Unloading excavation can increase the possibility of rock burst, especially for coal seam with rock parting. In order to explore the evolution process of rock burst under lateral unloading, the combination of in situ measures and numerical experiments is used to study. The following four points were addressed: (1) the coal seam with rock parting easily causes the stick-slip and instability along the interface, and the process of stick-slip and instability has hysteresis characteristics; (2) the greater the degree of unloading or the smaller the interface friction angle of the Coal-Rock Parting-Coal Structure (CRCS), the more likely it is for stick-slip and instability to occur; (3) the abnormal increase of shear stress and slip dissipation energy can be used as the precursory information of the stick-slip and instability of CRCS; (4) the damage intensity of rock burst induced by stick-slip and instability of CRCS can be reduced by reducing the unloading speed or increasing the roughness of interface. The research results can be used for early warning and controlling of dynamic disaster induced by stick-slip instability in coal seam with rock parking.

The slip-staggered rock burst is caused by the slip dislocation of the internal related structure, which mainly occurs in the fault, coal seam separation, and abnormal change area of coal seam dip angle. The coal seam separation is a typical occurrence structure in coal mines of China, which causes the transformation of coal and rock structures, and commonly the Coal-Rock Parting-Coal Structure (CRCS) is formed by rock parting upper and lower coal seams [1, 2]. The natural CRCS is in a stable triaxial stress state. The process of roadway excavation can cause the redistribution of surrounding rock stress and cause the horizontal stress to be gradually released, and the CRCS also changes from a three-dimensional stress state to a lateral unloading state [3-6]. As the interface of coal and rock parting is weak, the process of lateral unloading may cause stick-slip and instability along the weak surface, which easily leads to rock burst accidents.

In recent years, with the rapid development of science and technology, the research methods of rock mechanics are gradually enriched. The deformation and failure mechanism of unloading coal/rock mass is gradually revealed, and the mechanism of stick-slip instability of the contact surface is also constantly verified [7]. Such as He et al. [8-10] designed a true-triaxial rock burst test simulation system and simulated the lateral sudden unloading process caused by deep rock excavation. Lu et al. [11] studied the precursory characteristics of rock burst induced by fault stick-slip instability through field observations and biaxial direct shear friction experiments and explained the influence of friction coefficient on stick-slip instability. Liu et al. [12] confirmed that the rock parting structure also has the characteristics of stick-slip and instability under the influence of mining activities. Generally speaking, the current research focuses on the single-factor failure mechanism of coal/rock mass unloading failure or contact face stick-slip instability, but research on the coupling mechanism of unloading failure and contact face stick-slip instability is rare. Especially, the mechanism of stick-slip instability caused by lateral unloading. Therefore, it is particularly important to study the stick-slip instability mechanism of CRCS under the lateral unloading.

Numerical simulation has been widely accepted for its unique repeatability and data diversity, especially Universal Distinct Element Code (UDEC). The newly added triangular element can effectively simulate the fracture expansion of coal/rock mass, and the embedded fish program can also complete the tracking and positioning of fractures [13, 14]. Bai et al. [15] used a Discrete Element Method(DEM) investigation of the fracture mechanism of rock disc containing hole(s) and its influence on tensile strength and explored the effects of pore location, size, and quantity on its tensile strength and fracture. Zhang et al. [16] used the UDEC Trigon block model to study the initiation, propagation, and evolution of fractures in composite coal and rock samples and explored the influence of coal and rock height on the mechanical properties of composite coal and rock samples. Lu et al. [17] simulated the failure and instability process of coal seam with rock parting using UDEC discrete element software and pointed out the coupling instability mechanism between coal and rock fractures and contact surface slipping. The numerical results were compared with on-site measurements, and the two results were basically consistent, indicating the applicability of the UDEC Trigon block model.

Based on this, this paper takes the C5301 working face of Yunhe Coal Mine (YCM) as the research background of structural sliding induced by driving coal seam with rock parking and uses UDEC numerical simulation technology to study the stick-slip instability process of CRCS, and the influence of unloading speed and joint roughness coefficient (JRC) on the stick-slip instability of composite structure is studied and puts forward the prevention measures of stick-slip instability impact disaster induced by lateral unloading. The research results can be used for early warning and controlling of dynamic disaster induced by stick-slip instability in coal seam with rock parking.

