Study on Bursting Liability of Coal-like Material with Pores and Anchors Based on Impact Kinetic Energy Characteristics

Abstract

Drilling unloading, and bolt support are widely used in the practice of coal mine roadway engineering as the means of impact prevention and support. However, the evaluation index of intact coal body is still used in bursting liability evaluation, and the evaluation results obtained do not match with the actual dynamic phenomena in the field, resulting in inaccurate evaluation results and even bringing serious impact accidents. In this paper, uniaxial compression and uniaxial loading/unloading tests are conducted on specimens in different states, and common evaluation indexes are used to evaluate the bursting liability of specimens in different states, and the impact kinetic energy of crushed blocks during uniaxial compression is calculated. Based on this, the bursting liability criterion based on the impact kinetic energy of the crushed block is established and the common bursting liability evaluation index is modified. The bursting liability obtained by the bursting liability discrimination criterion based on the impact kinetic energy of the crushed block is more consistent with the laboratory dynamic phenomena. Therefore, the bursting liability evaluation results based on the impact kinetic energy of the crushed block are more consistent with the actual engineering. And the numerical simulation results verify the correctness of the bursting liability criterion based on the impact kinetic energy of the crushed block.

1. Introduction

Rock burst is a dynamic disaster phenomenon caused by sudden release of elastic deformation energy gathered in underground engineering surrounding rocks resulting from excavation or other external disturbances, which is extremely destructive and seriously threatens the safe and efficient production of coal mines. And it is one of the important disasters faced by coal mining at home and abroad [1,2,3,4]. For deep mining [5], the ground stress is always at a high level due to the high elastic energy stored in the rock. So how to evaluate the bursting liability of the surrounding rock becomes an important research topic to ensure safe production. Based on laboratory tests and field measurements, domestic and foreign experts have studied this key issue from the perspectives of energy evolution, time variation, and damage strength.

The occurrence of rock burst is a nonlinear dynamic process caused by the sudden release of steady-state energy accumulated in the coal and rock body within a very short period of time triggered by mining operations. Therefore, the entire deformation process of bump-prone coal samples taken from Zhaogezhuang Mine, Kaiping Basin in China was investigated by using infrared thermography and acoustic emission technique simultaneously and continuously. Uniaxial compression loading and cyclic loading tests on bump-prone coals were monitored by TIR observation system and acoustic emission in real time. The strain, acoustic emission and IRR features were analyzed comparatively to investigate the precursory characteristics of specimen failure [6]. Yang Lei et al. [7,8] carried out acoustic emission tests under uniaxial compression on coal bodies with strong, weak and no bursting liability, and analyzed the acoustic emission energy characteristics of coal bodies and the spatial and temporal evolution of localization events, which clarified the correlation between acoustic emission and bursting liability to a certain extent. Wang et al. [9] studied the relationship between the bursting liability of coal rock body and the rupture charge and acoustic emission characteristics of coal body and explored the charge law of the bursting liability and damage characteristics of coal rock body. Pan et al. [10] investigated the force-electric induction law during the deformation and damage of impact-prone coal bodies under uniaxial compression conditions and concluded that based on the difference of charge signals during the destabilization and damage of coal bodies with different bursting liabilities, the charge signals and the evolution characteristics of related parameters can be used to make a preliminary evaluation of the bursting liability of coal samples. Yao et al. [11] used electromagnetic waves and damage mechanics theory to initially analyze the relationship between electromagnetic radiation energy and loaded mechanical energy, and used experimental and energy theory to study the coupling relationship between electromagnetic radiation energy generated by deformation and damage of coal body under uniaxial compression conditions and energy accumulation and dissipation of loaded coal body, which provided a theoretical basis for electromagnetic radiation prediction of mine impact ground pressure hazard.

