## 3 Analysis of Test Results  
### Analysis of Variation Characteristics of Maximum Principal Stress  
The principal stress-strain relationship is depicted in Figure 5. Due to the large intermediate principal stress \(\sigma_{2}\), when it exceeds the loading capacity limit of the test system, the maximum principal stress results in Scheme III \(\sigma_{2}/\sigma_{3}\) ratios of 1.4, 1.6, and 1.8, which prevent the sandstone samples from being crushed. Consequently, this section focuses solely on comparing and analyzing the test results from Scheme I and Scheme II.  
Figure 4: Schematic diagram of true triaxial loading of sample.  
Figure 5: Relationship between principal stress and principal strain: (a) 600 m buried depth; (b) 1000 m buried depth.  
From the test curve, it is evident that the stress-strain curve initially exhibits a concave upward change due to the compaction and closure of original micro-cracks and defects, accompanied by a reduction in the sample's porosity. In the elastic stage, the curve demonstrates a clear linear relationship, indicative of elastic deformation where the strain continues to increase while adhering to [PERSON]'s law, with no new cracks forming. Upon reaching the crack initiation stress, the equilibrium between new and previously closed damage is maintained, preserving the linear relationship of the stress-strain curve. As the axial load advances to the expansion stress, the sample's cracks begin to expand unsteadily; the rate of new crack growth surpasses that of crack closure, and the stress-strain curve shifts to a nonlinear convex shape. Internally, the sample begins to connect and gradually penetrate, forming a macroscopic fracture surface. When the axial load attains peak strength, a sharp drop in stress occurs, and the sample becomes instantly unstable and fractures. At this point, although completely fractured, the sample retains significant residual strength due to the high confining pressure. As the axial strain increases under constant axial load, the specimen enters the residual stage, maintaining some bearing capacity despite being damaged.  
When the minimum principal stress \(\sigma_{3}\) remains constant, the peak stress, residual strength, peak strain, and \(\sigma_{2}/\sigma_{3}\) ratios are depicted in Figure 6a. A comparison of test data from 600 m and 1000 m depths shows that with an increase in intermediate principal stress, triaxial compressive strength, yield stress, and residual strength gradually increase, while axial peak strain initially decreases and then increases. At a buried depth of 600 m with \(\sigma_{2}\), the maximum failure principal stress \(\sigma_{1}\) increases by 48.45 MPa. Compared to the initial stage, the strength at each subsequent stage increases by 4.7%, 7.4%, and 16%, respectively. At a buried depth of 1000 m with \(\sigma_{2}\), the maximum failure principal stress \(\sigma_{1}\) increases by 59.57 MPa, with strength increases at each stage of 2%, 7.2%, and 14%, respectively, compared to the initial stage. The peak strain initially increased and then decreased, showing a generally downward trend, primarily due to the influence of high confining pressure. When \(\sigma_{2}/\sigma_{3}=1.6\), the maximum increase in peak stress is 133.89 MPa, which is 5.5% higher than the average increment, and the minimum increment in peak strain is 0.0265%, based on the comparison of sandstone specimens from 600 m and 1000 m buried depths.  
Figure 6: _Cont._  
As depicted in Figure 6b,c, the duration of each stage in the compression process of the sandstone samples initially increases and then decreases as \(\sigma_{2}\) increases. The compaction stage gradually shortens, while the durations of the elastic and plastic deformation stages correspondingly lengthen, with the plastic deformation stage lasting the longest. In the post-peak stage, due to the confining pressure, the rock experiences no significant stress drop, enhancing the rock's ductility.