Experiments on Mechanical Response and Energy Dissipation BehaviorofRockburst-ProneCoal SamplesUnder ImpactLoading

College of Mining, Liaoning Technical University, Fuxin, China 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, China Fuxin Hongdikan New Energy Co., Ltd, Fuxin, Liaoning Province, China School of Mechanical Engineering, Liaoning Technical University, Fuxin, China


Introduction
Coal and rock mass buried in deep is subjected to a complex geological environment with the depletion of shallow resources and the increase of coal mining depth [1,2]. Coal mass with great stored elastic energy may be subjected to strong impact loading when it is disturbed by mining operations, such as uncovering coal seam from rock mass, engineering blasting, roadway excavation, nearby coal seam mining, resulting in serious mine dynamic disasters such as rockburst, coal and gas outburst accompanyed with a large amount of released energy [3][4][5][6][7][8][9]. ese disasters may lead to great property losses and casualties. erefore, it is much significant to reveal the dynamic mechanical response of coal and rock mass under different impact loadings and the law of energy dissipation in the process of dynamic failure, which may provide a reliable theoretical basis for further understanding of the trigger mechanism of dynamic disasters [10].
Kolsky first proposed the Split Hopkinson Pressure Bar (SHPB) system in 1949 to investigate the dynamic responses [11]. e SHPB tests are usually conducted to determine dynamic properties of brittle materials including concrete, ceramics, rocks, and coals, under a wide range of impact loadings or strain rates of 10 −1 ∼10 −4 s −1 [12][13][14][15]. e coalrock mass under impact loading during coal mining and excavation will produce behavior dynamic responses with a high strain rate. ese dynamic responses include the variation of density, wave velocity, porosity, strength, scale effect, bedding effect, water effect, and energy dissipation [16][17][18][19][20]. Klepaczko et al. studied the elastic and viscoelastic properties of Nova Scotia coal over a wide range of strain rates (quasistatic to impact) [21]. Zhao et al. studied on energy dissipation characteristics of coal samples under impact loading [22]. Wang et al. studied the effects of low temperature gradient on dynamic mechanical properties of coal through Split Hopkinson Pressure Bar (SHPB) dynamic impact experiment [23]. Li [30,31]. Moreover, many techniques have also been introduced to modify the SHPB system [32][33][34]. e above research has an important role in promoting the study of mechanical properties of coal and rock under impact loading. Extensive suites of dynamic SHPB tests have been carried on rock and common coal materials, but only a few such dynamic tests have been completed on rockburstprone coals. Most of these experiments only obtained the dynamic stress-strain curve. Here, we supplement this dearth of observations by recovering a full suite of dynamic failure characteristics and energy dissipation laws to contrast the response of rockburst-prone coals (Xinzhouyao coals) against a control sample of rockburst resistant coals (Machang coals) by using the Split Hopkinson Pressure Bar (SHPB) experimental system to reveal the mechanism of coal mine dynamic disasters induced by impact load.

Split Hopkinson Pressure Bar (SHPB) System.
e SHPB system is composed of bullet, bullet velocimetry, incident bar, transmission bar, buffer bar, and damper, shown in Figure 1. e bullet is made of Cr alloy rigid with 37 mm in diameter and 300 mm in length. e incident and transmission bars are variable cross-section bars with 50 mm in diameter and 1200 mm in length. e diameter and length of the buffer bar are 50 mm and 1000 mm, respectively. e stress wave velocity in the pressure bar is 5190 m/s, the elastic modulus is 210 GPa, and the density is 7.8 × 10 3 kg/m 3 .

