# Mechanical and Energy Evolution Characteristics of Sandstone under True Triaxial Cyclic Loading
## 4 Conclusions  
The mechanical and energy evolution characteristics of sandstone under true triaxial cyclic loading were studied. The effects of different true triaxial stress paths on sandstone deformation and energy were systematically analyzed. The similarities and differences in the axial cycle under different \(\sigma_{2}\) conditions were compared, and the energy in each principal stress direction was determined. Moreover, the dissipated energy was quantitatively analyzed, and the mechanical and damage characteristics of sandstone under true triaxial cyclic loading were revealed. The following main conclusions were derived:  
1. Under the different stress paths, the axial bearing capacity and macroscopic failure characteristics of sandstone differed. The existence of confining pressure greatly improved the axial bearing capacity of the rock. The \(\sigma_{1}\) of sandstone under a true triaxial cycle was lower than that under true triaxial compression. Under uniaxial compression, sandstone mainly experienced shear failure. During true triaxial compression, sandstone was mainly subjected to tension-shear composite failure, and in the true triaxial cycle, sandstone mainly experienced tensile failure. This showed that the rock in the true triaxial environment in the project would reduce the axial strength of the rock and change its macroscopic failure characteristics from tensile-shear composite failure to tensile failure after repeated cyclic loading. Figure 15: Damage evolution curves of sandstone under different intermediate principal stresses. 2. In the process of true triaxial graded cyclic loading \(\sigma_{1}\) of sandstone, the stress-strain curves and failure characteristics under different \(\sigma_{2}\) conditions varied obviously. The larger \(\sigma_{2}\) was, the smaller the deformation in each principal stress direction was, and the failure mode gradually changed from tensile failure to shear failure. With the increase in the load rate, \(\sigma_{1}\), \(\varepsilon_{v}\), \(\varepsilon_{2}\), and \(\varepsilon_{3}\) decreased when sandstone was destroyed. The expansion point was advanced, but the expansion capacity increased. The increase of \(\sigma_{2}\) could improve the strength of rock under a true triaxial environment. The lower loading and unloading rate could reduce the damage to the rock mass and improve the safety of the project. 3. Under true triaxial cyclic loading, the input energy and elastic energy of sandstone in each principal stress direction increased nonlinearly. Similar to the direction of intermediate principal stress, in the two other principal stress directions, the dissipated energy increased nonlinearly with the increase in cyclic loading. Compared with the input energy and elastic energy in the \(\sigma_{1}\) and \(\sigma_{3}\) directions, the input energy and elastic energy in the \(\sigma_{2}\) direction increased with the increase in \(\sigma_{2}\). On the basis of the definition of the energy parameters, an energy analysis method of true triaxial graded cyclic load was proposed, which has important guiding significance for the analysis of rock dynamic disasters. 4. With graded cyclic load \(\sigma_{1}\), the total dissipated energy of sandstone increased exponentially. Therefore, the damage variable equation was established by combining all the dissipated energies. The damage variable equation clearly described the damage evolution law of sandstone under different \(\sigma_{2}\) values. The larger \(\sigma_{2}\) was, the smaller the critical damage variable \(D_{c}\) was. Therefore, the damage of sandstone under repeated loading and unloading could be reduced by reducing \(\sigma_{2}\). Conceptualization, C.D. and C.F. ; methodology, C.F. ; software, C.D. ; validation, G.Z., X.L. and C.D. ; formal analysis, G.Z. ; investigation, R.Q. and C.F. ; resources, C.D. and G.Z. ; data curation, C.F. ; writing--original draft preparation, C.F. ; writing--review and editing, C.D. ; visualization, X.L. ; supervision, C.F. ; project administration, M.Q. ; funding acquisition, C.D.