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. 2023 Jun 5;8(24):22159–22167. doi: 10.1021/acsomega.3c02453

Prediction of the Penetration Radius of Cumulative Blasting

Jinzhang Jia †,‡, Yumo Wu †,‡,*, Dan Zhao §, Bin Li ∥, Dongming Wang †,‡
PMCID: PMC10286281  PMID: 37360449

Abstract

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To improve the efficiency of coal seam gas extraction, the influence characteristics of different factors on the penetration effect of cumulative blasting were determined and the hole spacing was effectively predicted; in this work, we used ANSYS/LS-DYNA numerical simulation software to establish the penetration model of cumulative blasting. Combined with an orthogonal design scheme, the crack radius prediction of cumulative blasting was studied. A prediction model for predicting the fracture radius of cumulative blasting based on three groups of different factors was established. The results showed that the primary and secondary order of factors that affected the fracture radius of cumulative blasting was as follows: ground stress > gas pressure > coal firmness coefficient. The penetration effect decreased with increasing ground stress and decreased with an increase in the gas pressure and coal firmness coefficient. The industrial field test was carried out. The gas extraction concentration increased by 73.4% after cumulative blasting, and the effective crack radius of cumulative blasting was approximately 5.5–6 m. The maximum error of the numerical simulation was 1.2%, and the maximum error of the industrial field test was 6.22%, which proved that the crack radius prediction model of cumulative blasting was correct.

1. Introduction

Energy security is the cornerstone of national security. In recent years, energy security, coal production safety, clean coal utilization, and sustainable development of mines have become the focus of attention from all walks of life, which is also the key to achieve “carbon neutrality”.1,2 Gas disaster is one of the main factors affecting the safe mining of coal seam,3,4 and it is also an urgent problem to be solved in the research of coal seam development.5 The main methods of gas disaster prevention and control are the mining protective layer pressure relief and increase penetration method,6,7 high-energy liquid disturbance increase penetration method,8,9 the blasting pressure relief and increase penetration method,10,11 and the inert gas increase penetration method.12,13 These methods mainly have issues involving distribution that is not concentrated during the blasting process, which can easily cause energy loss and an uncertain fracture direction, resulting in a small range of fracture zones.14,15 Therefore, many scholars have proposed the increase penetration technology for cumulative blasting. This technology has concentrated energy and can control the direction of cracks, and its increase penetration effect more significant.16

Cumulative blasting is a blasting method designed to release the energy from the explosive explosion in the direction of poly-energy by the poly-energy effect, reducing or eliminating randomly generated cracks in other directions, thus improving the utilization rate of the shell hole, and its characteristics fully meet the requirements of safe coal mining.17 Under the premise of considering the complexity of coal seam structure, Zhao Dan et al.18 used numerical simulation software to simulate and analyze many factors affecting the blasting effect and optimized the gas extraction efficiency. Therefore, researchers in the industry have focused on determining the factors that affect blasting cracking and finding methods to improve prediction accuracy. Jia et al.19 studied the influence of different factors on the phase change cracking effect of liquid CO2 based on the gray correlation analysis method. The results showed that the gas pressure and ground stress directly affected the blasting cracking effect. Soliman20 and EI-Rabaa21 showed that the tensile strength theory could effectively predict the development of cracks. According to Jia et al.,22 the orthogonal design method was used to simulate and analyze the various factors affecting the fracturing radius of liquid CO2 phase change blasting, and the prediction model of blasting fracturing radius was obtained, which effectively predicted the field blasting range. According to the abovementioned analysis, many studies focused on cumulative blasting, but the effect was not found to be sufficiently rational and required improvement. Many factors will affect the cracking effect of cumulative blasting, mainly due to the complex underground geographical environment, and the propagation law of cracks after blasting was found to be relatively complex and less controllable.23 At the same time, there are few data processing contents related to the numerical simulation of cumulative blasting, and it is impossible to express the characteristic law of multi-factor affecting the effect of cumulative blasting. This will require the application of reasonable methods to optimize the structural design of cumulative blasting, enhance the controllability of crack propagation after blasting, and apply a series of mathematical algorithms to couple the factors affecting the cracking effect of cumulative blasting.

