# Blasting for Fracturing and Improving the Permeability of Deep, Soft, Outburst Prone Coal Seams Using Blasthole and Relief Hole Drilled into the Underlying Stratum: Optimal Hole Distance

Authors: Jianyu Zhang; Xingguo Zhao; Shigui Fu; Guodong Qiao; Xin Zhang; Shuai Yang
Journal: Geofluids
 (2022)

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## Abstract

To address the problems with deep-hole presplit blasting intended to fracture and improve the permeability of deeply buried, soft, high-gas-content coal seams, a method using a blasthole and a relief hole drilled into the underlying rock stratum was proposed. By establishing a theoretical model for this purpose, the stress wave propagation characteristics during the blasting process were analyzed, and the working mechanisms of the relief hole and the stress transmission characteristics were investigated. The blasting of the C13-1 coal seam in the Huainan mining area under different in situ stress conditions using different blasthole–relief hole distances was simulated using an implicit–explicit coupled method and the ANSYS/LS-DYNA software. The results showed that the blasting-induced stress wave was reflected from the coal–rock interface and transformed into a tensile wave owing to the different wave impedances of coal and rock, thereby fracturing the rock and coal masses better and achieving the intended permeability improvement effect. A free surface effect was produced near the relief hole during the blasting process, which directed the stress wave to propagate in the direction of the relief hole, thereby promoting fracturing in that direction. The in situ stress inhibited the blasting-induced fracturing in the coal mass. Thus, for blasting intended to improve the permeability of deeply buried coal masses, the blasthole–relief hole distance should be reduced to achieve better fracturing. Our results have a certain reference value for directional blasting intended to fracture and improve the permeability of deeply buried, soft, high-gas-content coal seams.


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## Body

## 1. Introduction

With the increasing operation depth of coal mines in China, some coal mines are gradually developing from low gas mines to high outburst mines [1, 2]. According to the statistics of coal mining accidents, gas outburst remains the major type of coal mining accident in China, and the prevention and control of gas hazards remain severely challenging [3–5]. Current outburst-prevention measures adopted at coal mines include protective seam mining [6, 7], large-area gas drainage [8, 9], coal seam water infusion [10, 11], hydraulic fracturing [12, 13], and presplit blasting [14–16]. Notably, methane in deep coal is also an important unconventional natural gas resources. Successful extraction of this natural gas could both improve energy supply and reduce the dangers of underground coal mining [17]. For low permeability coal seam, deep-hole presplit blasting remains an effective approach for improving the gas drainage efficiency of low-permeability coal seams.Many scholars have studied the deep-hole presplit blasting in coal seam. Liu et al. [18] found that the effect of drilling blasting with borehole cross the seam was better than that down the seam. Chu et al. [19] found that the blasting crack damage of coal body is the result of the joint action of explosion stress wave, detonation gas, and coal mine methane. Guo et al. [20] showed that the displacement compensation space provided by the relief hole and the surface properties of the hole wall enhanced the tangential tensile stress between the coal particles on and around the relief hole wall, which promoted the development and expansion of the radial cracks around the control hole. Cai [21] carried out a long hole loose blasting test on the -610MW2EB4 working face of Liyi Coal Mine in China and found that the antipermeability of coal seam was effectively improved after blasting, and the loose radius reached 3-3.5 m. Shang et al. [22] designed the drilling, charging, and hole sealing processes of coal seam blasting. Zhang [23] conducted gas extraction after presplitting blasting in C1201 working face of Chiyu Coal Mine in China and found that the concentration of gas extraction after blasting reached 1.93-3.2 times of the original, the flow rate of gas extraction reached 1.4-2.6 times of the original, and the influence radius reached 4.5 m. The above research has promoted the development of coal seam blasting to increase permeability. However, deep-hole presplit blasting does not produce the desired effect for soft, high-gas-content coal seams deeply buried between hard underlying and overlying strata. The problems include the rapid closing of blasting-induced fractures and a short duration of the permeability improvement effect. To address the above problems, a method for blasting soft, outburst-prone coal seams using a blasthole and a relief hole drilled into the underlying stratum was proposed. This outburst prevention method involves blasting the underlying stratum and controlling the direction of blasting-induced fracturing using a relief hole, and it realizes directional gas drainage from soft, high-gas-content coal seams.Therefore, in this study, a theoretical model was established for describing the stress wave propagation of blasting intended to fracture and improve the permeability of coal seams using a blasthole and a relief hole drilled into the underlying stratum. Furthermore, the working mechanisms of the relief hole and the transmission characteristics of the blasting-induced stress were analyzed. The fracturing induced by blasting using different blasthole–relief hole distances under different in situ stress conditions was investigated using an implicit–explicit coupled method and the ANSYS/LS-DYNA software. Our results have certain reference value for the blasting of soft, outburst-prone coal masses for outburst prevention.


