4.1. Characterization of Strength Properties with Lateral Pressure in Through-Type Hole-Cracked Rock-like Specimens
Biaxial compression tests of through-type hole-crack specimens are carried out, keeping the steady lateral pressure
σ2 at 0 MPa, 2 MPa, 4 MPa, and 6 MPa. As shown in
Figure 12, when there is no lateral pressure (
σ2 = 0 MPa), the peak strength of the specimen is 21.22 MPa. When the lateral pressure
σ2 = 2 MPa, the peak strength is 48.55 MPa: an increase of 273%, which significantly increased the peak strength of the specimen. Also, the peak strain is significantly reduced compared to no lateral pressure, due to the limitation of lateral stress. With the increase in lateral pressure, the peak strength of the specimens shows varying degrees of increase. At the lateral pressure
σ2 = 4 MPa, the peak strength of the specimen is 51.21 MPa, which is an increase of about 5.5% compared to the peak strength at
σ2 = 2 MPa. At the lateral pressure
σ2 = 6 MPa, the peak strength of the specimen is 61.44 MPa, which is a 16.7% increase compared to the peak strength at
σ2 = 4 MPa. According to the trend of peak stress and crack initiation stress shown in
Figure 13, both peak stress and crack initiation stress increase with the increase in lateral pressure. In particular, when the lateral pressure is increased from nothing to something, the increase in peak strength increases significantly. As the lateral pressure continues to increase, the increase in peak strength decreases. The mechanical properties of the specimens under different lateral pressures are shown in
Table 2.
Deformation is one of the important factors in determining the stability of rock masses. Therefore, a study of the specimen peak strain is carried out. The variation in peak strain with lateral stress in the test for through-type hole-cracked rocks is shown in
Figure 14. The strain value at peak strength is in the range of 3.5 × 10
−3–5 × 10
−3; it does not show an increase with the increase in lateral pressure, and the larger value of the peak strain appears at the lateral pressure
σ2 = 4 MPa. The lateral displacement of the specimens under different lateral pressures is also different, and the variation in lateral displacement with load is shown in
Figure 15. The lateral displacements change gently in the pre-loading period. The lateral displacement shows a sharp upward trend in the middle and late stages of loading, which is due to the beginning of severe plastic damage of the specimen and weakening of the bearing capacity, resulting in a significant increase in lateral displacement. As shown in
Figure 16, the peak lateral strain decreases with increasing lateral pressure. When the lateral pressure
σ2 = 2 MPa and
σ2 = 4 MPa, the reduction in lateral strain is smaller. At the lateral pressure
σ2 = 6 MPa, the lateral strain decreases significantly, reflecting that its lateral confinement effect becomes more prominent as the lateral pressure increases.
4.2. Strength Characteristics of Hole-Crack Specimens with Hole Depth Changes
In order to analyze the variation in the mechanical properties of the hole-crack rock with hole depth, specimens with hole depths of 0 mm, 20 mm, 40 mm, 60 mm, 80 mm, and 100 mm, and with penetration cracks, are made. The steady lateral pressure of
σ2 = 4 MPa is chosen for the test, and the axial stress–strain curve obtained is shown in
Figure 17. Under the action of lateral pressure, the peak strength of the specimen shows a decrease with the increase in hole depth, but the magnitude of change is relatively gentle, and the peak stress is maintained between 50 MPa–70 MPa.
The variation curve of peak stress and cracking stress is shown in
Figure 18. When the hole depth in the hole-crack specimen is from 40 mm to 60 mm, the peak stress decreases more significantly, by about 10%. In this process, the hole depth exceeds 50% of the specimen length. The main deformation area of the sample is the hole and crack area, which changes the stress distribution structure. Excessive deformation on the porous side leads to inconsistent deformation before and after the test, leading to unstable failure of the sample. This is also confirmed by the consistent trend of the crack initiation stress with the peak stress in the graph. Except for the rest of the hole depth variation stages, the peak stress decreases by about 3% for every 20 mm increase in hole depth.
Figure 19 shows the trend of the axial peak strain of the specimens. At 4 MPa lateral pressure, the axial peak strain does not increase linearly with increasing hole depth, and the maximum peak strain occurs at a hole depth of 60 mm. The variation in the lateral strain curve with axial stress is shown in
Figure 20. Due to the restraining effect of lateral pressure, the curve changes gently in the early stage with a small slope, and then the curve suddenly becomes steeper and the slope increases rapidly when it approaches the peak stress. The variation curve of lateral peak strain with hole depth is shown in
Figure 21. Similarly to the axial peak strain, the maximum value of the lateral peak strain occurs at a hole depth of 60 mm. The mechanical properties of the specimens with different hole depths under 4 MPa lateral pressure are shown in
Table 3.
