## 3 Unloading-Damaged Test Procedure  
### Triaxial Unloading Test Analysis  
A triaxial unloading test with constant axial unloading confining pressure is carried out to approximately simulate the stress path of slope excavation. The axial stress level is taken as 70%, and the axial pressure is kept constant to unload the surrounding pressure until the specimen is damaged. The surrounding pressure at the time of unloading damage is 3, 4, and 7.5 MPa, and the stress-strain curve is shown in Figure 4.  
Figure 3: Schematic diagram of temperature variation in the freeze-thaw cycle test. Figure 2: Homemade rock freezing and thawing jig. The unloading quantity [43] is used to characterize the degree of unloading damage and is calculated as:  
\[K=\left(\frac{\sigma_{3}-\sigma_{3}^{\prime}}{\sigma_{3}-\sigma_{d}}\right)\times 1 00\% \tag{1}\]  
where \(K\) is the confining pressure unloading quantity, \(\sigma_{3}\) is the initial confining pressure, \(\sigma_{3}^{\prime}\) is the target value of confining pressure unloading, and \(\sigma_{d}\) is the confining pressure value at failure. To analyze the damage-evolution process of the rock sample during the unloading stage, the unloading quantity is used as the damage classification criterion, and the strain confining pressure increment ratio is introduced ([PERSON] et al. [44]). The ratio of the strain increment caused by unloading confining pressure to the value of the confining pressure reduction is calculated (Equation (2)). This represents the physical quantity of how fast the axial or circumferential deformation increment changes with each unit of unloaded confining pressure, which better reflects the deformation response of the rock sample during the process of confining pressure unloading. \[\Delta\dot{\epsilon}_{i}=\frac{\Delta\epsilon_{i}}{\Delta\sigma_{3}} \tag{2}\]  
where \(\Delta\dot{\epsilon}_{i}\) is the strain confining pressure increment ratio (\(i\) = 1,3 represents axial strain and circumferential strain, respectively), \(\Delta\epsilon_{i}\) is the strain increment between the starting point of the unloading confining pressure and the target value of the confining pressure to the corresponding unloading quantity, and \(\Delta\sigma_{3}\) is the difference between the starting point of the unloading confining pressure and the corresponding unloading quantity corresponding to the confining pressure target value. As shown in Figure 5, the strain of the sample under the three groups of confining pressures gradually increases with increasing unloading quantity, and the axial and circumferential strain confining pressure increment ratios gradually increase, reflecting the influence of the size of the unloading quantity on the deformation response of the rock sample during the process of unloading confining pressure. It can be roughly divided into three stages: stage I (0-60% unloading capacity) is the slow section, where the microfractures inside the rock sample are affected by the unloading confining pressure, and the original closed state gradually opened but did not undergo expansion; stage II (60-90%) is the uniform section, with the increase in unloading quantity, the microfractures inside the rock sample continue to develop and expand, the pore structure is damaged to a certain extent, and the axial and circumferential deformation of the rock sample continues; stage III (90-100%) is the accelerated section, the pore fissures inside the rock sample develop,  
Figure 4: Triaxial unloading test stress-strain curve. expand, and connect, the structure is rapidly destroyed, and the axial and circumferential deformation increases rapidly. After the unloading quantity becomes greater than 60%, the rate of change of the axial and circumferential strain confining pressure increment ratio is significantly accelerated.