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Article

Energy Evolution Characteristics of Water-Saturated and Dry Anisotropic Coal under True Triaxial Stresses

by
Yubing Liu
1,2,*,
Enyuan Wang
1,2,
Dong Zhao
1,2 and
Li Zhang
1,2
1
School of Safety Engineering, China University of Mining and Technology, Xuzhou 221116, China
2
Key Laboratory of Gas and Fire Control for Coal Mines, China University of Mining and Technology, Ministry of Education, Xuzhou 221116, China
*
Author to whom correspondence should be addressed.
Sustainability 2023, 15(2), 1431; https://doi.org/10.3390/su15021431
Submission received: 28 November 2022 / Revised: 28 December 2022 / Accepted: 10 January 2023 / Published: 11 January 2023
(This article belongs to the Section Hazards and Sustainability)
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Abstract

:
During deep underground coal mining, water-injection-related engineering methods are generally carried out to reduce the hazards of coal dynamic disasters. The energy evolution characteristics of coal can better describe the deformation and failure processes, as it is more consistent with the in situ behavior of underground mining-induced coal. In this study, experimental efforts have been paid to the energy evolution characteristics of water-saturated and dry anisotropic coal under true triaxial stresses. The effects of water saturation, intermediate stress, and anisotropic weak planes of coal on the true triaxial energy evolution were systematically evaluated. The results show that the overall energy is weakened due to the water adsorption for water-saturated coal samples. The water-weakening effect on the overall energy of water-saturated coal is more pronounced when perpendicular to the bedding plane direction than in the other two cleat directions. The accumulation elastic energy anisotropy index of dry and water-saturated coal samples is higher than 100.00%. Both accumulation and residual elastic energy of dry and water-saturated coal samples show an increasing-then-decreasing trend with intermediate stress increase. The results obtained in this study help understand the in situ behavior of coal during deep underground mining and control coal dynamic disasters.

1. Introduction

Coal remains the second largest energy source worldwide, which accounts for 27.6% of the global primary energy consumption in 2017 [1]. China is the world’s largest coal producer and consumer [2]. With the shallow coal resources gradually exhausted, some countries such as Germany, France, and Poland, have already conducted deep underground coal mining and it will become common in the future [3,4]. The geological conditions of deep coal seams are significantly different from shallow coal seams. Compared with shallow-buried coal seams, deep coal seams are generally characterized by high in situ stress, high gas content, and low permeability [5,6]. Deep coal mining processes could cause coal dynamic disasters, and the associated accidents may occur more frequently [7,8].
Water content has a significant effect on the physical and geo-mechanical properties of the coal seam [9]. Some water-injection-related engineering methods (e.g., hydraulic fracturing, hydraulic cutting, and hydraulic flushing) are generally carried out during deep coal mining for coal dynamic disaster control and permeability enhancement [10,11,12,13]. After the water adsorption in coal seams, two effects could happen on the targeted areas. On the one hand, the existence of water will modify the coal structure, and the associated water wedge effect leads to a decrease in coal strength [14]. On the other hand, easy disintegration of coal and possible water inrush could be triggered due to a large amount of water injection [15,16,17]. Thus, deep coal mining activities under dry and water-saturated conditions could face different risk levels concerning potential coal dynamic disasters. Investigating and comparing the coal energy evolution characteristics under dry and water-saturated conditions is necessary to prevent and control the relevant engineering hazards during water-injection methods.
Numerous experimental effects have been investigated regarding the mechanical properties of water-saturated coal under uniaxial stress conditions (σ1 > σ2 = σ3 = 0) [18,19,20,21,22]. Their results show that the peak strength and elastic modulus of coal decrease significantly with the increase of moisture content. For most cases, this stress replication method is relatively simple. Some scholars have carried out triaxial stress tests (σ1 > σ2 = σ3) on water-saturated coal [23,24,25]. Compared with the results of uniaxial stress tests, the changes in the coal’s triaxial mechanical properties due to water content adsorption decrease significantly. Both the reduction of saturated-water content and the high confining pressure strengthening effect contribute to the decreases in the alteration of mechanical properties. Triaxial stress is also a simplified way of in situ stress as it neglects the influences of intermediate stress. True triaxial tests (σ1 > σ2 > σ3) have the benefit of examining the effect of intermediate stress. Some scholars have investigated the water-content variations on sandstone and shale’s mechanical properties under true triaxial stress conditions [26,27]. Their results found that increasing intermediate stress and decreasing water content resulted in higher stiffness and strength for the tested rock samples. When neglecting the effect of intermediate stress could lead to conservatively measured mechanical parameters for tested rock samples. Coal, a relatively weak rock with numerous natural fractures inside, could behave differently under certain tested stresses. Some true triaxial tests on water-saturated coal have examined its mechanical behavior [28,29], and they found that strength anisotropy decreases if considering water content.
As indicated by the experimental studies above, the existing water content in coal significantly impacts its mechanical properties, which could further contribute to the instability of the engineering structure constructed in the deep coal seams. The obtained mechanical parameters of coal with water content could be used to calculate the energy evolution during stress loading. The energy evolution characteristics of coal can better describe the deformation and failure processes, as it is more consistent with the in situ behavior of underground mining-induced coal. It is necessary to investigate the energy evolution characteristics of coal with water content under true triaxial stresses. Thus, in this paper, true triaxial tests were carried out on dry and water-saturated coal samples to examine the water content effect on the energy evolution characteristics. The effects of intermediate stresses and anisotropic weak planes of coal on the true triaxial energy evolution were also systematically evaluated. Implications for energy evolution used for the prediction of in situ behavior of coal during deep underground mining were further illustrated.

