Abstract
Taking raw coal and briquette coal samples with preset center holes as research objects, this paper makes a systematic analysis and research of crack evolution laws of the two different coal samples under the local load. The results show that the raw coal and briquette coal samples are different mainly in number, dimension, and complexity of the internal microstructures, so it is not right to replace raw coal with briquette coal when performing observational study of the crack evolution of microstructures; under the effect of local load, local property, randomness of crack initiation position, and crack initiation stress of raw coal samples are greater than those of briquette coal samples; law of instantaneous maximum effective cut-through rate of raw coal samples is more complex than that of briquette coals; under the effect of uniformly distributed load, end effect factor Fe, sample microstructure influencing factor Fs, and preset center hole factor Fh are the major factors influencing crack growth, among which the amplified end effect factor Fe and sample microstructure influencing factor Fs are dominant factors; under the effect of local load, local load influencing factor Fp, end effect factor Fe, sample microstructure influencing factor Fs, and preset center hole factor Fs are the major factors influencing crack growth, among which the local load influencing factor Fp, end effect factor Fe, and sample microstructure influencing factor Fs are dominant factors. Compared with briquette coal samples, raw coal samples are more sensitive to influencing factors, such as local load influencing factor Fp, end effect factor Fe, sample microstructure influencing factor Fs, and preset center hole factor Fh, and can aggravate the influence of these factors on the crack growth; the paper also puts forward a method for describing local load based on a coupling mechanical model of uniaxial compression and local shear.
1. Introduction
As geological materials formed under special geological conditions and environment, coal resources are characterized by porosity, aeolotropy, and heterogeneity. For the above three major reasons, it is significantly difficult to prepare coal samples for conducting mechanics experiment research with the standard size recommended by the International Society for Rock Mechanics. Furthermore, the rate of success is also rather low. As a result, in many experimental studies, briquette coal samples are usually used to replace raw coal samples to perform relevant experiments and studies. However, because the briquette coal samples cannot completely reflect the features of the internal structures of raw coal, it has been disputed whether using briquette coal samples for experiment can achieve the right law that can accurately show the features of raw coal. Under the same external mechanical conditions, whether surface crack evolution laws of the two kinds of samples is the same are identical and whether briquette coal samples can accurately reflect the surface crack evaluation law of raw coal samples needs further study.
Local load is a kind of nonuniform load, and when a sample is under the effect of local load, it will be an obvious local effect in its interior, such as local deformation, local stress concentration, etc., which can magnify the influence of load on the sample to some extent; in the samples, there are preset holes which can also intensify the local effect, including local stress concentration and increase of new cracks.
Scholars have carried out a large number of researches on the crack propagation law of the samples containing holes, mainly focusing on the conditions of uniaxial compression, biaxial compression, triaxial compression, and impact loading, whereas few studies on crack propagation law of holes under partial load. Yang et al. [1] have studied the features of the samples cracks with single hole on origination, initiation, propagation, evolution, and coalescence in uniaxial compression process by using scanning electron microscopy, which demonstrated that heterogeneity has a great influence on the crack propagation features of the samples. Nemat-Nasser and Horii [2, 3] conducted real-time observation researches on the cracks around single or multiple fissures of its development process in the simulated rock materials. Li et al. [4] used SHPB [5] to study the crack propagation characteristics and propagation velocity of plate-shaped specimens with round and oval holes. The results show that the average crack propagation velocity of marble sample is 100∼450 m/s under the loading strain rate of 30∼45 s−1. Tang et al. [6, 7] conducted compressive tests and numerical simulations on the axial splitting failure characteristics of brittle materials with prefabricated holes, which found that the origination and propagation of cracks started from the area of tensile stress concentration of the hole. Ma et al. [8] observed the circular holes failure process of the marble square slab with a central circular hole and the deformation field evolution under the condition of uniaxial compression. Carter et al. [9] studied the crack propagation features of granite with central holes under uniaxial compression. It is concluded that the distant field crack starts to evolve, when the initial crack length extends to the same length as the diameter of the central hole. Xu et al. [10, 11] summarized the microscopic evolution law of primary cracks in the process of shear failure of coal and studied the mesoevolution process of shear cracks in briquette samples under different gas pressures. Peng et al. [12] studied the cracks evolution and fractal features of coal containing gas (coal and briquette) in the process of shear failure. Zhao et al. [13] studied the crack propagation law of porous samples with partial load. It considered that the crack propagation is the coupling action result of loading conditions and macroscopic central pores. Scholars concentrated researches on the crack propagation features under uniform load and have achieved fruitful results. However, there are relatively few studies on the crack propagation law of porous media under local loads. In addition, it is still controversial whether the evolution law of surface cracks in briquette samples can be used to characterize the surface crack evolution of coal samples under the same external conditions, and few scholars carry out relevant research.
