## 3 Fracture Characteristics  
### Damage Behaviour after Freezing-Thawing  
Figure 2 is a damage diagram of quasi-sandstone after thawing for various freezing temperatures. It shows that the intact quasi-sandstone and the quasi-sandstone with different angle fissures have different degrees of surface spalling or crack propagation after thawing. There are two main types of frost-heaving fracture mode of the original fissure [52]: (i) Coplanar frost-heaving propagation cracks appear at the end of the prefabricated fissure, propagate along the direction of the original fissure for a certain distance, and gradually turn to the short side of the sample. These are called 'coplanar propagation cracks'. (ii) The two sides of the middle of the prefabricated fissure produce a frost-heave propagation crack in an approximately horizontal direction, which is called a 'horizontal propagation crack'.  
The damage and fracture characteristics of samples after thawing at different freezing temperatures were significantly different. For a freezing temperature \(T_{f}=-10\)\({}^{\circ}\)C, random flake spalling occurred on the surface and top of the intact quasi-sandstone samples after thawing, and the scale of spalling was small. The crack propagation laws caused by cracks with different dip angles were also different. When the fissure angle was \(0^{\circ}\), small flake spalling occurred on the surfaces of the sample, and a horizontally extended microcrack (coplanar propagation crack) appeared along with the tip position of the prefabricated fissure. When the fissure angle was \(45^{\circ}\), the flake spalling around the prefabricated fissure was large, and the spalling at the top was small. When the fissure angle was \(75^{\circ}\), the flake spalling amount on the surface of the sample was less than that of the specimen with a fissure angle of \(45^{\circ}\). The crack did not appear at the end of the prefabricated fissure, but near the top. This indicates that, for quasi-sandstone with fissure angles of \(0^{\circ}\), \(45^{\circ}\), and \(75^{\circ}\), the localised damage effect caused by thawing at \(T_{f}=-10\)\({}^{\circ}\)C decreases with the increase in fissure angle. The fracture characteristics of \(T_{f}=-20\)\({}^{\circ}\)C and \(T_{f}=-30\)\({}^{\circ}\)C quasi-sandstone after freezing-thawing were compared and analysed. With the decrease in freezing temperature, the amount of spalling at the top edge of quasi-sandstone samples increased gradually, and the number and penetration of new cracks initiated at the apex of the prefissure increased.  
Figure 2: Freeze–thaw damage of quasi-sandstone.  
Because of the large difference in potential propagation paths, the freeze-thaw temperatures of crack propagation required for quasi-sandstone fissures with various angles also differ. When the fissure angle is 0\({}^{\circ}\), the potential propagation path is 15 mm, and \(T_{f}=-10\)\({}^{\circ}\)C thawing produces obvious frost-heaving cracks. When the fissure angle is 75\({}^{\circ}\), the potential propagation path is 41 mm, so a freeze-thaw cycle at \(T_{f}=-30\)\({}^{\circ}\)C is needed to generate frost-heaving cracks, which is consistent with the results obtained by the principle of'minimum resistance area' proposed by [PERSON] et al. [24].