2. Experimental Setup and Procedures

2.1. Sample Materials

The tested coal samples were all collected from the No. 2461 working face in the Baijiao underground coal mine in Southeast China. The collected coal blocks were cut, ground, and processed into 10 × 10 × 10 cm3 standard cubes. After the preparation of intact cubes, the samples were scanned by the CT scanner to exclude the samples with macro-fractures induced during the sampling process. Half of the prepared coal samples were dried at 40 °C in the drying vessel for at least 24 h. The measured dry density of the coal sample is 1.55 g/cm3. The rest of the prepared coal samples were immersed in water for 7 days. The measured water-saturated density of the coal sample is 1.58 g/cm3. The basic mechanical parameters of the tested dry anthracite coal are measured where the uniaxial compressive strength is 20.03 MPa, and Young’s modulus is 3.42 GPa parallel to the bedding plane. The uniaxial compressive strength is 25.28 MPa, and Young’s modulus is 2.95 GPa perpendicular to the bedding plane [30]. The basic proximate parameters of the tested coal were measured as follows: fixed carbon Fc = 87.08%; ash content Ad = 7.48%; volatile matter Vdaf = 4.64%; vitrinite reflectance R0 = 2.85%; moisture content Mad = 0.80% [31]. The tested coal sample was classified as anthracite by ISO 11760 according to measured fixed carbon and vitrinite reflectance [32].

2.2. Apparatus and Procedures

The true triaxial experiment was carried out using the multi-functional true triaxial apparatus (TTG) (Figure 1). The TTG apparatus can apply a maximum of 400 MPa stress in X and Z directions and a maximum of 600 MPa stress in the Y direction. The deformation of the tested sample was measured by the fixed linear variable differential transformers (LVDTs) along the six loading pistons. The tested coal samples were all subjected to the same stress path. The hydrostatical stress condition was applied at a loading rate of 0.5 MPa/s to reach the stress level of 10 MPa. Then, the intermediate was increased at a loading rate of 0.5 MPa to reach the stress level of 15, 20, and 30 MPa, respectively. Finally, the maximum stress was increased at a loading rate of 0.002 mm/s with constant intermediate and minimum stress to obtain the peak and residual strengths of the tested coal samples. After each true triaxial compression test, the coal samples were orientated in three different directions (perpendicular to the bedding plane, face cleat, and butt cleat, respectively), and repeated stress loading paths were applied to the coal samples. In loading direction 1, the maximum principal stress was perpendicular to the bedding plane. In contrast, the maximum principal stress was perpendicular to the butt cleat and face cleat, respectively, in loading directions 2 and 3. The stress loading path and variations in loading directions are schematically shown in Figure 2. The applied stress loading path in this test is also suggested by the International Society for Rock Mechanics (ISRM) [33]. The workflow diagram of this experiment is shown in Figure 3.