4.3. Crack Extension Evolutionary Characteristics of Hole-Crack Specimens under Biaxial Loading
The images of hole-crack specimens during loading damage are collected, and the extended damage mechanisms such as crack initiation, extension, and penetration of the specimens are obtained by analyzing these images.
Figure 22,
Figure 23 and
Figure 24 represent the damage processes of the penetration hole-cracked specimens at different lateral pressures
σ2 = 2 MPa, 4 MPa, and 6 MPa.
Figure 25,
Figure 26,
Figure 27,
Figure 28 and
Figure 29 represent the damage process of hole-crack specimens with different hole depths at a steady lateral pressure
σ2 = 4 MPa.
- (1)
H = 100 mm, σ2 = 2 MPa
The secondary crack initiation point of the specimen is at the tip of the prefabricated crack. It is shown that the stress concentration caused by cracks is more pronounced during the compression process due to the difference in geometric characteristics of cracks and holes. The initial crack initiation angle is larger compared to the control test without lateral pressure. As shown in
Figure 22a, crack No. 1 is a standard wing crack with an extension angle of 90° at about 37% of the peak stress. With the increase in load, the No. 2 wing crack appears at 50% of the peak strength, and the No. 2 wing crack extension angle is also 90°. Unlike the results of the uniaxial control test, the expansion direction of the wing crack does not shift to the main stress direction with the increase in the load, but continues to expand in the crack initiation direction until penetration, and the wing crack gradually widens with the increase in the axial load, as shown in
Figure 22b, 1+. As the crack becomes wider, the slope of the curve decreases significantly at 82.4% of the peak. Near the peak strength, the potential energy is converted into the surface potential energy required for crack expansion due to the continuous expansion and widening of existing cracks, releasing most of the potential energy so that no new cracks are generated until the specimen is completely destroyed at the peak load. The stress–strain curve of the specimen and the crack stress point location are shown in
Figure 22c.
- (2)
H = 100 mm, σ2 = 4 MPa
When the lateral stress
σ2 = 4 MPa, the peak strength of the specimen is elevated and the initial cracking stress of the crack is higher at the same time. The initial crack at the No. 1 wing crack in
Figure 23a appears at 24 MPa, which is about 48% of the peak strength, followed by a No. 2 wing crack at 50% of the peak strength at the upper end of the pre-crack of the specimen, with an extension angle of about 90°. The precast hole is a penetration hole, so a stress concentration point is formed at the intersection of the hole and the crack, and the No. 3 wing crack in
Figure 23b appears at this intersection when the stress reaches 72% of the peak strength, and the extension angle is still 90°. All of the wing cracks do not shift the crack expansion angle during the expansion process, and all of them expand according to the initial crack angle until they penetrate the specimen. The stress–strain curves of the specimens are shown in
Figure 23c. The appearance of cracks 1 and 2 can be attributed to the extension of the prefabricated cracks without significant fluctuations in the stress–strain curves. However, the appearance of crack No. 3 lead to large stress fluctuations in the specimen, and although there is no complete loss of load capacity, the curve already shows obvious plastic characteristics, and then the specimen is rapidly destroyed.
- (3)
H = 100 mm, σ2 = 6 MPa
Unlike the specimens at lateral pressure
σ2 = 2 MPa and 4 MPa, when the lateral pressure
σ2 = 6 MPa, the initial cracking of the precast cracks appears at the crack tip and the secondary cracks start in the opposite direction, as in crack No.1 and 2 in
Figure 24a, which are in the anti-wing cracking direction. The initial cracking is at 30 MPa stress, which is about 48% of the peak strength. As the load continues to increase to the peak strength, cracks No. 1 and 2 continue to widen and new crack faces are created inside. After the upper and lower wing cracks penetrate the specimen, wing cracks No. 3 and 4 appear in
Figure 24b. From the
Figure 24c stress–strain curve, the appearance of cracks No. 3 and No. 4 leads to a significant stress retraction, and the residual stress is more obvious due to the presence of lateral pressure, but the specimen is completely destroyed at this time.
