## 3 Numerical Models and Parameter Selection  
### Numerical Model  
LS-DYNA 18.2 is a highly efficient non-linear dynamic analysis software that provides a high-energy explosive material model, is particularly well suited to handling high strain and high deformation problems. Due to these advantages, LS-DYNA has become an effective tool for researching and solving blasting-related problems, reproducing the explosive process while reducing experimental costs.  
Taking the tunnel project of Liyue Road in Chongqing as an example, the Arbitrary Lagrangian-Eulerian (ALE) algorithm is used in the LS-DYNA program to establish a single-layer solid quasi-3D model to improve the computational efficiency. In the ALE algorithm model, the blasting load is transferred from the Euler grid to the Lagrange grid, which belongs to the unidirectional coupling layering method in the computational multiscale method, and more accurate calculation results can be obtained [33]. The rock serves as the solid material and the remaining material serves as the fluid material, with air as the coupling medium. In the modeling of air interval charge structures, air also serves as the interval medium. To ensure that the model boundary does not affect the calculation results, the distance from the boundary to the hole should be increased and the non-reflective boundary conditions added reasonably to achieve the purpose of no damage at the boundary. The model was 2.4 m high and 1.8 m wide, the diameter and length of the blast hole were 0.04 m and 2.0 m, the length of the stemming material was 0.6 m, the interval media was 0.4 m, and the length of the upper and lower sections of explosives were 0.2 m and 0.4 m. The upper boundary of the model was a free surface, and the rest of the boundaries were set with no-reflection boundary conditions by the keyword BOUNDARY_NON_REFLECTING. Describe the blasting process using the combined JWL equation of state with high explosives. The kg-m-s unit system was used. Figure 3 illustrates the established model and meshing. The distance between the peripheral holes  
Figure 2: Location of damage monitoring units: (**a**) single-hole model, (**b**) double-hole model.  
in the project is 0.5 m. Therefore, unit I is placed at 0.25 m from the free surface as the monitoring reference unit for the damage effect evaluation.  
Three types of grids are illustrated in Figure 3. The Euler grids are used to describe the motion of a continuous medium such as a fluid or gas by dividing the space into a fixed grid of cells and tracking the motion of the fluid through these grids. The Euler grids are suitable for dealing with macroscopic motions of continuous media such as fluids or gases. Unlike the Euler grids, the Lagrange grids are a kind of body-following grids, whose nodes move and deform during the motion. When the deformation is large, it often results in mesh distortion and fails to obtain accurate results. The ALE grids combine the advantages of the Lagrange and Euler methods, and their grids can move and deform with the motion of fluids and solids, which is suitable for dealing with fluid-solid coupling problems, such as deformation under the action of blast shock waves, fluid-structure interactions, and other complex cases. In the fluid-solid coupling region, a multi-matter unit group is created, and the coupling relationship is established by the keyword CONSTRAINED-LAGRANGE-IN-SOLID. In this study, the numerical model is divided into a square grid with grid sides of 0.5 cm. The coupling width is 20 times the diameter of the blasting hole to ensure the accuracy of the calculations.