Numerical Simulation of Split-Hopkinson Pressure Bar Tests for the Combined Coal-Rock by Using the Holmquist–Johnson–Cook Model and Case Analysis of Outburst

In the coal and rock dynamic disasters, such as the rock burst, dynamic load damage often acts simultaneously on the combined coal and rock mass. Based on the split-Hopkinson pressure bar (SHPB) test of the combined coal and rock with a bullet velocity of 4.590–8.791m/s, the numerical model of four kinds of combined coal and rock with different sandstone-coal-sandstone ratios, including 1 :1 :1, 2 :1 :1, 1 :1 : 2, and 1 : 2 :1, is investigated. A finite element software (LS-DYNA) and the Holmquist–Johnson–Cook (HJC) constitutive model of rock are employed in these regards. .e stress waveform, the oscillation phenomenon of stress wave, and the damage process of the specimen in the impact test of the composite coal and rock are studied. .e obtained results show that the compression-shear failure is the main failure mode of the coal body and the tensile failure of the sandstone along the axial direction in the composite coal-rock specimens. Moreover, it is found that combination of coal and rock samples is mainly destroyed by the coal body, which has no correlation with the impact speed and combination mode. Finally, numerical simulation about Hongling coalmine extralarge tunnel malfunction is carried out. Obtained results showed the protruding and stress change processes of the coal seam of the tunnel exposing. It is found that the simulation results are in an excellent agreement with those from the field investigation. .e present study may provide a reference for further understanding the mechanism of the coal and rock dynamic disasters, such as the rock burst.


