# Experimental Study on Damage Constitutive Model of Rock under Thermo-Confining Pressure Coupling
## 3 Results and Discussion
### Analysis of Mechanical Properties of Rocks
#### 3.2.2 Analysis of Elastic Modulus for Different Rocks
In the range of 60 \({}^{\circ}\)C to 80 \({}^{\circ}\)C, at low confining pressures (0-15 MPa), the increase in temperature still causes \(E_{t}\) to increase, while at high confining pressures (15-25 MPa), \(E_{t}\) remains relatively unchanged and tends to stabilize. When the temperature reaches 120 \({}^{\circ}\)C, \(E_{t}\) significantly decreases, primarily due to high temperatures causing mineral particle expansion, generating thermal stress, weakening internal bonds, and intensifying crack propagation, which reduces the elastic modulus. Figure 11c,d indicate that the trend of \(E_{t}\) of gray sandstone differs from that of red sandstone. As temperature increases, \(E_{t}\) initially decreases and then increases. At room temperature (20 \({}^{\circ}\)C), when the confining pressure increases, \(E_{t}\) increases from 62.39 GPa to 65.18 GPa, an increase of 4.47%; at 40 \({}^{\circ}\)C, the increase is 7.74%; at 60 \({}^{\circ}\)C, the increase is 3.29%. The \(E_{t}\) of gray sandstone increases with confining pressure, but the rate of increase gradually decreases. This indicates that the effect of confining pressure on the closure of internal cracks in gray sandstone gradually reaches saturation. At 80 \({}^{\circ}\)C, \(E_{t}\) first decreases and then increases, reflecting the significant thermal expansion effect at high temperatures, leading to pore and crack expansion, but at high confining pressures, the closure effect dominates. At 120 \({}^{\circ}\)C, \(E_{t}\) increases with confining pressure, indicating that thermal expansion causes mineral particles to contact more closely. Figure 11e,f illustrate that the tangent elastic modulus \(E_{t}\) of shale is significantly affected by temperature and confining pressure. In the range of 20 \({}^{\circ}\)C to 60 \({}^{\circ}\)C, at low confining pressures (0-5 MPa), \(E_{t}\) first rises and then falls, while at high confining pressures (10-25 MPa), \(E_{t}\) gradually rises. High temperatures cause the closure effect of internal pores and cracks in shale to exceed the expansion effect, leading to an increase in \(E_{t}\). The differing trends in the development of elastic modulus for the four rock types under varying temperature and confining pressure conditions primarily stem from differences in their internal structures and mineral compositions. Granite and shale generally exhibit an increase in elastic modulus under high temperature and pressure, reflecting the thermal stability of their structures and the effect of confining pressure on fracture closure. In contrast, red sandstone and gray sandstone show a more complex response, particularly under high-temperature conditions. Their porosity and diverse mineral compositions can lead to a decrease in elastic modulus under certain conditions. Figure 11: Relationship between tangent elastic modulus and temperature, confining pressure for different rocks: (**a**) relationship between red sandstone tangent elastic modulus and temperature; (**b**) relationship between red sandstone tangent elastic modulus and confining pressures; (**c**) relationship between gray sandstone tangent elastic modulus and temperature; (**d**) relationship between gray sandstone tangent elastic modulus and confining pressures; (**e**) relationship between shale tangent elastic mod-ulus and temperature; (**f**) relationship between shale tangent elastic mod-ulus and confining pressures.