3.1. Analysis of Pre-Peak Loading and Unloading Results
The damage and softening degree of water on coal samples mainly depends on the mineral composition, particle composition, initial water content, stress state and other factors of coal samples [
32]. It can be seen from
Figure 3 that the difference of the initial water content makes the coal samples show different deformation properties during the whole deformation and failure process. The strength of the coal sample is larger in dry state, the deformation is larger in the whole failure process, the pre-peak deformation value is almost linear elastic, and the duration is longer. The water affects the self-properties of the coal sample, moisture enters into the pore and crack, wets the particles on the free surface, weakens the relationship between the particles, weakens the cohesion and internal friction coefficient of the coal sample, and causes the strength of the coal sample to decrease obviously. With the increase of water content, the deviatoric stress gradually decreases, from 0% to 0.15% of water content, the ultimate strength from 57.12 to 53.96 MPa, which decreases by 5.84%. Compared with the strength of the dry coal sample, when the water content of coal sample is 0.32%, the ultimate strength is 51.88 MPa, which decreases by 9.68%. When the moisture content of coal sample is 0.65%, the ultimate strength is 49.62 MPa, which decreases by 13.86%. It can be seen that the initial moisture content has a significant impact on the mechanical damage of the coal sample until the final fracture failure. Combined with the test results, the Mohr stress circle of each coal sample under different water content conditions is shown in
Figure 4. It can be seen that with the increase of water content, the center of the Mohr stress circle moves to the left, and the ultimate strength and peak strain decrease gradually.
In the pre-peak loading process, the specimen exhibits compression deformation in the axial direction and expansion deformation in the radial direction. According to the test results in
Figure 4, the deformation parameters under different stress states are listed in
Table 1. When the axial stress is loaded to 18.6 MPa, the axial, radial and volumetric strain of the specimens are different under different water content conditions. When the axial stress continues to be loaded to 25.85 MPa, the absolute values of the axial, radial and volumetric strain of the samples increase gradually under different water content conditions, but due to the anisotropy of the raw coal sample, the deformation difference is large. When the sample reaches its ultimate strength, the axial, radial and volumetric strain of coal samples decrease obviously with the increase of water content. Compared with the dry coal sample, the axial strain of the coal samples with water contents of 0.15%, 0.32% and 0.65% decreased by 4.98%, 11.59% and 17.99% respectively, the radial strain decreased by 40.4%, 14.46% and 17.43% respectively, and the volumetric strain decreased by 52.54%, 8.66% and 18.65%, respectively. It can be seen that with the increase of water content, the deformation amount of coal samples in all directions tends to decrease under the same stress.
According to the test results in
Table 1, the curves of peak intensity and peak axial strain of coal samples with water content under different water content conditions were drawn, and the relationships between peak strength, peak axial strain and water content were established. It can be seen that the relationship between peak intensity, peak axial strain and water content of coal samples obey quadratic polynomial, as shown in Equation (2), and the fitting curve is shown in
Figure 5.
where,
a1,
a2,
a3 are the fitted constants;
w is the water content;
is the peak axial strain at failure; and
σ′ is the deviatoric stress at failure (MPa).
3.2. Analysis of the Deformation Properties during Post-Peak Loading and Unloading
As there are fewer cracks in the sample, the permeability of the sample is 0 during the pre-peak loading and unloading process, and the permeability of the sample increases rapidly after the sample is destroyed. The permeability formula reflects the relationship between gas permeability and gas pressure, gas flow rate, sample length and cross-sectional area of the sample. It does not directly reflect the relationship between stress and permeability, but simply studies the relationship between axial stress, confining pressure or pore pressure (provided by gas pressure) and permeability can only explain the one-way action relationship. The permeability is the result of joint action of axial stress, confining pressure and gas pressure, which needs comprehensive consideration. Therefore, the study of the relationship between effective stress and permeability has more practical significance than the study of the relationship between a certain force and permeability alone, and it has a certain positive significance for studying coal and gas outburst.
