In open pit mining, road excavation, and other slope projects, bench blasting excavation technology can significantly improve the construction efficiency and velocity of the project progress. However, the bench blasting vibration effect seriously affects the safety of the surrounding buildings (structures) and the stability of the rock structure of the slope. Theoretical analyses, field tests, and numerical simulations have been used to research bench blasting vibration. To clarify the impact of blast vibration on buildings and provide a reference basis for blast vibration control and prediction of whether the structure is damaged, based on Sadovsky’s empirical formula, experts have proposed an elevation correction formula considering the high slope conditions.
In recent years, scholars at home and abroad have mainly focused on the vibration velocity of blasting seismic waves. The empirical formulae for the variation of blasting vibration velocity with explosive quantity and blast core distance have been summarized by using the method for dimensional analysis, and the prediction and assessment of blast vibration have been carried out accordingly [
1,
2,
3]. In terms of the propagation law of blasting vibration, Yin et al. [
4] investigated the attenuation law of blast vibration waves in nodal slopes using blast vibration signals monitored in situ from the blasting of different rock masses. Yu et al. [
5] and Tan et al. [
6] studied the blasting vibration variations in the slope areas of mines and reservoir projects and summarized the variations of blasting velocity inside the slope. Li et al. [
7] derived the blasting vibration response law of slopes in quarries by the regression analysis of many vibration test data. Wan et al. [
8] studied the propagation law of seismic waves in blasting of hydropower station projects through blasting vibration tests. Rafael Rodríguez et al. [
9] proposed a user-friendly methodology for determining the behavior of vibrations generated in any rock mass. Zhu et al. [
10] proposed a new method to predict the vibration velocity of multi-hole trenching blasting of laminated rock masses, which can be used for optimizing engineering blasting design and the blasting of the slope. In order to study the propagation law of blast vibration in soft rock tunnels, Chen et al. [
11] carried out an analysis and research on the measured data by blast vibration tests and used nonlinear regression and Fourier transform methods to provide a reference for the optimization of blast design in the Muzhailing tunnel or similar soft rock tunnels; Lin et al. [
12] proposed a superposition prediction method based on the propagation and superposition principles of blast vibration signals; Xiao et al. [
13] obtained the slope blasting vibration propagation law by fitting the Sadovsky formula based on field blasting vibration monitoring data; Gao et al. [
14] used regression analysis for the Sadovsky and the CRSRI blast vibration velocity prediction models during onsite operations; Zhang et al. [
15], through field blasting vibration monitoring and numerical simulation, proposed the propagation law of blasting vibration velocity in the high side wall, elucidated the local elevation amplification effect of blasting vibration velocity, and modified Sadovsky’s formula; Tian et al. [
16] used MATLAB to compile a signal processing program to analyze the propagation law of blast vibration in the stratum of shallow buried tunnels with oversized cross-sections. In terms of the research of dynamic response. Yan et al. [
17] studied the blasting vibration response law of slopes at different elevations by modifying the elevation formula and numerical simulation. Xie et al. [
18] used a modified DDA method to study the dynamic response of rocks under blast loads. Deng et al. [
19] derived an attenuation formula for the propagation velocity of elastic stress waves in elastomers based on the stress wave theory, which provides a reference for similar excavation blasting and vibration control methods to provide a reference for similar excavation blasting and vibration control methods. The blasting data measured and obtained in the actual project is complicated, time consuming, inconvenient, and has great limitations. Therefore, most scholars use finite element numerical simulation software to analyze the dynamic effect from seismic wave blasting, and then judge whether the buildings are damaged and destroyed from the structural material properties, providing reference for the blasting vibration control, hole network parameters, and design indicators [
20,
21,
22,
23,
24,
25,
26,
27]. Zhang et al. [
28] analyzed the propagation law of vibration in the civil air defense tunnel through field tests and numerical simulations and established a model for the relationship between peak vibration velocity and effective stress; Xu Wu et al. [
29] studied, based on theoretical analysis and numerical simulations, the effect of bench height on blasting seismic waves; Yang et al. [
30] used numerical simulations to study the vibration characteristics of slopes under blasting loads; Blair et al. [
31] used numerical models to study the dynamic response of the shaft wall under blasting loads at the bottom of the shaft wall; Jiang et al. [
32] analyzed literature on the study of the dynamic response law of pipelines using field tests, outdoor tests, and numerical simulations. In terms of the impact of blasting vibration on surface buildings, Esmatkhah et al. [
33] studied the settlement and damage caused by subway tunnel excavation through onsite monitoring and numerical simulation; Chaudhary et al. [
34] conducted a comparative assessment on the performance of conventional and advanced tunnel lining materials subjected to blast loading and used a three-dimensional nonlinear finite element analysis procedure. Tsang et al. [
35] presented a practical structural vulnerability assessment method for mine blast-induced vibrations. In general, blast vibration has been studied in-depth and a wealth of research results have been obtained. However, there are few reports on the research on vibration propagation law and the dynamic effect of bench blasting, and it is not comprehensive enough. Therefore, in order to ensure the safety of surrounding buildings (structures) during blasting, it is necessary to comprehensively and systematically study the vibration propagation laws and dynamic effects under the combined action of horizontal distance and elevation.
In view of this, based on the existing research, field tests and numerical calculations are carried out with the background of a step blasting project in a gravel mine in Guizhou Province, and regression analysis is carried out with the least squares method and SPSS software to study, more comprehensively and systematically, the vibration propagation law and dynamic effect under the joint action of horizontal distance and elevation, to provide a reference basis for controlling blasting vibration and predicting whether the structure is damaged.