## 2 Test Scheme Design
### Establishment of a Numerical Model  
The numerical calculation model of a three-dimensional \"explosive stratum building\" is established using a method similar to that used for the geological conditions of the Panjin coal mine. The blasting vibrations of the 2303 working face at the remaining 400 m are simulated and compared with the field monitoring data. The correctness of the numerical model is verified. Therefore, the model is used to simulate the influence of blasting vibrations on buildings final mining stage within 200 m of the advancing distance to working face, which ensure safe production and improves the mining rate of producing top coal in the final mining stage. In the numerical model, the geometric similarity ratio \(C_{h}\) is the ratio of actual thickness to the simulated thickness of the coal seam or rock layer, which is taken as 10. The similarity ratio of time \(C_{t}\) and velocity \(C_{v}\) is \(\sqrt{C_{h}}~{}=~{}3.162\). Due to using the same type of model, the similarity ratio of bulk density and elastic modulus is 1. Considering the influence of the charge on buildings, the blast hole is treated with an equivalent concentrated charge [34; 35; 36; 37; 38]. A similar model of 60 m \(\times\) 100 m \(\times\) 25 m is established and analyzed using ANSYS/LS-DYNA software, taking into account the thickness and model size of each simulated layer. The stratum and building models are shown in Figure 3. Because we used the unit system of g-cm-\(\mu\)s, the stress unit is Mbar (1 Mbar = 1 \(\times\) 10\({}^{11}\) Pa) and the velocity unit is 1 \(\times\) 10\({}^{6}\) cm/s. The surroundings and the bottom of the model are set as non-reflective boundary conditions to simulate the infinite region, and the ground (the top of the model) is set as a freed boundary. The chimney, the district office, and the science and technology building are fixed on the ground through the keyword CONTACT_AUTOMATIC_SURFACE_TO_SURFACE. Ground buildings, stratum and air are modeled using the Solid164 solid element. The maximum grid size is controlled within 0.4 m to meet the accuracy requirements of the wavelength of 1/10-1/8. The size of the stratum grid is relatively sparse, and the size of the building unit is refined to 2.5 cm. Local densification processing is used for the area around the blast hole and provides the connection between the stratum and buildings [39]. Figure 2: Monitoring of blasting vibrations. C25 concrete is adopted as the building material for the science and technology building and the district office, and the brick level of the chimney is MU15. The overall continuous model is used for analysis. The MAT_JOHNSON_HOLMQUIST_CONCRETE model is used for the rock and building materials; this model is widely used for blasting calculations. The rock's physical and mechanical parameters are shown in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rock** & \
\begin{tabular}{c} **Density** \\ **g/m3** \\ \end{tabular} &
\begin{tabular}{c} **Uniaxial Compressive** \\ **Strength MPa** \\ \end{tabular} & **Poisson Ratio** \\ \hline fine sandstone & 2.5 & 37.8 & 0.3 \\ silt stone & 2.56 & 48.2 & 0.31 \\ medium sandstone & 1.95 & 24.6 & 0.28 \\ grit stone & 2.42 & 25.6 & 0.32 \\ C25 & 2.4 & 25 & 0.22 \\ MU15 & 2.15 & 15 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical, mechanical, and building materials parameters. Figure 3: The numerical calculation model. Three scientists--[PERSON], [PERSON] and [PERSON]--have conducted in-depth research on the explosion phenomenon. Based on the experimental data and theoretical analysis, a Jones-Wilkins-Lee model describing explosive behavior is proposed as shown in Equation (1), in which the relationship between the pressure, volume, and energy release of material is established.