# Study on the Vibration Variation of Rock Slope Based on Numerical Simulation and Fitting Analysis
###### Abstract  
In engineering blasting, the slope surfaces in the blasting area exert various effects on the blast vibration velocity. For example, the slope effect and the whipping effect are generated in the slope area, which will influence the blast vibration velocity. The slope area is the key protection area for many projects; therefore, it is of practical value to explore the influence of slope surface on blast vibration speed for the prediction of blast vibration and protection against it. The influence of slope effect and whipping effect on blast vibration velocity in the slope area was analyzed by numerical simulation and fitting. The field monitoring data were fitted to the blast vibration velocity prediction formula. According to the obtained fitting formula, we inferred that vibration speed amplification occurred in the slope area. Numerical simulation was carried out using the ANSYS/LS-DYNA program. Using the above two methods, whether the slope effect and whip tip effect occurred in the study area was verified. By numerical simulation, we established three-dimensional (3D) slope models for four different working conditions. We simulated the complete blasting process and the consistency between the simulation results, and the field data proved the reliability of the numerical simulation. Based on the results of the numerical simulation, we explored the variation of blasting vibration velocity under different height difference conditions. Finally, we explored the distribution law of blasting vibration at the slope surface and inside the slope.  
blasting; fitting analysis; numerical simulation; blasting vibration velocity; whipping effect; slope effect +
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these studies were mostly conducted by combining field monitoring and theoretical analysis. With the development of computer technology, numerical simulation software has been widely applied to the study of slope blasting vibration distribution law. [PERSON] et al. [11] used ANSYS/LS-DYNA software to simulate the whole process of blast vibration propagation in the slope area of the mine site and summarized the stress state and deformation in the slope area. [PERSON] et al. [12] used FLAC 3D software to simulate the dynamic process of the slope under the influence of blasting load. [PERSON] et al. [13] used the UDEC method to simulate the stress wave propagation inside the slope and the change law during blasting. [PERSON] et al. [14] investigated the effect of blast vibration on slope stability using finite element analysis. In summary, studies on blast vibration in slope areas can be mainly conducted with three analysis methods, namely, field monitoring, theoretical analysis, and numerical simulation. The amplification of blast vibration inside the slope can be explained by the whipping effect [15] and the slope effect [16]. [PERSON] et al. [17], [PERSON] et al. [18], and [PERSON] et al. [19] demonstrated the existence of the whip effect at slopes and steps. [PERSON] et al. [20], [PERSON] et al. [21], and [PERSON] et al. [22] analyzed the influence of the internal slope effect on blast vibration velocity.  
In this paper, the distribution law of blasting vibration inside the slope was studied. Firstly, we monitored the blasting vibration at the site and obtained a blasting vibration prediction formula applicable to the geological conditions at the site by fitting analysis. According to the blasting vibration prediction formula, we preliminarily concluded that the amplification effect on vibration speed occurred inside the slope. Secondly, we established a three-dimensional model of the actual slope by means of numerical simulation. We compared the field monitoring data with the numerical simulation results to prove the reliability of the simulation results. Finally, in order to obtain the effect of slope angles on blast vibration speed, we set up four working conditions. Based on the numerical simulation results, we investigated the distribution law of blast vibration at the slope surface and inside the slope.