## 4 Energy Dynamics in Sandstone Subjected to CLU
### Evolution of Energy in Sandstone during CLU Tests  
The energy density for each phase of the rock specimens was determined using the stress-strain data from CLU tests at varying confining pressures, following the energy calculation methodology outlined in Section 4.1. Based on these calculations, graphs illustrating the relationship between input energy and strain, dissipated energy and strain, and the ratio of energy dissipation to strain were created, using the strain at each cycle's unloading point as the \(x\)-axis. Furthermore, stress-strain envelope curves were constructed for the CLU tests, utilizing the stress and strain values at the unloading points of each cycle, as depicted in Figure 8.  
Figure 8: \(Cont.\)  
Figure 7: Methodology for determining energy density in rock specimens in CLU tests. Figure 8 illustrates the following: (1) analogous to the conventional triaxial compression stress-strain profiles, the CLU stress-strain envelopes can also be categorized into five distinct stages: compaction stage I, elastic stage II, crack propagation stage III macroscopic failure stage IV, and residual stage V. This observation confirms the rock's ability to remember its deformation history [46; 47; 48]. The patterns of energy change in the rock specimens during triaxial CLU exhibit a peak-like shape, indicating a significant turning point in energy distribution. (2) Prior to attaining the maximum stress level, the total input energy, elastic strain energy, and dissipated energy all escalate with the increment in cycle number (or strain at the unloading point). Notably, the rise in elastic strain energy significantly surpasses that of dissipated energy. The slope of the elastic strain energy curve initially increases before declining. This phenomenon occurs as the rock samples predominantly store the input energy as elastic strain energy due to the continuous work performed by the external load in the pre-peak phase. The remaining energy is expended in compacting and closing micro-fractures, along with the propagation and merging of cracks within the rock samples. This demonstrates that the pre-peak phase of energy evolution in rock samples is characterized by energy accumulation, with the deformation primarily being elastic. As both the elastic strain energy and dissipated energy expand, the rock samples' capacity for energy storage and deformation diminishes, leading to failure. (3) Beyond the peak stress, there is a sharp decline in elastic strain energy coupled with a significant rise in dissipated energy (each curve exhibits a turning point). The peak elastic strain energy is reached just before peak stress, whereas the peak dissipated energy occurs after. This indicates that energy dissipation escalates continuously due to crack propagation and merging in the  
Figure 8: Envelopes of stress–strain and curves of energy density for rock samples subjected to triaxial CLU. rock samples around the peak stress (critical failure point), marking a significant alteration in their internal structure and a gradual loss of load-bearing capacity, leading to failure. Additionally, as cracks propagate and merge until a macroscopic fracture plane forms, the stored elastic strain energy in the rock is converted into other forms of energy, which are then dissipated and released, causing a significant reduction in elastic deformation energy and a substantial increase in dissipated energy. Figure 9 demonstrates that under various confining pressures, the patterns of energy density vs. strain curves for rock specimens exhibit similar trends. As depicted in Figure (a)a, the overall energy assimilated by the rock specimens escalates with every cycle of loading and unloading (axial strain) during the pre-peak phase, peaking at the stress's apex. This total energy intake reflects the rock's capacity to store strain energy. With an increase in confining pressure, rocks display a heightened ability to absorb energy.