## 4 Energy Dynamics in Sandstone Subjected to CLU
### Energy Distribution in Sandstone during CLU Tests  
The degradation of rocks fundamentally pertains to a thermodynamic issue, encompassing the processes of energy uptake, conversion, and dispersion. Throughout testing, rocks adhere to the principle of energy conservation and thermodynamic laws under any form of loading. A higher density of elastic energy indicates a rock's superior capability for elastic deformation, while an increased density of dissipated energy reflects more extensive damage during deformation. Consequently, the damage and deformation behavior of rock specimens during testing can be deduced by evaluating the ratios of elastic and dissipated energy. Figures 10 and 11 display the progression curves of these energy ratios for rock specimens, correlating with stress and strain during CLU under triaxial conditions. The fraction of energy associated with elastic deformation in the CLU tests of rock samples primarily indicates their capacity for elastic deformation and energy storage. Conversely, the dissipated energy ratio indicates the degree of internal damage and plastic deformation under specific stress or strain levels. According to Figure 11, we observe that (1) the profiles of the dissipated energy ratios across different confining pressures  
Figure 11: Development of dissipated energy ratios in rock samples during triaxial CLU. Figure 10: Progression of elastic strain energy ratios in rock samples subjected to triaxial CLU. resemble a spoon shape. Initially, as the cycle count (and corresponding strain at each unloading point) rises, the ratio decreases linearly (phase I), transitions into a steady state (phase II) and then gradually climbs (phase III) and sharply escalates (phase IV) before finally reaching a plateau (phase V). On the other hand, the trajectory of the elastic strain energy ratio exhibits a reverse pattern. (2) During the initial stages of loading, particularly in the pre-peak phase, the dissipated energy ratio in rock samples surpasses the elastic strain energy ratio, fluctuating between 0.6 and 0.8 under varying confining pressures. This predominance of dissipated energy in the early loading stages is attributed to the compaction of the rock samples, where energy is consumed in compacting and sealing off pores and pre-existing micro-fractures. Consequently, the samples exhibit low rigidity and limited capacity for accumulating elastic strain energy, resulting in a higher dissipated energy ratio. As the loading cycles progress, the rock samples advance through the elastic and plastic deformation phases, with the elastic strain energy ratio initially rising linearly and then stabilizing between 0.2 and 0.8, depending on the confining pressure. This increase signifies the sealing of pores and tiny cracks under stress, enhancing the capacity for elastic energy storage and, by extension, the elastic strain energy ratio. At this juncture, energy dissipation from the closure of pores and micro-fractures diminishes, highlighting the primacy of elastic energy accumulation until the peak stress is reached. Elevated confining pressures are shown to augment the ratio of elastic strain energy at peak stress, indicating enhanced efficiency in energy storage and a bolstered capacity for energy accumulation in the rock samples. This elevation also mitigates crack propagation and coalescence, thereby reducing energy dissipation and release upon failure, As shown in Figure 12. (3) In the phase following the peak, the dissipated energy ratio near the peak stress point progressively increases with additional cycles. This is attributed to the propagation and coalescence of micro-cracks into fracture planes, leading to the instantaneous release of stored elastic strain energy and a sudden surge in dissipated energy, as evidenced by the sharp rise in the dissipated energy ratio. Following this, the ratio declines as a new equilibrium is established post-failure under the impact of confining pressure, stabilizing the rock samples.