Therefore, in order to study the difference of crack evolution laws of raw coal and briquette coal samples under external conditions, this paper adopts local load as stress condition and selects cube raw coal and briquette coal samples with preset center holes to make systematical analysis of differences in laws presented by the two kinds of samples from perspectives of local features, crack initiation stress and position, maximum effective instantaneous penetration rate, etc.
2. Sample Preparation and Local Load
2.1. Preparation of Raw Coal Samples
All coal samples used in the experiment were taken from Ganhe Mine of Shanxi Huozhou Coal Electricity Group. A large block of raw coal was taken from the working face and transported to the laboratory after being wax-sealed. In the laboratory, the coal block was processed into standard cube samples of 70.0 mm × 70.0 mm × 70.0 mm, through wet processing including core drilling, cutting, and smoothing, according to the requirements for experimental method recommended by the International Society for Rock Mechanics and then, selected the samples without obvious stratification distribution and drilled an 8.0 mm vertical penetration hole in the center position of each sample, as shown in Figure 1.
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2.2. Preparation of Briquette Coal Samples
Raw coal for preparing briquette coal samples was also taken from Ganhe Mine of Shanxi Huozhou Coal Electricity Group. A large block of raw coal was taken from the working face and transported to the laboratory after being wax-sealed. In the laboratory, the coal block was pulverized, and the pulverized coal with granularity of less than 1.0 mm was selected for future use, and the selected pulverized coal was mixed uniformly with concrete and water in the proportion 10.0 : 2.4 : 1.6, the mixture was put into the self-developed mould of briquette coal preparation equipment (Figure 2), and then 5.0 MPa briquetting pressure was provided for 20.0 min to demould and they were kept still for two weeks. Then, an 8.0 mm vertical penetration hole was drilled in the center position of each sample, as shown in Figure 3.
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2.3. Local Load
During the experiment, local load was given according to the following steps: fixed the bottom of the sample, imposed the pressure from the top of the sample to realize the imposing of local load by changing the area of pressure action surface. That is, the load was imposed on the relative areas of S, 3S/4, 2S/4, and S/4 (S refers to the surface area of the sample loading surface), respectively, at a loading rate of 0.5 MPa/s to the designed loading value. In this way, local loading was realized, as shown in Figure 4.
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3. Influence of Local Load on the Crack Evolution of Raw Coal and Briquette Coal
3.1. Physical Inspection of Differences between the Two Types of Samples
Before the experiment, four means were used including weighing, strength testing, together with ultrasonic testing, and nuclear magnetic resonance detection to find out the difference between the raw coal samples and briquette coal samples. The weighting results show that the average mass of raw coal samples was about 440 g, while that of briquette coal samples was around 490 g; the strength test results indicate that the uniaxial compressive strength of the raw coal samples was about 1.82 MPa, while that of briquette coal samples was around 0.94 MPa; the ultrasonic test results reveal that the average speed of ultrasonic propagation in raw coal samples was about 1800 m/s, while that in briquette coal samples was 1100 m/s; the results of nuclear magnetic resonance imaging are shown in Figure 5.
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The area of the shadow part in the graph was the amount of pore structure within the scale range. According to Figure 5, porosity of briquette coal samples was about 15%, and the pore radius was within the scope of 0.01∼100 μm, and concentrating upon 1∼10 μm, with a maximum peak in around 1 μm, porosity of raw coal samples was about 5%, and the pore radius was within the scope of 0.001∼10 μm, concentrating upon 0.001∼0.1 μm, with a maximum peak in around 0.01 μm.
The results of the four studied mentioned above indicated that there exists a certain degree of difference between the briquette coal samples and the raw coal samples, mainly in number and dimension of pore structures, but from uniaxial compressive strength, propagation velocity of ultrasonic wave, porosity, and pore distribution, briquette coal samples and raw coal samples were greatly similar to each other. The main difference lied in the two aspects of the number of microstructures and the scale of microstructures.
