## 3 Results and Discussion
### Effects on the AE and Failure Behavior
#### 3.4.2 Variation in Acoustic Properties and Damage Stress
These microstructures then produced sliding friction under loading, resulting in increased energy consumption that was manifested in the extension  
Figure 16: The relationship between the AE behavior and the stress of samples with different F-T cycles under uniaxial compression conditions: (**a–d**) represent the samples that were subjected to 0, 5, 15, and 30 F-T cycles, respectively. of the III and IV stages. Additionally, the generation of friction between the cement and particles well explained the increasing AE rate. The cumulative AE parameters against stress values under loading are shown in Figure 17. With increasing F-T damage, the AE signals showed a continuous transition during loading, corresponding to the different stages of crack development. The cumulative AE rates increased with increasing F-T damage, except in the pre-peak stage. This is due to the fact that F-T damage changes the brittleness of the rock and prolongs the macroscopic crack failure phase before the peak. To better understand the variations in the AE behavior of the samples as a result of F-T action, the normalized stress values were plotted against the normalized cumulative AE rate. This plot provided helpful insight into identifying the stress levels at which fracturing changes due to F-T damage. Figure 17b showed that the acoustic properties of all the samples under F-T action follow an identical pattern. This indicated that the fracture tendency shifts at 70% to 95% of the peak stress. In addition, F-T damage led to early crack development. All the tested samples exhibited drastic AE rates in the initial stage, which gradually decreased after reaching the crack extension stress. To determine the effect of F-T damage on the crack development of the sample during loading, the point of AE transition was chosen as the stress threshold for crack development according to Figure 14, as shown in Figure 18.  
As [PERSON] et al. [38] reported, the stress threshold was helpful to determine the onset, coalescence, and propagation of the micro-cracks in rocks. Therefore, this study focused on the stress threshold of the sandstone in each deformation stage by analyzing the change  
Figure 17: Changes in the acoustic behavior and stress with different F-T cycles. (**a**) Stress; (**b**) Normalized stress. Figure 18: Acoustic behavior of the sandstone that was subjected to different F–T action. (**a**) Micro-cracks; (**b**) Macro-cracks. of AE behavior with the F-T cycles. At the same time, the stress threshold values were normalized by the peak stress to better understand the effect of F-T damage on them. Figure 18 shows the stress threshold values corresponding to each shift point in the loading process. From that, with the increase of F-T damage, the stress threshold for micro-cracks propagation and micro-cracks initiation decreased obviously. For example, the normalized stress threshold for micro-cracks propagation decreased from 0.734 (20.73 MPa) to 0.348 (5.04 MPa) after 30 F-T cycles. Also, the normalized stress threshold for macro-cracks initiation dropped from 0.932 (26.3 MPa) to 0.708 (9.8 MPa) after 30 F-T cycles. These phenomena indicated that micro-cracks appeared in rocks even under low-stress inputs with the increase of F-T damage, resulting in reducing the load-bearing capacity and strength. The strength can be considered as the result of the particle, bonding strength, and the particle chimeric action. However, with more F-T treatment, the stress-strain curves witnessed a diminishing trend of peak stress, signifying the deterioration of the mineral particle strength and bonding among minerals. Meanwhile, this degradation of strength can be considered as a change in rock brittleness on the stress-strain curve. [PERSON] et al. [32] believed that this change indicated that the rocks absorbed more energy before failure.