# Experimental Study on Damage Constitutive Model of Rock under Thermo-Confining Pressure Coupling
## 3 Results and Discussion  
### Failure Modes  
The crack characteristics of the four types of rocks, after conventional triaxial compression failure and uniaxial compression failure under temperature-stress coupling, are shown in Figure 3. It can be observed that the failure modes of red sandstone and shale under uniaxial stress and temperature-stress coupling are primarily characterized by shear failure. Under uniaxial stress, a macroscopic through-crack typically appears on the specimen surface, accompanied by several small micro-cracks. However, under the coupling of temperature and stress, the number of micro-cracks on the specimen surface decreases, with the failure characteristics focusing on a single main crack. Additionally, the angle of the crack relative to the principal stress direction increases. This phenomenon is primarily due to the generation of thermal stress, where temperature changes within the rock induce thermal stress. The action of thermal stress can make the internal stress field of the rock more uniform, reducing stress concentration and, consequently, the number of micro-cracks. Simultaneously, the complex stress state of thermal stress and confining pressure alters the propagation direction of the main crack, increasing its angle relative to the principal stress direction. These findings indicate that the coupling effect of temperature and confining pressure significantly influences the failure modes and characteristics of red sandstone and shale.  
Additionally, the failure modes of granite and gray sandstone exhibit bulging failure, with most cracks parallel to the principal stress direction under uniaxial stress. However, under the coupling of temperature and stress, the failure mode transitions to shear failure, and the shear plane of the specimen displays a \"Y\"-shaped shear surface. The primary reason for this is that uniaxial compression creates stress concentration zones within the rock perpendicular to the direction of the compressive stress. This stress concentration easily leads to bulging failure, characterized by expansion and cracking along the perpendicular  
Figure 3: Failure patterns of various rock types under triaxial and uniaxial compression: **(a)** failure patterns of granite under triaxial and uniaxial compression; **(b)** failure patterns of red sandstone under triaxial and uniaxial compression; **(c)** failure patterns of gray sandstone under triaxial and uniaxial compression; **(d)** failure patterns of shale under triaxial and uniaxial compression.  
direction. Conversely, under the combined effects of temperature and confining pressure, the internal stress field of the rock becomes more complex. Confining pressure inhibits bulging failure, while the changes in the rock at high temperatures make shear failure the primary failure mode. In this scenario, the rock is likelier to experience sliding and failure along weak planes under shear stress.  
When subjected to temperature-stress coupling, the fracture surface of the specimen during failure is relatively smooth and flat. In contrast, the fracture surface under uniaxial stress appears rough and uneven. Additionally, around the fracture surface under uniaxial conditions, multiple secondary cracks parallel to the main fracture surface and a few spalled fragments can be observed.