3.2. Local Features of Cracks in Two Samples
According to the designed experimental scheme, related experiments were carried out to observe the crack initiation of raw coal and briquette coal samples under different local loads, respectively, as shown in Figures 6–9.
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During the process of imposing a load by an action area of S on raw coal and briquette coal samples, a HD digital video camera was utilized to shoot the surfaces of the samples, and then pictures were extracted from the video frame by frame. The HD digital video camera is SONY HDR-PJ600, and the shooting used HD mode (1920 ∗ 1080/50i (FX, FH)). In the pictures, burst-mode cut-through failure instead of obvious progressive crack growth was observed, for the briquette coal samples, cracks generated were not obvious at the early stage, but suddenly increased when the load imposed was near the cracking load. In this case, when the two types of samples were close to failure, the number and width of the newly generated cracks, bending complexity of the cracks, and roughness of the cracks’ interior in the raw coal samples were obviously greater than those in the briquette coal samples. In the two types of samples, some of newly generated cracks started from the sample bottoms while some started from the edge of the preset center holes. The distribution of newborn cracks was relatively uniform, which occurs mostly at the end of the specimen and the circumjacent of the preset central hole and parts of the newly generated cracks did not pass through the preset center holes. In addition, the newly generated cracks had no obvious local features.
Local load was imposed on raw coal and briquette coal samples respectively, which was realized by changing the load action area (3S/4, 2S/4, and S/4). During the experimental process, an obvious process of crack initiation, development, and growth was found in the surface of raw coal samples, and the length, quantity, width, and evolution rate of newly generated cracks significantly increased with the intensification of the effect of local load. Besides, when the sample was destroyed, the penetration of the new crack was particularly prominent and the main control crack appeared in most of the specimens. However, there was no distinct changing of the original cracks which showed notable change after joining in new initiated cracks. In addition, most raw coal samples showed “flaking” with the evolution of new cracks, and their burst-mode brittle failure was evidently magnified. There was also an obvious process of crack initiation, development, and growth in the surface of briquette coal samples, but the quantity, width, and complexity of evolution process of newly generated cracks were significantly lower than those of the raw coal samples. When the briquette coal was close to failure, the newly generated crack caused by dominant factors is not a cut-through crack, but a crack composed of two-directional cracks connected by the preset center hole when the load action area covers the preset center hole; or a new crack generated near the center of the sample and in the edge of the load action area when the load action area not covers the preset center hole. Under the effect of local load, newly generated cracks in the surfaces of both raw coal and briquette coal samples were initiated from the bottoms of the samples, and they were obviously more in the edge of load action area than in other areas; there were almost no new cracks generated in the area without the effect of the partial load. Moreover, the distribution law of newly generated cracks in briquette coal samples was more obvious than that in raw coal samples. And local features of crack initiation in both types of samples were very notable, but local feature of cracks in raw coal samples was more visible than those in briquette coal samples.
3.3. Crack Initiation Position of the Two Types of Samples
Crack initiation position is an important indicator that reflects the sequence and evolution of cracks generated in samples. During the experiment, a HD digital video camera was utilized to catch the surfaces of the samples, and then pictures were extracted from the video frame by frame, and sequence of crack appearance in sample surfaces was obtained through comparing each picture. The sequence of cracks were marked, and the main cracks on the sample surface were depicted to study the initiation position of cracks generated in the two types of samples, as shown in Figure 10.
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In the above pictures, cracks were marked by numbers 1, 2, 3, and 4, and the sequence of crack initiation was a, b, c, and d. According to Figure 10, the effect of local load has a significant influence on the initiation positions of cracks in samples with the central hole. Under the effect of partial load on 3S/4 of the sample, there are two cut-through cracks generated in the raw coal sample, of which one does not pass through the center hole (crack #2 in raw coal, Figure 10(a)) and is initiated from the loading critical position (point b), and it cuts through the sample in advance of the other crack which passes through the center hole (crack #3 in raw coal, Figure 10(a)) and starts from the loading critical position around the center hole; there is only one cut-through crack generated in the briquette coal sample (crack #1 and crack #2 in briquette coal, Figure 10(a)). The crack starts from the loading critical position and gradually extends downwards to form crack #1, and in the same time, it starts from the periphery of the center hole and gradually extends downwards to form crack #2. The growth and cutting-through of crack #1 and crack #2 finally cut through the sample and caused its failure; under the effect of partial load on 2S/4 of the sample, the crack growth in both the raw coal and briquette coal samples is basically the same. That is, the crack starts from the loading critical position and gradually extends downwards to form crack #1, and in the same time, it starts from the periphery of the center hole and gradually extends downwards to form crack #2. The growth and cutting-through of crack #1 and crack #2 finally cut through the sample and finally caused the failure of the raw coal and briquette coal samples; under the effect of partial load on 1S/4 of the sample, the crack growth law in both the raw coal and briquette coal samples is basically the same. That is, only one cut-through crack is generated, only the quantity and complexity of cracks generated in raw coal samples are greater than those in briquette coal samples, and the crack starts from the load critical position and gradually extends towards the center hole from the edges, and moreover, all the cracks are within the scope of effect of the partial load and do not pass through the preset center hole.