According to the theory of geotechnical mechanics, the effective stress is the difference between the total stress acting on the coal seam and the fluid pressure existing in the pore or fissure, that is to say:
In the formula, σe is the average effective stress of coal sample, MPa; σ1 and σ3 are the axial stress and confining pressure of coal samples, respectively, MPa; p1 and p2 are the gas pressure at the inlet and outlet of raw coal samples, respectively, MPa.
The deformation parameters of each specimen under different stress states during the post-peak loading and unloading confining pressure are shown in
Table 2.
Table 2 shows that in the process of loading and unloading confining pressure post-peak, the axial direction of the sample is applied by the displacement control, which causes the axial strain to increase linearly during the process of loading and unloading confining pressure, that is, the axial direction of the sample is compressed deformation. During the process of loading and unloading confining pressure, the radial deformation of specimens is shrinkage with confining pressure loading, and expansion with confining pressure unloading. According to the test results in
Table 2, the relationship curves of axial strain-effective stress and radial strain-effective stress under different stress states were plotted as shown in
Figure 6.
As can be seen from
Figure 6, for the dry coal sample, the radial strain of the sample decreases from 2.37 × 10
−2 to 1.86 × 10
−2 after the first loading confining pressure, which decreases by 21.54%. After the first unloading confining pressure, the radial strain increases to 2.99 × 10
−2, which increases by 25.89%; the radial strain of the sample decreases to 2.60 × 10
−2 after the second loading confining pressure, which decreases by 12.83%. After the second unloading confining pressure, the radial strain increases to 3.43 × 10
−2, which increases by 15%; the radial strain of the sample decreases to 3.28 × 10
−2 after the third loading confining pressure, which decreases by 4.45%. After the third unloading confining pressure, the radial strain increases to 3.72 × 10
−2, which increases by 8.3%; the radial strain of the sample decreases to 3.54 × 10
−2 after the fourth loading confining pressure, which decreases by 4.48%. After the fourth unloading confining pressure, the radial strain increases to 3.99 × 10
−2, which increases by 7.29%.
For the coal sample with a water content of 0.15%, the radial strain of the sample decreases from 3.06 × 10−2 to 2.76 × 10−2 after the first loading confining pressure, which decreases by 10.03%. After the first unloading confining pressure, the radial strain increases to 3.42 × 10−2, which increases by 11.72%; the radial strain of the sample decreases to 3.27 × 10−2 after the second loading confining pressure, which decreases by 4.44%. After the second unloading confining pressure, the radial strain increases to 3.77 × 10−2, which increases by 10.06%; the radial strain of the sample decreases to 3.61 × 10−2 after the third loading confining pressure, which decreases by 4.2%. After the third unloading confining pressure, the radial strain increases to 4.01 × 10−2, which increases by 6.53%; the radial strain of the sample decreases to 3.83 × 10−2 after the fourth loading confining pressure, which decreases by 4.46%. After the fourth unloading confining pressure, the radial strain increases to 4.22 × 10−2, which increases by 5.21%.
For the coal sample with a water content of 0.32%, the radial strain of the sample decreases from 2.01 × 10−2 to 1.62 × 10−2 after the first loading confining pressure, which decreases by 20.67%. After the first unloading confining pressure, the radial strain increases to 2.76 × 10−2, which increases by 35.25%; the radial strain of the sample decreases to 2.32 × 10−2 after the second loading confining pressure, which decreases by 15.53%. After the second unloading confining pressure, the radial strain increases to 2.93 × 10−2, which increases by 6.5%. The radial strain of the sample decreases to 2.87 × 10−2 after the third loading confining pressure, which decreases by 2.18%. After the third unloading confining pressure, the radial strain increases to 3.26 × 10−2, which increases by 11.04%; the radial strain of the sample decreases to 3.26 × 10−2 after the fourth loading confining pressure, which decreases by 4.82%. After the fourth unloading confining pressure, the radial strain increases to 3.52 × 10−2, which increases by 8.01%.
