Evolution of Permeability and Sensitivity Analysis of Gas-Bearing Coal under Cyclic Dynamic Loading

Abstract

It is imperative to conduct experimental studies on the seepage behavior of gas-bearing coal under cyclic dynamic loading conditions. This paper focuses on the evolution of coal permeability under the combined effects of dynamic loading, static loading, and gas adsorption. The principal conclusions are as follows: (1) As the frequency and amplitude of dynamic loading increase, the development of pore and fissure structures within the coal body becomes increasingly pronounced during dynamic loading cycles, resulting in a gradual rise in permeability. Notably, as the coal approaches its yielding stage, the permeability can increase by up to 47%. (2) The permeability curve is divided into four regions: the compaction reduction zone, the oscillation zone, the gradual recovery zone, and the abrupt failure increase zone. Ultimately, in the failure phase, the permeability surges dramatically, potentially reaching four to five times the initial permeability. (3) When the static loading stage and dynamic load are constant, the rate of change in coal permeability decreases with increasing adsorption amounts. When the adsorption amount is constant, the rate of change in permeability of the coal under dynamic loading increases with the increase in the static loading stress stage, with the maximum increase reaching 75.2%. It can be concluded from the rate of change in permeability and the dynamic loading sensitivity coefficient that the permeability of coal is highly sensitive to cyclic dynamic loading, with increased sensitivity associated with larger static loading stages and decreased sensitivity with greater adsorption amounts.

1. Introduction

Due to the depletion of shallow coal resources, coal mining operations are progressively moving towards deeper deposits. Deep coal seams frequently experience repeated mining disturbances, resulting in cyclic dynamic loading on the coal layers. When subjected to such cyclic dynamic loading, the deformation of the coal body causes the propagation of fractures, which in turn affects the permeability of the coal, leading to abnormal gas outbursts in coal mines. In severe cases, this can result in catastrophic events such as gas explosions and coal and gas outbursts. Consequently, it is imperative to conduct experimental studies on the seepage behavior of gas-bearing coal under cyclic dynamic loading conditions.

Extensive research has been conducted by scholars both domestically and internationally on the permeability characteristics of coal rock masses [1,2,3,4,5,6,7]. Regarding the effects of coal matrix contraction and expansion on permeability, Bustin et al. [8] conducted preliminary studies on the relationship between adsorption expansion effects and permeability in coal samples under different gas purities. Wang et al. [9] investigated the relationship between coal matrix contraction and permeability under the adsorption of multiple gasses. Niu et al. [10] investigated the differential effects of gas adsorption on the swelling behavior of raw coal versus structural coal. Mojgan et al. [11] conducted experiments to identify the critical point at which the effect of gas pressure on coal matrix shrinkage changes, and they noted that this pressure is approximately 1.5 MPa. Larsen [12] and Liu [13] hypothesized, based on experimental results, that the effect of gas adsorption on the permeability of coal rock is primarily due to matrix contraction and expansion. Li et al. [14] investigated the effects of effective stress, matrix expansion and contraction, temperature, and moisture on coal rock permeability, and identified the principal influencing factors. Liu et al. [15] investigated the effects of various gasses on the permeability of coal rocks and analyzed the differences in adsorption of different gasses concerning the contraction and expansion of the coal matrix. Zhao et al. [16] examined the mechanisms by which gas adsorption affects the permeability of coal. Zhao [17] and Hu [18] fitted the relationship between permeability and gas pressure based on experimental results.

In terms of the impact of effective stress on permeability variations, Li et al. [14] investigated the sensitivity of permeability to stress and delineated the relationship between permeability and stress fluctuations. Bai et al. [19] investigated the variations in coal rock permeability across different stress stages. Lu [20] investigated the variations in coal rock permeability with respect to confining pressure and pore pressure, and observed that, with an increase in pore pressure, the permeability initially increased and then decreased. Fan et al. [21] analyzed the variation in coal rock permeability with effective stress and delineated the characteristics of initial permeability. Mitra et al. [22] investigated the variations in coal rock permeability with changes in pore pressure and effective stress under uniaxial compression test conditions and concluded that the rate of permeability change differed at various stages. Tang et al. [23] conducted experiments using a self-developed seepage testing apparatus. Based on the experimental results, they fitted the relationship between effective stress and permeability during the testing process and highlighted the discrepancies observed between the loading and unloading phases. Zhao et al. [24] derived an equation that elucidates the correlation between coal matrix permeability and effective stress, thereby laying the groundwork for the establishment of subsequent models. Li et al. [25] investigated the sensitivity of coal rock permeability to effective stress during loading. Peng et al. [26] examined the impact of scale effects on coal rock permeability and noted that sensitivity to effective stress varied at different scales. Yin et al. [27,28] not only explored the influence of effective stress on coal rock permeability but also analyzed the effects of strain on permeability.

