Coal seams are both source rocks and reservoirs of coalbed methane (CBM). Unlike conventional natural gas, CBM is mainly stored in an ads orbed state in pores of the coal reservoir matrix. Coal reservoirs in China have generally low permeability, (0.3-0.5) × 10^-3 μm² on average, and low porosity and pressure besides^[1]. For most coalbed methane wells, without stimulation measures, many wells don’t even have industrial development value^[2]. Hydraulic fracturing is one of the major CBM recovery techniques. Through hydraulic fracturing, the free and absorbed gases in coal reservoirs would enter the well along fractures to achieve large-scale mining^[3,4]. The study of crack initiation and damage mechanisms of CBM reservoirs can guide the design and construction of hydraulic fracturing, and improve the productivity of individual wells^[5].

The crack initiation strength and damage strength are important parameters in the reservoir failure process^[6]. The crack initiation strength of the coal reservoir refers to the critical strength at which cracks begin to sprout in the reservoir. And the damage strength indicates the strength of coal reservoir when a large number of cracks are interconnected, and is the starting point for the unsteady expansion of cracking. It can be seen that crack initiation strength and damage strength have important guiding significance for the parameter design of reservoir hydraulic fracturing. They are affected by many factors. The effects of a variety of factors on crack initiation and crack propagation of coal reservoirs, such as water saturation^[7,8], carbon dioxide saturation^[9,10], liquid nitrogen cooling^[11], temperature^[12], and confining pressure^[13], have been studied experimentally. Yang et al.^[14] and Feng et al.^[15] studied the evolution of acoustic emission events during crack initiation in, and damage to, coal reservoirs with a uniaxial compression test system. Jiang et al.^[16] studied the influence of the direction of maximum horizontal principal stress on the form of propagation of hydraulic fractures in coal seams with large inclination by physical simulation experiments. Zhang et al.^[17] analyzed the influences of geological factors such as in-situ stress conditions, coal structure, and roof and floor lithology on hydraulic fracturing effect of coal reservoir. Fan et al.^[18] studied the influences of fracturing fluid and fracturing technology on hydraulic fractures in coal seam.

The structural characteristics of coal reservoir are also an important factor affecting the hydraulic fracturing effect. Coal reservoirs are typical heterogeneous porous media, with many bedding planes, pores, cleats, and other structurally weak surfaces. The bedding is the first weak joint surface of the coal reservoir, and the cleat is the two sets of natural open fracture systems that are mutually perpendicular and perpendicular to the bedding planes in the coal reservoir. The one that extends longer is face cleat, while the one that is perpendicular and ends at the face cleat is the butt cleat. According to previous studies, the unique fracture system of coal reservoir has important effects on the mechanical properties and permeability of coal reservoir^[19,20], and the anisotropy evaluation of coal reservoir is particularly important^[21]. Ranjith et al.^[22] studied the effects of cleat density and direction on the strength of coal reservoir. Zhang et al.^[23], Kossovich et al.^[24], Zhao et al.^[25], and Liu et al.^[26] conducted experimental studies on coal reservoirs with different bedding angles, and found that the coal reservoir exhibits strong anisotropy in uniaxial compressive strength, elastic modulus, dynamic indirect tensile strength, and acoustic emission characteristics. Hao et al.^[27] studied the influences of bedding and cleats on the strength of coal reservoir and found that the strength of coal reservoir is mainly affected by bedding, but the effect of cleats cannot be ignored. The current researches on the effects of bedding and cleats on the mechanical properties of coal reservoir mainly focus on uniaxial compressive strength, tensile strength, elastic modulus, and so on. There is hardly any research on the effect of bedding and cleats on the crack initiation strength and damage strength.

The hydraulic fracturing technology for CBM development mainly draws on the hydraulic fracturing technology of conventional petroleum reservoirs^[28], but the mechanical properties of coal reservoirs are quite different from those of conventional petroleum reservoirs^[4]. Compared with other reservoirs, coal reservoirs not only have lower strength and elastic modulus, a longer non-linear compaction stage, but also have many weak structural surfaces such as bedding and cleats, and feature significant anisotropy in mechanical properties. Because of these differences, coal reservoirs have hydraulic fracturing mechanisms different from conventional petroleum reservoirs, and more complex mechanisms of crack initiation and damage^[29]. This makes the current theoretical calculation results of hydraulic fracture initiation of coal reservoirs deviate considerably from the real situation and unable to predict and design the crack initiation strength of hydraulic fracture in coal reservoirs.

