Study on Mechanical Response and Failure Characteristics of Coal Specimens Under the Coupling Effect of Joints and Drillings

Abstract

To investigate how joint density and drilling diameter impact the failure features of coal specimens, a numerical simulation test was conducted using PFC 2D 5.0 software. The mechanical characteristics, failure characteristics, and energy changes of borehole coal specimens with different joint densities and different drilling diameters were analyzed, and the sensitivity of the two was compared by range analysis. The results show that (1) the increase of joint density significantly reduces the bearing capacity of coal specimens, while the drilling diameter has little effect on the peak stress, but it will significantly change the failure path of coal specimens; (2) Under the condition of low joint density, the specimen is mainly characterized by tensile brittle failure, and the fragments are large. Increasing joint density shifts the specimen’s failure mode towards shear failure and produces smaller fragments; (3) With the increase of drilling diameter, the initiation and propagation of cracks are more likely to occur around the drilling, and the acoustic emission hot spots are more concentrated around the drilling. The increase of joint density leads to more complex crack distribution, and the distribution range of acoustic emission hot spots is expanded and the number is increased; (4) The joint density has a weakening effect on the elastic energy storage of coal specimens, and this weakening effect decreases with the increase of drilling diameter. and drilling affects the way of energy dissipation.

1. Introduction

The stability of coal and rock mass is of great significance to the safe mining of coal resources. Its interior not only contains primary cracks and holes, but also artificial drillings carried out by engineering practice, such as pressure relief holes, gas drainage holes, etc. The existence of drillings makes its structure more complicated [1,2,3]. The interaction between drilling and natural joints and joints formed by mining disturbance seriously affects the mechanical properties of coal and rock mass. Figure 1 graphically illustrates the pressure relief mechanism induced by drilling in jointed coal-rock masses.

At present, numerous studies have been conducted on coal joint and drilling. Some studies are carried out from an experimental aspect. Mu et al. [4] performed experimental investigations on coal specimens subjected to uniaxial compression, examining variations in mechanical properties and acoustic emission signature patterns under distinct loading orientations and joint inclination angles. It was found that the angle between the loading direction and the joint surface had a significant effect on the mechanical behavior and acoustic emission evolution patterns of specimens. Lai et al. [5] conducted uniaxial compression experiments and monitored the failure process and internal damage evolution process of coal specimens during loading. At the same time, the mechanical properties, failure modes, and energy transfer dynamics of coal specimens were also analyzed. By conducting similar material model tests on specimens containing prefabricated joints and fissures, Kulatilake et al. [6] revealed the correlation between the structural characteristics and mechanical response of jointed rock mass. Wu et al. [7] used the equivalent rock mass technology to study the engineering rock mass with random joint distribution and revealed fracture evolution mechanisms of different rock mass models. Han et al. [8] investigated how the joint dip angle affects the mechanical response of jointed rock masses subjected to uniaxial and biaxial compression. Through the uniaxial compression test of the horizontal pre-drilled coal specimen, Zhang et al. [9] examined the fracture patterns of the surrounding rock during staged and regional drilling operations. Wang et al. [10] carried out a uniaxial loading test on prefabricated borehole coal specimens and studied the variation law of dynamic failure susceptibility. Wang et al. [11] conducted uniaxial compression tests on self-made briquettes to explore the effect of drilling on the stability of coal specimens.

In addition, some scholars combine numerical simulation to study. Wang et al. [12] constructed a synthetic coal model based on the structural plane measurement and parameter calibration test, and then carried out uniaxial compression tests at different loading directions through numerical simulation to analyze the influence of the structural plane on the uniaxial compression mechanical behavior of the jointed coal. Cui et al. [13] studied the internal stress distribution and deformation characteristics of roadway surrounding rock with different jointed degrees through UDEC 4.0 and clarified the causes of large-scale rock expansion deformation in jointed soft rock roadway and the reasons for the deformation difference of rock strata at the junction. Jia et al. [14] studied the influence of joint density on the mechanical properties of rock mass by 3D printing experiment and numerical simulation. Through PFC numerical simulation, Fan et al. [15] divided the failure of rock mass with parallel joints into four categories: complete rock mass failure, plane failure, step-by-step failure, and splitting failure. Jia et al. [16] investigated the effects of drilling parameters (diameter, spacing, and depth) on the strength of the specimen via laboratory tests and examined crack propagation morphology and crack number under different parameter conditions by means of PFC. Ma et al. [17] combined numerical simulation with theoretical analysis to study borehole mechanical behavior and fracture evolution under complex conditions, identifying factors influencing failure modes in soft coal seams.

