3.1 Stress-strain curve
The stress-strain curve of the unfissured specimens (intact specimens) and those with pre-existing fissure are shown in Fig. 3. The stress-strain behavior of samples can be approximately divided into four typical stages, i.e. compaction, elastic deformation, crack growth and propagation, and strain-softening.
Figure 3a shows the stress-strain curve features of the unfissured specimens. The specimen compressive strength is 32.8MPa. The stress-strain curve shows brittle characteristics when it reaches peak stress.At the stage of compaction, the curve shows the downward concave shape and the nonlinear deformation at the beginning of loading, which is related to the closure of some primary pores. At the stage of elastic deformation, the curve exhibits the characteristics of linear increases. At the stage of crack growth and propagation, the curve deviates from elastic behavior and exhibits clearly nonlinear deformation. At the stage of strain-softening, the stress-strain curves drop rapidly which is associated with the penetration of the macroscopic cracks.
Figure 3b shows the stress-strain curve features of the specimens with a fissure angle of 0°. The compressive strength is 9.55MPa (29.1% of the unfissured specimens). The stage of compaction and elastic are similar to that of the unfissured specimens. At the stage of crack growth and propagation and strain-softening, however, the stress fluctuates many times and the curves look like an irregular zigzag.
Figure 3c shows the stress-strain curve features of the specimens with a fissure angle of 15°. The specimen compressive strength is 6.47MPa (19.7% of the unfissured specimens). The strain of peak stress is about 0.75%, which is lower than that of the others. Compared with the unfissured specimens, the yield phenomenon of the specimens with a fissure angle of 15° is more obvious and the post-peak stress shows a step-like drop.
Figure 3d shows the stress-strain curve features of the specimens with a fissure angle of 30°. The specimen compressive strength is 12.6MPa (38.4% of the unfissured specimens). The stress-strain curve is similar to that of 15°. The yield phenomenon is obvious before the peak stress and the stress decreases in a step-like way after the peak value.
Figure 3e shows the stress-strain curve features of the specimens with a fissure angle of 45°. The specimen compressive strength is 8.14MPa (24.8% of the unfissured specimens). This angle shows different characteristics in the stage of strain-softening. Different from other angles, the coal samples with a fissure angle of 45° show the characteristics of multi-stage stress drop, and the proportion of post-peak curve increases significantly.
Figure 3f shows the stress-strain curve features of the coal specimens with a fissure angle of 60°. The specimen compressive strength is 16.4MPa (50% of the unfissured specimens). Except for the high stress at each stage, the stress-strain curve of the specimen is similar to that of 15° and 30°. The yield phenomenon appears before the peak value, and the post-peak stress decreases in a step-like manner.
Based on the above analysis, the stress-strain curve of the unfissured specimens and those with pre-existing fissure can be divided into four-stage: compaction, elastic deformation, crack growth and propagation, and strain-softening. Due to the existence of pre-existing fissures, the stage duration of elastic deformation is greatly reduced and the crack growth and propagation stage enters in advance. The stage of crack growth and propagation and strain softening show different characteristics as the change of the fissure angle. According to the difference of stress-strain curve, the specimens are divided into four types (A, B, C, D).
Type A: the stage of crack growth and propagation is approximately linear, and the post-peak behavior in stress-strain curves shows a rapid drop. The compressive strength of this type is high and a large amount of elastic energy is accumulated in the loading process, which indicates that this type of coal specimen has a strong dynamic failure tendency. The unfissured specimens belong to this type.
Type B: At the stage of crack growth and propagation, the curve presents obvious yield characteristics even accompanied by a small stress drop. At the stage of strain-softening, the curve decreases step by step. The specimens with fissure angles of 15°, 30°, and 60° belong to this type.
Type C: At the stage of crack growth and propagation and strain-softening, the stress-strain curves present an irregular zigzag pattern. The compressive strength of this type is low and less elastic energy is accumulated, which indicates that the dynamic failure trend of this type is very weak. The specimens with a fissure angle of 0° belong to this type.
Type D: The post-peak behavior in the stress-strain curves shows the characteristics of multi-stage stress drop and the duration of the post-peak part is relatively long. the specimens with a fissure angle of 45° belong to this type.
