## 4 Example Simulation and Analysis of SPH in Tunnel and Underground Engineering
### Establishment of Numerical Simulation Model  
This numerical simulation primarily investigates the extent of the damage to and the dynamic response of rock under blasting impact loads. For this study, the rock material was modeled using the material model *MAT_272, also known as *MAT_RHT, which effectively characterizes the damage range. The physical and mechanical parameters of the surrounding rock, based on field measurements, are presented in Table 1.  
The high-energy explosive material model from the Ansys/LS-DYNA material library was selected to simulate the physical and chemical properties of explosives during the detonation process. The explosive is modeled as a uniform continuous medium using the keyword *MAT_HIGH_EXPLOSIVE_BURN. The material parameters were primarily referenced from the performance characteristics of granular viscous ammonium nitrate explosives provided by the mine. The specific explosive parameters are detailed in Table 2.  
To mitigate boundary effects, the tunnel section is positioned at the center of the model, with the distance from the boundary set to four times the tunnel diameter. The surrounding rock is modeled using the SHELL163 shell element. The finite element mesh model is constructed with Ansys 19.0/LS-DYNA, employing the SPH method to simulate the explosives. Particle distribution within the model is managed using LS-PrePost 4.0 post-processing software. In the vertical stress field, a uniform load is applied to the top of the model to account for self-weight. The initial stress values in the horizontal stress field are adjusted according to the vertical gradient. A fixed constraint is applied at the bottom of the model, while force constraints are imposed on the upper boundary to simulate various working conditions at different burial depths. Additionally, force constraints are applied to the left and right boundaries to represent the varying lateral pressure coefficient. The model simulates the blasting excavation process, as depicted in Figure 11. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Surrounding Rock Classification** & **Volumetric Weight/(kN/m3)** & **E/(GPa)** & **Poisson Ratio** & **Angle of Internal Friction/(\({}^{\circ}\))** & **Cohesion/(MPa)** \\ \hline Va & 19 & 1.65 & 0.37 & 24 & 0.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical and mechanical parameter values of surrounding rock. Figure 10: The process of tunnel face excavation by the blasting method. (**a**) Tunnel face disclosure; (**b**) Tunnel support schematic diagram. The model was extended into three dimensions, as depicted in Figure 14. From Figure 14a, it is observed that the tunnel structure adjacent to the tunnel face first experiences the blasting impact, occurring at approximately 4.3 ms. Over time, the blast-induced vibrations in the tunnel wall propagate radially from the inner center toward the periphery. During this phase, the vibration velocity distribution takes on an elliptical shape, with the affected area gradually expanding from the front side to the back side of the tunnel, reaching the inverted arch trestle at around 7.9 ms. The vibration velocity peaks during this process and subsequently begins to decay. The blast vibrations continue to propagate toward the rear side of the tunnel, ultimately affecting the entire tunnel structure by approximately 8.8 ms. Figure 14b reveals that the effective stress initially increases and then decreases along the tunnel's direction, with the maximum stress occurring at a distance of 2 m. This indicates that the region approximately 2 m from the blasting surface within the tunnel structure is a vulnerable area, prone to buckling. The highest circumferential effective stress at this location occurs at measuring point 1, situated at the center of the blasting side, which is the most susceptible to stress failure. Overall, the effective stress decreases initially and  
Figure 14: (**a**) Effective stress cloud diagram of tunnel structure. (**b**) Vibration velocity response of tunnel wall.