The main evaluation indexes used in production practice are the four indexes of specimen elastic energy index [12], impact energy index [13], uniaxial compressive strength and dynamic damage time [14], and the final evaluation results can be obtained by fuzzy algorithm. For field tests, the most ideal state is to monitor the mechanical response of the roadway support system by means of micro seismic monitoring, and stress and displacement monitoring during real coal bursts in the field. Many researchers have used this method to study the mechanical response characteristics of different support systems under dynamic loading conditions [15,16,17,18]. This evaluation method is widely used in the determination of rock bursting liability with its test operation convenience and the comprehensiveness of multi-indicator comprehensive evaluation method. However, since the evaluation angle of each indicator is different, there will be contradictions between evaluation indicators, which is mainly because the evaluation results of different evaluation indicators will be averaged in the weight distribution of fuzzy statistics and the evaluation results will be different from the actual situation to a certain extent [19]. Therefore, many scholars have studied coal rock bursting liability through new indicators, new methods and influencing factors. Gong et al. [20,21] used the area integration method to calculate the total input energy density, elastic energy density, and dissipation energy density values of rock specimens at different unloading points, investigated the quantitative relationship between the three and established a new criterion of rock burst propensity based on the linear energy storage law and the residual elastic energy index. Dai et al. [22] evaluated the bursting liability of coal by studying the modulus index and analyzed the correlation between the modulus index and other bursting liability indexes. Based on the results of experimental and numerical analyses, Zhao et al. [23] established the bursting liability criterion of material destabilization type under the plastic strain gradient theory, derived the damage characteristics and rupture surface morphology at different stress stages, and established the determination criterion of material impact destabilization before the occurrence of coal body damage from the perspective of static equilibrium and energy balance. Zhao et al. [24] established a fine-scale numerical model of coal rock bursting liability based on the granular flow theory and evaluated the bursting liability of coal rock with different homogeneous degrees by analyzing the energy evolution law during the uniaxial compression test. Jiang et al. [25] used the fine-scale test method to analyze the mechanism of mine rock burst occurrence and explore the relationship between the fine-scale structure of coal body and bursting liability by combining the coal mine impact case. Jiang et al. [26] Chen et al. [27] used micro seismic monitoring to study tectonically controlled impact hazards and used micro seismic events as a criterion for stress concentration near the structure and used the drilling method to determine the hazard level.

Drilling, unloading and bolt support are widely used in the practice of coal mine roadway engineering as the means of rock burst prevention and support [28,29,30,31,32]. However, the evaluation index of complete coal body is still used in bursting liability evaluation, and the results obtained do not match with the actual dynamic phenomenon on site, which causes inaccurate evaluation results, and even brings serious accidents. Therefore, it is necessary to study the bursting liability of pore-bearing and anchored coal bodies to be more in line with reality. In view of the above understanding, this paper conducts uniaxial compression tests and uniaxial loading and unloading tests on three types of specimens with different states: intact specimens, specimens with holes and anchored specimens. Based on this, a new method of bursting liability analysis based on the impact kinetic energy of the crushed block is proposed, and the evaluation method commonly used in production practice is modified. The correctness of the new method is verified by numerical simulation method, which provides a new method for the evaluation of bursting liability of the specimen.

2. Bursting Liability Analysis of Specimens in Different States

In this test, coal-like material specimens made of cement, river sand and water with a mass ratio of 3.2:1:0.68 were used. The length of the specimen is 50 mm, the width is 50 mm, the height is 100 mm, and the uniaxial compressive strength of the specimen is about 15 MPa, which is similar to the strength of the coal body in the common roadway surrounding rock. The specimen states are complete specimens, specimens with holes and anchored specimens, as shown in Figure 1. Uniaxial compression tests and uniaxial loading and unloading tests were performed on the specimens in different states, and three identical tests were conducted for each group of tests, and a total of 36 specimens in different states were prepared. The test was carried out on the RJW2000 rock mechanics testing machine, and the displacement meter was fixed at the same horizontal position on both sides of the specimen. The pre-tightening force of the bolt was measured by the through-axis sensor, and the data were collected by the DH3515 N data collection device. The specific test scheme is shown in

Table 1. Parameters of the test program.

Specimen Status	Number of Bolts (pcs)	Drill Hole Diameter (mm)	Preload Magnitude (kN)	Test Method
Complete specimen	0	0	0	Uniaxial compression test
	0	0	0	Uniaxial loading and unloading test
Specimen with holes	0	4	0	Uniaxial compression test
	0	4	0	Uniaxial loading and unloading test
	0	6	0	Uniaxial compression test
	0	6	0	Uniaxial loading and unloading test
Anchored specimen	4	0	0	Uniaxial compression test
	4	0	0	Uniaxial loading and unloading test
	4	0	0.03	Uniaxial compression test
	4	0	0.03	Uniaxial loading and unloading test
	4	0	0.05	Uniaxial compression test
	4	0	0.05	Uniaxial loading and unloading test

.

