## 4 Analysis Results and Discussion
### Failure Mechanism  
The ratio of risetime/amplitude (RA) and average frequency (AF) has been widely used for classifying the failure mechanism and crack mode in rock and concrete materials. Crack propagation in tensile mode corresponds to a high AF value and a low RA value. Conversely, a low AF value and a high RA value correspond to crack propagation in shear mode. When analyzing the RA-AF values of acoustic emission hits, outlier processing should be performed. The box plot outlier detection method can be considered, assuming that the raw data follow a normal distribution and filter out values that deviate more than three times from the mean. This method sequentially removes outliers in the RA and AF values. When analyzing the RA-AF values of acoustic emission events, it is necessary to consider the attenuation and dissipation effects of elastic waves during their propagation in the medium, which can affect the characteristic parameters of acoustic emission. It is recommended that the RA and AF values of acoustic emission events be determined by the RA and AF values of the initially triggered acoustic emission hits. In this study, the data collected by the acoustic emission monitoring system were filtered based on the criterion that a single event triggered at least 10 sensors. A total of 204 acoustic emission events were obtained through filtering. In the analysis, the overall micro-fracture analysis does not quantify the specific proportion of the two micro-fracture types using a transition line. Instead, the relative proportion of micro-crack types in the same mechanical environment is compared by analyzing the numerical differences in the RA-AF distribution. The results are shown in Figure 8a. As can be seen from the figure, the distribution range and density center of the RA values for the acoustic emission events in this experiment are 0-100 ms/V and 8 ms/V, respectively, while the distribution range and density center of the AF values are 0-140 kHz and 50 kHz, respectively. This shows that the cracks in this experiment are characterized by low RA values and relatively low AF values, or even moderate AF values, indicating that the cracks are mixed-mode cracks containing both tensile and shear components. The RA-AF relationship is more qualitative in understanding micro-fracture types through acoustic emission hits. Therefore, after using the RA-AF ratio to assess the differences in overall micro-fracture types during specimen failure, large amplitude acoustic emission events that contribute to the formation of dominant macroscopic cracks are selected. Considering the P-wave first motion polarity of each acoustic emission signal, the moment tensor inversion method is used to invert the source mechanism. This method allows for a deeper discussion of the differences in the main fracture types across the samples. [PERSON] et al. [31] defined [PERSON]'s function library for inverting the source mechanisms of mine microseismic events. They successfully inverted the source mechanisms of microseismic events induced by mining activities and distinguished between fault slip sources, mine pillar instability sources, and roof collapse sources based on the source mechanism solutions. In this section, the same method is applied to invert the source mechanisms of the dominant sample failures in the goat instability test using acoustic emission data. The results are then compared with DIC and RA-AF analysis results to analyze the relationship between macroscopic failure and microseismic source mechanisms. The moment tensor inversion results of the acoustic emission monitoring data are represented on a Hudson plot, as shown in Figure 8b. The source mechanism inversion results indicate that none of the 204 acoustic emission events are purely tensile or shear sources; all are mixed-type sources, which corresponds with the results from the RA-AF relationship.