# Laser Vibration Characteristics of Marble Specimens and Failure Criterion
## 3 Results
### Characteristics of AE Signals  
The parameter-based and waveform-based AE characteristics are plotted in Figure 3. The AE counts and cumulative AE counts curves are AE parameter characteristics, and the dominant frequency is AE waveform-based characteristics.  
Figure 2: Stress-strain relationship and failure mode of marble specimens in (a) Brazilian test and (b) uniaxial compression test.  
In Figure 3a, the AE activities in uniaxial compression experience gentle increase stage, quick increase stage, and rapid increase stage. In the gentle stage, the natural holes, cracks, and fissures are compressed as the axial compression stress is small. The AE counts are weak, and the cumulative AE count curves increase gently. As the axial compression stress increases, the AE activities gradually become intensive, and the cumulative AE counts curve quickly increases at 387.2 s, indicating unstable crack propagation. Unstable cracking forecasts the failure of marble specimens. Finally, the AE signals are notably released, and the cumulative AE counts curve sharply increases as the peak stress is achieved.  
In Figure 3b, the AE activities are weak in most of the loading process when the specimen is subjected to indirect tensile stress, and only the clam stage and sharp increase stage are identified. The released AE counts are relatively rare in the calm stage, and the cumulative AE counts curve starts to increase at 215.8 s, indicating unstable cracking behaviors.  
According to the statistical regularities of AE dominant frequency in this study, the AE dominant frequency higher than 200 kHz is high dominant frequency, while lower than 200 kHz is low dominant frequency. In the uniaxial compression test (Figure 3a), AE dominant frequency-intensive distributed in the low frequency band and dispersedly distributed in the high frequency band, while both low and high AE dominant frequencies became dense after 356.3 s. In the Brazilian tests (Figure 3b), the low AE dominant frequency distributes from initial loading to final failure of the specimen, while the high AE dominant frequency distributes from initial loading to final failure of the specimen.  
Figure 3: Evolution of AE and cumulative AE curves with time. (**a**) Uniaxial compression test; (**b**) Brazilian test.  
frequency major distributes around the failure moment, i.e., synchronous with the sour of cumulative AE counts curve at 215.8 s.  
On the one hand, the AE frequency characteristics can reveal the failure mechanism of rock. Compared Figure 3a,b, the tensile failure component is characterized by low dominant frequency AE signals, and the shear failure component is represented by high dominant frequency AE signals. This finding is consistent with [PERSON] et al. [28]. Combined with the failure morphologies in Figure 2, it can be concluded that the marble specimen in the Brazilian test failed due to tensile cracks. However, under uniaxial compression stress, tensile cracks are predominant, while shear cracks are control factors for its failure.  
On the other hand, forecasting the failure of rock mass with the AE method is related to the stress conditions. Under uniaxial compression stress, the occurrence of high AE dominant frequency is 30.9 s earlier than the sharp increase of cumulative AE counts (356.3 s and 387.2 s, respectively). However, the time advantage is not obvious for the specimen subjected to tensile stress, as the occurrence of high AE dominant frequency and the sharp increase of cumulative AE counts are synchronous. Cracks that develop quickly in brittle rock under tensile stress should be responsible for the difference.