## 3 Triaxial Cyclic Loading and Unloading Experiment on High-Strength Sandstone
### Energy Properties of Sandstone under Triaxial Cyclic Loading and Unloading
The elastic and dissipation energies of the samples were calculated using triaxial cyclic loading and unloading test stress-strain curves. The calculation of the energy density of the sample in cyclic loading and unloading at a certain stress level is shown in Figure 10. The elastic energy density \(U^{e}\) and dissipation energy density \(U^{d}\) are shown in Equation (9). \[\left. \begin{array}{l}U_{i}^{e}=\int_{\varepsilon_{i}^{d}}^{ \varepsilon_{i}}\sigma_{i}d\varepsilon_{i}\\ U_{i}^{d}=\int_{\varepsilon_{i}}^{\varepsilon_{i}}\sigma_{i}d\varepsilon_{i}- \int_{\varepsilon_{i}}^{\varepsilon_{i}^{d}}\sigma_{i}d\varepsilon_{i}\end{array} \right\} \tag{9}\]The cyclic loading count-energy density curve of the sample is shown in Figure 11. When the surrounding pressure of sandstone samples was kept constant, the total energy density \(U\), elastic energy density \(U^{e}\), and dissipation energy density \(U^{d}\) of the samples at the same level of cyclic loading and unloading phases showed an overall tendency to decrease with the increase in cycle count. From the dissipation energy density curve and the hysteresis loop area of the stress-strain curve, it can be concluded that there is energy loss in the sample during cyclic loading and unloading. The energy dissipation in a single cycle decreases with increasing cycle count. The total energy of the sample decreases significantly in the first four cycles. The energy density curves of the loaded sandstone samples are characterised by more pronounced stages. The dissipated energy in a single cycle of the sample increases as it enters the next higher stress level of the stress cycle. When analysed in conjunction with Figures 9 and 11, the energy density of the sample exhibits an aggregation of energy due to the incomplete unloading and small amplitude of the applied unloading stresses. Elastic energy occupies the main part. With the release of elastic energy and the increase in dissipation energy, the energy storage property of the sandstone sample decreases. The deformation of the loaded sandstone sample continues to increase until instability damage occurs. The total energy density, elastic energy density, and dissipated energy density curves of cyclically loaded samples at different surrounding pressures are shown in Figure 12. According to Figure 12a, the total energy density increases slowly with increasing cyclic stress levels at a surrounding pressure of 0 MPa. The increase in total energy density is more significant at a surrounding pressure of 20 MPa. In the first stage of the cycle, the total energy density was at a relatively low level for all surrounding pressure conditions. The total energy density at 0 MPa surrounding pressure is maintained at approximately 75 kJ/m\({}^{3}\), while the total energy density at 20 MPa surrounding pressure is close to approximately 262 kJ/m\({}^{3}\). During the third stage of cyclic loading, a significant increase in the total energy density for each surrounding pressure condition was observed. The sandstone samples showed the most significant increase in total energy density at 20 MPa surrounding pressure, with the total energy density increasing from approximately 300 kJ/m\({}^{3}\) to approximately 375 kJ/m\({}^{3}\). This shows that the energy absorption capacity of hard sandstone under higher surrounding pressure is significantly improved. According to Figure 12c, the dissipation energy densities of the hard sandstone samples in each surrounding pressure condition in the first cyclic loading and unloading stage at low stress levels fluctuate with the increase in cycle count. At 0 MPa surrounding pressure, the dissipation energy density of the samples fluctuated around 4.2 kJ/m\({}^{3}\), and at 20 MPa, the dissipation energy density fluctuated in a larger range (6.1 kJ/m\({}^{3}\)-16.5 kJ/m\({}^{3}\)). Significant peaks in dissipation energy density can be observed during the loading and unloading phases in the second stage of the cycle, especially at higher surrounding pressures (15 MPa\(\sim\)20 MPa).