## 3 Sandstone Energy Analysis
### Energy Density Analysis  
Based on the conventional triaxial compression test results of sandstone under different confining pressures, the change curves of the input energy, elastic strain energy, and dissipative energy densities of the sandstone with the axial strain were obtained according to Equation (5) and the results are shown in Figure 5.  
It can be observed from Figure 5 that under different confining pressures, the trends of changes in the sandstone input energy, elastic strain energy, and dissipative energy densities with the axial strain are the same. The input energy density always increased throughout the deformation and failure processes of the sandstone because, throughout the experimental process, the system always loaded the sandstone and continuously input energy into it. The elastic strain energy density increased gradually in the pre-peak stage, and the value was close to the input energy density, which indicates that the pre-peak input energy transformed into elastic strain energy and was stored in the sample. After the sandstone underwent failure, the elastic strain energy density decreased sharply, and the elastic strain energy stored before the peak was released rapidly. The dissipative energy density was extremely low in the pre-peak stage, whereas it increased sharply in the post-peak stage. The energy density curve shows that the accumulation of elastic strain energy was the main factor before the deformation and failure of sandstone, and this component of the energy was the driving force for the failure of the samples. Each sample had an elastic strain energy storage limit; when the amount of input energy that was converted into elastic strain energy exceeded this limit, the sample could no longer store energy and was damaged. Energy dissipation is the main form of sandstone failure. Most of the input energy of the external force was dissipated rapidly by crack initiation, propagation, coalescence, and friction on the fracture surface, resulting in a sharp increase in the post-peak dissipated energy density with strain and a continuous decrease in the elastic strain energy density. From the perspective of mechanics, the failure of sandstone was caused by the external load exceeding the compressive strength of the sample itself, while from the perspective of energy, it was caused by the fact that the elastic strain energy accumulated in the test system inside the sandstone sample exceeded its storage limit.  
The relationship between the confining pressure and peak input energy density U\({}_{FP}\) is shown in Figure 6. As shown in the figure, the peak input energy density U\({}_{FP}\) increased with increasing confining pressure. When the confining pressure was 0, 5, 10, 15, 20, and 25 MPa, U\({}_{FP}\) increased from 0.1507, 0.2081, 0.2619, 0.3364, and 0.4517 MJ/m\({}^{3}\) to 0.4917 MJ/m\({}^{3}\), respectively. The increases were 38.81%, 25.85%, 28.44%, 34.27%, and 8.86%, respectively. The U\({}_{FP}\) under a confining pressure of 25 MPa was 3.26 times that under uniaxial compression. This is because the larger the confining pressure is, the stronger the ability of sandstone to resist damage and deformation; thus, more energy must be absorbed when a failure occurs.