In view of this, this paper applies ANSYS/LS-DYNA numerical simulation software to establish the penetration model of cumulative blasting and apply orthogonal design and multiple linear regression analysis to simulate the three main factors affecting the fracturing effect of cumulative blasting, study the effect of multiple factors on cumulative blasting, and establish the prediction model of the fracturing radius of cumulative blasting by multiple factors. The prediction model can be used to increase gas penetration by different blasting methods.

2. Theory and Methods

2.1. Basic Principle of Cumulative Blasting

Cumulative blasting is a type of explosive strong impact and penetration principle produced by the energy-accumulating effect. It can be designed to release the energy of an explosive after an explosion along the energy-accumulating direction, reduce or eliminate cracks randomly generated in other directions, and result in the highest blasting efficiency. The cumulative blasting device is mainly composed of the shell of the blasting device, the cumulative groove, and the cumulative column,24 as shown in Figure 1. After blasting, the energy of the ordinary grain will disperse around, while the action area will be relatively average, equivalent to the size of the end area. This energy will be relatively dispersed, with a small damage effect. After blasting, the energy wave will eject along the vertical direction of the conical hole and gather in the vertical axis direction, forming a high-density, high-pressure, and high-speed energy column, making the blasting wave fully concentrated. Thus, the shaped charge will have significant advantages in directional blasting cracking. The blasting process of cumulative blasting in coal and rock mass can be divided into three stages.

  • (1)

    The shaped jet penetration stage

Figure 1.

Figure 1

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Cumulative blasting device model.

After an explosive undergoes an explosion, the energy will first impact the cumulative groove, and the rapid and violent chemical reaction will produce a high-temperature and high-speed energy-gathering jet that propagates into the coal-rock mass. The symmetrical energy-gathering cover will generate pressure collision and compress the detonation gas to the cumulative direction. The entire energy-gathering jet will completely penetrate the coal-rock mass in a very short amount of time, and the energy will form a penetrating initial crack along the diameter direction, which in turn will guide subsequent crack propagation., The velocity of the cumulative jet can be expressed as follows:25

2.1. 1

where uj is the jet velocity (m/s), u0 is the closing speed (m/s), γ is the closure angle, ω is the half cone angle, and δ is the deformation angle.

  • (2)

    The explosion stress wave action stage

The pressure generated by the explosion shock wave after the explosion will be much larger than the tensile strength of the coal body itself. The detonation wave generated by the explosion will penetrate the coal and rock mass for propagation. After the obstruction of the rock mass in the crushing area, it will gradually decay into a radial stress wave acting on the rock mass, with the radial tension greater than the tensile strength of the coal rock, forming a circumferential crack until it gradually decays into a seismic wave, so that the coal body only vibrates without deformation.26 The penetration velocity of the cumulative jet can be expressed as follows

2.1. 2

where u is the penetration velocity (m/s), ρ1 is the jet density, and ρ2 is the density of the coal rock mass.

  • (3)

    Quasi-static action stage of detonation gas

After the cumulative blasting, the gas wedge effect will be generated in the coal and rock mass, when the gas wedge enters the crack of the coal and rock mass, a quasi-static stress field will form, generating tensile stress at the tip of the original crack, and the crack will further expand outward in the coal body. After the end of the explosion stress wave action stage, the jet energy will be insufficient, the penetration speed will be reduced, the crack propagation energy of coal rock mass will be reduced, and finally, the shaped jet will stop penetration. The penetration speed of the cumulative jet in this process can be expressed as follows

2.1. 3

where L is the penetration depth (m), ρj is the effective jet length (m), and ρt is the effective jet time (s).

In the early stage of cumulative jet penetration, the crushing zone will be generated due to the explosion shock wave, and a fracture development zone will form by the action of the explosion stress wave. Finally, the expansion zone of the fracture will be generated due to the attenuation of the stress wave and the gas wedge of the detonation gas. The fracture zone of coal and rock mass after cumulative blasting is shown in Figure 2.

