A new digital surface crack image monitoring technology for coal failure

The experimental study on the variation law of coal fracture and stress was carried out in the laboratory and engineering fields, respectively. A multiparameter monitoring system including electromagnetic radiation and a high‐speed camera was built, and three stress paths, uniaxial compression, cyclic loading, and graded loading, were used to monitor the dynamic expansion process of surface cracks during uniaxial compression failure of coal specimens. Through the quantitative analysis of the electromagnetic radiation signal in the crack propagation process, it is found that the electromagnetic radiation and the stress change trend are consistent, and the electromagnetic radiation signal is ahead of the failure of coal‐generating rock mass 1–2 s. The surface crack changes after the peak value of electromagnetic radiation and presents a stepwise growth trend, crack length changes on the millisecond time scale, and the crack propagation speed is about 2000 mm/s. The surface cracks appear when the stress reaches a certain degree, and the propagation of the principal cracks is consistent with the failure of the specimen. The electromagnetic radiation value of the coal mass from static period to dynamic is analyzed by using electromagnetic radiation at the engineering site, and it was found that the electromagnetic radiation is consistent with the stress distribution of the mining face. Through normalization, the variation rule of electromagnetic radiation in laboratory and engineering sites is similar, but the peak value of electromagnetic radiation in engineering sites is more significant. Therefore, electromagnetic radiation has a good monitoring effect on the stress distribution and cracks propagation of underground coal mining working faces, which could guide the layout of underground drilling.


| INTRODUCTION
Coal is the most enormous one-time energy consumption in China, accounting for 58% of all energy, and the status of power dominant will not change for a long time. 1 Gas accidents such as gas overrun, gas combustion, gas explosion, and coal and gas outburst frequently occur in coal mines. Coal mine gas is still a critical problem affecting the safe and efficient production of coal mines. [2][3][4][5][6] The commonly used gas control methods in coal mines, such as the construction of gas extraction drilling holes, high drainage roadway, and protective layer mining. Those methods in essence reduce the action of mining stress, and increase the passage of gas flow in the coal body so that the gas is easier and faster released from the coal seam. [7][8][9][10] Given the common problems of high in situ stress, high gas content, and low permeability in China's coal mining areas, mining protective layers, drilling holes in the coal seam, drilling through the seam, water injection in the coal seam, hydraulic separation in the coal seam, and CO 2 blasting are widely adopted, and good results have been achieved. [11][12][13][14][15][16] However, the coal seam is a heterogeneous porous medium, which contains many impurities and is under a more complex stress environment. 17,18 Therefore, the gas geological conditions of each mine and each working face are not entirely consistent, and a convenient method is needed to test the development of coal cracks.
The process of coal compression failure is also the process of inoculation, occurrence, expansion, and penetration of many internal cracks. 19,20 The process of crack propagation is accompanied by coal rock stress, acoustic emission, electromagnetic radiation signals, coal rock surface cracks, and other signals. [21][22][23][24][25] Some of the research studies on crack failure process images are qualitative studies, which only describe the crack distribution of broken coal bodies. 26,27 The other part of the study is semi-quantitative, only at the partial time of crack growth, without a kind of continuous observation. 28 The study of coal mass cracks is divided into laboratory tests and engineering field measurements. In the laboratory, the loading methods include different stress paths such as compression failure, cyclic loading, and graded loading 29 ; the loading machines are divided into single-axis and three-axis 30,31 ; the observation methods include camera shooting and CT scanning. 32,33 At the engineering site, there are intuitive measurements of cracks with borehole endoscopes, and there are also signals derived from electromagnetic radiation and microseisms. [34][35][36][37] These research results play an essential role in promoting the understanding of crack propagation and distribution law and provide a reference for mutual verification in the laboratory and field.
Although the stress environment of the laboratory and the coal mine site is different, the stress change trend of the coal mine underground working face can be approximately simulated according to various stress paths. Affected by the intermittent advancement of the working face, the cutting of coal by the shearer, and the roof's collapse, the stress of the working face in the coal mine is intermittent and sudden. The compression failure test was carried out by three stress loading paths, uniaxial compression, cyclic loading, and graded loading, respectively. The stress change of the coal body in the underground working face was analogized.
The study of crack propagation law has a guiding role in the design of gas extraction [38][39][40] and the establishment of visualized three-dimensional (3D) space. [41][42][43] It is of great significance to the control of coal mine gas, and the prevention of coal and rock dynamic disasters. Therefore, this paper chooses to analyze the crack propagation process in detail, and combined with the stress in the failure process, discusses the change law of surface crack in the failure process of coal and rock, and provides guidance for on-site pressure relief, gas extraction, and rock burst warning.

