Experimental Study on the Mechanical Behavior of Coal under Triaxial Dynamic Compression

Abstract

The frequency and intensity of coal-rock dynamic incidents in underground coal mining, such as coal bumps and outbursts of coal and gas, tend to increase with mining depth. These dynamic incidents are closely related to the dynamic mechanical behavior of coal. In this experimental study, the dynamic mechanical behavior of coal was investigated with an active triaxial split Hopkinson pressure bar (SHPB) test system. In the test, the in-situ stress field for coal with an overburden depth of 100 m to 600 m was simulated and the dynamic loading tests of coal were undertaken under low, medium, and high loading rates. The results of the study show that the dynamic compression strength of coal increases with loading rate and axial and confining stress, and the effect of confining stress is more profound than that of axial stress. The results also reveal that the energy consumption and energy density per unit volume of coal are positively correlated with the depth and loading rate. This study may help gain insights into the occurrence mechanism of coal-rock dynamic incidents in underground coal mining.

1. Introduction

Coal still dominates national energy consumption and resource reserves, with coal accounting for 56.8% of China’s total energy consumption in 2020 [1]. Long and continuous large-scale coal mining has resulted in an increase in mining depth, leading to mining in high-stress environments and making the prevention and control of coal-rock dynamic disasters difficult [2,3,4]. Current theories cannot fully explain the mechanism of coal-rock dynamic disasters in high-stress environments [5,6,7,8].

The dynamic mechanical behavior and failure mechanism of coal is a popular research topic [9,10,11,12], and the split Hopkinson pressure bar (SHPB) is becoming an important means to investigate the dynamic mechanical properties of coal at medium to high strain rates (10²~10^4/s) [13,14,15,16]. Uniaxial dynamic loading has been used by previous researchers and many significant results have been obtained. Klepaczko conducted an early experimental study on coal dynamics under different strain rate ranges, demonstrating the rate dependence of coal under dynamic loading [17]. The effect of bedding directivity on coal was studied by uniaxial dynamic loading tests; energy dissipation and fractal dimension were analyzed, which proved the effect of bedding directivity on the dynamic behavior of coal was not significant with increasing strain rate. [12]. Specifically, numerical simulations and physical experiments on the strength properties of rocks under dynamic loading were carried out, and the strength enhancement coefficient was introduced with a good match to the experimental results [18]. Meanwhile, Feng et al. analyzed the damage behavior and mechanism of coal under uniaxial dynamic compression. The fragmentation behavior of coal at different loading rates was presented at the macroscopic level, where axial fracture is caused by the incident stress wave and lateral fracture is caused by the tensile stress of the reflected stress wave. [19]. Based on these investigations, the crack evolution and fractal characteristics of coal under impact loading were studied; the crack propagation rate is greater at 45° bedding angle than at other angles. Thus, the crack propagation rate was verified to be less than the Rayleigh wave velocity [20]. Li et al. analyzed the electromagnetic radiation and mechanical properties of coal under uniaxial impact loading, and concluded that incident energy magnitude is the dominant factor influencing the electromagnetic radiation energy of coal, and the gray correlation theory can better quantify the dynamic properties of coal [9].

However, coal is present underground in a three-dimensional stress field [21,22,23,24]. Through modification of the SHPB system, the coal dynamics test gradually switched from one-dimensional dynamic loading to triaxial combined dynamic and static loading. The mechanical behavior of rocks under coupled uniaxial dynamic and static loading was analyzed according to the stress environment, and this explained the coal bumps mechanism under high stress [25]. Feng et al. investigated the deformation and failure characteristics of coal under coupled dynamic and static loading, and concluded that there is correlation for coal between energy dissipation and loading rate, compression strength, and peak stress [26]. Xie et al. considered the stress field of coal at different depths, and confirmed the feasibility of a triaxial combined dynamic and static loading electromagnetic SHPB test system that could be realized [27]. Moreover, Liu et al. conducted a series of experimental studies on sandstone based on the true triaxial SHPB system, and found the constraint-dependent dynamic properties under multi-axial prestressing [28]. According to existing studies, Kong and Wang developed a triaxial SHPB system for gas-bearing coal, considered the effect of combined dynamic and static loading and gas pressure on the coal in the tests, and applied the control variable method to the axial and confining stress. From the test results, it was concluded that the confining stress increased the compressive strength of the coal in the dynamic loading test, and the axial stress decreased the compressive strength of the coal and reduced the ability of the coal to resist deformation [29,30,31]. Previous studies on coal dynamics focused more on uniaxial and triaxial combined dynamic and static loading, and rarely applied the realistic stress environment for coal in SHPB test parameters. Therefore, it is of great theoretical significance to carry out triaxial dynamic mechanical test research on coal with sufficient consideration of in-situ stress at different depths.

