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. 2026 Jan 23;16:6064. doi: 10.1038/s41598-026-35979-4

Influence of confining pressure and stress amplitude on the mechanical properties and permeability characteristics of coal

Huiming Yang 1, Dengke Qin 2,✉, Hao Liu 3,✉, Xiaoyan Sun 4, Qican Ran 2, Yulin Hu 2
PMCID: PMC12901259  PMID: 41578119

Abstract

To explore the influence mechanism of confining pressure and stress amplitude on the mechanical properties and permeability characteristics of coal samples, loading and unloading experiments with different confining pressures and amplitudes were performed with a triaxial test system. The stress‒strain, permeability and energy changes of the coal samples were monitored in real time, and the stress response, energy evolution, creep deformation and fracture distribution characteristics were systematically analyzed. The experimental results reveal that with increasing confining pressure, the peak stress and elastic modulus of coal samples increase significantly, the input energy and elastic energy increase synchronously, and the permeability and fracture ratio decrease significantly. High confining pressure effectively inhibits fracture expansion, making the structure of the coal sample more regular after destruction; as a whole, the fractal dimension decreases, and the structure tends to be simplified and densified. In contrast, the increase in loading and unloading amplitude accelerates the structural failure and fatigue damage process of coal samples, resulting in a decrease in peak strength, an increase in irreversible strain, crack expansion and penetration, an increase in the fracture proportion and fractal dimension, and a significant increase in permeability. The results of three-dimensional fracture reconstruction further confirm the significant effect of confining pressure and amplitude on the evolution of the fracture spatial structure. An increase in confining pressure helps to close microcracks and compact pore channels, whereas a large-amplitude disturbance induces fracture penetration and the formation of a flow network.

Keywords: Confining pressure, Amplitude, Mechanical properties, Permeability characteristics

Subject terms: Energy science and technology, Engineering, Materials science, Solid Earth sciences

Introduction

Coal resources have long dominated China’s energy structure and are the cornerstone of national energy security and economic development1–6. However, with the depletion of shallow coal resources, mining activities are constantly shifting deep. The environment of deep coal seams is characterized by “three high and one disturbance”, and its stress state is more complex than that of shallow coal seams. In this stress environment, the continuous action of high ground stress and the dynamic disturbance caused by frequent production activities (such as blasting, mechanical vibration, and periodic weighting) significantly increases the damage accumulation and instability risk of coal and rock masses7–15. The stable state of coal is closely related to the safety of underground engineering16–18.

During coal seam excavation, the coal body is repeatedly affected by various cyclic stress loading and unloading disturbances and in situ stress19.Under these conditions, the mechanical properties of coal and rock change, and damage gradually accumulates, which eventually results in the instability and failure of coal and rock masses. This process is also accompanied by the transformation of energy20. Therefore, determining the mechanical properties of coal and rock masses under the influence of cyclic disturbance and confining pressure (simulated in situ stress) is key to ensuring the stability of mining engineering21,22.

To better describe the mechanical properties of coal with different influencing factors, scholars have conducted much research on this topic23–27. Shen et al. revealed the irreversible residual deformation and failure process caused by the accumulation of internal damage to coal under cyclic loading28. Chen et al. investigated the fatigue process of granite under uniaxial compression cyclic loading using the fluorescence method29. Ran et al. obtained the hardening damage law of sandstone through multistage cyclic loading tests30. Zhou conducted a fatigue test on red sandstone and reported that its mechanical properties and life increased but then decreased with increasing frequency31. Liu et al. defined the damage variable on the basis of energy dissipation theory and constructed damage constitutive models for two kinds of typical rock under cyclic loading and unloading32. Zhang et al. proposed that with increasing confining pressure, the energy storage efficiency increased, and the energy release rate decreased. On this basis, the evolution characteristics of rock energy accumulation, dissipation and release behavior expressed by energy storage density and energy dissipation density are established23. Li et al. conducted uniaxial cyclic loading and unloading tests on sandstone and determined the evolution law of energy indices such as elastic energy, dissipation energy and damage energy of rock and further applied it to characterize the damage evolution of rock33. Wang et al. performed triaxial fatigue and unloading confining pressure tests and revealed the effects of the degree of fatigue damage and unloading rate on rock fracture and instability34.