The hole diameters of the fabricated specimens with holes are 4 mm and 6 mm, respectively, and the holes are located in the center of the specimen and crossed the whole specimen in parallel. There are 4 bolts in the anchored specimen, with 2 bolts on two adjacent sides. Magnesium alloy bolts with a diameter of 3 mm were chosen. The bolt tray is an aluminum alloy ring with 3 mm inner diameter and 15 mm outer diameter, and the magnesium alloy bolt was threaded at both ends, and the preload force was applied to the bolt by clamping the bolt tray with nuts, and the preload forces were 0 kN, 0.03 kN and 0.05 kN, respectively.

The uniaxial compression tests and uniaxial loading/unloading tests were performed on the specimens in different states to obtain the relevant test parameters. Figure 2 shows the compression tests of the specimens in different forms.

In the uniaxial loading and unloading test, it is necessary to set up three unloading points for three times in the pre-peak stage of the failure stress of the specimen. The stress at the unloading point is between 70 % and 80 % of the peak stress of uniaxial compression. The loads at unloading points of specimens in different states are shown in

Table 2. Loads at unloading points of specimens in different states.

Specimen Status	Uniaxial Compression Peak Load/MPa	Unloading Point 1 Load/MPa	Unloading Point 2 Load/MPa	Unloading Point 3 Load/MPa
Complete specimen	14.1	10.5	11.2	11.6
Specimen with hole (hole diameter 4 mm)	11.85	8.2	8.7	9.2
Specimen with hole (hole diameter 6 mm)	8.60	6.3	6.5	6.9
Anchored specimen (preload 0)	14.12	10.2	10.9	11.1
Anchored specimen (preload 0.03 kN)	14.27	9.5	10.1	10.5
Anchored specimen (preload 0.05 kN)	15.12	10.2	10.5	11.2

. Figure 3 shows uniaxial compression and unloading stress-strain curves of specimens in different states.

The bursting liability of the specimens is evaluated by fuzzy statistics of four indexes and the final results are obtained. The four evaluation indexes are: (i) uniaxial compressive strength R_C; (ii) impact energy index K_E; (iii) elastic energy index W_ET; and (iv) dynamic damage time D_t. Among them, uniaxial compressive strength R_C and dynamic damage time D_t can be obtained directly by the test. The remaining two indices are calculated as shown in Equation (1).

$$\left\{\begin{array}{c}{K}_E=\frac{E_s}{E_x}\\ W_{ET}=\frac{{\Phi }_{sp}}{{\Phi }_{st}}\end{array}\right.$$

(1)

In Equation (1), E_s and E_x are the deformation energy consumed after the peak, Φ_sp is the elastic strain energy, i.e., the area under the unloading curve, and Φ_st is the plastic strain energy, i.e., the area enveloped by the loading and unloading curves.

The impact energy index K_E and elastic energy index W_ET can be obtained by applying MATLAB software to the pre-peak and post-peak curves of the stress-strain curve obtained from uniaxial compression of the specimen and the loading and unloading curves of the stress-strain curve obtained from uniaxial loading and unloading of the specimen, respectively, by fitting and applying the integral calculation. The bursting liability of the specimens in different states was calculated and analyzed according to the “Classification of Coal Seam Bursting Liability and Method of Determination of Index” (MT/T174-2000), which is shown in

Table 3. Evaluation results of bursting liability of specimens in different states.

