Study on mechanical properties and energy evolution of gas-bearing coal with different bedding angles under impact loads

Abstract

To reveal the mechanical response and energy conversion mechanism of deep gas-bearing layered coal under impact loads, coal samples from a gas outburst mine in Gansu Province were taken as the research object. Based on a three-dimensional combined dynamic-static load testing system, impact tests were conducted on coal samples with different bedding angles β (0°, 30°, 45°, 60°, and 90°) under a gas pressure of 0.8 MPa. A preset axial static load of 2 MPa and confining pressure of 4 MPa were applied, followed by loading with an impact pressure of 0.6 MPa. The stress–strain curves, mechanical parameters, failure modes, and energy evolution laws were analyzed. The results show that the peak strength presents a U-shaped distribution with the change of bedding angle: it reaches the highest values at 0° (160.41 MPa) and 90° (164.66 MPa), and the lowest at 45° (124.96 MPa). This is because the shear stress concentration effect on the bedding plane is the strongest at 45°, making it easy for cracks to propagate along the bedding. The peak strain also shows a U-shaped trend, reaching 0.03 at 90°and stabilizing at 0.026 at 30°and 45°, which reflects the differences in the deformation mechanisms of coal samples under different angles. In terms of energy evolution, the total energy density (U) and dissipated energy density (U_d) are higher and grow faster at 0°and 90°, while the elastic energy density (U_e) shows obvious post-peak release only at 0°. In the range of 30°∼60°, the values of U and U_d are low, and the release of U_e is weak, which is consistent with the low energy consumption characteristics of shear failure along the bedding. The failure mode changes regularly with the bedding angle: multi-directional fragmentation at 0°, shear fragmentation along the bedding mainly at 30°∼45° (the most severe fragmentation at 45°), and cross-bedding splitting failure at 90°. The study confirms that bedding angle regulates the mechanical properties and energy distribution of coal by changing the stress distribution and crack propagation path. The research results can provide key quantitative parameter support for the assessment and prevention of dynamic disasters in deep gas-bearing coal.

Keywords

Gas-bearing coal bedding angle impact loads mechanical properties energy evolution

Introduction

Coal, as the main energy source in China's energy structure, holds an irreplaceable strategic position in ensuring national energy security and economic and social development.^1,2 With the increasing depletion of shallow coal resources, the mining depth has been continuously advancing to deep formations over 1000 m. By 2025, more than 80 mines in China have exceeded a mining depth of 1000 m, and some even reach over 1500 m.^3,4 The deep mining environment exhibits the “three highs and one disturbance” characteristics of “high stress, high gas content, and high temperature”, among which the occurrence frequency and damage intensity of coal-gas compound dynamic disasters (such as rock bursts and coal and gas outbursts) have increased significantly.^5,6 According to statistics from the National Mine Safety Administration, in the past 5 years, casualties caused by dynamic disasters in deep mines accounted for 35% of the total, with an average annual direct economic loss of over five billion yuan, which has become a core bottleneck restricting the safe and efficient mining of deep coal.^7,8 The essence of such disasters is a dynamic instability process where the mechanical equilibrium of gas-bearing coal is broken under mining disturbances (such as impact loads from blasting, roof collapse, and mechanical cutting), leading to the rapid release of internal energy and the massive emission of gas.^9,10 Therefore, revealing the mechanical response and energy conversion mechanism of gas-bearing coal under impact loads is a key scientific issue for preventing and controlling deep dynamic disasters.

Bedding planes are common primary weak planes in sedimentary rocks (coal), formed by differences in particle deposition and cementation during different geological periods. Their spatial distribution characteristics, especially the dip angle, directly determine the anisotropic mechanical behavior of coal.^11,12 Under impact loads, the bedding angle significantly affects the strength, deformation characteristics, and failure mode of coal by altering the internal stress transfer path, crack initiation location, and propagation direction of coal.¹³ For instance, when the bedding plane is parallel to the loading direction, coal is prone to interlayer slip failure; when the bedding plane is perpendicular to the loading direction, failure is dominated by trans-laminar splitting. Meanwhile, the presence of gas further exacerbates the deterioration effect of bedding weak planes.¹⁴ Gas molecules reduce the cohesion of the coal matrix through adsorption-desorption, and promote crack propagation via the “gas wedge effect”, forming a triple coupling effect of “gas-bedding-impact load” and making the mechanical properties of gas-bearing layered coal more complex.¹⁵ Therefore, clarifying the regulatory law of bedding angle on the impact on the mechanical behavior of gas-bearing coal is an important prerequisite for an in-depth understanding of the occurrence mechanism of deep dynamic disasters.

Scholars at home and abroad have conducted extensive research on the impact of the mechanical properties of coal. Regarding non-gas-bearing coal, Li et al.¹⁶ based on the Split Hopkinson Pressure Bar (SHPB) test system, found that the dynamic peak strength of coal is the lowest when the bedding angle is 45°, with shear being the dominant failure mode. Through energy analysis, Gao et al.¹⁷ pointed out that the presence of bedding reduces the elastic energy storage capacity of coal and increases the energy dissipation rate. For gas-bearing coal, Gao et al.¹⁸ showed through research that the increase in gas pressure linearly reduces the dynamic strength of coal, and this weakening effect intensifies with the increase in strain rate. Huang et al.¹⁹ found through numerical simulation that gas changes the internal stress distribution of coal, making it easier for cracks to propagate along bedding planes. Zhang et al.²⁰ conducted true triaxial tests on coal and rock, analyzed acoustic emission energy, temperature, and impact force, identified different disaster types based on variations in depth and gas pressure, and thus provided a basis for disaster prediction and control. Chen et al.²¹ constructed a uniaxial constitutive model of coal and rock using the structural ensemble dynamics method, verified the model, derived an instability criterion, and proposed a bursting liability index.