Regarding the influence of the Klinkenberg effect on gas permeability, Pirzada et al. [29] investigated the sensitivity of the Klinkenberg effect to confining pressure and pore pressure and identified the inflection point of this effect, while Talapatra et al. [30] conducted experimental studies on the aforementioned phenomenon, providing a quantitative analysis of the impact of the Klinkenberg effect on permeability reduction, and Wang et al. [31] analyzed the discrepancies of the Klinkenberg effect between briquette coal and raw coal.

The aforementioned studies primarily focused on the gas permeability characteristics of coal under static loading conditions. However, there is a paucity of research on the gas flow characteristics of coal under the combined effects of static load, dynamic load, and gas adsorption. The mechanisms of gas flow in coal under these combined influences remain to be further explored. This paper, utilizing self-developed instrumentation, investigates the impact of static load, dynamic load, and gas adsorption on the permeability of coal. The findings provide a theoretical foundation for understanding coal rock dynamic disaster mechanisms and gas extraction processes.

2. Experimental Apparatus

A self-developed three-axis solid–gas coupling test apparatus was used to measure the permeability of the coal under cyclic dynamic and static combined loads, as shown in Figure 1 [32]. It consisted of four key units: dynamic and static loading unit, three-axis confining pressure unit, fluid injection unit, and information acquisition unit. The challenges of the dynamic–static load combination, high-pressure sealing under dynamic loads, and permeability measurement during the full stress–strain process were solved. The apparatus, through an innovative structural design, incorporated a dynamically sealed piston in conjunction with an integrated loading cylinder, successfully achieving the dynamic and static combined loading of solid–gas coupled coal samples. The calibration of pressure in the experimental equipment was carried out using a high-precision manometer. The calibration pressure range extended from 0 to 60 MPa, and the calibration dynamic load frequency was from 0 to 10 Hz. The accuracy of the permeability measurement was ensured through calibration with a mass flow meter, with a calibration range of 0–50 L/min.

3. Experimental Scheme

The permeability of gas-containing coal under combined static and dynamic loading is closely related to factors such as static load, dynamic load, and the amount of gas adsorption. The experimental variables chosen for this test were the dynamic loading impact energy, the static loading stress stages, and the gas adsorption quantity. Dynamic impact energy is primarily achieved by adjusting the frequency and magnitude of the dynamic load. The static loading stress phase is divided into the compaction stage, the elastic stage, and the yield stage. The gas adsorption amount is adjusted through different adsorptive gasses at the same adsorption pressure, and all the gasses are in a gaseous form. The dynamic load along the trough of a mining face is mainly caused by the excavation process, and the source energy level in our study was about 100 J. Based on the magnitude of the energy and the compressive strength of the coal samples, it was determined that the dynamic load amplitude should not exceed 6.5 MPa. The dynamic load frequency band was mainly at 3–6 Hz, and the main deformation stage of coal and rock occurred within the first 300 cycles [33]. According to the storage conditions of the gas pressure in coal under the actual working conditions, the gas pressure was selected to be 1 MPa. At the same time, in order to create a triaxial stress environment and mitigate the differences in permeability arising from variations in effective stress, the confining pressure was maintained at a constant value of 1.5 MPa. The ambient temperature throughout the experiment was maintained at approximately 25 °C, with the adsorption time of the adsorptive gasses uniformly regulated to around 48 h. The detailed experimental plan is presented in

Table 1. Experimental plan.