3.2 Strength and deformation characteristics
The uniaxial compressive stress (UCS), elastic modulus(E), and the strain of the peak stress (Peak strain) can effectively indicate the strength and deformation characteristics of the specimen. Therefore, we statistically analyzed these three parameters. Table 1 shows the basic mechanical parameters of specimens with different fissure angles. The relation among UCS, E, and Peak strain and fissure angle is shown in Fig. 4
Table 1
Mechanical parameters of specimens containing a single fissure under uniaxial compression
Specimen
|
UCS/MPa
|
Average value/MPa
|
Standard deviation
|
E/GPa
|
Average value/GPa
|
Standard deviation
|
Peak strain/%
|
Average value/%
|
Standard deviation
|
a-1
|
31.62
|
32.8
|
1.1800
|
1.76
|
1.74
|
0.0200
|
2.30
|
2.39
|
0.0882
|
a-2
|
33.98
|
1.72
|
2.47
|
0°-1
|
10.16
|
9.55
|
0.4570
|
0.7
|
0.83
|
0.0990
|
2.46
|
1.77
|
0.5000
|
0°-2
|
9.43
|
0.85
|
1.56
|
0°-3
|
9.06
|
0.94
|
1.30
|
15°-1
|
6.38
|
6.47
|
0.0900
|
1.07
|
1.06
|
0.0050
|
0.79
|
0.79
|
0.0042
|
15°-2
|
6.56
|
1.06
|
0.78
|
30°-1
|
12.14
|
12.60
|
0.4374
|
1.10
|
1.25
|
0.1040
|
1.68
|
1.53
|
0.1209
|
30°-2
|
13.19
|
1.31
|
1.52
|
30°-3
|
12.48
|
1.33
|
1.38
|
45°-1
|
9.03
|
8.14
|
0.6405
|
1.20
|
1.19
|
0.0094
|
0.98
|
0.87
|
0.0780
|
45°-2
|
7.56
|
1.18
|
0.84
|
45°-3
|
7.82
|
1.20
|
0.79
|
60°-1
|
18.61
|
16.4
|
1.6112
|
1.53
|
1.46
|
0.0741
|
1.82
|
1.65
|
0.1199
|
60°-2
|
15.79
|
1.5
|
1.55
|
60°-3
|
14.81
|
1.36
|
1.58
|
As shown in Fig. 4a, the UCS of different fissure angles do not show an obvious pattern, which may be closely related to the primary fractures in the coal. The unfissured specimens have a UCS of 32.8MPa, but specimens with a single fissure get a UCS of 6.47 MPa (α = 15°) to 16.4MPa (α = 60°), with a reduction between 50% and 80%. According to Fig. 4b, the existence of fissure also significantly weakens the elastic modulus, and the E of specimens with different fissure angles does not show an obvious pattern. The minimum value of the elastic modulus is 0.83GPa with the fissure angle of 0°. This is due to the fact that the normal to the fissure direction is parallel to the loading direction, and the deformation were much larger than the others during the loading process. The Peak strain of specimens with a single fissure are lower than that of unfissured specimens, as shown in Fig. 4c. The reason is that the presence of fissure destroys the integrity of the specimens, resulting in failure under low strain.
Base on the above analyses, UCS, E, and Peak strain of specimens containing pre-existing fissure are all lower than that of the unfissured samples. The variation of uniaxial compressive stress, elastic modulus under different fissure angles is not obvious, which is closely related to the primary fractures the coal.
3.3 Crack evolution process
To study the crack evolution process of coal specimens containing a pre-existing fissure, the video monitoring was adopted during the test. Based on the combined results on stress and video monitoring, the real-time crack evolution process of specimens was analyzed in detail.
Figure 5a shows the stress-strain curve of the specimens with a fissure angle of 0° and the corresponding crack propagation sketch. At the stages of compaction and elastic deformation, the pre-existing fissures did not produce a visually observable closure. When the stress reaches to point a(σ = 5.17MPa), the specimen initiates the crack from the center of the fissure, but the crack is small and inconspicuous. With the increase of stress, the crack widens a lot and the pre-existing fissure begins to close. At point c(σ = 7.34MPa), a new tensile crack forms quickly at the left tip of the fissure resulting a minor stress drop. Afterwards, the fissure has been closed. When the specimen is loaded to 7.49MPa (point d), two cracks begin to generate from the tip of the fissure and propagate along the axial stress. Finally, more cracks appear as the increase of deformation, resulting in the reduction of loading capacity.