Figure 2.

Figure 2

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Principle diagram of cumulative blasting cracking.

2.2. Establishment of the Numerical Model

ANSYS/LS-DYNA-2019 software was used to establish the geometric cumulative blasting model. The size of the model was 16 m × 16 m × 0.1 m, and the diameter of the blasting hole was 89 mm. The model was composed of three parts, namely, the explosive, air, and coal rock. Subsequently, the fluid-solid coupling algorithm was adopted, where the explosive and air used the Euler algorithm, the coal rock used the Lagrange algorithm, the unit used the multi-material ALE algorithm, and the continuous medium model used the ALG algorithm.27 The single hole blasting grid was divided into 369,411 units, and the number of nodes was 742,344. A uniform load of 12 MPa was applied at the top of the model, and the horizontal stress was 18 MPa. The boundary conditions were as follows. The surface of the coal rock model was constrained, the two sides of model Z were unidirectional constraints, where the constraints in the Z direction were applied, and the model boundary consisted of the non-reflective interface boundary. The material parameters of coal and rock are shown in Table 1. To show the fracturing effect of cumulative blasting more clearly, *MAT_ADD_EROSION was added to the simulation to control the failure of the coal unit, it would fail and be deleted to represent a broken area. The model is shown in Figure 3.

Table 1. Coal Rock Material Parameters.

density (g·cm–3) elastic modulus (GPa) poisson ratio tensile strength (MPa) compressive strength (MPa) cohesion (MPa)
1.54 1.74 0.3 0.84 2.2 2.5
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Figure 3.

Figure 3

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Cumulative blasting model.

2.3. Orthogonal Design of the Numerical Simulation Scheme

The deformation characteristics and mechanism of the coal body will be affected by the external pressure, and the temperature at the time of tectonic deformation and coalification degree. Therefore, in this study, three groups of factors, namely, the ground stress, gas pressure, and coal firmness coefficient, were selected, which had a significant influence on coal body deformation.28 The three groups of influencing factors under the action of cumulative blasting were separately and comprehensively analyzed by the orthogonal design method to determine the influence of different influencing factors on the fracture radius of cumulative blasting, and the parameter equation for predicting the fracture radius of cumulative blasting was obtained.29

The orthogonal design method is to use the principle of orthogonality and mathematical statistics to select representative experiments from a large number of experimental data to simplify the amount of experiments. The orthogonal table is used to divide the multiple factors of the test at different levels, and the number of tests can be reduced under the premise of obtaining the best test results, so as to obtain the most scientific test data. In this paper, ANSYS/LS-DYNA software is used for numerical simulation, and the range method and variance method are used to analyze the results of orthogonal experiments. Through the difference analysis, the primary and secondary of the influencing factors and the size of the experimental error can be intuitively arranged, so as to confirm each other with the results of the range analysis, make up for the deficiency of the range analysis, and improve the accuracy of the test. Combining the orthogonal design method with the multiple linear regression analysis method can better describe the significance and influence effect of the three groups of factors and obtain the regression relational expression of the test index, which is the prediction model for predicting the cracking radius of concentrated energy blasting. In order to increase the accuracy and scope of application of the empirical equation, three horizontal factors were set in the orthogonal design, including in situ stress, gas pressure, and coal firmness coefficient. In order to increase the accuracy and scope of application of the parameter equation, the range of ground stress was set to 6–10 MPa, the range of gas pressure was set to 0.2–0.4 MPa, and the range of coal firmness coefficient was set to 0.5–0.7. These three factors were brought into the orthogonal design software for three-factor four-level operation. A column of horizontal factors was used for error analysis to obtain the orthogonal design scheme L9 (34), with a total of nine sets of comparison schemes, as shown in Table 2.

