Abstract
In order to study the influence of fissures on the burst tendency of coal, the test and numerical simulation of the burst tendency of coal with different burst angles were carried out. The evolution law of the burst tendency index of coal under the influence of burst angle was analyzed, and the mechanism of energy storage and release of coal under the influence of fissure angle was revealed. The results show that compared with the specimens without prefabricated cracks, the uniaxial compressive strength of the specimens with 0° cracks is reduced by 48.4%, the dynamic failure time is increased by 279.4%, the burst energy index is reduced by 54%, and the burst energy velocity index is reduced by 87.9%. After that, with the increase of prefabricated crack angle, the uniaxial compressive strength of coal increases gradually, the dynamic failure time decreases gradually, the burst energy index increases gradually, and the burst energy velocity index increases gradually. That is to say, the larger the crack angle contained in the coal body, the stronger the burst tendency of the coal body, but it is still lower than that of the complete coal body. With the increase of prefabricated crack angle, the proportion of prepeak elastic energy of coal body increases, the less energy dissipation in the whole loading process of coal body, and the faster energy release rate during failure. The research results can provide some theoretical support for the prevention and control of rock burst disaster.
1. Introduction
Coal is a typical heterogeneous material that contains a large number of joints, cracks, or structural planes inside. The instability and failure of coal mine roadways are caused by the initiation, expansion, and connection of internal cracks in the coal body [1–4]. With the gradual deepening of coal mining, the joint cracks of the roadway surrounding rock are more developed, loose, and broken, and the deformation of the roadway is aggravated [5–9]. The fracture of coal can be regarded as a process of energy conversion and transmission, and its final failure is a state instability phenomenon driven by energy. Many scholars believe that the essential mechanism of coal dynamic failure and rock burst can be revealed from the perspective of energy [10–14]. Therefore, it is of great engineering significance to study the burst failure and energy evolution of cracked coal.
At present, scholars at home and abroad have systematically studied the influence of crack dip angle, number and length on the strength, and deformation and failure characteristics of coal mass through laboratory tests and numerical simulation [15–19].
The whole process from loading deformation to destruction of coal body is accompanied by the accumulation and transformation of energy. Energy is the essential factor leading to the destruction of the coal bodies [19–26]. Many scholars have carried out a lot of research on energy and rock failure, but there are few studies on the energy of cracked coal, which still needs further research.
Previous studies have focused on the influence of crack angle, crack number, and crack length on the mechanical properties of coal and rock mass. Therefore, on the basis of previous studies, this paper fixed the crack length and crack number, prefabricated four kinds of coal with different crack angles, and carried out the impact tendency test of coal with different crack angles to study the impact failure characteristics of coal [27, 28]. Through the indoor test and numerical simulation of coal body with different fracture angles, the energy evolution process of coal body is analyzed and the energy evolution law of coal body is studied.
2. Indoor Experiment and Result Analysis
2.1. Specimen Preparation and Loading Scheme
The size of the coal in the test is 50 mm in diameter and 100 mm in height. The prefabricated crack is located in the center of the coal body. The crack size is 20 mm in length and 2 mm in width, and the crack penetrates the coal body. In order to reduce the individual difference of the sample, the longitudinal wave velocity of the coal sample was tested before the prefabricated crack, and the coal sample with the wave velocity between 1200 and 1500 m/s was selected for the prefabricated crack. According to the angle of the prefabricated crack, it is divided into five groups of tests, namely, no crack group, 0° crack group, 30° crack group, 60° crack group, and 90° crack group. Each group is tested on three specimens. The specific specimen preparation is shown in Figure 1.
The test loading system adopts an RLJW-2000 rock testing machine, axial compression is applied at a stress loading rate of 0.5 mm/min, and the load-displacement data of the sample are collected synchronously until the sample is destroyed.
2.2. Measurement of Burst Tendency
The burst tendency of coal refers to the ability and inherent properties of coal to accumulate energy and produce burst damage, which is a necessary condition for rock burst. Therefore, the determination of coal burst tendency is an important part of the prevention and control of rock burst, and the burst tendency index can be used to evaluate the risk of coal burst. In the national standard GB/T 25217.2-2010 determination of rock burst monitoring and prevention methods Part 2: classification of coal burst tendency and determination method of index, four indexes are given to measure the strength of burst tendency. At the same time, many researchers have also proposed many indexes to measure the burst tendency [29, 30].
In this test, four parameters in the national standard, namely, dynamic failure time DT, uniaxial compressive strength , burst energy index , and burst energy velocity index proposed by authoritative scholars [28], were selected to measure the burst tendency of coal body, which can be divided into no burst tendency, weak burst tendency, and strong burst tendency.
