# Study on the Vibration Variation of Rock Slope Based on Numerical Simulation and Fitting Analysis
## 4 Numerical Simulation of Slope Effect
### Analysis of Variation Law of Internal Vibration Velocity of Slope with Same Elevation  
In order to study the variation rule of vibration velocity (resultant velocity) within the range of 10 m inside the slope, six feature points, namely B1-B6, were set up. Their locations are shown in Figure 11.  
In this section, the resultant velocity (PPV) data were analyzed. The peak vibration velocity (resultant velocity) of each monitoring point under the four working conditions is shown in Figure 12.  
As can be seen from Figure 12, with the increase of horizontal distance (\(D\)), the attenuation effect was intensified. The peak particle velocities under conditions I-IV were attenuated from 6.83 cm/s, 6.10 cm/s, 4.36 cm/s, and 3.22 cm/s to 2.83 cm/s, 2.30 cm/s, 1.21 cm/s, and 0.86 cm/s, respectively, without an obvious amplification trend. The reasons are as follows. Firstly, compared with the top of the slope, the middle position of the slope had better stability and larger stiffness, where the influence of load and restraint was significantly stronger. Secondly, the increasing horizontal distance was accompanied by the assumption of energy by the blast vibration wave propagation, and therefore the vibration velocity kept attenuating.  
The attenuation rate was calculated by extracting the PPV of characteristic points B1 and B6 under working conditions I-IV. The attenuation rate statistics are shown in Figure 13.  
Figure 11: The feature points B1–B6.  
Figure 10: Comparison of amplification rate and attenuation rate.  
Figures 9 and 13 show similar regularity. The attenuation rate in Figure 14 is much larger than that shown in Figure 10 because of the different slope effects on feature points B\({}_{1}\) and B\({}_{6}\). In the interior of the slope, the influence of the slope effect on the blast vibration velocity was not significant. In Figure 12, the decay rate under condition I is the smallest (58.56%) and the decay rate under condition IV is slightly higher (73.29%) since different diffracted waves were generated due to various slope angles. There was also a difference in the range of the slope effect due to the diverse shapes of the slope structure.  
Slopes are the key areas to be protected in blasting projects. Therefore, the control and prediction of blasting vibration are critical to the safety of surrounding buildings and the stability of the slope. Blasting vibration field tests should be performed before the blasting. The specifications of explosives to be used for the blasting should be determined in advance, and the site safety work should be performed. With the acquired test data, data fitting was performed to obtain the blast vibration prediction formula. An accurate blast vibration prediction formula can provide a valuable reference for the blasting program. [PERSON]'s formula should be used for blast vibration prediction in flat terrain areas. For the prediction of blast vibration in the slope area, Equation (1) should be used. To comprehensively study the effect of blast vibration on the slope, field monitoring needs to be combined with numerical simulation. With numerical simulation, the peak mass vibration velocity, mass displacement, and unit stress state in the slope area can be obtained. The conclusion data  
Figure 12: The peak vibration velocity of points B\({}_{1}\)–B\({}_{6}\).  
Figure 13: The peak vibration velocity decay rate of points B\({}_{1}\) and B\({}_{6}\).  
obtained need to be evaluated based on relevant engineering specifications and existing research to further determine the degree of slope stability and the influence of vibration velocity. However, the numerical simulation method has certain limitations. In actual strata, there are often various complex geological bodies, faults, fracture zones, etc., and therefore, the propagation and attenuation law of blasting vibration propagation are more complicated. Numerical simulation results may be inaccurate for areas with complicated geological conditions.