## 2. Theoretical Mechanisms

### 2.1. Stress Wave Propagation Characteristics

Blasting-induced stress waves may be reflected from or transmitted through blasting media, depending on their wave impedance [24]. For blasting intended to fracture and improve the permeability of soft, outburst-prone coal seams using blastholes drilled into the underlying stratum, the blasting-induced stress wave propagates from the underlying stratum to the soft coal seam. The process of propagation of the blasting stress wave from the underlying stratum to the soft coal seam was modeled, as shown in Figure 1. In the figure, P is the longitudinal incident wave induced by blasting, which propagates from the underlying stratum to the soft coal seam, Pr is the longitudinal reflected wave, Sr is the horizontal reflected wave, Pt is the longitudinal transmitted wave, and St is the horizontal transmitted wave.Figure 1
The model of propagation of the blasting stress wave.Based on the continuity of stress wave propagation, the particle velocities and stresses on the two sides of the rock–coal interface during blasting can be expressed as(1)σi+σr=σt,(2)νi−νr=νt,where σi, σr, and σt are the stresses (MPa) induced by the incident, reflected, and transmitted waves, respectively, and υi, υr, and υt are the particle vibration velocities (m/s) of the incident, reflected, and transmitted waves, respectively.For a longitudinally propagating stress wave,(3)σi=ρ1Cp1νi,νi=σiρ1Cp1,σr=ρ1Cp1νr,νr=σrρ1Cp1,σt=ρ2Cp2νt,νt=σrρ2Cp2.By combining Equations (1), (2), and (3), σr and σt can be expressed as
(4)σr=σiρ2Cp2−ρ1Cp1ρ2Cp2+ρ1Cp1,(5)σt=σi2ρ2Cp2ρ2Cp2+ρ1Cp1,where ρ1 and ρ2 are the densities (kg/m3) of the rock stratum and coal seam, respectively, and CP1 and CP2 are the velocities (m/s) of the longitudinal waves propagating in the rock stratum and coal seam, respectively.Then, the reflection coefficientF can be expressed as
(6)F=ρ2Cp2−ρ1Cp1ρ2Cp2+ρ1Cp1.The transmission coefficientT can be expressed as
(7)T=2ρ2Cp2ρ2Cp2+ρ1Cp1.T and F satisfy the following relation:
(8)1+F=T.When the blasting stress wave is transmitted from the underlying stratum to the soft coal seam, becauseρ2Cp2<ρ1Cp1, F<0, and the incident and reflected waves have different signs, resulting in a tensile reflected wave on the coal–rock interface that reacts on the rock mass. As the tensile strength of the rock is much lower than its compressive strength, the tensile reflected wave can better fracture the rock side of the coal–rock interface. The weakness plane in the rock resulting from the fracturing disposes the blasting stress wave to propagate in that direction and, as the coal mass has a lower strength than the rock mass, finally leads to the formation of massive fractures in the soft coal mass, thereby improving its permeability.


### 2.2. Working Mechanisms of Relief Hole

The blasting produces a free surface effect at the relief hole, and the effect disposes the stress wave to propagate in the direction toward the relief hole. In addition, the blasting stress wave is reflected from the relief hole and transformed into a tensile stress wave, resulting in a stress concentration around the relief hole, which promotes further fracturing. Figure2 illustrates the range of fracturing induced by blasting using a relief hole [25].Figure 2
The range of fracturing.In Figure2, the blasthole (on the left) and relief hole (on the right) are designed to have the same radius and are located on the same horizontal line to simplify the model. After blasting, the stress wave is attenuated with distance; thus, the stress in any particle A can be expressed as [26]
(9)σr=P0Lr−α,(10)σθ=μ1−μσr,where p0 is the initial pressure after blasting (MPa), σr is the radial stress (MPa), σθ is the tangential stress (MPa), L is the distance from the particle to the center of the blasthole (m), r is the radius of the blasthole (m), α is the attenuation coefficient, and μ is the Poisson’s ratio of the material.When the blasting stress propagates to around the relief hole, the following equations can be derived based on the theory of elasticity [27]:
(11)σrr=121−k2σθ−σr+1−4k2+3k4σr+σθcos2θ,(12)σθθ=121−k2σθ−σr+1+3k4σr+σθcos2θ,(13)τrr=121+2k2−3k4σθ+σrcos2θ,where σrr is the radial stress in the relief hole (MPa), σθθ is the tangential stress in the relief hole (MPa), k=rb/L is an equation coefficient, and θ is the angle between the two lines connecting the particle to the blasthole and relief holes.According to blasting theory, the tensile strength of a rock mass is much lower than its compressive strength, and blasting fragments a rock mass mainly through tensile-stress-induced circumferential fractures. In the far field of blasting, the blasting stress wave is not sufficiently strong to fracture the rock mass. Thus, only the tangential tensile stress needs to be discussed here, and the minimum stress required to fracture the zone around the relief hole can be expressed as(14)σθθ=1+12k2+32k4σθ+32k4−12k2σr.


### 2.3. Effect of In Situ Stress on Relief Hole

The state of relief holes under in situ stress is shown in Figure3. The stress near the relief hole is [28]
(15)σrr=Px+Py21−ar2+Px−Py21−4ar2+3ar4cos2θ,σθθ=Px+Py21+ar2+Px−Py21+3ar4cos2θ,τrθ=Py−Px21+2ar23ar4sin2θ,where σrr is the radial stress in the relief hole (MPa), σθθ is the tangential stress in the relief hole (MPa), τrθ is the shear stress in the relief hole (MPa), a is the distance to the relief hole (cm), and r is the radius of relief hole (cm).
(1)
Whenθ=0, a=r, τrθ=0, σrr=0, and σθθ=−Px+3Py(2)
Whenθ=π/2, a=r, τrθ=0, σrr=0, and σθθ=3Px−PyFigure 3
The state of relief holes under in situ stress.Under the condition of in situ stress, the rock is subjected to tangential tensile stress in the direction of maximum principal stress and tangential compressive stress in the direction of minimum principal stress. The tensile strength of rock is less than the compressive strength. Therefore, the cracks will develop in the direction of the maximum principal stress.