The uniaxial compressive strength can reflect the ultimate bearing capacity of coal samples. The higher the uniaxial compressive strength, the stronger the bearing capacity of coal samples before failure, the more energy accumulated inside under the external force, and the greater the kinetic energy converted and released when the peak strength is reached. The dynamic failure time is used to measure the degree of burst tendency, which is the transient duration time of coal from the beginning to the end of the peak strength, as shown in Figure 2 [29]. The duration of the failure process is a comprehensive reflection of the dynamic characteristics of energy accumulation and dissipation, reflecting the speed of postpeak failure of coal samples.
The whole process of the stress-strain curve of coal contains rich information about burst tendency, which intuitively and comprehensively reflects the whole process from energy storage to energy consumption. It is of great significance to reveal the physical nature of burst tendency and analyze other burst tendency indexes. The burst energy index is calculated by dividing the prepeak total input energy by the postpeak failure dissipation energy in the stress-strain curve, as shown in Figure 3 [29]. The calculation formula is as follows:
In the formula, is the total input energy before the peak, and its value is the area enclosed by the prepeak curve and the coordinate axis; is the postpeak damage dissipation energy, and its value is the area enclosed by the postpeak curve and the coordinate axis.
The residual energy released per unit time during the failure process of coal samples represents the amount of elastic energy converted into kinetic energy per unit time, which also reflects the degree of burst tendency of coal. The burst energy velocity index is the ratio of the burst energy index to the dynamic failure time. The specific calculation formula is as follows:
The physical meaning of the index characterizes the ratio of energy accumulation and release during the compression process of coal samples per unit time and reflects the burst release ability of energy during the compression failure process of coal samples.
The determination methods of four burst tendency indexes are listed in Table 1.
2.3. The Final Failure Form of Coal
Figure 4 shows the final failure form of the coal specimen after uniaxial compression loading. It can be seen from Figure 4 that the damage degree of the 0° crack specimen is the smallest, and only a small number of fragments fall off along the crack tip. For the 30° crack specimen, some coal blocks are thrown along the crack area, and the whole crack area of the 60° crack specimen is basically completely destroyed, while the 90° crack specimen has large pieces of coal body spalling and throwing, and the degree of damage is the largest.
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2.4. Uniaxial Compressive Strength
The stress-time curve of coal containing prefabricated cracks with different angles is shown in Figure 5. When the crack angle is 0°, 30°, and 60°, the postpeak curve is a step-down curve; the new cracks in the specimen are slowly generated and expanded, and the specimen is slowly destroyed. When the prefabricated crack angle increases to 90°, the step-down characteristic of the postpeak curve of the specimen weakens, showing rapid failure and enhanced brittle failure characteristics.
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The statistics of uniaxial compressive strength of prefabricated cracks at different angles are shown in Table 2 and Figure 6. About the uniaxial compressive strength, compared with the specimens without prefabricated cracks, the uniaxial compressive strength of the coal is reduced by 48.4% when the crack angle is 0°, 44.9% when the crack angle is 30°, and 32.8% when the crack angle is 60°. The coal body with three crack angles shows a weak burst tendency; when the crack angle is 90°, the uniaxial compressive strength is reduced by 2%. In this case, it still shows a strong burst tendency. With the increase of prefabricated crack angle, the measured value of uniaxial compressive strength of coal specimens also increases, and a power function growth relationship is presented.
Since the coal is limited in the loading direction, there is free expansion space in the other two directions, so the microcracks are mainly tensile cracks parallel to the loading direction. In the mutual expansion and penetration of small tensile cracks, the prefabricated cracks play the role of bridging, so that the cracks generated inside the coal body with the increase of load can interact more easily, and then, the ability of the coal sample to withstand the load is reduced. Therefore, with the increase of the dip angle, the number of tensile cracks that can be connected by the prefabricated cracks of the same length along the loading direction is less and less, so the uniaxial compressive strength of the coal body is on the rise. Especially when the crack dip angle is 90°, the prefabricated crack has little effect on the uniaxial compressive strength of the coal body.
2.5. Dynamic Failure Time
The dynamic failure time of coal obtained from the stress-time curve is shown in Table 3 and Figure 7. Compared with the coal specimen without prefabricated cracks, the dynamic failure time increases by 279.4% when the crack angle is 0°, 236.7% when the crack angle is 30°, 171.8% when the crack angle is 60°, and 15.9% when the crack angle is 90°. According to the standard, there is no burst tendency. With the increase of crack angle, the measured value of dynamic failure time gradually decreases and finally shows a trend of power function decrease. The smaller the crack angle, the longer the dynamic failure time of the specimen. This is because with the increase of the crack angle, the projection length of the crack length in the vertical loading direction is smaller, so that the number of cracks in the coal body parallel to the loading direction is reduced, the damage degree of the coal body is reduced, and finally, the dynamic failure time of the coal body is reduced.