| Samples
To get closer to the reality of the coal mine rock bursts, raw coal was used for the test. The selected coal specimens come from the No. 4 coal seam of Shadunzi Coal Mine, which has the risk of rock burst and coal and gas outburst, and the coal seam dip angle is 6.5°.
Coal specimen preparation steps are as follows: (1) Collect coal blocks with a length, width, and height of 25 cm × 25 cm × 25 cm or more on-site and transport them to the laboratory; (2) drill the coal core in the laboratory; (3) use a cutting machine to cut the drilled coal core to a suitable length; (4) flatten the cut coal specimen with a ball mill, and then sand it with sandpaper; (5) put the obtained rock mechanics standard experimental piece of ϕ50mm × 100 mm and polished to achieve a surface roughness below 0.02 mm, with a grid of 1 cm × 1 cm on the surface, and put it in a sealed bag. Some samples are shown in Figure 1.

| Experimental system
The multiparameter monitoring system is mainly composed of four parts, which are the loading system, data acquisition system, electromagnetic radiation, and high-speed camera. The overall layout of the experimental design is shown in Figure 2 1. The loading system adopts the Tianchen WAW-1000 hydraulic universal test system, as shown in Figure 3, including a hydraulic press and servo control system. By operating on the computer with Maxtext software, parameters such as stress, strain, failure strength, and corresponding curves can be obtained.
2. The portable EME-HF mine intrinsically safe electromagnetic radiation monitoring system consists of a host, coils, and connecting wires, as shown in Figure 3. The acquisition, conversion, processing, storage, and alarm of the signal are completed automatically by the monitor. The electromagnetic radiation intensity mainly reflects the loading degree and deformation and fracture intensity of the coal and rock mass, and the number of pulses mainly demonstrates the frequency of the deformation and microfracture of the coal and rock mass. 3. The data acquisition system adopts the DH5981 portable data acquisition system, which cooperates with the DHDA dynamic signal acquisition and analysis system for data acquisition and processing. It can be plugged in or powered by a mobile power supply. The calculation frequency of load and displacement is 10,000Hz/s. 4. MemercamGX-3 high-speed camera with a maximum shooting rate of 198,000 frames per second. According to the image storage space and the surface crack propagation speed, after much debugging, the shooting frame number is set to 1500 frames per second; the image format is jpg, and the size is 512 × 384 pixels.

| Experimental scheme
To explore the occurrence rule of electromagnetic radiation of coal under different stress paths, three paths of uniaxial compression, cyclic loading, and staged loading were used to conduct uniaxial compression failure tests, and the loading speed was set to 0.5 MPa/s.

Uniaxial compression
To observe the surface crack propagation process, the loading method of uniaxial compression is adopted. According to the Detailed Rules for Prevention and Control of Coal Mine Rock Burst formulated by the State Administration of Coal Mine Safety of China, 44 the loading speed is set to 0.5 MPa/s.

Cyclic loading
The first cycle sets the strength to 70% of the single-shaft failure strength, then reduces it to 5%; The second cycle is loaded to 75% of the failure strength, then reduces to 5%; This process is repeated until the coal rock is destroyed. In this process, mechanical parameters such as stress and displacement, electromagnetic radiation pulse number, intensity, images of crack propagation, and other parameters were recorded.
F I G U R E 1 Coal samples and surface punctuation.
F I G U R E 2 Experimental system diagram.
F I G U R E 3 Electromagnetic radiometer.