## 2.1. Stress Wave Propagation Characteristics

Blasting-induced stress waves may be reflected from or transmitted through blasting media, depending on their wave impedance [24]. For blasting intended to fracture and improve the permeability of soft, outburst-prone coal seams using blastholes drilled into the underlying stratum, the blasting-induced stress wave propagates from the underlying stratum to the soft coal seam. The process of propagation of the blasting stress wave from the underlying stratum to the soft coal seam was modeled, as shown in Figure 1. In the figure, P is the longitudinal incident wave induced by blasting, which propagates from the underlying stratum to the soft coal seam, Pr is the longitudinal reflected wave, Sr is the horizontal reflected wave, Pt is the longitudinal transmitted wave, and St is the horizontal transmitted wave.Figure 1
The model of propagation of the blasting stress wave.Based on the continuity of stress wave propagation, the particle velocities and stresses on the two sides of the rock–coal interface during blasting can be expressed as(1)σi+σr=σt,(2)νi−νr=νt,where σi, σr, and σt are the stresses (MPa) induced by the incident, reflected, and transmitted waves, respectively, and υi, υr, and υt are the particle vibration velocities (m/s) of the incident, reflected, and transmitted waves, respectively.For a longitudinally propagating stress wave,(3)σi=ρ1Cp1νi,νi=σiρ1Cp1,σr=ρ1Cp1νr,νr=σrρ1Cp1,σt=ρ2Cp2νt,νt=σrρ2Cp2.By combining Equations (1), (2), and (3), σr and σt can be expressed as
(4)σr=σiρ2Cp2−ρ1Cp1ρ2Cp2+ρ1Cp1,(5)σt=σi2ρ2Cp2ρ2Cp2+ρ1Cp1,where ρ1 and ρ2 are the densities (kg/m3) of the rock stratum and coal seam, respectively, and CP1 and CP2 are the velocities (m/s) of the longitudinal waves propagating in the rock stratum and coal seam, respectively.Then, the reflection coefficientF can be expressed as
(6)F=ρ2Cp2−ρ1Cp1ρ2Cp2+ρ1Cp1.The transmission coefficientT can be expressed as
(7)T=2ρ2Cp2ρ2Cp2+ρ1Cp1.T and F satisfy the following relation:
(8)1+F=T.When the blasting stress wave is transmitted from the underlying stratum to the soft coal seam, becauseρ2Cp2<ρ1Cp1, F<0, and the incident and reflected waves have different signs, resulting in a tensile reflected wave on the coal–rock interface that reacts on the rock mass. As the tensile strength of the rock is much lower than its compressive strength, the tensile reflected wave can better fracture the rock side of the coal–rock interface. The weakness plane in the rock resulting from the fracturing disposes the blasting stress wave to propagate in that direction and, as the coal mass has a lower strength than the rock mass, finally leads to the formation of massive fractures in the soft coal mass, thereby improving its permeability.


## 2.2. Working Mechanisms of Relief Hole

The blasting produces a free surface effect at the relief hole, and the effect disposes the stress wave to propagate in the direction toward the relief hole. In addition, the blasting stress wave is reflected from the relief hole and transformed into a tensile stress wave, resulting in a stress concentration around the relief hole, which promotes further fracturing. Figure2 illustrates the range of fracturing induced by blasting using a relief hole [25].Figure 2
The range of fracturing.In Figure2, the blasthole (on the left) and relief hole (on the right) are designed to have the same radius and are located on the same horizontal line to simplify the model. After blasting, the stress wave is attenuated with distance; thus, the stress in any particle A can be expressed as [26]
(9)σr=P0Lr−α,(10)σθ=μ1−μσr,where p0 is the initial pressure after blasting (MPa), σr is the radial stress (MPa), σθ is the tangential stress (MPa), L is the distance from the particle to the center of the blasthole (m), r is the radius of the blasthole (m), α is the attenuation coefficient, and μ is the Poisson’s ratio of the material.When the blasting stress propagates to around the relief hole, the following equations can be derived based on the theory of elasticity [27]:
(11)σrr=121−k2σθ−σr+1−4k2+3k4σr+σθcos2θ,(12)σθθ=121−k2σθ−σr+1+3k4σr+σθcos2θ,(13)τrr=121+2k2−3k4σθ+σrcos2θ,where σrr is the radial stress in the relief hole (MPa), σθθ is the tangential stress in the relief hole (MPa), k=rb/L is an equation coefficient, and θ is the angle between the two lines connecting the particle to the blasthole and relief holes.According to blasting theory, the tensile strength of a rock mass is much lower than its compressive strength, and blasting fragments a rock mass mainly through tensile-stress-induced circumferential fractures. In the far field of blasting, the blasting stress wave is not sufficiently strong to fracture the rock mass. Thus, only the tangential tensile stress needs to be discussed here, and the minimum stress required to fracture the zone around the relief hole can be expressed as(14)σθθ=1+12k2+32k4σθ+32k4−12k2σr.