Basic Principles of the SHPB System.
In the experiment, high pressure nitrogen is used to provide impact loading for the bullet. e bullet moving velocity is controlled by the pressure on the incident bar. When the elastic stress wave propagates to the interface between the specimen and the incident bar, the stress wave will reflect and transmit. At the same time, an electrical signal is formed. All electrical signals are collected by strain gauges at both ends of the incident and transmission bars and delivered to the data acquisition system.
Based on the one-dimensional stress wave theory, the collected strain signal is processed by the three-wave method to obtain the dynamic stress-strain relationship of coal samples [23]: where σ s (t), ε s (t), _ ε s (t) are the dynamic stress, strain, and strain rate of coal samples respectively; A and A s represent the cross-sectional area of the elastic bar and coal sample, respectively; E represents the elastic modulus of the elastic bar; C 0 and L represent the longitudinal wave velocity of the elastic bar and the length of the specimen, respectively; ε i (t), ε r (t), ε t (t) represent the strain value of incident wave, reflected wave, and transmitted wave, respectively.
Let the cross-sectional area of the two bars be the same bar, the relation between the incident, reflected, and transmitted waver induced strain can be obtained： Substituting equation (2) into equation (1), the basic principles of the SHPB experiment can be obtained: e SHPB experiments involve five kinds of energies, including bullet carried energy, incident energy, reflected energy, transmitted energy, and dissipated energy. e incident, reflected, and transmitted energy of the test system can be expressed as follows [25]: where W I , W R , W T are incident, reflected, and transmitted energy, respectively; σ i , σ r , σ t are the stress corresponding to the incident wave, reflected wave, and transmitted wave on the pressure bar, respectively; ε i , ε r , ε t are the strains corresponding to the stress of each stress wave on the pressure bar; A is the cross-sectional area of pressure bar, A � πr 2 , r is 25 mm; E is the elastic modulus of the bar material, 210 GPa; C is the stress wave velocity in the one-dimensional state, C � ��� E/ρ, ρ is the material density of the pressure bar. According to the mass conservation law, the energy dissipation in the failure process of coal sample (W L ) can be expressed as follows:  Table 2.
In order to ensure the stable transmission of the transmitted wave, the vaseline reagent was evenly smeared on both ends of the coal sample to keep it fully lubricated and coupled with the two bars, and the transverse strain caused by the difference in Poisson's ratio between the bar and the coal sample was eliminated. e coal sample is placed between the incident bar and the transmission bar, as shown in Figure 2. Figure 3 shows the relationship between the average strain rate of two groups of coal samples and the impact velocity of bullets.

Effect of Impact Velocity on Strain Rate.
With the increase of impact velocity, the strain rate of both two groups of coal samples increases significantly. ere is an intersection point between the curves of the two groups of coal samples because the rockburst-prone coal sample is harder. Under the low impact velocity, the strain rate will rise faster. e initial strain rate of nonprone coal samples is small, as there are numerous small cracks within the coal sample to undergo a compaction deformation process in nonprone coal samples. However, the average strain rate of the nonprone coal sample increases with the impact velocity when the impact velocity reaches 8.71 m/s, indicating that the impact velocity at this time is the critical value. en, the strain rate will also increase with the impact velocity, which also meets the toughening effect of the impact velocity and the strain rate.

Dynamic Stress-Strain Curve.
Because the stress-strain curves of coal samples show good similarity under the same strain rate, a typical stress-strain curve is selected for each strain rate in order to compare the stress-strain curves of coal samples at different strain rates more intuitively as shown in Figure 4. At the same time, the static stress-strain curves of coal sample are shown in Figure 5. It can be found  that the static stress-strain relationship and the dynamic stress-strain relationship show obvious differences. e static stress-strain curve can be divided into four stages: compaction stage, elastic stage, plastic stage, and failure stage. e dynamic stress-strain curves of the two groups of coal samples are basically the same. e curve can be divided into five stages: the original nonlinear compaction stage, linear elastic stage, microfracture extension stage, plastic fracture propagation stage, and rapid unloading failure stage. e peak stress, peak strain, and elastic modulus can be extracted from the stress-strain curve of each coal sample. e basic mechanical parameters of the three coal samples at each strain rate are averaged in order to reduce the experimental error, and then the relationship between each mechanical parameter and the strain rate is analyzed.

Variation of Dynamic Elastic Modulus with Strain Rate.
In order to reflect the difference of each coal sample and the change rule of the elastic modulus of the coal sample with the strain rate, the elastic modulus obtained from three repeated experiments at each strain rate is retained in the image, and the fitting curve of the average elastic modulus and the strain rate is made, as shown in Figure 6. e dynamic elastic modulus of the two groups of coal samples increases with the strain rate, and the correlation between them is significant. e dynamic elastic modulus of rockburst-prone coal samples increases rapidly from 7.42 GPa to 27.56 GPa, with the strain rate from 87.76 s −1 to 116.83 s −1 , increased by 3.71 times, while the static elastic modulus of coal samples is 3.66 GPa, increased by 7.53 times. e dynamic elastic modulus of the nonprone coal samples increases from 1.14 GPa to 2.34 GPa, increased by 2.05 times, and the static elastic modulus is 0.85 MPa with 2.75 times of increment. e relation between dynamic elastic modulus and strain rate of two groups of coal samples is fitted as follows:

