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Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39300131
64151
10.1038/s41598-024-64151-z
Article
Damage and energy characteristics of coal rock combinations with inclined coal seams under axial loading
Du Xuanhong 15349419043@163.com

12
Lei Wulin xakjdxwl@163.com

1
Zhang Hengyan 1
Wen Zhaohui 1
Zhao Ruirui 1
Chen Zhiheng 2
Yu Lan 1
Zheng Chao 1
Liu Jinhe 1
Xing Erjun 3
Jiang Shengling 1
Yang Rili 1
Cao Juheng 1
1 https://ror.org/03wcn4h12 grid.488147.6 0000 0004 1797 7475 College of New Energy, Longdong University, Qingyang, 745000 Gansu People’s Republic of China
2 https://ror.org/046fkpt18 grid.440720.5 0000 0004 1759 0801 College of Safety Science and Engineering, Xi’an University of Science and Technology, Xi’an, 710054 People’s Republic of China
3 College of Safety Engineering, Lanzhou Resources & Environment Voc-Tech University, Lanzhou, 730000 Gansu People’s Republic of China
19 9 2024
19 9 2024
2024
14 2188129 12 2023
5 6 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
A single load compression test of rock-coal-rock assemblages (RCRs) containing coal bodies with different inclinations was carried out with the research background of mining deep, large-steep coal seams. It was found that the larger the inclination angle of the coal body in the RCR samples, the larger the compaction stage of the samples and the smaller the uniaxial compressive strength value. In addition, both the maximum acoustic emission (AE) energy of the samples and the cumulative AE energy at the moment of destruction decreased with the increase of the inclination angle of the coal body in the form of exponential relativities. Also, the input energy and ultimate elastic energy of the samples at the peak stress moment decreased with increased inclination angle of the coal body. Furthermore, both of them changed with the inclination angle of the coal body in accordance with the exponential relationship; meanwhile, when the applied load exceeded the peak strength, the dissipative energy of the RCR samples increased rapidly due to the loss of load-bearing capacity. At the peak moment, the percentage of dissipated energy of the samples increased exponentially with the increase of the inclination angle of the coal body. This study has certain reference significance for the prevention and control of dynamic disasters during the mining of large angle coal seams.

Subject terms

Energy science and technology
Energy harvesting
Energy storage
Fossil fuels
Transverse research project of Longdong University: Determination of alkane gas components and isotopes in Longfeng coal mine, Lindong.901314030901/901 Du Xuanhong issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

The strength of the rock body is closely related to the safety of underground engineering. Among them, the destabilisation of the deep rock mass is closely related to its own strength and other properties, which also affects the possibility of deep dynamic disasters to a certain extent1. In particular, the conditions under which coal seams exist and the environment in which they are mined have become more complex in deep mining projects2,3. At the same time, during deep mining, coal seams are often not horizontal coal seams, the possibility of large inclination coal seams greatly increases, so that the mining of coal seams and contains a certain degree of difficulty, due to the influence of the inclination. The appearance of the mine pressure law and the pattern of stress distribution has a typical asymmetric characteristic, so the mining environment of the steep large inclination coal seams to be more complex, with the impact of the ground pressure and other disasters occurring likely to be high4,5. By the excavation effect of the excavation layer, the underground mining will produce a certain degree of damage to the top and bottom of the damage, and the excavation of the mining layer is actually a type of energy accumulation and release of the process6–8, and the top plate—the coal seam—the bottom plate as a whole, are involved in this process9–11. Therefore, to grasp the law of energy change during the actual coal seam excavation, an in-depth study should be carried out from the perspective of the “whole”.

In China, deep mining has opened up on a large scale with frequent dynamic disasters12–14. Dynamic hazards, such as impact ground pressure, are often devastating, so an enormous time and energy have been dedicated to the study of dynamic hazards in underground mines, with crucial contributions being made to the safe production of mines15,16. For the research on impact ground pressure, China commenced to enter the stage of independent theoretical cognition after the 1980s, and the three criteria17, instability theory18, and three-factor mechanism19 appeared; after years of refinement and development, scholars have put forward the intensity weakening and impact reduction theory20, impact initiation theory21, and the impact perturbation response to the destabilisation theory22, and so on. Based upon the above theories, the theories and the prevention and control technology system of impact ground pressure in the process of on-site practice have been improved23,24. These theories have made a vital contribution to solving the impact ground pressure geopressure hazards in shallow mines in China25. However, with the continuous increase of mining depth, the shallow mining methods and experiences are not compatible with the deep mining conditions, the loading mode of coal and rock masses has changed26–28. which makes the existing theories and technical systems lag behind the actual situation, and compared with the shallow part, the ground stress is larger in the deep mining, the stratum structure is complicated, and the number of disaster-causing factors increases. This results in the lowering of the threshold of the occurrence of impact pressure; accordingly, the research on the disaster of impact pressure under the complex factors of the deep part is still not slackened.