## 2.3. Effect of In Situ Stress on Relief Hole

The state of relief holes under in situ stress is shown in Figure3. The stress near the relief hole is [28]
(15)σrr=Px+Py21−ar2+Px−Py21−4ar2+3ar4cos2θ,σθθ=Px+Py21+ar2+Px−Py21+3ar4cos2θ,τrθ=Py−Px21+2ar23ar4sin2θ,where σrr is the radial stress in the relief hole (MPa), σθθ is the tangential stress in the relief hole (MPa), τrθ is the shear stress in the relief hole (MPa), a is the distance to the relief hole (cm), and r is the radius of relief hole (cm).
(1)
Whenθ=0, a=r, τrθ=0, σrr=0, and σθθ=−Px+3Py(2)
Whenθ=π/2, a=r, τrθ=0, σrr=0, and σθθ=3Px−PyFigure 3
The state of relief holes under in situ stress.Under the condition of in situ stress, the rock is subjected to tangential tensile stress in the direction of maximum principal stress and tangential compressive stress in the direction of minimum principal stress. The tensile strength of rock is less than the compressive strength. Therefore, the cracks will develop in the direction of the maximum principal stress.


## 3. Numerical Simulation Calculation Scheme

### 3.1. Numerical Modeling

A numerical calculation model was established for the C13-1 coal seam in the Huainan mining area using the ANSYS/LS-DYNA software. The C13-1 coal seam has an average thickness of 4.5 m and horizontal bedding. It mainly consists of lumpy durain mixed with strips of bright vitrain and thus is semidark and semibright coal. The C13-1 coal seam had a measured gas pressure of 3.8 MPa, an initial gas emission rateΔp of 4, a coal sturdiness coefficient f of 0.61, a comprehensive index D of 16, and a K value of 6.6. The coal seam was predicted to have a risk of gas outburst. The coal seam had a high gas content and low permeability and was underlain by a fine sandstone stratum [29].Figure4 illustrates the model of the coal seam. The model had the dimensions of 600×600 cm. It was configured with an arc-roof roadway (60 cm in width and 90 cm in height) located 60 cm above the coal–rock interface and 60 cm from the right boundary of the model, and a blasthole in the underlying stratum of the roadway (360 cm (210 cm for blasting and 150 cm for stemming) in length and 60 cm in diameter) inclined at an angle of 25° to the horizontal line. The blasting of the coal seam was simulated using the blasthole alone and a relief hole with a length of 360 cm and different distances (180, 300, and 420 cm, or 3, 5, and 7 times the hole diameter, respectively) to the blasthole. A horizontal in situ stress σx was applied to the right boundary of the model, a vertical in situ stress σy was applied to the upper boundary, and displacement constraints were applied to the left and bottom boundaries. The boundaries were defined as nonreflecting to reproduce the actual situation better, thus eliminating their potential influence on the tensile reflected wave.Figure 4
Numerical calculation model: (a) blasting model without relief hole; (b) blasting model with relief hole.
(a)(b)


### 3.2. Coal, Rock, and Stemming Models

The coal, rock, and blasthole stemming were defined using the∗MAT_JOHNSON_HOLMQUIST_COOK(HJC) model, and the ∗MAT_ADD_EROSION failure criterion was added for describing the tensile failure of the coal, rock, and blasthole stemming during the blasting process. The Holmquist–Johnson–Cook (HJC) model, an improved version of the Johnson–Cook model, expresses the equivalent strength of a rock mass as the function of its pressure, strain rate, and damage and considers the combined effects of strain rate, hydrostatic pressure, and cumulative damage on rock strength. This model has been widely used in the simulation calculation of impact-induced large rock deformations [30]. Table 1 shows the physiomechanical parameters of the coal, rock, and blasthole stemming selected for the simulation.Table 1
The physiomechanical parameters of the coal, rock, and blasthole stemming.
Nameρ/(g·m-3)E/GPaμσbc/MpaRm/MpaCoal1.3805.30.320.457.2Rock2.58333.40.2353.1969.592Hole sealing1.6201.310.093.110.98Note:ρ is the material density. E is the elasticity modulus. μ is the Poisson ratio. σbc is the compressive strength. Rm is the tensile strength.


### 3.3. Explosive Material and State Equation

The explosive material was defined using∗MAT_HIGH_EXPLOSIVE_BURN. The Jones–Wilkins–Lee (JWL) state equation was used to describe the process of the external work of blasting and the expansion and driving of explosion products [31]. The JWL state equation is expressed as
(16)P=A1−ωR1Ve−R1V+B1−ωR2V+ωE0V,where P is the blasting pressure (Pa); A and B are the explosive parameters (Pa); R1, R2, and ω are the explosive characteristic parameters (dimensionless); E0 is the internal energy of the blasting products (J/m3); and V is the initial relative volume (dimensionless). Table 2 shows the configuration of the explosive parameters.Table 2
The configuration of the explosive parameters.
ρ/kg·m-3D/m·s-1A/PaB/PaR1R2ωE0/J·m-3120032003.73×10113.74×1094.150.90.356×109Note:ρ is the material density. D is the detonation velocity.


