Numerical Investigation of Influences of Drilling Arrangements on the Mechanical Behavior and Energy Evolution of Coal Models

State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China College of Mining and Safety Engineering, Shandong University of Science and Technology, Qingdao 266590, China National Demonstration Center for Experimental Mining Engineering Education, Shandong University of Science and Technology, Qingdao 266590, China


Introduction
With the worldwide economic and social development, the shallow mineral resources are gradually depleted, and the depth of mining or tunnelling is deeper and deeper [1][2][3][4].Rock burst has become one of the serious dynamic disasters in deep exploitation [5][6][7][8][9][10].According to the statistics, there were more than 140 coal mines threatened by rock bursts in China [11].Fortunately, scholars have achieved a series of significant achievements related to rock bursts in mechanisms, monitoring, and warning techniques, and preventing and controlling techniques [12,13].Despite decades of researches, some aspects still need to be improved, and its control remains a critical research point.
e commonly used mitigation methods include destress blasting performed in coal seams and compete rock layers, water infusion of coal seam, and destress drilling [14,15].Among these methods, the destress drilling method also has become popular due to its convenient construction in China [11,16], and scholars have done lots of work related to destress drilling.Regarding the experimental and numerical researches, Liu et al. [11] studied the relief mechanism of destress drilling for rock burst prevention through laboratory tests and proposed a method for determining the drilling parameters; Jia et al. [17] researched the destress mechanism of largediameter drilling by laboratory and numerical studies; and Liu et al. [18], Li et al. [19], and Yi et al. [20] numerically researched the diameter, space, and length of the drilling hole on the destress effect.Regarding the theoretical and field researches, Zhu et al. [16] proposed an energy dissipation index method for determining drilling parameters, and Song et al. [21] and Ma et al. [22] researched the collaborative control of destress drilling and roadway support.
Above researches mainly focus on the destress mechanism and on the destress effect by comparing parameters, but the drilling arrangement also has an essential influence on the destress effect of the drilling method.However, there are few literatures trying to reveal the influences of drilling arrangements on the destress effect of the drilling method systematically.erefore, this paper first introduced the rock burst mitigation mechanism of destress drilling performed in coal seams.en, we numerically investigated the influences of various drilling arrangements, including the drilling diameter, the number of drilling holes in one row, and the number of drilling rows, on the mechanical properties of coal models.Based on the test results, the energy evolution influenced by various drilling arrangements and their influencing mechanisms on the destress effect of the drilling method were analyzed and discussed.is study can provide a basic reference for understanding the influences of drilling arrangements on the destress effect of drilling method.

Rock Burst Mitigation Mechanism of Destress Drilling Method
As one of the widely used methods for mitigating rock bursts in China, the destress drilling method is that drilling boreholes with large-diameters in the stress or possible stress concentration areas in coal seams.When drilling boreholes in the stress concentration area, X-shape areas of plastic deformation will form around these holes [23].If the density of drilling boreholes is high enough, these plastic areas will be connected each other and thus a larger destressed area will form, leading to the transfer of high stress concentration area into the deep coal wall, as shown in Figure 1.Generally speaking, the destress drilling method mainly functions through stopping the formation or mitigating the stress concentration of high stress concentration areas [11].When it is used for premitigating stress concentration, its prevention mechanism of rock bursts is changing the mechanical parameters of coal/rock and decreasing its ability of strain energy accumulation; when it is used for preventing rock bursts, its prevention mechanism is dissipating the accumulated strain energy and increasing the resistant force.for simulating granular materials and compact materials, respectively.ere are two advantages for the PBM: first, parallel bonds can transmit both forces and moments between particles; second, bond breakage can lead to immediate decrease in macrostiffness.us, the PBM can be more realistic for simulating rock materials because the bonds can break in either tension or shearing as the stiffness reduces [24].In this paper, we chose the PBM to carry out the numerical simulation.