Table 2. Orthogonal Table of the Simulation Scheme.

group ground stress (MPa) gas pressure (MPa) coal firmness coefficient blank column
a 6 0.2 0.5 0
b 6 0.3 0.7 0
c 6 0.4 0.8 0
d 8 0.2 0.7 0
e 8 0.3 0.8 0
f 8 0.4 0.5 0
g 10 0.2 0.8 0
h 10 0.3 0.5 0
i 10 0.4 0.7 0
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A certain mine in Jincheng City, Shanxi Province was selected as the industrial experimental site of concentrated energy blasting, and real-time data monitoring was carried out at the project site. The measured data of underground coal mine in the engineering site were as follows: the in situ stress measured by the hole method was 8.2 MPa, the gas pressure measured by the direct method was 0.40 MPa, and the firmness coefficient of coal measured by grouping was 0.61. The measured data of coal sample properties were substituted into the prediction model of crack radius of energy-gathering blasting, which can be used to verify the accuracy of the prediction model.

2.4. Design of the Hole Arrangement Parameters in the Test Blasting Site

To investigate the influence of the cumulative blasting cracking test on the gas pre-drainage effect, the gas drainage duration of the coal seam after the cumulative blasting was calculated and analyzed. The aperture of the fracturing hole was set to 89 mm, and four observation holes were arranged on the left and right sides. The distances between observation holes A1–A4 and fracture holes were 3, 4, 5, and 6 m, respectively, while the distances between observation holes A5–A8 and fracture holes were 3.5, 4.5, 5.5, and 6.5 m, respectively. A9 is a natural drainage hole. The drilling arrangement is shown in Figure 4. To avoid the influence of an explosion shock wave, a natural drainage hole was arranged at 30 m on the right side of the observation hole. After 30 days of gas extraction, the natural gas emissions and the changes in the coal seam permeability coefficient were compared, and we could analyze the effect of gas extraction after cumulative blasting.

Figure 4.

Figure 4

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Field test hole arrangement method.

2.5. Determination Principle of the Effective Fracture Radius

To verify the accuracy of the numerical simulation of cumulative blasting and the rationality of the prediction model, a mine in Jincheng City, Shanxi Province, was selected to conduct the industrial test of cumulative blasting. The desorption gas amount of the coal seam was 5.54 m3/t, and the original gas pressure of the coal seam was 0.40 MPa. In this study, the pressure index method was used to determine the crack radius range after cumulative blasting.30 This method referred to the setting of gas pre-drainage indicators, as shown in Table 3. The parameters obtained from the Langmuir equation and industrial analysis of the coal samples by the gas laboratory were used to calculate the residual gas content of the coal body after extraction technology. The calculations were conducted by using eqs 4–6, with the results indicating that hat WCC = 6.1 m3/t, WCY = 10.08 m3/t, the residual gas pressure of the coal seam was 0.21 MPa, and the gas pressure of the coal seam decreased by 48%

2.5. 4

where WCY is the residual gas volume (m3/t), a, b denote the adsorption constants, PCY is the residual relative gas pressure of the coal seam (MPa), Pa indicates the standard atmospheric pressure (0.101325 MPa), Ad is the coal ash (%), Mad is the coal moisture (%), π denotes the porosity of the coal (%), and λ is the apparent density of the coal (t/m3)

2.5. 5

where Wj is the desorption gas amount of coal (m3/t), and WCC is the residual gas content of coal under standard atmospheric pressure, which could be calculated as follows

2.5. 6

Table 3. Coal Adsorption Constant Analysis.

adsorption constants
 coal quality analysis
 volumetric weight  
a (m3/t) b (Mpa–1) Mad (%) Ad (%) volatile (%) λ (t/m3) porosity (%)
32.668 0.999 0.69 13.28 19.64 1.35 5.41
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3. Results and Discussions

3.1. Numerical Simulation Results Analysis

The damage cloud map of the model at different times was dynamically depicted using LS-PREPOST post-processing software. By concealing the explosives and the air units, the effective stress of the coal materials could be more intuitively understood. The simulated crack radius results of cumulative blasting under the nine orthogonal schemes are shown in Figure 5.

Figure 5.

Figure 5

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Cracking effect diagrams under the coupling of three factors.

The results of the orthogonal design of the numerical simulation of cumulative blasting were calculated, and range analysis was carried out. The calculation results are shown in Table 4.