### 3.4. Air Material and State Equation

The air material was defined using∗MAT_NULL. The state equation of air was expressed as a linear polynomial (LINEAR_POLYNOMIAL) [32]. The state equation is expressed as
(17)p=C0+C1μ+C2μ2+C3μ3+C4+C5μ+C6μ2E,where p is the pressure (Pa), μ is the specific volume (dimensionless), C0–C6 are the coefficients of the polynomial, and E is the internal energy per unit volume (J/m3). Table 3 shows the configuration of the air parameters.Table 3
The configuration of the air parameters.
ρ/kg·m-3C0C1C2C3C4C5C6E0/J·m-31.02500000.40.402.5×102Note:ρ is the material density.


### 3.5. In Situ Stress Loading Scheme

Three mining depths (0, 1000, and 1500 m) were simulated, and the corresponding in situ stresses were calculated using the formula proposed by Heidbach et al. [33] and applied in the X and Y directions. Table 4 shows the in situ stresses for the three different mining depths simulated.Table 4
The parameters of in situ stresses.
ProjectH/mσx/MPaσy/MPa10002100052.3541.693150073.3558.19Note:H is the mining depth. σx is the horizontal stress. σy is the vertical stress.


## 3.1. Numerical Modeling

A numerical calculation model was established for the C13-1 coal seam in the Huainan mining area using the ANSYS/LS-DYNA software. The C13-1 coal seam has an average thickness of 4.5 m and horizontal bedding. It mainly consists of lumpy durain mixed with strips of bright vitrain and thus is semidark and semibright coal. The C13-1 coal seam had a measured gas pressure of 3.8 MPa, an initial gas emission rateΔp of 4, a coal sturdiness coefficient f of 0.61, a comprehensive index D of 16, and a K value of 6.6. The coal seam was predicted to have a risk of gas outburst. The coal seam had a high gas content and low permeability and was underlain by a fine sandstone stratum [29].Figure4 illustrates the model of the coal seam. The model had the dimensions of 600×600 cm. It was configured with an arc-roof roadway (60 cm in width and 90 cm in height) located 60 cm above the coal–rock interface and 60 cm from the right boundary of the model, and a blasthole in the underlying stratum of the roadway (360 cm (210 cm for blasting and 150 cm for stemming) in length and 60 cm in diameter) inclined at an angle of 25° to the horizontal line. The blasting of the coal seam was simulated using the blasthole alone and a relief hole with a length of 360 cm and different distances (180, 300, and 420 cm, or 3, 5, and 7 times the hole diameter, respectively) to the blasthole. A horizontal in situ stress σx was applied to the right boundary of the model, a vertical in situ stress σy was applied to the upper boundary, and displacement constraints were applied to the left and bottom boundaries. The boundaries were defined as nonreflecting to reproduce the actual situation better, thus eliminating their potential influence on the tensile reflected wave.Figure 4
Numerical calculation model: (a) blasting model without relief hole; (b) blasting model with relief hole.
(a)(b)


## 3.2. Coal, Rock, and Stemming Models

The coal, rock, and blasthole stemming were defined using the∗MAT_JOHNSON_HOLMQUIST_COOK(HJC) model, and the ∗MAT_ADD_EROSION failure criterion was added for describing the tensile failure of the coal, rock, and blasthole stemming during the blasting process. The Holmquist–Johnson–Cook (HJC) model, an improved version of the Johnson–Cook model, expresses the equivalent strength of a rock mass as the function of its pressure, strain rate, and damage and considers the combined effects of strain rate, hydrostatic pressure, and cumulative damage on rock strength. This model has been widely used in the simulation calculation of impact-induced large rock deformations [30]. Table 1 shows the physiomechanical parameters of the coal, rock, and blasthole stemming selected for the simulation.Table 1
The physiomechanical parameters of the coal, rock, and blasthole stemming.
Nameρ/(g·m-3)E/GPaμσbc/MpaRm/MpaCoal1.3805.30.320.457.2Rock2.58333.40.2353.1969.592Hole sealing1.6201.310.093.110.98Note:ρ is the material density. E is the elasticity modulus. μ is the Poisson ratio. σbc is the compressive strength. Rm is the tensile strength.


## 3.3. Explosive Material and State Equation

The explosive material was defined using∗MAT_HIGH_EXPLOSIVE_BURN. The Jones–Wilkins–Lee (JWL) state equation was used to describe the process of the external work of blasting and the expansion and driving of explosion products [31]. The JWL state equation is expressed as
(16)P=A1−ωR1Ve−R1V+B1−ωR2V+ωE0V,where P is the blasting pressure (Pa); A and B are the explosive parameters (Pa); R1, R2, and ω are the explosive characteristic parameters (dimensionless); E0 is the internal energy of the blasting products (J/m3); and V is the initial relative volume (dimensionless). Table 2 shows the configuration of the explosive parameters.Table 2
The configuration of the explosive parameters.
ρ/kg·m-3D/m·s-1A/PaB/PaR1R2ωE0/J·m-3120032003.73×10113.74×1094.150.90.356×109Note:ρ is the material density. D is the detonation velocity.


