## 2 Materials and Methods  
### Unloaded Sample Preparation  
Sandstone samples were prepared in standard cylinders [23], 100 mm in height and 50 mm in diameter. The rock samples with similar properties were selected by the method of longitudinal wave velocity measurement. The average quality of the selected rock sample is 419.64 g, density is 2.15 g:cm\({}^{-3}\), longitudinal wave velocity is 2294 m:s\({}^{-1}\), porosity is 14.95%, and uniaxial strength is 62.8 MPa. The sandstone samples and triaxial test equipment are shown in Figure 1.  
In the process of engineering slope excavation, there are different excavation levels and different excavation rates for the rock mass within different areas. In this paper, the values of the confining pressure of sandstone specimens at the time of unloading damage were determined by pretesting the common sandstone samples for unloading confining pressure damage. After comparing the changes in the stress-strain curve in the unloading test and the morphological characteristics of the sample, 75% of the confining pressure unloading (i.e., 75% of the confining pressure value from the beginning of unloading under the corresponding confining pressure to the confining pressure value at the time of unloading damage) was finally selected as the change in confining pressure in this unloading test. The formula for the value of confining pressure unloading is as follows:  
\[\Delta\sigma_{3}=\left(\frac{\sigma_{3}-\sigma_{3}^{i}}{\sigma_{3}-\sigma_{d }}\right)\times 100\% \tag{1}\]  
where \(\sigma_{3}^{i}\) is the confining pressure at the end of the unloading, \(\sigma_{3}\) is the initial design confining pressure, and \(\sigma_{d}\) is the final confining pressure when the sample is damaged. The stress paths taken in this unloading test are presented in Figure 2 and the loading or unloading rates for each phase are labelled. Step I: The rock sample has specific pore structure characteristics under the original ground stress environment when it was not mined, the stress state of the rock sample changed after mining, and the structural characteristics changed accordingly. Therefore, when preparing unloaded damaged rock samples, we first simulate the initial stress state of the rock sample by loading the hydrostatic pressure (\(\sigma_{1}=\sigma_{3}\)), as well as not destroying the pore structure characteristics, as in section _oa_ in Figure 2. Step II: Keeping the confining pressure \(\sigma_{3}\) constant, continue to load the axial pressure \(\sigma_{1}\) to 75% of the peak triaxial strength, corresponding to the confining pressure value, as in section _ab_ in Figure 2. Step III: Simulate the excavation disturbance process by the method of unloading the confining pressure, keep the axial pressure \(\sigma_{1}\) unchanged, and unload the confining pressure \(\sigma_{3}\) to the set value, as in section _bc_ in Figure 2. Step IV: Unload the axial pressure to the set value (end of this stage, \(\sigma_{1}=\sigma_{3}\)), as in section _cd_ in Figure 2. Step V: Unload the hydrostatic pressure stage, as in the section _do_ in Figure 2.  
Figure 1: Sandstone specimens and triaxial test equipment (where (**c**) shows the displacement sensors, consisting of two axial displacement sensors parallel to the height direction of the specimen and a chain displacement sensor around the middle of the specimen. When the specimen is compressed, the axial displacement sensor is compressed at the same time, and the lateral displacement sensor is elongated with the lateral expansion of the sample, with the height of the sample being compressed and the size of the radial expansion able to be measured to obtain the axial and lateral strains. The measuring accuracy is 0.001 mm). (**a**) Sandstone specimens; (**b**) triaxial test equipment; (**c**) displacement sensors. Two initial confining pressure values were set in this test: 15 MPa and 21 MPa. Two points need to be clarified.