2.3. Energy Evolution Calculation

During the true triaxial stress loading process, the coal samples underwent four energy stages: energy input, accumulation, dissipation, and transformation. The energy evolution characteristics are schematically shown in Figure 4. When assuming no heat exchange between the loading system and the outer environment, the total energy of the coal sample is equal to the applied energy by the stress loading process. According to the conservative energy laws, the input energy is the sum of elastic energy and dissipated energy as the following correlations [34,35]:
U = U d + U e
where U refers to the input energy from the loading stress, Ud refers to the dissipated energy from deformation to failure of coal samples, Ue refers to the elastic energy inside the coal sample.
And the elastic energy can be calculated as follows:
U e = 1 2 ( σ 1 ε 1 + σ 2 ε 2 + σ 3 ε 3 )
where σ1, σ2, σ3 refer to the maximum stress, the intermediate stress, and the minimum stress, respectively, and ε1, ε1, ε1 refer to the strains corresponding to σ1, σ2, σ3, respectively.
U d = ∫ 0 ε 1 σ 1 d ε 1 + ∫ 0 ε 2 σ 2 d ε 2 + ∫ 0 ε 3 σ 3 d ε 3
The elastic strain has the following equations according to generalized Hooke’s law as follows:
ε ei = 1 E u ( σ i − υ u ( σ j + σ k ) )
where E and ν refer to the elastic modulus and Poisson’s ratio, respectively.
The elastic energy of coal could be calculated as follows:
U e = 1 2 E ( σ 1 2 + σ 2 2 + σ 3 2 − 2 ν ( σ 1 σ 2 + σ 2 σ 3 + σ 1 σ 3 ) )
Then, the dissipated energy of coal could be obtained as follows:
U d = ∫ 0 ε 1 σ 1 d ε 1 + ∫ 0 ε 2 σ 2 d ε 2 + ∫ 0 ε 3 σ 3 d ε 3 − 1 2 E ( σ 1 2 + σ 2 2 + σ 3 2 − 2 ν ( σ 1 σ 2 + σ 2 σ 3 + σ 1 σ 3 ) )

3. Results and Analysis

3.1. Energy Evolution Characteristics of Dry and Water-Saturated Coal under Different True Triaxial Stresses

Figure 5 and Figure 6 present the strain and energy evolution curves of dry and water-saturated coal under different intermediate stresses and loading directions from deformation to ultimate failure. The energy evolution characteristics are similar for dry and water-saturated coal. The outer mechanical energy is uninterruptedly applied to the tested coal samples as the total energy rises. During the stress-loading process, the elastic energy of dry and water-saturated coal accumulates, and the dissipated energy gradually increases. In the pre-loading stage, the elastic energy is the primary energy form as the narrows and closes of pre-existing fractures in this stage. The dissipated energy growth rate increases with the stress loading as the differential stress loading is applied to the coal samples. When the dry and water-saturated coal reaches the peak strength and enters the post-peak stage, the dissipated energy gradually becomes the pre-dominated energy, and the elastic energy experiences a steady decrease. When approaching the residual strength, the elastic and dissipated energy has a stable ascending or descending rate.
For water-saturated coal samples, the overall energy is weakened due to the water adsorption, as indicated by the lower values in the total, elastic, and dissipated energy evolution curves than dry coal samples. The water-weakening effect on the overall energy of water-saturated coal is more pronounced when perpendicular to the bedding plane direction than in the other two cleat directions. In the post-peak regions, most water-saturated coal samples have a higher growth rate than the dry coal samples for the dissipated energy curve, leading to faster energy releases. The pre-existing natural weak planes significantly affect the mechanical properties of coal, as demonstrated by relevant experimental studies [28,37]. Generally, when loaded perpendicular to bedding planes, the peak strength of coal is higher than the results tested parallel to cleat directions [38,39]. As shown in Figure 6, at the same intermediate stresses, the elastic and total energy of dry and water-saturated coal samples are higher in pre-peak stages when tested perpendicular to the bedding planes. For example, the elastic energy at peak strength of dry coal samples under 15 MPa intermediate stress is 0.516 MJ/m3 in the bedding plane direction, while the values are lower to 0.383 MJ/m3 and 0.334 MJ/m3 in the face and butt cleat direction, respectively. The total energy of dry coal samples at peak strength under 15 MPa intermediate stress is 0.811 MJ/m3 in the bedding plane direction, while the values are lower to 0.748 MJ/m3 and 0.492 MJ/m3 in the face and butt cleat direction, respectively.