Numerical Specimens with Various Drilling Arrangements and Simulation
Procedure.e height and width of numerical specimen were 100 mm and 50 mm, respectively [25].e numerical specimen was discretized into 11,693 particles.e particle size followed a uniform distribution varying from 0.3 to 0.4 mm. e density was about 1600 kg/m 3 .After generating the specimen, we established coal models with various drilling arrangements by deleting ball particles.e drilling arrangement mainly includes three parameters, that is, drilling diameter, number of drilling holes in one row, and number of drilling rows.Since this paper mainly researches the influences of drilling arrangements on the destress effect in detail, three kinds of test schemes were designed; that is, scheme I considering the influence of drilling diameter, scheme II considering the influence of the number of drilling holes in one row, and scheme III considering the influence of the number of drilling rows, as shown in Figure 2. In scheme I, the numbers of drilling holes and drilling rows are all set to 1 while the drilling diameter varied from 3 to 10 mm, as shown in Figure 2(a); in scheme II, the number of drilling rows and the drilling diameter are set to 1 and 3 mm, respectively, while the number of drilling holes in one row varied from 1 to 4, as shown in Figure 2(b); in scheme III, the number of drilling holes and the drilling diameter are set to 3 and 3 mm, respectively, while the number of drilling rows varied from 1 to 4, as shown in Figure 2(c).Detailed description of test schemes is listed in Table 1.Advances in Civil Engineering An external displacement was applied on the top of the specimen in the axial direction.e loading rate must be low for ensuring that the specimen remained in a quasistatic state throughout the simulation process.Zhang and Wong [26] researched the in uence of loading rate on the mechanical behavior of specimens containing pre ssures, which showed that the crack initiation stress, and uniaxial compressive strength remained steady when the loading rate increased from 0.005 m/s to 0.08 m/s.erefore, the loading rate of 0.05 m/s was chosen in this numerical simulation, and the loading was applied until the failure occurred.

Con rmation for Microparameters of Rock-Like Material
3.2.1.Con rming Method for Microparameters.Determining the microparameters for numerical simulation is di cult by experiment, but it is essential to establish a correlation between the macrobehavior and microparameters for validating the particle properties used in numerical specimens.
e macrobehavior includes the stress-strain curve, peak stress, elastic modulus, and failure mode [27][28][29].e trial and error method was used in con rming the microparameters.e macrobehavior of coal material obtained by experiment was used to calibrate the microparameters.After each trial, the macroscopic results obtained by the numerical simulation were used to compare with the experimental results.is process was repeated until the numerical results were similar to the experimental results.
e microparameters used in the PFC2D model are listed in Table 2. e elastic modulus of the particle is 0.45 GPa. e ratio of normal to shear sti ness of the particle and the parallel bond is 2.5.e particle friction is 0.5.e values of parallelbond normal strength (σ n ) and parallel-bond shear strength (τ n ) are 10.5 MPa and 8.75 MPa, respectively.

Calibration of Microparameters by Experimental
Results.
e comparison between experimental and numerical stress-strain curves under uniaxial compression is shown in Figure 3.It can be seen that both the numerical curve and the experimental curve include elastic deformation stage, crack initiation and growth stages, and unstable failure stage.However, the experiment specimen also has the stage of compaction and nonlinear deformation at low stress levels, which are not observed in the numerical specimen.
is is because the experimental specimen contains primary cracks, pores, and voids.
e comparison of mechanical parameters between the experimental results and the numerical results is listed in Table 3.In Table 3, σ c is de ned as the uniaxial compressive strength, and E refers to the slope of the linear part of the stress-strain curve.In accordance with Table 3, it shows clearly that the simulated peak stress and elastic modulus are almost equal to those obtained by the experiment.
e comparison between the experimental and numerical failure modes is depicted in Figure 4. Figure 4 illustrates that the failure mode of rock-like specimen is axial splitting under numerical simulation, which is similar to that obtained by experiment.e comparisons shown in Figures 3 and 4 calibrate the rightness and reasonability of microparameters used in Table 2.

Overall Stress-Strain Curves.
Stress-strain curves of specimens with di erent drilling arrangements under uniaxial compression are shown in Figure 5.In accordance with Figure 5, we can conclude that the compression strength of specimens decreases gradually as increasing the drilling diameters, the number of drilling holes in one row, or the number of drilling rows, which will be analyzed in detail in the following sections.
Table 4 lists the mechanical properties of specimens with di erent drilling arrangements, that is, the uniaxial compressive  4 Advances in Civil Engineering strength (σ c ), the elastic modulus (E), and the peak axial strain (ε 1max ) corresponding to the strain at peak stress.In accordance with the numerical results listed in Table 4, generally, the deformation and strength behaviors of specimens are found depending on the drilling arrangement.