1.1. Field Investigation

1.1.1. Geological Conditions

The YCM is located in Jining City, Shandong Province, China. Figure 1 shows the plane layout of the C5301 longwall face. The elevation of the C5301 longwall face is from −600 m to −684 m, and the average is −642 m. The thickness of the mining #3 coal seam is 5.4–10.3 m with an average of 8.1 m, and the dip angle is 9°–20° with an average of 14°. Table 1 shows the lithology of coal and rock strata in the longwall face. There is a rock parting in the coal seam of the C5301 longwall face (in Figure 1). The rock parting is composed of siltstone and pyrite loose crystal, with a thickness of 0.5–7 m, which is gradually thinned from the northwest to the southeast.

Table 1

The lithology of coal and rock strata.

Serial numberLevel/mThickness/mGeologicalFormationsRock stratumNotes
1−600.83.85graphicMudstone
2−605.44.60Siltstone
3−606.91.50Medium sandstone
4−619.99.97Siltstone
5−623.76.80Fine sandstone
6−630.87.10SiltstoneMain roof
7−631.91.10MudstoneImmediate roof
8−640.08.103# coalMining
9−648.13.10MudstoneImmediate floor
10−651.21.70SiltstoneMain floor
Serial numberLevel/mThickness/mGeologicalFormationsRock stratumNotes
1−600.83.85graphicMudstone
2−605.44.60Siltstone
3−606.91.50Medium sandstone
4−619.99.97Siltstone
5−623.76.80Fine sandstone
6−630.87.10SiltstoneMain roof
7−631.91.10MudstoneImmediate roof
8−640.08.103# coalMining
9−648.13.10MudstoneImmediate floor
10−651.21.70SiltstoneMain floor
Figure 1

The plane layout of the C5301 longwall face.

Figure 1

The plane layout of the C5301 longwall face.

Microseism (MS) is a monitoring method that uses the wave effects produced by rock fracture to carry out positioning, which is widely used in coal mine and tunnel engineering [18, 19]. The KJ648 MS system and nineteen geophones were installed in the YCM. The system can complete the functions of real-time monitoring, data processing, and three-dimensional visualization of the source. Based on the principle of microseismic arrival time difference and arrival time difference quotient [20]. A total of four geophones were arranged around the C5301 longwall face (in Figure 1), which were named as C5301p1, C5301p2, C5301g1, and C5301g2, respectively. Table 2 shows the three-dimensional coordinates of four geophones.

Table 2

Three-dimensional coordinates of four geophones.

Sensor numberEast/mNorth/mElevation/m
C5301p15486.608087.30−674.30
C5301p25516.148028.75−655.45
C5301g15570.708007.30−665.70
C5301g25599.858179.39−650.00
Sensor numberEast/mNorth/mElevation/m
C5301p15486.608087.30−674.30
C5301p25516.148028.75−655.45
C5301g15570.708007.30−665.70
C5301g25599.858179.39−650.00

1.1.2. Stick-Slip Instability Induced by Excavation

From December 10, 2018, to January 10, 2019, the advancing distance of the C5301 longwall face was 116 m. During the roadway excavation, large energy MS event frequently occurred in the rock parting area, which was possibly associated with the stick-slip instability of the CRCS.

The variations of MS events and peak energy during the headentry excavation are shown in Figure 2. Both event counts and peak energy show a distinct “accumulation-release-accumulation” cycle. Lu et al. [21] pointed out that there is an obvious vibration mutation during the fault stick-slip and instability process, which is a typical energy accumulation process. This is consistent with the characteristics of vibration change caused by the excavation in the rock parting area. It was observed that when the energy accumulated to the condition of slip, the slip and instability process will occur along the interface of CRCS. Meanwhile, due to the irregularity of the interface, the friction coefficient gradually changes with the roughness of the interface during slip and instability. Therefore, the slip and instability process of the CRCS shows the “slip-stability-slip” phenomenon, which is consistent with the fault stick-slip instability.

Figure 2

The variation curves of MS events and peak energy. Note: the shadow area is the process of stress accumulation and release.

Figure 2

The variation curves of MS events and peak energy. Note: the shadow area is the process of stress accumulation and release.