Although extensive research exists on jointed coal-rock masses and drilling in coal from various perspectives, few scholars have studied the coupling effect of joints and drilling. In practical engineering, drilling may become a channel for crack propagation on the joint surface and accelerate rock mass failure. The existence of joints may also limit the range of stress release around the drilling, forming a local stress concentration area. The complexity of this coupling effect makes it impossible to accurately predict the mechanical behavior of rock mass by single-factor analysis. Based on this, the numerical simulation of coal specimens with drilling and joints is carried out in this paper. The research results can provide theoretical and data support for deep coal mining.

2. Numerical Modelling

2.1. Numerical Simulation Test Model Establishment

Coal is a non-continuous medium material, and the PFC (particle flow code) can effectively deal with such problems [18]. The basic unit is rigid spherical particles (balls) with different particle sizes, which form contact and interact through bonding. When the simulation test is carried out, the speed condition is applied to the set rigid boundary wall to realize the force displacement mode loading. During the loading process, the displacement of the spherical particles is calculated by Newton’s law of motion, and the particles follow the force−displacement motion equation during the movement [19,20]. Figure 2 illustrates the PFC linear and PB bonding models, while Figure 3 depicts their tangential and normal mechanical responses.

When the contact stress reaches the threshold of the bond strength, the contact failure produces micro-cracks, so the failure mechanism of the specimen can be analyzed from the microscopic level.

Based on laboratory coal specimen dimensions, the established uniaxial compression numerical model measures 100 mm in height and 50 mm in width. Key particle parameters include R_min = 0.33 mm, R_max/R_min = 1.5, density = 2.0 kg/m³, and damping coefficient = 0.7. The final generated model has a total of 8107 particles and 20,386 contacts.

In view of the fact that the joints with angles of 135° and 45° have the most significant influence on the project in the actual working conditions, and the effects of the two are similar, this paper selects the joints with an angle of 135° as the research object and only changes the joint density and the drilling diameter of the specimens for research. In the generated model, randomly distributed parallel joints are added by giving it a smooth joint model [21]. Figure 4 illustrates models with varying joint densities and drilling diameters.

It can be seen from Figure 4 that the joint densities are 0, 20, 40, 60, 80, and 100 m/m², and the drilling diameters are 0, 4, and 8 mm, respectively. A total of 18 models with different variables are selected. The parallel bond (PB) model simulates the intact coal, while the smooth joint (SJ) model represents the embedded joints.

2.2. Parameter Calibration

Calibrating the microscopic parameters of the initial numerical model is essential to match the macroscopic mechanical properties of real coal specimens. At present, the most commonly used method is the “trial and error method”, which calibrates the microscopic parameters that have a great influence on macroscopic mechanics, that is, repeated debugging [22], until the stress-strain curves of numerical simulation and laboratory test tend to be consistent. The ultimately calibrated micro-mechanical parameters are presented in

Table 1. Microscopic mechanical parameters of numerical simulation.

Group	Microscopic Mechanical Parameters	Symbol and Units	Value
Linear bond group	Effective modulus	GPa	0.1
	Normal to shear stiffness ratio	1	1.5
	coefficient of friction	1	0.5
Parallel bond group	Effective modulus	GPa	1.25
	Normal to shear stiffness ratio	1	1.5
	Friction coefficient	1	0.5
	Tensile strength	MPa	13.97
	Binding strength	MPa	13.5
Smooth-joint group	Normal stiffness	GPa	0.27
	Tangential stiffness	GPa	0.14
	Friction coefficient	1	0.5
	Binding strength	MPa	0.0

. The comparison between numerical simulation test and laboratory test results is shown in Figure 5, and the comparison between test and simulated specimen failure modes is shown in Figure 6.

As shown in Figure 5 and Figure 6, the numerical simulation results are closely consistent with the laboratory test results. Compared with the laboratory test, the relative errors of peak stress and peak strain are 2.71% and 1.14%, respectively, and the relative error of elastic modulus is 5.35%. The observed damage pattern largely aligns with the outcomes of laboratory tests. However, due to the uniform distribution of particles in PFC, there is no compaction stage, leading to some discrepancies between the stress-strain curve and the experimental findings.