Table 4. Range Analysis of the Cracking Radius.

horizontal group ground stress (MPa) gas pressure (MPa) coal firmness coefficient blank column
mean point 1 5.900 5.467 5.533 5.533
mean point 2 5.500 5.567 5.567 5.600
mean point 3 5.333 5.700 5.633 5.600
range value 0.567 0.233 0.100 0.067
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According to the fracturing radius range analysis results of cumulative blasting, as shown in Table 4, we observed that the influence degree of the three factors affecting the fracturing effect of the cumulative blasting from high to low was as follows: ground stress > gas pressure > coal firmness coefficient. An intuitive analysis of the mean results presented in the table is shown in Figure 6.

Figure 6.

Figure 6

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Intuitive analysis chart of the influence of various factors on the fracture radius.

By calculating the range and mean value of the numerical simulation results of cumulative blasting, and drawing an intuitive analysis diagram, the influence degree of the different influencing factors on the crack radius of the cumulative blasting could be clearly observed.

  • (1)

    With an increase in the ground stress, the fracture radius of cumulative blasting decreased, mainly due to the influence of ground stress on the closure degree and the permeability of the coal body itself; thus, with an increase in ground stress, the development of cracks after fracture of the coal body was inhibited.

  • (2)

    With an increase in gas pressure, the crack radius of cumulative blasting increased, mainly because the expansion degree of cracks after coal cracking was affected by the gas pressure in coal.

  • (3)

    With an increase in the coal firmness coefficient, the crack radius of cumulative blasting increased. Mainly due to the coal body under the action of blasting stress, the lower the hardness, the easier it was to break into a crushing circle, which was not conducive to the conduction of stress waves and resulted in certain side effects on the development of cracks.

To study the primary and secondary order of the cracking effect of cumulative blasting, the confidence levels were 90, 95, and 99%. Variance analysis of the results of cumulative blasting was carried out, and the solution is shown in Table 5.

Table 5. Variance Analysis of Orthogonal Design.

        F marginal value
 significance
influencing factor square of deviance degree of freedom F-ratio a = 0.1 a = 0.05 a = 0.01 a = 0.1 a = 0.05 a = 0.01
ground stress (MPa) 0.509 3 62.429 5.390 9.280 29.50 * * *
gas pressure (MPa) 0.082 3 17.429 5.390 9.280 29.50 * * *
coal firmness coefficient 0.016 3 6.714 5.390 9.280 29.50 * * *
error 0.01 3              
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Through the analysis of variance of cumulative blasting, we found that by comparing the F ratio of the three influencing factors, which followed the order ground stress > gas pressure > coal firmness coefficient, in situ stress had the greatest influence on the cracking effect of cumulative blasting, followed by the gas pressure and coal firmness coefficient, which was consistent with the range analysis results. When the confidence levels were 90, 95, and 99%, respectively, the significance of the three was higher, and the sum of squared errors was smaller than the sum of squared errors, which proved that the orthogonal test was reasonable.

By analyzing each factor and by visually analyzing the influence of each factor on the fracture radius shown in Figure 6, we found that the influence factors and the simulation results could be described by a linear relationship. The fracture prediction radius of cumulative blasting was y, the ground stress was x1, the gas pressure was x2, and the coal body firmness coefficient was x3. The orthogonal test data were subjected to multiple regression analysis, and the index coefficient results are shown in Table 6. Thus, the prediction model between y and x was obtained, as shown in eq 7, with R2 representing the goodness of fit, and a larger R2 indicating a better fitting effect.

3.1. 7

In Table 6, b0 is the constant of the crack prediction radius equation of cumulative blasting, and b1–b3 is the influence factor coefficient. Therefore, the prediction model of the crack radius of cumulative blasting can be calculated as shown in eq 7, where R2 represents the goodness of fit. The larger the value is, the better the fitting effect is. R2 = 0.982, indicating that the goodness of fit is high. In order to further prove the rationality of the prediction model, a simulation comparison test and error analysis can be carried out.

