## 3 Results and Discussion
### Effects on the AE and Failure Behavior
#### 3.4.2 Variation in Acoustic Properties and Damage Stress  
The acoustic profiles that were obtained from uniaxial compressive tests are shown in Figure 16. The deduction of F-T damage based on acoustic signals was divided into four stages following Figure 14[40], including (I) crack closure stage where some acoustic signals were recorded; (II) new cracks began to appear, showing an increase in acoustic signals; (III) interaction among cracks began to intensify, resulting in micro-cracks propagation and coalescence with lots of acoustic signals; and (IV) the appearance of macro-cracks led to unstable fracture propagation resulting in final failure. Figure 16 presents an obvious demarcation and a different variation in the AE-stress relationship of the sample with a  
Figure 14: The relationship between the AE signal and stress with rock deformation (after [39]). different amounts of FT cycles applied, indicating that the F-T damage has a vital effect on the fracture process of the tested samples, including micro-crack initiation, their coalescence, propagation, and eventually macro-cracks formation. Consequently, the tested samples exhibited different deformation behavior under loading with the variation of the F-T damage. Here, it is necessary to point out that visible damage refers to the propagation of the macro-cracks. Besides, the crack germination stage (II) of the sample decreased with the increasing F-T action, while the macro-cracks damage zone (IV) widened with the increasing F-T cycles. As the compression progresses, the AE rate that was produced by the test samples decreased significantly due to the coalescence of micro-cracks in stage II [41]. When the samples entered the failure phase, the deformation changed from micro-cracks coalescence to micro-cracks propagation, forming macro-cracks damage zones, while the AE rate showed a dramatic increase. The extent of F-T damage dramatically affected the macro-cracks generation and subsequent propagation. Therefore, these results proved that the F-T damage largely controls the AE behavior of the tested samples under uniaxial compressive loads. Figure 15: Relationship between the AE counts, cumulative AE counts, and the time of samples with different numbers of F-T cycles under uniaxial compression condition: (**a–d**) represent the tested samples that were subjected to 0, 5, 15, and 30 F-T cycles, respectively. Furthermore, the crack propagation of the sample under loading was varied with F-T cycles. The tested samples without F-T damage showed an obvious elastic deformation (II) process and prolonged the initiation and coalescence of micro-cracks but limited micro-cracks propagation and macro-cracks initiation (Figure 16a). These results indicated that the samples in the fresh state require sufficient stress to provide energy for the micro-cracks propagation before the failure, i.e., it is hard for micro-cracks of untreated samples to propagate due to the stability of the sample microstructure. However, with the increase of F-T action, the elastic deformation tended to decrease (II), while the propagation phase of the micro-cracks presented an increasing trend with a high AE rate before sample failure (III stage). This was probably due to the volumetric expansion that was introduced by the phase transformation of the water and ice in the cracks or pores [1]. These processes promoted the initiation and coalescence of micro-cracks, thereby reducing the energy that was provided by stress in the elastic deformation stage. As the study of [PERSON] et al. [22], the F-T action had a significant deterioration effect on the bonding strength of rocks. This conclusion strongly proved that the F-T damage caused a decrease of resistance to the micro-cracks growth under loading, thereby facilitating the micro-cracks to initiate and coalesce (stage II) effortlessly with less stress input, matching with Figure 16. At the same time, the deterioration of the bonding and particles in the samples promoted the micro-cracks initiation and propagation.