Variation of Peak Stress with Strain Rate.
e relationship between strain rates and peak stress is shown in Figure 7. e same impact loading was applied on the two groups of coal samples. With the increase of strain rate, the peak stress of the rockburst-prone coal samples increases from 31.25 MPa to 117.64 MPa, increased by 3.76 times. e peak stress increases from 19.24 MPa to 98.14 MPa, increased by 5.1 times, while the static peak stress is 17.73 MPa, increased by 5.54 times. e dynamic peak   strain and strain rate of the two groups of coal samples increase approximately linearly in the range of 6.31∼10.82 m/s. As the impact velocity reaches 11.64 m/s, the dynamic peak stress of outburst prone coal sample increases faster. e reason may be that there is a certain strain rate critical value in coal samples. When it exceeds this critical value, the internal stress accumulation rate of coal increases and the outburst prone coal seam is more likely to trigger a rockburst disaster. Relations between the dynamic peak stress and strain rate for the two groups of coal samples can be fitted as follows:

Variation of Peak Strain with Strain Rate.
e relationship between peak strain and strain rate is shown in Figure 8. e peak strain of rockburst-prone coal samples  Shock and Vibration increases from 1.96 × 10 −3 to 7.73 × 10 −3 in the strain rate range of 87.76-168.83 s −1 . Within the same strain rate range, the peak strain of nonprone coal samples increases from 1.31 × 10 −3 to 10.43 × 10 −3 , showing an obvious increase with strain rate under dynamic compression. Because the nonprone coal samples are looser with a large number of internal cracks developed, the deformation needs an excessive time, and then the peak strain will increase with the strain rate at a faster speed. e relations between peak strain and strain rate of coal samples are fitted as follows:

Relationship between Dynamic Increment Factor and
Strain Rate. Dynamic increment factor (DIF) is the ratio of dynamic compressive strength to static compressive strength [24].
DIF � σ f σ fs , (9) where σ f is the dynamic compressive strength of the coal sample, and σ fs is the static compressive strength of the coal samples. e curves of dynamic increment factors of two groups of coal samples at different strain rates are shown in Figure 9.
e DIF of rockburst-prone and nonprone coal samples show a significant strain rate increasing effect. Under the condition of low strain rate, the DIF of rockburst-prone coal samples rapidly increases, while the DIF of nonprone coal samples increases more significantly, as well as the dynamic compressive strength.

Effect of Impact Velocity on Stress Wave
Energy. e variation of stress wave energy of coal samples with impact velocity is shown in Figure 10

Variation of Dissipated Energy with Strain Rate.
e curves of dissipated energy versus strain rate of both rockburst-prone and nonprone coal samples are shown in Figure 11. e dissipated energy for crushing coal samples rises rapidly with the increase of strain rate, showing a significant strain rate effect. e strain rate of rockburstprone coal samples is in the range of 87.76-168.83 s −1 , and the dissipated energy increased from 9.83 J to 82.45 J by an increment of 8.39 times. e strain rate of the nonprone coal sample is in the range of 67.43-220.28 s −1 , and the dissipated energy increases from 5.45 J to 77.90 J by an increment of Shock and Vibration 14.29 times. With the increase of the strain rate, the original cracks of the coal sample could extend and develop, and new cracks would be generated, so the energy used for the destruction of the coal sample continues to increase. e dissipated energy of rockburst-prone coal sample grows faster, and the rate of the increase of the dissipated energy is more stable.

Conclusions
(1) e strain rate of both two groups of coal samples increases significantly with the increase of impact velocity, but there is a turning point in the strain rate change of the nonprone coal sample. e static stress-strain relationship and the dynamic stressstrain relationship show obvious differences. e dynamic stress-strain curve can be divided into four stages: the initial nonlinear compaction stage, the linear elastic stage, the microfracture evolution stage, the plastic fracturing stage, and the rapid unloading stage. (2) e dynamic elastic modulus of coal samples increases with the increase of strain rate. However, the dynamic elastic modulus and strain rate strengthening characteristics of rockburst-prone coal samples are more significant. e peak stress and peak strain of both rockburst-prone and nonprone coal samples show an obvious increase effect with strain rate under impact loading. low strain rate, the rate correlation between rockburst-prone and nonprone coal samples is similar. However, with the increase of strain rate, the strain rate strengthening of rockburst-prone coal is more significant. (4) With the increase of impact velocity, the incident, reflected, and transmitted energy of both rockburstprone and nonprone coals increase with varying degrees. e energy of the rockburst-prone coal sample is more likely to be concentrated than that of nonprone coal sample, and the dissipated energy is greater with obvious strain rate correlation.

Data Availability
e experimental data used to support the findings of this study are included within the article.

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