## 3.4. Air Material and State Equation

The air material was defined using∗MAT_NULL. The state equation of air was expressed as a linear polynomial (LINEAR_POLYNOMIAL) [32]. The state equation is expressed as
(17)p=C0+C1μ+C2μ2+C3μ3+C4+C5μ+C6μ2E,where p is the pressure (Pa), μ is the specific volume (dimensionless), C0–C6 are the coefficients of the polynomial, and E is the internal energy per unit volume (J/m3). Table 3 shows the configuration of the air parameters.Table 3
The configuration of the air parameters.
ρ/kg·m-3C0C1C2C3C4C5C6E0/J·m-31.02500000.40.402.5×102Note:ρ is the material density.


## 3.5. In Situ Stress Loading Scheme

Three mining depths (0, 1000, and 1500 m) were simulated, and the corresponding in situ stresses were calculated using the formula proposed by Heidbach et al. [33] and applied in the X and Y directions. Table 4 shows the in situ stresses for the three different mining depths simulated.Table 4
The parameters of in situ stresses.
ProjectH/mσx/MPaσy/MPa10002100052.3541.693150073.3558.19Note:H is the mining depth. σx is the horizontal stress. σy is the vertical stress.


## 4. Results and Analysis

### 4.1. Analysis of Fracturing

Figure5 shows the blasting outputs at different mining depths and blasthole–relief hole distances. The ratio of the fractured area to the total area of coal mass, n, was calculated by performing image processing using MATLAB. Table 5 shows the corresponding results. Figure 6 shows the explosion crack box dimension fitting curve. Table 6 shows the fractal dimension of each case. The n of 5 times hole spacing increased by 3.49%, 1.05%, and 1.00%, and the fractal dimension increased by 1.89%, 0.29%, and 0.05%, compared with that of no relief hole, 3 times hole spacing, and 7 times hole spacing. When the buried depth is 0 m, the development of 5 times hole spacing crack is better than other conditions. Figure 4(a) shows the blasting outputs at the mining depth of 0 m and different blasthole–relief hole distances. At the mining depth of 0 m, blasting using different blasthole–relief hole distances fractured a large area of the coal mass, confirming the feasibility of blasting to fracture and improve the permeability of soft coal masses using a blasthole and a relief hole drilled into the underlying stratum. A further analysis of the blasting outputs showed that all the blasting configurations produced several fractures at the coal–rock interface and near the roadway. The reason behind the formation of massive fractures at the coal–rock interface has been analyzed in Section 1 and is not elaborated here. The reason behind the formation of massive fractures along the roadway is that the roadway can be considered as an air-filled cavity that produces a free surface effect and promotes fracturing in that direction. Therefore, the supporting structure of the roadway should be reinforced during floor blasting to avoid excessive damage to the roadway due to blasting vibration and affect the stability of the roadway. Figure 4(b) shows the blasting outputs at the mining depth of 1000 m and different blasthole–relief hole distances. The coal mass was significantly less fractured when compared with that at the mining depth of 0 m, indicating that the in situ stress inhibited the blasting-induced fracturing. The n of 3 times hole spacing increased by 8.93%, 4.15%, and 7.68%, and the fractal dimension increased by 19.12%, 4.08%, and 10.95%, compared with that at no relief hole, 5 times hole spacing, and 7 times hole spacing. Figure 4(c) shows the blasting outputs at the mining depth of 1500 m and different blasthole–relief hole distances. At this mining depth, the blasting failed to fracture a large area of the coal mass. The n of 3 times hole spacing increased by 1.92%, 1.32%, and 1.37%, and the fractal dimension increased by 13.59%, 6.78%, and 6.81%, compared with that at no relief hole, 5 times hole spacing, and 7 times hole spacing. The fracturing results showed that the in situ stress inhibited the blasting-induced fracturing in the coal mass. Thus, for the blasting of deeply buried coal masses for permeability improvement, the blasthole–relief hole distance should be reduced to achieve better fracturing.Figure 5
The blasting outputs at different mining depths and blasthole–relief hole distances.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)Table 5
The parameters of fracture area ratio.
Mining depthSingle blast hole3 times hole spacing5 times hole spacing7 times hole spacing0 m10.06%12.50%13.55%12.55%1000 m1.85%10.78%6.63%3.14%1500 m0.47%2.39%1.07%1.02%Figure 6
Explosion crack box dimension fitting curve.
(a)(b)(c)Table 6
The fractal dimension of each case.
Mining depthSingle blast hole3 times hole spacing5 times hole spacing7 times hole spacing0 m1.54921.57401.57851.57771000 m1.30661.55651.49551.40291500 m1.19591.35841.27221.2718


### 4.2. Analysis of Stress Transmission

Temporal variations in the stresses at two points (points 1 and 2, which were located 100 and 300 cm, respectively, above the central line of the coal–rock interface) were measured. Figure7 shows the stress–time curves. For a given mining depth, the maximum stress produced by blasting using a relief hole was larger than that produced by blasting using no relief hole, indicating that the addition of the relief hole decreased the stress wave attenuation rate and increased the range of stress wave propagation. A larger initial in situ stress led to a larger effective stress sustained after blasting, indicating that the magnitude of the initial in situ stress was a major factor affecting the postblasting stress state in the coal mass. Thus, for the blasting of deeply buried coal masses for permeability improvement, the effect of the in situ stress should be fully considered, and the effects of the in situ stress and blasting should be synergized to achieve the optimal blasting output. At the mining depth of 0 m, the maximum effective stress at the blasthole–relief hole distance of five times the hole diameter was larger than that for the blasthole–relief hole distances of three and seven times the hole diameter. At the mining depths of 1000 and 1500 m, the maximum stress at the blasthole–relief hole distance of three times the hole diameter was larger than that at the other blasthole–relief hole distances. The stress–time curves further indicate that, for the blasting of deeply buried coal masses for permeability improvement, the blasthole–relief hole distance should be reduced to achieve better blasting output.Figure 7
The stress–time curves.
(a)(b)(c)(d)(e)(f)