Specimen Status	Uniaxial Compressive Strength/MPa			Dynamic Damage Time/ms			Elastic Energy Index			Impact Energy Index
Complete specimen	11.2	14.9	15.9	540	270	410	2.7	1.8	2.1	5.2	5.4	4.7
Average value	14.1 (strong)			406 (weak)			2.2 (weak)			5.1 (strong)
Specimen with hole (hole diameter 4 mm)	11.5	11.7	12.3	970	1370	450	2.8	1.8	1.5	5.4	5.1	5.4
Average value	11.8 (weak)			930 (None)			2.0 (weak)			5.3 (strong)
Specimen with hole (hole diameter 6 mm)	8.27	9.35	8.2	470	750	950	2.1	1.6	1.3	3.2	7.4	7.2
Average value	8.6 (weak)			717 (None)			1.6 (None)			5.9 (strong)
Anchorage specimen (preload 0)	13.6	14.1	14.2	270	460	110	2.1	1.9	2.3	6.7	6.5	6.5
Average value	14.12 (strong)			280 (weak)			2.1 (weak)			6.6 (strong)
Anchorage specimen (preload 0.03 kN)	14.2	14.1	14.4	260	240	160	1.8	3.1	2.1	7.4	7.6	7.4
Average value	14.2 (strong)			220 (weak)			2.3 (weak)			7.5 (strong)
Anchorage specimen (preload force 0.05 kN)	14.8	15.2	15.2	460	420	570	2.2	2.9	2.2	5.7	5.5	4.7
Average value	15.1 (strong)			483 (weak)			2.4 (weak)			5.3 (strong)

.

Combined with the bursting liability evaluation results of specimens in different states in Table 3, the fuzzy mathematical method was applied to comprehensively evaluate the four indexes in the table. The evaluation results are: strong bursting liability for both intact and anchored specimens, weak bursting liability for specimens with holes (hole diameter 4 mm), and no bursting liability for specimens with holes (hole diameter 6 mm).

3. Bursting Liability Correction Based on Impact Kinetic Energy

From the evaluation results of the commonly used bursting liability indexes, it can be seen that drilling has a significant reduction effect on the bursting liability of the specimen, and the bursting liability of the specimen gradually decreases with the increase in drilling diameter. However, for the anchored specimen, the specimen is strong bursting liability based on the commonly used evaluation indexes, which is not consistent with the actual dynamic phenomenon in the laboratory and the actual field. During the compression tests on the anchored specimens, the dynamic phenomena of the specimen dynamic phenomenon was not obvious, and most of the blocks fell around the specimens except for a few broken blocks thrown far away. It can be seen that although the anchored specimens were evaluated as strong bursting liability, they did not necessarily have obvious bursting liability phenomena, so the bursting liability should be evaluated comprehensively in combination with the dynamic phenomena.

In the uniaxial compression test, the throwing phenomenon of the broken blocks is the most intuitive expression of the impact of the test specimens. The energy consumed by the broken block throwing is the impact kinetic energy of the broken blocks. Therefore, the bursting liability evaluation method can be proposed based on the impact kinetic energy of the broken block. The specific operations are as follows.

(1)

After the uniaxial compression test of the specimen is completed, the broken blocks are collected according to the throwing distance classification. Assuming that the broken blocks are all thrown from the type of center part of the specimen, the distance ranges are 0~5 cm, 5~10 cm, 10~15 cm, 15~30 cm, 30~45 cm, 45~60 cm, respectively, and the total mass of broken blocks in the regional range is counted.

(2)

Since the indenter and the test bench of the test equipment are gradually lowered in a step type, the falling height of the crushing blocks in the range of 0~5 cm is 0, the falling height of the crushing blocks in the range of 5~10 cm is 5 cm, the falling height of the crushing blocks in the range of 10 cm~15 cm is 30 cm, and the falling height of the crushing blocks in the range of 15 cm~60 cm is 40 cm, as shown in Figure 4. Assuming that the crushing blocks are thrown as a flat throwing path, the initial velocity of the crushing block can be calculated according to the equation of flat throwing motion, the throwing distance and throwing height.

According to the throwing distance and throwing height, the initial velocities of the broken blocks in different throwing distances were calculated by combining the equations of flat throwing motion, see

Table 4. Initial velocity of crushed blocks in different throwing distance ranges.

Throwing Distance/cm	0~5 cm	5~10 cm	10~15 cm	15~30 cm	30~45 cm	45~60 cm
Initial velocity/m·s−1	0.3	0.5	0.6	1.1	1.8	2.4

.