3. Analysis of Simulation Results

3.1. Mechanical Characteristics Analysis

3.1.1. Characteristics of Stress-Strain Curve

Compared with the intact specimens, the specimens with drillings and joints have great differences in stress-strain curve characteristics, failure modes, and crack evolution, as shown in Figure 7.

It can be seen from Figure 7 that the whole loading process can be divided into three stages according to the characteristics of the stress-strain curve and crack number curve, namely the elastic stage (OA stage), plastic stage (AC stage), and failure stage (CD stage). During initial loading, the specimen exhibits linear elastic behavior with no crack development. When loaded to point A, cracks began to appear in the specimen. With the continuous increase of axial strain, the number of cracks increased slowly, resulting in intermittent failure of the specimen [23]. Both the stress-strain curve and the crack curve fluctuated slightly, as shown in point B in the figure. Continue to load to point C, the number of cracks increases faster, and the specimen gradually failed. When it reaches point C, the specimen fails, the bearing capacity of the specimen begins to decrease, and cracks propagate rapidly, leading to ultimate specimen failure.

Compared with intact specimens, the peak stress and peak strain of the joint specimen with drillings are significantly reduced, and the brittleness is weakened. Drilling and joint conditions alter both crack initiation points and propagation paths. The crack initiates at the joint and propagates to both sides of the joint. The first occurrence of intermittent damage was ahead of time, and the number of pre-peak intermittent damage increased. After point C, the crack growth rate and stress drop rate both slow down.

3.1.2. Peak Stress and Elastic Modulus

The joint specimens containing different drillings are loaded, and the obtained peak stress is shown in Figure 8, and the elastic modulus is shown in Figure 9.

As evident in Figure 8, when the joint density within the specimen rises, the peak stress of the three different aperture specimens shows a downward trend, and the decline rate decelerates progressively as joint density increases; the joint density increases from 0 m/m² to 60 m/m², the peak stress of the three aperture specimens decreased from 26.88 MPa, 23.87 MPa, and 22.82 MPa to 5.64 MPa, 5.88 MPa, and 5.50 MPa, respectively, with a decrease of 79.02%, 75.37%, and 75.90%, respectively. The joint density increased from 60 m/m² to 100 m/m², and the peak stress reached 4.00 MPa, 3.75 MPa, and 4.01 MPa, respectively. In addition, as joint density increases, the disparity in peak stress between specimens with different apertures diminishes.

As illustrated in Figure 9, the elastic modulus of the specimens is less affected by the drilling diameter, but exhibits a significant dependence on joints, undergoing a linear reduction as the joint density rises. As joint density progressively increases from an initial state of 0 m/m² to 100 m/m², the elastic modulus of the specimen without drilling decreases from 1.59 GPa to 0.73 GPa, with a decrease of 54.09%. The elastic modulus of the specimen with 4 mm drilling decreased from 1.56 GPa to 0.71 GPa, with a decrease of 55.35%. The elastic modulus of the specimen with 8 mm drilling decreased from 1.54 GPa to 0.70 GPa, with a decrease of 54.55%.

3.2. Analysis of Failure Characteristics

3.2.1. Fragmentation Size

To systematically elucidate the dual effects of joint density and drilling diameter on specimen failure mechanisms, the fracture state of each specimen is derived, as shown in Figure 10.

From Figure 10 and the previous analysis, it can be seen that when the joint density is low, the specimen structure is relatively complete, and the stress distribution is more uniform when loaded. The failure mode is mainly tensile failure, which is caused by local tensile stress concentration. The fragments produced during the failure are large, and the whole presents brittle failure. The rapid expansion of the crack causes the rapid release of energy. As joint density escalates, the continuity of the specimen decreases significantly, and a large number of potential slip surfaces are formed inside the specimen. The stress transfer and crack propagation are affected by the joint. The stress tends to transfer along the joint surface, and the energy dissipation mechanism changes accordingly. The energy is released mainly through the friction slip of the joint surface, which makes the specimen show the failure characteristics of progressive shear slip, and the fragments produced during the failure are smaller.