However, there are still obvious shortcomings in existing research: first, most studies focus on a single gas pressure or a single bedding angle, lacking systematic comparative analysis of mechanical parameters and energy evolution of gas-bearing coal under different bedding angles, which makes it difficult to reveal the quantitative influence law of bedding angles. Second, the research on the coupling mechanism of “bedding angle-mechanical properties-energy evolution-failure mode” is insufficient, especially the lack of in-depth theoretical analysis from the perspectives of stress distribution and crack propagation path. Third, there is a difference between the test conditions and the on-site reality; some studies do not consider the initial static load (axial pressure, confining pressure) conditions of deep mines, which limits the engineering applicability of the research results.^22,23

To address the aforementioned research gaps, this study takes layered coal from deep high-gas mines as the research object. Based on the SHPB test system combined with a gas permeation loading device, impact load tests were conducted on coal samples with different bedding angles (0°, 30°, 45°, 60°, and 90°) under a gas pressure of 0.8 MPa. The test design strictly simulates on-site working conditions, with a preset axial static load of 2 MPa and confining pressure of 4 MPa. Dynamic loads were applied through an impact pressure of 0.6 MPa, while stress–strain data and failure characteristics were collected simultaneously. Based on the principle of energy conservation, the total energy density (U), elastic energy density (U_e), and dissipated energy density (U_d) were calculated. The research aims to achieve three objectives: first, to reveal the influence law of bedding angles on the dynamic peak strength and peak strain of gas-bearing coal; second, to clarify the energy conversion mechanism of gas-bearing coal under different bedding angles and establish a quantitative relationship between energy parameters and bedding angles; third, to determine the evolution law of failure modes controlled by bedding angles and analyze their mechanical essence from the perspectives of stress distribution and crack propagation. The research results can obtain the mechanical parameters of gas-bearing coal under different bedding angles, directly providing a quantitative basis for the risk assessment of dynamic disasters in deep mines. They also offer technical support for the optimization of mining schemes for layered coal seams, the design of support strength, and the selection of disaster early warning indicators, which holds significant practical significance for ensuring the safe and efficient mining of deep coal resources.

Experiment

Sample collection and preparation

The deep coal samples with bedding used in this study were collected from a gas outburst mine in Gansu Province, and all samples were taken from the same sampling location. The sampling process is as follows: (1) To maintain the integrity of the selected coal samples with bedding, when selecting the parent coal blocks, those with larger volumes were preferred as much as possible. (2) The on-site coal samples with bedding were numbered, with their sampling locations noted. Meanwhile, the appearance of the samples and the key characteristics of their bedding structures were described and recorded. (3) The collected coal samples were sealed with plastic film. To preserve the original structural properties of the coal samples with bedding, they were sealed with plastic film immediately after collection underground and then transported to the ground for subsequent coring operations. (4) After sampling, the coal samples with bedding were handled gently during transportation to avoid damage and maintain their original structural state. The outer surfaces of the samples were sealed with paraffin, and foam pads were placed around the samples in the packing boxes before transportation to the laboratory. Before coring, the basic physical parameters of the coal blocks were tested: (1) Density: Measured by the drainage method, with an average value of 1.42 g/cm³ and a coefficient of variation ≤ 1.2% among different sampling positions. (2) Porosity: Measured by the helium pycnometry method, with an average value of 8.7% and a coefficient of variation ≤ 1.5%. After coring samples with different bedding angles (0°, 30°, 45°, 60°, and 90°), three parallel samples were randomly selected for each angle to retest the above parameters. The results showed that the density of samples with different bedding angles ranged from 1.40 to 1.43 g/cm³, and the porosity ranged from 8.5% to 8.9%, with no significant statistical difference. This indicates that the inherent physical homogeneity of samples with different bedding angles is ensured, and the subsequent differences in mechanical properties and energy evolution can be attributed to the regulation of bedding angles rather than sample inhomogeneity. The processing process of the coal samples with bedding is as follows: (1) Coring: To study the influence of bedding angles on the mechanical response characteristics of coal samples with bedding under gas pressure and dynamic loads, coring was conducted at five different bedding angles (0°, 30°, 45°, 60°, and 90°) on the collected parent coal blocks to obtain standard-sized coal samples with bedding in a planned manner. During coring, the coal block with bedding was first fixed in a fixture, and then drilled using a drill. To prevent excessive temperature from affecting the mechanical behavior of the coal samples with bedding, the drill bit was cooled with cold water during the drilling process, and a vertical coring machine was used for coring. (2) Cutting: The ends of the cored coal samples with bedding were generally uneven. To make the processed samples suitable for the Hopkinson dynamic load test, the cored samples were cut. After cutting, the size and end flatness of the coal samples with bedding were ensured to meet the test requirements. (3) Polishing: To conduct effective Hopkinson dynamic load tests on the coal samples with bedding, the two ends of the cut samples were polished to ensure their flatness. The coal samples required for the dynamic compression test were processed into standard cylindrical specimens with a size of 100 × 50 mm, with the end flatness controlled within 0.02 mm and no obvious cracks on the specimen surface, after which they could be used for the test. The sample selection is shown in Figure 1.