Practically speaking, on-site monitoring is the most direct way to grasp the actual stress state of the coal rock body, using monitoring data, with existing theoretical knowledge to predict the possibility of disaster, so as to develop preventive means to forestall the disaster before it occurs, can achieve better results29–31. At the same time, many scholars have also explored the stress transfer and crack evolution law of coal rock body by means of numerical calculation. This is cost-effective and applicable and can realise the research work under a variety of complex conditions. With this method, the difficulty of researching the dynamic disaster of mines has been greatly reduced, and the visualisation of the process of the disaster can be realised32–34. At the same time, the conditions can be varied to realise the likelihood of power hazards occurring under the influence of different factors or under multiple influences35,36, in order to facilitate the acquisition of threshold values for the occurrence of power hazards under various conditions. In addition, scholars are also accustomed to taking rock samples and coal samples as test objects to exam the corresponding properties of the samples in a certain state by applying different external forces or other experimental conditions, so as to achieve certain experimental purposes. Ren et al.37 carried out loading tests on rock samples, studied the fractal characteristics of the destruction process of the samples, and grasped the mechanism of rockburst phenomenon during the destruction of the rock. Zheng38 conducted uniaxial experiments under static loading to investigate the rockburst process; some have also used cyclic loading as an external experimental condition to scrutinise the damage process of the samples and analyse the energy properties of the samples accordingly39–41. Some scholars have also conducted loading tests with different combinations of coal-rock composites to study the energy evolution of the material when loaded, thus analysing the occurrence mechanism of high-energy dynamic disasters in mines42–44.

Meanwhile, foreign scholars have also conducted research on mine dynamic disasters. Rock burst is a major threat to coal mining in the United States. Iannacchione et al.45 analyzed rock burst accidents in the United States and explored their prediction and control methods. Swolkień et al.46 discussed the joint impact of gas disasters and rockburst on coal mine safety. Mishra et al.47 studied the failure characteristics of coal and rock masses obtained from a coal mine in West Virginia and Hiawatha under axial and transverse strain control modes. Simmons et al.48 studied the composite failure mechanism of coal bearing rock masses. Khan et al.49 explored the energy evolution characteristics of coal under different loading rates.

In summary, scholars have studied the occurrence mechanism and characteristics of power disasters in mines from theories, experiments, engineering, etc. However, the occurrence of dynamic disasters is not only caused by the damage to a single coal body or a single rock body, but also by the interaction of stress, damage and energy between the coal body and the rock body under the influence of mining. At the same time, the interaction between coal and rock bodies in large inclined coal seams is more complicated. Therefore, we used different angles of coal and top and bottom rock bodies as raw materials to make coal and rock combinations with different inclinations, and carried out a loading test on the combination of samples under the action of a single load, so as to analyse the damage and energy characteristics of the combinations with different inclination angles. The purpose of this study was to appraise the characteristics and mechanism of dynamic disasters in coal seam mining with large inclination angle by means of energy transfer.

Experimental process

The raw materials required (obtained mainly from Henan Province, China) for the tests consisted of roof rocks, coal bodies, and floor rocks. The approximate depth of the sampling site was 800 m. Once the raw materials were obtained from the mine, they were labelled so that there would be no confusion among the raw materials when making the composite samples. Once sufficient raw materials were obtained, a box containing wood chips was prepared and the raw materials were loaded into it and transported to the laboratory in a relatively smooth manner.

During the processing of the samples, the raw material needs to be processed in specified dimensions and angles, and the combination samples produced must meet the standards of the test samples50; the parameters of sample making are shown in Fig. 1. After obtaining the required sample parts, according to the “top rock—coal—bottom rock” order of bonding sample parts, the interface bonding material selection of AB adhesive, after bonding the sample size should be Ф 50 mm × 100 mm. to receive the final “inclined rock—coal—rock combination samples”. The final “inclined rock-coal-rock combination sample” (RCR sample), the different inclined RCR samples were labelled as RCR-0, RCR-10, RCR-20, RCR-30, RCR-45, individually, and the completed RCR samples needed to be maintained at a constant temperature of 25 ℃ for 7 days.Figure 1 Sample making parameters.