In this work, the anisotropy of crack initiation strength and damage strength of coal reservoirs is studied, which is helpful for us to understand the crack initiation strength and damage strength of coal reservoirs with different bedding and cleat angles. The research results provide guidance for the prediction and design of hydraulic fracture initiation pressure, help us understand the occurrence and development direction of hydraulic fractures in coal reservoirs with different bedding and cleat directions, and provide guidance for the optimization of full-scale hydraulic fracturing.

The coal reservoir samples used in this work were taken from the 14# coal seam in the Xinzhouyao mine of Datong city. The Xinzhouyao mine has high CBM content, with a CBM emission of 32.55 m³/t. The 14# coal seam belongs to the Jurassic Datong Formation, with a buried depth of 350 m, a coal thickness of 0 to 4.62 m, and an average coal thickness of 1.44 m. The coal belongs to bituminous coal. The 14# coal consists of bright coal and dark coal, with a hard texture, high fracture flatness, and a Protodyakonov coefficient of 3.0 to 4.5.

With widely distributed endogenous fissures, the matrix of the 14# coal seam has significant bedding and cleat structures. To further understand the bedding characteristic of the coal reservoir, the ultrahigh-resolution field emission scanning electron microscope (HIACHISU8010) of China University of Petroleum (Beijing) was used to scan the coal samples, the scanning results are shown in Fig. 1. It can be seen that compared with other reservoirs, the coal reservoir has a large number of weak structural planes such as cleats, and cracks developed inside, and is badly fractured. The beddings are uniform and parallel, and about 80 μm from each other. The break direction of the bedding is basically perpendicular to the direction of the bedding distribution. The direction of cleat is basically perpendicular to the direction of bedding. The cracks in the coal sample are irregularly distributed: most are parallel to the bedding planes, while a small number are at angles with the bedding. The cracks vary in size, and can be up to 100 μm or only a few microns long. From the microscopic point of view, the existence of these bedding planes, cleats, and cracks inside the coal reservoir is bound to lead to anisotropy in the macroscopic mechanical properties of the coal reservoir.

To reduce the discreteness of the samples, the coal reservoir samples were all taken from the same location in the 14# coal seam. According to the method and specification for rock mechanics samples recommended by the International Society of Rock Mechanics, the coal reservoir was sampled as shown in Fig. 2. When drilling samples with different bedding angles, the side parallel to the bedding was fixed to ensure that the direction of the bit and the bedding direction were at an angle, and finally the samples were processed into φ 25 mm × 50 mm standard ones with different bedding angles. After drilling, the fracture network system angles of the three sets of coal reservoir samples are: when the bedding was at any inclination and the inclination angle of 0°, the face cleat was 0° in inclination and 90° in inclination angle, and the butt cleat was 90° in inclination and inclination angle; when the bedding was 0° in inclination and 45° in inclination angle, the face cleat was 180° in inclination and 45° in inclination angle, and the butt cleat was 90° in inclination and 90° in inclination angle; when the bedding was 0° in inclination and 90° in inclination angle, the face cleat was at any angle in inclination and 0° in inclination angle, and the butt cleat was 90° in inclination and 90° in inclination angle. Fig. 2 shows that the beddings, face cleats, and butt cleats are perpendicular with each other. When the bedding angle is determined, the angles of face cleat and butt cleat are determined, therefore, only the bedding angle (0°, 45°, 90°) is used to describe the fracture network system of the coal reservoir. Six samples at each bedding angle were prepared, making a total of 18 samples. Among them, the coal reservoir samples with a bedding angle of 0° (horizontal bedding) are recorded as Z group; the coal reservoir samples with a bedding angle of 45° are recorded as F group; the coal reservoir samples with a bedding angle of 90° (vertical bedding) are recorded as N group. Each sample was cut and polished after drilling to ensure that the parallel deviation between the two ends of the sample was no more than 0.05 mm, the size deviation of two ends was no more than 0.2 mm, the end surface was perpendicular to the sample axis, and the maximum angular deviation didn’t exceed 0.25°.

