Comparison of Energy Evolution Characteristics of Intact and Fractured Coal under True Triaxial Progressive Stress Loading

Abstract

The underground coal mining process is closely associated with frequent energy storage and consumption of coal mass with natural and induced fractures. Exploring the energy evolution characteristics of intact and fractured coal samples could be helpful for dynamic disaster control. In this study, laboratory true triaxial tests on the energy evolution characteristics of intact and fractured coal samples have been carried out and systematically discussed. The results show that the brittleness and peak strength are weakened due to the presence of macro-fractures in coal. The mean peak strength and brittleness for fractured coal are 29.00% and 74.59% lower than the intact coal samples. For both intact and fractured coal, the energy evolution curves are closely related to the deformation stages under true triaxial stresses. When subjected to the same intermediate stress, intact coal stores more elastic strain energy compared to fractured coal. Additionally, the rate of dissipative energy variation is two–three times lower in fractured coal samples compared to intact coal samples.

1. Introduction

As coal resources are gradually exhausted in shallow areas in China, deep underground coal mining operations will become more common. The number of 1000 m level depth underground coal mines in China has reached more than 50, with the deepest depth of 1510 m [1]. Severe dynamic disasters, e.g., gas outbursts, coal bursts, and coal–gas compound dynamic disasters, could occur more frequently when underground coal mines enter deep mining [2,3,4,5]. The safety of a deep coal mining method is closely linked to the geo-stress conditions, coal fracture forms, and gas-containing features in situ [6,7,8,9]. Investigating the energy evolution characteristics of coal under a deep underground mining environment with gas and fractures helps reveal the mechanism of dynamic disasters.

Coal seams are naturally fractured formations with cleats that are oriented perpendicular to the bedding planes [10,11,12]. In regions near fault and mining-induced areas, macro-fractures with large apertures are distributed in coal seams [13]. Both natural and induced fractures are important to deep underground mining because they can cause coal mass instability under applied high geo-stresses or excavation-induced stresses [14,15,16]. Identifying the influences of fractures-induced weakening on energy evolution with stress is critical in supporting deep mining design and operations. To date, extensive laboratory measurements on energy evolution intact coal, with natural fractures under uniaxial and triaxial stress conditions, have been explored [17,18,19,20,21,22]. During the unloading process, the fracture growth is related to the conversion of energy input into dissipation energy, leading to coal failure. Increasing the depth will advance this conversion, leading to faster coal failure. Under cyclic loading and unloading, coal failure is related to the mechanism of energy storage and consumption, and is affected by the energy storage and consumption limit. There is a cyclic hysteresis of mechanical behavior and an enhancement in coal strength under cycle loading higher than that of uniaxial compression. In actual coal mining, gas is adsorbed in the coal seams. Gas adsorption in coal will have a wedged-opening effect on fractures and cause a significant decrease in the strength of coal [23,24,25,26,27]. Experimental measurements of the energy evolution of intact coal under triaxial stresses have been reported [28,29,30]. The energy density shows a nonlinear growth trend with stress. The total input energy density, elastic energy density, and dissipated energy density increase with the increase in stress.

The in situ geo-stresses measured in deep underground coal mines indicate that the coal seams are generally in unequal 3D stress environments [6]. Confining pressure applied to the intact coal samples under triaxial stresses can only increase with 2D equal stresses while uniaxial tests can apply 1D stress without confinement [31]. The inconsistency of the laboratory and in situ, with regard to the stress replication in the two above tests, has certain limits. Some researchers have carried out true triaxial tests on the energy evolution of intact coal under replicated unequal 3D stresses [32,33]. With the increase in intermediate principal stress, sandstone and coal change from brittle to semi-brittle. The inclusion of gas-absorbed intact coal under true triaxial stresses has also been reported [34,35,36]. The pre-existing fractures have a great impact on the failure modes, strength levels, and permeability levels. Through true triaxial tests, the great impact of intermediate stress on the mechanical characteristics of intact coal has been identified [37]. The failure plane angle of coal and the ratio of residual strength to peak strength increases linearly with the intermediate principal stress. During deep underground coal mining, complex geological structures, e.g., faults, synclines, and anticlines, are randomly distributed [38,39,40]. The high tectonic stress near geological structures can significantly affect the fracturing behavior of coal. Therefore, the energy evolution and fracturing mechanism of intact coal under highly unequal 3D geo-stress and gas-pressure conditions need further discussion.