Number	Frequency and Magnitude of Dynamic Load	Static Load Stress Phase	Gas
1	2.50 MPa, 3 Hz	0.45 σc	CH4
2	2.50 MPa, 4 Hz	0.45 σc	CH4
3	2.50 MPa, 5 Hz	0.45 σc	CH4
4	2.50 MPa, 6 Hz	0.45 σc	CH4
5	3.75 MPa, 3 Hz	0.45 σc	CH4
6	5.00 MPa, 3 Hz	0.45 σc	CH4
7	6.25 MPa, 3 Hz	0.45 σc	CH4
8	2.50 MPa, 3 Hz	0.3 σc	CH4
9	2.50 MPa, 3 Hz	0.6 σc	CH4
10	2.50 MPa, 3 Hz	0.75 σc	CH4
11	2.50 MPa, 3 Hz	0.45 σc	CO2
12	2.50 MPa, 3 Hz	0.45 σc	N2
13	2.50 MPa, 3 Hz	0.45 σc	He

, where σ_c is the triaxial compressive strength.

In order to ensure the comparability of the experimental data, a testing loading path was designed, as illustrated in Figure 2. The sample was initially subjected to a predeterminable confining pressure, after which it was infused with a predefined pressure of gas. After the gas adsorption had reached an equilibrium, a static load was applied to the sample until it reached the designated value. On this basis, a cyclic dynamic load was applied with the predetermined amplitude and frequency. After the dynamic loading disturbance ended, it was returned to the uniform predetermined stress state of 2 MPa, and we conducted the permeability test.

4. Results and Discussion

4.1. The Influence of the Cyclic Loading Frequency on the Permeability

The variation in coal permeability with the frequency of cyclic dynamic loading is illustrated in Figure 3. It is evident that there is a positive correlation between the permeability of the coal body and the frequency of cyclic dynamic loading. To better visualize the variation in permeability with the dynamic loading frequency, we defined the ratio of permeability at a given dynamic load frequency to the permeability without dynamic loading conditions as the ratio of values. When the coal body was undisturbed by dynamic loading, its permeability was approximately 0.0135 μm². However, after being subjected to cyclic dynamic loading with an amplitude of 2.5 MPa and a frequency of 6 Hz, the permeability increased to 0.0176 μm², reflecting an increase of approximately 30.1%. The increases in permeability at the other three dynamic loading frequencies were 7.2% (3 Hz), 16.3% (4 Hz), and 23.8% (5 Hz), respectively. It is, therefore, evident that cyclic dynamic loading has a significantly pronounced effect on increasing the permeability of coal bodies. The pores and fractures within the coal mass serve as the primary conduits for gas seepage. Under the continuous influence of cyclic loading, the primary pores and fractures further develop, resulting in an increased permeability. As the frequency of dynamic loading increases, a certain number of secondary fractures will develop, leading to a phenomenon where permeability continues to rise with the ongoing increase in dynamic loading frequency. Moreover, under the influence of cyclic dynamic loading, the gas adsorption equilibrium within the coal matrix is disrupted, further enhancing the gas adsorption and expansion effects. Thus, it is evident that the greater the external disturbance to the coal seam, the faster the gas migration within the seam, making it more prone to abnormal gas outbursts. Simultaneously, for coal seams from which gas can be extracted, external disturbances can enhance their permeability, thereby improving the efficiency of gas extraction. Furthermore, as the load frequency increases, the enhancement of transmittance becomes more pronounced.

4.2. The Influence of the Cyclic Loading Amplitude on the Permeability

The variation in coal permeability with the amplitude of cyclic dynamic loading is illustrated in Figure 4. It is evident from the figure that the permeability of coal is positively correlated with the amplitude of cyclic dynamic loads. At amplitudes of 2.5 MPa, 3.75 MPa, 5 MPa, and 6.25 MPa, the permeabilities are recorded to be 0.0144 um², 0.0154 um², 0.017 um², and 0.0193 um², respectively, with growth rates of 7.2%, 14.3%, 26.1%, and 43%. It is evident that the amplitude of dynamic loading exerts a more pronounced effect on the increase in permeability. The reasons for the increase in permeability are fundamentally consistent with those for different frequencies. The sharp 43% increase in permeability at an amplitude of 6.25 MPa is due to the fact that, at this stage, the cyclic dynamic loading is in the yield phase of the coal body stress–strain curve. Consequently, the degree of damage is greater, and the development of fractures is more pronounced. For coal seams from which it is difficult to extract gas, one method employed is to enhance the amplitude of vibrational loading.