The experimental equipment is shown in Fig. 2. The loading rate was 0.001 mm/s, and the AE signals when the RCR samples were loaded were monitored by the SH-II AE system, six AE sensor probes were selected during the monitoring period, and the probes were fixed on the specimen surface with elastic tape. At the same time, a coupling agent (petroleum jelly) was applied at the probes with the purpose of preventing the loss of AE signals.Figure 2 Experimental equipment.

Coal damage and energy calculation model

Damage model based upon AE energy

With the development and updating of monitoring technology and equipment, many scholars have found that elastic waves will be emitted when the material is damaged, and the elastic waves can be collected and converted into AE signals by AE equipment, with the AE signals having a sound correspondence with the damage of the material. Meanwhile, the AE energy and cumulative AE energy among the AE parameters can better reflect the damage evolution of materials51. Based upon this, in this paper, AE energy and accumulated AE energy were employed to characterise the damage properties of RCR samples with different inclination angles.

The damage variables defined by Kachanov52 was as follows:1 D=AdA

where Ad is the damaged section area and A is the section area in the undamaged state.

If the cumulative AE energy for complete destruction of the entire section A of the non-destructive material is Em, the AE energy Ew per unit area of destruction is as follows:2 Ew=EmA

The cumulative AE energy when the damage area is Ad is Ed with the following expression:3 Ed=EwAd=EmAAd

By joining Eqs. (1) and (3), the damage variable equation based on AE energy can be obtained as follows:4 D=EdEm

Energy calculation model

When a single load is applied to the RCR sample, a continuous energy input is formed, and setting the process without heat exchange phenomena, the RCR sample continuously stores and releases energy. Thus, the loading process of the RCR sample is the energy evolution process53. According to conservation of energy, the following relationship exists between input energy (W), elastic energy (We) and dissipative energy (Wd):5 W=We+Wd

The relationship equation for W is as follows:6 W=∫01σ1dε1+∫02σ2dε2+∫03σ3dε3

The relational equation for We is as follows:7 We=12σ1ε1+σ2ε2+σ3ε3

It follows from the generalised Hooker’s law:8 ε1=1Etσ1-νtσ2+σ3ε2=1Etσ2-νtσ1+σ3ε3=1Etσ3-νtσ1+σ2

Joining Eqs. (7) and (8):9 We=12Etσ12+σ22+σ32-2νtσ1σ3+σ2σ3+σ1σ2

where σi is the principal stress, εi is the strain corresponding to the principal stress, Et is the modulus of elasticity, and νt is Poisson’s ratio.

The following relationship exists for a single load:10 σ2=0σ3=0

Joining Eqs. (6) and (10):11 W=∫01σ1dε1

Further processing of Eq. (11) yields:12 W=∑1n12σi+1+σiεi+1-εi

Joining Eqs. (9) and (10):13 We=σ122Et

Equations (5), (12) and (13) lead to the following dissipated energy calculation equation:14 Wd=∑1n12σi+1+σiεi+1-εi-σ122Et

Experimental results and analysis

Mechanical and AE characteristics of the RCR samples

After the single-load compression test of RCR samples, the samples will be ruptured by the force, and the rupture location will generate damage signals and release them in the form of elastic waves to the surroundings. The AE equipment will glean the elastic waves released during the rupture of the samples and convert them into AE signals. According to the data of the changes of the samples stress–strain-AE signals during the test period, the characteristics of the AE energy of RCR samples with different inclinations at different periods of stress–strain will be mapped out, as shown in Fig. 3.Figure 3 Stress–strain and AE energy-strain curves for RCR samples: (A) α = 0°, (B) α = 10°, (C) α = 20°, (D) α = 30°, and (E) α = 45°.

Analysing the stress–strain curve in Fig. 3, it was found that as the inclination angle of the coal body in the RCR sample increased, the compaction stage of the sample grew longer, and its uniaxial compressive strength was smaller. At the same time, the larger the inclination angle of the coal body, the larger the axial proportion of the coal body in the sample. In addition, there was an interface effect, so the strength of the sample decreased when the inclination angle increased. To clarify the influence of the inclination angle of the coal body in the RCR samples on the strength of the samples themselves, the uniaxial compressive strength change curves of the RCR samples under different inclination angles were plotted (Fig. 4).Figure 4 Ultimate strength of RCR samples with different inclination angles.