The impact kinetic energy of the crushed blocks in different distance ranges was calculated by counting the crushed blocks in different throwing distance ranges and combining with the kinetic energy theorem. For the broken blocks in the range of 0~5 cm, most of them are broken blocks which are destroyed and dislodged during the compression process, and the impact kinetic energy of the broken blocks in this range has no obvious effect on the bursting liability of the specimen. Therefore, only the broken blocks and their impact kinetic energy in the range of 5~60 cm were counted, which can be seen in

Table 5. Impact kinetic energy of broken blocks of specimens in different states.

Specimen Conditions	Specimen Number	Crushing Block Throwing Distance										Remote Mass Ratio	Impact Total Kinetic Energy /10−3 J
		5~10 cm		10~15 cm		15~30 cm		30~45 cm		45~60 cm
		Mass/g	Impact Kinetic Energy/10−3 J	Mass/g	Impact Kinetic Energy/10−3 J	Mass/g	Impact Kinetic Energy/10−3 J	Mass/g	Impact Kinetic Energy/10−3 J	Mass/g	Impact Kinetic Energy/10−3 J
Complete specimens	W1	23	1.84	23	4.14	11	6.66	23	37.26	6	0	0.87	49.90
	W2	26	2.08	14	2.52	9	5.45	17	27.54	5	0	0.78	37.59
	W3	27	2.16	10	1.80	10	6.05	16	25.92	6	0	0.86	35.93
Specimens with hole (hole diameter 4 mm)	H4-1	18	1.44	8	1.44	7	4.24	2	3.24	0	0	0.35	10.36
	H4-2	19	1.52	6	1.08	5	3.03	1	1.62	2	0	0.32	7.25
	H4-3	17	1.36	10	1.80	4	2.42	3	4.86	0	0	0.26	10.44
Specimens with holes (hole diameter 6 mm)	H6-1	24	1.92	3	0.54	2	1.21	1	1.62	0	0	0.11	5.29
	H6-2	25	2.00	16	2.88	0	0.00	0	0.00	0	0	0.00	4.88
	H6-3	30	2.40	12	2.16	3	1.82	0	0.00	1	0	0.10	6.38
Anchored specimens (preload 0)	M0-1	15	1.20	9	1.62	5	3.03	2	3.24	0	0	0.29	9.09
	M0-2	16	1.28	6	1.08	2	1.21	2	3.24	1	0	0.23	6.81
	M0-3	14	1.12	9	1.62	1	0.61	3	4.86	2	0	0.26	8.21
Anchored specimens (preload 0.03 kN)	M3-1	26	2.08	6	1.08	6	3.63	1	1.62	2	0	0.28	8.41
	M3-2	25	2.00	14	2.52	7	4.24	7	11.34	3	0	0.44	20.10
	M3-3	22	1.76	5	0.90	6	3.63	4	6.48	0	0	0.37	12.77
Anchored specimens (preload 0.05 kN)	M5-1	41	3.28	7	1.26	4	2.42	1	1.62	5	0	0.21	8.58
	M5-2	19	1.52	18	3.24	10	6.05	7	11.34	4	0	0.57	22.15
	M5-3	18	1.44	14	2.52	4	2.42	3	4.86	4	0	0.34	11.24

.

In the reference [24], the mass of the crushed blocks with a throwing distance less than 15 cm in the uniaxial compression tests is defined as the near-field throwing mass, and the mass of the crushed blocks over 15 cm is defined as the far-field throwing mass. The far-field mass ratio is defined as the far-field ejection mass divided by the near-field ejection mass. And the far-field mass ratio is used as the standard to classify the bursting liability of the specimens. When the far-field mass ratio is 0, the specimens have no bursting liability. When the far-field mass ratio is 0–0.4, the specimens have light bursting liability. When the far-field mass ratio is 0.4–0.6, the specimens have medium bursting liability. And when the far-field mass ratio is greater than 0.6, the specimens have strong bursting liability. The method in the reference [24] takes into account the effect of broken blocks within 0–5 cm on the bursting liability of the specimens. However, in practice, the broken blocks are scattered around the specimens during compression of all specimens, so there is no significant effect of the broken blocks in this range on the bursting liability of the specimens. Therefore, based on the method in the reference [24], the impact kinetic energy of broken blocks in the range of 5~60 cm is considered, and the evaluation method of specimen bursting liability is proposed.