4.3. The Influence of the Static Load Stage on the Permeability

The variation in permeability with the static load stage of the cyclic dynamic load is illustrated in Figure 5. It is evident that there is a positive correlation between the permeability of the coal body and the static load stage. When the static load stages are 0.3 σ_c, 0.45 σ_c, 0.6 σ_c, and 0.75 σ_c, the permeability of the coal samples is observed to be 0.0137 μm², 0.0144 μm², 0.0152 μm², and 0.0198 μm², with corresponding growth rates of 2%, 7.1%, 13.1%, and 47.2%, respectively. During the elastic stage of coal, the impact of cyclic dynamic loading on permeability is not significant. This is because, during this phase, the internal damage to the coal body is minimal, and the resulting plastic deformations and newly formed cracks are also relatively few. However, before and during the yield stage of the coal mass, its permeability significantly increases, with a maximum increase of up to 47.2% compared to the permeability without dynamic loading. The reason is that, during this stage, the application of cyclic dynamic loads significantly exacerbates the internal damage to the coal body, leading to the expansion of primary fractures and the formation of numerous secondary fractures. It is evident that, when coal seams are subjected to higher stress conditions, they are more prone to damage and abnormal gas outbursts when disturbed by external dynamic loads.

4.4. The Influence of Adsorbed Gas on the Permeability

Gas adsorption capacity is measured through gasses at identical pressures but of different types, thereby ensuring the comparability of the permeability results. The adsorption capacity was measured for the following four gases, in ascending order: He, N₂, CH₄, and CO₂. The variation in permeability with the capacity of gas adsorption is illustrated in Figure 6. It is evident that there is an inverse correlation between the permeability of the coal body and the gas adsorption capacity. As the capacity for gas adsorption increases, the permeability of the coal samples is 0.0186 μm², 0.0172 μm², 0.0144 μm², and 0.0132 μm², respectively. Taking the permeability of the non-adsorptive inert gas He as the baseline, the reductions in permeability for the other three gasses are 8%, 23%, and 29.2%, respectively. Thus, it is evident that gas adsorption exerts an inhibitory effect on the permeability of the coal body. The reason is that, after the coal body adsorbs gas, it undergoes adsorption-induced swelling and deformation. However, constrained by the confining pressure, deformation can only occur inwardly, thereby compressing the internal seepage pathways of the coal body and consequently reducing its permeability. As the amount of adsorption increases, so does the degree of adsorption-induced swelling and deformation, resulting in a more significant reduction in permeability.

4.5. The Permeability Behavior of Coal in the Full Stress–Strain Process

To more intuitively illustrate the overall evolution of coal permeability under cyclic dynamic loading, we also obtained the stress–strain versus permeability relationship curves of the coal body under such loading, as depicted in Figure 7. There exists a notable coupling relationship between the stress of the coal samples, the axial strain, and the permeability. The stress–strain curve of coal can be classified into four distinct phases: the compaction stage, the elastic oscillation stage, the plastic deformation stage, and the failure stage. Correspondingly, the permeability curve is divided into four regions: the compaction reduction zone (I), the oscillation zone (II), the gradual recovery zone (III), and the abrupt increase zone of failure (IV).

The compaction reduction zone (I): From the initial compression point to the lowest permeability point before the application of cyclic loading, this phase corresponds to the consolidation stage and the elastic deformation stage of the stress–strain curve. During this period, the permeability of the coal samples exhibited a non-linear decreasing trend, with the rate of decrease gradually decelerating, ultimately reducing by approximately 50% of the initial permeability. The reason is that, under the gradual application of an axial load, the inherent fissures within the coal body are progressively compacted. This leads to a reduction in the connectivity of the fissures, consequently decreasing the porosity. The channels through which gas molecules flow become narrower and fewer, resulting in a noticeable decline in permeability.

The oscillation zone (II): This zone exhibits a propensity towards coupled resonance in permeability during the application phase of cyclic dynamic loading, which evolves in tandem with the imposition of cyclic dynamic loads. The permeability after the application of a dynamic load should exceed that before the application, as cyclic dynamic loading induces irreversible plastic deformation in the coal matrix, leading to a gradual accumulation of damage and an increase in the pathways available for gas flow.

The gradual recovery zone (III): From the end of the oscillatory zone in the permeability curve to the point of sudden slope increase, this stage corresponds to the plastic deformation phase of the stress–strain curve. During this period, with the increase in axial stress, permeability also exhibits growth. Due to the external load, the coal body framework undergoes irrecoverable plastic deformation, leading to a gradual accumulation of damage and destruction. Numerous new fissures emerge, develop, and stabilize, thereby causing the permeability to progressively recover.