By analysing the ultimate strengths of RCR samples with different coal body inclinations, it was found that the larger the coal body inclination in RCR samples, the smaller the value of the ultimate strengths of the samples. Meanwhile, the ultimate strengths of the samples decreased in a linear manner with the increase of the coal body inclination.

Further analysis of Fig. 3 revealed that there were differences in the AE energy characteristics of RCR samples at different deformation stages. Among which, in the compaction stage, because of the presence of interfacial friction and initial damage, the AE signals of the samples were more obvious and increased with the increase of the inclination angle of the coal body; in the elasticity stage, the distribution of the AE signals of the samples was uniform, which was in line with the deformation characteristics of the stage. After the entry into the plastic stage, the AE after the peak stage, as the sample reached the maximum bearing capacity, the continuous application of external force made the sample rapidly destroyed, the AE signal further increased, and the AE energy reached the maximum value when the sample underwent macroscopic destruction. To clarify the influence of the inclination angle of the coal body on the rupture signals of the samples in the RCR samples, the maximum value of the AE energy (Emax) and the cumulative AE energy (Ed) at the time of destruction of the samples were plotted with the variation of inclination angle of the coal body, as shown in Fig. 5.Figure 5 AE energy of RCR samples: (A) maximum AE energy, and (B) accumulated AE energy at rupture.

From Fig. 5, it can be seen that the maximum AE energy of the RCR samples decreased in an exponential relational manner with increasing coal body inclination, and the cumulative AE energy at the moment of destruction of the samples also decreased in an exponential relational manner with increasing coal body inclination. Here, both of them varied with the coal body inclination in RCR samples as listed in Table 1.Table 1 Relational equation for the variation of AE energy with coal body inclination for RCR samples.

AE energy type	Equation	a	b	c	R2	
Emax	E=ae-αb+c	40.33	38.39	15.28	0.98	
Ed	1142.21	85.63	− 78.54	0.99	

RCR samples damage characteristics based upon AE energy

To facilitate the analysis of the damage state of the RCR samples at various stages before destruction, it is first assumed that the samples are completely destroyed at the moment when the RCR samples reach the maximum AE energy, and the damage variable of the samples at that moment is one.

Based upon the above assumptions, according to Eq. (4), combined with the data in Fig. 3, the damage-strain curve of the RCR samples is shown in Fig. 6.Figure 6 Damage evolution of RCR samples: (A) α = 0°, (B) α = 10°, (C) α = 20°, (D) α = 30°, (E) α = 45°.

According to the evolution curve of damage with axial strain of RCR samples in Fig. 6, it was found that the samples went through three processes from the beginning to the rupture, namely, initial damage, stable development of damage, and rapid development54–56. And the development of damage of RCR samples was attributed to the decrease of internal cohesion due to the generation of micro-porous fissures and cracks inside the samples under the action of a single load, which resulted in the gradual deterioration of the RCR samples and their eventual destruction.

In the first damage stage, due to the existence of microfractures in the sample, the internal fissures of the sample were compacted under the axial pressure at the beginning of the test, but compared with the AE energy generated by the rupture of the sample, the AE energy generated by the compression of the initial microfractures was small, and thus the damage in this stage was small overall.

In the second damage stage, the RCR samples enter the elastic–plastic deformation stage, the samples are continuously compressed, and the new cracks inside the combined samples begin to be generated and gradually developed; the new cracks of the samples are relatively slow in the process of germination and development, so the damage development is stable.

In the third damage stage, the RCR sample completely crosses the yield point and enters the plastic deformation stage, internal fissures are generated in large quantities and developed rapidly, and the corresponding AE signals are increased, which makes the AE energy increase, so the damage of the sample in this stage develops quickly.

Energy characteristics of RCR samples

According to the stress and strain data of the RCR sample after a single load, the energy data of the sample can be calculated by combining Eqs. (12), (13), and (14); the energy curve of the RCR sample after a single load is shown in Fig. 7:Figure 7 RCR sample energy profile: (A) α = 0°, (B) α = 10°, (C) α = 20°, (D) α = 30°, and (E) α = 45°.