To compare the discreteness of coal reservoir samples, the axial longitudinal wave velocities of the 18 samples were tested. The test results are shown in Table 1. It can be seen from the table that the wave velocities of samples are mainly affected by the bedding angle. Because the wave velocities of samples F5 and N5 differ widely from the wave velocities of other samples at the same bedding angle, samples F5 and N5 were eliminated.

The coal reservoir samples were loaded in an MTS815.04 rock mechanics testing machine at Wuhan Institute of Coal and Rock Mechanics, Chinese Academy of Sciences, and uniaxial compression testing was conducted under strain control. The loading rate was 5.0 × 10^-6 mm/s. The DISP acoustic emission signal acquisition system produced by PAC Company was used to study the evolution of acoustic emission events of coal under uniaxial loading. In the process of the experiment, the loading and the monitoring of acoustic emission were carried out simultaneously.

The methods used to determine the crack initiation strength and damage strength of coal reservoir include crack volume strain method, acoustic emission parameter value method, lateral strain and volume strain curve observation method, and moving point regression method. Crack volume strain method is the most commonly used at present. Therefore, crack volume strain method was used to determine uniaxial crack initiation strength and damage strength of coal reservoirs in this study.

The crack volume strain method was first proposed by Martin^[30] to calculate the crack initiation strength of rock and has since been widely used^[31,32]. Since the volume strain of coal is generally unable to be measured directly, the following equation was used to calculate approximately:

By subtracting the elastic volume strain from the volume strain, the crack volume strain reflecting crack closure and opening during loading can be obtained. The elastic volume strain and crack volume strain are calculated by the following formulas:

The typical crack volume strain curve of the coal reservoir sample under uniaxial compression is shown in Fig. 3. The coal reservoir sample is the F1 sample with a bedding angle of 45°. In crack closure stage (Stage I), the crack volume strain is positive and the slope of the curve is positive, which indicate that the volume of the coal reservoir sample is decreasing; in the elastic stage (Stage II), theoretically, the increment of coal volume strain is equal to the increment of elastic volume strain, but there is a little difference between the two because coal has a non-linear elastic stage; in stable crack growth stage (Stage III) and non-stable crack growth stage (Stage IV), the total volume strain includes the volume increase caused by crack opening, leading to a negative slope of the crack volume strain curve. Therefore, the stress corresponding to the inflection point where the slope of the crack volume strain curve is zero is the crack initiation strength; the stress corresponding to the point where the slope of the total volumetric strain curve is zero is the damage strength. Accordingly, the F1 sample is determined to have a crack initiation strength of 6.9 MPa and damage strength of 17.5 MPa.

Fig. 4 shows the examples of crack volume strain curves of coal reservoir samples with different bedding angles. Due to sensor failure, the parameters of sample N6 were not obtained. According to the above method, it can be concluded that the samples have crack initiation strength between 4.7 and 10.4 MPa and damage strength between 7.8 and 47.6 MPa. It can be seen that the strength of coal reservoirs shows significant anisotropy due to the influence of fracture network systems such as bedding and cleats in them. The index used to measure the anisotropy of rock strength is the degree of anisotropy^[33]:

Through calculation, the degree of anisotropy of uniaxial compressive strength of the coal reservoir is 1.94. Similarly, the degree of anisotropy of crack initiation strength is 1.49 and the degree of anisotropy of damage strength is 2.31.

To analyze the anisotropy of crack initiation strength and damage strength, the variations of crack initiation strength, damage strength, compressive strength, crack initiation ratio (the ratio of the crack initiation strength to the compressive strength), and damage ratio (the ratio of the damage strength to the compressive strength) with bedding angle were studied (Figs. 5 and 6).

It can be seen from Fig. 5 that the crack initiation strength first decreases and then increases with the increase of bedding angle. When the bedding angle is 0°, the average value of the crack initiation strength is the largest (9.28 MPa); when the bedding angle is 45°, the average value of the crack initiation strength significantly reduces (6.24 MPa); when the bedding angle is 90°, the crack initiation stress is not much different from that at the bedding angle of 45°, with an average of 6.80 MPa. The damage strength also shows the similar variation trend. The compressive strength decreases with the increase of the bedding angle, but the compressive strength at the bedding angle of 45° is not much different from that at the bedding angle of 90°.