In the non-drilling specimen, the failure first occurs in the area with large joint density, which extends to both ends of the specimen. For the specimen with a drilling diameter of 4 mm, when the joint density is small (20 m/m²), the failure of the specimen begins at the position where the joint density of the specimen is large, and then gradually expands to the drilling and the upper end of the specimen, and the existence of the drilling changes the failure path of the specimen. When the joint density is greater than 20 m/m², the specimen is also damaged at the drilling position. With the further increase of the joint density, the local destructiveness of the specimen is enhanced, and the damage gradually concentrates on the drilling. Compared with the specimen with a 4 mm aperture, the specimen with a drilling diameter of 8 mm has a more obvious concentration of damage to the drilling and a more obvious change in the crack propagation path. Compared with the specimen without drilling, the specimen with drilling produces smaller fragments when it fails. The specimen with a drilling of 8 mm has a smaller fragment size than the specimen with a drilling of 4 mm.

3.2.2. Hot Spot Analysis of Acoustic Emission

The acoustic emission hot spot diagram can reflect the distribution characteristics of elastic energy released by activities such as crack generation and expansion in the specimen during the loading process. The hot spot area is the location of a high incidence of acoustic emission events and strong energy release, which can intuitively show the active area of damage evolution inside the specimen. Figure 11 is the acoustic emission hot spot diagram of the specimen when loaded to the peak stress, so as to further reveal the failure characteristics of the specimen.

According to the acoustic emission hot spot diagram shown in Figure 11, it can be seen that when the joint density of the specimen changes, the crack distribution and propagation mode of the specimen also change. For non-drilling specimens, when the joint density is low, the number of acoustic emission hot spots is small, and the hot spot distribution and crack distribution are relatively concentrated, and the crack propagation path is relatively simple; as joint density rises, the distribution of cracks becomes complicated, the phenomenon of coalescing fractures becomes obvious, the number of hot spots increases, and the distribution range expands. This demonstrates that the joint has a guiding and disturbing effect on the crack propagation, which makes the energy release more dispersed and frequent during the crack propagation process.

Compared with the specimen without drilling, the specimen with a drilling diameter of 4 mm, the crack and the distribution of acoustic emission hot spots are both affected by the dual effects of drilling and joints; drilling will lead to local stress concentration and guide the initiation and propagation of cracks; the increase of joint density makes the crack propagation more complicated, and the combination of the two makes the crack propagation path more tortuous; the existence of drilling makes the hot spots more concentrated around the drilling. With the increase of joint density, the distribution range of hot spots is wider and the number is also increased, which also reflects the dynamic change of energy release during crack propagation.

When the aperture increases to 8 mm, the influence of the drilling on the crack propagation is more significant, and the crack is easier to initiate and propagate around the drilling. With the increase in joint density, the distribution of cracks is more complex, and the interaction between drillings and joints may lead to more branching and interweaving of crack propagation. The distribution of acoustic emission hot spots shows the influence of large drillings on energy release. The hot spots may be more concentrated around the drilling and in the joint-intensive areas, indicating that these areas are the main areas for crack propagation and energy release. With the change of joint density, the distribution and strength of hot spots will change accordingly.

Therefore, the increase in the aperture makes the effect of the drilling on crack propagation and acoustic emission more obvious. When the drilling diameter is larger, the initiation and propagation of cracks are more likely to occur around the drilling, and the acoustic emission hot spots are more concentrated around the drilling. The increase in joint density leads to a more complex crack distribution, and the distribution range and number of acoustic emission hot spots increase, reflecting the increase and dispersion of energy release during crack propagation. When the drilling and joints work together, the crack propagation path and acoustic emission characteristics are comprehensively affected by the two, and the interaction may lead to new modes and energy release characteristics of crack propagation.

3.2.3. Specimen Damage Analysis

The radial strain is used to characterize the damage variable during the loading process of the specimen. The change of the damage variable during the loading process of each specimen is shown in Figure 12.

$$D={\displaystyle \frac{{\epsilon }_h}{{\epsilon }_t}}$$

(1)

In the formula, D denotes the damage variable, ε_h represents the specimen’s radial strain under loading, and ε_t is the radial strain when the specimen is completely failed.

Figure 12 shows that as joint density increases, the damage curve gradually flattens out and the damage starting point advances. When the joint density increases from 0 m/m² to 100 m/m², the initial damage strain of the specimen with a drilling diameter of 0 mm decreases from 1.77% to 0.52%. The initial damage strain of the specimen with a drilling diameter of 4 mm is reduced from 1.53% to 0.42%. The initial damage strain of the specimen with a drilling diameter of 8 mm decreased from 1.48% to 0.34%. With the increase in the diameter of the borehole, the initial strain of the damage gradually advances. The damage curve gradually becomes gentle and smooth, and the step characteristics are weakened. This is mainly because the increase in joint density creates more weak surfaces or defects inside the specimen. In the process of stress, these joints will disperse stress, which makes the stress concentration phenomenon relatively weakened. Therefore, the development of damage is no longer as sharp as when the joint density is low, but relatively smooth, resulting in a gradual flattening of the damage curve. Because the existence of joints reduces the overall strength of the specimen, the specimen begins to exhibit the initiation and propagation of micro-cracks at a lower strain level, that is, the damage initiation. With the increase in joint density, this effect is more obvious, so that the damage initiation point will be advanced.