Figure 1.

Sample selection.

Experimental equipment and plan

The equipment used in this study is a three-dimensional combined dynamic-static load testing system, which mainly consists of an air compression tank, a pressure gauge, a cylindrical projectile, an infrared velocimeter, a wave shaper, an incident bar, a transmission bar, an energy absorption device, a data acquisition and processing system, an oscilloscope, a dynamic strain gauge, a vacuum pumping device, and a gas storage system. Compared with the traditional one-dimensional combined dynamic-static load system, it is additionally equipped with a confining pressure device to meet the requirement for confining pressure conditions in the test process. Test data during the experiment were obtained by the strain data acquisition unit, which is composed of strain gauges attached to the incident bar and transmission bar, a strain gauge wiring bridge box, an ultra-dynamic strain gauge, and a high-speed acquisition system. The gas storage during the test was monitored in real time by measuring the gas flow at the outlet of the sealed chamber with a gas flowmeter. The incident bar in the test was fixed, and the sample was clamped between the incident bar and the transmission bar in the test chamber by an axial hydraulic loading device to apply axial static load. Confining pressure was applied by injecting hydraulic oil into the upper part of the test chamber through a confining pressure device, and a confining pressure rubber sleeve was designed inside the test chamber to isolate the sample from the hydraulic oil. Gas was supplied from a steel gas cylinder to the inlet after passing through a pressure-reducing valve, for inflating the coal sample in the test chamber. It should be noted that before inflation, a vacuum pump must be used to evacuate the sample and its auxiliary pipelines in the test chamber. The equipment is shown in Figure 2. To study the mechanical properties and energy evolution of gas-bearing coal with different bedding angles under impact loads, the test scheme was designed as follows: Appropriate values of impact pressure, confining pressure, and axial pressure for the coal sample test were determined through preliminary tests. First, an axial static load of 2 MPa and a confining pressure of 4 MPa were applied to the bedding samples with bedding angles of 0°, 30°, 45°, 60°, and 90° via a preloading axial pressure device. Then, the pressure valve was adjusted to control the tank pressure to an impact pressure of 0.6 MPa for impact loading. Considering the on-site mine gas conditions, the gas pressure was set to 0.8 MPa.

Figure 2.

SHPB experimental system.

Validation verification

During the impact test of coal samples, the pulse signals of the incident bar and transmission bar are usually measured by strain gauges attached to the middle of the bars. Figure 3 shows the stress balance diagram obtained after the impact test of a typical sample. It can be seen from Figure 3 that before and after impact loading, the superposition curve of incident stress and reflected stress is basically consistent with the transmission stress curve, thus meeting the stress balance condition.^24,25

Figure 3.

Dynamic stress balance diagram.

Data processing

Since coal samples are inhomogeneous and anisotropic materials, based on the assumptions of one-dimensional elastic stress waves and homogeneity, the following formulas are used to calculate their strain rate $\dot{ε} (t)$ , strain and stress $σ_{s} (t)$ ^26,27:

ε (t) = \frac{C_{0}}{L_{S}} [ε_{I} (t) - ε_{R} (t) - ε_{T} (t)] d t

(1)

\dot{ε} (t) = \frac{C_{0}}{L_{S}} [ε_{I} (t) - ε_{R} (t) - ε_{T} (t)]

(2)

σ_{s} (t) = \frac{S_{B} E_{0}}{2 S_{S}} [ε_{I} (t) - ε_{R} (t) - ε_{T} (t)]

(3)

where

S_{B}

is the radial cross-sectional area of the bar, mm²;

S_{S}

is the radial cross-sectional area of the coal sample, mm²;

ε_{I} (t), ε_{R} (t), ε_{T} (t)

are incident strain, reflection strain, and transmission strain, respectively.

ρ_{0}

is the density of the rod, kg/m³;

C_{0}

is the propagation velocity of stress waves inside the bar, m/s;

E_{0}

is the elastic modulus of the rod, GPa.

Test results and analysis

Stress–strain curve characteristics

Figure 4 shows the typical dynamic impact stress–strain curves of coal samples with different bedding angles.

Figure 4.

Stress–strain curves of different bedding angles.