This study focused on the in-situ stress field for coal with overburden depths of 100 m to 600 m, and the active triaxial SHPB test system was used to investigate the dynamic mechanical behavior of coal. Dynamic loading tests of coal at low, medium, and high loading rates were undertaken in axial and confining stress related to different depths. In this paper, the stress–strain curve, the dynamic compression strength, the correlation of failure strain and loading rate, and the energy dissipation of coal during dynamic loading are analyzed. The test results can provide a theoretical basis for the mechanism of coal-rock dynamic disasters and a valuable reference for the monitoring and early detection of dynamic disasters.

2. Experiment

2.1. Sample Preparation

The effect of tectonic movements and in-situ stress fields on coal at different depths influences the success rate of raw coal coring. In this study, the coal specimens required for the experiments were collected from the 2-2 coal seam of Zhang Minggou coal mine in Yulin, Shanxi Province, China. The location of coal specimens are as shown in Figure 1. The coal seam in this area is less influenced by geological and tectonic movements, and the coal fractures and weathering degree are comparable. Large pieces of raw coal were taken out from the 2-2 coal seam at a burial depth of 76.0 m, drilled (the coring direction is vertical to the raw coal bedding), processed, and polished into Ø50 × 25 mm cylindrical specimens with a length-to-diameter ratio of 0.5. The end face of the specimen is vertical to the axis with a maximum deviation not more than 0.25°, the flatness tolerance of the two end faces is less than 0.01 mm, and the parallelism tolerance of the two end faces is less than 0.02 mm, as shown in Figure 2, following the ISRM rock dynamics test standard.

To reduce the error of the coal specimens in the dynamic loading rate experiment, wave velocity and density tests for the processed coal specimens were carried out, and specimens with similar parameters were selected for the test. The basic physical and mechanical parameters of the specimens are shown in

Table 1. Physical parameters and mechanical properties of coal specimens.

Specimen	Uniaxial Compressive Strength/MPa	Density/(g/cm3)	Wave Speed /(m/s)	Poisson’s Ratio	Elastic Modulus /GPa	Failure Strain
Raw coal	37.21	1.30	1338.63	0.20	1.79	0.024

.

2.2. Triaxial Split Hopkinson Press Bar System

To truly simulate the stress environment around coal at different depths, the in-situ stress multifunctional geomaterial dynamic testing system was used for the test, which is a modified active triaxial SHPB test system, developed independently by the Rock Engineering Catastrophe and Protection Laboratory of Tianjin University. The system, as shown in Figure 3, consists of five main parts: the SHPB main bars, the bullet launch subsystem, the axial loading subsystem, the active confining stress loading subsystem, and the data acquisition subsystem.

The main bars include a strike bar (Ø50 × 350 mm), an incident bar (Ø50 × 3000 mm), and a transmission bar (Ø50 × 1800 mm), which are produced of alloy steel with an elastic modulus of 211 GPa and a wave velocity of 5270 m/s, and the diameter of 50 mm can significantly reduce the dispersion effect of the stress wave in the propagation process. The bullet launch subsystem includes an air compressor, a high-pressure gas chamber, and a strike bar. The air is compressed through the compressor to the high-pressure gas chamber, whose gas valve is adjusted to the required air pressure for impact loading to drive the strike bar. The axial loading subsystem mainly includes a kinetic energy trap and axial compression device; the kinetic energy trap can limit the position of the incident bar so that the axial compression device drives the transmissive bar to achieve axial stress. The active confining stress loading subsystem, as shown in Figure 4a, includes the confining device and hydraulic pump. The hydraulic pump is filled with oil so the confining device can realize active confining stress, and the coal specimen is wrapped with the jacket and the rubber ring to isolate the hydraulic oil inside the device. The triaxial dynamic loading for the coal specimen is shown in Figure 4b. The data acquisition subsystem consists of a super dynamic strain gauge and an oscilloscope to extract, amplify, and record the signals generated in the triaxial dynamic loading.