- (4)
H = 0 mm, σ2 = 4 MPa
At this time, the lateral pressure
σ2 = 4 MPa and the specimen contains only prefabricated single cracks, the crack extension evolution process and stress–strain curve obtained are shown in
Figure 25. As shown in
Figure 25a, the starting point of the secondary crack appears at the tip of the precast crack and the standard wing crack appears at the upper end, appearing and expanding at an angle of extension of 90°. For example, the No. 1 crack appears at 53% of the peak strength with a stress of about 35 MPa, and the No. 2 wing crack appears at 40 MPa; the No. 3 anti-wing crack appears at about 70% of the peak strength. Compared with no lateral pressure, the wing cracks appear later and have a larger crack initiation angle. There is no tendency of vertical bias in the direction of secondary wing crack expansion. This is similar to the results of biaxial compression tests on specimens with penetration holes, indicating that lateral stresses have an effect on the direction of crack extension.
- (5)
H = 20 mm, σ2 = 4 MPa
When the depth of the hole H = 20 mm, under a lateral pressure of 4 MPa, the secondary crack propagation and stress–strain curve of the sample are shown in
Figure 26. The wing cracks No. 1 and No. 2 at the upper and lower ends of the specimen appear at an extension angle of 90°, and there is no shift in the direction of the main stress during the extension. The presence of the holes causes the wing cracks to appear earlier, at about 34 MPa, which is at 54% of the peak stress. When the stress reaches 70% of the peak stress, the hole undergoes significant dislocation along the prefabricated crack, leading to the appearance of the No. 3 anti-wing crack, which extends vertically, as shown in
Figure 26b. When the load exceeds 70% of the peak strength, the wing crack penetrates and widens significantly, and the No. 4 crack with vertical splitting appears at the side of the hole, and the specimen reaches the peak strength after the No. 4 crack appears. The stress–strain curve is shown in
Figure 26c, and the specimen has a certain residual stress under the lateral pressure after the peak.
- (6)
H = 40 mm, σ2 = 4 MPa
At H = 40 mm, the No. 1 wing crack appears first at 54% of the peak strength, as shown in
Figure 27a. As the load increases, the width of the No. 1 crack increases and the No. 2 wing crack with a cracking angle of 90° appears at the lower end, when the load is about 60% of the peak stress. The wing cracks in the upper and lower of the specimen widen continuously under the axial load, causing obvious dislocation of the holes along the prefabricated cracks. And, the internal cracks gradually crack completely leading to the splitting of the specimen into two parts, as shown in
Figure 27b. The stress–strain curve develops a clear plastic characteristic after the obvious widening of crack No. 1, with the continued widening of cracks No. 1 and No. 2, as shown in
Figure 27c where the specimen reaches its peak after position 1+.
- (7)
H = 60 mm, σ2 = 4 MPa
When H = 60 mm, the hole size exceeds 50% of the specimen, and at 50% of the peak strength, the first secondary crack appears as an anti-wing crack at the upper end, such as crack No. 1 in
Figure 28a. The wing crack No. 2 appears at the lower end of the precast crack when the stress increases to 55% of the peak strength. As the load increases, the surface of the specimen falls off severely, and wing cracks are generated at the upper end of the prefabricated cracks. During the propagation process, the direction of propagation shifts towards the direction of the main stress, as shown in crack No.3 in the figure. The appearance of crack No. 3 leads to a significant fluctuation in stress, as shown in point 3 in
Figure 28c. As the load approaches the peak stress, the holes are more misaligned along the precast cracks under the axial stress, producing shear cracks along the precast cracks, as shown in cracks 4 and 5 in
Figure 28b.
- (8)
H = 80 mm, σ2 = 4 MPa
When H = 80 mm, the hole is close to penetration, the stress–strain curve compression phase is also relatively long, and the specimen strength is low and close to that of the penetration specimen. The initial crack of the specimen is an anti-wing crack. Crack No. 1 in
Figure 29a, which appears at the lower end point of the upper precast crack, has a strength of about 48.8% of the peak strength. At 55% of the peak strength, a No. 2 wing crack appears at the lower end of the prefabricated crack, with a 90° crack initiation angle. As shown in
Figure 29b, the anti-wing crack gradually shifts to the axial stress direction with the expansion of the crack. And, as the load increases, the secondary crack gradually widens through the specimen, and the stress reaches the peak after penetration, and the specimen is divided into two parts by the prefabricated crack and the secondary crack, as shown in
Figure 29c, and the stress decreases rapidly.