3.4. Crack Initiation Stress Analysis of Two Samples
Because it is impossible to directly observe the internal crack initiation of coal, the stress corresponding to crack initiation on sample surface shall only be defined as the crack initiation stress; at the same time, considering the impacts of load-carrying area on coal sample crack initiation stress, the load-carrying area shall take the average value of load-applying area and base area as effective area for calculation of crack initiation stress. The relation curves between loading-carrying conditions and crack initiation stress of two kinds of samples are as shown in Figure 11.
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As can be seen from the crack initiation stress data of the two samples in Figure 11 that when the load-carrying areas of raw coal sample and briquette coal sample are between S/4 and 2S/4, the change of crack initiation stress is relatively significant; when the load-carrying area is between 2S/4 and 3S/4, the change of crack initiation stress is relatively relaxed; when the load-carrying area exceeds 3S/4, the change of crack initiation stress becomes significant again; a clear “reverse S” relation is presented between relative load-carrying area and crack initiation stress of two kinds of samples; it is only that the degrees of significant and gentle changes have slight difference. Under the same stress condition, the crack initiation stress of briquette coal is clearly smaller than that of raw coal; when there is same degree of change in stress condition, the degree of change in crack initiation stress of briquette coal is also clearly smaller than that of raw coal. The consistency in change regulations of crack initiation stress of raw coal sample is poor, and the impact regulation on it of local load action is also not consistent; the large difference between groups of raw coal sample crack initiation stresses also explains why the regularity in raw coal crack growth is poor; to study the change features of crack initiation stress of raw coal sample from perspective of statistical regularity, the averaging treatment was conducted to obtain data of crack initiation stress of two groups of raw coal sample and it can be found that with the weakening of local load effects (which is the increase of the ratio between load-applying area and base area), the crack initiation stress of raw coal sample presents gradual increasing trend which is also consistent with the regulation as mentioned above where the raw coal sample damages under uniform distribution of load are mostly presented to be burst-mode damages, that is, the value of stress for crack initiation is large and even is close to failure load sometimes. The regularity of crack initiation stress change of briquette coal sample is relatively strong, and the regularity of impact on it of local load action is also relatively strong which means that the homogeneous degree of briquette coal sample is clearly better than that of raw coal and the complexity of its internal structure is far lower than that of raw coal.
3.5. Instantaneous Maximum Effective Cut-Through Rate of Crack
To compare the differences on crack growth of raw coal and briquette coal samples caused by local load, the method of extracting the videos taken by high-speed cameras as per each frame to obtain the high-definition images of each moment (with interval of 0.02 s) is adopted and the effective penetration size of crack at each moment is measured based on images to obtain the effective penetration rate of crack at each moment under the local load action; instantaneous maximum effective cut-through rate is selected and its data to obtain the instantaneous maximum effective cut-through rate of cracks are organized, as shown in Figure 12.
