## 3 Results and Discussion  
### The Stratification Effects of Rock's Splitting Characteristics  
#### 3.1.1 Tensile Strength and Failure Mode Analysis  
The tensile strength of the specimen can be expressed as follows:  
\[\sigma_{\text{t}}=\frac{2P_{\text{max}}}{\pi DB} \tag{1}\]  
Figure 3: Schematic diagram of loading with different stratification numbers and stratification angles (**upper** portion: intact specimens; **lower** portion: pre-cracked specimens).  
Figure 2: Tensile test system diagram.  
where \(\sigma_{\rm t}\) represents the tensile strength of the rock, \(B\) represents the specimen length(thickness), \(D\) represents the diameter, and \(P_{\rm max}\) represents the failure load.  
The experimental results, as shown in Figure 4, indicate that the number of stratification planes and the stratification angle significantly affect the tensile strength of the rock. Specifically, the tensile strength of layered rocks decreases with an increasing number of stratification planes. This is mainly because the weaker the stratification planes, the higher the probability of failure along these planes, leading to a gradual decrease in tensile strength. As the stratification angle increases, the failure mode of the rock transitions from internal matrix fracture to shear splitting along the stratification planes. The shear failure along the stratification planes mainly relies on the bonding strength of the dolomitic glue in the rock, which is relatively low. Therefore, with an increasing stratification angle, failure along the stratification planes becomes easier, resulting in a reduction in overall tensile strength.  
Table 2 shows the final failure modes of the layered rock specimens. It can be seen that the number of stratification planes has a relatively minor impact on the failure mode of the disks. The diversity in failure modes is mainly caused by the different angles of the stratification planes. The interactions between particles within the rock and the bonding strength between layers vary with the angle of the stratification planes relative to the loading direction, resulting in different failure behaviors.  
Based on the stress state, deformation characteristics, and crack morphology, the failure modes of layered rock can be categorized into four types: stratification tensile, stratification tensile-shear, matrix tensile, and matrix tensile-shear.  
* Stratification Tensile Type (\(\theta=90^{\circ}\)):  
When \(\theta=90^{\circ}\), the specimen typically splits along the central stratification plane into two halves. The opening of the stratification plane provides space for lateral deformation, resulting in the lowest tensile strength.
* Stratification Tensile-Shear Type (\(\theta=45^{\circ}\), \(60^{\circ}\)):  
When \(\theta\) is \(45^{\circ}\)or \(60^{\circ}\), the failure mode of the rock changes. The rock does not fully crack along the stratification plane, nor does it form continuous cracks through the upper and lower loading points. Instead, it splits by a crack at a certain angle to the stratification plane, but the angle of this crack is not fixed, with noticeable peeling of the stratification plane within the crack. The tensile strength slowly decreases as \(\theta\) increases within this range.  
Figure 4: Tensile strength for different stratification numbers and stratification angles.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Angle Type** & \(0^{\circ}\) & \(30^{\circ}\) & \(45^{\circ}\) & \(60^{\circ}\) \\ \hline One stratification & & \\ Two stratifications & & \\ Three stratifications & & \\ Four stratifications & & \\ Five stratifications & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Failure patterns of rock specimens with different stratification numbers and stratification angles.