The abrupt increase zone of failure (IV): From the point of the sharp increase in the slope of the permeability curve until the conclusion of the test, this phase corresponds to the peak strength and post-peak phase of the stress–strain curve. During this period, the permeability curve of the coal samples exhibits an almost vertical ascent. Compared to the initial permeability, the permeability at the end of this stage has increased by approximately a factor of two.

The stress–permeability temporal curve of coal under cyclic loading is illustrated in Figure 8. It is evident that the stress loading curve of the coal body and the variation in permeability exhibit a synchronous resonance pattern. When the cyclic load is applied and the stress returns to its pre-load level, the permeability fails to revert to its original state and actually increases to a certain extent. The reason for this lies in the fact that, during the application of dynamic loading, the internal fissures within the coal body further develop, leading to the widening and proliferation of seepage pathways, which, to a certain extent, increases the permeability of the coal body. Based on the experimental conclusions, it is essential to continuously monitor the gas concentration at the working face during field construction to determine whether mining disturbances have caused a sudden increase in permeability of the coal seam at the working face, thereby minimizing the risk of disasters such as coal and gas outbursts.

The increase in permeability of the coal mass during different cyclic dynamic loading processes is illustrated in Figure 9. As the amplitude of the cyclic dynamic load increases, the increment in permeability of the coal mass during the application of the dynamic load also rises. This indicates that, with the increase in the dynamic load amplitude, the damage within the coal mass becomes more pronounced, leading to the more extensive development of fractures.

The coupling curve of permeability increases, and the yield strain of coal under different cyclic dynamic loading is illustrated in Figure 10. As the amplitude of dynamic loading increases, the yield strain during the dynamic loading process also grows. This indicates that the coal body is subjected to further compression; however, an increase in permeability is observed. The reason for this is that, during this process, fractures radially expand further, leading to a continuous rise in permeability.

Following cyclic loading, the maximum permeability of the coal body during failure also increases, as illustrated in Figure 11. When the cyclic loading amplitudes are 2.5 MPa, 3.75 MPa, 5 MPa, and 6.25 MPa, the maximum permeability values of the coal body are 0.0255 μm², 0.0286 μm², 0.0321 μm², and 0.0386 μm², respectively. Compared to the baseline value of 0.0135 μm², these represent increases of 88.9%, 111.9%, 137.8%, and 185.9%, respectively. It is evident that the application of dynamic loading not only enhances the current permeability of the coal body but also significantly contributes to the increase in its maximum permeability upon failure.

5. Sensitivity Analysis of Permeability to Cyclic Loading

As the depth of coal seam mining increases, the geostress (static load), gas pressure (gas adsorption), and dynamic load disturbances continuously change. The permeability of gas-bearing coal is not constant but rather a function of certain influencing factors. Given the numerous factors affecting coal seam permeability, this paper focuses on analyzing the impact of static and dynamic loads and gas adsorption. The deep coal rock mass itself is complex in structure, surrounded by a challenging environment and subject to rapidly changing evolutionary patterns. Ordinary control variable methods fall short in adequately describing these patterns; thus, a sensitivity coefficient for coal permeability is defined to characterize them.

5.1. Fitting of the Permeability Variation Curve

Figure 12 illustrates the variation in coal rock permeability with respect to the frequency of cyclic dynamic loading. Under the condition of a fixed static load phase, the permeability of the coal rock increases in an exponential manner with the rise in the cyclic dynamic load. Initially, as the frequency of cyclic dynamic loading increases, the energy imparted by the load rises slowly, resulting in minimal damage and fewer fractures within the coal mass. Consequently, the rate of increase in permeability is gradual. However, as the frequency of cyclic dynamic loading continues to rise, the rate of energy increase accelerates, leading to a corresponding rapid increase in permeability.

Fitting the curve in Figure 12 reveals that, when the adsorptive gas and static load phase are held constant, the permeability of the coal rock increases exponentially with the frequency v of cyclic dynamic loading:

$$\mathit{k}\mathit{=}{\mathit{a}}_{\mathbf{0}}{\mathit{e}}^{{\mathit{b}}_{\mathbf{0}}\mathit{v}}$$

where k represents the permeability of the coal body, and a₀ and b₀ are both fitting constants. a₀ signifies the magnitude of permeability, while b₀ indicates the rate of change in permeability.

