# 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
#### 4.2.3 Influence of Circumferential Pressure on Specimen Cracking  
(1)Influence of circumferential pressure on crack expansion and rupture state of specimens  
Figure 28 showcases the expansion fracture shape and crack distribution characteristics of two-hole specimens under different enclosure pressures. The final crack areas for the four specimens were measured as 52.1 mm\({}^{2}\), 45.8 mm\({}^{2}\), 41.3 mm\({}^{2}\), and 38.7 mm\({}^{2}\), respectively. It can be observed that as the pressure increases, the fracture surface decreases from 4 to 2. This indicates that the response of the two-hole specimens to expansion fracturing is influenced by the magnitude of the surrounding pressure. Additionally, there is an inverse relationship between the enclosure pressure and the size of the cracks' expansion range and their degree of fragmentation.  
Figure 28: Expansion cracking pattern and crack distribution characteristics of double-hole specimens under different circumferential pressures.  
Figure 27: Changing the law of expansion pressure of specimens with different hole spacings.  
Moving on to Figure 29, it illustrates the relationship between the number of internal cracks in the double-hole specimen and the application of expansion pressure with various peripheral pressures. According to the curve, there is a negative correlation between the peripheral pressure and both the crack initiation time and the crack count in the specimen. Additionally, the growth rate of the number of cracks in each of the four types of specimens follows a similar pattern: initially fast, then slow, and then fast again. The increase in circumferential pressure has an inhibitory effect on the fracture initiation time and the overall number of cracks, but it does not impact the crack growth rate.  
2. The change rule of expansion pressure and the size of fracturing expansion pressure under different peripheral pressures  
Figure 30 portrays the variation in expansion pressure in double-hole specimens under different circumferential pressures. Figure 30a demonstrates that each specimen's peak expansion development pattern is essentially the same, with a peak expansion pressure ranging from 42.3 MPa to 46.1 MPa.  
Furthermore, Figure 30b illustrates the magnitude of the expansion pressure during double-hole penetration and at the time of fracture. It can be observed that the circumferential pressure has a gradient effect on the cracking of double-hole specimens. There is a positive correlation between the perimeter pressure and the expansion pressure at fracture. Additionally, when the perimeter pressure is lowered, there is more unloading of the expansion pressure at the time of the specimen's rupture, leading to greater fluctuations. This suggests that a high perimeter pressure depletes the specimen's expansion pressure more, while a low perimeter pressure is more conducive to the extension of the specimen's crack, resulting in a greater release of expansion potential energy.  
Figure 29: Variation curves of the number of expansion-cracking cracks in double-hole specimens under different circumferential pressures.