## 3 Results and Analysis
### Acoustic Emission Analysis  
During the compression process of rock-like materials, the change in the internal structure of the materials will release elastic waves of different frequencies and different energies, which is called rock-like acoustic emission [31]. By monitoring the acoustic emission parameters of rock-like specimens throughout the compression process, a clearer understanding can be gained regarding the initiation and propagation of cracks within these specimens, thereby enhancing comprehension of the entire rock failure mechanism [32; 33; 34]. The acoustic emission ringing count refers to the number of oscillations of the acoustic emission signal exceeding the threshold value signal, which can be divided into ringing count and cumulative ringing count. Acoustic emission ringing count can reflect the intensity and frequency of the signal, which is widely used in the evaluation of acoustic emission activity. The schematic diagram of the acoustic emission ringing count principle is shown in Figure 8.  
The relationship curves of the acoustic emission ringing count, cumulative ringing count, stress, and time during the loading process of rock-like specimens with different proportions are depicted in Figure 9.  
Figure 8: Schematic diagram of the acoustic emission ringing count principle. Figure 9: Acoustic emission ringing count, cumulative ringing count, stress, and time curve. A1–C4 are the numbers of rock-like specimens. I–IV is the four stages of changing the cumulative ringing count curve of acoustic emission. The analysis in Figure 9 revealed that the variation patterns of the acoustic emission ringing count and cumulative ringing count of rock-like specimens with different proportions exhibited certain similarities. In the initial compaction stage, the original pores and cracks in the specimen underwent compaction without any generation of new cracks. Consequently, a minimal number of acoustic emission events were observed during this stage, and no major acoustic emission events occurred. With the continuous increase in stress, the material entered the elastic stage, and new micro-cracks were generated inside the material. At this time, loud emission events occasionally occurred, and the frequency of acoustic emission events in this stage was higher than that in the initial compaction stage. As the loading continued, the rock-like specimen entered the damage stage, and an obvious acoustic emission phenomenon appeared in this stage. During this period, as stress continued to increase, the pores and cracks within the specimen gradually interconnected and merged, leading to frequent occurrences of acoustic emission events. When loaded near the stress peak of the material, a large energy event was generated, and the acoustic emission ringing count reached its maximum. The maximum value of the acoustic emission ringing count usually did not occur at the peak stress point of the specimen, and often lagged behind the peak stress point for a while. The specimen eventually entered the post-failure stage, wherein it retained a certain residual strength, maintained its bearing capacity, and still produced acoustic emission events. Without the addition of gypsum, the rock-like specimens exhibited rapid failure, followed by a sharp decrease in stress after reaching the peak of the stress-strain curve, and there was a low occurrence rate of large acoustic emission events during the post-failure stage. The maximum acoustic emission ringing counts of specimens A1-A4 were 14,101, 15,672, 18,771, and 22,569 times, respectively. The maximum acoustic emission ringing counts of specimens C1-C4 were 7164, 8329, 9642, and 11,109 times, respectively. It was found that the maximum value of the acoustic emission ringing counts was positively correlated with the cement content in the specimen. The maximum acoustic emission ringing counts of specimens B1-B4 were 14,140, 12,072, 10,800, and 7164 times, respectively.