## 2 Experimental Methodology
### Testing Procedure  
A triaxial rock mechanics test system was used to conduct both the DTT and BST, as shown in Figure 3a. The test set-up for DTT is shown in Figure 3b. A loading cylinder with a diameter of 25 mm was positioned at the upper end of the specimen, while an annular plate with a diameter of 120 mm and a high friction coefficient was placed at the lower end. To prevent specimen slippage during initial loading, a pre-loading force of 0.5 kN was applied. The test was then conducted in displacement control mode at a loading speed of 0.05 mm/min. To monitor damage in the DTT specimens during loading, a DS5 series full-information acoustic emission (AE) signal analyzer with a transmission speed of 10 M per channel was utilized. Three AE probes were attached to either side of the specimen and secured with fixers. Vaseline was applied to the fixers to minimize noise interference. The test set-up for BST were shown in Figure 3c,d. Flat loading platens were positioned at the upper and lower ends of the specimen. A pre-loading force of 0.5 kN was applied before the test began, and the test was conducted in displacement control mode at a loading speed of 0.1 mm/min. Due to the smaller size of the BST specimens and the relative simplicity of monitoring internal damage, only two AE probes were installed on the back of the specimen using fixers.  
Figure 3: Test set-up for DTT and BST. (**a**) Set-up for rock mechanics test system, (**b**) Set-up for DTT, (**c**) Set-up for BST, and (**d**) AE probe configuration for BTS.  
Figure 2: Specim preparation of BST with different loading angles. (**a**) Schematic diagram of shale coring, and (**b**) Typical shale specimen for BST.  
The direct tensile strength can be determined by the following equation [23]:  
\[\sigma_{\text{td}}=\frac{F}{A}=\frac{F}{\pi\Big{[}\Big{(}\frac{d_{2}}{2}\Big{)}^{ 2}-\Big{(}\frac{d_{1}+2b_{1}}{2}\Big{)}^{2}\Big{]}} \tag{1}\]  
where \(\sigma_{\text{td}}\) is the tensile determined by the DTT, MPa; \(F\) is the peak load, kN; \(d_{1}\) and \(b_{1}\) are the inner diameter and thickness of the annular slot drilled from the upper end of the specimen, mm; \(d_{2}\) is the inner diameter of the annular slot drilled from the lower end of the specimen, mm.  
The indirect tensile strength can be determined by the following equation:  
\[\sigma_{\text{ti-iso}}=\frac{2P}{\pi Dt} \tag{2}\]  
where \(\sigma_{\text{ti-iso}}\) is the isotropic tensile strength determined by the BST, MPa; \(P\) is the peak load, kN; \(D\) is the diameter of the Brazilian disk, mm; \(t\) is the thickness of the Brazilian disk, mm.  
It is important to note that although Equation (2) is commonly used to calculate the indirect tensile strength of rocks, it only considers the functional relationship between indirect tensile strength, peak load, specimen thickness, and diameter. It does not account for the influence of rock anisotropy. To address this limitation, [PERSON] and [PERSON] [24] proposed a new equation for calculating indirect tensile strength, which incorporates the effects of rock elastic anisotropy:  
\[\begin{array}{l}\sigma_{\text{ti-ani}}=\frac{2P}{\pi Dt}\Big{[}\big{(}E/E \prime\big{)}^{\frac{1}{4}\cos(2\beta)}-\frac{(b-1)\cos 4\beta}{4}\Big{]}\\ b=\frac{\sqrt{ET}}{2}\Big{(}\frac{1}{G}-\frac{2\pi\prime}{E\prime}\Big{)}\end{array} \tag{3}\]  
where \(\sigma_{\text{ti-ani}}\) is the anisotropic tensile strength determined by the BST, MPa; \(E\) is the elastic modulus parallel to the bedding plane, GPa; \(E^{\prime}\) is the elastic modulus perpendicular to the bedding plane, GPa; \(G^{\prime}\) is the shear modulus perpendicular to the bedding plane, GPa; \(v^{\prime}\) is the Poisson's ratio perpendicular to the bedding plane; \(\beta\) is the loading angle, (\({}^{\circ}\)). According to [PERSON] et al. [25], we set \(E\) = 20.53 GPa, \(E^{\prime}\) = 15.21 GPa, \(v\) = 0.17, \(v^{\prime}\) = 0.19, and \(G^{\prime}\) = 7.17 GPa.