## 3 Results
### Failure Mode
In the fractures perpendicular to the x to y direction, the most obvious perforating fracture surface passed through the tunnel and was perpendicular to the interface. Additionally, owing to the interface sliding traction, as the distance to the interface decreased, the curvature increased and the fracture surface was thus formed. The same fracture mode appeared in the 30\({}^{\circ}\), 60\({}^{\circ}\), and 75\({}^{\circ}\) samples. The curvature of the fracture surface increased with the dip angle. A large number of incomplete cracks appeared in the sample with the 45\({}^{\circ}\) angle, and these cracks were distributed on both sides of the interface, which caused concentrated destruction of the rock surrounding the tunnel. For the 90\({}^{\circ}\) sample, the number of fracture surfaces parallel to the y to z direction significantly increased, and many fractures appeared in the tunnel. The cracks in the tunnel gradually increased with the dip angle, and the damage degree gradually became more severe. The test results revealed that, under the influence of an interface with different dip angles, the rock surrounding a tunnel without support mainly undergoes tensile failure (Figure 9a), shear failure (Figure 9b), slip along the interface (Figure 9c), collapse failure (Figure 9d), and bending failure (Figure 9e). A fracture surface parallel to the maximum principal stress is produced under axial pressure because the surrounding rock is brittle. The relationship between the ultimate strain and the loading speed is very small, and the brittle tensile fracture is controlled by tensile strain. Figure 9: Diagram of failure mechanism. (**a**) is tensile failure. (**b**) is slide-shear failure. (**c**) is slide-broken failure. (**d**) is compression-bend failure. (**e**) is compression-shear failure. Shear failure contains brittle and plastic deformation. When the load provided by the maximum principal stress is higher than the maximum static friction force of the interface, the interface maintains stability, the surrounding rock near the interface is subjected to traction, and plastic shear deformation occurs. Consequently, a large number of parallel pinnate fissures appear along the interface. This phenomenon is obvious in the 15\({}^{\circ}\)-45\({}^{\circ}\) samples. Brittle deformation forms vertical cracks, and plastic deformation forms pinnate fractures. These two types of crack extend and connect, and form a curved fracture pattern. The degree of bending reflects the strength of the shear action on the surrounding rock, and as the curvature of the fracture surface increases, shear failure is the main failure of the surrounding rock. Slide deformation occurs under axial stress, and is dominated by the internal friction angle of the interface. Slip deformation occurs when the dip angle of the interface is higher than its internal friction angle. The typical signs of slip deformation are the fracture of the slip plane and the occurrence of a broken rock mass at the inner wall of the tunnel. Collapse failure often occurs in the rock surrounding the slab crack medium and the rock's failure condition is closely related to the elastic curve shape of the slab crack deformation. When the inclination angle was 90\({}^{\circ}\), the surrounding rock underwent elastic deformation toward the tunnel under compression stress, collapse failure occurred, and a curved fracture surface formed in the surrounding rock. The failure mechanism of the bending failure was the same as that of the beam. The surrounding rock at the top of the chamber bent and deformed under the action of pressure. Failure occurred when the tensile strength of the rock was reached. The characteristic of bending failure is that the fracture surface converges to the bending middle point in the rock mass, and the most typical example is the sample with an inclination angle of 0\({}^{\circ}\). In summary, three kinds of cracks with different mechanical behaviors appeared in the course of the test, namely, tensile crack, shear crack, and tensile shear crack.