Introduction
Studies show that as the coal mining depth increases, the geostress and gas pressure increase significantly, and the geological occurrence becomes very complicated. Moreover, the coal-rock dynamic disasters, such as the impact pressure and coal and gas outburst, increase [1]. e coal seams are deposited underground in the form of coal-rock interbeds [2]. However, these seams are not separately distributed, and they may be connected to each other. Investigating different mining methods for various working conditions showed that the coal body itself is destroyed during the mining process, and the rock mass adjacent to the top and bottom plates is damaged. It is found that this results in the overall instability of the coal-rock interbed [3]. erefore, the interaction between rocks and coal seams should be considered during the mining process [4]. In recent years, studying the dynamic and static mechanical parameters of the combined coal-rock has been widely concerned by many researchers. Liu et al. [5] carried out uniaxial compression experiments on 13 coal-rock combinations and found that the compressive strength of coal samples increases as the rock strength increases while it decreases as the coal-rock height ratio increases. Guo et al. [6] found that the tensile strength of the layer-crack structure decreases as the fissure length (or width) increases through uniaxial compression and Brazilian tests. Chen et al. [7] conducted an experiment on the deformation and destruction behavior of coal-rock combinations under the uniaxial compression. ey found that mechanical properties and deformation-destructive characteristics of the coal-rock composites are mainly depend on the coal composition and its percentage in the coalrock. Gong et al. [8] studied the effect of low loading rate on the mechanical behavior of coal-rock combined body. Moreover, Gong et al. [9] used a split-Hopkinson pressure bar (SHPB) device to perform high strain rate dynamic compression tests on a variety of coal-rock combinations. ey showed that the dynamic stress-strain curve of the coal-rock has double peak characteristics in the high loading rates. Zhao et al. [10] employed the FLAC3D software to simulate and study the damage evolution of the coal-rock with different combinations. ey found that the overall damage rate increases as the coal seam thickness increases. Furthermore, Fu et al. [11] employed the RFPA 2D software to numerically investigate the mechanical properties and acoustic emission characteristics of coal-rock under different confining pressures and dip angles. ey concluded that the stress-strain curves of different coal-rock combinations are similar, and the peak strength is close to the uniaxial compressive strength of the coal. Reviewing the literature indicated that majority of studies on the mechanical characteristics of the coal-rock with different combinations are focused on static or slow loading conditions [5][6][7][8][9][10][11]. In other words, the dynamic mechanical properties of coal-rock with different combinations under the impact loading have not been deeply studied yet.
Recently, the SHPB has been widely used for studying the dynamic mechanical properties of materials [12] and has achieved reasonable results in soft materials [13,14], metallic materials [15,16], and brittle materials [17,18]. e improved SHPB test device can be utilized to study the dynamic mechanical properties of materials for different conditions [19,20]. Doan and Billi [21] investigated the high strain rate behavior of unconfined Carrara marble through a set of experiments with a split-Hopkinson pressure bar. Zhang et al. [22] made discussion and comparisons on the dynamic fracture processes and specimen fragments in the clay brick to explain the dynamic enhancement in brick mechanical properties. Gong et al. [23] obtained the effects of high strain rates and low confining pressures on the dynamic mechanical properties of sandstone experimentally with a modified triaxial SHPB system. However, due to the limitations in test equipment and experimental methods, there are not enough experimental research studies on the impact damage of the coal and rock. On the contrary, numerical methods can resolve the problems. rough numerical simulation, the stress and strain variations inside the coalrock can be calculated. erefore, the propagation and damage characteristics of stress waves in the coal and rock can be analyzed, and the limitations in the laboratory analysis of the dynamic load are covered. Holmqusist et al. [24] proposed the Holmquist-Johnson-Cook (HJC) constitutive model for the concrete and rock under high strain rate and large deformation problems. e HJC model has been used for dynamic failure analysis of the coal and rock, and it has achieved satisfactory results [25,26] considering the mechanical similarity between the coal and rock and the ordinary rock and concrete materials. ey utilized the concrete HJC constitutive model to investigate coal samples and simulated the damage process of coal samples under different impact velocities. ey showed that the numerical results are in a good agreement with those from the experiment. Li et al. [26,27] used the HJC constitutive model and commercial finite element software, called LS-DYNA, to numerically investigate the coal-rock SHPB test and the coal-rock SHPB passive confining pressure test. ey found that the simulation results have a good similarity with the experimental results.
In order to explore the evolution law of the combined impact damage of the coal-rock, it is intended to perform the SHPB test for different coal-rock combination ratios, including 1 : 1 : 1, 2 : 1 : 1, 1 : 1 : 2, and 1 : 2 : 1. Moreover, the LS-DYNA finite element analysis software and the HJC constitutive model are employed to construct the damage evolution and dynamic fracture process of the combined coal-rock in the dynamic impact test. en, the feasibility and effectiveness of the HJC constitutive model will be verified by comparing the numerical simulation results with those from the experimental results. Because the previous research on the dynamic mechanical characteristics of combined coal-rock under impact load has not been carried out in depth, this paper studies the dynamic characteristics of coal-rock samples under instantaneous impact failure by taking the actual coal-rock composite structure under the impact load as the research object and further verifies with the actual case, so as to further study the dynamic mechanical characteristics. It is intended to provide an experimental basis for further understanding the occurrence mechanism of the coal-rock dynamic disasters, such as the rock burst, coalmine rock disaster monitoring, and early warning, which is of great significance from safety points of view.

SHPB Test Device
e combined coal-rock dynamic impact test is completed with the SHPB testing device of the China University of Mining and Technology (Beijing). It should be indicated that the SHPB device consists of a striker (bullet), an incident bar, and a transmission bar. is test device uses a special shaped double-cone spindle with a total length of 540 mm, where the cone ratio of the bullet is 310 : 100 : 130 [28]. e approximately half-sine loading wave was generated by the spindle-shaped bullet, which has been suggested as the ideal loading waveform for SHPB testing device [29,30]. It should be indicated that this shape of the loading wave is more suitable for the dynamic test of the coal-rock brittle materials [31]. e specific size of the bullet is shown in Figure 1.
In the experiment, the "top-coal-base" composite coalrock sample MY1-MY23 was produced. It should be indicated that the MY6 test failed. A total of 22 impact compression tests are carried out in the present study, with sample height ratios of 1 : 1 : 1 (MY1-MY5), 2 : 1 : 1 (MY7-MY12), 1 : 1 : 2 (MY13-MY18), and 1 : 2 : 1 (MY19-MY23). In order to minimize the inertia effect of the test piece and satisfy the internal stresses, it is assumed that all samples are uniform [32]. According to the best aspect ratio calculation recommended by Davies and Hunter [33], the diameter, length, and the aspect ratio of the coal-rock cylindrical specimen are set to D � 75 mm, L � 40 mm, and L/ D � 8/15, respectively [26]. Moreover, in order to reduce the influence of the interface friction during the test, the Vaseline lubrication is applied between the elastic bar and the test piece interface [34]. Figure 2 shows configurations of different experimental combined coal-rock samples.
Combined with the physical parameters of the actual pressure bar, both the incident bar and the transmission bar adopt a linear elastic model of steel material, where the diameter, length, and density are 75 mm, 2000 mm, and ρ � 7800 kg/m3, respectively. Moreover, the elastic modulus and Poisson's ratio are E � 206 GPa and ] � 0.36, respectively. Finally, the impact velocity v is 4.590 to 8.791 m/s, and the specific experimental data are shown in Table 1 [31]. Figure 3, the HJC constitutive equation uses a three-stage polynomial equation of state to describe the relationship between the coal-rock pressure (p) and the volumetric strain (μ), in the elastic phase (OA segment), plastic phase (AB segment), and the dense compaction phase of the material (BC segment) [24]. ese phases are described in the following:

HJC Dynamic Constitutive Model. As shown in
(1) Elastic phase (p w < p c ): the hydrostatic pressure (p w ) of the material has linear correlation with the volumetric strain (μ) of the material: where K e � R ' c /3 (1 − 2]) and ] are the bulk modulus of the material and Poisson's ratio of the coal sample, respectively [31].
(2) Plastic phase (p c ≤ p w ≤ p l ): in this phase, the hydrostatic pressure is calculated from the following equation: where μ l , μ c , and p l are the compacted volume strain corresponding to the compaction pressure, crushed volume deformation of the material during the uniaxial compression, and the compaction pressure, respectively. In the unloading section, the governing equations are where K 1 denotes the plastic bulk modulus. Moreover, p max and μ max are the maximum volume pressure and volume strain achieved before unloading, respectively [24].
(3) Completely compact phase (p w > p l ): in the loading section, the hydrostatic pressure is calculated as where k 1 , k 2 , and k 3 are constants and μ is the corrected volume strain.
In the unloading section, e HJC constitutive model uses the dynamic damage factor D to describe the damage of the material, which is expressed as the cumulative plastic strain and the volumetric strain: where Δε p and Δμ p are the equivalent plastic strain increment and plastic volume strain increment, respectively.

Advances in Civil Engineering
hydrostatic pressure and the maximum tensile strength of coal and rock masses, respectively. Finally, D 1 and D 2 are damage constants [27].

Determination of Parameters of Common Coal
Materials. In the LS-DYNA software, the HJC constitutive model is defined as the " * mat_johnson_holmquist_concrete," which has 21 parameters. It should be indicated that model parameters of the coal material are selected in accordance with the Xie Beijing experiment [25]. Table 2 shows the selected parameters.

Determination of Rock Material Parameters.
Because the stress-strain curve of sandstone and coal is very different [35], the relevant literature parameters were consulted to establish the sandstone material model [36]. It is intended to investigate the influence of the combination type and impact velocity changes in the simulation results. e    Table 3.

Establishment of the Finite Element
Model. According to the actual size of the test, the bullet, pressure bar, and threedimensional solid elements of the combined coal-rock specimen (Solid164) are established. Considering the structure symmetry, only a quarter of the test device and the test piece are modeled. en, the model is meshed, and the bullet and the input and transmission bars are divided into 20 parts in the radial direction, 54 pieces in the axial direction of the bullet, and 200 parts in the axial direction of the incident and transmission bars. Moreover, the bullet and the pressure bar are divided into 1 part per 10 mm in the axial direction. In order to reflect the impact damage process of the combined coal-rock specimens more directly, the combined coal-rock specimens are finely meshed so that the combined specimens are divided into 20 parts in radial directions and the axial direction is divided into 1 mm long each, as shown in Figure 4. e bullet and the incident bar are in automatic contact with the surface and the erosion contact between the pressure bar and the test piece. By neglecting the friction between the contact surfaces, the contact algorithm of the penalty function is used to reduce the hourglass effect. It should be indicated that the value of the contact stiffness penalty function factor (f ) is set to 2 [24]. Based on the actual SHPB test, the simulation is performed by applying the loading speed to the bullet directly. Due to the short length of rods and the combined coal-rock specimens in the SHPB test, the attenuation of the stress waves in the rod and the specimen is ignored in the simulation [37].