Fitting the remote mass ratio to the total kinetic energy of the impact in Table 5, a scatter plot of the impact kinetic energy-remote mass ratio is obtained, see Figure 5.

From Figure 5, it can be seen that the impact kinetic energy of the crushed blocks is positively correlated with the far-field mass ratio. And MATLAB is used to regress the two relationships. The results are as follows.

$$\begin{array}{c}W=47.04Q^2+4.42Q+4.49\hfill \\ R^2=0.94462\hfill \end{array}$$

(2)

In Equation (2), W is the impact kinetic energy with a value of 10⁻³ J; Q is the far-field mass ratio; R² is the coefficient of determination.

According to Equation (2), the bursting liability of the specimen is graded by using the far-field mass ratio as the standard. And the bursting liability of the specimen is discriminated based on the impact kinetic energy of the crushed block as shown in Figure 6.

The impact kinetic energy of the same group of specimens is averaged and the impact propensity of different specimens based on the impact kinetic energy of the crushed blocks can be obtained by combining Figure 6, as shown in

Table 6. Bursting liability of different specimens based on the impact kinetic energy of the crushed blocks.

Specimen Form	Complete Specimen	Specimen with Hole (Hole Diameter 4 mm)	Specimens with Hole (Hole Diameter 6 mm)	Anchored Specimen (Preload 0)	Anchored Specimen (Preload 0.03 kN)	Anchored Specimen (Preload 0.05 kN)
Impact kinetic energy/10−3 J	41.14	9.35	5.52	8.03	13.76	13.99
Impact propensity	strong	weak	weak	weak	weak	weak

.

From Table 6, it can be seen that the impact kinetic energy of the specimen with hole (hole diameter 4 mm) is 77.3% lower than that of the complete specimen. The impact kinetic energy of the specimen with hole (hole diameter 6 mm) was 86.6% lower than that of the complete specimen. The impact kinetic energy of the anchored specimen (preload 0) was reduced by 80.5% compared with that of the complete specimen. The impact kinetic energy of anchored specimen (preload 0.03 kN) is 66.6% lower than that of the complete specimen. The impact kinetic energy of the anchored specimen (preload 0.05 kN) is 66.0% lower than that of the complete specimen. The drilling and anchoring of the specimens can effectively reduce the bursting liability of the specimens. The complete specimens have strong bursting liability, while specimens with holes and anchored specimens have weak bursting liability. The bursting liability of complete specimens and specimens with holes are more consistent with the evaluation results of common bursting liability index. And only the bursting liability of anchored specimens is not consistent, but the evaluation results of bursting liability of specimens based on impact kinetic energy are more consistent with the laboratory dynamic phenomenon. Therefore, the evaluation results of bursting liability of specimens based on impact kinetic energy of crushed blocks are more in line with the reality. According to the above conclusions, the existing bursting liability evaluation indexes are revised based on the impact kinetic energy of the crushed block, and the revised results are shown in

Table 7. Modified Level 3 Bursting Liability Evaluation Indexes.

Common Impact Propensity Evaluation Results	None		Weak		Strong
Impact propensity evaluation results based on the impact kinetic energy of the crushed block	Weak	Weak	None	Weak	None	Weak	Strong
Modified results	Weak		None	Weak	Weak		Strong

.

According to Table 7, when the bursting liability evaluation result based on the impact kinetic energy of the crushing blocks is consistent with the common bursting liability evaluation result, the evaluation result is unchanged. When the bursting liability evaluation result based on the impact kinetic energy of the crushing block is higher than the common bursting liability evaluation result, the bursting liability evaluation result based on the impact kinetic energy of the crushing block shall prevail. When the bursting liability evaluation result based on the impact kinetic energy of the crushed block is lower than the common bursting liability evaluation result, the common bursting liability evaluation result level will be reduced by one level as the correction result.