Compared with intact coal, fractured coal with macro-fractures exhibits strong nonlinearity in energy and fracturing behavior. Experimental efforts have also been made in fractured coal with regular geometry under stresses. By manually creating macro-fractures with flat surfaces, the fracturing characteristics have been conducted under uniaxial and triaxial stresses [41,42,43,44,45]. With the increase in pre-existing fractures number, the size of the failure shape increased linearly, the total energy and elastic energy decreased, and the dissipation energy increased. However, for the drilled borehole images in deep underground coal mines, the rough surfaces of induced macro-fractures are more common [46,47]. The grain-interface stiffness mismatch in induced macro-fractures will have a great effect on the energy and fracturing behavior. Measurements of the damage and fracturing behavior of the fractured coal with fracturing-induced macro-fractures, under uniaxial and triaxial stresses, have been carried out [48,49,50]. Laboratory observations of coal subjected to true triaxial stresses have so far been limited to intact samples, and relevant experimental studies on fractured coal samples are still limited. Necessary comparisons of the energy evolution characteristics between intact and fractured coal need to be assessed clearly.

In this experiment, we conducted an experiment to compare the energy evolution characteristics of intact and fractured coal samples under varying true-triaxial progressive stress loads. We analyzed the energy evolution characteristics at different intermediate stresses and calculated elastic energy, dissipated energy, and total energy to reveal the fracture mechanism. The implications for research results of predicting the in situ behavior of coal in both intact and fractured regions were further discussed.

2. Experimental Setup and Methodology

2.1. Sample Materials and Preparation

The intact and fractured coal samples are both initially cut out from the same coal blocks, collected from the Baijiao coal mine in Sichuan province, China. Each intact coal sample is cut into a cubic shape with a size of 100 mm × 100 mm × 100 mm. To manually create macro-fractures, the fractured coal cubic sample undergoes progressive true triaxial loading first until it reaches residual strength by using the intact coal cubic sample. The stress is loaded at displacement control mode at 0.002 mm/s. The σ₃ remains at 10 MPa, and the preset magnitudes of σ₂ are varied at 15, 20, and 30 MPa, respectively. The macro-fractures have double-shear shapes with a mean length of 110 mm, width of 1.2 mm, and an average angle of 53° from the horizontal direction. The intact and fractured coal samples are dried out for at least 24 h at 40 °C in a drying vessel to remove the moisture content.

2.2. Experimental Setup and Procedure

The true triaxial experiments are carried out on the multi-functional true triaxial geophysical (TTG) apparatus, as shown in Figure 1 [7]. The TTG apparatus is an automatic control system with a confining pressure range of 0 to 40 MPa, 3D loading stress range of 0 to 600 MPa in two directions and 0 to 400 MPa in one direction, and strain measurements of linear variable differential transform (LVDT) with a maximum range of 40 mm. Gas flow properties can also be measured through the flow rate measurements at the gas outlet with a maximum flow rate of 5 L/min.

The true triaxial tests experimental procedure for the intact and fractured coal samples is as follows: (a) the intact and fractured coal samples are prepared and installed with a heat-shrink tube on the center of the loading plate. (b) A hydrostatic stress of 10 MPa is applied to the coal samples. (c) The intact and fractured coal samples undergo carbon dioxide gas adsorption for 48 h under stressed conditions. (d) A 3D unequal stress state of σ₁ = 20 MPa, σ₂ = 15 MPa, and σ₃ = 10 MPa is applied to the intact and fractured coal samples. (e) The σ₁ is loaded at displacement control mode at 0.002 mm/s until the residual strength is reached. During the progressive loading, the σ₃ remains at 10 MPa, and the preset magnitudes of σ₂ are varied at 15, 20, and 30 MPa, respectively.

3. Results

3.1. Results of True Triaxial Loading Test

The test results for the intact and fractured coal samples under true triaxial progressive stress loading conditions are listed in

Table 1. Test results of intact and fractured coal samples subjected to true triaxial progressive stresses.

Test Number	Peak Strength (MPa)	Residual Strength (MPa)	Elastic Modulus (GPa)	Post-Peak Modulus (GPa)
Coal-I-15#	63.40	37.51	3.33	−1.65
Coal-I-20#	72.56	46.40	3.24	−2.47
Coal-I-30#	63.90	44.52	2.87	−4.63
Coal-F-15#	46.52	45.64	2.99	−0.17
Coal-F-20#	52.42	38.22	3.56	−0.65
Coal-F-30#	42.96	38.27	3.05	−0.65

Test numbers refer to the intact and fractured coal samples tested under different intermediate stresses, i.e., Coal-I-15# represents intact coal samples subjected to 15 MPa intermediate stress, and Coal-F-15# represents fractured coal samples subjected to 15 MPa intermediate stress.

