# Safety Assessment of the Cover-and-Cut Method Under Blasting Vibration Induced by Tunnel Excavation
## 2 Numerical Modeling and Parameter Selection  
### Numerical Modeling of Dynamic Responses in Tunnel Construction  
This study employed FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions) to simulate the dynamic soil-structure interaction during tunnel construction under blast-induced vibrations. The model incorporated key structural components, including the diaphragm wall, central pillar, and roof, as well as the surrounding rock mass. The tunnel geometry and material properties were based on field data from the Guizhou University Station site.The numerical simulation model of the subway tunnel, established by FLAC3D6.0 software, is shown in Figure 4.  
This study employs a three-dimensional finite element model (FEM) to simulate the dynamic response of the underground metro station and its surrounding environment. The model is built based on specific parameters of the underground geological structure and calibrated with actual engineering cases. To ensure the accuracy of the model, the \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Depth** & **Bore** & **Hole** & **Row** & **Single Hole** & **Filling** \\ \hline L (m) & diameter (mm) & distance a (m) & spacing b (m) & Charge Q (kg) & length (m) \\
1.2 & 40 & 1.0 & 0.8 & 0.3 & \(\geq 0.8\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Blasting scheme parameter table. Figure 3: Blast hole and delay layout diagram. Figure 2: Section of the subway tunnel in the cover-and-cut method. following methods were used to determine its parameters: First, the model was calibrated using field vibration monitoring data to ensure that the model's response under various vibration source conditions matches the actual measured data. Second, numerical optimization algorithms were applied to adjust the parameters of the geological layer's elastic modulus, Poisson's ratio, and metro car vibration characteristics, thereby improving the model's precision. Model Construction and Setup: The foundation pit structure was modeled as reinforced concrete integrated with the surrounding rock, treated as a uniform, continuous, isotropic medium. Mechanical properties of the rock mass were defined using the Mohr-Coulomb failure criterion, and the Saint-Venant principle was applied to minimize boundary effects. The model dimensions were set to 10 times the actual structure size (length, width, and depth) to reduce boundary interference. Mesh sensitivity analysis was conducted to ensure accuracy. A coarse mesh was initially used for preliminary simulations, with subsequent refinement around high-stress areas, such as the blasting zone and critical structural elements. The final grid size of 0.5 m in these regions provided a balance between computational efficiency and precision. Additionally, a convergence analysis verified the stability of the model, with no significant variation (less than 2%) in peak vibration velocities observed upon further mesh refinement or reduction of the time step size. Boundary Conditions and Soil-Structure Interaction: Boundary conditions were set to realistically replicate field constraints. The model's base was fixed to represent bedrock, while lateral boundaries used free-field conditions to prevent wave reflections. Contact elements were employed to simulate the interaction between the soil and structural components, ensuring accurate representation of the dynamic response. Dynamic Loading and Frequency Analysis: Blast-induced loads were applied to simulate multiple blasting cycles. Parameters such as charge weight and the distance from the blast source were calibrated to reflect real-world conditions. The simulation revealed that vibration intensity decreased with distance from the blast, with higher frequencies dominating near the source and lower frequencies propagating further. This frequency-dependent behavior highlighted the significance of considering the natural resonance frequencies of nearby structures, as they may amplify vibrations and lead to potential damage.