It can be seen from Fig. 6 that the crack initiation ratio values range from 0.17 to 0.35, with an average of 0.25. With the increase of the bedding angle, the crack initiation ratio increases in general. The damage ratio values range in a large span from 0.33 to 0.98, with an average of 0.81. With the increase of the bedding angle, the damage ratio decreases first and then increases. At the bedding angle of 45°, the damage ratio is the smallest.

The variation of acoustic emission event count and cumulative energy with time during the uniaxial compression of a typical coal reservoir sample Z5 with a bedding angle of 0° is shown in Fig. 7. In the crack closure stage (Stage I), some AE events occurred, indicating that some crystals in the CBM reservoir had friction and

extrusion when the cracks closed, producing a small number of low energy AE events. In the elastic stage (stage II), the AE events of the CBM reservoir sample were more than that in stage I, but still low in energy. In the stage of stable crack growth (Stage III), the AE counts and cumulative energy began to rise gradually, indicating that microcracks began to appear inside the CBM reservoir sample in this stage. In the stage of instable crack growth (Stage IV), the AE count and cumulative energy increased significantly, indicating that the cracks in the CBM reservoir sample rapidly expanded and connected with each other. When the stress approached the compressive strength, the AE events were very active. With the penetration of the macroscopic cracks, the AE count reached the maximum at the peak compressive strength.

The variation trends of cumulative count and cumulative energy of acoustic emission with the bedding angle are shown in Fig. 8. It can be seen that the AE characteristics also have recognizable bedding effect. The cumulative count of the samples with a bedding angle of 45° is slightly larger than the samples with a bedding angle of 0°. The samples with a bedding angle of 90° have the least cumulative count. The results indicate that the samples with a bedding angle of 45° had the most frequent AE activities during the uniaxial compression process, followed by the samples with a bedding angle of 0°, and the samples with a bedding angle of 90° had the fewest. This indicates that the samples with the bedding angle of 45° had the most frequent crack generation and propagation under the same stress conditions. But from the cumulative energy, the coal reservoir samples with a bedding angle of 0° had the largest cumulative energy released on average. These results may be attributed to the fact that AE events occurred throughout the whole compression process of the samples with the bedding angle of 0°, resulting in a relatively large number of AE counts. The failure is mainly caused by the fracture of the matrix in the coal reservoir, so these samples had the largest cumulative energy released. But for the coal samples with the bedding angle of 45°, the slip failure occurred along the bedding plane during the loading process, so there was more friction between bedding planes, and the cumulative count was the largest. However, slip failure between the bedding planes took dominance, and so the cumulative energy released was smaller. For the samples with the bedding angle of 90°, the bedding direction was consistent with the loading direction. When the stress was low, the bedding planes were not squeezed, so the count and energy were less. When the stress was high, microcracks began to occur in the samples, so the cumulative count and cumulative energy began to increase. The failure is mainly induced by tensional failure between bedding planes with less energy released, so the cumulative count and cumulative energy were both small.

The variation curves of AE cumulative count with stress level (ratio of axial stress to compressive strength) of the samples are shown in Fig. 9. The part of the abscissa where the stress level that exceeds 100% represents the stress level after reaching the peak strength, for example, 120% on the abscissa represents the stress level of 80% after reaching the peak strength. It can be seen from Fig. 9 that the samples with different bedding angles had different stress levels corresponding to the gradual and significant increases of the cumulative count of AE. During the uniaxial compression of coal reservoir samples, AE signals are generated when the cracks initiate and grow. The gradual increase of AE activities indicates that microcracks began to turn up inside the coal reservoir sample. The stress at this point is the crack initiation strength. The significant increase of AE activity marks the rapid propagation and connection of cracks in the coal reservoir sample. The stress at this point is the damage strength. For the samples with the bedding angle of 0°, the stress level at which the cumulative count of the AE starts to gradually grow is between 22% and 45%, mostly below 40%, and on average 34.47%. The stress level at which the cumulative energy of AE starts to grow significantly is between 73% and 88%, on average 81.18%. For the samples with the bedding angle of 45°, the stress level at which the cumulative count of the AE starts to gradually grow is between 25% and 46%, on average 37.38%. The stress levels at which the cumulative count of the AE starts to significantly grow are more discrete, with the minimum of 59%, the maximum of 91%, and an average of 76.17%. For the samples with the bedding angle of 90°, the stress level at which the cumulative count of the AE starts to gradually grow is between 35% and 48%, on average 43.04%. The stress level at which the cumulative count of the AE starts to grow significantly is between 75% and 95%, on average 85.85%. These results show that the crack initiation ratio of coal reservoirs determined by the cumulative count of the AE increases with the increase of bedding angle, while the damage ratio determined by the cumulative count decreases firstly and then increases with the increase of bedding angle, and is the smallest at the bedding angle of 45°. This is consistent with the previous conclusion obtained by the crack volume strain method.

