# Experimental Study on Damage Constitutive Model of Rock under Thermo-Confining Pressure Coupling
## 3 Results and Discussion
### Analysis of Mechanical Properties of Rocks  
#### 3.2.1 Analysis of Stress-Strain Curves for Different Rocks  
Figures 4 and 5 illustrate the stress-strain curves of granite under different temperatures and confining pressures. From Figure 4a,f, it can be observed that the yield stage of granite is not distinct, the crack development stage is short, and the stress immediately drops after reaching the peak, resulting in failure accompanied by a noticeable cracking sound, indicative of brittle failure. When granite samples are loaded to the stress limit, they remain in the elastic stage. Under the same confining pressure conditions, the slope of the curve increases with rising temperature, while the separation between the curves at different temperatures decreases as the confining pressure increases. This is primarily due to the reduction of pores between mineral particles within the microstructure of the rock sample as the confining pressure increases, and the confining effect induced by the increase in confining pressure surpasses the thermal expansion effect caused by the rise in temperature. As illustrated in Figure 5, when the temperature remains constant, the stress-strain curves progressively converge with the increase in confining pressure. This indicates that granite is more sensitive to changes in confining pressure under lower confining conditions. However, once a certain confining pressure threshold is reached, the slope of the curve stabilizes, indicating that the deformation behavior of the rock tends to become consistent. Comparing Figure 5a,e, it is evident that, at a confining pressure of 25 MPa and a temperature of 120 \({}^{\circ}\)C, the compressive strength and peak strain of granite are both greater than those under normal conditions. It indicates that the coupled effects of temperature and stress can enhance the density of the mineral substructure within the rock sample, thereby increasing its load-bearing capacity and improving its ductility. Figure 6 shows the stress-strain curves of red sandstone under different temperature and confining pressure conditions. From Figure 6a,b, it can be observed that the curves of red sandstone mainly exhibit four stages: the pore crack compaction stage, the linear elastic deformation stage, the microcrack development stage, and the post-failure stage. The nonlinear characteristics of the crack closure and compaction stage in red sandstone are not obvious, and the curve quickly enters the elastic deformation stage, showing linear variation characteristics. Comparing Figure 6c,d, it is found that the slope of the curve in the elastic stage gradually increases. The confining pressure restricts the lateral deformation of the rock sample and the expansion of internal cracks, enhancing the closure degree of internal cracks and thus increasing the load-bearing capacity of the sample. Moreover, the compressive strength and peak strain of red sandstone decrease under high-temperature and high-pressure conditions. Higher temperatures cause a crack expansion in red sandstone, reducing its density. The influence of plastic deformation at elevated temperatures outweighs the confining pressure's restrictive effect, thereby decreasing the sample's load-bearing capacity. Consequently, temperature becomes the primary factor determining the compressive strength of red sandstone. Figure 4: Stress–strain curves of granite under different temperature conditions: (**a**) granite \(\sigma_{3}=0\) MPa; (**b**) granite \(\sigma_{3}=5\) MPa; (**c**) granite \(\sigma_{3}=10\) MPa; (**d**) granite \(\sigma_{3}=15\) MPa; (**e**) granite \(\sigma_{3}=20\) MPa; (**f**) granite \(\sigma_{3}=25\) MPa.