Table 2. Results of fitting of permeability.

Static Load Stage	Gas Type	a0	b0	R2
0.3σc	He	0.0123	0.0693	0.9973
	N2	0.0116	0.0688	0.9813
	CH4	0.0107	0.0683	0.9963
	CO2	0.0105	0.0667	0.9972
0.45σc	He	0.0129	0.0705	0.9980
	N2	0.0121	0.0758	0.9967
	CH4	0.0116	0.0686	0.9732
	CO2	0.0113	0.0629	0.9651
0.6σc	He	0.0133	0.0814	0.9584
	N2	0.0131	0.0777	0.9663
	CH4	0.0122	0.0723	0.9913
	CO2	0.0119	0.0695	0.9842

presents the fitting results of the permeability of the coal body for various gasses across different phases of static loading, along with the R² values, illustrating that the exponential function yields a commendable fit.

5.2. Evaluation Parameters for Cyclic Load Sensitivity

The sensitivity of coal permeability to the frequency of cyclic dynamic loading is analyzed from two perspectives, primarily concerning the rate of permeability change and the permeability dynamic loading sensitivity coefficient. These two parameters reflect the magnitude and the rate of change in permeability, respectively.

The rate of change in permeability described in this paper refers to the variation in permeability induced by cyclic loading frequencies during the static load phase and with a fixed type of gas.

$${\mathit{D}}_{\mathit{v}}\mathit{=}{\displaystyle \frac{{\mathit{k}}_{\mathit{i}}\mathit{-}{\mathit{k}}_{\mathbf{0}}}{{\mathit{k}}_{\mathbf{0}}}}$$

where D_v represents the rate of change in coal permeability, indicating the magnitude of permeability variation. k₀ denotes the initial permeability of the coal body, in μm². k_i signifies the permeability after an increase in dynamic loading frequency, in μm².

The dynamic load sensitivity coefficient of permeability refers to the relative change in coal rock permeability caused by an increase of 1 Hz in the frequency of cyclic dynamic loading, while the static loading phase and the type of gas are held constant. Based on the characteristics of the functions presented in this paper, the dynamic load sensitivity coefficient of permeability can be expressed using the following equation.

$${\mathit{C}}_{\mathit{v}}\mathit{=}{\displaystyle \frac{\mathbf{1}}{{\mathit{k}}_{\mathbf{0}}}}{\displaystyle \frac{\mathsf{\partial }\mathit{k}}{\mathsf{\partial }\mathit{v}}}$$

where C_v represents the coefficient of dynamic load sensitivity, in Hz⁻¹. $\partial k$ signifies the variation in permeability, in µm². $\partial v$ denotes the change in dynamic load frequency, in Hz. A higher C_v value indicates a greater sensitivity of permeability to dynamic loads, while a lower C_v value reflects a reduced sensitivity.

5.3. Sensitivity Analysis of Cyclic Load

The results of the calculation for the variation rate of coal body permeability under different cyclic dynamic loading frequencies are presented in

Table 3. Calculation results of permeability change rate.

Static Load Stage	Dv (%)
	He	N2	CH4	CO2
0.3σc	48.8	45.6	29.6	25.6
0.45σc	57.6	52	40.8	32.8
0.6σc	75.2	68.8	51.2	45.6

. When the static loading stage is constant, the permeability variation rate of the coal body decreases as the adsorption amount increases, although it remains positive throughout. This indicates that cyclic dynamic loading increases the permeability of the coal body, but the extent of this increase diminishes as the adsorption amount grows. When the adsorption amount is constant, the variation rate of coal body permeability increases with the increase in the static loading stage, with the maximum increase reaching 75.2%. Hence, it is evident that coal body permeability is highly sensitive to cyclic dynamic loading, with a greater sensitivity associated with larger static loading stages. Conversely, higher adsorption amounts lead to reduced sensitivity.

Substitute Equation (1) into (3) to derive the relationship between the coefficient of dynamic sensitivity of permeability C_v and the dynamic loading frequency ν.

$${\mathit{C}}_{\mathit{v}}={\mathit{a}}_1{\mathit{e}}^{{\mathit{b}}_1\mathit{v}}$$

where a₁ and b₁ are both fitting constants. The value of a₁ is related to the magnitude of coal permeability. b₁ reflects the rate of change in the dynamic loading sensitivity coefficient, with a greater value of b₁ indicating a faster rate of change in the dynamic loading sensitivity factor. The relationship between the dynamic loading sensitivity coefficient and the dynamic loading frequency also follows an exponential function, with a greater dynamic loading frequency resulting in a higher sensitivity coefficient. The calculated results are presented in

Table 4. Calculation results of the dynamic load sensitivity coefficient.

