## 3 Analysis of Test Results
### Deformation Characteristic Analysis  
The stress-strain curves under different intermediate principal stresses are shown in Figure 7, wherein the volumetric strain calculation formula of \(\varepsilon_{\rm V}\) is:  
\[\varepsilon_{\rm V}=\Delta V/V=\varepsilon_{1}+\varepsilon_{2}+\varepsilon_{3} \tag{4}\]  
Observing Figure 7 reveals that \(\sigma_{2}\) has a significant influence on \(\varepsilon_{\rm V}\), and distinct stages are evident during the specimen's expansion in the stress loading process. In the initial  
Figure 6: Relationship between intermediate principal stress and failure stress and time: (**a**) relationship between the maximum failure principal stress and the intermediate principal stress; (**b**) stress time relationship diagram of each stage of 600 m; (**c**) relationship between stress and time at each stage of 1000 m.  
stage of loading, as \(\sigma_{1}\) increases, micro-cracks in the rock specimen are compacted and closed, causing all directional strains to be positive and the model to be in a compressed state. Here, \(\epsilon_{\rm V}\) typically exhibits a linear increasing trend, and the deformation at this stage varies positively with increases in \(\sigma_{2}\) and negatively with decreases. During the elastic phase, the growth rate of \(\epsilon_{1}\) is notably higher than that of the lateral strain, \(\epsilon_{\rm V}\) remains positive, and the specimen's deformation is primarily axial compression, with the total model deformation increasing gradually. In the yield stage, as \(\sigma_{1}\) continues to rise, the internal cracks of the specimen rapidly expand and penetrate, leading to an increased growth rate of lateral strain, predominantly \(\epsilon_{3}\), causing \(\epsilon_{\rm V}\) to increase in the opposite direction. This transition marks the change from a volumetric compression state to an expansion state. In the failure stage, through-cracks form a fracture surface that spans the entire specimen, ultimately leading to its destruction, and the deformation stabilizes at a maximum value. Comparing the volumetric strain across the three stages shows that the volumetric deformation at a 600 m burial depth is more pronounced than that at 1000 m.  
To better characterize the damage degree of deep sandstone under the influence of mining disturbance, the fracturing coefficient is introduced as \(\xi\), and the corresponding expression is:  
\[\xi=\frac{\epsilon_{v1}-\epsilon_{v2}}{\epsilon_{v2}} \tag{5}\]  
where \(\epsilon_{v1}\) represents the volume strain at the peak strength point of the sandstone specimen, and \(\epsilon_{v2}\) denotes the volume strain under the initial in situ stress environment. Calculations show that \(\xi\),600 m = 0.028, \(\xi\)1000 m = 0.242, and \(\xi\)1400 m = 1.075, indicating that the fracturing coefficient at 1400 m exceeds 1. This suggests that the volume strain of the sandstone sample progressively decreases from the initial stress state to the peak strength point, reflecting compressive deformation. This occurs because the increases in maximum horizontal strain and minimum horizontal strain are smaller than those in axial strain throughout the loading process, leading to the volume strain at the peak strength point being lower than at the initial stress state's end. Conversely, \(\xi\)600 m and \(\xi\)1000 m are less than 1, showing that the volume strain of sandstone specimens increases progressively from the initial stress state to the peak strength point, indicating swelling deformation. This happens because the increments of maximum and minimum horizontal strains exceed the axial strain during the loading process under 600 m and 1000 m stress conditions. The sequence \(\xi\)1400 m > \(\xi\)1000 m > \(\xi\)600 m demonstrates how different burial depths significantly influence the degree and mode of rock failure. This research indicates that as intermediate principal stress increases, the volume strain decreases and the extent of compressive deformation of sandstone specimens diminishes, exhibiting significant dilation.