The above research from different perspectives improves the understanding of the mechanism of coal and rock disasters and is important for the scientific control and guidance of mining engineering design35–38. However, until now, most of the research has focused on the damage deformation or failure behavior of coal and rock under the influence of only the confining pressure or amplitude. In contrast, a coal seam faces a complex stress environment under the combined action of confining pressure, cyclic disturbance and other factors in the stratum39. There are significant differences in mechanical properties, energy dissipation, crack propagation and permeability during the process of coal damage and failure with different loading and unloading amplitudes and different confining pressures. Therefore, exploring the mechanical properties and permeability characteristics of coal samples under the influence of confining pressure and amplitude is important. In this paper, by setting stress paths with different confining pressures and different amplitudes and considering the effect of confining pressure and amplitude, several stress environments to which coal samples may be subjected are simulated, and the basic properties of coal samples in this environment are discussed. The research in this paper provides reference data for the stability and permeability of coal seams.

Experimental methods

To explore the mechanical characteristics of coal under disturbance and elucidate the deformation parameters, permeability characteristics and their interrelationships, a triaxial experimental system was used to perform cyclic loading tests on the samples. The experimental equipment and stress path are shown in Fig. 1. In the experiment, the gas was CO2, and the inlet pressure was 1 MPa (the adsorption characteristics of CO2 and methane are similar, and for safety reasons, CO2 was chosen for the experiment)40,41. The coal sample used in the experiment was collected from a coal mine in Shenmu, Shaanxi Province. The sample was a cylindrical coal sample with a diameter of 50 mm and a height of 100 mm, and the drilling direction was perpendicular to the coal seam bedding surface. In addition, the mineral composition of the coal sample was determined by X-ray diffraction analysis: kaolinite (50.1%), quartz (24.6%), kaolin group (14.1%), and nisbite (11.2%). The sample density is approximately 1.29–1.31 g/cm3, the wave velocity is 2040 ± 30 (m/s), and the initial porosity is approximately 6.5 ± 0.3%. All the samples were stored at room temperature for 48 h to ensure that the experimental results were not affected by moisture.

Fig. 1.

Fig. 1

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Experimental equipment and the stress path.

Specific experimental operation steps: (1) The amplitude of cyclic loading and unloading was maintained at 20% of the peak stress, and the confining pressure was changed to 5 MPa, 10 MPa and 15 MPa; (2) The confining pressure was maintained at 5 MPa, and the cyclic loading and unloading amplitude was changed to 5%, 10%, and 15% of the peak stress. In addition, one stress gradient was subjected to 20 cycles of loading and unloading. After each cycle of loading and unloading, the load was maintained at 50% and 80% of the corresponding peak stress for two hours (creep), after which it failed. At the same time as loading and unloading, a gas permeability of 1 MPa is introduced, and the measuring points are shown in Fig. 1b.

The design of the stress path is based on the common stress disturbance modes during the process of deep coal seam excavation: periodic excavation disturbance (corresponding to cyclic loading and unloading) and continuous ground stress (corresponding to confining pressure). Two-stage creep tests (conducted at 50% and 80% of the peak stress) are designed to simulate the rheological behavior of coal in the temporary support or stress adjustment stage during the advancing process of the underground working face to investigate the time-dependent deformation and permeability evolution characteristics42,43.

Results

Mechanical properties of the coal samples under different confining pressures

Stress‒strain curves

The stress‒strain curves of coal samples under different confining pressures are shown in Fig. 2. The coal sample was damaged after two cycles of loading and unloading and two creeps. With increasing confining pressure, the peak strain of the coal sample increases gradually from 3.95% to 5.67%. The strain of the second creep stage also gradually increases with increasing confining pressure. When the confining pressure is 15 MPa, the strain of the second coal sample increases by approximately 0.5%; whereas the strain of the second coal sample increases by approximately 0.1% under the first two confining pressure conditions.

Fig. 2.

Fig. 2

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Stress‒strain curves of coal samples under different confining pressures.