As can be seen from Figure 4, all five stress-strain curves indicate that coal samples with different bedding angles undergo four stages: compaction stage, elastic stage, unstable crack propagation stage, and post-peak stage, with the compaction stage being short in all cases. For coal samples with a bedding angle of 0°, the initial compaction stage of the stress-strain curve is extremely short. After the internal initial microcracks of the coal sample are quickly compacted, it enters the elastic stage, where the stress increases approximately linearly with strain, showing good elastic deformation capacity. When entering the unstable crack propagation stage, the stress still shows an upward trend but the growth rate slows down, indicating that cracks are gradually propagating but still subject to certain constraints. The peak stress is relatively high, reaching approximately 160 MPa. A significant “strain rebound” phenomenon occurs in the post-peak stage, which means that the internal structure of the coal sample undergoes drastic adjustments after the peak, and the strain changes in the opposite direction during the stress decline process. The physical essence of this phenomenon lies in two aspects: first, before the peak, the coal matrix and bedding interfaces store a large amount of elastic potential energy under axial impact loading; second, after reaching the peak stress, the internal microcracks of the coal sample (especially trans-bedding cracks) rapidly penetrate, leading to sudden reorganization of the internal structure. During this structural reorganization, the stored elastic potential energy is quickly released, driving the coal sample to produce a small amount of reverse deformation, which is manifested as “strain rebound” in the stress-strain curve. This is a unique mechanical response of coal samples at this bedding angle. For coal samples with a bedding angle of 30°, the compaction stage is also short. In the elastic stage, the linear relationship between stress and strain is obvious, and the elastic modulus is relatively stable. After entering the unstable crack propagation stage, the upward trend of the curve becomes relatively gentle, and the stress growth rate decreases significantly. This indicates that the internal crack propagation process of the coal sample at this bedding angle is more moderate, and the crack propagation resistance changes under the interaction between bedding and matrix. The peak stress is approximately 130 MPa. In the post-peak stage, the stress shows a continuous downward trend without strain rebound, and the coal sample is mainly damaged by continuous deformation after the peak. For coal samples with a bedding angle of 45°, the compaction stage is short, consistent with that of samples at other angles. In the elastic stage, the stress increases linearly with strain, and the stress level in this stage is similar to that of coal samples with a 30° bedding angle. The unstable crack propagation stage also appears relatively gentle, with stress rising slowly to the peak. This indicates that at a 45° bedding angle, the initiation and propagation of internal cracks in the coal sample are significantly affected by the bedding, and the propagation resistance of cracks along and across the bedding tends to be balanced, resulting in a gentle curve in this stage. The peak stress is slightly lower than that of coal samples with 0° and 90° bedding angles. In the post-peak stage, the stress decreases continuously and the deformation develops continuously. For coal samples with a bedding angle of 60°, the compaction stage remains short. In the elastic stage, the stress increases linearly with strain. After entering the unstable crack propagation stage, the curve rises as gently as that of coal samples with 30° and 45° bedding angles. This indicates that at a 60° bedding angle, the internal crack propagation mechanism of the coal sample has certain commonalities with that at 30° and 45°; the inhibitory or guiding effect of bedding on crack propagation slows down the stress growth in this stage. The peak stress falls in the same range as that of coal samples with 30° and 45° bedding angles. In the post-peak stage, the stress decreases continuously, and the coal sample is gradually damaged. For coal samples with a bedding angle of 90°, the compaction stage is extremely short and almost negligible. In the elastic stage, the stress rises rapidly and linearly, showing strong elastic deformation characteristics. In the unstable crack propagation stage, the stress continues to rise, but the rate slows down. The peak stress is relatively high, close to that of coal samples with a 0° bedding angle, reaching approximately 160 MPa. The “strain rebound” phenomenon also occurs in the post-peak stage, which is consistent with the mechanical response of coal samples with a 0° bedding angle. This reflects that when the bedding angles are 0° and 90°, the bedding distribution of the coal sample presents extreme states of “horizontal” and “vertical” (relative to the loading direction). Under such states, the instability adjustment mode of the internal structure of the coal sample after the peak is similar, leading to the same strain rebound phenomenon. In summary, the bedding angle has a significant regulatory effect on the stress-strain characteristics of coal samples. In terms of deformation stages, all coal samples with different angles follow the stage division of “compaction-elasticity-unstable crack propagation-post-peak,” and the compaction stage is generally short—this indicates that the internal initial microcracks of the coal samples are less developed or distributed relatively uniformly. In terms of mechanical characteristics, coal samples with 0° and 90° bedding angles, due to the extreme distribution of bedding (parallel and perpendicular to the loading direction), show higher peak stress and a unique post-peak strain rebound phenomenon. In contrast, coal samples with 30°, 45°, and 60° bedding angles, as the bedding forms a certain angle with the loading direction, have a gentler unstable crack propagation stage, relatively lower peak stress, no strain rebound in the post-peak stage, and are mainly damaged by continuous deformation. This difference is essentially caused by the bedding angle, leading to variations in internal stress concentration, crack propagation paths, and interface interaction between bedding and matrix of the coal sample. It also provides a key basis for an in-depth understanding of the mechanical behavior and catastrophic failure mechanism of layered coal under dynamic load disturbance.

Mechanical parameter analysis

Based on the stress-strain curves, mechanical parameters such as peak compressive strength and peak strain are extracted.

Peak compressive strength

Figure 5 shows the relationship curve between bedding angle and peak compressive strength.

Figure 5.

Peak compressive strength of different bedding angles.

As can be seen from Figure 5, the relationship curve between peak strength and bedding angle shows that the peak strength presents an obvious law of “first decreasing and then increasing” with the change of bedding angle. When the bedding angle is 0°, the peak strength reaches 160.41 MPa. As the bedding angle increases to 30°, the peak strength decreases to 129.17 MPa, and further drops to the minimum value of 124.96 MPa at 45°. After that, when the bedding angle increases to 60°, the peak strength rises back to 135.88 MPa, and reaches the maximum value of 164.66 MPa at 90°. The formation of this law is closely related to the regulatory effect of bedding on the internal stress distribution and crack propagation path of coal samples. When the bedding angle is 0°, under axial loading, the bedding planes mainly bear shear and extrusion forces. The interface adhesion between the coal matrix and bedding planes, together with the strength of the coal matrix itself, resists the external load. At this time, the stress concentration phenomenon is relatively weak, and cracks are difficult to propagate rapidly along the bedding planes, so the peak strength is relatively high. When the bedding angle is 90°, the loading stress is mainly borne by the coal matrix. The existence of bedding planes has little hindering effect on the transmission of axial stress, allowing the overall bearing capacity of the coal matrix to be well exerted. Meanwhile, cracks need to cross the bedding planes during propagation, facing great resistance, so the peak strength is also at a high level. When the bedding angle is 30°, 45°, or 60°, the internal stress distribution of the coal sample becomes complex. Taking 45°as an example, the angle between the bedding plane and the loading direction easily causes obvious shear stress concentration at the bedding plane. When the stress reaches the shear strength of the bedding plane, cracks will preferentially initiate and propagate along the bedding planes. This failure mode along the bedding planes significantly reduces the overall bearing capacity of the coal sample, leading to a sharp drop in peak strength. Around 45°, the angle between the bedding plane and the loading direction makes the shear stress concentration effect the most prominent, and the “path dependence” of crack propagation along the bedding planes is the strongest, so the peak strength is the lowest. When the bedding angle increases from 45° to 60°, the angle between the bedding plane and the loading direction gradually deviates from the most unfavorable shear angle, the degree of stress concentration is alleviated, and the role of the coal matrix in bearing load is gradually enhanced, so the peak strength begins to rise.