Table 6. Empirical Equation of Orthogonal Design.

  b0 b1 b2 b3 R2
y 6.155 –0.142 1.167 0.310 0.982
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To verify the rationality of the prediction model for predicting the fracture radius of cumulative blasting, in this work, we substituted the measured data of an underground coal mine in the field of cumulative blasting engineering into the prediction model of the fracture radius of cumulative blasting, where the ground stress was 8.2 MPa, the gas pressure was 0.40 MPa, and coal firmness coefficient was 0.61. The predicted fracture radius of cumulative blasting was 5.65 m, according to the calculation. To verify the rationality of the prediction, the measured data were applied to the numerical simulation for verification, and the damage evolution cloud map of the coal and rock was obtained, as shown in Figure 7.

Figure 7.

Figure 7

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Simulation verification of cumulative blasting.

According to the numerical simulation of single hole verification, we observed that when the original model parameter conditions were unchanged, and the three parameter values, i.e., ground stress of 8.2 MPa, gas pressure of 0.40 MPa, and coal firmness coefficient of 0.61, were changed, the fracture radius of cumulative blasting was 5.58 m, the error was 1.2%, and the error was small, which proved that the empirical equation was reasonable for numerical simulation calculations.

3.2. Analysis of Field Engineering Application Test Results

The investigation of the extraction radius of the cumulative blasting involved installing the gas pressure meter after the sealing mortar was completely solidified after the pressure measurement borehole was sealed. The measurement record time was 30 days, and the measurement results are shown in Figure 8. The measurement results were analyzed by the pressure index method, and the residual gas volume of the coal body after the extraction technology was calculated by the parameters obtained from the industrial analysis of the coal sample by the Langmuir equation and the gas laboratory, so as to calculate the residual gas pressure and the gas pressure drop index of the coal seam.

Figure 8.

Figure 8

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Pressure change diagrams of the observation holes at the measuring points.

After cumulative blasting, the energy first impacted the cumulative groove and produced a squeezing effect on the symmetrical cumulative groove plane, crushing it. The energy formed a penetrating initial crack along the diameter direction, and then, the jet generated by the blasting started to move freely. Finally, under the action of the cumulative effect, the initial crack generated a high-temperature, high-speed cumulative jet, which propagated into the coal and rock mass, generating radial tensile stress. The cumulative jet started to penetrate the coal and rock mass, causing radial cracks in the coal and rock mass. As shown in Figure 8, the gas pressure measured by the observation holes on both sides of the fracturing hole decreased with time, and the farther away from the fracturing hole during the initial stage of extraction, the greater the pressure indication, with an increasing trend during the process, and the pressure indication of the near pressure measurement hole was less than that of the remote hole. Because the observation holes A1 and A5 were close to the broken zone of coal damage after cumulative blasting, the coal body formed large cracks under the action of the cumulative jet, and gas could be quickly transmitted. Because the observation holes A2 and A6 were in the middle of the blasting area, the influence of blasting stress was relatively reduced, and the fracture development effect in this area was better, which was helpful for gas conduction, as the observation holes A3 and A7 were in the crack propagation area, which was the end area affected by cumulative blasting. This area consisted of the energy attenuation area of the blasting stress wave, and the crack propagation degree of the coal body was small, which caused the gas conduction velocity to slow down and the concentration to decrease. As the observation holes A4 and A8 were in the vibration zone after cumulative blasting, the stress wave in this area was attenuated, and it no longer caused damage to the coal body. However, due to the close distance to the blasting influence range, the gas would also be transmitted to the observation hole along the coal body crack. The pressure value of measuring point A3, which was 5 m away from the fracturing hole, was greater than that of measuring points A1 and A2, and the pressure value of measuring point A7, which was 5.5 m away from the fracturing hole, was greater than that of measuring points A4 and A3. When the axial spacing of the fracturing device was 5–5.5 m, the distribution of the fracture network was more uniform, the fracture development was better, and thus, gas extraction was smoother. With the passage of gas extraction time, the gas pressure gradually decreased; the greater the distance between the observation hole and the extraction hole, the more the time that was required to drop to the effective extraction line. When the extraction reached the 30th day, the pressure values of the six measuring points A1, A2, A3, A5, A6, and A7 decreased below the 48% effective line, while the pressure values of the two observation holes A4 and A8 decreased by less than 48%. The results showed that after 30 days of drilling pressure measurement, the effective fracture radius of cumulative blasting was more than 5.5 m but less than 6 m, the maximum error was about 6.22%, and the error was small, which further proved that the prediction model was reasonable.