The theoretical principles for triaxial dynamic compression follow two basic assumptions: the one-dimensional stress wave theory and the stress homogenization assumption [15]. The dynamic response for the coal specimen can be obtained from the strain gauges on the incident and transmitted bars during dynamic tests, and the incident, reflected, and transmitted strains can be obtained by the strain-voltage conversion coefficients with Equation (1), and then calculated by substituting in Equation (2) to obtain the specimen stress (${\sigma }_{\left(t\right)}$), strain (${\epsilon }_{\left(t\right)}$), and strain rate (${\stackrel{•}{\epsilon }}_{\left(t\right)}$), respectively [32].

$${\epsilon }_{(t)}=\frac{2\Delta U_{(t)}}{K_1{K}_2{U}_0}$$

(1)

where ${\epsilon }_{\left(t\right)}$ is the strain, $U_{\left(t\right)}$ is the voltage output by strain gauge, $K_1$ is the sensitivity coefficient of the strain gauge, $K_2$ is the amplification coefficient of the super dynamic strain gauge, and $U_0$ is the supply bridge voltage.

$$\begin{array}{l}{\sigma }_{(\mathrm{t})}=\frac{AE}{2A_{\mathrm{s}}}\left[{\epsilon }_{i(t)}+{\epsilon }_{r(t)}+{\epsilon }_{t(t)}\right]\\ {\epsilon }_{(\mathrm{t})}=\frac{C}{L_{\mathrm{s}}}{\displaystyle {\int }_0^t\left[{\epsilon }_{i(t)}-{\epsilon }_{r(t)}-{\epsilon }_{t(t)}\right]}dt\\ {\stackrel{•}{\epsilon }}_{(\mathrm{t})}=\frac{C}{L_{\mathrm{s}}}\left[{\epsilon }_{i(t)}-{\epsilon }_{r(t)}-{\epsilon }_{t(t)}\right]\end{array}$$

(2)

where i, r, and t are the incident, reflected, and transmitted waves, respectively, $A$ is the cross-sectional area of the bar, $E$ is the elastic modulus of the bar, $C$ is the wave velocity of the elastic bar, and $A_s$ and $L_s$ are the cross-sectional area and length of the coal specimen.

$P_1$, and $P_2$ are the stress in the end faces of the incident and transmitted bars of the coal specimen, respectively, represented with Equation (3).

$$\begin{array}{l}{P}_1=AE({\epsilon }_i+{\epsilon }_r)\\ P_2=AE{\epsilon }_t\end{array}$$

(3)

The ends of the coal specimen satisfy the dynamic stress balance and the internal stress homogenization, which means $P_1=P_2$. Thus Equation (2) can be written as Equation (4).

$$\begin{array}{l}{\sigma }_{(\mathrm{t})}=\frac{AE}{A_{\mathrm{s}}}{\epsilon }_{t(t)}\\ {\epsilon }_{(\mathrm{t})}=-\frac{2C}{L_{\mathrm{s}}}{\displaystyle {\int }_0^t{\epsilon }_{r(t)}}{d}_t\\ {\stackrel{•}{\epsilon }}_{(\mathrm{t})}=-\frac{2C}{L_{\mathrm{s}}}{\epsilon }_{r(t)}\end{array}$$

(4)