An increase in drilling diameter modifies the local stress state within the specimen. There will be a large stress concentration area around the large-aperture drilling. When the force is applied, deformation and damage are more likely to occur near the drilling. As the aperture increases, the influence range of this local stress concentration expands, making the development of damage more continuous and stable, so that the damage curve becomes gentle, and the original step characteristics are weakened. The large-aperture drilling makes the specimen begin to show obvious damage at a lower strain level. This is because the stress concentration effect around the drilling makes the specimen reach the critical state of damage under a small strain, which in turn triggers the initiation and propagation of micro-cracks, so the initial strain of damage gradually advances.

Increasing joint density and drilling diameter significantly influences the specimen’s damage evolution, and there is an interaction between the two. In the mining work, the existence of joints and drilling will change the stress distribution and damage evolution law of the surrounding rock, and corresponding support and reinforcement measures need to be taken to deal with it.

3.3. Energy Evolution

3.3.1. Analysis of Elastic Energy at Peak Value

The elastic energy at the specimen’s peak stress represents the energy absorbed and stored before loading to the bearing limit during the uniaxial loading process. By analyzing it, the absorption and release ability of coal energy during the mining process can be further understood, which provides an important basis for the evaluation of the mechanical stability of coal. The elastic energy stored when each specimen reaches the peak stress is analyzed, as shown in Figure 13.

From Figure 13, it can be seen that when the specimen is loaded to the peak stress, the elastic energy stored inside the specimen is affected by both the drilling diameter and the joint density. As the joint density increases, the interference effect of the drilling diameter on the elastic energy of the specimen is weakened. With the increase of joint density from 0 to 60 m/m², the storage of elastic energy of three kinds of aperture specimens showed significant changes: the specimen with a drilling diameter of 0 mm was reduced from 1.26 KJ to 0.17 KJ, which was reduced by 1.09 KJ; the specimen with a drilling diameter of 0 mm is reduced from 0.97 KJ to 0.14 KJ, a decrease of 0.83 KJ; the specimen with a drilling diameter of 0 mm was reduced from 0.88 KJ to 0.10 KJ, a decrease of 0.78 KJ, and the decrease was relatively small. The above results show that the increase of drilling diameter can inhibit the weakening effect of joint density on the elastic energy storage of the specimen to a certain extent.

When the joint density continues to increase and exceeds 60 m/m², the influence of joint density and drilling diameter on the energy storage capacity of the drilling becomes extremely weak. This shows that when the joint development degree is high, the energy storage characteristics of the specimen tend to be stable, and the interference effect of joint density and drilling diameter on it is no longer significant.

3.3.2. Dissipative Energy Analysis

Dissipative energy refers to the energy consumed by irreversible deformation, such as crack initiation and propagation, friction slip between particles and joint surfaces during loading. By analyzing the energy dissipation characteristics during the loading process, the failure characteristics and damage evolution of the specimen can be further analyzed. Figure 14 shows the energy dissipation of specimens with different drilling diameters and different joint densities under loading. Figure 15 shows the energy dissipation when the specimens are completely failed.

As shown in Figure 14 and combined with the failure characteristics of the specimen in Figure 10, after the peak stress of the jointless specimen is reached, the crack quickly penetrates the specimen, and the elastic energy stored in the specimen is quickly released, and the energy is rapidly dissipated, so that the specimen loses its bearing capacity instantly and brittle failure occurs. As the joint density rises, the failure path and direction of the specimen have changed significantly, and the failure process has become more complex and diverse. The failure mode has gradually changed from tensile failure to shear failure, and the way of energy dissipation has also changed. In addition to the energy used to generate cracks, it is also necessary to consume energy to overcome the mutual friction between joint surfaces. With the increase in joint density, the dissipation energy gradually shows a step-by-step growth, and the number of steps is also increasing, but the growth rate of dissipation energy slows down. This indicates that as the quantity of joints rises, there is a corresponding increase in the number of vulnerable spots within the specimen. Moreover, the failure process of the joint surface is a stepped slip, and the slip process is not continuous.