In uences of Drilling Arrangements on the Strength and Deformation Parameters.
Figure 6 shows the in uence of the drilling diameter on the mechanical properties of specimens.
From Figure 6, it can be seen that the elastic modulus remains stable with the increase of drilling diameter.e uniaxial  Advances in Civil Engineering compressive strength and peak strain, however, show a di erent trend.Both of the two parameters decrease gradually with the increase of drilling diameter.For example, when the drilling diameter increases from 3 to 10 mm, the uniaxial compressive strength and peak strain vary from 11.48 to 8.64 MPa and from 1.7863 to 1.3926 × 10 −2 , respectively.In addition, the decreasing percentage of uniaxial compressive strength is 0.78-25.32%compared with the intact specimen.
Figure 7 shows the in uence of number of drilling holes in one row on the mechanical properties of specimens.From Figure 7, it can be seen that the elastic modulus remains stable with the increase of number of drilling holes in one row, whose variation law is similar to the in uence of drilling diameter.In contrast, the uniaxial compressive strength and peak strain remain steady rst and then decrease gradually as increasing the number of drilling holes in one row.When the number of drilling holes increases from 1 to 2, the uniaxial compressive strength and peak strain vary from 11.48 to 11.41 MPa and 1.7863 to 1.7804 × 10 −2 , but when the number increases from 2 to 4, these two parameters decrease from 11.41 to 10.46 MPa and from 1.7804 to 1.6510 × 10 −2 , respectively.Compared with the intact specimen, the decreasing percentage of uniaxial compressive strength is only 0.78-9.59%,which is far lesser than the cause of increasing the drilling diameter.
Figure 8 shows the in uence of number of drilling rows on the mechanical properties of specimens.From Figure 8, it can be seen that the deformation parameters, that is, the elastic modulus and peak strain, are not obviously in uenced by the number of drilling rows.But, the uniaxial compressive strength decreases gradually with the increase of number of drilling rows.For example, as the number of drilling rows increases from 1 to 4, the uniaxial compressive strength decreases from 11.01 to 9.63 MPa.Compared with the intact specimen, the decreasing percentage of the uniaxial compressive strength is only 4.84-16.77%.

In uences of Drilling Arrangements on Failure
Modes. Figure 9 gives the failure modes of specimens with various drilling arrangements.Figures 9(a) and 9(b) clearly show that the in uence of drilling diameter or number of drilling holes in one row on the failure mode of specimens is not obvious.For specimens with di erent drilling diameters, shear failure accompanied with splitting failure is the main failure mode and the shear zone just propagates across the drilling hole, but for specimens with di erent numbers of drilling holes in one row, splitting failure accompanied with shear failure is the main failure mode.However, the number of drilling rows in uences the failure mode of specimens greatly, as shown in Figure 9(c).When the number of drilling rows is 1 or 3, splitting failure is the main failure mode, but when the number of drilling rows is 2 or 4, shear failure is the main failure mode.