In summary, the bedding angle changes the degree of internal stress concentration of the coal sample and the dominant path of crack propagation, resulting in the law that the peak strength “first decreases and then increases” with the bedding angle. The peak strength is relatively high at 0°and 90°, and the lowest around 45°. This law provides an important quantitative basis for an in-depth understanding of the strength characteristics and catastrophic failure mechanism of layered coal under dynamic load disturbance.

Peak strain

Peak strain reflects the deformation degree of coal samples when they reach peak stress under impact loads, and embodies their deformation capacity and deformation reserve before failure. Figure 6 shows the relationship curve between bedding angle and peak strain.

Figure 6.

Peak strain of different bedding angle.

As can be seen from Figure 6, the peak strain generally shows a U-shaped trend with the change of bedding angle. When the bedding angle is 0°, the peak strain is 0.027; as the bedding angle increases to 30° and 45°, the peak strain decreases to 0.026 and remains stable; when the bedding angle continues to increase to 60°, the peak strain rises back to 0.027; at 90°, the peak strain increases significantly to 0.03. The formation of this law is closely related to the influence of bedding angle on the deformation mechanism and crack propagation path of coal samples. When the bedding angle is 0°, under axial loading, the relative slip between bedding planes is subject to certain constraints. At the same time, the elastic deformation of the coal matrix and the initial propagation of microcracks jointly contribute to the deformation, so the peak strain is relatively large. When the bedding angle is 30° and 45°, the bedding plane forms a certain angle with the loading direction. At this time, the internal deformation of the coal sample is mainly manifested as the coupling of shear deformation along the bedding plane and compression deformation of the coal matrix. Under this deformation mode, cracks are prone to initiate and propagate along the bedding plane, and the resistance to deformation is relatively balanced, resulting in a decrease in peak strain, which remains at 0.026. When the bedding angle is 60°, the angle between the bedding plane and the loading direction gradually deviates from the angle most prone to shear deformation, the role of the coal matrix in deformation is enhanced, and the deformation mechanism transitions to a mode similar to that at 0°, so the peak strain rises back to 0.027. When the bedding angle is 90°, the loading stress is mainly borne by the coal matrix. During the deformation process, the coal matrix needs to overcome the lateral resistance of the bedding planes, and the propagation of microcracks needs to cross the bedding planes. This process produces a large amount of deformation, so the peak strain increases significantly to 0.03.

In summary, the bedding angle changes the internal deformation mechanism and crack propagation path of the coal sample, leading to a U-shaped change trend of peak strain. The deformation is relatively large at 0°and 60°; the resistance to deformation is more balanced at 30° and 45°, resulting in the lowest peak strain; at 90°, due to the combined effect of coal matrix deformation and cross-bedding crack propagation, the peak strain reaches the maximum. This law provides a key basis for an in-depth understanding of the deformation characteristics of layered coal under dynamic load disturbance.

Analysis of failure modes

There are significant differences in the failure modes of coal samples with different bedding angles under impact loads, and Figure 7 shows the failure morphologies of each bedding coal sample.

Figure 7.

The destruction patterns of each bedding coal sample.

