## 4 Test Result
### Mechanical Characteristic Analysis  
#### 4.2.1 Influence of Crack Angle on Cracking Characteristics  
Figure 7 depicts the influence of variations in fracture inclination angle on the crack initiation sequence and propagation pattern in the specimen. As shown in Figure 7a, when the fracture inclination angle is 0\({}^{\circ}\), the first crack (Crack 1) initiates at a certain distance to the left of the upper part of the fracture. While Crack 1 propagates along the loading direction, Crack 2 initiates at the same distance below the fracture, Crack 3 initiates at a certain distance below the lower right end of elliptical hole 2, Crack 4 initiates at a certain  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Materials** & **Parameters** & **Value** \\ \hline \multirow{4}{*}{Solid elements} & Density/kg\(\cdot\)m\({}^{-3}\) & 2500 \\  & [PERSON]’s modulus/GPa & 15 \\  & Poisson’s ratio & 0.3 \\  & \(K_{n0}/\)GPa\(\cdot\)mm\({}^{-1}\) & 15 \\  & \(K_{s0}/\)GPa\(\cdot\)mm\({}^{-1}\) & 5.28 \\  & \(K_{t0}/\)GPa\(\cdot\)mm\({}^{-1}\) & 5.28 \\  & \(t_{n}/\)MPa & 5.5 \\  & \(t_{n}/\)MPa & 20 \\  & \(t_{t}/\)MPa & 20 \\  & Model-I fracture energy/N/mm & 0.055 \\  & Model-II fracture energy N/mm & 0.16 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters applied in the model.  
Figure 5: Embedding of zero-thickness cohesive elements for the Brazilian model.  
distance above the upper left end of elliptical hole 2, Crack 5 initiates at a certain distance below the lower right end of elliptical hole 1, and Crack 6 initiates at a certain distance above the upper left end of elliptical hole 1. As the external load increases, Cracks 1, 2, 3, 4, 5, and 6 all propagate radially. The cracks continue to expand and intersect, and the specimen enters a stage of crack coalescence. Ultimately, the fracture becomes fully connected, and local closure occurs between Crack 1 and Crack 2, leading to failure of the specimen.  
As shown in Figure 7b, when the fracture inclination angle is 15\({}^{\circ}\), the initiation points of Cracks 1 and 2 shift to the right and left, respectively. Ultimately, no closure of the fracture is observed.  
Figure 7c illustrates that when the fracture inclination angle is 60\({}^{\circ}\), the initiation points of Cracks 1 and 2 shift to the left and right ends of the fracture, and the initiation points of Cracks 3, 4, and 5 also change. For example, Crack 3 initiates at a certain distance below the lower right end of elliptical hole 1. Again, no closure of the fracture is observed.  
Figure 6: Evolution process of cohesive elements:(**a**) Initial state(**b**) Crack initiation (**c**) Crack propagation (**d**) Crack propagation (**e**) Crack coalescence.  
Figure 7: _Cont._  
Figure 7d demonstrates that when the fracture inclination angle is 90\({}^{\circ}\), the initiation points of Cracks 1, 2, 3, 5, and 6 all change. For instance, Crack 6 initiates at a certain distance below the lower right end of elliptical hole 1, and Crack 2 initiates at a certain distance below the lower right end of elliptical hole 2. As the external load increases, Crack 5 barely propagates. Ultimately, no closure of the fracture is observed in this case as well.  
As observed in Figure 7e, when the fracture inclination angle reaches 150\({}^{\circ}\), the initiation points of Cracks 1, 2, 4, and 5 undergo changes. Specifically, Crack 4 initiates at a certain distance below the lower right end of elliptical cavity 1, while Crack 5 initiates at  
Figure 7: Effect of fissure angle on the fracture evolution of rock-like materials with hole-fissures under Brazilian tests: (**a**) fissure angle 0\({}^{\circ}\), (**b**) fissure angle 15\({}^{\circ}\), (**c**) fissure angle 60\({}^{\circ}\), (**d**) fissure angle 90\({}^{\circ}\), (**e**) fissure angle 150\({}^{\circ}\).  
a certain distance above the upper left end of elliptical cavity 2. Ultimately, the fracture exhibits an overall closure phenomenon.