Elastic modulus and irreversible strain

The elastic modulus characterizes the ability of rock materials to resist deformation under external disturbances and is an important mechanical index of rock. In this paper, the average slope of the approximate straight line section of the stress‒strain curve of the cyclic loading section and the unloading section is selected to calculate the elastic modulus. The evolution of the elastic modulus of the sample during different confining pressure loading and unloading stages is shown in the following figure.

Different confining pressures significantly affect the increase in the elastic modulus and irreversible strain of the sample, as shown in Fig. 3a. First, with the same number of loading and unloading cycles and with increasing confining pressure, the increase in the elastic modulus of the sample also increases, and the increase at 15 MPa is more obvious than that at 10 MPa. With respect to each stress gradient under the same confining pressure, the average elastic modulus increases gradually with increasing number of loading and unloading cycles. When the confining pressure is 15 MPa, the average elastic modulus increases the fastest; that is, the slope is the greatest. When the confining pressure is 5 MPa, the average elastic modulus increases slowly.

Fig. 3.

Fig. 3

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Variations in the elastic modulus and cumulative irreversible strain of coal samples under different confining pressures: (a) elastic modulus and (b) cumulative irreversible strain.

The irreversible strain is another important index for characterizing the mechanical properties of rock. The calculation principle of the irreversible strain of rock is shown in Fig. 4. The calculation formula is as follows:

graphic file with name d33e418.gif 1
Fig. 4.

Fig. 4

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Calculation principles of cumulative irreversible strain.

where Inline graphic represents the irreversible axial strain in the total cycle and n denotes the number of cycles. In addition, Inline graphic and Inline graphic denote the final strain at the end of the cycle and the initial strain at the beginning of the cycle, respectively.

The cumulative irreversible strain of the sample during the entire cyclic loading and unloading stage is shown in Fig. 3b. With increasing confining pressure, the irreversible strain of the sample gradually accumulates. However, the first stress step may have less effect on the coal sample because the lower limit of the cyclic loading and unloading amplitude is only 20% of the peak stress, so irreversible strain accumulation is lower. The second stress step clearly indicates that the irreversible strain accumulation rate increases with increasing confining pressure. When the confining pressure is 15 MPa, the cumulative effect is the most obvious, indicating that the confining pressure may accelerate the failure of the coal sample in the near failure stage and that a greater circumferential force causes the failure of the sample.

Energy characteristics of the coal samples under different confining pressures

During the loading and unloading process, the coal sample does not exchange with the external energy; thus, the total input energy can be converted to the elastic energy and dissipation energy stored in the sample44–46, as shown in Fig. 5.

Fig. 5.

Fig. 5

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Calculation principles of strain energy.

The changes in elastic energy and dissipation energy can reflect the internal damage law of the coal samples under cyclic loading and unloading. The method for calculating the strain energy is shown in Formula (2)47.

graphic file with name d33e481.gif 2

where U represents the total strain energy, kJ/m3; Ue denotes the releasable elastic strain energy stored per unit volume, kJ/m3; Ud indicates the dissipated strain energy, kJ/m3; and f₁ represents the input energy function during the cyclic loading and unloading of the samples, and its integral from the starting point of the strain to the end is used to calculate the input energy; f₂ denotes the dissipated energy function, and its integral (the area contained in the loading and unloading curve) is used to calculate the dissipated energy; ε’ indicates the strain at the beginning of loading/unloading; and ε’’ represents the strain at the end. An increase in dissipation energy indicates irreversible damage, such as friction slip of the original crack surface and the formation of new microcracks in the coal sample. An increase in the proportion of elastic energy means that the coal sample tends to store more energy. Once the stress exceeds the threshold, this energy may be quickly released, controlling the instability of the macroscopic crack.

By substituting the triaxial compression test data into Eq. (2), the energy values of coal samples under different confining pressures can be obtained. The energy evolution law of coal samples under different confining pressures are shown in Fig. 6. Under the same amplitude loading and unloading conditions, with increasing confining pressure, the input energy and elastic energy of coal samples increase. Under the same confining pressure conditions, the loading and unloading cycle is 20% of the peak stress. However, because the lower limit of the second stress step is 50% of the peak stress and the lower limit of the first stress step is only 20% of the peak stress, the input energy and elastic energy in the second stress step increase compared with those in the first stress step. In addition, in contrast, the dissipation energy of the two stress steps under loading and unloading at 5 MPa and 10 MPa did not significantly increase, and the dissipation energy of the second stress step at 15 MPa was greater than that of the first stress step. This may be attributed to the excessive compaction of coal samples under high axial pressure and confining pressure. Different confining pressures significantly affect the overall energy evolution of coal samples.