Figure 3 shows the plane location of the sources in the C5301 longwall face. At the beginning of the C5301 headentry excavation, the source was mainly concentrated on the area where the thickness of the rock parting obviously changed. On December 22, 2018, an MS event with the energy of 3.39 × 105 J was located (>105 J), defined as a strong mine earthquake, which is called Strong Mine Earthquake (SME). Through the analysis, it was caused by the disturbance of the initial excavation, which led to the stick-slip and instability of CRCS in the −725 north headentry. With the roadway advancing to the rock parting area, the sources gradually transferred to both sides and rear of the roadway. From December 26, 2018, to January 10, 2019, three large energy MS events occurred, with the energy of 1.70 × 105, 1.20 × 105, and 1.43 × 105 J, respectively, two of which were located near the roadway. It was proved that the stick-slip instability of CRCS induced by roadway excavation has obvious hysteresis characteristics.

Figure 3

The source locations of the C5301 longwall face. (a) December 10, 2018, to December 25, 2018. (b) December 26, 2018, to January 10, 2019

Figure 3

The source locations of the C5301 longwall face. (a) December 10, 2018, to December 25, 2018. (b) December 26, 2018, to January 10, 2019

2.1. Slip Mechanism of Unloading Instability

The horizontal stress is a step-type decreasing trend as the deep rock mass is excavated [22]. Based on the occurrence characteristics of rock parting in the C5301 longwall face, the mechanical model of stick-slip and instability of CRCS under lateral unloading was established. Figure 4 shows the stress conditions of CRCS.

Figure 4

The stress conditions of CRCS.

Figure 4

The stress conditions of CRCS.

 Fx=σ3h+σθl tanθτθlτ1lσ3(h+l tanθ)
(1)

Where σθ is the normal stress, σ3 and σ′3 are the horizontal stress, τ1 and τθ are the shear stress, l and h are the model width and height, θ is the angle of interface.

Assuming that the coal and rock blocks are rigid and there is no damage in the block, then

 Fx>0
(2)

When the horizontal stress decreases gradually by lateral unloading, then

σ 3=σ 3NΔδ
(3)

Where N and Δδ are unloading step and unloading gradient. Therefore

NΔδ>A
(4)

If

A=τθ+τ1+σ3 tanθσθ tanθhl+tanθ
(5)

Then, A is a fixed value. Therefore,

NΔδ>A
(6)

The slip and instability of CRCS are closely related to unloading steps and gradient under lateral unloading. The longer the unloading step, the larger the unloading gradient, and the easier the slip of CRCS.

The friction force of the interface also has an important influence on the slip and instability of CRCS. When the CRCS is slipping, the normal stress and shear stress of the interface can be expressed as

{τ1τmax=c+μστ1τmax=cμσ
(7)

Where φ is the friction angle.

Substituting the equation (7) into the equation (4):

NΔδ(hl+tanθ)σ3tanθσ1>2tanφ+tan2φtanθtanθ1+tanφtanθ
(8)

If

f(φ)=2 tanφ+tan2φ tanθtanθ1+tanφ tanθ
(9)

Then

df(φ)dφ=sec2(φθ)+sec2 φ>0
(10)

This shows that f(φ) is a monotone-increasing function. Therefore, the higher the friction angle, the more stable the CRCS.

2.2. Stick-Slip Mechanism of Structural Instability

The slipping of the interface includes stick and steady slips. Stick-slip refers to the slipping process if the shear stress of the interface continuously increases and decreases sharply during slipping, while the steady slip refers to the slipping process when the shear stress of the contact surface is basically stable [23]. Figure 5 shows the process of stick-slip instability, which is divided into four processes: initial occlusion, upslope, downslope, and reocclusion. During the process of slipping upslope, normal stress (σ) plays a negative role, otherwise σ plays a positive role. According to Jaeger’s law of friction:

{τ1τmax=c+μσττmax=cμσ
(11)
Figure 5

The process of stick-slip instability.

Figure 5

The process of stick-slip instability.

Δτ=τ1τ1=2μσ
(12)

Where τ1 andτʹ1 are the shear stress of interface on the upslope and downslope, respectively, τmax and τmax ʹ are the maximum shear stress of interface on the upslope and downslope, respectively, μ and σ are the friction coefficient and normal stress of interface, c is the cohesion of interface, Δτ is the fluctuating value of shear stress of interface during upslope and downslope.

Assuming that the slope angles on both sides are consistent and the block is not ruptured, the shear stress will fluctuate with the upslope and downslope of the interface, and the fluctuation value of shear stress is Δτ=2μσ. At the same time, when the horizontal stress F generated by lateral unloading is constant, the slip velocity of the interface will fluctuate with the change of the shear stress, which is also the reason for stick-slip.