Staged loading
Although uniaxial and cyclic loading can obtain the compressive strength of coal and rock and the damage of cyclic loading, it does not reflect the damaging effect of loading time on coal specimens. To simulate the long-term stress of the coal wall in the coal mine, the creeping form of hierarchical loading is adopted as the loading method. Taking 10%, 30%, 50%, 70%, 90%, and 110% of the uniaxial compressive strength as the set target values, the loading speed was set to 0.5 MPa/s. According to the staged loading creep process, the deformation of 1000 s is less than 0.01 mm, which can be considered stable, and the force in each stage is set to be maintained for 7200 s.

| Automatic crack identification and calculation
To quickly obtain the surface crack propagation parameters in the process of compression failure, a large-scale automatic crack identification and quantitative calculation program were written. The specific processing steps are as follows: 1. Use the imgDiff function in MATLAB to find the difference between the images, and use the loop function to meet the requirements of image batch processing quickly. 2. Call the saved image with differences, perform grayscale processing on the image, intercept the cracked area, lock the principal cracked area with a difference, intercept this area, and save it as a new image. 3. Binarize the captured images of the difference in cracks, the cracks are black, and the background is white.
4. Use the I = bwmorph() function to refine the image in MATLAB to obtain the width of a single pixel. 5. Count the situation of the pixels, get the length and width of the crack, and then calculate the area of the crack.

| Electromagnetic radiation and stress
Failure process of uniaxial compression With the increased stress, the electromagnetic radiation signal of coal specimen SC24 also changes. The coal specimen was destroyed between 36 and 37 s, and the electromagnetic radiation signal was the strongest at this time, as shown in Figure 4. The stress-time curve is not a smoothly increasing curve, indicating that the coal specimen is not a homogeneous medium. The intensity of the electromagnetic radiation signal increases with stress, and the signal reaches a peak when the coal specimen is destroyed. In the process of stress increase, the electromagnetic radiation has a small rise at about 29 s, which is consistent with the trend of stress change. The time is advanced by about 2 s, indicating that the electromagnetic radiation signal is ahead of the crack generation and expansion process.
Failure process of cyclic loading During each cycle, as the stress increases, the displacement appears, and the EMR signal increases; and vice versa, as shown in Figure 5. In the first cycle, after the stress exceeds a particular value, the number of electromagnetic radiation pulses reaches a small peak. Although there is a signal when the pressure is relieved, the sign is tiny; after the force of the next cycle exceeds the peak value of the previous process, the EMR signal again increases, which is the memory effect of electromagnetic radiation. This cycle is repeated until the coal specimen is broken. The electromagnetic radiation during cyclic loading is different from that of uniaxial compression, and the signal peak in the final destruction stage is more minor. At around 370 s, although the stress decreases, the electromagnetic radiation increases sharply. In the early warning process, you need to be alert to the situation where the signals are frequent, but the peak value is small. This process is not only easy to misjudge, but also a dangerous area. Therefore, when this phenomenon occurs, it is necessary to monitor it at any time and take pressure relief measures in advance.

Failure process of staged loading
In the process of graded loading, electromagnetic radiation changes rapidly in the time of stress increase, decreases slowly in the time of stress maintenance in the overall stability, and reaches the peak at the last specimen failure, as shown in Figure 6. In this process, electromagnetic radiation and stress change trends are similar, but not the same. At about 23,000 s, the electromagnetic radiation signal mutated without apparent changes in stress, which may be caused by small internal cracks, deformation, and rupture. It shows that in the stress-holding stage, although there is no deformation or visible cracks outside, the internal cracks are not fixed. Under the action of sizeable constant stress, the development and propagation process of cracks appeared in the coal body, which indirectly indicated that there were primary joints in the coal body on the one hand, and rheological properties of the coal specimen itself on the other hand.

| Surface cracks and stress
The principal cracks leading to failure in the compression failure process of coal specimen SC24 were monitored, and the expansion of surface cracks was staged and abrupt, as shown in Figure 7. To find out the propagation law of surface cracks more intuitively, the length, propagation rate, and area of surface cracks were counted and compared with the stress, as shown in Figure 8. In the three-time intervals of A, B, and C, although the stress is increasing slowly, the length, and area of the cracks all change rapidly. To quantize the expansion of the crack at this stage, the length, area, expansion rate, and stress of the crack correspond to the time accuracy of 2 ms, and the rapidity of crack expansion can be seen.
A cyclic loading test was carried out on coal specimen SC31-2, and the crack development on the surface of the specimen was monitored. The surface cracks started to propagate in the first cycle stage, but the specimen failed abruptly in the fifth cycle stage, as shown in Figure 9.
A graded loading test was carried out on coal specimen SC13, and the crack development on the surface of the specimen was monitored, the surface crack propagates after a few seconds of stress retention in the fifth stage, as shown in Figure 10.