Influences of Drilling Arrangements on the Energy Evolution
4.1.Energy Parameters.Although scholars have proposed many indexes for evaluating the bursting liability of coal seam, there are little researches related to the bursting liability evaluation of destressed coal seam.Zhu et al. [16] put forward a new index, that is, dissipation energy index (X E ), to improve this issue.is index is used in this section to analyze the in uences of drilling arrangements on the energy evolution of specimens before peak stress.X E is the ratio of the released accumulative strain energy after destressing (ΔS) to the accumulated strain energy before destressing (S 1 ), as shown in Figure 10(a).X E is calculated in the following equation:  6 Advances in Civil Engineering Besides using the above index, the bursting energy index (K E ) also is used to study the in uences of drilling arrangements on the energy evolution.As shown in Figure 10(b), K E refers to the ratio of the accumulative strain energy before peak stress (F S ) to the released energy after peak stress (F X ) under uniaxial compression condition [30,31].
is index considers the energy transformation during the deformation and failure processes of rock or coal specimens.K E is calculated in the following equation: 4.2.In uences of Drilling Arrangements.Employing ( 1) and ( 2), the dissipation energy and bursting energy indexes of specimens with di erent drilling arrangements are determined Advances in Civil Engineering and summarized in Table 5. Figure 11 depicts the energy evolution curves of these specimens with various drilling arrangements.
As shown in Figures 11(a) and 11(b), in uences of drilling diameter or the number of drilling holes in one row on the energy evolution law are similar.As increasing the drilling diameter or number of drilling holes in one row, the energy dissipation index increases nonlinearly.When the drilling diameter and number of drilling holes increase from 3 to 5 mm and from 1 to 2, respectively, their corresponding variations of energy dissipation index are only 1.01-3.35%and 1.01-2.51%.But when the drilling diameter and number of drilling holes increase from 8 to 10 mm and from 3 to 4, the corresponding variations reach about 24.35-41.93%and 10.12-14.89%,respectively.However, the bursting energy index rst decreases slowly and then rapidly as increasing the drilling diameter or number of drilling holes in one row, which shows an opposite trend compared with the energy dissipation index.For example, when the drilling diameter varies from 3 to 8 mm, the bursting energy index decreases from 9.13 to 7.17, but when the drilling diameter is 10 mm, this index is only 4.00; when the number of drilling holes in one row increases from 1 to 4, the bursting energy index varies from 9.13 to 7.74. is phenomenon reveals that increasing the drilling diameter for the destress drilling method might be more e ective than increasing the number of drilling holes in one row.
Although the energy dissipation index also increases as increasing the number of drilling rows, the variation law of bursting energy index is not obvious, as shown in Figure 11(c).When the number of drilling rows increases from 1 to 4, the energy dissipation index varies from 10.12% to 26.17%, but the bursting energy index rst increases from 8.76 to 11.93 and decreases to 4.89 and then increases to 10.17. is phenomenon is very interesting.Perhaps there are two reasons causing this result.First, as increasing the number of defects of specimens, its bearing capacity will be weakened, certainly causing the decrease of ability of strain energy accumulation.Second, the in uence of the number of drilling rows on the failure modes is more serious than that of the drilling diameter or number of drilling holes in one row, but the energy consumed by the failure of specimens varies greatly depending on the failure modes.For example, when the number of drilling rows is 2, the failure mode is shear failure and the bursting energy index is high.is result shows that choosing a proper drilling arrangement is essential for mitigating rock bursts; that is, if the drilling arrangement that leads to the energy consumed by the coal failure is small, rock bursts might occur.

Discussions
As introduced in Section 2, the prevention mechanism of destress drilling performed in coal seam is given in Figure 1.We can explain the in uence of drilling arrangements on the prevention mechanism of the drilling method based on the above results.Overall, the strain accumulation ability of   Advances in Civil Engineering coal seam decreases nonlinearly with the increase of the number or area of defects, but its decreasing degree varies greatly depending on the drilling arrangement.In addition, the drilling arrangement also in uences the consumed energy of coal failure through a ecting the failure mode, especially for the number of drilling rows.
In aspect of the in uences of drilling diameter and number of drilling holes in one row, their in uencing Advances in Civil Engineering mechanisms are similar.Although the strain accumulation ability of coal decreases with the increase of drilling diameter or number of drilling holes in one row, the failure mode of coal almost remains stable.
at means the variation of consumed energy of coal failure is small according to the least energy principle of dynamic failure of rock mass [32][33][34].at is to say, the influencing mechanism of increasing the drilling diameter or number of drilling holes in one row mainly is to decrease the energy accumulation ability of coal without affecting the consumed energy of coal failure, as shown in Figure 12(a).erefore, the bursting liability of coal seam can be weakened.However, the influencing mechanism of number of drilling rows shows a difference in the consumed energy of coal failure through affecting the failure mode.As increasing the number of drilling rows, if the coal failure consumes lesser energy than before, the bursting energy index may increase, and vice versa. is result is mainly influenced by the failure mode, as shown in Figure 12(b).So far, Figure 12 gives the influencing mechanism of drilling arrangement on the prevention mechanism of destress drilling method.