For the coal sample with a water content of 0.65%, the radial strain of the sample decreases from 0.95 × 10−2 to 0.63 × 10−2 after the first loading confining pressure, which decreases by 33.93%. After the first unloading confining pressure, the radial strain increases to 1.20 × 10−2, which increases by 26.43%; the radial strain of the sample decreases to 0.83 × 10−2 after the second loading confining pressure, which decreases by 30.35%. After the second unloading confining pressure, the radial strain increases to 1.46 × 10−2, which increases by 21.74%. The radial strain of the sample decreases to 1.07 × 10−2 after the third loading confining pressure, which decreases by 26.24%. After the third unloading confining pressure, the radial strain increases to 1.70 × 10−2, which increases by 17.03%; The radial strain of the sample decreases to 1.32 × 10−2 after the fourth loading confining pressure, which decreases by 22.65%. After the fourth unloading confining pressure, the radial strain increases to 2.09 × 10−2, which increases by 22.83%.
In summary, with the increase cyclic loading and unloading confining pressure times, the radial strain decrement and increment of raw coal sample after loading and unloading confining pressure gradually decrease.
3.3. Analysis of the Permeability Properties during Post-Peak Loading and Unloading
Based on the test results, the relationship curves deviatoric stress-axial strain-permeability of coal samples with different water content under loading and unloading confining pressure are shown in
Figure 7.
According to the deviatoric stress-axial strain-permeability curve of the sample in
Figure 7, the permeability of each sample under different stress states is shown in
Table 2. The permeability-effective stress curves of specimens under different stress states were plotted, as shown in
Figure 8.
It can be seen that the permeability change of each sample during the post-peak loading and unloading process is as follows: for the dry coal sample, the permeability decreases by 63.54% after the first loading confining pressure, and the permeability increases by 6.43% after unloading confining pressure. After the second loading of confining pressure, the permeability decreases by 56.43%, and the permeability increases by 20.24% after the unloading confining pressure. After the third loading confining pressure, the permeability decreases by 58.99%, and the permeability increases by 24.75% after the unloading confining pressure. After the fourth loading confining pressure, the permeability decreases by 60.16%, and the permeability increases by 11.68% after the unloading confining pressure; for the coal sample with a water content of 0.15%, the permeability decreases by 21.55% after the first loading confining pressure, and the permeability recovered to 87.56% of the initial permeability after unloading confining pressure. After the second loading confining pressure, the permeability decreases by 56.43%, and the permeability increases by 35.61% after the unloading confining pressure. After the third loading confining pressure, the permeability decreases by 15.99%, and the permeability increases by 36.84% after unloading confining pressure. After the fourth loading confining pressure, the permeability decreases by 23.33%, and the permeability increases by 34.72% after unloading confining pressure; for the coal sample with a water content of 0.32%, the permeability decreases by 45.1% after the first loading confining pressure, and the permeability recovered to 90.2% of the initial permeability after unloading confining pressure. After the second loading confining pressure, the permeability decreases by 23.91%, and the permeability increases by 23.91% after the unloading confining pressure. After the third loading confining pressure, the permeability decreases by 31.58%, and the permeability increases by 58.97% after unloading confining pressure. After the fourth loading confining pressure, the permeability decreases by 30.65%, and the permeability increases by 74.42% after unloading confining pressure; for the coal sample with a water content of 0.65%, the permeability decreases by 77.28% after the first loading confining pressure, and the permeability increases by 15.11% after unloading confining pressure. After the second loading of confining pressure, the permeability decreases by 76.06%, and the permeability increases by 15.4% after the unloading confining pressure. After the third loading confining pressure, the permeability decreases by 66.41%, and the permeability increases by 13.73% after the unloading confining pressure. After the fourth loading confining pressure, the permeability decreases by 62.63%, and the permeability increases by 10.11% after the unloading confining pressure.