| 2101
In the loading failure test of the coal specimen under different stress paths, it is found that cracks will occur on the surface of the specimen, and the cracks will expand with the increase of stress until the specimen ruptures. The time for cracks to appear in cyclic and graded loading is different from that of uniaxial loading. Part of the failure is in the process of stress increase, and some specimens are damaged during stress reduction or the process of stress maintenance, as shown in Tables 1 and 2.

| Electromagnetic radiation and surface cracks
To quantitatively compare the multiparameter signals observed in the test, the number of electromagnetic radiation pulses, surface crack length, stress, and displacement are used as parameters, and the sample SC24 is taken as an example for analysis, as shown in Figure 11. Although stress is a common monitoring method, according to the F I G U R E 9 Principal crack propagation process of coal sample SC31-2.
F I G U R E 10 Principal crack propagation process of coal sample SC13. parameters in the experiment, the failure of the specimen cannot be predicted well in advance at about 29 s. Both electromagnetic radiation and surface cracks can be quickly identified, and there are apparent electromagnetic radiation peaks and surface crack propagation at 29 and 32 s. Electromagnetic radiation, a commonly used noncontact monitoring and monitoring method for coal and rock dynamic disasters in underground mines is more consistent with the length signal of surface cracks, and can intuitively show the process and suddenness of specimen failure. Therefore, the experiment proves from the laboratory that the image processing of surface cracks can become a new early warning parameter of coal-rock dynamic disasters in underground coal mines.
The surface cracks selected to be observed in the experiment are the principal cracks that lead to the failure of the specimen. They are the intuitive reaction of the internal failure of the specimen, which can represent the failure process of the crack. Therefore, by monitoring the changes of electromagnetic radiation pulses in the underground working face, in addition to the stress changes of the coal body, the development of cracks in the coal seam can also be obtained, which provides a reference for coalrock dynamic disasters and gas drainage in coal mines.

| Test site and scheme
The portable EME-HF mine intrinsically safe electromagnetic radiation meter predicts the dynamic disaster of coal and rock by receiving the electromagnetic radiation signal generated during the deformation and rupture of the coal and rock mass. To study the variation law of electromagnetic radiation at the coal mine site, tracking monitoring was carried out on the N4106 working face of the Shadunzi Coal Mine. The layout of the measuring points is shown in Figure 12.
The test scheme is as follows: (1) The electromagnetic radiation signal of the coal wall is monitored every 10 m in the return air slot along the mining direction from the working face. (2) A measuring point is selected on the coal wall near the working face in the return air slot, and continuously observes the change of the electromagnetic radiation with the advancement of the working face.
Through the continuous observation of the electromagnetic radiation of the mining face for 1 month, a large amount of data is obtained, and the electromagnetic radiation of the coal body in the static period (stress unchanged) and dynamic period (stress increase) are analyzed.

| Electromagnetic radiation of the coal body in the static period
In the return airway, 10 measuring points are arranged in sequence on the coal wall in the advancing direction from the working face, and the distance between adjacent measuring points is 10 m. The maximum energy value and the number of pulses are recorded, as shown in Figure 13. As it moves away from the working surface, the energy value and the pulse number have the same trend, first increasing and then decreasing, then tending to a stable weight. Among them, there is a higher peak around 20 m and a lower peak around 60 m, but the peak at 60 m is slightly higher than the stable value behind.
The electromagnetic radiation distributed along the roadway is in the shape of an asymmetric hump. The hump near the end of the working face is higher, which is different from the stress distribution curve of the coal body in the traditional working face direction, as shown in Figure 14. The stress distribution has a peak near the F I G U R E 12 Electromagnetic radiation measuring point layout.
F I G U R E 13 Distribution diagram of coal electromagnetic radiation in return airway of N4106 working face. end of the working face and gradually decreases to the original stress in other places. The difference between the electromagnetic radiation and the stress distribution can be explained by the electromagnetic radiation signal during the uniaxial compression of the coal specimen: before reaching the stress peak, the electromagnetic radiation has a small signal peak. This is because many small cracks begin to appear inside the specimen at this time, and these newly generated small cracks or the expansion process of the original cracks will generate electromagnetic radiation signals.

