# Study on the Vibration Variation of Rock Slope Based on Numerical Simulation and Fitting Analysis
## 4 Numerical Simulation of Slope Effect  
Based on the construction conditions at the site, we conducted a numerical simulation using the ANSYS/LS-DYNA program. The ground investigation data showed that the surface plain fill was cleared and that the stratum was mainly composed of medium-weathered granite. We adopted the relevant parameters provided in the exploration data to define the physical properties of the medium-weathered granite. In the actual project, the slope height was 15 m, and the horizontal distance (\(H_{\text{L}}\), from the foot to the top of the slope) was 6 m. In order to investigate the effect of slope angles on blasting vibration, we fixed the height of the slope in the 3D model to 15 m. We built four slope models with horizontal distances (\(H_{\text{L}}\)) of 6 m, 12 m, 18 m, and 24 m and slope angles of 68.20\({}^{\circ}\), 51.34\({}^{\circ}\), 39.80\({}^{\circ}\), and 32\({}^{\circ}\), respectively. The model for working condition II was divided into a total of 182,568 meshes. The fine meshes ensured the accuracy of the calculation and saved calculation time. The mesh quality and calculation accuracy are high enough for subsequent studies. The model is shown in Figure 2.  
For the constraint conditions, the top surface of the model was set as the free surface, and other surfaces were set as nonreflecting boundaries to simulate an infinite stratigraphic space. As for the load conditions, since this study focused on the vibration velocity variation of the  
Figure 2: The 3D model of numerical simulation of work condition II.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fitting Results of Traditional** & **Coefficient of Correlation** & **Type of Vibration Velocity** & **Average Error Rate (\%)** \\ \hline \(V=0.0696\left(\frac{\text{O}^{\frac{1}{8}}}{\text{R}}\right)^{0.165}\) & R\({}^{2}=0.902\) & Vertical & 94.74\% \\ \(V=0.0709\left(\frac{\text{O}^{\frac{1}{8}}}{\text{R}}\right)^{0.185}\) & R\({}^{2}=0.905\) & Horizontal & 93.24\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: The error rates of [PERSON]’s fitting formula.  
masses at the surface and the shallow stratigraphic interior, the effect of crustal stress was not considered. The detailed data for the four operating conditions are shown in Table 4.  
The elastic-plastic material model was selected as the rock-soil mass model, and the keyword was \"MAT_PLASTIC_KINEMATIC. Based on the site geological survey data, the selected mechanical parameters are shown in Table 5.  
The explosive weight was 3.6 kg, and only one explosion was carried out. ANSYS/LS-DYNA software, which involves the numerical simulation of rock explosives, generally uses the 2 # emulsion explosive material model with the keyword \"MAT_HIGH_EXPLOSIVE_BURN. This keyword must be defined with the equation of state; otherwise, there will be calculation errors. The equation of state keyword was \"EOS_JWL, which contains the explosive-related internal energy parameter. In the case of the definition of the state equation, explosives in the explosion process, the explosion pressure, volume changes, and energy signal characteristics can be accurately described. The state equation is shown below [28]:  
\[P=A\bigg{(}1-\frac{\omega}{R_{1}V}\bigg{)}e^{-R_{1}V}+B\bigg{(}1-\frac{\omega}{ R_{2}V}\bigg{)}e^{-R_{2}V}+\frac{\omega E_{0}}{V} \tag{4}\]  
where \(P\) is the pressure; \(V\) is the initial relative volume; \(E_{0}\) is the internal energy constant; \(A\), \(B\), \(R_{1}\), \(R_{2}\), \(\omega\) are the characteristic parameters, and for certain explosives, the value is constant.  
Detailed parameters are shown in Table 6.