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It is shown in Figure 12 that the correlation curves of raw coal samples and briquette coal samples present two kinds of different forms. The crack growth of raw coal samples is usually related to fracture, pore systems, load conditions, and preset center hole, while the crack growth of briquette coal samples can only be deemed to be related to load conditions and preset center hole. For the raw coal sample, there is clear difference between groups. But as a whole (mainly presenting on the average value), the increase of instantaneous maximum effective cut-through rate of crack presents the “three-phase” change regulation of increasing first and slow transition latter and then sharply increasing. Therefore, it can be considered that under the condition of only considering the crack and pore system of raw coal sample, the instantaneous maximum effective cut-through rate of crack presents increased trend with the increase of load-carrying area, while when considering the preset center hole, there will be an impact range (2S/4∼3S/4) and within this range, the preset center hole weakens the trend of increasing of instantaneous maximum effective cut-through rate of crack to present the feature of gentle transition. For the briquette coal sample, because the fracture and pore system of sample is usually single, it can be considered that the instantaneous maximum effective cut-through rate of crack is only closely related to load conditions and preset center hole and it presents the “two-phase” change regulation of reducing first and then increasing with the increasing of load-carrying area; when the relative load-carrying area is less than certain critical load-carrying area, the smaller the relative load-carrying area, the greater the instantaneous maximum effective cut-through rate of sample surface crack; after exceeding the critical value, when the stress concentration caused by continuous increasing of load-carrying area is gradually weakened while the preset center hole causes the stress concentration action in sample and such action is gradually strengthened and takes the leading position, it will cause the instantaneous maximum effective cut-through rate of sample crack during this phase to present increase trend with increase of load-carrying area. The difference between change regulations of instantaneous maximum effective cut-through rate of cracks of raw coal sample and briquette coal sample can exactly explain the inducement through which the damages on raw coal present burst-mode while damages on briquette coal present gradual mode.
4. Discussion
When adopting cube sample to conduct mechanical properties test, the end effect will be intensified due to the change of the sample shape. By changing the loading area SJ to change the uniform load to a partial load, the difference in load-carrying areas causes the difference in end face bearing range of sample; and the difference in load-carrying area will change the stress conditions in sample so as to change the deformation process of sample into combination of several typical deformation processes, which will present the deformation features clearly different from that under even distribution of load. For the samples of raw coal and briquette coal, the quantity, size, and complexity of microstructures in raw coal samples are all larger than that of briquette coal samples; therefore, when bearing the same load, the effective bearing area SD will be less than the actual bearing area SC; due to the clear increase of quantity, size, and complexity of shapes of microstructures, when bearing the same load, the stress concentration generated on the end of internal microstructures of raw coal will be clearly larger than that of briquette coal; the stress concentration on end of microstructures will cause guiding functions on crack evolution which will cause generation and growth of raw coal sample cracks to be more complex; when the cracks on sample generated due to end effect is connected with preset center hole, the stress concentration caused by crack center hole will be superimposed with the two factors mentioned above to further magnify the promotion on coal sample crack evolution of local load and make this change process more complex. Therefore, the four aspects including the factor Fp of local load action, factor Fe of magnified end effect, factor Fs of internal microstructure action in sample and factor Fh of preset center hole shall be separately taken into consideration to study the theoretical model of crack evolution of sample under local load action.
4.1. Condition of Even Distribution of Load
Under the action of even distribution of load, the sample is under uniaxial compression state and overall deformation features can comply with typical uniaxial compression theory. While the localization feature, crack initiation position, crack initiation stress, and instantaneous maximum effective cut-through rate of sample surface crack will be impacted by three aspects including factor Fe of magnified end effect, factor Fs of internal microstructure of sample and factor Fh of preset center hole, of which the factor Fe of magnified end effect and factor Fs of internal microstructure of sample are main controlling factors, and its theoretical model is as shown in Figure 13(a).
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Because of adopting cube sample, the frictional effect between load-applying pressure head and sample shall be larger, the end effect factor Fe will be magnified, and the transverse strains (ε3h) with different distance from end in sample in the end effect area will be unevenly increased with the increasing of distance, which will cause the shear stress among sample cross sections in the end effect impact area and make samples more easily being “torn” and generate more cracks on the end. For raw coal samples, the quantity, size, and complexity of microstructures in samples will increase the factor Fs of microstructure action, cause the stress concentration on end of each microstructure clearer, and increase the chances for such microstructure to participate in crack growth which is presented, as there will be surface cracks with more quantity, larger size, and more complex evolution directions in samples, as shown in Figure 13(b); for briquette coal samples, the microstructure in samples is relatively simple and the intensifying action on crack growth of factor Fs of microstructure action is not that clear; the end effect factor Fe plays the main control function, which is therefore presented as that cracks are more likely to appear on sample end face with small quantity and relatively simple crack evolution directions, as shown in Figure 13(c).