| Electromagnetic radiation of the coal body in the dynamic period
To analyze the influence of the advancement of the working face on the electromagnetic radiation of the coal body, a distance of 400 m from the mining stop line was set as the reference point, and paint was sprayed on the coal wall as a mark. A recording was made as shown in Figure 15. When the distance from the working face to the measuring point is more excellent than 70 m, the impact of mining is small, the coal body is not depressurized, and the electromagnetic radiation is in a stable range within this range. When the working face is 50-70 m away from the measuring point, it begins to be affected by mining, fractures develop in the coal body, and the electromagnetic radiation in this range has a small peak value. When the working face is advanced to about 18 m from the measuring point, it is located at the roof caving step distance, where the stress is concentrated, and the electromagnetic radiation is relatively dense.
Through the monitoring of the electromagnetic radiation of the coal body near the mining face and the later data analysis, it can be obtained: 1. The electromagnetic radiation value has an excellent corresponding relationship with the stress value. The electromagnetic radiation pulse value and energy value increase with the increase of the coal body stress; the distribution range is relatively consistent with the distribution trend of the stress distribution map of the coal body, and there are apparent differences in the electromagnetic radiation signals in the pressure relief area, the stress concentration area, and the original rock stress area. 2. There is a big difference between electromagnetic radiation and stress at a distance of 50-70 m from the working face, where the stress change is not apparent, but fine cracks develop inside the coal body, and the electromagnetic radiation increases. 3. The electromagnetic radiation value of the coal wall is measured by static and dynamic measurement, which verifies that the relationship between electromagnetic radiation and crack propagation and coal fracture under uniaxial loading in the laboratory is consistent, which can guide Live application.

| The relationship between electromagnetic radiation and stress
Through laboratory experiments and engineering field measurements, the stress change curve of the specimen in the laboratory is similar to the stress change curve of the coal mine underground working face, and the electromagnetic radiation energy value of the coal mass has a positive correlation with the stress. According to the electrical coupling model of coalrock deformation and failure, the relationship between EMR pulse and coal-rock stress-strain is 45,46 F I G U R E 14 Stress distribution of working face.
F I G U R E 15 Variation of electromagnetic radiation at 400 m with the working surface.
In the formula, ε is the strain of coal microelement; ∑N is the cumulative number of electromagnetic radiation pulses when strain increases to ε during the loading process; N 0 is the number of electromagnetic radiation pulses of specimen completely destroyed; M is the distribution scale of Weibull distribution; ε 0 is the form parameter characterized by strain.
The relationship between damage factor D and electromagnetic radiation pulse is as follows: The relationship between damage factor D and elastic modulus is where, E is the elastic modulus after damage; E 0 is the initial nondestructive elastic modulus.
Combining Formulas (1)-(3), in the 1D case, the constitutive relation of coal and rock materials expressed by the number of electromagnetic radiation pulses is where σ is the stress.

| Similarities and differences between laboratory and engineering field dynamic load
With the coal-cutting machine mining, working face advance, and working face hydraulic support constantly rising and falling, the coal mass stress in the engineering site is continually changing. To simulate this change, uniaxial compression, cyclic loading, and graded loading tests were used in the laboratory. The electromagnetic radiation changes of the coal wall in the direction of the working face, and with the advance of the working face were measured in the engineering field, and good observation results were achieved. However, there is a big difference between the laboratory and the field. First of all, the compression failure in the laboratory is regular, according to the set compression failure rate (0.5 MPa/s); although the working face presents regularity as a whole, the stress variation presents discontinuity and inhomogeneity in different mining process periods such as coal-cutting and maintenance. Second, the laboratory can avoid a lot of interference, but there are often various emergencies in the field, so the test conditions cannot be maintained under certain conditions.
To explore the similarity of the electromagnetic radiation curves of the compression failure process in the laboratory and the engineering site, the normalization method was used to process the experimental data. Taking the number of electromagnetic radiation pulses in Figures 4 and 15 as a parameter, the time of compression failure in the laboratory and the distance of the engineering site are uniformly defined as the process of compression failure. The processing result is shown in Figure 16. Among them, the abscissa 0 represents no compression, 1 represents compression failure; the ordinate 0 represents the number of pulses is 0, and 1 represents the maximum number of pulses. It can be seen from Figure 16 that the electromagnetic radiation in the laboratory and the engineering site has the same trend of change. The difference is that the peak value of the electromagnetic radiation at the engineering site is more prominent, which may be due to the more intense coal and rock damage and more abundant crack development in the engineering site. The laboratory is a simplification and approximation of the field conditions. Although the conditions cannot be guaranteed to be consistent, there are relatively constant laws. Therefore, the laboratory can provide specific guidance for the field.