3.1. Numerical Model

Based on the field survey and mechanical analysis of the rock parting structure, a numerical model of UDEC is established to study the stick-slip and instability of CRCS caused by lateral unloading, and the numerical model is shown in Figure 6. The width and height of the model are 50 and 100 mm, respectively, and two rigid loading plates are set at the top and bottom. The bottom loading plate is fixed, the top loading plate maintains the axial constant load σ1, and the initial confining pressure is set to σ3. The method of lateral unloading is used to simulate the process of slow unloading of horizontal stress after roadway excavation, and the unit of force unloading speed is Pa/step. The structural plane is set as a wave-shaped occluded structure to simulate the stick-slip effect caused by the slip of the structural plane.

Figure 6

Numerical model.

Figure 6

Numerical model.

3.2. Calibration of Microparameters

In the UDEC discrete element, rock is considered to be a structure composed of rock blocks and joint surfaces. The block and joint have their own microparameters. These microparameters cannot be directly obtained through the laboratory mechanical test, so the inversion calibration is required before the simulation [24, 25]. The parameters calibration process is as follows:

First, the deformation module (E) and Poisson’s ratio (μ) of coal and rock parting are obtained by uniaxial compression experiment. According to International Society for Rock Mechanics(ISRM), coal and rock parting samples with a diameter of 50 mm and a height of 100 m were used for uniaxial compression calibration testing, and the numerical model was consistent with the calibration sample size [26]. Figure 7 shows the numerical and experimental results of coal and rock parting samples under uniaxial compression.

Figure 7

Numerical and experimental results of coal and rock parting samples under uniaxial compression. (a) Coal. (b) Rock parting.

Figure 7

Numerical and experimental results of coal and rock parting samples under uniaxial compression. (a) Coal. (b) Rock parting.

The bulk modulus (K) and shear modulus (G) of the blocks in the numerical model can be calculated with the following equation (13) and equation (14) [27]. Table 3 shows the microparameters of coal and rock parting blocks after calibration.

Table 3

The microparameters of blocks after calibration.

MineralBlock properties
Density (kg/m3)K/GPaG/GPa
Coal14003.071.40
Rock parting24005.912.79
MineralBlock properties
Density (kg/m3)K/GPaG/GPa
Coal14003.071.40
Rock parting24005.912.79
K=E3(12μ)
(13)
G=E2(1+μ)
(14)

The normal stiffness kn and shear stiffness ks of joints are obtained by equation (15) and equation (16) [27]. Table 4 shows the normal and shear stiffness of joints after calibration.

Table 4

The normal and shear stiffness of joints after calibration.

Mineralkn(GPa/m)ks (GPa/m)
Coal58762350.4
Rock parting14,4885795.2
Contact surface58762350.4
Mineralkn(GPa/m)ks (GPa/m)
Coal58762350.4
Rock parting14,4885795.2
Contact surface58762350.4
kn=n[K + (4/3)GΔZmin]1n10
(15)
ks=0.4kn
(16)

Where ΔΖmin is the smallest width of the zone adjoining the contact in the vertical direction.

Second, Brazil disc testing is used to calibrate the cohesion (c), friction angle (φ), and tensile strength (σt) of contacts. Brazil disc used a disk specimen with a diameter of 50 mm and a thickness of 25 mm, and the numerical model was consistent with the calibration sample size [28]. Figure 8 shows the numerical and experimental results of coal and rock parting samples under Brazil disc testing.

Figure 8

Numerical and experimental results of coal and rock parting samples under Brazil disc testing. (a) Coal. (b) Rock parting.

Figure 8

Numerical and experimental results of coal and rock parting samples under Brazil disc testing. (a) Coal. (b) Rock parting.

The tensile strength of Brazil disc numerical testing is calculated by Eq. (17) [15]. Table 5 shows the microparameters of joints after calibration.

Table 5

The microparameters of joints after calibration.

MineralCoh.(MPa)Fri.(°)Ten. strength(MPa)Res. coh.(MPa)Res. fri.(°)Res. ten. strength(MPa)
Coal2.7241.00200
Rock Parting6.4303.40240
Contact surface0.6160.20100
MineralCoh.(MPa)Fri.(°)Ten. strength(MPa)Res. coh.(MPa)Res. fri.(°)Res. ten. strength(MPa)
Coal2.7241.00200
Rock Parting6.4303.40240
Contact surface0.6160.20100
σt=2FπDt
(17)

Where D is the diameter, t is the thickness, and F is the applied diametrical load when failure.