4.2. Conditions of Local Load
Under local load action, the stress state of sample can be simplified as the model shown in Figure 14 which includes two parts: part of uniaxial compression and part without local load action; the critical plane between two parts is the shear action belt formed under local load action. Therefore, factors impacting localization feature, crack initiation position, crack initiation stress, and instantaneous maximum effective cut-through rate shall also be divided into three parts, which is that the impact factors on localization feature, crack initiation position, crack initiation stress and instantaneous maximum effective cut-through rate shall be consistent with that under even distribution of load while the part without local load action has no significant crack evolution. The localization feature, crack initiation position, crack initiation stress, and instantaneous maximum effective cut-through rate of surface cracks of shear action belt is impacted by four aspects including factor Fp of local load action, factor Fe of end effect, factor Fs of internal microstructure action in samples and factor Fh of preset center hole, of which the factor Fp of local load action, factor Fe of end effect and factor Fs of internal microstructure action in samples are main controlling factors.
Because the shear action belt is the critical zone between zone under impact of local load and zone without impact of local load, there is obvious stress concentration caused by local load boundary which plays obvious shear action to the sample. The shear strength of coal sample is clearly less than uniaxial compression strength which will cause this zone to more easily generate new cracks which is the action of factor Fp of load action. Factor Fe of end effect will form “torn” zone in sample to cause more new cracks through the differences in deformation natures and sizes between two parts of the critical zone; the factor Fs of internal microstructure in sample mainly plays the functions of reducing the equivalent area of shearing surface in this shear action belt, increasing shear stress actually applied on this surface so as to play promotion action on the crack evolution. If the shear surface in shear action belt is near to preset center hole, the cracks generated by factor Fe of magnified end effect will be easier to be connected with preset center hole which will cause factor Fe of magnified end effect to be coupled with factor Fh of preset center hole to be in action presented as that on one hand, the stress concentration caused by both of them are superimposed and one the other hand, the existing of preset center hole will reduce the equivalent area of shear surface in shear action belt but increase the shear stress applied on shear surface so as to cause cracks to be easily generated and developed. For the raw coal sample, the complexity of its internal structure will reduce the equivalent area of shear surface in shear action belt more obviously but increase the shear stress applied on shear surface so as to more easily cause cracks generated due to end effect to be connected with preset center hole which will be more favorable to the generation and evolution of cracks, thus causing cracks with larger quantity and sizes and increasing complexity in crack evolution paths, as shown in Figure 15(b), while due to relative simple internal microstructure of briquette coal, the two actions mentioned above are not obvious, and the impacts caused by local load on its crack growth will not be obvious as that of raw coal sample, as shown in Figure 15(c).
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5. Conclusion
Through the serial tests and study conducted, mainly following conclusions can be obtained:(1)The main differences between raw coal sample and briquette coal sample are manifested on aspects including quantity, size, and complexity, etc. of internal microstructure. The mechanical test can be conducted by using briquette coal sample to replace the raw coal sample which, however, is not applicable for observation and study on microscopic crack evolution.(2)Under local load action, the localization feature appeared on raw coal sample cracks is obviously higher than that of briquette coal sample; the randomness of crack initiation positions is clearly higher than that of briquette coal sample; the crack initiation stress is obviously greater than that of briquette coal sample, and the regulations on instantaneous maximum effective cut-through rate of raw coal sample cracks are obviously more complex than that of briquette coal sample.(3)Under even distribution of load, factor Fe of end effect, Fs of internal microstructure in sample, and Fh of preset center hole are the main factors impacting crack growth and the magnified factor Fe of end effect and factor Fs of internal microstructure in sample are main controlling factors.(4)Under local load action, the mechanical model can be simplified into combination of uniaxial compression and local shear; the crack growth are impacted by four aspects including factor Fp of local load action, factor Fe of end effect, factor Fs of internal microstructure action of sample, and factor Fh of preset center hole, of which the factor Fp of local load action, factor Fe of end effect, and factor Fs of internal microstructure action of sample are main controlling factors.(5)Compared with briquette coal sample, the raw coal sample is more sensitive to the factors including factor Fp of local load action, factor Fe of end effect, factor Fs of internal microstructure action of sample, and factor Fh of preset center hole, etc., and can intensify the impacts of those factors on crack growth.
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
Financial support for this work is provided by the National Natural Science Foundation of China (Grant no. 51474220), the Research Fund of State and Local Joint Engineering Laboratory for Gas Drainage & Ground Control of Deep Mines (Henan Polytechnic University) (Grant no. G201603), the Research Fund of State Key Laboratory Cultivation Base for Gas Geology and Gas Control (Henan Polytechnic University) (Grant no. WS2017A06), and the Fundamental Research Funds for the Central Universities (Grant no. 2009QZ03).