## 3 Fracture Characteristics
### Fracture Characteristics after Freeze-Thaw and Triaxial Compression  
According to [PERSON] et al. [52], frost-heaving cracks have different effects on the fracture mode of quasi-sandstones with a single fissure at different angles under uniaxial compression. According to the research of [PERSON] et al. [53] on the crack coalescence of single-fissured rock, with the increase in ambient pressure, the failure mode of quasi-rock gradually becomes ductile, and the crack propagation in quasi-rock is more complicated. Single-fissured rock under triaxial compression mainly has three kinds of through fracture form [54]: tensile, shear and tensile-shear mixed failure. The main branch cracks at the prefissured apex of rock under triaxial compression are [55]: (1) wing crack, (2) secondary inclined crack, (3) secondary coplanar crack, (4) branch crack and (5) inclined crack, as shown in Figure 3. For the saturated macro-fissures in this experiment, the freeze-thaw cycle with a freezing temperature of \(-10\)\({}^{\circ}\)C can drive the fissure tip to initiate new macro-frost-heaving cracks. It is necessary to study the influence of frost-heaving cracks on the fracture mode of triaxial compression. Therefore, typical failure samples with a confining pressure of 2 MPa and freezing temperatures of unfrozen, \(-10\), \(-20\) and \(-30\)\({}^{\circ}\)C, are selected for analysis, and the fracture failure diagram of quasi-sandstone with three kinds of single-fissured angles at four freezing temperatures is obtained, as shown in Figure 4. The intact rock sample shows tensile-shear failure under triaxial compression without freezing, and the single-fissured sample is a shear-slipped failure. Tensile cracks are mainly produced in rock samples without prefabricated fissures, and shear oblique cracks appear at the upper end. When \(\theta=0\)\({}^{\circ}\), the fracture mode of the sample mainly presents as secondary inclined cracks (2) at both ends of the prefabricated fissure. When \(\theta=45\)\({}^{\circ}\), the secondary coplanar crack (3) initiates at the apex of the prefissure, and its initiation direction is along the direction of the prefabricated crack. When it extends to a certain extent, the upper and lower cracks (3) deflect toward the orientation of the maximum main stress until the end of the sample. When \(\theta=75\)\({}^{\circ}\), two secondary coplanar cracks (3) initiate at the apex of prefissure, and its initiation direction is the same as that of the prefabricated fissure. When it extends to a certain extent, the upper crack (3) deflects toward the orientation of the major principal stress until the end of the  
Figure 3: Crack propagation at prefabricated fissure tip. rock sample, and the lower crack (3) propagates tortuously along the orientation of the resultant force of the maximum main stress and the minimum main stress until reaching the lateral face of the sample. When \(T_{f}=-10\)\({}^{\circ}\)C, the \(0^{\circ}\) fissure specimen under triaxial compression is a tensile-shear mixed failure, and the other samples are all shear failure. There is only one shear oblique crack penetrating specimen in the intact quasi-sandstone. Because of the freeze-thaw effect, the number of secondary inclined cracks (2) along the prefissure tip of the quasi-sandstone with a fissure angle of \(0^{\circ}\) increases. When loaded, the prefissure is closed first, and then the fracture along the frost-heaving cracks at both ends is produced and finally sheared. For the quasi-sandstone with a \(45^{\circ}\) angle fissure, compared with the fracture mode without freezing, the difference is that the cracks (3) in the upper and lower parts extend along the coplanar direction of the prefabricated fissure, and then they extend in the orientation of the maximum main stress until the side edge of the sample. Frost-heaving cracks do not occur in the \(75^{\circ}\) inclination prefissured sample owing to freezing and thawing, so the final fracture mode is the same as that in the unfrozen state.