2.3. Experimental Scheme

For realistic simulation of in-situ stress of coal at different depths, theoretical analysis of the distribution characteristics of the underground stress field in current domestic coal mines, and comprehensive consideration of the bedding directivity of the coal specimens during coring are required. In the test, the vertical in-situ stress at different depths was used as the axial stress of the specimens, and the average horizontal principal stress was used as the confining stress of specimens. Hoek and Brown gave an empirical equation based on the global in-situ stress measurement sites. The vertical in-situ stress at the different depths can be calculated with Equation (5) [33].

$${\sigma }_v=\gamma h=0.027h$$

(5)

where ${\sigma }_v$ is the vertical in-situ stress, MPa; $\gamma$ is the overlying rock layer capacity,$0.027 \left(\mathrm{MPa}/\mathrm{m}\right)$; and $h$ is the buried depth for test points, $\mathrm{m}$.

Kang conducted 204 in-situ stress tests in 13 mining areas, 6 provinces, 49 coal mines (mining depth from 69.2 m to 1283 m) in China. The coefficient $k$ for the average horizontal principal stress to the vertical in-situ stress can be calculated with Equation (6) [34].

$$k=\frac{{\sigma }_H+{\sigma }_h}{2{\sigma }_v}$$

(6)

where ${\sigma }_H$ is the maximum horizontal principal stress, and ${\sigma }_h$ is the minimum horizontal principal stress.

Based on the linear regression of the in-situ stress test data, the coefficient relationship between the average horizontal principal stress and the vertical in-situ stress is proposed, and Equation (6) can be written as Equation (7).

$$k=\frac{116.5}{h}+0.7$$

(7)

Therefore, based on Equations (5)–(7), the vertical in-situ stress and the average horizontal principal stress for the mining depth of 100–600 m were calculated as the axial and confining stress parameters, respectively, as shown in

Table 2. Experimental scheme and test results.

No.	Depth/m	Axial Stress /MPa	Confining Stress/MPa	Loading Rate	Dynamic Compression Strength/MPa	Failure Strain	Whether Completely Fragmented	Energy Consumption/J	Energy Dissipation Rate	Energy Density /J/cm3
1-1	100	2.7	5.04	957	83.09	0.04	√	222.81	0.49	4.54
1-2	100	2.7	5.04	987	95.11	0.028	√	285.43	0.55	5.82
1-3	100	2.7	5.04	1327	110.42	0.027	√	332.79	0.58	6.78
2-1	200	5.4	6.93	648	81.99	0.04	×	154.65	0.47	3.15
2-2	200	5.4	6.93	935	89.65	0.046	√	317.36	0.45	6.47
2-3	200	5.4	6.93	1276	118.07	0.038	√	376.84	0.46	7.68
3-1	300	8.1	8.82	747	89.65	0.033	×	187.45	0.52	3.82
3-2	300	8.1	8.82	1205	108.23	0.048	×	435.46	0.47	8.88
3-3	300	8.1	8.82	1212	114.79	0.056	×	456.36	0.47	9.30
4-1	400	10.8	10.71	723	94.57	0.043	×	303.26	0.65	6.18
4-2	400	10.8	10.71	952	101.67	0.051	×	329.83	0.47	6.72
4-3	400	10.8	10.71	1039	110.42	0.016	√	425.92	0.45	8.68
5-1	500	13.5	12.60	958	104.95	0.033	×	203.21	0.49	4.14
5-2	500	13.5	12.60	1022	111.51	0.052	×	326.80	0.45	6.66
5-3	500	13.5	12.60	1313	102.76	0.011	√	390.28	0.37	7.95
6-1	600	16.2	14.49	1129	113.70	0.047	×	372.58	0.50	7.59
6-2	600	16.2	14.49	1332	135.56	0.054	×	406.21	0.45	8.28

.

In the experiment scheme, three coal specimens were selected under the axial and confining stress parameters determined at each depth group. According to the different disturbances of the coal mines, the dynamic loading tests of coal were undertaken under low, medium, and high loading rates, and the dynamic mechanical behavior and energy dissipation of the coal were investigated. The low loading rate can simulate the disturbance to the coal microelements caused by rock drilling, roof stress, or mining stress; the medium loading rate can simulate the dynamic loading to the coal microelements during small mine shocks; and the high loading rate can simulate the high dynamic loading to the coal microelements during the dynamic disasters such as coal bumps and outbursts of coal and gas.