Static Load Stage	Gas Type	a1	b1
0.3σc	He	0.0682	0.0693
	N2	0.0638	0.0688
	CH4	0.0585	0.0683
	CO2	0.0560	0.0667
0.45σc	He	0.0728	0.0705
	N2	0.0734	0.0758
	CH4	0.0637	0.0686
	CO2	0.0569	0.0629
0.6σc	He	0.0866	0.0814
	N2	0.0814	0.0777
	CH4	0.0706	0.0723
	CO2	0.0662	0.0695

.

The coefficient of the dynamic load sensitivity of permeability exhibits a pattern similar to that of the rate of change in permeability. The permeability of the coal body shows a pronounced sensitivity to dynamic load frequency, with this sensitivity diminishing as the adsorbed gas quantity increases and increasing as the static load phase extends.

With the increase in the cyclic dynamic load frequency and amplitude, the working face is damaged and prone to disasters such as coal and gas outbursts. Therefore, in practical engineering, blasting excavation or high-frequency mechanical disturbance should be avoided as much as possible for high-pressure coal seams. When the stress level of the coal seam to be mined is high, such as the coal seam in the yield stage, the change in the permeability of the coal seam and the cracking and damage state of the coal seam should be focused on during the mining process. When the gas content of the coal seam being mined is high, corresponding measures should be taken to relieve pressure before normal mining activities can be carried out. This article mainly focuses on the influence of dynamic load and gas pressure on coal permeability, but, in practical engineering, harsh environments such as ones with high temperature and humidity may also be encountered. Therefore, more detailed research is needed for the above-mentioned harsh environment.

6. Conclusions

This paper focuses on the evolution of coal permeability under the combined effects of dynamic loading, static loading, and gas adsorption. It considers the influence of critical factors such as the dynamic load frequency and amplitude, the static load stage, and the types of adsorbed gasses. The principal conclusions are as follows.

(1)

As the frequency and amplitude of dynamic loading increase, the development of pore and fissure structures within the coal body becomes increasingly pronounced during the dynamic loading cycles, resulting in a gradual rise in permeability. Notably, as the coal approaches its yielding stage, the permeability can increase by up to 47%. However, with the enhancement of gas adsorption, the permeability of the coal body gradually diminishes.

(2)

The permeability curve is divided into four regions: the compaction reduction zone, the oscillation zone, the gradual recovery zone, and the abrupt increase zone of failure. It is noteworthy that the permeability and stress–strain relationship exhibit a phenomenon of resonance at the same frequency, with the permeability of the coal body gradually increasing during dynamic load cycling. Ultimately, in the failure phase, the permeability surges dramatically, potentially reaching values of four to five times the initial permeability.

(3)

A sensitivity analysis of permeability to dynamic and static loading and gas adsorption was conducted, defining two evaluation parameters: the rate of change in permeability and the dynamic loading sensitivity coefficient of permeability. When the static load stage was constant, the rate of change in permeability of the coal under dynamic loading decreased with increasing adsorption amounts. When the adsorption amount was constant, the rate of change in permeability of the coal under dynamic loading increased with the increase in the static loading stress stage, with the maximum increase reaching 75.2%. It can thus be concluded from the rate of change in permeability and the dynamic loading sensitivity coefficient that the permeability of coal is highly sensitive to cyclic dynamic loading, with an increased sensitivity associated with larger static loading stages and decreased sensitivity with greater adsorption amounts.

In the realm of equipment designed for cyclic loading, it is imperative to undertake regular maintenance and upkeep to ensure its long-term stable operation, which incurs a certain maintenance cost. Although enhancing cyclic loading can improve methane extraction efficiency, the process may have a discernible environmental impact due to methane emissions. Therefore, additional funds must be allocated for environmental protection and remediation efforts. By employing cyclic loading fracturing technology, fractures can be induced within the coal seam, boosting methane extraction efficiency and increasing energy yield. An enhanced methane extraction efficiency contributes to reducing gas accumulation in coal mines, thereby mitigating the risk of gas explosions and safeguarding miners’ safety.