. The average peak strength of intact coal is 66.62 MPa. The average peak strength of fractured coal is 47.3 MPa. It can be seen that the true triaxial peak strength of the fractured coal samples is 29.00% with an average value of 19.32 MPa lower than the intact sample. The fractured coal samples have a certain resistance to the outer load but are lower than the intact one due to the weak planes formed from macro-fractures. Furthermore, the fractured coal could undergo secondary failure with the load. The post-peak modulus of fractured coal samples is significantly lower than intact samples. Figure 2 shows the comparisons of the stress–strain curve of intact and fractured coal samples under different intermediate stresses. Both the intact and fractured coal samples show an increasing-then-decreasing trend with the intermediate stress. The main difference in the shape of the stress–strain curve for intact and fractured coal samples falls into the post-peak stage. The decreasing rate of stress with strain is not apparent for fractured coal samples.

For further quantitatively evaluating the mechanical property, the brittleness of coal can be calculated as the B₁ and B₂ indices as follows:

$$B_1=\frac{d{W}_{\mathrm{r}}}{d{W}_{\mathrm{e}}}=1-\frac{E}{M}$$

(1)

$$B_2=\frac{d{W}_{\mathrm{a}}}{d{W}_{\mathrm{e}}}=\frac{E}{M}$$

(2)

where B₁ and B₂ represent the brittleness indices of coal. W_r, W_e, and W_a separately represent the post-peak rupture energy, withdrawn elastic energy, and additional (or released) energy, respectively. E represents the elastic modulus of coal. M represents the post-peak modulus.

The brittleness of the intact and fractured coal samples is summarized in Figure 3. The detailed data on the brittleness of the intact and fractured coal samples are shown in

Table 2. The detailed data of brittleness of intact and fractured coal samples.

Test Number	B1	B2
Coal-I-15#	2.02	−1.02
Coal-I-20#	2.31	−1.31
Coal-I-30#	1.62	−0.62
Coal-F-15#	18.59	−17.59
Coal-F-20#	6.48	−6.48
Coal-F-30#	5.69	−4.69

. It can be seen that the brittleness of intact coal is significantly higher than the fractured coal. The mean brittleness of the intact coal is 2.35, and the fractured coal is 9.25. The mean brittleness for the fractured coal is 74.59% lower than the intact coal samples. This indicates that the fractured coal behaves with greater ductile properties when subjected to differential true triaxial stresses. The coal samples with macro-fractures inside could undergo larger deformation when loaded entering into the post-peak stage than the coal with natural cleats.

3.2. Strain Energy Evolution Curves of True Triaxial Loading Test

The calculation of the strain energy evolution for coal and rock with loading can be obtained based on the strain energy formula [51,52]. Figure 4 presents the typical curve of the stress and energy with increasing strain for intact and fractured coal samples under an intermediate stress of 30 MPa. The corresponding curve of strain energy for intact and fractured coal samples can be divided into several stages according to the deformation stages. In the quasi-elastic deformation stage and micro-fracture occurrence stage, the elastic strain energy (U_e) is the main source of the total strain energy (U), while the dissipative strain energy (U_d) is relatively low. This indicates that the energy of stress loading mainly transits to elastic strain energy in coal samples for both intact and fractured coal. Entering into the development of the micro-fractures stage, the total and elastic strain energy curves gradually bifurcate. Meanwhile, the dissipative energy strain curve experiences a sharp increase with strain, transiting the energy to the development of micro-fractures. During the strain softening and post-failure stage, the peak value is reached for the elastic strain energy curve, while the dissipative strain energy curve shows a sharp increase. This indicates that the macro-fractures develop, propagate, and experience the slip of a broken plane, where the dissipative strain energy dominates. In the post-peak regions, there is an obvious difference in the elastic strain energy for intact and fractured coal samples. No significant decrease is observed in the curves of elastic strain energy for fractured coal samples, which means that fractured coal mainly behaves showing ductile behavior.

$$U=U_{\mathrm{e}}+U_{\mathrm{d}}$$

(3)

$$U={\displaystyle {\int }_0^{{\epsilon }_1}{\sigma }_1\mathrm{d}{\epsilon }_1+{\displaystyle {\int }_0^{{\epsilon }_2}{\sigma }_2\mathrm{d}{\epsilon }_2}+}{\displaystyle {\int }_0^{{\epsilon }_3}{\sigma }_3\mathrm{d}{\epsilon }_3}$$

(4)

$$U_e=\frac{1}{2}{\sigma }_1{\epsilon }_1^e+\frac{1}{2}{\sigma }_2{\epsilon }_2^e+\frac{1}{2}{\sigma }_3{\epsilon }_3^e$$

(5)

where ε_i (i = 1, 2, 3) represents the total strain in each direction and ${\epsilon }_i^e$ represents the related elastic strain.