2.4. Experimental Procedures

The 18 specimens were divided into six groups for the test as shown in Figure 5. (1) The two ends of the coal specimens were tinted with vacuum grease and were placed coaxially between the incident bar and transmitted bar. Meanwhile, the suitable shaper was chosen at the front of the incident bar; (2) the coal specimen was loaded to a preset stress by means of the axial compression device; (3) the confining device was sealed with hydraulic oil to load to the preset confining stress; (4) the air was compressed by the air compressor, and then the air valve was adjusted to the preset air pressure for the test; (5) the data acquisition system was adjusted to the state “waiting for trigger”, and then the launch switch was pressed and the test data were recorded; and (6) once the test was completed, the confining stress was unloaded first, and the fragmented specimen was removed and saved in a sealed bag for subsequent analysis.

3. Results and Discussion

3.1. Stress Equilibrium

The results of triaxial dynamic compression tests on coal with different depths are shown in Table 2, including loading rate, dynamic compression strength, failure strain, fragmentation condition, energy consumption, energy dissipation rate, and energy density of the coal specimens.

In the test, the original waveform signals of the incident, reflected, and transmitted waves were collected, as shown in Figure 6a. Meanwhile, the dynamic stress balance of the coal specimens was reached, as shown in Figure 6b, which was in accordance with the recommended specification of ISRM [32]. Therefore, the dynamic loading process was sufficient for the dynamic stress at the ends of the incident bar and transmitted bar to reach balance, and the stress is homogenized across the coal specimen, and there is a constant loading rate before the peak load [16].

3.2. Stress–Strain Behavior

The dynamic stress–strain curves of coal with three different loading rates under different depth stress fields are shown in Figure 7. From Figure 7, it is shown that the dynamic stress–strain curves of the coal with different loading rates in the realistic stress field from 100 m to 600 m have significant variability. The stress–strain curve of coal under low loading rate at the same depth with the same axial and confining stress went through the fracture compacting period, linear elastic deformation period, elastoplastic period, plastic deformation period, and strain softening period, which is better in line with the stress–strain curve of conventional compression tests of coal [35,36,37], according to the previous studies on the combined dynamic and static loading of coal [30]. The stress–strain curve of the coal specimen is almost without the fracture compacting period. In this study, the mechanical behavior of coal under high loading rates well verified the results of previous studies, and none of its stress–strain curves showed the fracture compacting period. From Figure 7a–d, it can be seen that when the coal depth is below 500 m, the horizontal principal stress and vertical in-situ stress of the coal at this depth are small, which means the axial and confining stress in the test are small. The smaller axial stress does not allow the internal fracture of the coal to be completely compacted, therefore, both show the classical stress–strain in each phase with a low loading rate, while the high loading rate makes the coal leap over the fracture compacting phase and reach the elastic deformation phase directly during the dynamic loading process. From Figure 7e,f, it can be seen that when the coal depth reaches 500 m, the axial stress parameter at this depth has allowed the internal fracture of the coal to be compacted; therefore, the dynamic stress–strain curve no longer shows the fracture compacting period, regardless of whether the loading rate is high or low. In addition, with the increasing depth, the stress–strain curves all showed that the elastic deformation phase of the coal line became smaller and smaller, and the elastoplastic deformation period became longer.