2.6. Burst Energy Index
Through the analysis of stress-strain curve data, the final calculated coal burst energy index is shown in Table 4 and Figure 8. Compared with the coal specimen without prefabricated cracks, the burst energy index is reduced by 54% when the crack angle is 0°, 42.2% when the crack angle is 30°, 24.4% when the crack angle is 60°, and 11.9% when the crack angle is 90°. As the crack angle increases, the measured value of the burst energy index gradually increases, showing a linear growth trend. The smaller the crack angle, the smaller the burst energy index of the coal, and the less severe the damage. The results also verify the influence principle of fracture angle on uniaxial compressive strength and dynamic failure time of coal.
2.7. Burst Energy Velocity Index
According to the average value of burst energy index and dynamic failure time and combined with formula (2), the final burst energy velocity index of coal is shown in Table 5 and Figure 9. According to the standard, the coal without prefabricated cracks has weak burst tendency. Compared with the coal without prefabricated cracks, the burst energy velocity index decreases by 87.9% when the crack angle is 0°, 82.6% when the crack angle is 30°, and 72.2% when the crack angle is 60°. The coal with these three abovementioned crack angles shows no burst tendency. When the crack angle is 90°, the burst energy velocity index is reduced by 23.9%, and this crack angle still shows a weak burst tendency. With the increase of crack angle, the measured value of burst energy velocity index increases gradually, showing a trend of power function growth. The smaller the crack angle, the smaller the burst energy velocity index of coal, and the less the elastic energy converted into kinetic energy per unit time.
3. Numerical Simulation and Result Analysis
3.1. Simulation Scheme
In order to study the energy evolution law of coal with prefabricated cracks at different angles, PFC numerical simulation software is used to establish a numerical model similar to the laboratory test. The model size is 50 mm × 100 mm, and the prefabricated crack angles are 0°, 15°, 30°, 45°, 60°, 75°, and 90°. The crack length is 20 mm, and the width is 2 mm. The crack is located at the center of the model.
In this simulation, the parallel bond model is used to simulate the mechanical behavior of coal. The parameters are compared by the trial and error method and indoor test. The stress-strain curve of the complete specimen is shown in Figure 10. The specific parameters of the model are listed in Table 6.
In PFC, rock crack and macroparameters are closely related to the size of particles, which is called the size effect. With increasing of L/R (i.e. the ratio of specimen size to particle radius), the influence of the size effect decreases. Based on works by Zhao et al., when the value of L/R is greater than 120, the size of particles has little influence on macro parameters of the specimen [31]. So in this paper, in order to reduce the size effect, the radius of the particles was set 0.4∼0.5 mm, and L/R was 220.
In the simulation, the coal is prefabricated with cracks at different angles, and then, uniaxial loading is carried out to destroy the coal. The changes of stress, elastic energy, dissipation energy, and input energy in the whole process are recorded, and the energy evolution law of the coal body is analyzed.
3.2. Failure Form of Specimen
After uniaxial loading to failure, the crack expansion of coal under different crack angles is shown in Figure 11. From the diagram, it can be seen that after uniaxial loading, the tip of the prefabricated crack will be destroyed first. With the increase of the angle of the prefabricated crack, the generated crack gradually expands to the diagonal direction. When the angle of the prefabricated crack is small, the damage range is basically near the prefabricated crack. The larger the angle of the prefabricated crack, the larger the damage range, which is basically similar to the indoor test results.
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3.3. The Energy Calculation Method
In PFC2D simulation, the strain energy accumulated in the specimen includes two parts. One is the contact strain energy stored at all contacts, and the other is the parallel-bond strain energy stored in parallel bonds. The strain energy can be expressed aswhere
In Equations (4) and (5), , , and are the normal force, shear force, and the moment in the parallel bond i, respectively; and are the normal force and shear force in the contact i, respectively; Ai and Ii are the area and inertia moment of the bond cross section, respectively; is the number of contacts; and is the number of parallel bonds.
3.4. Energy Evolution Process of Coal with Different Crack Angles
During the loading process of the coal, the stress and energy evolution curve of the whole process can show the loading and failure process inside the coal during the whole process. The energy evolution law in the process of coal loading and failure is analyzed, respectively, as shown in Figure 12.
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It can be seen from Figure 9 that as the prefabricated crack angle increases, the strain at failure gradually increases. When the prefabricated crack angle is 0°, the strain is 0.148%, and when it is 90°, the strain is 0.18%. The greater the angle of the prefabricated crack, the greater the uniaxial compressive strength and the greater the peak elastic energy; the larger the prefabricated crack angle is, the faster the release rate of stress and elastic energy in the postpeak failure stage is, the faster the dissipation energy increases, and the more severe the damage is.