The above analysis shows that during the post-peak loading and unloading confining pressure, the permeability of the sample gradually decreases with the loading confining pressure and increases with the unloading confining pressure, the permeability of the coal sample increases in wave shape with the increase of axial strain, that is, the permeability increases after each loading and unloading confining pressure compared with that after the previous loading and unloading confining pressure. The possible reason is that the specimen has been destroyed in the process of post-peak loading and unloading confining pressure, and macro-penetrating cracks are generated inside the specimen, and the axial stress is always applied by displacement control. At this time, loading confining pressure can make the macro-cracks produced by sample failure close slowly, resulting in a non-linear decrease in permeability; while unloading confining pressure can make the closed macro-cracks open slowly, but at the same time, under the combined action of axial stress, the cracks in the sample further expand, cracks increase and new cracks are generated, and the gas through the sample capacity increases, resulting in the permeability of the sample after each loading and unloading confining pressure being greater than that of the previous loading and unloading confining pressure.
In conclusion, the permeability of coal sample is closely related to confining pressure during loading and unloading. Due to the limitation of the length of the space, this paper only draws the deviatoric stress-confining pressure-permeability curves of water content 0.65% sample during loading and unloading confining pressure post-peak as shown in
Figure 9.
It can be seen from
Figure 9 that with the loading of the confining pressure, the deviatoric stress increases linearly, and the permeability decreases nonlinearly. When the confining pressure is loaded to about 98% of the predetermined value, the deviatoric stress increases rapidly, and the permeability decreases rapidly. Perhaps it is because under the confining pressure of the raw coal sample, the internal crack and part of the raw coal sample are closed by pressure, which makes the gas flow passage narrow, resulting in a non-linear decrease of gas permeability. When the confining pressure of the specimen is close to the predetermined value of 9 MPa, the confining pressure loading rate automatically decreases under the influence of the test system, and the axial pressure is always in the displacement control uniform loading process, resulting in a rapid increase of the axial stress of the sample, the corresponding deviatoric stress of the specimen increases rapidly, and the permeability of the specimen decreases rapidly. With the unloading of confining pressure, the deviatoric stress of the specimen continues to increase. The deviatoric stress of the specimen reaches the maximum when the confining pressure is unloaded to 5.705 MPa during the first loading and unloading process. The deviatoric stress of the specimen reaches the maximum when the confining pressure is unloaded to 5.975 MPa during the second loading and unloading process. The deviatoric stress of the specimen reaches the maximum when the confining pressure is unloaded to 5.8 MPa during the third loading and unloading process. The deviatoric stress of the specimen reaches the maximum when the confining pressure is unloaded to 5.78 MPa during the fourth loading and unloading process, that is, when the confining pressure is unloaded to an average of about 5.815 MPa (64.61% of the initial confining pressure unloading value), the deviatoric stress of the sample reaches the maximum, and in this process, the permeability of the sample increases slowly, but the rate of increase is small. With the continuous unloading confining pressure, the deviatoric stress of the specimen changes from gradually increasing to decreasing gradually. During this process, the permeability of the sample continues to increase, and the increasing rate is increasing. The possible reason is as follows: at the initial stage of unloading confining pressure, the axial stress of the specimen continues to increase under the control of displacement, that is, the deviatoric stress of the specimen increases gradually. However, the unloading confining pressure cannot effectively open the closed cracks during this process, which leads to a slow increase of the permeability of the sample. When the confining pressure is unloaded to a certain value, the axial stress of the specimen begins to decrease with the unloading confining pressure, that is, there is a turning point in the change of deviatoric stress during the post-peak unloading confining pressure. During the process of unloading confining pressure, the closed cracks and pores of the sample gradually open and expand, and generate new cracks, which results in a non-linear increase of the permeability of the sample and an increasing rate of increase. The difficulty of gas flow in the coal body depends on the development degree of the seepage channel such as cracks and pores in the raw coal sample. The more developed seepage channel is, the more beneficial the gas flow in the coal body will be.
Based on the test results in
Figure 9, the relationship between permeability and effective stress during each loading and unloading process is shown in
Figure 10, and the relationship is established. It can be seen that the permeability and effective stress of the sample are subject to the ExpDec1 function distribution, as shown in Equation (4).
where,
b1,
b2,
b3 are fitting constants.
It can be seen from
Figure 10 that the gas permeability decreases exponentially with the increase of the effective stress, and increases exponentially with the decrease of the effective stress.