Figure 5 shows the variations of total strain energy with strain for the intact and fractured coal samples under different intermediate stresses. It can be seen that the total strain energy increases with the strain for both intact and fractured coal samples. The total strain energy for fractured coal is slightly lower than the value obtained for intact coal. The relationship between the total strain energy at failure and the intermediate stress for intact and fractured coal samples is shown in Figure 6. It can be seen that the total strain energy increases with intermediate stress for fractured coal, while the total strain energy shows an increasing-then-decreasing trend with intermediate stress for intact coal. Under the same intermediate stress, except for 30 MPa, the value of the total strain is higher for intact coal than for fractured coal as the sample absorbs more energy during stress loading.

The variation curves of elastic strain energy with strain for intact and fractured coal samples are shown in Figure 7. It can be seen that the relationships between elastic strain energy and strain for both intact and fractured coal show different obvious deformation stages, and it is similar to the stress–strain curves. In the development of the micro-fractures stage, the elastic strain energy curves increase slowly with strain. A linear increase in the elastic strain energy curve is observed in the elastic stage. As the coal samples lose the bearing ability, the growth rate gradually decreases. A more obvious platform is observed for the fractured coal than the intact coal. After entering into the strain-softening and post-peak stage, the elastic strain energy decreases sharply with strain for the intact coal samples. For the fractured coal samples, the elastic strain energy shows a gentle decrease with strain, which exhibits a plastic deformation after failure. Figure 8 shows the variations of elastic strain energy of intact and fractured coal samples with intermediate stress at failure. Both the intact and fractured coal samples show an increasing-then-decreasing trend with the increase in intermediate stresses. Under the same intermediate stress, the magnitude of elastic strain energy for intact coal is higher than that for fractured coal.

In Figure 9, the relationship curves of the dissipative strain energy with strain are presented, which shows some obvious stages during evolution for intact and fractured coal. At the micro-fracture development and elastic deformation stages, the dissipative strain energy is in relatively low magnitudes, indicating that the absorbed energy in coal samples is converted into elastic strain energy. When approaching failure, the micro-fractures connect and new macro-fractures are formed in the coal samples, the dissipative strain energy increases sharply with the strain. It can be seen that the dissipative curves for intact and fractured coal show a rapid increase after reaching the critical failure point. The intensive slips are formed in asperities on the newly formed broken plane, which contributes to the sharp increases. Most of the absorbed energy is converted into dissipative energy in intact and fractured coal at this stage. The dissipative strain energy of the intact and fractured coal samples at failure is plotted against the intermediate stresses in Figure 10. The dissipative energy of intact coal shows an increasing-then-decreasing trend with intermediate stress at failure, while an increasing trend is observed in fractured coal. However, for weak fractured coal, the dissipative strain energy occupies most of the total energy under high intermediate stress, resulting in large deformation like weak rock [12].

4. Discussion

4.1. Dissipative Energy Variation Rate Analysis of Intact and Fractured Coal under Different True Triaxial Stress Paths

The coal accumulative damage and failure during stress loading are mainly induced by the energy release and dissipation. The dissipative energy provides the intrinsic power for the connections and developments of the micro- and macro- fractures. The energy released during stress loading contributes to the failure of intact and fractured coal. The dissipative energy variation rate could be quantitively calculated as follows:

$$U_{\mathrm{dr}}=\frac{U_{d1}-U_{d2}}{t_{d1}-t_{d2}}$$

(6)

where U_dr is the dissipative energy variation rate, U_d1 and U_d2 are the dissipative energy during stress loading, and t_d1 and t_d2 are the corresponding loading time. Figure 11 presents the pre-peak and post-peak dissipative energy variation rate data of intact and fractured coal samples under different true triaxial paths. For the intact coal, the pre-peak dissipative energy variation rate shows an increasing-then-decreasing trend with intermediate stress. In the post-peak region, the values of the dissipative energy variation rate for both the intact and fractured coal are significantly higher than the values obtained in the pre-peak regions. This indicates that the macro- fractures develop and asperities slide mainly in the post-peak regions. In comparison with the intact coal samples, the values of dissipative energy variation rate for the fractured coal samples are 2–3 times lower, which means that fracture coal undergoes less abrupt damage in the post-peak regions and shows plastic behavior [53,54].

