## 4 Acoustic Emission Characterization
### Spatio-Temporal Evolution of Acoustic Emission Rupture Instability  
RA - AF, as important parameters of acoustic emission, are often used to describe the crack pattern classification, and the cut line directly affects the division of the crack category. According to the relevant research, the cut line is taken as RA:AF = 1:100. They are given by:  
\[RA=\frac{T_{g}}{A} \tag{19}\]  
\[AF=\frac{C}{T_{p}} \tag{20}\]  
where T\({}_{g}\), T\({}_{p}\), and C denote the acoustic emission rise time, upper emission duration, and acoustic emission ring number, respectively.  
By applying Equations (19) and (20), \(RA\) and \(AF\) are calculated, with \(RA\) and \(AF\) denoting shear fractures and tensile fractures, respectively. Figure 13 presents the proportion of different types of cracks formed during the entire loading process of sandstone. Calculations reveal that shear cracks account for 44% of the total, while tensile cracks make up 56%. This indicates that more tensile cracks are generated during the entire loading process of sandstone, and the primary mode of failure is tensile rupture.  
Acoustic emission (AE) amplitude and AE energy can both reflect the degree of rock damage to a certain extent. Relevant studies have shown that there is a characteristic power law relationship between AE amplitude and energy. Referring to the calculation method of the Richter scale for earthquakes, the AE energy level can be taken as:  
\[E_{s}=lgE \tag{21}\]  
In the formula, E represents the acoustic emission energy.  
Figure 12: Relationship between load cycle rating and FR value.  
Figure 14 illustrates the changes in energy levels of shear and tensile cracks during the failure process of sandstone. From the figure, it can be observed that during the compaction stage of pre-existing microcracks, the energy level of shear cracks shows a certain upward trend, while the energy level of tensile cracks has almost no signal, indicating that shear cracks dominate during the compaction stage. As the material enters the linear elastic stage, there are no signals for either tensile or shear crack energy levels, suggesting no damage occurs in this phase. When entering the stable crack propagation stage, the energy level of tensile cracks begins to show signals, with some points reaching an energy level of 1.5, while the energy level of shear cracks is almost zero, indicating that tensile cracks dominate in this stage. In the unstable crack propagation stage, shear crack energy levels start to show signals but are lower compared to tensile crack energy levels, so tensile cracks still dominate. Upon reaching the peak stage, the energy level of shear cracks increases dramatically, with the highest level reaching 4, while the energy level of tensile cracks is lower and the number of signals is also lower. Concurrently, experiments have found that multiple shear fracture surfaces occur at the moment of failure, with shear cracks dominating. From these observations, it is found that before failure, the energy level is almost below 2, but at the time of failure, the energy level reaches 4. Therefore, this phenomenon can be used as a precursor to rock failure.  
Figure 13: Percentage of cracks. (AF denotes tensile cracking; RA denotes shear cracking).