Fig. 10 shows the curves of AE cumulative energy with stress of the samples. It can be seen that the samples with different bedding angles differ in stress levels corresponding to the gradual and significant growth of the cumulative energy of AE too. For the samples with the bedding angle of 0°, the average stress levels at which the cumulative energy starts to grow gradually and then significantly are 36.01% and 78.28%, respectively. For the samples with the bedding angle of 45°, the average stress levels at which the cumulative energy starts to grow gradually and then significantly are 36.48% and 73.63%, respectively. For the samples with the bedding angle of 90°, the average stress levels at which the cumulative energy starts to grow gradually and then significantly are 41.11% and 86.71%, respectively. These results show that the crack initiation ratio of coal reservoir (as determined by the cumulative energy of AE) increases with increase of bedding angle. The damage ratio determined by cumulative energy first decreases, then increases with the increase of bedding angle and is the smallest at the bedding angle of 45°. This is consistent with the conclusion based on the acoustic emission count.

It can also be seen from Fig. 10 that some samples with the bedding angles of 0° and 45° had several energy surges before the peak compressive strength. This may be because the direction of bedding is inconsistent with the loading direction, so the bedding inhibits the growth of vertical cracks, and it is difficult for the cracks to penetrate the samples at once. In contrast, the samples with a bedding angle of 90° had only one energy surge before the peak compressive strength. This is because the direction of the bedding of these samples is parallel to the loading direction, and the bedding cannot inhibit the growth of the vertical cracks, so the vertical cracks rapidly penetrate the samples and release most energy.

The amplitude of an AE event can be used to describe the intensity of the AE event. Analysis of the amplitude distribution of the AE events during the axial compression process of the coal reservoir samples can give up a better understanding on the process of crack initiation and damage in the CBM reservoirs.

The amplitude distribution of the AE events can be described by the parameter b. Parameter b was originally used in the field of earthquake. Gutenberg and Richter proposed the Gutenberg-Richter (G-R) relation in 1941^[34]:

At present, research on the parameter b is not limited to the field of earthquakes. There are many calculation methods for the value of b, such as the least square and maximum likelihood estimation methods^[35]. In this study, the maximum likelihood estimation method was used to calculate the value of b:

The b-value during the uniaxial compression of each sample was calculated by Eq. (6), and the calculation results are shown in Fig. 11. The dynamic characteristics of the b-value have specific physical meaning. The increase of b-value means the proportion of small-scale events increases, and the cracking is dominated by small-scale fractures. The b-value keeping constant indicates that the large- and small-scale AE events are relatively stable in proportion. The decrease of b-value means that the proportion of large-scale events increases, and the cracking is dominated by large-scale fractures. Fluctuation of the b-value in a small range indicates that the cracks propagate slowly and steadily. Sudden leap of b-value a large range means a sudden change of failure process and represents suddenly instable propagation.

It can be seen from Fig. 11 the dynamic variations of the b-values of the coal reservoir samples with different bedding angles have some common characteristics. The samples have higher b-values before reaching the peak compressive strength, which indicates that when the stress level is relatively low, the cracks turning up are largely small ones. When the stress level increases, the value of b decreases, which indicates that the large number of small-scale fractures connect with each other and go through the coal sample, and the cracking is dominated by large-scale fractures at this point. The dynamic changes of b values of the coal reservoir samples with different bedding angles also show some different characteristics. The samples with a bedding angle of 0° have steady decrease of b variation magnitude with the increase of stress level, indicating that the failure of the samples with a bedding angle of 0° is mainly steady propagation of large-scale fractures. Out of the samples with the bedding angle of 45°, some (F2, F4) have drop of b-values when the stress is higher, suggesting that these samples have stable micro-cracks in the initial stage of loading, then when the stress level is high, cracks connect with each other and go through the samples, resulting in instable propagation, which is a process of steady propagation of fractures. The b-values of the remaining samples (F1, F3, F6) fluctuate in a large range in all the stages of uniaxial compression, indicating that these samples have unstable proportions of large- and small-scale fractures at all stages, and the failure of this type of sample is due to sudden-instability of fractures. The samples with the bedding angle of 90° have b-values fluctuating in a large range. For these samples, the fractures at different scales are relatively stable in the initial stage of loading, but when the stress reaches peak, the cracks rapidly propagate along the bedding plane. The cracks in this type of sample propagate quite violently, resulting in sudden failure of the samples.