From Fig. 7, it can be seen that the total energy of the RCR sample continues to increase with the increase of axial strain. This is because the entire test process of the testing machine is doing work on the sample. That is, the sample has a fixed input energy; the elastic energy of the RCR sample with the increase of axial strain first increases and then decreases, and in the moment of the peak stress point of the elastic energy to reach the maximum value, this is because the sample’s input energy exceeds its own peak stress point, resulting in the sample rupture. This is because the input energy of the sample exceeds its own energy storage limit when it jumps over the peak stress point, which leads to the rupture of the sample, and the energy that cannot be stored in the sample is converted into dissipative energy, which is employed to support the rupture of the sample. Meanwhile, the dissipative energy of the RCR sample increases slowly with the increased of axial strain, and then increases rapidly when the stress exceeds the yield point, which is because the sample enters into the plastic stage after jumping over the yield point, and a large number of cracks are sprouted and develop in the internal cracks, which leads to the increase of energy consumption. Further analyses revealed that the energy value of the RCR samples decreases with the increase of the inclination angle of the coal body in the samples, among which the maximum elastic energy is the most obvious.

According to the energy curves of the RCR samples at each inclination angle, it is obvious to find that the input total energy, elastic energy and dissipative energy at the moment of the peak stress point are different and show a certain regularity. To grasp this regularity, the energy magnitude of the RCR samples at the moment of the maximum stress under the conditions of different inclination angles was assessed. Among them, the trend of the total energy input into the RCR samples at the moment of maximum stress is illustrated in Fig. 8.Figure 8 Trend of total energy of RCR samples at the moment of peak stress.

According to Fig. 8, when the inclination angle of the coal body in the RCR samples increases, the input energy of the samples at the peak stress moment decreases, and the trend of the change between the two is in accordance with the exponential relationship equation. The input energy decreased by 6.45% when the coal body inclination angle increased from 0° to 10°, 7.48% when the coal body inclination angle increased from 10° to 20°, 10.88% when the coal body inclination angle increased from 20° to 30°, and 41.42% when the coal body inclination angle increased from 30° to 45°, which shows that the coal body inclination angle has a greater influence on the input energy. Input energy has a greater effect.

Conservation of energy tells us that there is an input of energy, so there must be an output of energy and the two are equal. During the loading period of the RCR sample, the input energy has two directions, elastic energy and dissipative energy, in which the elastic energy is stored inside the RCR sample. The elastic energy is stored inside the RCR sample, and there is an energy storage limit for each inclination angle of the RCR sample; when the input energy exceeds this limit, the sample will be destroyed. In practical engineering, if the accumulation of energy jumps over the limit of energy storage value of the coal body or rock body itself, then it will break out the power disaster, threatening safer production. Based upon this, it is necessary to grasp the limiting energy storage value of RCR samples, and the limiting energy storage value of RCR samples with different angles is shown in Fig. 9.Figure 9 Trend of limiting energy storage for RCR samples.

According to Fig. 9, when the inclination angle of the coal body in the RCR samples increases, the ultimate storage energy of the samples decreases, and the trend of the change between the two is in accordance with the exponential relationship equation. When the inclination angle of the coal body increased from 0° to 10°, the ultimate energy storage decreased by 9.17%, when the inclination angle of the coal body increased from 10° to 20°, the ultimate energy storage decreased by 11.64%, when the inclination angle of the coal body increased from 20° to 30°, the ultimate energy storage decreased by 13.27%, and when the inclination angle of the coal body increased from 30° to 45°, the ultimate energy storage decreased by 46.05%, which demonstrates that the inclination angle of the coal body has a greater influence on the ultimate energy storage of the RCR sample. This shows that the inclination angle of the coal body had a greater effect on the ultimate storage energy of the RCR sample itself. This illustrates that in practical engineering, when the inclination angle of the coal seam is larger, the ultimate energy storage capacity of the coal body and its top and bottom plate as a whole is smaller, and under the influence of mining activities, the energy accumulation of the coal body will readily exceed its own energy storage capacity, which results in a high-energy kinetic disaster and threatens safe production.

Collating the fitted equation of energy versus coal body inclination in the RCR samples in Figs. 8 and 9 yielded an equation for the variation of energy versus coal body inclination, as shown in Table 2.Table 2 RCR sample energy versus coal body inclination equation.

Energy density	Equation	a	b	c	R2	
W	W=-aeαb+c	6.00	21.67	83.34	0.99	
We	10.79	32.95	61.81	0.99	

According to the above analysis, the energy characteristics of RCR samples at the point of stress maximum can be known. However, in fact, after the project is disturbed, the coal rock body will continue to undergo the process of stress increase and decrease. At the same time, the force of RCR samples is also a continuous process, and this process is accompanied by the conversion of energy, and the distribution of elastic and dissipative energy ratios of different inclination angles of the RCR samples is not clear; the dissipation of energy can indirectly reflect the sample’s damage information. To clarify this issue, it is necessary to analyse the proportion of the RCR samples of the energy dissipation. In addition, the calculation of the proportion of the energy dissipation is shows in the following equations:15 rd=WdW

Based upon Eq. (15), combined with the energy evolution data of the RCR samples, the energy dissipation percentage data were calculated and shown in Fig. 10.Figure 10 Percentage of energy dissipation in RCR samples: (A) α = 0°, (B) α = 10°, (C) α = 20°, (D) α = 30°, and (E) α = 45°.