Combined with Figure 15, it can be seen that the influence of drilling on the dissipation energy of different types of specimens is different. For the jointless specimen, the effect of drilling is more significant, which can reduce the dissipation energy (In the jointless specimen, the dissipation energy is 752.78 J when the specimen is completely failed; the dissipation energy of the specimen with 4 mm aperture drilling is 564.97 J, which is 187.81 J lower than that of the specimen without drilling. The dissipation energy of the specimen with 8 mm drilling is 549.91 J, which is 202.87 J lower than that of the specimen without drilling, and it can slow down the release rate of dissipation energy. For the jointed specimen, the drilling has little effect on the magnitude of the dissipated energy, mainly affecting the energy release process, which can make the energy release of the jointed specimen more uniform during the loading process. The specific performance is as follows: the drilling increases the number of steps of energy dissipation and reduces the energy gradient of a single step. As the joint density rises, the dissipation energy of the three types of aperture specimens exhibits a decreasing tendency.

4. Discussion

4.1. Effect on the Spacing of Pressure Relief Holes

Combined with the Method for Determining the Physical and Mechanical Properties of Coal and Rock [24], the influence of joint density and drilling diameter on the K value in the calculation of pressure relief hole spacing is analyzed, as follows:

$$L=kd\sqrt{1+{\displaystyle \frac{1}{N}}}$$

(2)

$$N={\displaystyle \frac{\lambda }{E}}$$

(3)

In the formula, N is the deformation modulus index, zero dimension; E and λ are the pre-peak elastic modulus and post-peak softening modulus of the specimen, respectively, and the unit is MPa; k is the risk correction coefficient of pressure relief drilling spacing; d is the diameter of the drill bit for pressure relief drilling, and the unit is m; L is the spacing of pressure relief drillings, and the unit is m. By analyzing the influence of joint density and drilling diameter on N, the influence of the two on the spacing L can be obtained. The N values of joint specimens with different drillings are shown in Figure 16.

Figure 16 shows N values decreasing with increasing joint density in specimens of different apertures: when the joint density increases from 0 to 100 m/m², N values for specimens with apertures of 0, 4, and 8 mm fall from 18.50, 13.20 and 6.36 to 0.54, 0.90 and 0.32, respectively, which decrease by 17.96, 12.3 and 6.04, respectively. The steepest drop in N value occurs between 0 and 20 m/m² joint density, followed by a slower decline up to 100 m/m². When the joint density is not more than 40 m/m², the N value gradually decreases with the increase of drilling diameter.

4.2. Sensitivity Analysis

The range analysis method is used to calculate the strength of the specimen obtained by the numerical simulation test, and the sensitivity analysis is carried out by setting the two factors of drilling diameter and joint density. The range analysis method needs to calculate the range of the two factors first. By comparing the range R, the influence degree of the two factors on the test index is judged [25]. The larger the range value is, the more sensitive the factor is.

$$R=\max \{K_{avg}\}-\min \{K_{avg}\}=\max \{{\displaystyle \frac{{\displaystyle {\sum }_{k=1}^n{Y}_{ijk}}}{n}}\}-\min \{{\displaystyle \frac{{\displaystyle {\sum }_{k=1}^n{Y}_{ijk}}}{n}}\}$$

(4)

In the formula, K_avg represents the average value of the test data Y at each level of each factor; n denotes the number of tests; Y_ijk represents the outcome index from the k-th test at factor j’s i-th level.

Table 2. Specimen strength and range values of two influencing factors.

	Levels	Drilling Diameter	Joint Density
K	0	64.71 MPa	73.57 MPa
	4	60.27 MPa	-
	8	58.37 MPa	-
	20	-	41.01 MPa
	40	-	26.17 MPa
	60	-	17.02 MPa
	80	-	13.82 MPa
	100	-	11.76 MPa
Kavg	0	10.79 MPa	24.52 MPa
	4	10.04 MPa	-
	8	9.73 MPa	-
	20	-	13.67 MPa
	40	-	8.72 MPa
	60	-	5.67 MPa
	80	-	4.61 MPa
	100	-	3.92 MPa
Best level		8 mm	100 m/m2
Number of levels		3	6
R		10.57 MPa	20.60 MPa

Note: “-“ means that there are no data at this level; K is the sum of Y-values for each factor level; the optimal level represents the corresponding level when the K_avg value is the largest for each factor; levels refer to the distinct settings per factor.

presents the range analysis results.