Finally, the microparameters of contact are adjusted repeatedly until the microparameters of numerical simulations and laboratory tests are consistent.

Table 6 shows the error values of uniaxial compressive strength and tensile strength. The errors of uniaxial compressive strength are 2.19% and 1.49%, respectively, and the tensile strength are 5.08% and 1.33%, respectively, with relatively small errors. Therefore, it was proved that the microparameters can better reflect the macromechanical properties of coal and rock parting, and the microparameters are feasible.

Table 6

Comparison of experimental and numerical results.

MineralUCS (MPa)Error/%BTS (MPaError/%
ExperimentSimulationExperimentSimulation
Coal5.485.362.190.590.625.08
Rock parting14.8014.581.491.501.521.33
MineralUCS (MPa)Error/%BTS (MPaError/%
ExperimentSimulationExperimentSimulation
Coal5.485.362.190.590.625.08
Rock parting14.8014.581.491.501.521.33

UCS, Uniaxial Compressive Strength. BTS, Brazilian Testing Strength.

3.3. Setting of Interface

During the coal seam deposition process, the coal and the rock parting will occupy each other, presenting a curved occlusion-up interface. In order to quantitatively analyze the roughness of the interface, the JRC is introduced. The JRC was first proposed by Barton [29], and ten standard curves were provided. Initially, the JRC of the fracture profile was obtained by visual comparison and reference evaluation. But this method has obvious experience, blindness, and randomness. Afterward, many scholars have been working on the quantitative measurement of JRC by different methods. Tse and Cruden [30] obtained the relationship between JRC and the root-mean-square Z2 satisfies Eq. (18) by studying Barton’s standard contour curve.

JRC=32.2+32.471lgZ2
(18)
Z2=1L i=1n(yi+1yi)2xi+1xi
(19)

Where L is the total span of interface,xi+1 and xi are the axial coordinate of the first i+1 and the first i joint discrete points of xi , respectively, yi+1 and yi are the y axis coordinates of the first i+1 and the first i joint discrete points, respectively, and n is the number of discrete points on the interface. There is a close correspondence between JRC and Z2 with the correlation coefficient of 0.9863. In order to simulate the effect of JRC on the stick-slip and instability of CRCS, different JRC parameters are chosen as the initial occlusion up interface.

Figure 9 shows the variation curve of shear stress, shear displacement, and fracture development of interface under lateral unloading. With the slip and instability of the CRCS under lateral unloading, the shear stress shows a wave-like change characteristic, and the shear displacement shows a step-type change of “slip-stable-slip.” The fracture of the interface shows “rupture-intact-rupture” feature. These three typical characteristics are consistent with the results of a stick-slip experiment conducted by Lu et al. [11]. Under lateral unloading, the interface shear stress, shear displacement, and crack development process can be divided into the following four stages:

  1. Shear stress reversal stage: At this time of stress balance, the initial shear stress direction of the interface is along the negative direction of the X-axis. After unloading, the shear stress value gradually decreases until the final shear stress is 0. This phenomenon is caused by the change of the direction of static friction on the interface due to lateral unloading.

  2. Shear stress accumulation stage: The shear stress gradually accumulates without obvious shear slip and crack development. It should be noted that the microshear displacement is microdeformation caused by the different elastic modulus of the coal and rock. The accumulation of shear stress is the main reason for the stick-slip hysteresis characteristics of the interface.

  3. The precursor of stick-slip and instability stage: At this stage, the cracks begin to develop, but the number is relatively small. The shear displacement is basically unchanged, but the accumulation of shear stress obviously increases until the shear stress peak. The abnormal increase of the shear stress can be used as the precursor of the stick-slip and instability.

  4. Stick-slip and instability stage: With the decrease of the waveform of the shear stress on the interface, the shear displacement and cracks show a step-by-step growth. Shear stress, shear displacement, and crack development show obvious stick-slip characteristics.

Figure 9

Variation curve of shear stress, shear displacement, and crack development.

Figure 9

Variation curve of shear stress, shear displacement, and crack development.