As can be seen from Figure 7, coal samples with different bedding angles exhibit significantly different failure characteristics under impact loads, and this pattern is closely related to the regulatory effect of bedding angles on the internal stress distribution and crack propagation paths of coal samples. For coal samples with a bedding angle β = 0°( Figure 7(a)), the failure morphology appears as fragmented blocks with multiple sets of vertical and horizontal cracks interwoven, and the coal sample is broken into a large number of fine particles. This is because when the bedding planes are parallel to the loading direction, under axial impact loads, the normal stress between bedding planes is relatively large while the shear stress is relatively small. Cracks not only initiate and propagate along the bedding planes but also form trans-bedding vertical cracks in the coal matrix. The interweaving of multi-directional cracks eventually leads to severe fragmented failure of the coal sample. This failure mode indicates that the stress concentration areas of the 0° bedding coal sample under impact loads are relatively scattered, and cracks in multiple areas propagate simultaneously and penetrate the coal sample, resulting in an extremely high overall fragmentation degree. For coal samples with a bedding angle β = 30° (Figure 7(b), (d), (e)), the failure morphology shows a coexistence of large blocks and fine particles, with obvious shear displacement along the bedding planes in some coal blocks. When the bedding planes form a 30° angle with the loading direction, according to the shear failure theory in rock mechanics, the shear stress component on the bedding planes is relatively large while the normal stress component is moderately small, which easily causes shear stress concentration at the bedding planes. When the stress reaches the shear strength of the bedding planes, cracks preferentially initiate and propagate along the bedding planes, leading to shear failure of the coal sample along the bedding planes and forming large block failure areas. At the same time, during the shear failure process, some secondary cracks are also generated in the coal matrix; the propagation of these cracks forms fine particles, eventually resulting in the failure characteristic of coexisting large blocks and fine particles. For coal samples with a bedding angle β = 45° ( Figure 7(c)), the sample is almost completely broken into fine particles after failure, with the most significant fragmentation degree among all angles. From the perspective of mechanical principles, 45° is the most unfavorable angle for material shear failure—at this angle, the shear stress on the bedding planes reaches the maximum value, while the normal stress component is relatively small, making the shear resistance of the bedding planes the weakest. Under impact loads, the shear stress concentration effect at the bedding planes is extremely strong; cracks initiate and propagate rapidly and extensively along the bedding planes. After these cracks intersect and connect, they quickly split the coal sample into fine particles. Therefore, the failure morphology of the 45° bedding coal sample is dominated by extremely fine particles, reflecting that the coal sample at this angle has the weakest impact failure resistance. Combined with the analysis of the mechanical properties of coal samples with bedding angles of 60° and 90° in the test scheme, when the bedding angle is 60°, its failure characteristics gradually transition to the failure mode of the 0° bedding coal sample. At this time, the angle between the bedding planes and the loading direction gradually increases, the shear stress component on the bedding planes decreases, and the normal stress component increases. The tendency of cracks to propagate along the bedding planes weakens, while the tendency of trans-bedding crack propagation strengthens. Eventually, the failure morphology gradually changes from being dominated by inter-bedding shear to multi-directional fragmentation. For coal samples with a bedding angle β = 90°, the failure morphology presents blocky failure, and the coal sample mainly undergoes trans-bedding splitting failure. This is because when the bedding planes are perpendicular to the loading direction, the normal stress on the bedding planes is extremely large while the shear stress is minimal. The internal stress of the coal sample is mainly borne by the coal matrix, and the initiation and propagation of cracks need to cross the bedding planes. However, the propagation resistance of trans-bedding cracks is relatively large, so the propagation range and degree of cracks are limited. As a result, the coal sample eventually shows blocky failure with a relatively low fragmentation degree.

In summary, the bedding angle changes the distribution ratio of shear stress and normal stress on the bedding planes, controlling the initiation location, propagation direction, and penetration degree of internal cracks in the coal sample. This leads to a regular variation in failure characteristics: from multi-directional fragmented failure at 0°, to inter-bedding shear fragmentation at 30°∼45°(most significant at 45°), and to trans-bedding splitting block failure at 90°. Among them, the failure of coal samples with bedding angles of 30°, 45°, and 60° is dominated by inter-bedding shear, with the strongest shear failure effect at 45°; the failure of coal samples with bedding angles of 0° and 90° is dominated by multi-directional fragmentation and trans-bedding splitting, respectively. This pattern is essentially the result of bedding angles regulating the failure mechanism of coal samples, and also provides an intuitive morphological basis for an in-depth understanding of the catastrophic failure process of layered coal under dynamic load disturbance.

Analysis of energy dissipation law

During the combined dynamic-static loading test of coal samples with bedding, the energy transmitted from the test bars to the coal sample is mainly composed of three parts. The first part is the external input energy obtained from the external environment; the second part is the internal energy conversion of the coal sample with bedding from the energy transmitted by the test bars during the test; the third part is the external output energy. For the external input energy, it mainly refers to the incident energy transmitted by the test projectile during the combined dynamic-static test. For the coal sample with bedding, its internal energy conversion mainly involves the absorption energy of the coal sample being converted into elastic deformation energy and plastic deformation energy, which are generated during the elastic deformation stage and plastic deformation stage of the coal sample with bedding, respectively. For the external output energy, it mainly includes the reflected energy and transmitted energy output by the combined dynamic-static loading test system after testing the coal sample with bedding. In addition, a part of it is the sum of the energy converted into the fragmented ejection of the entire coal body during the energy conversion process of the coal sample with bedding and the energy released by the sample failure; this sum is called kinetic energy and thermal energy. Among the above parts, the relationship between the incident energy, reflected energy, transmitted energy, and absorbed energy of the coal sample with bedding has been mainly introduced. The following content will further deepen the research on the failure of the coal sample with bedding, focusing on the law of change in the process where the absorbed energy is converted into elastic energy and plastic energy during the failure of the coal sample with bedding. This research is crucial for understanding the dynamic study of coal with bedding. Therefore, combined with the first law of thermodynamics, the following formula is used to calculate the total energy U of the coal sample with bedding during the entire process of the combined dynamic-static loading test. The calculation formula is as follows:^28,29

U = U_{e} + U_{d}

(4)

In the formula, U_e and U_d, respectively, represent the elastic deformation energy and plastic deformation energy of the test coal during the elastic deformation stage and plastic deformation stage under combined dynamic-static loading. In the specific test process, the specimen is in a uniaxial loading state in the combined dynamic-static loading test system used for the test. Therefore, the total energy density U, elastic energy density U_e, and dissipated energy density U_d of the coal sample with bedding satisfy the following calculation formulas:^30,31

U = \int σ d ε

(5)

U_{e} = σ^{2} / 2 E

(6)

U_{d} = U - U_{e} = \int σ d ε - σ^{2} / 2 E

(7)

In the formula, U, U_e, and U_d, respectively, represent the input energy, elastic energy, and dissipated energy, with the unit of MJ/m³; E is the tangent elastic modulus, with the unit of MPa.