3.2. Accumulation and Residual Elastic Energy Analysis of Dry and Water-Saturated Coal under Different True Triaxial Stresses

The accumulation elastic energy of coal, Uea, is defined as the elastic energy at peak strength, reflecting the energy storage capability before failure. The residual elastic energy of coal, Uer, is measured at peak strength and reflects the energy release capability after failure. Detailed data of calculated accumulated and residual elastic energy of dry and water-saturated coal samples under different intermediate stresses and loading directions are listed in Table 1. Figure 7 and Figure 8 show the 3D scatter diagram of accumulation and residual elastic energy for dry and water-saturated coal samples under different conditions determined by the surface fitting. As presented in Figure 7 and Figure 8, both accumulation and residual elastic energy of dry and water-saturated coal samples show an increasing-then-decreasing trend with intermediate stress increase. This trend is because, with the increase of intermediate stress, the peak and residual strength increases first and then decreases, showing the associated increasing-then-decreasing trend. It also means that the coal failure needs more energy input at a relatively higher intermediate stress, but once it approaches a critical value, less input energy is needed. When the underground mining is near the geological structures (e.g., fault, anticline, and syncline), the coal seams have higher tectonic stress. Thus, the coal failure energy needed could vary with the tectonic stress, and the associated hazards reducing methods should be adjusted according to the measured in situ stress conditions.
The loading direction also dramatically affects coal’s accumulation and residual elastic energy. At the same intermediate stress, the dry and water-saturated coal samples have higher values for accumulation and residual elastic energy in loading direction 1 (perpendicular to bedding plane) than for loading direction 2 (parallel to face cleat plane) and loading direction 3 (parallel to butt cleat plane). To further evaluate the difference between the bedding plane direction and cleat direction, an energy anisotropy index is introduced and defined as follows:
A e v = 2 U e be U e fa + U e bu × 100 %
where A e v is the elastic energy anisotropic index, U e be is the elastic energy in the bedding plane direction, U e fa is the elastic energy in the face cleat direction, U e bu is the elastic energy in the butt cleat direction.
The calculated accumulation and residual elastic energy anisotropy indices are shown in Figure 9. For all the accumulation elastic energy anisotropy index of dry and water-saturated coal, samples are higher than 100.00%, and the values are from 135.91% to 153.07% for dry coal samples, from 141.05% to 163.74% for water-saturated coal samples. Most of the residual elastic energy anisotropy indexes of dry and water-saturated coal samples are higher than 100.00%, except for the result tested under 30 MPa intermediate stress for dry coal samples. The calculated values of residual elastic energy anisotropy index are from 77.87% to 136.71% for dry coal samples and from 139.56% to 169.67% for water-saturated coal samples.

3.3. Dissipated Energy Variation Rate Analysis of Dry and Water-Saturated Coal under Different True Triaxial Stresses

The dissipated energy variation rate, Udr, represents the conversion efficiency and is closely related to the deformation and failure of coal. Coal’s dissipated energy variation rate can be calculated as the increment of dissipated energy in the pre-peak and post-peak stages divided by the corresponding stress loading time. Detailed data of calculated dissipated energy variation rate of dry and water-saturated coal samples under different intermediate stresses and loading directions are listed in Table 2. Figure 10 and Figure 11 show the 3D scatter diagram of pre-peak and post-peak dissipated energy variation rates for dry and water-saturated coal samples under different conditions determined by the surface fitting. Both pre-peak dissipated energy variation rates of dry coal samples show an increasing-then-decreasing trend with intermediate stress increase. The values of the post-peak dissipated energy variation rate are significantly higher than those in the pre-peak loading stage, meaning that catastrophic damage mainly develops in the post-peak loading stage. For water-saturated coal samples, all the values of pre-peak and post-peak dissipated energy variations rate under different intermediate stresses and loading directions are lower than the dry coal samples. The difference indicates that the absorbed water content in coal samples could significantly reduce the abrupt damage in both the pre-peak and post-peak loading stages. The interaction of water molecules and clay minerals in the coal matrix could contribute to this less damage of water-saturated coal sampled during loading, induced by the softening and reduction in the friction after water absorption [28,40,41].