Stick-slip and instability of CRCS are accompanied with the formation, development, and intersection of cracks. The acoustic emission (AE) monitoring system is often used in the lab to monitor the internal damage. However, the AE can only effectively monitor the number of cracks and can not accurately describe the internal damage. Therefore, in order to quantitatively analyze the internal damage of CRCS, a fish function is used to record the total length of cracks as well as the length of shear and tensile cracks caused by stick-slip and instability of CRCS. The damage parameter (D) is proposed according to the analysis of Gao [13] and Wu [31].

D=DT+DS=LT+LSLO
(20)

Where DT is the damage parameter of tensile cracks, DS is the damage parameter of shear cracks, LO is the total contact length, LS is the total length of shear cracks, and LT is the total length of tensile cracks. The D is between 0 and 1, the closer it is to 1, the higher the damage degree. Figure 10 shows the crack evolution process of CRCS through lateral unloading. Figure 11 shows the contact damage rate of the interface.

Figure 10

The crack evolutions of CRCS under lateral unloading. Note: Red represents a shear crack, and blue represents a tensile crack.

Figure 10

The crack evolutions of CRCS under lateral unloading. Note: Red represents a shear crack, and blue represents a tensile crack.

Figure 11

The damage rate of contact. (a) The upper coal. (b) The rock parting. (c) The lower coal. (d) The upper and lower interface.

Figure 11

The damage rate of contact. (a) The upper coal. (b) The rock parting. (c) The lower coal. (d) The upper and lower interface.

At the initial unloading state, the shear stress accumulated inside the structure is small, and the structure only produces micro shear deformation. With the increase of unloading degree, the accumulated shear stress in coal-rock mass and structural plane increases gradually. When the accumulated shear stress exceeds the shear strength of the contact, the contact will slip or crack. At point (a), the unloading time is 1.54 ms, and the cracks first developed at the contact surface between the lower coal and the rock parking until the contact surface is completely broken when d = 1. The fracture development type is a shear fracture. At point (b), the shear stress accumulated on the upper interface reaches a peak. At this time, the cracks development on the upper interface occurs, and the cracks in the lower interface show a gradual closure trend. The upper and lower coal begin to produce shear failure along the top and bottom corners under the action of shear stress and gradually extend into the interior of the coal. At point (c), the cracks of the upper interface expand rapidly, and the cracks in the upper and lower coal gradually penetrate under the shear stress, but the development of cracks in the coal around the upper and lower interfaces is relatively small. This phenomenon is due to the fact that the slip unloading of coal and rock contact surface reduces the shear stress concentration degree around coal. Figure 12 shows the shear stress at points P1 and P2 in the upper coal. The shear stress at point P1 is significantly higher than that at point P2, which is a good confirmation of the accuracy of the concept. At point (d), the cracks are substantially completely penetrated. The cracks damage parameter is D = 0.19 of the upper coal, and the fracture damage parameter is D= 0.22 of the lower coal. The fracture damage value is basically equal. The ratio of the shear damage parameter (DS) and the tensile damage parameter (DT) is close to 9:1. In general, during the process of unloading instability of CRCS, the instability of coal is dominated by shear cracks, and the failure of coal is characterized by the fracture instability toward the unloading surface, the rock damage parameter is D0, and the crack development is less. However, the damage parameter of the upper interface is D1, and the damage is also dominated by shear cracks. The instability of the rock is attributed to slip instability toward the unloading surface. For the whole CRCS, the fracture on the nonunloading side is dominated by shear cracks, and the crack on the unloading side is dominated by the tensile cracks.

Figure 12

The shear stresses at points P1 and P2 in upper coal.

Figure 12

The shear stresses at points P1 and P2 in upper coal.

5.1. Energy Dissipation Characteristics

The process of stick-slip and instability of CRCS is accompanied by energy dissipation. The energy dissipation is mainly divided into two parts: one part is the energy dissipated by friction slip between blocks and the other part is the energy released in the form of kinetic energy. In this paper, a fish function is used to monitor energy dissipated in slip (Ujf) and kinetic energy (Uk). The Ujf was calculated by summing the energy dissipated in slip at every single contact that fails in shear [27].

Uif=i=1nc12( fs+fs)us
(21)

Where nc is the number of contacts, fs and s are the current and previous shear forces at the contact, respectively, and usis the increment of shear displacement during a time step.

The Ukwas calculated by summing the kinetic energy of each grid point [27].

Uk=i=1ngp12mi(ui)2
(22)

Where ngp is the number of grid points, mi is the mass of grid point, and i and ui is the velocity at grid point i at the current time step.