Fig. 6.

Fig. 6

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Energy characteristics of coal samples at different confining pressures: (a) 5 MPa, (b) 10 MPa, and (c) 15 MPa.

Time-varying law of axial strain of coal samples under different confining pressures

The variation characteristics of the first creep stage of the axial strain of coal samples under different confining pressures are shown in Fig. 7. Different confining pressures significantly affect the change in strain of coal samples during the creep stage. When the confining pressure is constant, the axial strain of the coal sample increases gradually but increases abruptly. With increasing confining pressure, the strain growth rate gradually changed from accelerated to uniform.

Fig. 7.

Fig. 7

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Axial strain of coal samples at different confining pressures: (a) 5 MPa, (b) 10 MPa, (c) 15 MPa, and (d) growth rate.

Permeability characteristics of coal samples under different confining pressures

In this paper, the transient pressure pulse method is used in the permeability measurement48, assuming that the gas is an ideal gas, the coal is a uniform porous medium, the gas flows from the high-pressure chamber to the low-pressure chamber through the core, and the volume of the two chambers is equal; then, the commonly used expression for determining permeability is as follows49:

graphic file with name d33e591.gif 3

where K represents the permeability, ml; µ denotes the viscosity coefficient, Pa·s; Inline graphic indicates the average gas compression factor; V represents the gas volume at both ends of the sample in m³; Inline graphic and Inline graphic denotes the pressure differences between the initial and t times at both ends of the sample in Pa; p0u and p0d indicate the import pressure and the export pressure before the experiment in Pa; A represents the cross-sectional area of the sample in m³; L denotes the length of the sample in m; and t indicates the test time in s.

During the experiments, the axial strain and flow rate of the coal samples were monitored in real time, and the permeability of the coal samples was calculated by Formula (3), as shown in the following figure. Figure 8 reflects the interaction between the permeability and strain of the coal samples under different confining pressures. When the confining pressure is constant, with increasing cyclic loading and unloading, the coal body is compacted, the strain increases gradually, and the gas flow channel inside the coal body gradually closes; thus, the permeability decreases. In addition, with increasing confining pressure, the overall decreasing trend of permeability tends to be gradual. This occurred because the increase in confining pressure resulted in compaction of the coal sample, closure of primary cracks in the coal sample and reduction in gas flow channels.

Fig. 8.

Fig. 8

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Permeability variation law of coal samples at different confining pressures: (a) 5 MPa, (b) 10 MPa, and (c) 15 MPa.

Three-dimensional fracture reconstruction

The three-dimensional reconstruction model of the fracture channel clearly reveals the internal fracture channel morphology of the coal sample after fracture. Three-dimensional reconstruction models of the block and the fracture channel after the failure of the coal sample are shown in Fig. 9. The expansion, penetration and degree of fracture can be visually observed from the model. A comparison of the three-dimensional reconstruction models under different confining pressures reveals significant differences. When the confining pressure is 5 MPa, the degree of fragmentation of the coal sample is greater, the fracture development is more extensive, and the crack distribution inside the rock is more complex, indicating that the coal sample is subjected to more severe stress under these conditions, resulting in significant structural damage. Under other confining pressure conditions, the three-dimensional reconstruction model of the coal sample after failure is relatively complete as a whole. Although the fracture undergoes expansion, the degree of fragmentation is relatively small, the connectivity and stability of the fracture channel are good, and the block connected by the fracture structure is also large.

Fig. 9.

Fig. 9

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Three-dimensional scanning and fracture extraction map: (a) 5 MPa, (b) 10 MPa, and (c) 15 MPa.(Produced by Avizo 2019.1: after computed tomography (CT) scanning, the three-dimensional shape (gray part) of the sample generated in software, and the blue part is the crack inside the sample, which is exposed after certain processing.).

