## 3 Analysis of Test Results
### Energy Characteristics  
There are numerous characteristic parameters associated with acoustic emission [22]. Due to the similarity in the patterns derived from experimental data, the acoustic emission  
Figure 8: Full stress–strain relationship under different burial depths and the same stress ratio: (a) \(\alpha_{2}/\alpha_{3}=1.2\); (b) \(\alpha_{2}/\alpha_{3}=1.4\); (c) \(\alpha_{2}/\alpha_{3}=1.6\); (d) \(\alpha_{2}/\alpha_{3}=1.8\). energy (ENE) for each stage preceding and succeeding the rock's peak strength has been identified and distinguished by [PERSON] et al. (2018). Additionally, the damage evolution characteristics of rock during compression failure are analyzed. The modified damage variable D is represented by both the acoustic emission event count and the cumulative event count, which are defined as follows:  
\[D=(1-\frac{\sigma_{\rm C}}{\sigma_{p}})\frac{C_{d}}{C_{0}} \tag{6}\]  
where D is the damage variable, C\({}_{\rm d}\) is the sum of acoustic emission counts in the whole process of rock compression failure, C\({}_{0}\) is the acoustic emission event count in the stage, \(\sigma_{\rm C}\) is the residual strength, and \(\sigma_{\rm P}\) is the peak intensity. The change trend of the damage variable curve in Figure 9 indicates that the damage process can be divided into four stages: initial damage stage (OA), stable damage development stage (AB), rapid damage development stage (BC), and damage failure stage (CD). It corresponds to the steady, slow increasing, active, and attenuation phases of acoustic emission energy, respectively. OA stage: during this initial compaction phase, small cracks and dense voids within the rock are progressively compressed and merged. Consequently, micro-cracks and fissures become scarce, leading to sparse acoustic emission signals and low acoustic emission energy. Only a minimal amount of elastic waves are released, resulting in a low damage variable for the rock. AB stage: this stage marks the end of rock compaction and transitions into the elastic deformation phase. Numerous large new cracks appear locally within the rock sample, leading to significant accumulation of strain energy. As this energy is released, there is a gradual increase in acoustic emission energy and a further increase in auditory emission activity. BC stage: as the rock progresses into the stable fracture stage, continuous axial pressure induces the formation of many new cracks, alongside the expansion of existing ones. Rock particles within the failure zone are compacted and abraded under axial load, causing local failure zones to converge and create a macro-fracture surface. This interaction between cracks intensifies, leading to rapid increases in both acoustic emission counts and energy. Shortly after the macroscopic failure of the rock samples, acoustic emission energy peaks. During this stage, the loading exceeds the rock's damage threshold, causing acoustic emission events to escalate rapidly and the rate of sandstone damage to accelerate. CD stage: upon entering the residual plastic flow stage, the rock sample retains a certain level of bearing capacity, despite the confining pressure. Increased axial load continues to induce numerous secondary cracks, in addition to significant primary fissures. At this juncture, the damage variable value reaches 1. Observational insights from Figure 9: the peak in acoustic emission energy from red sandstone slightly lags behind the macroscopic failure time of the rock samples. This delay suggests that confining pressure helps mitigate the failure of rock by enhancing micro-element strength and stiffness and reducing crack sliding. Not only does this improve the rock's failure strength but also boosts its post-peak bearing capacity. The variation in horizontal stress differences further influences the deflection stress of the material. According to the cohesive crack model, extensive damage at the crack tip correlates with increased accumulated energy from crack initiation to failure.