| Application of electromagnetic radiation monitoring in gas extraction
Through laboratory tests, it was found that the crack propagation was accompanied by the occurrence of F I G U R E 16 Comparison of electromagnetic radiation during loading and compression failure in laboratory and engineering site after normalization. electromagnetic radiation signals. Given the unclear development of internal cracks in the coal body under the coal mine, which leads to the unsatisfactory effect of coal gas drainage and pressure relief, it is proposed to use the electromagnetic radiation intensity of the underground coal body to reverse the development of coal body internal cracks.
China's coal mine underground working face mining currently implements a three-shift work system, with one shift for maintenance and two shifts for production, each change in 8 h. Is it possible to simplify this to a circular loading process? Under the combined action of the power of the coal cutter and the overlying pressure of the coal body, the stress on the coal body along the mining direction of the working face changes continuously, and the development of its internal cracks is essential for the arrangement of the gas drilling and the prevention of coal and coal. It is of great significance to gas outbursts and to eliminate stress concentration.
Currently, test methods such as acoustic emission and CT scanning can dynamically locate the inside of specimens, but there are some problems such as unintuitive spatial positioning of acoustic emission, slow CT scanning speed, and small scanning area. 47,48 Through the program of largescale automatic quantitative identification and calculation, it can monitor the damage of the coal mass and the spatial position of the crack in real-time, and it can correspond to the stress. The process of surface crack propagation is accurate to the time scale of 1 ms; the length and area of the surface crack can be calculated to obtain feedback on the crack propagation and the failure of the coal specimen. Through laboratory tests, the development of cracks in the coal body can be fed back according to the variation of electromagnetic radiation signal, guiding for taking other pressure relief measures and drilling layout.
Electromagnetic radiation has advantages over standard coal mine monitoring methods such as drilling cuttings and microseismic monitoring. First of all, electromagnetic radiation is a noncontact measurement method, and the quality is lighter than handheld measurement. Second, the whole measurement can be carried out quickly in intermittent coal mining. Third, the abnormal areas of other monitoring indicators can be rapidly verified. Finally, coal seam water injection, pressure relief drilling, hydraulic punching, and other measures before and after the close monitoring. 49

| CONCLUSIONS
In the process of coal specimen loading damage, electromagnetic radiation monitoring electromagnetic radiation signals of coal specimens and high-speed camera shooting specimen surface crack propagation were used and the stress-time curves were compared. The characteristics of crack propagation and stress failure stage of the coal wall surface were analyzed, and the variation law of electromagnetic radiation of coal wall in situ is obtained. The multisource information, such as strain, electromagnetic radiation, and image, was obtained through a comprehensive analysis of the test data. The conclusions are as follows: 1. In the uniaxial compression process, electromagnetic radiation and surface crack length will be changed with the stress increase. With the rise of stress to a particular stage, the amplitude of electromagnetic radiation begins to increase and reaches the maximum when the specimen was destroyed. When the stress comes to a particular value, the length of the surface crack increases rapidly, and then the increase is not apparent in the following time stage. These two stages continue to cycle until the coal specimen is broken. The peak value of the electromagnetic radiation signal leads to crack initiation, propagation, and penetration for 1-2 s. By comparing with the electromagnetic radiation that has been maturely applied, it is proved that surface cracking is feasible as a monitoring method. 2. By processing the images of the crack propagation process on the surface of coal specimens, the images containing cracks and changes in crack length are automatically screened out, and then the crack length and crack propagation rate are quantitatively analyzed. The calculated results show that the crack length changes on the millisecond time scale, and the crack propagation speed is about 2000 mm/s. 3. Through the comparison of laboratory and engineering field tests, it is found that the stress change trend of the coal mass in these two cases is consistent. Therefore, it is proposed to compare the correlation between electromagnetic radiation and crack propagation when the specimen destroying in the laboratory, then estimate the change of electromagnetic radiation with the working face. The development of cracks in different areas during advancement provides a reference for eliminating stress concentration areas and gas drainage borehole arrangements.