## 3 Results and Discussion
### The Stratification Effects of Rock's Splitting Characteristics
#### 3.1.2 Contribution of AE Characteristic Parameters
Under these conditions, the interactions between cracks become more complex, and the crack propagation speed increases, producing a higher proportion of high-frequency AE signals, thus increasing the proportion of high-frequency signals. The frequency distribution characteristics of the AE signals further validate the crack propagation features of bedded rock samples under different loading angles, as well as the variations in tensile strength, as described in Section 3.1.1. Figure 6: The proportion of high-frequency signals varies with the stratification number at \(\theta=0^{\circ}\). Figure 7: The proportion of high-frequency signals varies with the stratification angle. As previously discussed, the failure mode is significantly correlated with the stratification angle. However, there is no consensus regarding the relationship between the dominant frequency characteristics of AE signals and rock failure modes. [PERSON] et al. (2018) investigated the frequency characteristics of AE signals under three loading conditions: direct tension, Brazilian splitting, and uniaxial compression, finding that low-frequency AE signals originate from tensile fractures, while high-frequency signals stem from shear fractures. [PERSON] (2018) and [PERSON] (2019) concluded from their AE tests that tensile rupture in rock specimens generates higher-frequency AE signals, whereas shear fractures produce lower-frequency signals. To more accurately analyze the failure mechanisms of seismic sources, we generally examine two key AE parameters: the AF and RA. As shown in Figure 8, high AF values and low RA values are typically associated with tensile failure, while low AF values and high RA values correspond to shear failure. By observing the changes in the RA and AF values of the AE signals over time during the fracture process of this specimen, the characteristics of microcrack evolution during shear and tensile failure at different load levels are revealed. As shown in Figure 9, during the early elastic failure stage, both RA and AF values remain relatively stable, indicating that shear and tensile failures within the rock are relatively stable at this stage. Around 157 s, when the load level of the specimen approaches 90% of the maximum load (Pmax), the RA and AF values begin to change. Specifically, the RA value gradually decreases with fluctuations, while the AF value shows an upward trend. This indicates that, during the initiation and propagation of new cracks, a significant number of tensile cracks start to form. After the specimen reaches the peak load, the RA value rapidly increases, while the AF value quickly decreases. This phenomenon reflects that, during the fracture process, the coalescence of microcracks forms microcracks. The uneven stress at the crack tip causes the microcrack to change direction and propagate along the weak planes, resulting in the formation of a substantial number of shear cracks. Consequently, in the macroscopic failure stage, shear failures become more prevalent. When the number of acoustic emission (AE) signals is large, it becomes challenging to effectively observe the data distribution. In recent years, kernel density estimation (KDE), a non-parametric estimation method, has frequently been employed for data density estimation research. The KDE algorithm can be utilized to identify the concentration regions of RA and AF values during the fracture process. Furthermore, the primary advantage of  
Figure 8: Correlation of RA-AF values with fracture patterns. the KDE method lies in its enhanced capacity for data point visualization. The estimated value of the multivariate data density \(P(\text{z})\) is calculated using the following formula [40]:  
\[P(\text{z})=\frac{1}{m\hbar}\sum_{i=1}^{n}K(\frac{z-z_{i}}{h}) \tag{2}\]  
Prior to performing the KDE calculation, the original AE data for different stratification numbers and angles were screened to exclude data points where both the RA and AF values were zero, as these points do not provide useful information for analyzing fracture modes.