Fig. 12 shows the proportions of AE events of different amplitude segments of the samples with different bedding angles at peak strength. It can be seen that the coal reservoir samples with a bedding angle of 90° have much less large amplitude AE events than the samples with a bedding angle of 0°. The samples with a bedding angle of 45° show two different situations, some have more small- amplitude events, while the others have more large-amplitude events.

Based on the above analysis, the coal reservoir samples with the bedding angle of 90° have sudden failure and a lower proportion of large-scale fractures. In comparison, the coal reservoir samples with the bedding angle of 0° have failure caused by steady propagation of fractures and higher proportion of large-scale fractures. The coal reservoir samples with the bedding angle of 45° have two types of failure, one type features the steady propagation of fractures and larger proportion of small-scale fractures; the other type features sudden instability and larger proportion of large-scale fractures. This is because the bedding angle of these samples is in a certain angle with the loading direction, both some small-scale fractures between the bedding and some large-scale cracks along the bedding planes may turn up.

Hydraulic fracturing is an important technique that can increase permeability and production during the development of CBM. Micro-seismic monitoring technology and AE are often used to monitor cracking initiation and propagation in deep strata. It can be seen from the previous results that the AE activities in the coal samples show different characteristics when the cracks initiate and propagate in the samples. AE can also be used to determine the crack initiation strength and damage strength of the coal reservoir. However, the applicability of AE count and AE energy in assessing the crack initiation and damage of the coal reservoir with bedding has not been discussed before. Therefore, in this work, the crack initiation strengths and damage strengths calculated by the crack volume strain method and the acoustic emission method were compared and analyzed. It can be seen from Table 2, for most samples, the crack initiation strength and damage strength obtained from the cumulative AE counts are relatively close to that obtained from the cumulative AE energy. This is because during uniaxial compression of the coal reservoir, crack initiation and propagation are accompanied by AE events. As the number of AE events increases, a large amount of energy is usually released. However, the results of some samples are quite different, for example, the sample F4.

Taking the results of the crack volume strain method as the reference, the results obtained from the cumulative AE count and cumulative energy were compared, as shown in Fig. 13. It can be seen from Fig. 13(a), the average difference between the crack initiation strengths obtained by the cumulative count and crack volume strain method is 55.7%, the average difference between the crack initiation strengths obtained by the cumulative energy and crack volume strain method is 53.1%. It can be seen from Fig. 13(b), the average difference between the crack initiation strengths obtained by the cumulative count and crack volume strain method is 7.8%, the average difference between the crack initiation strengths obtained by the cumulative energy and crack volume strain method is 4.9%. The above results show that the results calculated by the cumulative energy method are closer to those of crack volumetric strain method than the cumulative count method. When the acoustic emission parameters are used to determine the crack initiation and penetration of coal reservoirs, the results obtained by the cumulative energy method are more accurate.

When the bedding angle of the coal reservoir sample is 0°, the bedding plane is perpendicular to the applied stress. According to the Jager failure criterion, the cracks will gradually expand and penetrate the rock matrix, as shown in Fig. 14(a). In this case, the bedding has no effect on the crack propagation and failure of the coal reservoir matrix. Therefore, when the bedding angle is 0°, the crack initiation strength and damage strength are both larger.