Figure 8 shows the calculated energy evolution curves of coal samples with different bedding angles during the uniaxial compression process.

Figure 8.

Strain–energy curves for different bedding angles.

As can be seen from Figure 8, The strain-energy curves (total energy U, elastic energy U_e, and dissipated energy U_d) across bedding angles of 0°, 30°, 45°, 60°, and 90° exhibit distinct and systematic patterns, which can be attributed to the combined effects of bedding angle-controlled crack propagation paths and the gas wedge effect. Starting with the total energy density U, it presents a clear U-shaped distribution with respect to bedding angles. At 0° and 90°, U increases sharply with strain, reaching peak values of approximately 3.8 and 7.2 MJ/m³, respectively. This is because at 0°, the coal sample undergoes multi-directional fragmentation, forming an interconnected three-dimensional fracture network that requires substantial energy input for crack initiation and propagation. At 90°, cracks need to propagate across the bedding, encountering significant resistance, thus also demanding high energy. In contrast, within the 30°∼60° range, U rises much more slowly, with a value of around 2.2 MJ/m³ at 45°, as cracks propagate directionally along the bedding, creating a more efficient and less energy-consuming fracture path. Turning to the elastic energy density U_e, its behavior is highly angle-dependent. At 0°, U_e accumulates steadily, peaking at about 1.8 MJ/m³, and then shows a noticeable post-peak drop, releasing approximately 0.8 MJ/m³. This elastic rebound is a result of the multi-directional fragmented failure, where the sudden loss of structural integrity allows stored elastic energy to be released. For bedding angles of 30°∼90°, U_e plateaus early, reaching peaks of only 1.0∼1.5 MJ/m³, and exhibits very weak post-peak release, with a reduction amplitude of less than 0.2 MJ/m³. This indicates that at these angles, most of the elastic energy is dissipated rather than stored, as the failure modes are dominated by plastic shear deformation or cross-bedding splitting, which do not allow for significant elastic energy accumulation. The dissipated energy density U_d follows a trend consistent with U. At 0°and 90°, U_d grows rapidly, reaching around 2.5 MJ/m³ and 6.0 MJ/m³, respectively. The high dissipated energy at 0° is due to the energy consumed in generating and propagating numerous multi-directional cracks, as well as the friction between fragmented particles. At 90°, the energy is dissipated in overcoming the resistance of cross-bedding crack propagation. In the 30°∼60° range, U_d increases slowly, with a value of approximately 1.5 MJ/m³ at 45°, as the directional propagation of cracks along the bedding minimizes energy loss from unnecessary crack branching or particle friction. The underlying mechanisms for these patterns lie in how bedding angles regulate crack propagation paths and the action of the gas wedge effect. Bedding angles of 0° and 90° lead to complex fracture networks, either multi-directional or cross-bedding, which are energy-intensive. The gas wedge effect further influences these processes: at medium angles (30°∼60°), where shear stress is concentrated on the bedding planes, gas tends to accumulate at the bedding interfaces, generating splitting forces that promote directional crack propagation along the bedding, thus reducing energy consumption. In contrast, at 0° and 90°, the fracture networks are more complex, leading to a more uniform distribution of gas and a more dispersed gas wedge effect, which does not significantly aid in reducing energy demand for crack propagation. Collectively, these factors result in the distinct strain-energy relationships observed across different bedding angles.

Discussion

Regulation mechanism of bedding angle on mechanical properties and its engineering implications

The observed U-shaped evolution law of strength and strain in this study is highly consistent with the “weak plane-controlled failure” theory in rock mechanics. The phenomenon that the peak strength is the lowest at 45° confirms the mechanical characteristic that the shear stress on the bedding plane reaches the theoretical maximum at this angle, which is consistent with the conclusion of “weak plane-dominated damage” discovered by Wang Enyuan et al. in triaxial coal impact tests.³² From an engineering perspective, if the angle between the stope advance direction and the bedding strike falls within the range of 30°∼60°, the coal mass is more prone to low-strength failure under dynamic loads such as blasting impact, and it is necessary to focus on strengthening the support strength. For coal seam areas with bedding angles of 0° and 90°, although the peak strength is relatively high, the sudden release characteristic of post-peak elastic energy of the 0° coal sample indicates the risk of impact tendency, and attention should be paid to the dynamic response caused by the sudden release of energy.

Physical essence analysis of energy evolution law

The angular differences in energy parameters stem from the damage evolution paths controlled by bedding. For 0° coal samples, multi-directional cracks interweave and propagate, with large crack surface areas and mutual penetration, resulting in high total energy dissipation. At 90°, the propagation of cross-bedding cracks needs to overcome the resistance of bedding interfaces, leading to high energy consumption intensity and thus a relatively high value of U_d. In the medium-angle range, cracks propagate directionally along bedding planes with more concentrated paths, resulting in low energy dissipation efficiency. This is similar to the research conclusion that “the bedding effect of water-saturated coal causes differences in energy parameters.” The differentiated characteristics of elastic energy release reflect that 0° coal samples have more sufficient elastic deformation reserves, leading to more intense elastic rebound when post-peak structural instability occurs. In contrast, medium-angle coal samples are dominated by plastic shear deformation with limited elastic energy storage. This finding can provide a reference for selecting energy indicators in rock burst early warning.

