# Study on Mechanism of Static Blasting-Induced Hard Rock Fracture Expansion
## 4 Numerical Simulation Analysis of Static Blasting Fracturing Influencing Factors
### Software Calculation Principles and Modeling
#### 4.1.2 Modeling and Verification  
(1) Model size and boundary conditions To mitigate the formation of drilled holes, a circular wall is strategically positioned, and an additional wall is erected around the periphery to confine the model's boundaries. These two specimen models were created using PFC2D software, as depicted in Figure 20. The dimensions of the single-hole specimen are 200 mm by 200 mm, while the double-hole specimen measures 1000 mm by 1000 mm. The center hole of the single-hole specimen has a diameter of 30 mm, and there is no circumferential pressure exerted. This specimen serves the purpose of validating the experimental model. The model is subjected to the same peripheral pressure, denoted as p, while the double-hole specimen has a hole diameter Rd and a spacing D. The peak expansion pressure size in the hole, as determined by prior experiments on the expansion pressure of different aperture sizes in the pill volume of actual testing, shall be retained in the simulation of single and double-hole expansion pressure fracture specimens. This simulation involves the utilization of the pill volume and a servo mechanism within the round hole to replicate the expansion pressure of the crusher. Figure 19: Boundary wall servo mechanism. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Parallel Bond** & **Parallel Bonded** & **Particle** & **Parallel Bond** & **Parallel Bond** & **Particle** & **Parallel Bonded** \\
**Normal** & **Tangential** & **Friction** & **Normal** & **Tangential** & **Contact** & **Effective** \\
**Stiffness** & **Stiffness** & **Coefficient** & **Strength** & **Strength** & **Modulus** & **Modulus** \\ \hline \(\overline{k}_{n}\) & \(\overline{k}_{s}\) & \(\mu\) & \(\overline{\tau}_{c}\) & \(\overline{\sigma}_{c}\) & \(E_{c}\) & \(\overline{\mathbb{F}}_{c}\) \\ \hline \end{tabular}
\end{table} 
Table 5: Parallel bonding model parameters. Calibration and model parameter validation  
The model is initially calibrated, as depicted in Figure 21, utilizing parameters from Table 6. This calibration involves simulating a single-hole specimen without peripheral pressure expansion cracking, investigating the development pattern of expansion pressure in a single-hole specimen, and comparing the measured expansion pressure changes obtained from an experiment with steel pipes. The results indicate that the initial increase rate is rapid, followed by a gradual slowdown, suggesting a similar development trend between the simulated and measured expansion pressures. The simulated expansion pressure reaches a maximum of 29.2 MPa, while the experimental expansion pressure reaches a maximum of 43.5 MPa, indicating a disparity between the two maximum expansion pressures. This discrepancy can be attributed to the steel pipe's ability to maintain its structural integrity and the freedom of expansion pressure to develop, in contrast to the simulated specimen's crack expansion and the inability of drilled holes to maintain hole integrity, resulting in partial loss of expansion pressure. Consequently, the steel pipe does not require the expansion pressure to reach its maximum at the hole diameter for fracture to occur. Figure 21: Comparison of patterns of change in expansion pressure. Figure 20: PFC2D numerical modeling. The fracture morphology of the single-hole specimen and the simulated crack extension are depicted in the image, showcasing a remarkable consistency with the laboratory method and results of single-hole expansion cracking. Initially, the specimen exhibits the development of a longitudinal crack along the vertical hole boundary, concurrently generating a transverse crack perpendicular to the longitudinal crack. This transverse crack expands along the path of least resistance towards the free surface. With the progression of expansion pressure, the width of the cracks gradually widens, ultimately resulting in the formation of a T-type damage pattern.