4.2. Characterization of Energy Ratios of Intact and Fractured Coal under Different True Triaxial Stress Paths

From the deformation to failure stages, intact and fractured coal samples undergo complex energy transmission and dissipation. To further evaluate the energy evolution process during stress loading, two energy ratios are defined as follows:

$$K_{\mathrm{et}}=\frac{U_{\mathrm{e}}}{U}$$

(7)

$$K_{\mathrm{dt}}=\frac{U_{\mathrm{d}}}{U}$$

(8)

where K_dt and K_et separately characterize the energy storage and dissipation capacities of coal.

Figure 12 and Figure 13 present the elastic and dissipative strain energy ratio variation of intact and fractured coal samples under different true triaxial stress paths. For most of the intact and fractured coal samples, the elastic strain energy ratio shows an increasing-then-decreasing trend with strain under different intermediate stresses. This means that the energy storage capability variation with stress loading has no difference for the intact and fractured coal samples. For the peak and valley values of elastic energy ratio in the post-peak region, the fractured coal samples have higher values than the intact coal samples. In contrast, for the dissipative strain energy ratios, the intact and fractured coal samples show a decreasing-then-increasing trend with strain under different intermediate stresses. For the peak and valley values of dissipative energy ratio in the post-peak region, the intact coal samples have higher values than the fractured coal samples. The intermediate stress has little influence on the variations of elastic and dissipative strain energy ratios for both intact and fractured coal samples. This explains the phenomenon that the larger energy is dissipated for macro- fractures sliding and developments for the fractured coal.

4.3. Application Guidance for Underground Coal Mining

Underground coal mining, especially for the kilometer-depth underground coal mines, is generally executed in areas under coupled high in situ and tectonic stresses and with high gassy conditions. Dynamic disasters, e.g., coal and gas outbursts and coal bursts, could be triggered by the instability of coal mass containing different fracture formations [2,55]. The laboratory tests could provide a certain reference for engineering applications since the dynamic disaster could not be easily replicated. Laboratory tests on the energy evolution characteristics of both intact and fractured coal samples at different true triaxial stresses were systematically studied in this work. Concerning the comparison of the instability of coal mass containing natural and induced fractures, the experimental results show that the presence of macro-fractures has a great influence on the coal samples. The fractured coal with macro-fractures inside behaves in larger deformation, especially in the post-peak stage, than the intact coal. The elastic energy storage capability for fractured coal is significantly lower than the intact coal, and less abrupt failure occurs once the fractured coal loses its bearing ability. Monitoring methods, e.g., ultrasonic indicators and borehole camera systems could help identify and detect fractured areas in deep underground coal mines. Relevant support and control measures should be adjusted according to different intact and fractured areas instead of remaining the same. Furthermore, our experimental results show that the energy characteristics of intact and fractured coal samples are influenced by intermediate stress. Both the intact and fractured coal samples’ elastic strain energy at failure show an increasing-then-decreasing trend with the increase in intermediate stresses. Intermediate stress enhances the brittleness of both intact and fractured coal samples. Therefore, special attention should also be paid to the tectonic stresses in the field. The overcoring method and hydraulic fracturing method are the two most commonly used measurements of in situ stresses, which can directly obtain the tectonic stresses.

5. Conclusions

In the present work, true triaxial progressive compression experiments were carried out on intact and fractured coal samples to obtain the energy evolution characteristics. The influences of fractures and intermediate stresses on the total strain energy, elastic strain energy, and dissipative strain energy characteristics of intact and fractured coal samples were systematically analyzed and discussed. The implications for field applications were further illustrated. The main conclusions of this paper are summarized as follows:

(1)

The presence of macro-fractures acts as a weakening agent. The mean peak strength and brittleness for fractured coal are 29.00% and 74.59% lower than the intact coal samples. The fractured coal behaves with greater ductile properties when subjected to differential true triaxial stresses. The energy evolution curves are closely related to the deformation stages under true triaxial stresses for both intact and fractured coal.

(2)

When approaching the failure point of intact coal samples, the total, elastic, and dissipative strain energies show an increasing-then-decreasing trend with intermediate stress. For fractured coal samples, the total energy and dissipative strain energies at failure increase with intermediate stress, and the elastic strain energy shows an increasing-then-decreasing trend. Under the same intermediate stress, the magnitude of elastic strain energy for intact coal is higher than that for fractured coal.

(3)

The values of the dissipative energy variation rate for the fractured coal samples are two–three times lower than for the intact coal samples. The elastic strain energy ratio shows an increasing-then-decreasing trend with strain under different intermediate stresses for most of the intact and fractured coal samples. For the peak and valley values of dissipative energy ratio in the post-peak region, the intact coal samples have higher values than the fractured coal samples.