According to Table 2, the average strength distribution map of the specimen under different drilling diameters and different joint densities is obtained, as shown in Figure 17.

Combined with Table 2 and Figure 17, joint density has a greater effect on specimen peak stress.

4.3. Coal Strength Weakening and Engineering Risk Early Warning

In view of the fact that the joint (fracture) network has a significant weakening effect on the macroscopic mechanical properties of coal, and directly determines its overall strength and stability. The coupling effect of joints (natural fissures) and drillings (artificial disturbances) will form a significant synergistic effect. This effect leads to a significant weakening of the strength of the coal around the borehole, which is very prone to failure near the borehole wall or the coal wall. This is the key cause of engineering instability problems such as coal wall spalling and borehole collapse.

When designing the roadway support structure or formulating the drilling construction scheme, it is necessary to quantitatively evaluate and scientifically investigate the effects that affect mechanical coefficients such as the macroscopic compressive strength of coal according to the key joint parameters (such as dip angle, density, connectivity and filling characteristics, etc.) obtained by the on-site refined geological survey, and determine the reasonable strength reduction coefficient accordingly, so as to ensure that the support parameters or construction technology match the actual bearing capacity of the surrounding rock. To avoid overestimating the actual bearing capacity of the jointed coal body, resulting in insufficient support or borehole instability, so as to ensure the safety and reliability of engineering design and construction.

5. Conclusions

In this paper, PFC 2D numerical software is used to systematically investigate the effects of drilling diameter and joint density on compressive strength, elastic modulus, failure characteristics, deformation progression, and energy evolution of coal specimens, and compared with the indoor test results. The following conclusions are drawn:

• According to the characteristics of the stress-strain curve and crack number curve, the loading process progression evolves through three distinct phases: elasticity, plasticity, and failure. Compared with the intact specimen, the peak stress and strain of the specimen with drilling joints are significantly reduced, the brittleness is weakened, the crack initiation position and crack propagation path are changed, the intermittent failure is advanced, and the number of times is increased, and the post-peak crack growth and stress drop rate are slowed down. As the joint density increases, peak stress exhibits progressive attenuation in specimens with enlarged borehole diameters, and the decrease gradually slows down, and the difference in peak stress of the specimens with different drilling gradually decreases. The elastic modulus of the specimen is less affected by the drilling diameter, and is greatly affected by the joint density, and decreases linearly with the increase in the joint density.
• When the joint density is low, the specimen structure is complete, the stress distribution is uniform, the failure is mainly tensile failure, and the fragments are large and brittle. With the increase in joint density, the continuity of the specimen decreases, forming a potential slip surface, and the stress is transmitted along the joint surface. In addition to generating cracks to consume energy, it can also release energy through friction slip. The failure is progressive shear slip, and the fragments are small. The failure of the specimen with a 0 mm drilling diameter begins in the area with a large joint density. 4 mm aperture specimen, the initial position of failure is similar when the joint density is small, and it expands to the drilling and the upper end. When the density is greater than 20 m/m², the failure occurs during the drilling, and the local destructiveness is enhanced. The failure of the 8 mm aperture specimen is more obvious during the drilling. The change of joint density, crack distribution, and propagation mode has an effect on the distribution of acoustic emission hot spots. The interaction of holes and joints affects crack propagation and energy release. The increase in joint density and drilling diameter makes the damage curve gentle, and the damage starting point advances.
• When the specimen is loaded to the peak stress, the elastic energy is affected by the drilling diameter and the joint density. The joint density increases, and the aperture interference effect is weakened. When the joint density increases from 0 to 60 m/m², the elastic energy storage of the three kinds of aperture specimens decreases significantly, and the increase of aperture can inhibit the weakening of elastic energy storage by joint density to a certain extent. When the joint density exceeds 60 m/m², the energy storage characteristics tend to be stable. When the jointless specimen fails, the elastic energy is released rapidly, and brittle failure occurs. With the increase of joint density, the failure path and form change, and the dissipated energy increases step by step, and the speed slows down. The drilling has a significant effect on the dissipated energy of the jointless specimen. For the jointed specimen, it mainly affects the energy release process and makes the energy release more uniform. As the joint density increases, the dissipated energy decreases when the three aperture specimens fail.