## 3 Numerical Computing Model
### Simulation of Transverse Tunnel Blasting Construction
#### 3.2.2 Blasting Equivalent Load  
The complexity of the research problem renders it difficult to establish every element of the explosion process. Although the research problem is complex, we can analyze blast waves using empirical formulas and monitoring data from vibration measuring points.  
Building on the research findings of [21], the maximum detonation pressure resulting from an explosion can be determined using the following calculation:  
\[P_{b}=\frac{\rho_{c}\upsilon^{2}}{4} \tag{4}\]  
In the formula: \(P_{b}\) is the maximum detonation pressure; \(\rho_{c}\) is the charge density; \(\rho_{c}=1000\) kg/m\({}^{3}\); \(\upsilon\) is the explosive detonation speed; and \(\upsilon=3400\) m/s.  
Due to variations in gas and rock properties, as well as contact conditions, the pressure of the explosive gas and the resulting detonation pressure may not be equivalent. Under explosion dynamics, the maximum impact force on the perforation wall can be determined when the perforation is filled with explosives, as follows:  
\[P_{max}=\frac{2\rho_{0}c_{p}}{\rho_{0}c_{p}+\rho_{c}V}P_{b} \tag{5}\]  
In the formula: \(P_{max}\) is the maximum impact pressure on the pore wall. \(\rho_{0}\) and \(C_{p}\) are rock density and p-wave velocity.  
To calculate the correct formula for non-full charge conditions, it is necessary to consider the proportional relationship between the single hole charge and the hole volume. This relationship can be described as follows:  
\[P_{max}^{{}^{\prime}}=\left(\frac{1}{D/d}\right)^{\upsilon\upsilon}\cdot \frac{V_{0}}{V}\cdot P_{max} \tag{6}\]  
To accurately calculate the necessary values for this project, the formula below incorporates specific parameters, such as \(D\) (blast hole diameter) set to 42 mm, \(d\) (cartridge diameter) at 32 mm, \(V_{0}\) (charge volume), \(V\) (blast volume), \(n\) (ratio of the length of the propellant charge to the diameter of the projectile), \(\beta\) (cylindrical charging coefficient), and \(\upsilon\) (adiabatic index of gas). It should be noted that \(\upsilon\) is assumed to be 1.4.  
Based on the construction plan, the second section of the stepped structure was designed to hold the largest amount of explosives when using a single ignition point. As a result of this, the potential exists for significant adverse impacts on existing tunnels. A  
Figure 5: The layout of the blasting holes for vehicle passage.  
minimal impact was observed during later-stage blasting, as there was enough clearance space available. Accordingly, the blasting load excitation parameters for this section were calculated using Equation (5). The calculation yielded a maximum impact pressure for a single blast hole of \(P^{\prime}_{max}\) = 1019.60 MPa. At present, the parabolic and triangular blasting load curves are the most commonly used ameter determination. The calculation results reveal the equivalent blasting load curve of the ones. The triangular load curve model was chosen to simulate the blasting in this paper because of its ease of use and parsatellite holes at the upper bench, as illustrated in Figure 6.