### 4.3. Analysis of Optimal Blasthole–Relief Hole Distance

The maximum loads induced by the blasting stress wave yielded by the series of simulations were analyzed to identify the optimal blasthole–relief hole distance at different mining depths. Figure8 shows the results. As the mining depth increased, the maximum stress loads at both points 1 and 2 decreased, indicating that the in situ stress inhibited the propagation of the blasting stress wave. At the mining depth of 0 m, the maximum stress load at the blasthole–relief hole distance of five times the hole diameter was significantly larger than that at the blasthole–relief hole distances of three and seven times the hole diameter, and the maximum stress loads at the blasthole–relief hole distances of three and seven times the hole diameter were approximately equal. At the mining depth of 1000 m, the maximum stress load at the blasthole–relief hole distance of five times the hole diameter decreased rapidly with time. At point 1, the maximum stress load at the blasthole–relief hole distance of five times the hole diameter was larger than that at the blasthole–relief hole distances of three and seven times the hole diameter. In contrast, at point 2, the maximum stress at the blasthole–relief hole distance of three times the hole diameter was larger than that at the blasthole–relief hole distances of five and seven times the hole diameter. These results indicate that, under these operating conditions, a blasthole–relief hole distance of five times the hole diameter better disposed the blasting energy to be distributed in the horizontal near field between the blasthole and the relief hole and promoted the fracturing in the horizontal near field but did not effectively direct the fracturing in the far field when compared with a blasthole–relief hole distance of three times the hole diameter. By contrast, a blasthole–relief hole distance of three times the hole diameter led to lower energy dissipation in the near field of blasting and slower attenuation and longer-distance transmission of the blasting stress wave and promoted the fracturing in the far field. At the mining depth of 1500 m, a blasthole–relief hole distance of three times the hole diameter performed much better in terms of the maximum stress load when compared with the other blasthole–empty hole distances.Figure 8
The peak variation curve of stress loading amplitude.
(a)(b)


## 4.1. Analysis of Fracturing

Figure5 shows the blasting outputs at different mining depths and blasthole–relief hole distances. The ratio of the fractured area to the total area of coal mass, n, was calculated by performing image processing using MATLAB. Table 5 shows the corresponding results. Figure 6 shows the explosion crack box dimension fitting curve. Table 6 shows the fractal dimension of each case. The n of 5 times hole spacing increased by 3.49%, 1.05%, and 1.00%, and the fractal dimension increased by 1.89%, 0.29%, and 0.05%, compared with that of no relief hole, 3 times hole spacing, and 7 times hole spacing. When the buried depth is 0 m, the development of 5 times hole spacing crack is better than other conditions. Figure 4(a) shows the blasting outputs at the mining depth of 0 m and different blasthole–relief hole distances. At the mining depth of 0 m, blasting using different blasthole–relief hole distances fractured a large area of the coal mass, confirming the feasibility of blasting to fracture and improve the permeability of soft coal masses using a blasthole and a relief hole drilled into the underlying stratum. A further analysis of the blasting outputs showed that all the blasting configurations produced several fractures at the coal–rock interface and near the roadway. The reason behind the formation of massive fractures at the coal–rock interface has been analyzed in Section 1 and is not elaborated here. The reason behind the formation of massive fractures along the roadway is that the roadway can be considered as an air-filled cavity that produces a free surface effect and promotes fracturing in that direction. Therefore, the supporting structure of the roadway should be reinforced during floor blasting to avoid excessive damage to the roadway due to blasting vibration and affect the stability of the roadway. Figure 4(b) shows the blasting outputs at the mining depth of 1000 m and different blasthole–relief hole distances. The coal mass was significantly less fractured when compared with that at the mining depth of 0 m, indicating that the in situ stress inhibited the blasting-induced fracturing. The n of 3 times hole spacing increased by 8.93%, 4.15%, and 7.68%, and the fractal dimension increased by 19.12%, 4.08%, and 10.95%, compared with that at no relief hole, 5 times hole spacing, and 7 times hole spacing. Figure 4(c) shows the blasting outputs at the mining depth of 1500 m and different blasthole–relief hole distances. At this mining depth, the blasting failed to fracture a large area of the coal mass. The n of 3 times hole spacing increased by 1.92%, 1.32%, and 1.37%, and the fractal dimension increased by 13.59%, 6.78%, and 6.81%, compared with that at no relief hole, 5 times hole spacing, and 7 times hole spacing. The fracturing results showed that the in situ stress inhibited the blasting-induced fracturing in the coal mass. Thus, for the blasting of deeply buried coal masses for permeability improvement, the blasthole–relief hole distance should be reduced to achieve better fracturing.Figure 5
The blasting outputs at different mining depths and blasthole–relief hole distances.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)Table 5
The parameters of fracture area ratio.
Mining depthSingle blast hole3 times hole spacing5 times hole spacing7 times hole spacing0 m10.06%12.50%13.55%12.55%1000 m1.85%10.78%6.63%3.14%1500 m0.47%2.39%1.07%1.02%Figure 6
Explosion crack box dimension fitting curve.
(a)(b)(c)Table 6
The fractal dimension of each case.
Mining depthSingle blast hole3 times hole spacing5 times hole spacing7 times hole spacing0 m1.54921.57401.57851.57771000 m1.30661.55651.49551.40291500 m1.19591.35841.27221.2718