3.5. Energy Storage Law of Coal with Different Crack Angles
Compared with the noncracked coal, the uniaxial compressive strength and elastic energy peak of the cracked coal will change, resulting in the change of the maximum energy storage of the coal. Therefore, the uniaxial compressive strength and elastic energy peak of the nonprefabricated crack and different prefabricated crack angles are compared and analyzed.
Figure 13 shows the uniaxial compressive strength curve at different crack angles. The uniaxial compressive strength of coal without prefabricated cracks is 18.38 MPa. It decreases by 31.23% when the prefabricated crack angle is 0°, 30.85% when the prefabricated crack angle is 15°, 25.79% when the prefabricated crack angle is 30°, 26.33% when the prefabricated crack angle is 45°, 16.81% when the prefabricated crack angle is 60°, 9.96% when the prefabricated crack angle is 75°, and 6.69% when the prefabricated crack angle is 90°. The greater the prefabricated crack angle of the coal body, the greater the uniaxial compressive strength increases in a power function, and the smaller the reduction is compared with the nonprefabricated crack, which is basically the same as the test results.
Figure 14 shows the peak curve of elastic energy at different crack angles. When there is no prefabricated crack, the peak value of elastic energy of coal is 93.67 J. It is reduced by 49.72% when the prefabricated crack angle is 0°, 47.91% when the prefabricated crack angle is 15°, 43.39% when the prefabricated crack angle is 30°, 45.5% when the prefabricated crack angle is 45°, 35.35% when the prefabricated crack angle is 60°, 27.15% at 75°, and 18.46% at 90°. The larger the prefabricated crack angle of the coal body, the peak value of the elastic energy increases in a power function, but it is still lower than the peak value of the elastic energy of the coal body without prefabricated cracks.
3.6. Energy Dissipation and Release Law of Coal with Different Crack Angles
During the whole loading process of the coal, there will be some energy dissipation. When the peak point is reached, the difference between the input energy and the elastic energy represents the energy dissipation during the whole loading process. Therefore, the elastic energy ratio (the ratio of the elastic energy peak to the input energy) is defined to analyze the energy dissipation law during the loading process of the coal.
Figure 15 shows the elastic energy ratio curve at different crack angles. When there is no prefabricated crack, the proportion of elastic energy of coal is 89.35%. It is reduced by 24.83% when the prefabricated crack angle is 0°, 18.75% when the prefabricated crack angle is 15°, 8.24% when the prefabricated crack angle is 30°, 9.68% when the prefabricated crack angle is 45°, 4.85% when the prefabricated crack angle is 60°, 2.18% at 75°, and 2.64% at 90°. The larger the prefabricated crack angle of coal body is, the larger the proportion of elastic energy is, showing a power function. Compared with no prefabricated crack, the smaller the reduction range is, the less the energy dissipation in the whole loading process of coal body is.
In the loading process of the whole coal body, the proportion of elastic energy can reflect the energy storage and dissipation characteristics inside the coal body. The postpeak energy release rate (i.e., failure energy release rate) can reflect the speed of energy release after coal failure. The slower the postpeak energy release rate is, the lower the burst risk of postpeak failure is. Figure 16 shows the energy release rate curves of coal with different crack angles after failure. For the postpeak failure stage, when the prefabricated crack angle is 0°, the elastic energy release amount of each 1% strain is 143.1 J, and the elastic energy release amount of each 1% strain increases by 8.04% at 15°. At 30°, the elastic energy release amount of each 1% strain increases by 126.62%. At 45°, the elastic energy release amount of each 1% strain increases by 215.37%. At 60°, the elastic energy release amount of each 1% strain increases by 217.96%. The elastic energy release per 1% strain at 75° increased by 640.04%, and the elastic energy release per 1% strain at 90° increased by 929.07%. The larger the prefabricated crack angle of the coal body, the elastic energy release amount per 1% strain produced increases in a power function, and the faster the energy release rate is.
4. Conclusions
The indoor test and numerical simulation of coal body under different crack angles were carried out. The burst tendency test of coal body with different crack angles was carried out, and the energy evolution law of coal body under different crack angles was analyzed. The main conclusions are as follows.
Compared with the specimens without prefabricated cracks, the uniaxial compressive strength of the specimens with 0° cracks decreased by 48.4%, the dynamic failure time increased by 279.4%, the burst energy index decreased by 54%, and the burst energy velocity index decreased by 87.9%. After that, with the increase of prefabricated crack angle, the uniaxial compressive strength of coal increases gradually, the dynamic failure time decreases gradually, the burst energy index increases gradually, and the burst energy velocity index increases gradually.
With the increase of prefabricated crack angle, the proportion of elastic energy in front of the peak of coal increases in a power function. The less energy dissipation in the whole loading process of coal, the faster the energy release rate.
The research results can provide some theoretical support for the prevention and control of rock burst disaster.
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This research was funded by Shandong Energy Group, grant no. SNKJ2022BJ01-R27.