Three-dimensional models of the block and the fracture channel after the failure of the coal sample are constructed. To further quantify the number of fractures, the top-hat algorithm50 is used to quantitatively calculate the fracture volume extracted by the above segmentation. The ratio of the fracture volume Vf to the total volume V is defined as the fracture volume ratio S of the coal sample after failure43. The calculation results are shown in Fig. 10. With increasing confining pressure, the number of cracks after the failure of coal samples decreases significantly. When the confining pressure increases to 10 MPa, the proportion of cracks after the failure of coal samples decreases by approximately 15%. The fractal dimension can reflect the internal pore distribution of coal and the tortuosity of the boundary. With increasing confining pressure, the fractal dimension of the coal sample decreases gradually, which indicates that the internal pore distribution is gradually regularized after the failure of the sample and confirms the above findings. These two phenomena reveal that an increase in confining pressure improves the ability of coal samples to resist deformation.

Fig. 10.

Fig. 10

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Fracture proportion and fractal dimension of coal samples under different confining pressures.

Mechanical properties of coal samples with different amplitudes

Stress‒strain curves

The stress‒strain curves of coal samples with different amplitudes are shown in Fig. 11. With increasing cyclic amplitude, the peak stress of the coal sample gradually decreases. Under a loading and unloading gradient of 5%, the peak stress of the coal sample is 77.58 MPa; under a loading and unloading gradient of 10%, the peak stress of the coal sample is reduced to 69.69 MPa; and under a loading and unloading gradient of 15%, the peak stress of the coal sample decreases to 67.65 MPa.

Fig. 11.

Fig. 11

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Stress‒strain curves of coal samples with different amplitudes.

Elastic modulus and irreversible strain

The variations in the elastic modulus and irreversible strain of coal samples under different amplitudes of loading and unloading are shown in Fig. 12. With the same number of loading and unloading cycles, with increasing amplitude, the elastic modulus of the sample decreases but then increases, and the increase in #3 is more obvious than that in #2. In each stress step with the same amplitude, the average elastic modulus gradually increases with increasing number of loading and unloading cycles. When the amplitude is 15%, the average elastic modulus increases the fastest (Fig. 12a). In addition, with increasing amplitude, the irreversible strain of the sample gradually accumulates (Fig. 12b). With increasing cyclic amplitude, the cumulative irreversible strain increases but then decreases, and the final cumulative irreversible strain increases with increasing amplitude. The cumulative amount of irreversible strain with an amplitude of 15% is the greatest, approximately 0.4%.

Fig. 12.

Fig. 12

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With different amplitudes: (a) elastic modulus of coal sample and (b) cumulative irreversible strain.

Energy analysis

By substituting the triaxial compression test data into Eq. (2), the energy values of coal samples under different confining pressures can be obtained. Fig. 13 shows the energy evolution law of coal samples under different amplitudes. Under loading and unloading conditions of the same amplitude, with increasing number of cycles, the input energy and elastic energy in the coal sample increase, and the second stress step significantly increases compared with the first stress step. In addition, with increasing amplitude, the input energy and elastic energy increase significantly, and the dissipation energy tends to decrease as a whole.

Fig. 13.

Fig. 13

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Energy variation law of coal samples with different amplitudes: (a) 5%, (b) 10%, and (c) 15%.

Time-varying characteristics of axial strain

The variation characteristics of the first creep stage of the axial strain of coal samples under different amplitudes are shown in Fig. 14. The cyclic loading and unloading of different amplitudes significantly affect the strain change during the subsequent creep stage of the coal sample. When the amplitude is 5% and 10%, the axial strain tends to increase slowly and rapidly, respectively. When the amplitude is 15%, the axial strain tends to increase gradually, and the growth rate also tends to increase steadily.

Fig. 14.

Fig. 14

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Time-varying law of axial strain in the first creep stage of coal samples with different amplitudes: (a) 5%, (b)10%, (c)15%, and (d) growth rate.

Three-dimensional fracture reconstruction

Three-dimensional reconstruction models of blocks and fracture channels after coal sample failure with different amplitudes of disturbance are shown in Fig. 15. A comparison of the three-dimensional reconstruction models at different amplitudes reveals significant differences. When the amplitude is 5% of the peak stress, the degree of damage to the coal sample is low, or the coal does not penetrate the coal sample, and the overall structure of the coal sample is relatively complete. When the amplitude is 10% or even 15% of the peak stress, the cracks in the coal sample increase significantly, and at least one main crack passes through the coal sample. The loading and unloading of a larger value significantly affect the degree of damage to coal samples.

