## 3 Results and Discussion
### Fracture Failure Process Analysis Subjected to F-T Conditions
#### 3.2.2 Fracture Failure Process Analysis Based on AE Signal Indirect Parameters  
Based on the correlation between the indirect parameters including average frequency (AF) and rise angle (RA), the fracture failure modes are classified and are calculated by the following equations:  
\[\text{AF}=\text{counts/duration}, \tag{1}\]  
\[\text{RA}=\text{Rise time/Amplitude} \tag{2}\]  
According to the comparative analysis between AF and RA, there are two kinds of fracture failure modes, i.e., the smaller RA and larger AF represent the tensile crack, and the larger RA and smaller AF indicate the shear crack, which is shown in Figure 7.  
Figure 6: _Cont_.  
Figure 8 illustrates the relations between cumulative RA and AF values for bitumen specimens subjected to F-T conditions during the whole stage of compression load. The clustering center of the shear as well as the tensile cracks can be obtained by using the  
Figure 6: The AE direct parameters (amplitude and count) versus tensile load level for asphalt mixture subjected to F-T conditions: **(a)** AE amplitude/count vs. load level under 0 cycle; **(b)** AE amplitude/count vs. load level under 3 cycles; **(c)** AE amplitude/count vs. load level under 9 cycles; **(d)** AE amplitude/count vs. load level under 15 cycles; **(e)** AE amplitude/count vs. load level under 21 cycles.  
Figure 7: The crack classification based on RA and AF.  
hierarchical cluster method. As the F-T condition continues, the failure mode of the bitumen specimens is mainly shear crack, in which the F-T condition continues; these data points of shear cracks successively account for 66.65%, 63.39%, 61.22%, 59.78%, 58.47%, 54.92%. 52.69% and 52.47% of the asphalt mixture. Based on the clustering algorithm, the cluster centroids of shear cracks and tensile cracks of the asphalt mixture present a certain decreasing tendency with F-T cycles. Therefore, under the effect of compression load, in the F-T pre-treatment, compression failure for the bitumen mix is mainly the shear failure mode. As the F-T condition continues, the failure mode changes to the combined effect of shear and tensile cracks. These findings are consistent with that of [PERSON] et al. [24].  
Figure 8: \(Cont.\)  
2. Tensile fracture failure analysis under F-T conditions  
Figure 9 illustrates the relations between cumulative RA and AF values for bitumen specimens subjected to F-T conditions during the whole stage of tensile load. The cluster centroids of the shear and the tensile cracks are also calculated using the hierarchical cluster algorithm. The cluster centroids of shear cracks and tensile cracks present a certain decreasing tendency with the F-T condition. The failure mode of the asphalt mixture specimens is still mainly a shear crack. As the F-T condition continues, these data points of shear cracks successively account for 78.16 to 58.13% of asphalt mixture. As the F-T condition continues, the failure mode is changed from shear failure to shear and tension modes. These findings could provide an explanation for the fracture failure of asphalt mixture, contributing to the existing state of the art.  
Figure 8: Compressive fracture mode classification based on the AE indirect parameters for asphalt mixture subjected to F-T conditions: (**a**) 0 cycle; (**b**) 3 cycles; (**c**) 6 cycles; (**d**) 9 cycles; (**e**) 12 cycles; (**f**) 15 cycle; (**g**) 18 cycles; (**h**) 21 cycles.  
Figure 9: _Cont._