamic stability of the laminar split structure in the coal wall of roadway, deriving the minimum critical load for instability of the laminar split structure under two constraint conditions: simply supported at both ends and fixed at both ends. Second, using discrete element software, the paper analyzes the influence of disturbing load on the stability and energy accumulation characteristics of the surrounding rock of the roadway. It examines the variation patterns of stress in the surrounding rock, deformation of both sides and roof‐floor, distribution of plastic zones, and energy accumulation characteristics with respect to time t and the intensity of disturbing load pmax. Finally, the paper analyzes the stability of surrounding rock in a mine involved in a rock burst accident. The research results provide a basis and reference for analyzing the risk of rock burst under similar conditions.
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Details
; Bu, Wankui 1 ; Qiu, Jun 2 ; Ma, Long 3 ; Qin, Hao 2 ; Li, Yajun 1 ; Zhang, Weishe 1 ; Li, Pengxiang 1 ; Zhang, Dong 1 ; Li, Peng 1 ; Jia, Chen 3 1 College of Urban Construction, Heze University, Heze, China
2 Institute of Shanghai Special Equipment Inspection and Technical Research, Shanghai, China
3 Shandong Provincial Lunan Geology and Exploration Institute (Shandong Provincial Bureau of Geology and Mineral Resources No.2 Geological Brigade), Jining, China