## 4 Discussion
### Discussion on the Characteristic of Different Fracture Modes of Granite Samples  
As an effective means of damage assessment, AE is often combined with resistivity, electromagnetic radiation, ultrasonic and other non-destructive testing methods to evaluate the damage of structures and materials. There are two main ways to judge the crack type: firstly, the parameter method,i.e., judging the internal fracture mode of the sample in accordance with RA value and AF value (RA = rising time/amplitude, AF = ringing count/duration). Studies indicate that AE signals with low AF and high RA values usually represent the generation or development of shear cracks, while high AF and low RA values represent the generation or development of tensile cracks. Secondly, quantitative inversion of moment tensor, i.e., achieving the properties, volume, spatial orientation and other parameters of the micro-crack after solving moment tenser by the first wave amplitude of six different spatial position sensors. However, this method is relatively complex due to involvement of the calibration test or deconvolution process of the sensor before the experiment as well as containment of the solution of the dynamic green functions. In this paper, the AE parameter method is used to study the relationship between the spatial distribution pattern of micro-cracks and its properties. Taking the pore rock as an example, the AE signal observation value during the rupture of the sample is shown in Figure 5, and the crack types over different spatial distributions according to the AE localization results are shown in Figure 6.  
It can be seen from Figure 5 that the fracture modes during the damage of the sample are tensile and shear composite crack and are mainly composed of tensile cracks. Take the right half of the hole rock as an example for analysis. As the stress increases, the crack spatial distribution is as shown in Figure 6. The tensile crack is indicated by a blue circle, and the shear crack is indicated by a red square. In the early stage of the loading failure process (the stress is less than 20% of the peak stress), the micro-cracks of the hole rocks are distributed in a dispersed manner, and the damage of the rock sample was weak. AE events were mainly caused by the closure of the original defects in the sample. With the increase of stress (about 60% of the peak stress), micro-cracks begin to appear around the prefabricated holes, indicating that stress concentration began to appear around the holes, and shear  
Figure 5: Distribution of AE parameters of RA versus AF. Figure 6: Spatial distribution of micro -cracks with an increase of stress. (**a**) 20% of tress; (**b**) 60% of stress; (**c**) 100% of stress. cracks began to appear above and around the holes, but tensile cracks still dominated at this time. With the increase of stress, the number of new shear cracks begin to increase and connect with each other and then gradually form macroscopic cracks. When the peak stress was reached, the connection between the old and new cracks led to the structural instability of the sample, which finally leads to macroscopic fractures appearing above and below the hole and penetrating the wall surface of the hole. Certainly, the change of resistivity value can be used as a monitoring method to evaluate the damage status of samples under load. The continuum damage mechanics model, fiber-bundle model, the time-dependent and stress-dependent model can also be established to quantify the damage and these theoretical results are consistent with the experimental results. [PERSON] et al. analysed the correlation between different modes of crack development and resistivity in the process of specimen damage by establishing a continuous damage mechanics model, and concluded that the relationship between damage and time is a power function, which provided theoretical support for the early warning of sample instability [21]. [PERSON] et al.