## 4.2. Analysis of Stress Transmission

Temporal variations in the stresses at two points (points 1 and 2, which were located 100 and 300 cm, respectively, above the central line of the coal–rock interface) were measured. Figure7 shows the stress–time curves. For a given mining depth, the maximum stress produced by blasting using a relief hole was larger than that produced by blasting using no relief hole, indicating that the addition of the relief hole decreased the stress wave attenuation rate and increased the range of stress wave propagation. A larger initial in situ stress led to a larger effective stress sustained after blasting, indicating that the magnitude of the initial in situ stress was a major factor affecting the postblasting stress state in the coal mass. Thus, for the blasting of deeply buried coal masses for permeability improvement, the effect of the in situ stress should be fully considered, and the effects of the in situ stress and blasting should be synergized to achieve the optimal blasting output. At the mining depth of 0 m, the maximum effective stress at the blasthole–relief hole distance of five times the hole diameter was larger than that for the blasthole–relief hole distances of three and seven times the hole diameter. At the mining depths of 1000 and 1500 m, the maximum stress at the blasthole–relief hole distance of three times the hole diameter was larger than that at the other blasthole–relief hole distances. The stress–time curves further indicate that, for the blasting of deeply buried coal masses for permeability improvement, the blasthole–relief hole distance should be reduced to achieve better blasting output.Figure 7
The stress–time curves.
(a)(b)(c)(d)(e)(f)


## 4.3. Analysis of Optimal Blasthole–Relief Hole Distance

The maximum loads induced by the blasting stress wave yielded by the series of simulations were analyzed to identify the optimal blasthole–relief hole distance at different mining depths. Figure8 shows the results. As the mining depth increased, the maximum stress loads at both points 1 and 2 decreased, indicating that the in situ stress inhibited the propagation of the blasting stress wave. At the mining depth of 0 m, the maximum stress load at the blasthole–relief hole distance of five times the hole diameter was significantly larger than that at the blasthole–relief hole distances of three and seven times the hole diameter, and the maximum stress loads at the blasthole–relief hole distances of three and seven times the hole diameter were approximately equal. At the mining depth of 1000 m, the maximum stress load at the blasthole–relief hole distance of five times the hole diameter decreased rapidly with time. At point 1, the maximum stress load at the blasthole–relief hole distance of five times the hole diameter was larger than that at the blasthole–relief hole distances of three and seven times the hole diameter. In contrast, at point 2, the maximum stress at the blasthole–relief hole distance of three times the hole diameter was larger than that at the blasthole–relief hole distances of five and seven times the hole diameter. These results indicate that, under these operating conditions, a blasthole–relief hole distance of five times the hole diameter better disposed the blasting energy to be distributed in the horizontal near field between the blasthole and the relief hole and promoted the fracturing in the horizontal near field but did not effectively direct the fracturing in the far field when compared with a blasthole–relief hole distance of three times the hole diameter. By contrast, a blasthole–relief hole distance of three times the hole diameter led to lower energy dissipation in the near field of blasting and slower attenuation and longer-distance transmission of the blasting stress wave and promoted the fracturing in the far field. At the mining depth of 1500 m, a blasthole–relief hole distance of three times the hole diameter performed much better in terms of the maximum stress load when compared with the other blasthole–empty hole distances.Figure 8
The peak variation curve of stress loading amplitude.
(a)(b)


## 5. Conclusion

We draw the following conclusions from this study.Owing to the different wave impedances of coal and rock, the blasting stress wave was reflected from the coal–rock interface and transformed into a tensile wave, which promoted the fracturing on the rock side. The fracturing-induced weakness plane in the rock directed the blasting stress wave to develop in that direction, thereby better fracturing the soft coal mass and realizing the intended permeability improvement effect.A free surface effect was produced near the relief hole during the blasting process, which directed the blasting stress wave to propagate in the direction of the relief hole, thus promoting fracturing in that direction. In deep rock, in suit stress will produce stress concentration at the relief hole. After blasting, cracks will develop along the direction of maximum principal stress.The in situ stress inhibited blasting-induced fracturing in the coal mass. For the blasting of deeply buried coal masses for permeability improvement, the blasthole–relief hole distance should be reduced for better fracturing.The supporting structure of the roadway should be reinforced during underlying stratum blasting to avoid excessive damage to the roadway due to blasting vibration and affect the stability of the roadway.An appropriate blasthole–relief hole distance should be selected for blasting. An inappropriate blasthole–relief hole distance will dispose the blasting energy to be distributed in the horizontal near field between the blasthole and the relief hole and promote fracturing in the horizontal near field but fail to direct fracturing in the far field effectively. An excessively large blasthole–relief hole distance will also fail to direct the stress wave propagation effectively.



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*Source: 7008131-2022-07-22.xml*