## 1 Introduction  
Practical engineering experience demonstrates that rock masses in intricate stress environments often undergo cyclic loading and unloading (CLU) phenomena, stemming from excavation-induced disturbances within deep geochemical undertakings, such as coal mining, the development of pumped hydroelectric energy storage facilities, and the excavation of underground caverns. These occurrences are common and have been documented in various studies and projects [1; 2; 3; 4]. This gives rise to problems pertaining to surrounding rock stability and causes severe engineering disasters [5; 6; 7; 8]. From a mechanical perspective, natural rocks possess numerous defects, including primary microcracks. Deformation and failure under load occur through a process whereby the localized rupture of microcracks propagates and eventually leads to a through-break failure along the rupture surface. This progression results in the catastrophic instability of the surrounding rock mass. The rock failure mode during this process is intrinsically linked to energy conversion and reflects a state instability phenomenon driven by energy [9; 10]. Consequently, investigating the patterns of the progression of energy and deterioration in geological materials subjected to cyclic loading holds crucial practical value for mitigating disasters during the construction and maintenance of underground infrastructure. Currently, researchers from both China and the international community have effectively analyzed patterns of rock damage through an energy-centric perspective. (1) Investigations into the development of energy and the process of failure in geological materials subjected to single-axis pressure environments include the following: [PERSON] et al. [11] examined how energy is dissipated and transformed during uniaxial CLU, focusing on the significance of elastic deformation energy in causing rock failure. [PERSON] et al. [12] investigated the patterns of energy build-up and release in rocks under similar conditions, delving into the stress-strain dynamics and acoustic emission (AE) traits of the samples throughout their deformation and breaking point. Through uniaxial compression experiments, [PERSON] et al. [13] investigated the behavior of energy transformations within rocks, establishing a clear connection between the pace of energy dissipation and the rock's durability. [PERSON] et al. [14] merged practical uniaxial compression tests with computational simulations to investigate how energy shifts and morphs during episodes of strain bursts within coal-rock mixtures. [PERSON] et al. [15] assessed how the ratio of height to diameter in rocks impacts the storage and release of energy during uniaxial cyclic stress, in addition to examining its effect on compressive strength, deformation behaviors, and modes of failure. [PERSON] et al. [16; 17] investigated how varying rates of loading influence the patterns of energy change and the failure properties of rocks subjected to unconfined compression. [PERSON] et al. [18] utilized X-ray computerized tomography (CT) imaging to track the changes in microstructural features and pore dynamics in rock samples under unconfined pressure, identifying a link between the rate of energy dissipation and the magnitude of the external force applied. (2) Investigations into the progression of energy and the breakdown process in rocks under triaxial stress conditions include the following: [PERSON] et al. [19] explored how rock brittleness correlates with its energy development under varying confining pressures. [PERSON] et al. [20] executed triaxial load and unload experiments on marble to observe the energy changes during deformation, formulating a non-linear model for rock energy evolution. [PERSON] et al. [21] delved into the mechanical behaviors and energy shifts in sandstone, particularly during the unloading phase under various initial confining pressures. [PERSON] et al.