Figure 5b shows the stress-strain curve of the specimens with a fissure angle of 15° and the corresponding crack propagation sketch. The stress reduction of the specimen mainly occurs in the post-peak stage, and the reduction usually corresponds to the macro crack propagation. When the stress reaches to point a(σ = 4.54MPa), the specimen initiates and propagate along the normal direction of the fissure. When the stress reaches 6.25MPa (point c), a crack generates near the under tip of the fissure. At point e(σ = 5.63MPa), the initial crack redevelops and propagates along the loading direction, corresponding to the significant decrease of stress. At this point, the pre-existing fissure has closed. Then, the stress gradually diminishes as the crack propagation on the left side of the specimen.
Figure 5c shows the stress-strain curve of the specimens with a fissure angle of 30° and the corresponding crack propagation sketch. It can be observed that stress drop in the stress-strain curve indicates a macro crack propagation. When the specimen is loaded to point a(σ = 9.61MPa), the specimen begins to initiate the wing crack 1,2 from the fissure, which can be seen with the naked eyes. When the stress is loaded to 12.22MPa (point e), the crack 3 emerges from the upper tip of the fissure and grows towards the loading direction, which presents an “H” type. At the point f, the pre-existing fissure has completely closed. When the specimen is loaded to point g(σ = 7.83MPa), cracks develop to the boundary, and the sample is expanded which leads to the loss of the bearing capacity.
Figure 5d shows the stress-strain curve of the specimens with a fissure angle of 45° and the corresponding crack propagation sketch. The pre-peak curve of the sample is smooth, and the post-peak stress presents a multistage decreasing trend. At point b(σ = 7.82MPa), the crack emanates from the lower tip of the fissure. When the stress reaches 6.71MPa (point d), a new crack develops quickly which leads to the expansion of the specimen. Then, the crack propagates downwards to the bottom when the stress reaches 5.96MPa (point f). Meanwhile, particles ejected from the right of the specimen, accompanied by an ejection sound. At this time, the fissure is almost close. With increasing axial deformation, the stress of the specimen steadily diminishes.
Figure 5e shows the stress-strain curve of the coal specimens with a fissure angle of 60° and the corresponding crack propagation sketch. As can be seen in the figure, macro cracks develop around the fissure from point a (σ = 13.95MPa) to point c(σ = 16.04MPa), during which many stress fluctuations occur. At point d (16.15MPa), coal ejection and fissure closure are observed. Afterward, when the coal is loaded to 18.61MPa (point g), coal ejection occurs once more, resulting in a rapid loss of supporting.
In brief, it can be concluded that the fissure angle has an effect on the initiation location of the initial crack. For the fissure angle of 0°, the initial crack is generated in the center of the pre-existing fissure. With the increase of fissure angle, the location transfers to the tip of the fissure. According to the state of the pre-existing fissure, the failure process of the sample can be divided into two stages: the stage of fissure closure, and the stage of failure. In the stage of fissure closure, the cracks are generated around the fissure, mainly leading to the closure of the fissure. And the cracks generally propagate towards the loading direction. In the failure stage, the failure mode of the specimens is dominated by the comprehensive action of the primary fracture, pre-existing fissure, and the cracks initiated in the previous stage. And the coal specimens lose most of the bearing capacity due to structural failure.
3.4 Failure mode
To investigate the influence of the fissure angle on the failure mode of specimens, the failure pattern of coal specimens with fissure angles of 0°,15°,30°,45°,60° and without fissure were selected for analysis, as shown in Fig. 6.
Figure 6a shows the failure pattern of the coal sample with a fissure angle of 0°. It can be seen that the failure of this type is mainly caused by tensile cracks generated at the tips of the fissure, which is a typical tensile failure mode. Figure 6b gives the failure pattern with a fissure angle of 15°. The failure of the type is mainly the result of the upward development of the tensile wing cracks, and the failure mode is tensile. Figure 6c-e present the failure pattern with fissure angles of 30°, 45°, and 60°, respectively. There are obvious tensile and shear cracks in all of them, which indicates that the failure mode is a tensile-shear composite. At the same time, dynamic ejection also occurs during loading. The unfissured coal specimens is typically subject to splitting failure (Fig. 6f), indicating a tensile failure mechanism.
According to the above research, tensile failure occurs in the unfissured specimens and the specimens with a lower fissure angle. With the increase of the fissure angle, the failure mechanism alters to the composite failure of tensile and shear. Meanwhile, the dynamic ejection of particles gradually appears in the process of compression. For the fissure angles of 0° and 15°, there is no obvious ejection. For the fissure angles of 45° and 30°, large particle ejection occurs. For the fissure angle of 60°, there is an obvious dynamic ejection in the middle of the specimen.