Waveform of Stress Waves.
In this section, the stress waveform results of the combined coal-rock under some typical speeds are presented. Figure 5 shows the measured and simulated stress waveform curves at the middle of the incident and transmission bars at different speeds, including 5.008 m/s (combined coal MY1), 7.671 m/s (combined coal MY7), 6.660 m/s (combined coal-rock MY13), and 5.880 m/s (combined coal-rock MY23). Figure 5 shows good consistency between simulated and measured stress waveform trends. It is observed that the incident wave grows in a stepwise manner. Focusing on the incidence wave, the measured peak values of the incidence wave at the four bullet speeds in the experiment are 101.96, 164.94, 133.46, and 132.26 MPa, respectively; the simulated peak values of the incidence wave measured by the corresponding four bullet speeds are 104.35, 165.10, 139.15, and 131.82 MPa, respectively. It is found that the peak value of the simulated incidence wave is slightly higher than the peak value of the measured incidence wave, and there is little discrepancy between the two values. Since the propagation of the experimental stress wave in the bar decreases with time, the stress wave in the numerical simulation does not decrease. When the wave reaches interface between two different impedances, the wave reflection and transmission occur at the interface. When the stress wave reaches the transmission bar, it passes through three sections with different wave impedances and the incident wave reflection causes it to rise in three steps. However, the measured incident wave does not exhibit a stepwise growth because the stress-strain acquisition rate is low. Moreover, the end faces of the bars are flat in the numerical simulation, and the combined coal and rock specimens in the experiment inevitably have defects.
is results in loss of stress wave during the wave propagation. Because of the nonuniformity in the coal-rock, the stress waveform in the experiment is different from that of the numerical simulation in terms of incident and reflected wave width and rise. Numerical simulation of the stress waveform is also associated with a certain oscillation phenomenon. However, the stress waveform distributions obtained from the numerical simulation and experiment are consistent with the overall trend of transmission wave rise. ere are a lot of microcracks and micropores in the combined coal-rock, which will produce significant evolution damage under impact load, especially under the condition of medium and high strain rate. And the internal material of the combined coal-rock is not uniform. ese factors make the stress-strain curve in Figure 6 fluctuate, but Figure 6 shows good consistency between simulated and measured stress-strain waveform trends. Because the simulation is carried out under ideal conditions, there are some differences due to small external interference. Although the simulated and measured values are slightly different, there are only minor differences. erefore, the numerical simulation results can replace the experiments, which can be used to test and analyze the dynamic test of the combined coal-rock.

Dynamic Stress Equilibrium Curves.
In order to obtain effective test data, the stress balance at both ends of the sample is achieved during the test, as shown in Figure 7. Figure 7 shows the dynamic stress balance curves of the four specimens at the corresponding bullet speed. e stresstime curve of the interface between the incident rod and the sample (incident + reflection in the figure) is calculated from the incident signal plus the reflected signal; the stress-time curve of the interface between the transmission rod and the sample (transmission in the figure) is calculated by the transmission signal. It can be seen from the figure that the       Advances in Civil Engineering stress balance of each sample is relatively good in the whole loading process.