3.4. Ratio of Elastic Energy to Total Energy Variation Analysis of Dry and Water-Saturated Coal under Different True Triaxial Stresses

During the true triaxial loading experiments, the energy of dry and water-saturated coal samples varies significantly, leading to different energy distribution characteristics. The elastic energy ratio is defined as the ratio of elastic energy to total energy during progressive deformation, which could characterize the elastic energy distribution characteristics of dry and water-saturated coal samples under different test conditions. Figure 12 presents the elastic energy ratio evolution of dry and water-saturated coal samples under different intermediate stresses and loading directions. As shown in Figure 12, different trends of elastic energy ratio evolution are observed with the increase of loading strain. The elastic energy ratio evolution of dry coal samples mainly behaves as an increasing-then-decreasing trend. In contrast, the elastic energy ratio evolution shows a decreasing trend for most water-saturated coal samples. It indicates that dissipated energy gradually domains the process from deformation to failure for water-saturated coal samples compared to dry coal samples. Similar results have also been found in dry and water-saturated sandstone with less percentage of elastic energy—no significant changes in elastic energy ratio evolution variations under different intermediate stresses and loading directions [42]. The elastic energy ratio evolution curves present a more rapid decrease with increased strain when entering the post-peak stage for the dry and water-saturated coal samples. In the post-peak stage, more dissipated energy develops for dry and water-saturated coal samples, and this feature is independent of the water content.

4. Discussion

The above research demonstrates that water saturation and loading direction greatly influence the energy evolution of coal samples. The energy evolution characteristics of coal are different for dry and water-saturated conditions. For example, for water-saturated coal, the overall energy is weakened with the lower values in the total, elastic, and dissipated energy evolution curves than in dry coal samples. This water-weakening effect has also been found in other water-saturated sedimentary rocks [43,44]. Moreover, all the values of the pre-peak and post-peak dissipated energy variations rate of water-saturated coal samples are lower than dry coal samples. This is because water adsorption decreases sliding friction and specific surface energy [45]. In addition, the reaction between water content and the mineral components (i.e., kaolinite) in the coal matrix could also lower coal energy compared with dry coal samples [40]. Some researchers found the anisotropic energy characteristics for shale and bedded sandstone samples mainly behaved in transverse isotropy [46,47,48]. Different from shale and sandstone, coal has three natural, mutually perpendicular weak planes, which could be regarded as orthogonal anisotropy in energy characteristics. In this study, the energy characteristics of dry and water-saturated coal samples at different loading directions differ. For example, dry and water-saturated coal samples have higher values for accumulation and residual elastic energy in loading direction 1 (perpendicular to the bedding plane) than for loading direction 2 (parallel to face cleat plane) and loading direction 3 (parallel to butt cleat plane). Experimental results on the confining pressure have shown it has a certain effect on the energy evolution of coal [49,50]. Meanwhile, intermediate stress will also significantly affect the dry and water-saturated coal energy evolution, as found in the experimental results. The accumulation and residual elastic energy of dry and water-saturated coal samples show an increasing-then-decreasing trend with intermediate stress increase.
As more and more underground coal mines enter deep coal mining in the future, higher risks of dynamic disasters could be posed during coal production [51,52,53,54,55]. Water-injection methods, i.e., hydraulic flushing and cutting and hydraulic fracturing, could be further adapted to decrease the overall energy of coal seams and reduce potential dynamic disasters of deep coal mining. The experimental analysis of this study also shows that the effects of anisotropic cleats and bedding planes in coal and the intermediate stress have a nonnegligible effect on the energy evolution of coal, which should be considered during deep coal mining. For example, when deep underground mining is conducted near the geological structures, the coal failure energy needed could vary with the tectonic stress. The associated water-injection hazards reducing methods should be adjusted according to the measured in situ stress conditions. In addition, the dip angle of the excavated coal seams could also significantly affect the working face’s stability due to the anisotropic energy characteristics for the dry and water-saturated coal observed in the tests. The support and control methods should be redesigned according to the cleats and bedding plane direction for safety mining.

5. Conclusions

This paper studied the anisotropic energy evolution characteristics of dry and water-saturated coal samples subjected to true triaxial stresses. The effects of intermediate stresses and anisotropic weak planes of coal on the true triaxial energy evolution were also systematically evaluated. The following conclusions could be obtained:
(1)
For water-saturated coal samples, the overall energy is weakened due to the water adsorption, as indicated by the lower values in the total, elastic, and dissipated energy evolution curves than dry coal samples. In addition, all the values of pre-peak and post-peak dissipated energy variations rates of water-saturated coal samples under different intermediate stresses and loading directions are lower than the dry coal samples. The elastic energy ratio evolution of dry coal samples mainly behaves as an increasing-then-decreasing trend. In contrast, the elastic energy ratio evolution shows a decreasing trend for most water-saturated coal samples.
(2)
The water-weakening effect on the overall energy of water-saturated coal is more pronounced when perpendicular to the bedding plane direction than in the other two cleat directions. At the same intermediate stresses, the elastic and total energy of dry and water-saturated coal samples were higher in pre-peak stages when tested perpendicular to the bedding planes. Moreover, at the same intermediate stress, the dry and water-saturated coal samples have higher values for accumulation and residual elastic energy when tested perpendicular to the bedding plane than parallel to the face cleat plane and butt cleat plane.
(3)
Both accumulation and residual elastic energy of dry and water-saturated coal samples show an increasing-then-decreasing trend with intermediate stress increase. In addition, both pre-peak dissipated energy variation rates of dry coal samples show an increasing-then-decreasing trend with intermediate stress increase.

