## 3 Results  
### Energy Evolution  
By integrating the stress-strain curve, it is possible to calculate the input energy resulting from external forces acting upon the rock, the elastic energy stored within the rock, and the dissipated energy generated by rock damage. As shown in Figure 3, the input energy is represented by the area beneath the loading curve, while the elastic energy is represented by the area beneath the unloading curve, and the dissipated energy is represented by the area between the loading and unloading curves. Figure 3: Energy evolution relationship during loading and unloading test. Figure 2: The sandstone samples. By calculating the integral area of the stress-strain curve, the energy density of input energy, elastic energy, and dissipated energy for each loading and unloading cycle can be obtained. Under uniaxial conditions, the energy density only needs to be calculated based on the axial stress-strain curve. In the case of conventional triaxial loading, the dissipated energy can be obtained by subtracting the elastic energy in the axial and circumferential directions from the input energy, as expressed by Equation (1) below. It is assumed that positive external work is performed on the rock, while negative work is carried out by the rock on the external environment. \[A=W_{1}+W_{3}-U_{1}-U_{3} \tag{1}\]  
where \(A\) represents the dissipated energy; \(W_{1}\) represents the input energy in the axial direction; \(W_{3}\) represents the input energy in the circumferential direction; \(U_{1}\) represents the elastic energy in the axial direction; and \(U_{3}\) represents the elastic energy in the circumferential direction. The energy curves within the rock under various confining pressures are presented in Figure 4. The axial strain is plotted on the horizontal axis, while the energy density is depicted on the left vertical axis, and the axial stress is illustrated on the right vertical axis. The different colored dotted lines correspond to the three distinct energy curves, while the smooth curve represents the axial stress-strain relationship. From Figure 4, it can be observed that during the loading process under different confining pressures, the energy evolution within the rock exhibits distinct converging characteristics. In the initial compaction stage of the stress curve, the primary cracks and pores within the rock are compressed and closed, leading to a gradual increase in the input  
Figure 4: Energy density curves under different confining pressures (**(a)**: 5 MPa, **(b)**: 10 MPa, **(c)**: 20 MPa, **(d)**: 30 MPa). energy and corresponding elastic energy. Prior to the stress peak, the variation trend of rock elastic energy aligns roughly with the stress-strain trend of the rock, wherein the elastic energy undergoes an initial slow increase and then approximates a linear growth. In the elastic stage of the stress curve, the increased hardness of the rock enhances its energy storage capacity. The level of damage within the rock remains relatively low, resulting in minimal dissipated energy, with the external energy primarily being converted into elastic energy stored within the rock. Before yielding, when the rock is relatively intact, the energy from external forces is primarily transformed into elastic energy, which typically reaches its maximum value near the stress peak. After entering the post-peak softening stage of the rock loading process, cracks rapidly propagate and connect within the rock, leading to the rapid loss of overall integrity, with the rock mass being fragmented into multiple blocks. At this stage, interblock sliding occurs accompanied by distinct cracking sounds, and the elastic energy within the rock is rapidly released. Consequently, the stored elastic energy within the rock declines rapidly as the stress decreases, while the energy density of the dissipated energy gradually increases. In the residual stage of the stress curve, severe damage occurs within the rock due to the formation and propagation of primary cracks.