## 2 Materials and Methods
### Testing Procedure for Intact and Pre-Cracked Brazilian Disk Specimens  
The experimental setup and loading schematic are shown in Figure 2. The tensile tests on the layered rock were performed using the WHY-300/10 microcomputer-controlled loading system (Shanghai Hualong Testing Instrument Co., Ltd., Shanghai, China). This apparatus features a dual-channel, dual-sensor configuration, with a test force capacity of 300 kN in the primary channel and 10 kN in the secondary channel, maintaining a relative error within 1%. To comprehensively capture the entire process of crack initiation and propagation, the loading rate for the specimens was set at a low rate of 0.12 mm/min. The PCI-2 AE monitoring system produced by the PAC company was used to collect AE signals during the rock fracture process (Physical Acoustics Corporation, Princeton, NJ, USA). Two MINI-30 AE sensors (each with a diameter and height of 9 mm) were symmetrically fixed on both sides of the loading direction (Physical Acoustics Corporation, Princeton, NJ, USA). These sensors have a detection frequency range of 125-750 kHz and a resonant frequency of 300 (\(\pm\)10%) kHz, which can better collect the AE signals of granite's fracture process. The pre-amplifier gain and threshold value of the AE system were set to 40 dB, with a sampling rate of 10 Msps and a sampling length of 5 kb. The waveform definition parameters for PDT, HDT, and HLT were set to 50 \(\upmu\)s, 200 \(\upmu\)s, and 300 \(\upmu\)s, respectively [33]. During the experiment, the sensors were attached to both sides of the specimen in the loading direction. To ensure good contact between the sensors and the loading boards, petroleum jelly was applied to the contact areas. Additionally, to obtain the displacement and strain fields around the initial crack tip region, a high-definition camera was used to capture scatter images of the rock specimens' surface, with an image resolution of 4090 \(\times\) 3000 and a sampling rate of 6 Hz.  
To study the stratification effects in layered rocks during the Brazilian splitting test, the tests were conducted at different stratification loading angles of 0\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), and 90\({}^{\circ}\), with the number of layers being 1, 2, 3, 4, and 5. The loading schematic is shown in Figure 3. Three replicates were selected for each group of specimens, and the sandstone specimens were set as the control group. Each specimen without prefabricated cracks was named \"stratification number-loading angle-1/2/3\", and each specimen with prefabricated cracks was named \"Y stratification number-loading angle-1/2/3\". For the 90\({}^{\circ}\) inclination angle, the loading of layered disk specimens without prefabricated cracks was conducted in two forms: through the stratification plane, and not through the stratification plane, so only one-layer and four-layer specimens were selected as typical specimens for the 90\({}^{\circ}\) inclination angle.  
\begin{table}
\begin{tabular}{c c c} \hline
**Rock Type** & **Specimen Size/mm** & **Quantities** \\ \hline  & 250 \(\times\) 240 \(\times\) 30 & 20 \\  & 250 \(\times\) 240 \(\times\) 18 & 2 \\ Green sandstone & 250 \(\times\) 240 \(\times\) 12.5 & 4 \\  & 250 \(\times\) 240 \(\times\) 10 & 6 \\  & 250 \(\times\) 240 \(\times\) 8.5 & 8 \\ \hline \end{tabular}
\end{table}
Table 1: Size and number of rock cube flakes.