Analysis of the Failure Process of the Combined Coal and
Rock. High-speed photography is utilized to capture the failure process of the combined coal-rock SHPB test. Moreover, the impact process of the combined coal-rock is analyzed and compared with the simulated combined coalrock failure process, as shown in Figure 8. Figure 8(a) indicates that, for the combined coal-rock of 1 : 1 : 1 affected at a speed of 5.008 m/s, the stress waves reach the sample at t � 395.96 μs and the coal is damaged by the compression shearing. When t � 545.9 μs, the rear end of the sandstone is subjected to the axial and tensile cracking and the damage is completed at t � 800.94 μs. During the whole test, the coal edge is sprayed in the radial direction, while the sandstone is maintained a certain degree of integrity. It should be indicated that this situation is in good agreement with the actual test process. Figure 8(b) indicates that, for the 2 : 1 : 1 combined coal-rock with an impact velocity of 7.671 m/s, the stress waves reach the sample at t � 398.93 μs and the coal is damaged by the compression and shear. When t � 434.96 μs, the sandstone is subjected to the axial and tensile cracking and damage is completed at t � 788.97 μs. roughout the experiment, the edge of the coal is sprayed radially along the compression shear, while the sandstone is maintained in a good integrity. In the actual experimental failure process, the sandstone instability produces radial cracks at the front end. Simulation result indicates that the rear sandstone creates radial cracks. e analysis shows that the front-end sandstone has cracks and creates radial cracks, when it is subjected to impact loads. Furthermore, Figure 8(c) shows that, for the 1 : 1 : 2 combined coal-rock with an impact velocity of 6.660 m/s, the stress waves reach the sample at t � 392.92 μs and the coal is damaged by compression shearing. When t � 431.99 μs, the rear end sandstone is subjected to the axial cracking and tensile cracking and the damage is completed at t � 761.98 μs. During the whole test, the edge of the coal is sprayed radially in the radial direction, while the sandstone is maintained in a good integrity. is condition is in a good agreement with the actual experimental failure process. Finally, Figure 8(d) illustrates that, for the 1 : 2 : 1 combination coal-rock with an impact velocity of 5.880 m/s, the stress waves reach the sample at t � 389.99 μs and the coal is damaged by the compression shearing. When t � 404.99 μs, the rear end sandstone is subjected to the axial and tensile cracking and the damage was completed at t � 779.94 μs. During the test, the edge of the coal is sprayed radially in the radial direction and the sandstone is maintained in a certain degree of integrity. Due to the equipment failure, the experimental process cannot be captured in this case. In addition, due to parameter settings, some element failures are lost and can be further simulated and verified later.
It is observed that, in the combined coal-rock SHPB impact test, the coal body first suffers damage and the sandstone produces the tensile damage. ese damages are mainly caused by the coal body damage and have no clear correlation with the impact speed and the combination mode.
e main failure modes of coal bodies are compression and shear failure, and the failure modes of sandstone are tensile failure along the axial direction. Furthermore, the edge of the coal is sprayed radially in the radial direction. It is found that the greater the impact velocity, the more severe the damage. Tensile damage occurs in the back-end sandstone, and the front sandstone still maintains good integrity.

Case Simulation
Shenling Group Hongling coalmine is located in Nanhong Village, Honglingbao Town, Sujiatun District, Shenyang City. e coalfield strata of the minefield are intercontinental sediments of sea and land, and the lithology is composed of sandstone and mudstone interbeds. e average dip angle of the coalfield in the minefield is 30°. It should be indicated that the Hongling coalmine is a mine with coal and gas outburst. e mine development method is a multilevel partitioning method for the main well. e ventilation method is the central diagonal type. e coal is mined by the blasting method, and the punching and blasting technique is utilized for the excavation. Over the years, there have been more than 140 coal and gas outburst accidents in the Hongling coalmine, including 15 accidents caused by the coal seam of tunnel exposing (more than 10% of total mine accidents). Moreover, among 55 casualties of the Hongling coalmine, 43 miners died in the coal seam of tunnel exposing, which accounts for almost 80% of the total casualties, due to outstanding accidents. Moreover, the largest coal and gas outburst in the Hongling coalmine was a prominent accident that occurred after the 12 th coal seam of the tunnel exposing on June 20, 1996. e outstanding coal volume is 5390 t, which is a large-scale prominent. e forehead coal seam is 4.2 m thick, and the inclination angle is 37° [38]. Figure 9 shows a cross-sectional view of the coal and gas outburst accidents.

Numerical Simulation Model.
Taking the largest coal and gas outburst in the Hongling coalmine as an example, Ansys and LS-DYNA finite element software are used to visualize the stress distribution law for the surrounding rocks during the outburst process. e length, width, and height of the calculation model are set to 50 m, 3 m, and 50 m, respectively. Moreover, the thickness of the coal seam and the inclination angle are set to 5 m and 30°, respectively. Figure 10 indicates that the roadway is 40 m long, 3 m wide, and 3 m high. e left-and right-side boundaries of the model are constrained by the X-direction, while the bottom boundary is confined to the Y-direction. e applied ground stress to the model is obtained by the field measurement. e initial horizontal direction ground stress is σ � 18 MPa.