Fig. 15.

Fig. 15

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Three-dimensional scanning and fracture extraction maps: (a) 5%, (b) 10%, and (c) 15%.(The processing method is the same as in Fig. 9).

The fracture volume ratio and fractal dimension are also used to quantitatively analyze the fracture situation after failure of the coal samples with different amplitudes, as shown in Fig. 16. With increasing amplitude, the fracture proportion and fractal dimension of the coal sample after failure increase. When the loading and unloading amplitude is 15%, the fracture proportion increases significantly, indicating that when the loading and unloading amplitude increases, the damage to the coal sample qualitatively changes. At this amplitude, the degree of damage to the coal sample is essentially the same, whereas the fractal dimension decreases slightly at an amplitude of 15%. As shown in Fig. 15, the fracture shape at this time is more regular than that at the amplitude of 10%, and the block distinction of the entire coal sample is more obvious because the fractal dimension usually increases with increasing loading and unloading amplitude. This finding reflects the complexity of the coal sample structure after failure, but it may fluctuate or decrease after the coal sample structure is severely damaged.

Fig. 16.

Fig. 16

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Fracture proportion and fractal dimension of coal samples with different amplitudes.

Permeability

During the experiments, the axial strain and flow rate of the coal samples were monitored in real time, and the permeability of the coal samples was calculated by Formula (3). As shown in Fig. 17, with increasing loading and unloading amplitude, the strain of the coal samples gradually increased, and the permeability gradually increased. When the amplitude is 15%, the permeability and strain of the sample are significantly greater than 5% and 10%, respectively. The increase in loading and unloading amplitude has a significant damaging effect on coal samples, which expands the internal cracks of the sample and results in the formation of a new channel for gas circulation.

Fig. 17.

Fig. 17

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Variation characteristics of the permeability and strain of coal samples with different amplitudes: (a) 5%, (b) 10%, and (c) 15%.

Discussions

Mechanical response mechanism of coal samples to confining pressure and amplitude

In this study, we discuss the mechanical properties and energy characteristics of coal samples under different confining pressures and loading and unloading amplitudes through experiments. The results indicate that the confining pressure and loading and unloading amplitude significantly affect the elastic modulus, irreversible strain and energy characteristics of coal samples. In particular, the higher confining pressure results in an increase in the degree of circumferential compaction of the coal sample, limits the expansion of the crack, increases the friction between the particles, and improves the strength of the coal sample (as shown in Fig. 18). As the stress amplitude increases, the degree of fatigue damage to the coal sample increases, and the strength of the coal sample decreases. When the amplitude increases from 5% to 15%, the peak stress of the coal sample decreases by approximately 12.8%, indicating that the increase in the dynamic disturbance amplitude improves the initiation and propagation of internal microcracks (as shown in Fig. 19).

Fig. 18.

Fig. 18

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Variation in peak stress with confining pressure.

Fig. 19.

Fig. 19

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Variation in peak stress with amplitude.

A higher confining pressure can inhibit the dissipation of energy, which decreases the internal dissipation energy of coal samples is reduced. Moreover, the elastic modulus tends to increase with increasing confining pressure, indicating that the resistance of coal to external disturbance increases under high confining pressure. A higher confining pressure delays the fatigue damage process of coal by limiting the accumulation of dissipated energy, but a confining pressure that is too high accelerates the fracture and increases the dissipation of energy when the coal sample is close to failure (as shown in Fig. 20). Similarly, higher amplitude loading and unloading significantly increase the input energy and elastic energy, indicating that coal is more inclined to energy storage rather than dissipation, but this situation may increase the risk of sudden instability. Excessive amplitude loading and unloading also reduce the input energy and elastic energy (as shown in Fig. 21), and the amount of dissipated energy continues to increase.

Fig. 20.

Fig. 20

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Accumulated dissipation energy of coal samples under different confining pressures.

Fig. 21.

