## 3 Results
### The Evolution Law of Displacement Field
Figure 7 depicts the final failure mode characterized by a central straight fissure, taking a prefabricated crack angle of 0\({}^{\circ}\) as an illustrative example, the joint plane angle is perpendicular to the loading direction, and the displacement variation in the joint end region is minimal, exhibiting a vertically distributed state of displacement change. When it is loaded to the compaction  
Figure 6: Digital speckle image acquisition system. moment, there is a small displacement change in the end region of the circular disk, and there is no obvious deformation feature on the surface of the circular disk. As the loading progresses to the stabilization moment, a significant increase in displacement is observed at the end of the circular disk surface, accompanied by small deformations appearing on both sides of the joint. The deformation increases from the center of the circular disk to the loading end. Upon reaching the cracking moment, the deformation area at the end of the circular disk surface continues to expand, extending to both sides of the joint, and the deformation on both sides of the joint notably intensifies. At the failure moment, the deformation area on both sides of the joint connects with the end region of the circular disk, and the overall displacement of the surface of the circular disk at the loading axis is the largest. Furthermore, deformation zones emerge at the joint ends, extending toward the edge of the circular disk. Nevertheless, these deformations remain relatively small in magnitude and lack macroscopic visibility. Figure 8 exhibits the case where the final failure mode corresponds to a crack tip wing fissure, specifically considering a prefabricated crack angle of 30\({}^{\circ}\). In this configuration, the displacement at the joint end region increases significantly compared to that of the 0\({}^{\circ}\) joint specimen. Upon reaching the compaction moment, the change is similar to the joint angle of 0\({}^{\circ}\). At the stabilization moment, there are deformation zones at the joint end and loading end, with larger deformation at the loading end. As the loading progresses to the cracking moment, the deformation in both regions gradually increases and approaches each other, and the extension direction is close to the macroscopic crack. Finally, upon reaching the failure moment, the two deformation zones become fully connected, presenting a macroscopically visible wing-shaped crack. Figure 8: Surface displacement contour maps of crack tip wing fissure failure mode (taking a prefabricated crack angle of 30\({}^{\circ}\) as an illustrative example) at different loading times: (**a**) stable state. (**b**) Initiation state. (**c**) Failure state. Figure 7: Surface displacement contour maps of central straight fissure failure mode (taking a prefabricated crack angle of 0\({}^{\circ}\) as an illustrative example) at different loading times: (**a**) stable state. (**b**) Initiation state. (**c**) Failure state. Figure 9 depicts the scenario where the final failure mode corresponds to a crack tip edge straight fissure, specifically considering a prefabricated crack angle of 90\({}^{\circ}\). In this case, the joint plane angle inclines toward the loading direction, and the displacement variation exhibits a vertically distributed state due to the presence of vertical joints. However, due to the presence of vertical joints, the displacement at the disk's center point is relatively smaller. Upon reaching the compaction moment, a minor deformation zone emerges at the loading end of the circular disk, while no significant changes are observed in other areas. As the loading progresses to the stabilization moment, the deformation zone at the end of the circular disk extends toward the end of the vertical joint, with the deformation zone at the joint end exhibiting a smaller extent of deformation. Advancing to the cracking stage, the deformation zone at the joint end intensifies and gradually connects with the loading end.