## 4 Test Result Analysis  
### Type I and Type II Failure Modes  
The general trend of each set of curves is consistent with the stress-strain curves. The rising section was in a smooth \"S\" shape, and the slope of the curve gradually increased. Then, the stress-strain curves showed a linear rise, with the rate of rise gradually decreasing as the peak stress approached. Near the peak, the specimens with prefabricated cracks produced a short-term flat cross-section, followed by a sharp decrease in specimen strength. Comparative results showed that the peak stresses were suppressed to varying degrees in all fracture groups, with Type IV fractures having the lowest peak stresses.  
There are two main types of cracks, tensile cracks and shear cracks, which are distinguished according to the direction of growth of the crack. Tensile cracks are cracks created along the axial direction when an axial force is applied to the specimen; shear cracks are cracks created perpendicular to the shear direction [21]. Cracks in between are defined as mixed tensile and shear cracks.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Materials** & **Rock-like Materials** & **Value** \\ \hline \multirow{4}{*}{Rock-like materials} & Poisson ratio & 0.238 \\  & Young’s modulus \(E\) (GPa) & 14.435 \\  & Uniaxial compressive strength, & 39.419 \\  & UCS (MPa) & \\ \hline \multirow{4}{*}{Particle parameters} & \(R\) (mm) & 0.6–0.9 \\  & Particle stiffness ratio (\(k^{n}/k^{s}\)) & 1.15 \\  & Particle friction & 1.6 \\ \hline \multirow{4}{*}{Parameters of simulated specimen} & Tensile strength \(\overline{\sigma}_{t}\) (MPa) & 39.6 \\  & Cohesion \(\overline{c}\) (MPa) & 39.6 \\  & Elastic modulus \(\overline{E}_{c}\) (MPa) & 18.7 \\  & Particle porosity & 0.04 \\  & Density & 2387 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experimental data and numerical simulation parameters for intact sample.  
Figure 5: Numerical simulation and experimental data comparison: (**a**) peak stress; (**b**) Young’s modulus.  
From the Type I stress-strain curve (Figure 6a), it can be seen: From point O to point a is the compaction stage of the original fracture of the specimen; from point a to point b, the curve grows linearly without micro-cracks (Figure 7a). In stage 2, after the curve passes through point b, the tensile crack starts from the lower edge of the specimen and gradually develops into a large-scale crack along the loading direction (Figure 7b). Unstable extension cracks were generated in stage 3 (Figure 7c), and mixed tensile-shear cracks began to appear. In stage 4, the crack width increases and continues to widen until it penetrates the entire specimen, and the specimen fails in strength (Figures 7d and 8). Type II: After the appearance of the two tips of the prefabricated cracks, the micro-cracks expand along the direction of maximum stress (vertically in this study) to form cracks on a macroscopic scale. The courses of the two cracks are approximately parallel (Figures 6b and 9b). The orientation of the two cracks changes abruptly near the edge (Figure 9c). The extension direction of the cracks tends to the near corner of the specimen. At the same time, the rock bridge between the prefabricated cracks breaks, and the two macroscopic cracks merge (Figures 9d and 10).  
Figure 8: Photographs and numerical simulation results of specimens at the end of loading (Type I): (**a**) experimental; (**b**) numerical.  
Figure 10: Photographs and numerical simulation results of specimens at the end of loading (Type II): (**a**) experimental; (**b**) numerical.  
Figure 9: The evolution of the principal strain field on the surface of Type II specimen: (**a**) Stage 1, (**b**) Stage 2; (**c**) Stage 3; and (**d**) Stage 4.