Fig. 21

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Cumulative dissipation energy characteristics of coal samples with different amplitudes.

Permeability response characteristics of coal samples to confining pressure and amplitude

An increase in confining pressure causes a significant decrease in coal permeability (measuring point 13 is selected, as shown in Fig. 22). The permeability under the 10 MPa confining pressure is 95% lower than that under the 5 MPa confining pressure, whereas the permeability under the 15 MPa confining pressure is 90% lower than that under the 5 MPa confining pressure. In addition, the results of three-dimensional fracture reconstruction reveal that the primary fractures in the coal body are closed under high confining pressure and that the gas flow channel changes from macroscopic fractures to micropores. Notably, when the confining pressure is 15 MPa, the permeability decreases slowly, indicating that the coal body forms a stable closed fracture network, which further validates the “closed–open” dual effect of confining pressure on the seepage channel.

Fig. 22.

Fig. 22

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Permeability variation law of the 13th measuring point under different confining pressures.

An increase in the stress amplitude significantly increases the permeability by inducing secondary crack propagation (selecting measuring point 10, as shown in Fig. 23). When the amplitude is 10%, the damage effect of loading and unloading on coal samples remains slight; thus, the permeability almost does not increase. When the amplitude is 15%, the permeability increases sharply. This phenomenon is directly related to the accumulation of axial strain and the increase in fracture penetration, resulting in a positive feedback mechanism of strain increase–crack propagation–permeability increase. However, high-amplitude disturbances may cause premature failure of coal, and balancing the stability of permeable structures in engineering is necessary.

Fig. 23.

Fig. 23

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Permeability variation law of the 10th measuring point under different amplitudes.

Confining pressure‒amplitude competition mechanism

As shown in Fig. 24, this study systematically reveals the effects of confining pressure (static stress) and stress amplitude (dynamic disturbance) on the mechanical properties and permeability characteristics of coal samples. The results indicate that they significantly affect the deformation mode, energy response, and permeability behavior of coal samples and exhibit nonlinear characteristics. An increase in confining pressure can increase the strength and stiffness of coal samples, increase the storage rate of elastic properties, reduce permeability, and improve structural stability. However, when the coal sample approaches failure, excessive confining pressure enables the accumulation of irreversible strain and accelerates failure. An increase in the stress amplitude will increase the energy accumulation inside the coal sample, whereas excessive stress amplitude loading and unloading will exacerbate fatigue damage, induce crack propagation, reduce strength, and sharply increase permeability. In terms of fracture morphology, as the confining pressure increases, the proportion of fractures after coal sample failure significantly decreases, and the fractal dimension decreases, indicating that the fracture structure tends to simplify and close. This microstructural change confirms the macroscopic phenomenon of increased elastic modulus and decreased permeability. In contrast, under high-amplitude disturbances, the proportion of cracks and fractal dimension increase significantly, indicating that internal cracks expand and penetrate, resulting in the formation of a complex flow network, a macroscopic decrease in strength and a sharp increase in permeability. Different confining pressures and amplitudes significantly affect the changes in the elastic modulus, irreversible strain, input energy, and dissipated energy, resulting in the formation of a competitive mechanism of “confining pressure crack suppression disturbance crack” under the combined action.

Fig. 24.

Fig. 24

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Confining pressure and amplitude competition mechanism.

On the basis of the experimental results, a preliminary inference can be made about the quantitative threshold of competitive effects. For example, to suppress the significant crack propagation and permeability increase induced by a 15% stress amplitude disturbance, the required confining pressure threshold is estimated to be between 10 MPa and 12 MPa. This inference is based mainly on the finding that under a 20% amplitude disturbance, a confining pressure of 10 MPa can significantly suppress permeability and simplify the fracture structure after failure (Figs. 8 and 10), indicating that its suppression ability is much stronger than that at a confining pressure of 5 MPa. Therefore, it is expected to effectively limit stronger 15% amplitude disturbances. This quantitative estimation provides a preliminary reference scale for balancing “confining pressure stability” and “disturbance enhanced transparency” in engineering. However, the determination of precise thresholds requires systematic research in future design experiments.