Figure 13 shows the curves of energy dissipated in slip and kinetic energy. At the initial unloading stage, the values of Ujf and Uk are relatively small and increase gradually with the unloading time, and both have a strong coupling with the overall change. At the stick-slip precursor stage, the Ujf reaches the high value quickly, and then keeps basically stable, while the value of Uk is always around 0. This shows that the response of Ujf to stick-slip and instability is earlier than Uk. At the stage of stick-slip and instability, the dissipation energy increases rapidly, and the peak value of energy Ujf fluctuates with the stick-slip and instability of CRCS, but the kinetic energy increases gradually. With the stick-slip and instability, the peak value of Uk presents fluctuating rise, which indicates that the Ujf caused by stick-slip and instability of CRCS tends to be stable gradually under the unloading, while the Uk of CRCS increases gradually.

Figure 13

The dissipated energy and kinetic energy.

Figure 13

The dissipated energy and kinetic energy.

In general, lateral unloading can induce the stick-slip and instability of CRCS. From the analysis of the characteristics of stick-slip and instability, it can be found that the abnormal increase of shear stress can be used as the precursor information of the stick-slip and instability of CRCS, and the peak point of the shear stress can be used as the starting point of stick-slip and instability. Based on the analysis of crack development characteristics, the instability of coal is characterized by fracture, and the instability of rock parting is shown as slipping. Based on the analysis of energy dissipation characteristics, the response of slip dissipation energy to stick slip and instability is earlier than kinetic energy, and the abnormal increase of slip dissipation energy can also be used as a precursor of stick slip and instability. With stick slip, the kinetic energy of CRCS gradually increases, which is also a direct reason for the occurrence of the slip-induced rock burst.

6.1. Unloading Speed

The roadway excavation speed is different, so the unloading speed of the stress is different in the surrounding rock mass. In general, the faster the excavation speed, the faster the stress unloading speed. In order to investigate the effect of unloading speed on the stick slip and instability of CRCS, the process of simulating stick slip and instability of CRCS is carried out under different unloading speeds. Figure 14 shows the curve of horizontal stress and time at different unloading speeds.

Figure 14

The curve of horizontal stress and time at different unloading speeds.

Figure 14

The curve of horizontal stress and time at different unloading speeds.

Figure 15 shows the shear stress and shear displacement curves of the interface at different unloading speeds. For shear stress, the stress accumulation rate at the accumulation stage becomes faster as the unloading speed increases, but the peak shear stress is basically stable. This shows that the peak value of the shear stress of the interface is independent of the unloading speed. After the shear stress reaches the peak and the unloading speed is 40 Pa/step, the shear stress of the interface produces a sudden drop with a velocity of 0.12 MPa, the sudden drop time is 0.02 ms, and the number of peak cracks is 39. The sudden drop in shear stress and peak crack numbers show that the interface has an obvious fracture phenomenon. When the unloading velocity is 25 Pa/step, the shear stress decreases by 0.01 MPa, the sudden drop time is 0.02 ms, the number of peak cracks is 36, and the fracture velocity and peak crack numbers gradually slow down. When the unloading speed is 15 Pa/step, there is no obvious shear stress drop after the peak value. This shows that with the decrease in unloading speed, the instability characteristics of the interface will change from fracture instability to stick slip and instability. For the variation curve of shear displacement, the smaller the unloading speed, the more obvious the slip-stability-slip phenomenon of shear displacement. It can be concluded that the unloading speed affects the stick slip and instability of CRCS. The smaller the unloading speed, the more obvious the stick slip and instability. On the contrary, the larger the unloading speed, the more obvious the fracture instability.

Figure 15

Shear stress, shear displacement, and fracture development curves of interface with unloading speeds.

Figure 15

Shear stress, shear displacement, and fracture development curves of interface with unloading speeds.

From Figure 16, with the increase in unloading speed, the total energy released gradually decreases. The coefficient of determination is 0.99567, which indicates that there is an obvious power function relationship between the energy released by lateral unloading and the unloading speed. When the unloading speed is 15 Pa/step, the total released energy is 47.23 J, and when the unloading speed is 40 Pa/step, the total energy released is 16.71 J, the released energy is reduced by 2.8 times, while the shear displacement is only increased by 0.25 times. The results show that the smaller the unloading speed, the more the total released energy, and the stronger the CRCS stability.

Figure 16

The fitting curve between total energy released and unloading speed.