Consideration on the coupling effect of gas and bedding

This test was conducted under a gas pressure of 0.8 MPa. The presence of gas promotes crack propagation through the “gas wedge effect,” which may exacerbate the deterioration degree of bedding weak planes. Combined with relevant studies, it is known that the increase in gas pressure will reduce the dynamic parameters of coal. It is inferred that under higher gas pressure, the weakening effect of bedding angle on strength may be more significant. In the future, it is necessary to supplement multi-gas pressure gradient tests to explore the triple coupling mechanism of gas-bedding-impact load. In addition, the influence of gas on energy evolution in the test can be further quantified by refining the energy calculation model. For example, introducing a gas expansion energy correction term to improve the energy balance equation of gas-containing coal. To address this gap, specific subsequent test schemes are proposed based on the current results, such as multi-gas pressure gradient test design, supplementary test of gas seepage-stress coupling, and microscopic characterization of post-failure samples. In addition, based on the failure morphology of coal, it can be initially inferred that the bedding angle dominates the morphology of gas seepage channels by regulating the crack propagation path. When the bedding angle is 0°, the coal sample undergoes multi-directional fragmentation, forming an interconnected three-dimensional fracture network. Gas seepage exhibits the characteristic of “global connectivity” and achieves the highest seepage efficiency. When the bedding angle ranges from 30° to 60°, cracks propagate directionally along the bedding, forming unidirectionally connected bedding fracture channels. Gas seepage is restricted to the direction of the bedding, showing the characteristic of “directional seepage.” It has relatively low seepage resistance but significant directionality. When the bedding angle is 90°, cracks need to propagate across the bedding, and the formed cracks are mostly discontinuous short fractures. Gas seepage presents the characteristic of “local blockage” and has the lowest seepage efficiency. Meanwhile, gas further expands the bedding cracks through the “gas wedge effect” during the seepage process. For medium-angle bedding (30°∼60°), shear stress is concentrated on the bedding plane. Gas tends to accumulate at the bedding interface and generate splitting force, which intensifies the separation of the bedding. In contrast, the fracture networks of 0°and 90°bedding are more complex, with uniform gas distribution, leading to a relatively dispersed wedge effect.

Experimental limitations and research prospects

In this study, a fixed impact air pressure (0.6 MPa) and confining pressure (4 MPa) were used, and the synergistic effect of strain rate and confining pressure was not considered. Existing studies have shown that the dynamic strength of coal has a linear positive correlation with strain rate. In subsequent research, multi-impact air pressure tests can be carried out to reveal the coupling effect of bedding angle and strain rate. Meanwhile, the test did not monitor the change of gas seepage during the impact process. However, there is a strong correlation between fracture propagation and seepage field evolution. By combining in-situ seepage testing with CT 3D reconstruction technology, the influence of bedding-controlled fracture structure on gas migration can be further clarified, providing a more comprehensive perspective for the study of coal and gas outburst mechanisms.

Conclusion

The peak strength shows a significant U-shaped distribution with the bedding angle. It reaches 160.41 and 164.66 MPa at 0° and 90°, respectively, and drops to 124.96 MPa at 45°. This indicates that the coal mass has the strongest bearing capacity when the bedding is parallel or perpendicular to the loading direction, and the weakest bearing capacity under the shear stress concentration effect at 45°.

The evolution of peak strain presents a U-shaped law. The peak strain is the largest (0.03) at 90°and at a low level (0.026) at 30°and 45°. This reflects that when the bedding is perpendicular to the loading direction, the deformation of the coal matrix and the propagation of cross-bedding cracks jointly lead to large deformation; while in the medium-angle range, the shear deformation along the bedding is more balanced in terms of constraint.

Energy evolution has obvious angular dependence: the total energy density (U) and dissipated energy density (U_d) are higher at 0° and 90°; the elastic energy density (U_e) shows significant post-peak release only at 0°; the energy storage capacity is weak and the total dissipation is low in the medium-angle range, which is consistent with the low energy consumption characteristic of shear failure along the bedding.

The failure mode changes regularly with the bedding angle, ranging from multi-directional fragmentation at 0°, shear fragmentation along the bedding at 30°∼45°, to cross-bedding splitting failure at 90°. This is essentially the result of the change in the ratio of shear stress to normal stress on the bedding plane controlling the dominant path of crack propagation.

Footnotes

Authors’ Contribution

Xiaoyang Cheng and Linchao Dai: conceptualization. Linchao Dai: methodology. Xiaoyang Cheng, Linchao Dai, and Yang Pu: validation. Xiaoyang Cheng and Linchao Dai: formal analysis. Junjie Guo: investigation. Xiaoyang Cheng and Yang Pu: resources. Linchao Dai: data curation. Xiaoyang Cheng and Linchao Dai: writing—original draft preparation. Xiaoyang Cheng and Linchao Dai: writing—review and editing. Yang Pu and Junjie Guo: visualization. Junjie Guo: supervision. Xiaoyang Cheng: project administration. Xiaoyang Cheng and Linchao Dai: funding acquisition. All authors have read and agreed to the published version of the manuscript.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by the National Natural Science Foundation of China (52474276), the National Key R&D Program of China (2024YFC3013805), the Natural Science Foundation of Chongqing (CSTB2024NSCQ-MSX0384), the Key Project of Science and Technology Innovation and Entrepreneurship Fund of Tiandi Technology Co., Ltd (2024-2-TD-CYD003, 2023-2-TD-ZD001), and the Key Science and Technology Project of Ministry of Emergency Management of the People's Republic of China (2024EMST070703).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability statement

The authors declare that all data supporting the findings of this study are available within the article.

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