According to previous studies, =when the stress–strain curve showed an obvious post-peak stress rebound in the process of the compression test, it means the coal was damaged but not completely fragmented; when the stress–strain curve showed obvious post-peak stress softening, it means that the coal was completely fragmented [38,39,40]. Based on these understandings, whether each group of coal specimens was completely fragmented was determined in the test. A specific analysis of the stress–strain curves under dynamic loading of coal at different depths yields: From Figure 7a, the 100 m in-situ stress field coal specimens were fragmented at all three loading rates, and the peak strength of the coal increased as the loading rate of the specimens increased from 1-1 to 1-3, but the failure strain corresponding to the peak strength decreased gradually. From Figure 7b, although coal specimen 2-1 has similar dynamic strength as 1-1, the stress–strain curve of 2-1 shows a significant post-peak rebound of its coal, indicating that the strength required for coal damage is higher with increasing depth; specimen 2-3 has a greater dynamic test loading rate than 2-2 and thus has a higher dynamic compression strength, but the failure strain is still decreasing. From Figure 7c, none of the specimens are completely fragmented, and as the loading rate increases from 3-1 to 3-3, the peak strength corresponds to the failure strain but shows a gradual increase. From Figure 7d, coal specimen 4-3 was completely fragmented at high loading rates under the test parameters of 400 m depth, 10.8 MPa axial stress, and 10.71 MPa confining stress, but the failure strain corresponding to the peak strength decreased suddenly, with a greater tendency to decrease than that of the completely fragmented specimens in 100 m and 200 m. From Figure 7e, at a depth of 500 m, the confining stress of the coal reaches 12.6 MPa, and the stress–strain curves of specimens 5-1 and 5-2 under the action of high loading rate also show an obvious rebound, indicating that there is still some residual strength after the peak of the coal under the action of high confining stress, and it is more difficult to make the specimens undergo complete fragmentation. Specifically, the dynamic mechanical behavior of the coal at 500 m depth verifies a sudden increase in failure strain at high loading rates, which is comparable to the results for specimen 4-3 at high loading rates. From Figure 7f, the dynamic loading rate of the coal specimen has reached the maximum value of the SHPB system in the test at a depth of 600 m with an axial stress of 16.2 MPa and confining stress of 14.49 MPa. Combining the stress–strain curve of the coal and the analysis of the macroscopic damage characteristics of the coal after the test, it can be concluded that the specimen is not completely fragmented. Therefore, the system might be modified, or the specimen diameter might be reduced to achieve a higher loading rate if the test is to be continued.

3.3. The Relationship between Failure Strain and Dynamic Compressive Strength with Various Loading Rates

Dynamic compressive strength and failure strain are important parameters of the dynamic mechanics of coal, while the loading rate determines the magnitude of the impact load applied to the coal specimen in each test [16,32]. Based on existing investigations for coal-rock dynamics, the loading rate is related to the dynamic mechanical behavior of coal, which means rate dependence [41,42,43]. The dynamic mechanical parameters of coal at different depths versus the loading rate are shown in Figure 8a,b. To visualize the relationship between dynamic compression strength, failure strain, and loading rate, low, medium, and high loading rates are represented in the horizontal coordinates of Figure 8a,b, instead of direct values.

Figure 8a shows that the dynamic compression strength of the specimens steadily increases with a higher loading rate at the same depth, and the coal specimens show a good rate dependence in the triaxial dynamic test. In the previous study on the triaxial dynamics of coal, the controlled variable method was used to show that varying the confining stress limits the deformation of the coal and increases the compressive strength; the axial stress reduces the ability of the coal to resist deformation, and the coal is more vulnerable to damage by impact [29]. In this study, from Figure 8a, it can be concluded that the dynamic compression strength of coal increases with increasing depth for the same loading rate level. The average growth rate of compression strength with increasing depth was 6.24%, 7.82%, and 0.43% for three loading rates: low, medium, and high, respectively. These results indicate that although both the axial stress and the confining stress parameters are increasing, the dynamic compression strength of the coal still increases. Thus, the effect of the confining stress on the dynamic compression strength of coal is more profound than the axial stress. Meanwhile, these results also reveal that the horizontal principal stress has a greater effect on the breeding process of coal-rock dynamic incidents than the vertical in-situ stress, and the effect becomes more obvious with the increase in mining depth.

The relationship between coal failure strain and loading rate in the test is shown in Figure 8b. The damage strain appears to vary with increasing loading rate; incompletely fragmented and completely fragmented coal at different depths reveal different properties. To demonstrate more clearly the variability of failure strain and loading rate for coal in different fragmentation states, Figure 9a,b shows the test failure strain versus loading rate for incomplete and complete fragmentation, respectively.