When the bedding angle of the coal reservoir sample is 45°, as the bedding plane and the loading direction intersect obliquely, the cracks would initiate and propagate almost along the bedding plane. At the same time, due to the complexity of the fracture system (as exemplified by the bedding and cleats of the coal reservoir), local tensile failure would appear (Fig. 14b). The strength of the coal reservoir is manifested as the strength of the bedding plane, and the strength of the bedding plane is much smaller than the matrix strength of the coal reservoir, which leads to smaller crack initiation strength and damage strength of the coal reservoir with a bedding angle of 45°. When the bedding angle of the coal reservoir sample is 90°, the bedding plane is parallel to the loading direction. Due to the presence of bedding planes, the coal reservoir samples are prone to tensile fracturing due to the lateral strain exceeding its limiting value (Fig. 14c). The cracks of this type of sample gradually turn up along the outer edge and propagate constantly toward the inner coal reservoir. Due to the low tensile strength of the coal reservoir bedding plane, the crack initiation strength and damage strength of coal reservoir with a bedding angle of 90° are also smaller.

Compared with the sample with a bedding angle of 90°, the crack initiation strength and damage strength of the sample with a bedding angle of 45° are lower. This is because, although the failures of samples with bedding angles of 45° and 90° are both closely related to bedding, according to the previous analysis of AE cumulative event count, cumulative energy, and failure mode, it can be seen that, only when the stress is quite high, cracks in the sample with a bedding angle of 90° begin to propagate rapidly, therefore, the crack initiation strength and damage strength of the sample with a bedding angle of 90° are slightly larger than that of the sample with a bedding angle of 45°.

The mechanical properties of coal reservoirs show obvious anisotropy. For the coal reservoir samples taken from 14# coal seam in Xinzhouyao of Datong city, the degree of anisotropy of uniaxial compressive strength of the coal reservoir is 1.94, the degree of anisotropy of crack initiation strength is 1.49, and the degree of anisotropy of damage strength is 2.31. The compressive strength decreases with the increase of bedding angle, but the compressive strength of the sample with a bedding angle of 45° is not much different that with a bedding angle of 90°. Both crack initiation strength and damage strength first decrease and then increase with the increase of bedding angle. When the bedding angle is 0°, the crack initiation strength and damage strength are the highest, followed by those at 90°, and those at 45° are the lowest. The crack initiation strength of the sample with a bedding angle of 0° is 1.49 times that of the sample with a bedding angle of 45° and 1.37 times that of the sample with a bedding angle of 90°. The damage strength of the sample with a bedding angle of 0° is 2.31 times that of the sample with a bedding angle of 45° and 1.92 times that of the sample with a bedding angle of 90°.

The coal reservoir samples with the bedding angle of 90° have the smallest cumulative count and cumulative energy of AE events under uniaxial compression, and have only one energy surge before the compressive strength The coal reservoir samples with the bedding angle of 45° have the largest cumulative count of AE events. The coal reservoir samples with the bedding angle of 0° have the largest cumulative energy of AE. The coal reservoir samples with the bedding angles of 0° or 45° have several energy surges before the compressive strength.

The failure of the coal reservoir samples with the bedding angle of 0° is the process of steady fracture propagation dominated by large-scale fractures. The failure of the samples with the bedding angle of 90° is mainly due to sudden instability of fractures, with a lower proportion of large-scale ones. The coal reservoir samples with the bedding angle of 45° have two types of failure, one type is the result of steady propagation of fractures, mainly small-scale ones; the other type of failure is the result of sudden instability of fractures, mainly large-scale ones.

Compared with the cumulative AE event count, the cumulative energy of AE events is more suitable for determining the crack initiation strength and damage strength of coal reservoir.

In addition to bedding and cleats, coal reservoirs may also have natural fractures, which will affect their mechanical properties. The effects of natural fractures on crack initiation strength and damage strength of coal reservoirs will be researched further.

a, b—constant;

A_i—the amplitude of the i-th acoustic emission event;

A_min—the minimum amplitude of the AE events;

E—elastic modulus obtained from the experimental stress- strain curve of the linear elastic stage of the sample, MPa;

R_c—anisotropy degree, dimensionless;

M—magnitude;

N—the number of earthquakes in the range of M+ΔM;

n—the total number of AE events;

ε₁—axial strain, dimensionless;

ε₃—circumferential strain, dimensionless;

ε_v—volume strain, dimensionless;

ε_vc—crack volume strain, dimensionless;

ε_ve—elastic volume strain, dimensionless;

σ₁—axial stress, MPa;

σ_c—compressive strength, MPa;

σ_cmax, σ_cmin—maximum and minimum values of average uniaxial compressive strength of samples at different bedding angles, MPa;

υ—Poisson’s ratio obtained from the experimental stress-strain curve of the linear elastic stage of the sample, dimensionless.