Author Contributions

Conceptualization, Y.L. and E.W.; methodology, Y.L.; validation, Y.L., D.Z. and L.Z.; formal analysis, D.Z.; investigation, Y.L.; resources, Y.L.; data curation, D.Z. and L.Z.; writing—original draft preparation, Y.L.; writing—review and editing, E.W.; supervision, E.W.; project administration, E.W.; funding acquisition, Y.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research is funded by the National Natural Science Foundation of China (52104231), the Postdoctoral Science Foundation of China (2020M681775), and the Fundamental Research Funds for the Central Universities (2021QN1088).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data used to support the finding of this study are available from the corresponding author upon request.

Acknowledgments

The authors would like to thank the support of the laboratory and university.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Schematic diagram and photograph of the true triaxial test apparatus [34].
Figure 1. Schematic diagram and photograph of the true triaxial test apparatus [34].
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Figure 2. Schematic diagram of the stress loading path and variations in loading directions: (a) stress loading path; (b) variations in loading directions [28].
Figure 2. Schematic diagram of the stress loading path and variations in loading directions: (a) stress loading path; (b) variations in loading directions [28].
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Figure 3. Workflow diagram of the true triaxial experiment.
Figure 3. Workflow diagram of the true triaxial experiment.
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Figure 4. Energy evolution characteristics of tested coal samples (modified from [36]).
Figure 4. Energy evolution characteristics of tested coal samples (modified from [36]).
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Figure 5. Stress-strain curves and energy evolution curves of dry coal samples under different intermediate stresses and loading directions: (a) Loading direction 1; (b) Loading direction 2; (c) Loading direction 3.
Figure 5. Stress-strain curves and energy evolution curves of dry coal samples under different intermediate stresses and loading directions: (a) Loading direction 1; (b) Loading direction 2; (c) Loading direction 3.
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Figure 6. Energy evolution curves of water-saturated coal samples under different intermediate stresses and loading directions: (a) loading direction 1; (b) loading direction 2; (c) loading direction 3.
Figure 6. Energy evolution curves of water-saturated coal samples under different intermediate stresses and loading directions: (a) loading direction 1; (b) loading direction 2; (c) loading direction 3.
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Figure 7. Nonlinear fitting surfaces of accumulation elastic energy data of dry and water-saturated coal samples under different intermediate stresses and loading directions: (a) dry coal samples; (b) water-saturated coal samples.
Figure 7. Nonlinear fitting surfaces of accumulation elastic energy data of dry and water-saturated coal samples under different intermediate stresses and loading directions: (a) dry coal samples; (b) water-saturated coal samples.
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Figure 8. Nonlinear fitting surfaces of residual elastic energy data of dry and water-saturated coal samples under different intermediate stresses and loading directions: (a) dry coal samples; (b) water-saturated coal samples.
Figure 8. Nonlinear fitting surfaces of residual elastic energy data of dry and water-saturated coal samples under different intermediate stresses and loading directions: (a) dry coal samples; (b) water-saturated coal samples.
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Figure 9. Accumulation and residual elastic energy anisotropy index of dry and water-saturated coal samples under different intermediate stresses: (a) accumulation elastic energy; (b) residual elastic energy.
Figure 9. Accumulation and residual elastic energy anisotropy index of dry and water-saturated coal samples under different intermediate stresses: (a) accumulation elastic energy; (b) residual elastic energy.