4. Numerical Simulation Validation of Impact Propensity of Pore-Containing and Anchored Specimens

The discrete unit method is a widely used method for analyzing discontinuous media. When this method is used to analyze a rock mass consisting of a series of blocks combined, these blocks are joined together by nodal surfaces and each block can be considered as a complete continuous region. The joints between the blocks represent preset discontinuity surfaces, and the intact blocks and the joints follow their own ontological criteria. The blocks of the model can be freely moved and turned over and can fall out of the rock when damage occurs, which can better simulate the damage fragmentation of the blocks under uniaxial compression tests.

In order to verify the correctness of the bursting liability evaluation method based on the impact kinetic energy of the crushed blocks, a two-dimensional numerical model containing a random nodal mechanism was established using the discrete element software UDEC for simulations to verify the correctness of the evaluation method. The model size is L × H = 60 × 110 m, and the specimen size is L × H = 50 × 100 mm. There is a pressure plate on the top and bottom of the specimen for loading the specimen. The lower platen of the specimen is constrained to be displaced and the specimen is pressurized by the upper platen, which is given a vertical velocity of 0.1 mm/s. And use the Struct Cable command to set the anchor bolts, use the Brick command to set the anchor plate, the anchor plate size is 10 mm ∗ 10 mm ∗ 5 mm, connected to the anchor bolts. The physical mechanical parameters of the rock mass and the mechanical parameters of the joints in the model are shown in

Table 8. Mechanical parameters of rock masses and joint.

Mechanical Parameters of Rock Mass					Nodal Mechanical Parameters
Bulk Modulus K/GPa	Shear Modulus G/GPa	Tensile Strength σt/MPa	Cohesion C/MPa	Internal Friction angle φ/°	Normal Stiffness Kn/GPa/m	Tangential Stiffness Ks/GPa/m
1.5	0.6	1.6	2.9	43	3.76	2.30

, and the parameters of the anchor bolt are shown in

Table 9. Mechanical parameters of anchor bolts.

Parameters	Density Kg/m3	Elastic Modulus GPa	Tensile Yield Force N	Shear Stiffness of Grout N/m	Normal Stiffness of Grout N/m
Anchor bolts	7500	98.6	5.00 × 105	1.12 × 109	1.75 × 109

. and the numerical models established for different states are shown in Figure 7.

During the compression test of the specimen, the maximum unbalance force in the specimen corresponds to the maximum value of the force on the specimen. When the specimen is destabilized by compression, the maximum unbalance force decreases rapidly. And when the unbalance force appears to fluctuate horizontally, no more loading is carried out and the specimen compression test is finished. The uniaxial compression stress-strain curves obtained for different forms of specimens are shown in Figure 8. As can be seen from Figure 8, the trends of the stress-strain curves of the numerical simulation results are more consistent with the laboratory test curves, and the analysis indicates that the established two-dimensional numerical model with random nodal joints can better simulate the mechanical parameters of real coal samples.

According to the nodal surface contact criterion, tensile damage is considered to occur at the contact surface when the normal stress at the contact surface is zero, while shear damage is considered to occur at the contact surface when the shear stress at the contact surface is greater than the ultimate shear strength. By writing the corresponding program in the built-in Fish language of UDEC, the velocity of the block with tensile and shear damage at the contact surface in the numerical simulation is monitored and the area of the block is calculated, and then the impact kinetic energy of the block is calculated to obtain the impact kinetic energy of the numerically simulated specimen. Figure 9 shows the block velocities of the specimens in different states after the completion of compression.

The velocity of blocks of specimens in different states are counted and the impact kinetic energy is calculated, and the impact kinetic energy and bursting liability of the specimens in different states are obtained according to the bursting liability discrimination criteria in Figure 6, as shown in

Table 10. Impact kinetic energy and bursting liability of specimens in different states of numerical simulation.

	Specimen Conditions	Complete Specimen	Hole-Containing Specimen (Hole Diameter 4 mm)	Hole-Containing Specimen (Hole Diameter 6 mm)	Anchored Specimen (Preload 0)	Anchored Specimen (Preload 0.03 kN)	Anchored Specimen (Preload 0.05 kN)
Test Data
Impact kinetic energy/10−3 J	Laboratory Testing	41.14	9.35	5.52	8.03	13.76	13.99
	Numerical simulation	45.83	8.48	5.95	9.49	11.97	13.05
	Error %	11.4	9.3	7.8	18.2	13.2	6.7
Bursting liability	Laboratory test	Strong	Weak	Weak	Weak	Weak	Weak
	Numerical simulation	Strong	Weak	Weak	Weak	Weak	Weak

.