Figure 16

The fitting curve between total energy released and unloading speed.

6.2. Joint Roughness Coefficient

In order to further explore the influence of JRC value on the stick slip and instability, the numerical simulation of UDEC is carried out by using the curved structural surfaces with different roughness coefficients. Figure 17 shows three types of JRC, and the JRC values are 4.42, 13.44, and 23.58, respectively. From Figure 18, it can be proved that with the increase of JRC, the interface changes from smooth to rough.

Figure 17

Three types of joint roughness coefficient.

Figure 17

Three types of joint roughness coefficient.

Figure 18

Shear stress, shear displacement, and fracture development curves of interface with JRC.

Figure 18

Shear stress, shear displacement, and fracture development curves of interface with JRC.

From Figure 18, with the increase of JRC, the peaks of shear stress are 0.98, 0.87, and 0.62 MPa, the stress drop is 0.22, 0.13, and 0.02 MPa, the shear displacements are 23.54 × 10-5, 7.29 × 10-5, and 0.4 × 10-5 m, respectively, and the complete times of cracks development on the interface are 2.58, 2.97, and 3.15 seconds, respectively. The results show that the peak shear stress, stress drop, and shear displacement are inversely proportional to JRC, and the complete development time of cracks on the interface is proportional to the JRC. The smaller the JRC value, the smoother the structural plane, the higher the degree of shear stress accumulation, and the larger the peak stress drop, and the interface is characterized by fracture instability. The rougher the interface, the greater the JRC value, the greater the variation of shear stress after a peak value, and the longer the fracture development time of the interface, and the instability type is stick slip and failure.

From Figure 19, the total energy released by the stick slip and instability satisfies the quadratic function relationship with the JRC, and the coefficient of determination is 0.98167. As the JRC value increases, the total energy released under the unloading path increases gradually. It indicates that the greater the roughness of the interface, the more stable the CRCS.

Figure 19

The fitting curve between total energy released and JRC.

Figure 19

The fitting curve between total energy released and JRC.

It is observed that with the gradual release of horizontal stress, the CRCS will produce slip instability along the interface. Both the unloading speed and the JRC can affect the slip instability of CRCS. When the unloading speed is reduced and the JRC is increased, the shear displacement generated by the slip decreases gradually, and the total energy released increases gradually; the instability of the interface can be transferred from break-slip to stick-slip, and the CRCS will stabilize gradually. Therefore, the stability of the CRCS can be increased by reducing the unloading speed around the roadway or increasing the JRC of the interface (such as timely support, improving support strength, grouting reinforcement, blasting rock parting, etc.), which will reduce the possibility of impact disaster accidents.

  1. Based on the analysis of field data, this paper puts forward the research subject of stick-slip instability along the coal rock contact surface when unloading excavation of coal seam with rock parking. At the same time, the stick-slip instability has obvious hysteresis characteristics that are pointed out. This hysteresis characteristic provides the possibility to prevent the impact disaster accident induced by unloading excavation of coal seam with rock parking.

  2. Based on the analysis of the occurrence state of coal seam with rock parking, a theoretical model of CRCS is proposed. Through theoretical calculation, it is pointed out that the unloading speed and roughness of the contact surface will affect the stick-slip instability of the CRCS.

  3. A self-compiled unloading program is used to test the numerical model under lateral unloading. The results show that the stick-slip instability along the contact surface is the main reason for the instability of the CRCS. Meanwhile, the rapid increase of shear stress and the abnormal increase of slip dissipation energy are the precursory signals of stick-slip instability.

  4. The effects of unloading speed and roughness of contact surface on the stick-slip instability of CRCS are studied by changing the parameters of the numerical model. The methods to reduce the unloading speed of coal/rock mass around the roadway and increase the roughness of contact surface are put forward to prevent the impact accidents induced by unloading excavation of coal seam with rock parking.

The data in this manuscript are available. https://doi.org/10.5061/dryad.41ns1rndr.

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

We gratefully wish to acknowledge The Key Scientific Research Projects for Higher Education of Henan Province (23A440012, 24A440011) and The Key R & D and promotion projects in Henan Province (212102310030) and Collaborative Innovation Center for Prevention and Control of Mountain Geological Hazards of Zhejiang Province (PCMGH-2022-05) and Interdisciplinary Sciences Project (NGJC-2022-02), Nanyang Institute of Technology and Doctoral Research Start-up Fund Project, Nanyang Institute of Technology.

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