## 4 Numerical Simulation Analysis  
### Establishment of Numerical Simulation Model  
In this study, we constructed a three-hole three-dimensional numerical simulation model with consistent model dimensions, material constitutive properties, charging methods, charge lengths, stemming lengths, boundary conditions, and mesh precision. By varying the detonation time of the explosives within the holes, a numerical simulation of pre-splitting blasting was conducted by using different inter-hole delay times.  
The three-hole three-dimensional numerical simulation model had dimensions of 640 cm \(\times\) 400 cm \(\times\) 500 cm. The drill bit used in the mining site had a diameter of 120 mm; thus, the hole diameter was determined to be 120 mm. Based on the research conclusions and recommendations of other researchers [35] regarding pre-splitting blasting with a radial decoupling charging factor of 2 to 4 and a hole spacing of 8 to 12 times the hole diameter, combined with engineering practices and the researchers' experience of mining site, a radial decoupling charging factor of 3.75 was ultimately determined (with the decoupling zone filled with water medium), and the hole spacing was set at 120 cm. The charge length was set at 4 m, and the stemming length was set at 1 m; detonation occurs at the bottom of the hole. The explosive used was No. 2 rock emulsion explosive, and the stemming material was the same as the rock material. The specific blasting parameters for the numerical simulation of sequential pre-splitting blasting are shown in Table 8.  
To closely align with real-world conditions, non-reflecting boundary conditions were set around the perimeter and bottom of the model to simulate an infinite rock domain, while the top surface of the model was left without specific boundary conditions, defaulting to a free surface. The numerical simulation algorithm employed a fluid-structure interaction (FSI) approach, where the rock, as a structural component, was modeled using the  
Figure 7: Numerical simulation of blasting funnel test and field comparison.  
Lagrangian algorithm, and water, air, and explosives, as fluids, were modeled using the Arbitrary Lagrangian-Eulerian (ALE) algorithm. Additionally, a certain flow space was designated as the coupling domain.  
In a study on pre-splitting blasting, [PERSON] et al. [36] found that sequential hole detonation with a delay time of 12 ms results in a higher half-hole rate for the pre-split holes. [PERSON] [37] conducted model tests using high-speed photography and concluded that the complete formation of pre-split cracks takes approximately 18 ms. [PERSON] et al. [38] proposed a theoretical model for selecting the delay time in millisecond blasting and verified it through field tests, suggesting an optimal inter-hole delay time of 24 ms.  
Therefore, four three-hole three-dimensional simulation models were constructed. The detonation of the explosives was defined using the keyword *INITIAL_DETONATION in LS-DYNA's detonation point definition function. The delay detonation times for the blast holes were set at 0 ms (simultaneous detonation), 12 ms, 18 ms, and 24 ms, respectively. The specific numerical simulation models are shown in Figure 8.