From Table 10, it can be seen that the impact kinetic energy of the numerically simulated specimens in different states is basically the same as that of the laboratory test specimens, and the error is maintained in the range of 6.7% to 18.2%. According to the bursting liability criteria based on the impact kinetic energy of the crushed blocks, it is concluded that the bursting liability of the laboratory test specimens is consistent with that of the numerical simulation specimens. The numerical simulation results verified the correctness of the bursting liability criterion based on the impact kinetic energy of the crushed block.

5. Discussion

The bursting liability evaluation indexes and evaluation methods commonly used nowadays are inaccurate for the bursting liability evaluation results of specimens in some states. In order to obtain more accurate evaluation results and make the evaluation results more consistent with the dynamic phenomena, this paper conducted uniaxial compression tests on the specimens in different states, and counted the impact kinetic energy of the crushed blocks in the range of 5~60 cm from the center of the specimen during the compression process. Based on this, the bursting liability criterion based on the impact kinetic energy of the crushed blocks is established, and the common bursting liability evaluation indexes are modified.

The bursting liability evaluation results based on the impact kinetic energy of the crushed blocks are more consistent with the laboratory dynamic phenomena, such as anchored specimens. Anchorage support is widely used in roadway support, and the results obtained by using the commonly used bursting liability evaluation indexes and the bursting liability discrimination criteria based on the impact kinetic energy of crushed masses are not consistent. But the evaluation results obtained by the bursting liability discrimination criteria based on the impact kinetic energy of crushed masses are more consistent with the dynamic phenomena in the laboratory. Therefore, the evaluation results derived from the discriminant of bursting liability based on the impact kinetic energy of the crushed block are more accurate and can better guide the field production. If the wrong evaluation results are used to guide the field production, it may cause serious impact accidents. Therefore, the bursting liability discrimination criteria based on the impact of kinetic energy of crushed blocks derived in this paper is of great significance to guide the site.

However, there are some limitations in this study, especially when counting the impact kinetic energy of broken blocks. In this study, only the impact kinetic energy of larger blocks was counted, but the impact kinetic energy of smaller blocks and small blocks broken into powder form was not counted. Although smaller blocks and small blocks broken into powder form have less influence on the evaluation results, they still need to be counted, which is the next problem to be solved in this study. That is, how to quickly and accurately count the impact kinetic energy of all crushed blocks during the experiment.

6. Conclusions

(1)

For the anchored specimens, the specimens were concluded to be strongly bursting liability according to the commonly used evaluation indexes, but the specimens did not have obvious dynamic phenomena during the compression test in the laboratory. Therefore, although the specimen is evaluated as strong bursting liability by the common evaluation indexes, it does not necessarily have obvious impact dynamic phenomenon, which indicates that there is an error in the evaluation of bursting liability of the common evaluation indexes for some state specimens.

(2)

In the uniaxial compression test, the throwing phenomenon of the crushed blocks is the most intuitive expression of the impact of the specimen. Based on the impact kinetic energy of the crushed block, the bursting liability criterion based on the impact kinetic energy of the crushed blocks is established, and the common bursting liability evaluation indexes are modified. When the bursting liability evaluation results based on the impact kinetic energy of the crushing block are consistent with the common bursting liability evaluation results, the evaluation results are unchanged; when the former is higher than the latter, the former prevails; when the former is lower than the latter, the common impact propensity evaluation result level is reduced by one level as the correction result.

(3)

A two-dimensional numerical model with random nodal theory was established by using the discrete element software UDEC to simulate the bursting liability of specimens in different states. The simulation results show that the impact of kinetic energy of the numerically simulated specimens in different states is basically the same as that of the laboratory test specimens. The bursting liability of the laboratory test specimens is consistent with that of the numerically simulated specimens based on the impact kinetic energy of the crushed block. The numerical simulation results verify the correctness of the bursting liability criterion based on the impact kinetic energy of the crushed block.