# Study on the Vibration Variation of Rock Slope Based on Numerical Simulation and Fitting Analysis
## 4 Numerical Simulation of Slope Effect
### Vibration Response Analysis of Slope Blasting  
The numerical simulation pictures showed that the vibration velocity was amplified in the small area above the middle of the slope. Figure 6b-d shows the movement of the area where a larger vibration velocity appears. At time 0.004 s, a larger vibration velocity started to appear in the middle of the slope; at 0.005 s, the area was pushed upward; at 0.006 s, the area was at the top of the slope. The movement of the area can be attributed to the slope effect and whip effect. As the slope foot was close to the explosion center, the energy propagated outward in the form of a shock wave in the area near the explosion. The wave front velocity, pressure, and particle movement velocity of the explosion shock wave were very large, and the attenuation  
Figure 5: Vibration velocities in the vertical and horizontal directions. Figure 6: Numerical simulation results of blast vibration velocity of the slope. was not significant. Therefore, the feature points (A1-A6) were set above the middle of the slope in order to better study the blasting vibration changes, as shown in Figure 7.  
In this section, the resultant velocity (peak particle velocity, PPV) data were analyzed. The distribution results of slope blasting resultant velocity under four working conditions are shown in Figure 8. It can be seen that in the propagation process of blasting vibration, the resultant velocity was affected by both the attenuation effect and amplification effect, which had their respective dominant scopes. With the increase of the slope, the vibration velocity of the slope also increased, and the blasting vibration velocity of the slope presented different degrees of attenuation. Within the range from feature point A\({}_{3}\) to A\({}_{6}\), there was a small degree of amplification under working conditions I and II, with the velocity increasing from 3.89 cm/s and 3.62 cm/s to 5.35 cm/s and 4.32 cm/s, respectively. The blasting vibration velocity increased by 37.5% and 19.3%, respectively. The attenuation effect was weakened and the whipping effect was intensified. Vibration velocity amplification was more likely to occur in the area close to the top of the slope than in the middle part of the slope. Under working conditions III and IV, the slope was relatively small, and under the influence of surface stiffness and stability, the vibration velocity attenuation of B\({}_{4}\)-B\({}_{6}\) point slowed down, and the vibration velocity amplification was not significant. The amplification rate data were obtained from feature point A\({}_{3}\) to point A\({}_{6}\) since the amplification phenomenon was mostly found there, as shown in Figure 9. The attenuation  
Figure 8: The vibration variation curve of the slope. Figure 7: The feature points A\({}_{1}\)–A\({}_{6}\). rate data were collected from the characteristic points A\({}_{1}\) and A\({}_{6}\), considering that the amplification effect had a very limited range, while the attenuation effect was always present. As far as the slope surface is concerned, the amplification phenomenon occurred locally, but overall, the blasting vibration showed an attenuation trend. In Figure 9, with the decrease of the slope angle and the increase of the horizontal distance (\(D\)), the vibration speed at the middle and the top of the slope gradually declined under working conditions I-IV. This phenomenon can be attributed to the slope effect. The area near the bottom of the slope belonged to the topographic abrupt change zone. When the blasting vibration propagates to this area, it will generate a bypass shot and then form a new vibration source. At the same time, when the blasting vibration propagates to the slope surface, it will cause the slope surface to produce a dynamic response. Under the combined effect, the vibration velocity at the slope surface showed an amplification trend [16].