Variation Law of the Outburst Stress Field.
In underground explosive operations, the shock wave generated by the blasting transmits the large amount of the blasting energy to the surrounding area. In severe cases, this energy can cause  10 Advances in Civil Engineering protrusion in the process of the coal seam of the tunnel exposing. e stress wave disturbance caused by the excavation blasting is also simplified into a semisinusoidal pulse. e dynamic stress-strain curve obtained by the coal-fired SHPB test is taken as the maximum peak of the half-sinusoidal pulse amplitude of 20 MPa. e constitutive parameters of coal materials and sandstone are presented in Tables 2 and 3, respectively. e numerical simulation is used to realize the visualization of the prominent dynamic disasters of the coal seam of the tunnel exposing. e obtained results from the numerical simulation are shown in Figure 11. Figure 11 shows the variation in the coal seam stress of the tunnel exposing. It is observed that when t � 2.8 μs, the disturbing stress wave contacts the coal seam and the coal       seam begins to crack. Moreover, it is found that when t � 14.8 μs, the coal seam is destroyed by the compressive stress wave. As the compressive stress wave continues to expand deep inside the coal seam, the crack gradually expands, the coal seam is notched at t � 38.8 μs, and the stress propagates in the rock stratum in three directions. When t � 116.8 μs, the gap size generated by the coal seam decreases, and then, it increases with the stress waves transmission. Finally, when t � 218.9 μs, a large cavity is formed deep in the coal seam with the increase in the notch. Figure 11 indicates that the coal seam and the surrounding rock mass are in a weak equilibrium state, when the coal is uncovered. It is found that the disturbance caused by the excavation blasting, instantaneously, destroys the equilibrium state, and the coal body loses the lateral support. It should be indicated that the strength of the coal body is much lower than the strength of the rock mass. erefore, in the coal body near the exposed surface, microrupture occurs due to the unloading action. With the expansion of the microfracture in the coal body, the highstress zone advances to the deep part of the coal body and the elastic potential in the coal seam is immediately released. Coal is thrown toward the roadway under the crustal stress, and it is called coal outburst. en, when the stress of coal and rock returns to the equilibrium state, the appearance of coal outburst stops. It is observed that the obtained outburst shape by the simulation results (Figure 11) agrees well with the results of the field investigation after the outburst (Figure 9). Furthermore, it is found that the bursting hole has a small cavity and the bursting hole expands along the interface between the coal body and the top and bottom plates in the horizontal and uphill directions.

Conclusions
In the present work, the constitutive model of the rock coal HJC is applied in the finite element software (LS-DYNA) to simulate the combined coal-rock SHPB test. e stress wave oscillation phenomenon and damage process of the specimen during the impact test of the combined coal-rock are simulated to construct the stress waveform. e present study shows that the simulation results have good similarity with those from the experiment. It is concluded that the parameters for the simulation are properly selected. Furthermore, the conclusions of this study are as follows: (1) e failure mode of the coal body is mainly due to the compression and shear failure. e failure mode of the sandstone is mainly originated from the tensile failure along the axial direction, which is mainly caused by the coal body damage. It is found that this failure does not have clear correlation with the impact velocity and material combination. (2) During the destruction process, the edge of the coal is sprayed radially in the radial direction. It is found that the greater the impact velocity, the more severe the damage, while the sandstone remains intact.
(3) Comparing the simulation results with the experimental results, the HJC constitutive model of coal and rock can reproduce the dynamic process of coal and rock under impact. (4) e dynamic constitutive model parameters of the coal and sandstone HJC are applied to the numerical simulation model of the coal seam of the tunnel exposing. Processes of the coal protruding and the stress change are presented. It is found that the simulation results are in a good agreement with the results of the on-site investigation after the outburst. ese results are important for further understanding the mechanism of the protruding coal in the coal seam of the tunnel exposing.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.