From Figure 9a, the failure strain of coal is gradually increasing with the increasing loading rate at the same depth, which indicates that the internal cracks of coal in the incompletely fragmented state propagate to form damage, but there is still a bearing margin after the peak load. Moreover, the failure strain of coal is gradually becoming larger with the increase in depth, which illustrates the deeper the depth, the higher dynamic load required for the occurrence of the dynamic disaster. From Figure 9b, it can be concluded that the failure strain is decreasing while the coal is in the in-situ stress state and complete fragmentation after impact loading. The decreasing trend becomes larger with increasing depth, which also confirms the conclusion analyzed in the stress–strain curve. From Figure 8b and Figure 9b, it can be shown that when the coal depth reaches 400 m and the high loading rate leads to complete coal fragmentation, the failure strain suddenly decreases and is even smaller than the failure strain at static loading uniaxial compressive strength. This might be related to the greater depth of coal resulting in large axial and confining stress parameters. The triaxial pre-loading of the coal leads to expansion of the internal fractures, which causes partial deformation before the dynamic load is applied and reduces its damage strain. This also implies that when coal is under the higher horizontal principal stress and vertical in-situ stress in the process of dynamic disaster breeding, the internal accumulated elastic deformation energy causes the coal to damage. However, there is still the potential for a dynamic incident when the dynamic loading occurs.

From Figure 7d,e and Figure 9b, it can be concluded that the failure strains of specimens 4-3 and 5-3 suddenly drop in the high loading rate, which is lower than the failure strains of coal in the uniaxial compression state. Therefore, discussion and analysis of this phenomenon are necessary to better reveal its causes. The stress–time curves and theoretical curves of specimens 4-3 and 5-3 are shown in Figure 10. It can be shown that both specimens were unloaded before reaching the desired peak strength during dynamic loading, and the stress dropped suddenly to lose the load-bearing capacity, which is comparable to rock fracturing [44]. It is clear from Figure 10 that axial and confining stress parameters increase with increasing overburden depth of coal. Pre-loading makes internal fractures appear in the coal with extension penetration before dynamic loading, which reduces the compressive strength of coal. As a result, slight strain in the coal occurred during dynamic loading, and the specimens were completely broken before reaching peak loading. Thus, large variability in the test results appeared. The result also verifies that the in-situ stress changes the physical and mechanical properties of coal during the breeding process of the dynamic disaster. Finally, there are dynamic disasters such as low parameters, low index of outburst, and extrusion.

3.4. Energy Dissipation

In the SHPB test, the energy consumption of the coal specimen can be given by the following equation [12,45]

$$W=W_i-(W_r+W_t)$$

(8)

where $W$ is the energy consumption of the coal specimen, and $W_i$, $W_r$, and $W_t$ are the energy carried by the incident, reflected, and transmitted waves, respectively, which can be calculated from Equation (9) as follows.

$$\begin{array}{l}{W}_i=AEC{\displaystyle {\int }_0^t{\mathsf{\epsilon }}_{(i)}{}^2}dt\\ W_r=AEC{\displaystyle {\int }_0^t{\mathsf{\epsilon }}_{(r)}{}^2}dt\\ W_t=AEC{\displaystyle {\int }_0^t{\mathsf{\epsilon }}_{(t)}{}^2}dt\end{array}$$

(9)

where $A$ is the cross-sectional area of the bar, $E$ is the elastic modulus of the bar, $C$ is the wave speed of the elastic rod, and ${\epsilon }_{\left(i\right)}$, ${\epsilon }_{\left(r\right)}$, and ${\epsilon }_{\left(t\right)}$ are the incident, reflected, and transmitted strains with time, respectively.

In the test, the energy dissipation rate and energy density of the coal specimen can be determined by Equation (10).

$$\begin{array}{l}N=\frac{W}{W_i}\\ e_d=\frac{W_{}}{V}\end{array}$$

(10)

where $N$ is the energy dissipation rate of the coal specimen, $e_d$. is the energy density of the coal specimen, and $V$ is the volume of the specimen.

