## 4 Strength Characteristics and Crack Evolution of Hole-Crack Specimens under Biaxial Compression
### Crack Extension Evolutionary Characteristics of Hole-Crack Specimens under Biaxial Loading
(3) H = 100 mm, \(\sigma_{2}\) = 6 MPa  
Unlike the specimens at lateral pressure \(\sigma_{2}\) = 2 MPa and 4 MPa, when the lateral pressure \(\sigma_{2}\) = 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, \(\sigma_{2}\) = 4 MPa  
At this time, the lateral pressure \(\sigma_{2}\) = 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\({}^{\circ}\). 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 specimenswith penetration holes, indicating that lateral stresses have an effect on the direction of crack extension. (5) H = 20 mm, \(\sigma_{2}\) = 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\({}^{\circ}\), 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, \(\sigma_{2}\) = 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\({}^{\circ}\) 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+.