The gas concentration and gas flow data measured for 30 days at observation hole A3, which was 5.5 m from the fracturing hole, and natural extraction hole A5 was analyzed, as shown in Figure 9a,b.

Figure 9.

Figure 9

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Gas extraction data.

According to the comparison curve of gas extraction concentration between observation hole A3 and natural drainage hole A5 in Figure 9a, the average gas extraction concentration of a single hole after cumulative blasting was 43.84%, while that of the natural drainage hole was 25.28%, and the average gas extraction concentration increased by 73.4%. According to the comparison curve of gas extraction flow between observation hole A3 and natural drainage hole A5 in Figure 9b, the average gas extraction flow of a single hole after cumulative blasting was 8.8%, while the average gas extraction flow of natural drainage hole was 3.13%. The average gas extraction flow of cumulative blasting was 2.81 times that of the natural drainage hole. This showed that cumulative blasting could effectively improve gas extraction and gas extraction flow, with a good effect on gas extraction.

4. Conclusions

  • (1)

    Based on the orthogonal design of the three factors that affected the fracturing effect of cumulative blasting, numerical simulations of cumulative blasting were carried out using ANSYS-LSDYNA numerical simulation software. Through range and variance analyses, the primary and secondary order of factors affecting the fracturing radius of cumulative blasting followed: ground stress > gas pressure > coal firmness coefficient. The fracturing radius decreased with an increase in ground stress, which increased with an increase in gas pressure and coal firmness coefficient, and showed a linear relationship.

  • (2)

    Based on the multiple regression analysis of the numerical simulation results, a prediction model of the fracture radius of cumulative blasting under the coupling conditions of three different factors (ground stress, gas pressure, and coal firmness coefficient) was established. Numerical simulation verification is carried out. The maximum error of the numerical simulations was 1.2%, and the maximum error of the industrial field test was 6.22%. Furthermore, the error was small, which proved that the prediction model of the crack radius of cumulative blasting was correct, and the prediction model could be used to predict the field blasting range, which had a certain reference value for the study of gas-reflection hole distribution.

  • (3)

    The pressure index method was used to test and analyze the effect of gas extraction after cumulative blasting. The results showed that the gas pressure measured by the observation holes on both sides of the cumulative blasting hole decreased with time; the farther the distance from the fracturing hole in the initial stage of extraction, the greater the pressure index, and the more the trend increased. The pressure index of the closest pressure measuring borehole was smaller than that of the farthest borehole, and the main reason was that the attenuation of stress waves after blasting led to different effects of fracture development in different regions. The crack propagation law of on-site cumulative blasting was consistent with the theoretical analysis results. The gas extraction concentration of the observation hole that was 5.5 m away from the cumulative blasting hole was 2.81 times that of the natural drainage hole, and the gas extraction concentration increased by 73.4%. Therefore, cumulative blasting could effectively improve the permeability of the coal seam, with a good effect on gas extraction.

Author Contributions

Conceptualization: Jinzhang Jia, Yumo Wu. Data curation: Jinzhang Jia, Yumo Wu, Bin Li. Formal analysis: Yumo Wu, Bin Li. Funding acquisition: Jinzhang Jia. Investigation: Jinzhang Jia, Yumo Wu, Dan Zhao. Methodology: Jinzhang Jia, Yumo Wu. Software: Yumo Wu, Bin Li, Dan Zhao. Validation: Jinzhang Jia, Dan Zhao, Dongming Wang. Visualization: Yumo Wu, Bin Li. Writing – original draft: Jinzhang Jia, Yumo Wu, Bin Li, Dan Zhao. Writing – review & editing: Yumo Wu., Dan Zhao.

The authors declare no competing financial interest.

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