# Study on Mechanism of Static Blasting-Induced Hard Rock Fracture Expansion
## 4 Numerical Simulation Analysis of Static Blasting Fracturing Influencing Factors
### Simulation Analysis of Cracking of Double-Hole Specimens with Different Influencing Factors  
#### 4.2.1 Influence of Pore Size on Specimen Cracking  
(1) Influence of pore size on crack expansion and rupture state of specimens  
Figure 22 illustrates the expansion fracture morphology and crack dispersion characteristics of double-hole specimens with different hole diameters. The crack areas of the four specimens are 23.6 mm\({}^{2}\), 38.7 mm\({}^{2}\), 46.2 mm\({}^{2}\), and 77.1 mm\({}^{2}\), respectively. This sequence indicates that the size of the hole diameter restricts the fracturing effect and the range of crack expansion, with a positive correlation between the hole diameter and the fracturing effect. As the hole diameter gradually increases, the fracture surface transitions from none to three blocks.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Particle Size** & **Density** & **Young’s Modulus** & **Coefficient of** **Friction** & **Rigidity Ratio** \\ \hline
0.5–0.75 & 3500 & 1.0 & 0.577 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 6: PFC2D numerical model parameters.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Experimental** & **Diameter of Hole** & **Pitsch of Hole (mm)** & **Pressurization** & **Maximum Expansion** \\
**Program** & **(mm)** & **(MPa)** & **Pressure in the Hole (MPa)** \\ \hline \hline \multirow{4}{*}{I} & 30 & & & 43.5 \\  & 35 & & & 58.8 \\  & 40 & & & 69.5 \\  & 45 & & 2 & 75.1 \\  & & 300 & & \\ II & 35 & 400 & & \\  & & 500 & & \\  & & & 0.5 & 58.8 \\ III & 35 & 400 & 1.5 & \\  & & & 2 & \\ \hline \hline \end{tabular}
\end{table}
Table 7: Experimental scheme and parameters for simulating expansion cracking in double-hole specimens.  
Figure 23 shows the variation in the number of internal cracks in the double-hole specimen under the influence of expansion pressure. The graph reveals that the frequency of cracks increases with an increase in the diameter of the hole. Specifically, as the hole diameter increases from 30 mm to 45 mm, the internal crack count of the specimen grows from 348 to 1180, an approximately 2.4-fold increase, within the same fracturing steps.  
Figure 23: Variation curves of the number of expansion fracture cracks in double-hole specimens with different hole diameters.  
Figure 22: Expansion cracking pattern and crack distribution characteristics of double-hole specimens with different pore sizes.  
2. The change rule of expansion pressure and the size of fracturing expansion pressure under different hole diameters  
Figure 24 illustrates the change in expansion pressure for each specimen. According to Figure 24a, the peak expansion trend of the specimens is essentially the same, with peak expansion pressures ranging from 38.9 MPa to 46.1 MPa. Figure 24b shows the size of the expansion pressure at the time of double-hole penetration and fracturing. This figure demonstrates that as the pore diameter increases, the connecting distance between the periphery of the double holes becomes shorter. As a result, the crack connection time is reduced, and the required expansion pressure decreases, allowing the crack to expand towards the free surface and form the fracture surface at an earlier stage. This provides further evidence of the positive correlation between the pore size and the impact of fracturing, as a larger pore size enables the extension of the crack towards the free surface, leading to the early formation of the fracture surface.