In terms of energy response, this study revealed an increase in energy storage efficiency (elastic energy ratio) and an inhibition of dissipation under high confining pressure, which is consistent with the main conclusion of Zhang et al. that confining pressure increases rock energy storage capacity23, confirming the general law that hydrostatic pressure induces energy elastic storage. However, in this study, under the condition of dynamic and static load coupling, when the amplitude of the dynamic disturbance increases, the coal sample tends to accumulate elastic energy quickly, guiding the sudden release of energy. This is different from the behavior described by Liu et al.‘s damage model based on energy dissipation, which is more suitable for monotonic or low-frequency cyclic loading32. This difference highlights the particularity of the failure mechanism of coal rock from progressive damage dominated by dissipation to brittle instability dominated by energy accumulation under the specific condition of high-amplitude dynamic disturbance. Therefore, the “competition mechanism” revealed in this study not only integrates the stability effect of static pressure but also emphasizes the key role of strong dynamic loading in inducing sudden disasters of coal and rock and improves the understanding of the particularity of coal and rock failure in deep environments.

The mechanics and seepage behavior of coal in complex stress environments are regulated by many factors, and the confining pressure stability and disturbance induction effect should be comprehensively considered. In engineering practice, in the deep high confining pressure (≥ 15 MPa) area, the amplitude of the dynamic disturbance stress should be controlled within 10% of the peak stress to utilize the stability effect of the confining pressure to prevent severe failure of the coal and rock mass and the release of concentrated energy. In shallow mining or gas extraction areas oriented by increased permeability, the disturbance amplitude can moderately increase to approximately 15% of the peak stress to facilitate the communication of the fracture network and improve the permeability of the coal seam.

Conclusions

In this study, combined tests of cyclic loading and gas seepage were performed in terms of the mechanical and seepage characteristics of coal in complex stress environments (static confining pressure and dynamic disturbance amplitude). The deformation behavior, energy evolution and permeability evolution of coal samples under different confining pressures and amplitudes were systematically analyzed. The main conclusions are as follows:

  1. As the confining pressure increases, the peak stress of the coal sample increases gradually (by 36.5%), and the elastic modulus and the slope of the stress‒strain curve increase synchronously. The high confining pressure effectively compacted the internal cracks of the coal sample, reduced the accumulation of irreversible strain and dissipated energy, and increased the anti-disturbance ability of the coal sample. Moreover, the permeability decreases significantly and tends to be stable under high confining pressure, indicating that the fracture network is fully closed and that the flow capacity is limited.

  2. Under the condition of a fixed confining pressure, an increase in the disturbance amplitude significantly reduces the peak strength of coal samples, and the irreversible strain significantly increases. The input energy and elastic energy accumulate faster, reflecting that the failure mode of the coal body tends to be “energy storage–burst release”. In addition, the high amplitude causes an increase in fracture penetration, and the permeability sharply increases. Three-dimensional fracture reconstruction validates the effect of fracture expansion on flow capacity.

  3. The confining pressure is involved mainly in crack compaction and structural stability, and the amplitude promotes crack propagation and energy damage accumulation. Under the combined action of the two, the coal sample clearly has a nonlinear response mechanism, which is reflected in many aspects, such as the evolution rate of the elastic modulus, the irreversible strain growth trend and the permeability‒strain coupling relationship. Under high confining pressure conditions, the disturbance amplitude should be controlled to prevent sudden damage and concentrated energy release. In the dominant area of extraction, the disturbance amplitude can be moderately increased to improve the permeability of the coal seam.

Prospect

This article qualitatively explores the competitive characteristics of amplitude and confining pressure in coal samples, which can provide some reference for on-site work. In future work, quantitative research will continue to be conducted to construct specific models to explain the problems.

Author contributions

H.M. Y -Manuscript main textD.K. Q-Paper diagramH. L-ReviewX.Y. S-methodQ.C.R-Guide the experimentY.L. H-proofread.

Funding

This work was supported by the Open Fund Project Funded by State Key Laboratory of Coal Mine Disaster Prevention and Control(2022SKLKF02)and the National Natural Science Foundation of China (52274246).

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s note

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

Contributor Information

Dengke Qin, Email: 1784048968@qq.com.

Hao Liu, Email: liuhaocqu@cqu.edu.cn.

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Associated Data

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Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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