# Mechanical and Energy Evolution Characteristics of Sandstone under True Triaxial Cyclic Loading
## 3 Test Results and Analysis
### Analysis of Deformation and Failure Characteristics of Specimens
#### 3.1.3 Strength and Deformation Analysis of Sandstone under Graded Cyclic Loading \(\sigma_{1}\)
generated inside were not completely closed, and new cracks were produced, resulting in a reduction in the energy required for crack development and the acceleration of crack propagation. When the sandstone was destroyed, the maximum load that could be borne in the \(\sigma_{1}\) direction was small, and the deformation in the \(\sigma_{1}\) direction was reduced, so the deformation in the \(\sigma_{2}\) and the \(\sigma_{3}\) directions was also reduced. Figure 7c indicates that the rock expanded during damage, and the expansion point appeared in advance with the increase in the loading and unloading rate. When the rock was damaged, the expansion characteristics became increasingly obvious, indicating that under the condition of true triaxial graded cyclic load \(\sigma_{1}\), the loading rate played a leading role in the expansion of the rock. 1.4 Analysis of Acoustic Emission and Failure Characteristics of Sandstone under Graded Cyclic Loading \(\sigma_{1}\)  
The microscopic failure (cracks, fissures, etc.) inside a rock is closely related to its external macroscopic failure form. Acoustic emission can detect the energy accumulated and released by the microscopic fracture of rocks under the action of external force and can send signals in the form of a stress wave. However, the energy released by the development and closure of rock cracks and pores under different load conditions differs greatly, resulting in different macroscopic damage phenomena [28]. Therefore, the internal relationship between acoustic emission characteristics and macroscopic failure phenomena can be established by combining acoustic emission parameters, such as ringing count and energy, as shown in Figure 8.  
Figure 7: Stress–strain curves of sandstone under different true triaxial loading rates. (**a**) \(\sigma_{2}\) = 20 MPa, (**b**) \(\sigma_{2}\) = 20 MPa, (**c**) \(\sigma_{2}\) = 20 MPa. In this study, the acoustic emission characteristics of sandstone under different \(\sigma_{2}\) conditions were generally similar and could be divided into active, quiet, and explosion periods. In the active period, the sandstone entered the compaction stage, the primary pores and cracks inside the rock were closed under the action of stress, and the mutual friction between the internal grains produced abundant acoustic emission signals. The rock entered the quiet period of acoustic emission signal after compaction. At this stage, acoustic emission signals appeared in each loading and unloading cycle, but the acoustic emission signals were relatively few and stable, indicating that the cracks in the rock were developing steadily. The acoustic emission during the unloading process was small because the microstructure of the rock rebounded and opened during the unloading failure process, so the acoustic emission signal during the quiet period was mainly concentrated in the loading part. The sudden increase in acoustic emission signals in the explosion period indicated that the rock entered the failure stage, and the internal cracks and pores developed rapidly and produced new cracks at the same time. The new and old cracks interlaced with each other to form macroscopic failure. Figure 8: Acoustic emission and failure characteristics of rock under different \(\sigma_{2}\) conditions. (**a**) \(\sigma_{2}=20\) MP, (**b**) \(\sigma_{2}=40\) MP, (**c**) \(\sigma_{2}=60\) MP. Figure 8 shows that the cumulative energy of acoustic emission under the different \(\sigma_{2}\) conditions had a consistent upward trend, and the increase in each energy was closely related to the microscopic damage inside the rock. The smaller \(\sigma_{2}\) was, the greater the increase was in each loading energy and cumulative A.E. energy before the rock was destroyed. When \(\sigma_{2}\) = 20 MPa, the sandstone formed a failure feature dominated by tension and supplemented by a tension-shear composite. In the macroscopic state, additional tension and shear cracks were formed, and the damage was severe, accompanied by a large amount of debris.