Figure 11 shows the energy dissipation in coal specimens at different depths. From the energy perspective, it is easy to understand the absorption of incident wave energy by the coal and the energy required for its fragmentation. Figure 11a shows that the coal during triaxial dynamic loading, regardless of the depth, exhibits good homogeneity of growth in energy consumption. For the same depth, the energy consumption of the coal steadily increases with loading rate and approaches linearity. For the same level of loading rate, the energy consumption corresponding to the greater depth of the coal also increases steadily. It is interesting to note that the fracture energy of coal increases with depth, so the critical value of stress level for the occurrence of dynamic disasters increases as well. Figure 11b shows that the majority of the coal energy dissipation rate ranges between 0.4 and 0.5, indicating that the energy transmitted by the incident wave is absorbed well by the coal for fragmentation. Figure 11c shows the energy density of the coal specimen, which also reveals a steady increase in inhomogeneity with depth and loading rate. In comparison with the results of previous studies on energy dissipation during uniaxial dynamic loading of coal [9,12,26], the energy consumption, energy density, and energy dissipation rate of coal in this study are higher. The reasons might be as follows: (1) The coal specimens in this test are produced from raw coal and the uniaxial compression strength is higher than that of tectonic coal. Thus, a higher loading rate and crushing energy are required for the higher-strength coal. (2) The previous research on coal energy dissipation used uniaxial dynamic loading. However, in this study, the coal in this test is in the triaxial preloading environment. During dynamic loading, the compressive strength and resistance to deformation of coal are increased by the confining stress. As a result, the energy dissipation rate of coal is increased. In addition, these results could determine the energy per unit volume of coal completely fragmented at different depths, which could be applied in coal seams with impact or prominence tendencies. Additionally, the critical value of the energy level per unit of coal might be calculated for dynamic disasters.

3.5. Prospects

The dynamic mechanical behavior of coal with different in-situ stress fields is of great benefit to the study of the occurrence mechanisms of coal-rock dynamic incidents. Based on the above discussions, prospects on this hot topic could be analyzed as per the following perspectives.

(1)

The in-situ stress in coal mines increases with overburden depth. The SHPB test system could be modified to achieve larger loading rates. Thus, the dynamic mechanical behavior of coal at depths higher than 600 m might be simulated.

(2)

In this study, the depth gradient for the two groups of tests was 100 m. It is suggested to reduce the depth gradient and divide the loading rate into multiple groups for experimental studies. This could quantify the complete fragmentation energy for coal at different depths.

4. Conclusions

In this paper, the dynamic compression tests of coal under in-situ stress fields with different overburden depths were successfully carried out on a triaxial SHPB test system. The dynamic mechanical behavior and the rate dependence of coal at different depths, and the energy dissipation of specimen fragmentation were analyzed and discussed, and the main conclusions were drawn as follows.

(1)

With increasing depth, the effect of the confining stress on the dynamic compression strength of coal is more profound than the axial stress under the same loading rate. The results indicated that the horizontal principal stress plays a main role in the mechanical properties of coal, more than vertical in-situ stress, which are mutually verified. The monitoring of horizontal principal stress should be focused on in the prediction of dynamic incidents.

(2)

The dynamic compression strength and failure strain of coal gradually increase with depth. Meanwhile, the energy dissipation and energy density per unit volume of coal also increase with depth. Higher critical energy is required for dynamic incidents in a deep mine. Thus, the damage degree of the accident might be drastic in a case of a dynamic disaster at the depth of deep mining.

(3)

During the dynamic loading of coal under in-situ stress conditions, the relationship between the failure strains of incompletely and completely fragmented specimens and the loading rate is variable. The coal could be completely fragmented and the failure strain is decreasing at high loading rates. Furthermore, the failure strain decreases suddenly when the loading rate is high enough. However, the failure strain of incompletely fragmented coal increases with the loading rate.

The findings of this study show that the horizontal principal stress of coal seams could be effectively monitored to predict and control coal-rock dynamic incidents. The results reveal the dynamic mechanical behavior of coal during coal-rock dynamic incidents, which might provide a theoretical basis and valuable reference for the mechanisms of coal-rock dynamic disasters.