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Figure 10. Nonlinear fitting surfaces of pre-peak dissipated energy variation rate data of dry and water-saturated coal samples under different intermediate stresses and loading directions: (a) dry coal samples; (b) water-saturated coal samples.
Figure 10. Nonlinear fitting surfaces of pre-peak dissipated energy variation rate data of dry and water-saturated coal samples under different intermediate stresses and loading directions: (a) dry coal samples; (b) water-saturated coal samples.
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Figure 11. Nonlinear fitting surfaces of post-peak dissipated energy variation rate data of dry and water-saturated coal samples under different intermediate stresses and loading directions: (a) dry coal samples; (b) water-saturated coal samples.
Figure 11. Nonlinear fitting surfaces of post-peak dissipated energy variation rate data of dry and water-saturated coal samples under different intermediate stresses and loading directions: (a) dry coal samples; (b) water-saturated coal samples.
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Figure 12. Elastic energy ratio variation data of dry and water-saturated coal samples under different intermediate stresses and loading directions: (a) loading direction 1; (b) loading direction 2; (c) loading direction 3.
Figure 12. Elastic energy ratio variation data of dry and water-saturated coal samples under different intermediate stresses and loading directions: (a) loading direction 1; (b) loading direction 2; (c) loading direction 3.
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Table
Table 1. Summary of accumulation and residual elastic energy of dry and water-saturated coal samples under different intermediate stresses and loading directions.
Table 1. Summary of accumulation and residual elastic energy of dry and water-saturated coal samples under different intermediate stresses and loading directions.
Sample IDAccumulation Elastic Energy (MJ/m3)Residual Elastic Energy (MJ/m3)Sample IDAccumulation Elastic Energy (MJ/m3)Residual Elastic Energy (MJ/m3)
Coal-15-1D0.5160.162Coal-15-1W0.2890.163
Coal-20-1D0.6850.284Coal-20-1W0.4420.224
Coal-30-1D0.5610.241Coal-30-1W0.2680.207
Coal-15-2D0.3830.117Coal-15-2W0.1750.122
Coal-20-2D0.5180.359Coal-20-2W0.2400.172
Coal-30-2D0.4060.365Coal-30-2W0.1540.074
Coal-15-3D0.3340.120Coal-15-3W0.1780.089
Coal-20-3D0.4900.180Coal-20-3W0.3750.149
Coal-30-3D0.3270.254Coal-30-3W0.2260.170
Sample ID refers to initially fractured coal samples tested under different conditions, i.e., Coal-15-1 denotes the initially fractured coal sample subjected to 15 MPa intermediate stress in the stress loading direction 1.
Table
Table 2. Summary of dissipated energy variation rate of dry and water-saturated coal samples under different intermediate stresses and loading directions.
Table 2. Summary of dissipated energy variation rate of dry and water-saturated coal samples under different intermediate stresses and loading directions.
Sample IDPre-Peak Dissipated Energy Variation Rate (KJ/m3·s)Post-Peak Dissipated Energy Variation Rate (KJ/m3·s)Sample IDPre-Peak Dissipated Energy Variation Rate (KJ/m3·s)Post-Peak Dissipated Energy Variation Rate (KJ/m3·s)
Coal-15-1D0.5153.377Coal-15-1W0.2221.173
Coal-20-1D0.5674.622Coal-20-1W0.3863.329
Coal-30-1D0.4635.777Coal-30-1W0.7464.779
Coal-15-2D0.2732.505Coal-15-2W0.3241.670
Coal-20-2D0.5364.118Coal-20-2W0.5571.741
Coal-30-2D0.3812.727Coal-30-2W0.5231.520
Coal-15-3D0.3302.237Coal-15-3W0.4561.733
Coal-20-3D0.6063.148Coal-20-3W0.5002.289
Coal-30-3D0.5712.357Coal-30-3W0.4331.860
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Liu, Y.; Wang, E.; Zhao, D.; Zhang, L. Energy Evolution Characteristics of Water-Saturated and Dry Anisotropic Coal under True Triaxial Stresses. Sustainability 2023, 15, 1431. https://doi.org/10.3390/su15021431

AMA Style

Liu Y, Wang E, Zhao D, Zhang L. Energy Evolution Characteristics of Water-Saturated and Dry Anisotropic Coal under True Triaxial Stresses. Sustainability. 2023; 15(2):1431. https://doi.org/10.3390/su15021431

Chicago/Turabian Style

Liu, Yubing, Enyuan Wang, Dong Zhao, and Li Zhang. 2023. "Energy Evolution Characteristics of Water-Saturated and Dry Anisotropic Coal under True Triaxial Stresses" Sustainability 15, no. 2: 1431. https://doi.org/10.3390/su15021431

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