# Triaxial Loading and Unloading Tests on Dry and Saturated Sandstone Specimens
## 3 Results
### Energy Evolution of Rock Failure
Meanwhile, since the rock is still under the effect of axial loading in this stage, the energy is still absorbed from the test machine. The absorbed energy is mainly converted into \(U_{d}\), which is used for the development and expansion of micro-cracks within the rock. When reaching the failure point (C'), \(U_{d}\) and circumferential strain energy (\(U_{3}\)) grow rapidly, and the stress-time curve falls down immediately. At this moment, \(U_{e}\) releases rapidly because of the propagation of rock cracks. Following the point C', almost all of the releasable strain energy is released. Meanwhile, \(U_{d}\) and \(U_{3}\) increase to the maximum value. Finally, the rock specimen fails violently due to the unloading of confining pressure. Undoubtedly, there are some differences in the energy evolution laws of the rocks under different confining pressure conditions, particularly in the elastic deformation stage in triaxial loading and unloading process. During the elastic deformation stage, the curves of \(U\) and \(U_{e}\) almost overlap when the rock specimen is under low initial confining pressure, and almost all of the absorbed energy is converted into \(U_{e}\). However, when the rock is under high initial confining pressure, the curves of \(U\) and \(U_{e}\) begin to separate, and the absorbed energy is basically stored as \(U_{e}\), and partially converted as \(U_{d}\). It is manifested that the internal damage has occurred earlier under the high initial confining pressure conditions, and the internal micro-cracks of rock begin to develop and propagate during the elastic deformation stage. Especially for the saturated sandstone under high initial confining pressures, the curves of \(U\) and \(U_{e}\) separate significantly in Figure 9h, which signifies that the water effect on rock energy evolution are nonnegligible, and it has a significant influence on the deformation and failure process of rock under high initial confining pressures. In addition, the curves separate at the point where the axial stress is about 80% of the peak strength for low initial confining pressure condition, while the curves separate at the point where the axial stress is about 60% of the peak strength under high initial confining pressure. It also indicates that the internal damage and micro-cracks develop earlier under high initial confining pressure than that under low confining pressure conditions. The dissipation of energy leads to the development and propagation of internal cracks, which is the main reason of rock failure. It has been proved that the use of \(U_{d}\)/\(U\) is more favorable to analyze rock deformation and failure process instead of dissipative strain energy (\(U_{d}\)) [25; 43]. The variation curves of \(U_{d}\)/\(U\) with the loading time under different confining pressures are shown in Figure 10.  
Figure 9: Typical strain energy and axial stress time curves: (**a**) TC-D-10; (**b**) TC-D-40; (**c**) TC-S-10; (**d**) TC-S-40; (**e**) TU-D-10; (**f**) TU-D-40; (**g**) TU-S-10; (**h**) TU-S-40. The \(U_{d}\)/\(U\) exhibits some typical evolution stages as shown in Figure 10. In the conventional triaxial compression test, it increases initially, then decreases, and then increases slowly; finally, it increases rapidly at the failure stage of the rock. However, the curve increases initially, and then it decreases to a nearly smooth platform; finally, it increases sharply in unloading tests. During the failure stage, the elastic strain energy accumulated within the rock releases instantaneously, prompting rock fractures and damages. Meanwhile, it has been testified that the faster dissipation of rock energy causes the crack to propagate and penetrate faster, and then the failure of the rock occurs more suddenly [42; 44]. In the conventional triaxial compression test, the energy dissipation curve increases along a skew line, showing a gradual increase trend.