Conclusions
In this study, the rock burst mitigation mechanism of the destress drilling method performed in coal seam was first introduced.en, a systematic numerical simulation by PFC2D was conducted to research the mechanical properties of coal models with various drilling arrangements under uniaxial compression tests.e following conclusions can be summarized: (1) e drilling arrangement mainly influences the bearing capacity of coal models.e uniaxial compressive strength increases nonlinearly with the increase of the drilling diameter, number of drilling holes in one row, or number of drilling rows.Among the three factors, the influencing degree in order from strong to weak is the drilling diameter, number of drilling holes in one row, and number of drilling rows.Compared with intact specimens, their decreasing percentages of uniaxial compressive strength are 0.78-25.31%,4.84-16.78%,and 0.78-9.59%,respectively.However, the elastic modulus remains stable as increasing the number of these defects.is phenomenon might be caused by that materials are homogeneous and defects could only decrease the structural bearing capacity in simulating process.(2) For specimens with different drilling diameters, shear failure accompanied with splitting failure is the main failure mode, but for specimens with different numbers of drilling holes in one row, splitting failure accompanied with shear failure is the main failure mode.However, it might be splitting or shear failure for specimens with different numbers of drilling rows.(3) e energy dissipation index increases nonlinearly with the increase of drilling diameter or number of drilling holes in one row, but the bursting energy index shows an opposite variation law, which decreases slowly and then rapidly.In addition, the energy dissipation index increases linearly as increasing the number of drilling rows, but the variation law of bursting energy index is not obvious due to the influence of different failure modes.(4) e influencing mechanism of drilling diameter or number of drilling holes in one row on the prevention mechanism of the destress drilling method is to decrease the energy accumulation ability of coal without affecting the consumed energy of coal failure, as shown in Figure 12(a).However, the number of drilling rows influences not only the energy accumulation ability, but also the consumed energy of coal failure, as shown in Figure 12(b).As increasing the number of drilling rows, if the coal failure consumes lesser energy than before, the bursting energy index might increase, and vice versa.
Although the analysis results above all were obtained by numerical simulation, it still reveals some variation laws about the influences of various drilling arrangements on the mechanical properties and failure mechanisms of specimens.We all know that the homogeneity of rock or rock-like materials is often hard to be controlled, but in the PFC2D numerical simulation process, the material is homogeneous.
us, we can study the influences of drilling arrangements without influences of other factors, especially material differences.erefore, the results obtained in this paper can also provide a reference for understanding the influencing mechanism of drilling arrangement on the rock burst mitigation mechanism of the destress drilling method.Of course, we will continue to do laboratory tests in the future to enrich the research and prove the viewpoint in this paper.

3. 1 .
Discrete Element Model 3.1.1.Microbond Model.In PFC2D, there are two kinds of failure modes between particles, that is, the shear failure and the tension failure.It has two different bond models-contact bond model (CBM) and parallel bond model (PBM)-generally used

Figure 1 :
Figure 1: Sketch of destress drilling in coal seam.

Figure 2 :
Figure 2: Schematic diagram of test schemes.(a) Specimens with di erent drilling diameters.(b) Specimens with di erent numbers of drilling holes.(c) Specimens with di erent numbers of drilling rows.

Table 2 :Figure 3 :
Figure 3: Comparison between experimental and numerical stressstrain curves of coal under uniaxial compression.

Figure 5 :
Figure 5: Stress-strain curves of specimens with di erent drilling arrangements under uniaxial compression.(a) Di erent drilling diameters.(b) Di erent numbers of drilling holes.(c) Di erent numbers of drilling rows.

Figure 6 :
Figure 6: In uence of drilling diameter on the mechanical properties of specimens.UCS: uniaxial compressive strength.

Figure 7 :Figure 8 :
Figure 7: In uence of number of drilling holes in one row on the mechanical properties of specimens.

Figure 9 :
Figure 9: Failure modes of specimens with various drilling arrangements.(a) Di erent drilling diameters.(b) Di erent numbers of drilling holes in one row.(c) Di erent numbers of drilling rows.

Figure 10 :
Figure 10: Sketch of the calculations of X E and K E .(a) Calculation of X E .(b) Calculation of K E .

Figure 11 :Figure 12 :
Figure 11: Energy evolution curves of specimens with various drilling arrangements.(a) Di erent drilling diameters.(b) Di erent numbers of drilling holes in one row.(c) Di erent numbers of drilling rows.

Table 3 :
Comparison between the experimental and numerical mechanical parameters.
Figure 4: Comparison between experimental and numerical failure modes of coal under uniaxial compression test.e black and red dots represent the tensile microcrack and shear microcrack, respectively.
Note.R D , N H , and N R are the drilling diameter, the number of drilling holes in one row, and the number of drilling rows, respectively.

Table 4 :
Mechanical properties of specimens with di erent drilling arrangements.

Table 5 :
Energy indexes of specimens with di erent drilling arrangements.