As can be seen from Fig. 10, RCR samples have end effect and interface effect, resulting in the need to overcome the interface friction and end effect in the early stage of compression of the sample. Therefore, the input energy is converted into dissipated energy in large quantities, so the dissipated energy of the coal samples at the beginning of loading is relatively large. As the angle of inclination of the coal body in the RCR sample increases, the dissipated energy share can be as high as 1. With the continuous action of a single load, the sample engages the elastic deformation stage. When the RCR sample enters the plastic deformation stage, a large number of rupture points or rupture lines start to appear in the sample; the rapid development of this process of deformation is irreversible and consumes a large amount of energy, so the dissipated energy ratio begins to show a turnaround, positive growth. When the peak strength is reached, the RCR sample also reaches the maximum load-bearing capacity, and under the continued action of the load, the sample undergoes large-area damage due to the stresses exceeding its own load-bearing capacity. Thus, the cracks inside the sample after the peak are promptly connected and form a macroscopic fracture surface, a process that consumes a large amount of energy, making the dissipative energy share increase further.

According to the above analysis, the RCR sample reaches the maximum load-bearing capacity at the moment of peak stress, and when the stress exceeds the peak moment, the dissipative energy of the RCR sample increases rapidly due to the reduction of load-bearing capacity. To grasp the percentage of dissipated energy of RCR samples at the peak moment, the dissipative energy distribution curves of RCR samples at different inclination angles were plotted, as shown in Fig. 11.Figure 11 Distribution of the percentage of dissipative energy of RCR samples at the peak moment.

From Fig. 11, it can be seen that the dissipative energy share of the RCR sample increased by 5.88% when the coal body inclination angle increased from 0° to 10°, the parameter increased by 5.56% when the coal body inclination angle increased from 10° to 20°, the parameter increased by 7.89% when the coal body inclination angle increased from 20° to 30°, and the parameter increased by 8.89% as the coal body inclination angle increased from 30° to 45°. At the peak moment, the percentage of dissipative energy of the RCR sample increased with the increase of the inclination angle of the coal body within the sample, and the growth relationship between the two conformed to an exponential function.

Conclusions

The AE energy of the samples had a tendency to decrease with the increase of the inclination angle of the coal body. In addition, both the maximum AE energy and the cumulative AE energy of the samples at the time of destruction decreased with the increase of the angle of the coal body in the form of an exponential relation.

According to the energy distribution curves of the RCR samples, it was found that all the energies of the samples had a tendency to decrease with the increase of the inclination angle of the coal body, among which the elastic energy and the total energy exhibited the most obvious performance. Meanwhile, when the inclination angle of the coal body in the RCR samples increased, the input energy and ultimate elastic energy of the samples at the time of the peak stress decreased. And both of them changed with the inclination angle of the coal body in accordance with the exponential relationship.

The RCR sample reached the maximum load-bearing capacity at the peak stress moment, and when the applied stress exceeded the peak stress, the dissipative energy of the RCR sample increased promptly due to the loss of load-bearing capacity. At the peak moment, the percentage of dissipative energy of the RCR samples increased with the increase of the inclination angle of the coal body within the samples, and the growth relationship between the two conformed to the exponential function.

Acknowledgements

Transverse research project of Longdong University: Determination of alkane gas components and isotopes in Longfeng coal mine, Lindong (901314030901/901).

Author contributions

X.D.: Conceptualisation, software, writing—original draft preparation. W.L.: Software, data curation, writing—reviewing and editing. H.Z.: Writing—reviewing and editing. Z.W.: Writing—reviewing and editing. R.Z.: Software. Z.C.: Writing—reviewing and editing. L.Y.: Method, software, data curation. C.Z.: Software, data curation. J.L.: Writing—reviewing and editing. E.X.: Writing—reviewing and editing. S.J.: Writing—reviewing and editing. R.Y.: Writing—reviewing and editing. J.C.: Writing—reviewing and editing.

Data availability

The datasets generated and /or analysed during the current study are available from the corresponding author upon reasonable request and permission.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

These authors contributed equally: Xuanhong Du and Wulin Lei.
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