## 2 Vibration Control Methods
### Single-Shot Vibration Waveform Reconstruction and Multi-Hole Vibration Superposition Method  
In multi-hole bench blasting, the vibrations are the superposition of single-hole vibration waves from blast holes at different locations, sequenced according to their arrival times. The spatiotemporal relationship between blast holes and monitoring points not only influences the arrival sequence of vibration waves but also affects the characteristics of the single-hole vibration curves. Based on the aforementioned methodology, the arrival time sequence of vibration waves from each blast hole can be determined. To predict multi-hole blast vibrations, it is also necessary to obtain the vibration curves for holes at various locations. However, in practical blasting engineering, it is challenging to measure the vibration curves of each blast hole on-site. Variations in blast-induced vibrations among holes arise from differences in charge, propagation distance, site factors, and other parameters. Therefore, this section utilizes measured single-hole vibration curves as baseline profiles and reconstructs the single-hole vibration curves at the monitoring point for blast holes at different locations by accounting for variations in these influencing factors. Subsequently, the reconstructed single-hole vibration curves are superimposed according to their arrival times, and the effectiveness of vibration control is evaluated based on the reduction in predicted vibration velocity. 1. _Determination of the scaling factor for vibration curves at arbitrary blast hole locations._  
Differences in blasting vibration from one blast hole to another are due to differences in charge, distance, and site factors. Using the measured vibration data from single holes, a mapping relationship is established between the \(PPV\) and factors such as the charge weight, spatial distance, and site conditions, aiming to cover the experimental area as comprehensively as possible, as shown in Equation (4). \[V_{\max}=\lambda Q^{\pi}R^{\beta} \tag{4}\]  
where \(V_{\max}\) is the peak vibration velocity of a single hole (unit: cm/s); \(Q\) denotes the charge weight per hole (unit: kg); \(R\) represents the propagation distance between the blast source and monitoring point(unit: m); \(\lambda\), \(\alpha\), and \(\beta\) are constant parameters for site factors related to lithology and geological conditions, and their values were obtained by regression analysis of field experimental data. In accordance with the blasting vibration attenuation principle, \(V_{\max}\) exhibits an inverse relationship with the distance \(R\), resulting in a negative value for coefficient \(\beta\). Due to differences in charge and spatial distance to the monitoring point between any blast hole and the measured hole, the peak vibration velocities of individual holes differ from that of the measured hole. The ratio between these two values is defined as the scaling factor, and the scaling factor for the \(i\)-th blast hole is given by Equation (5). \[A(Q_{0},R_{0},Q_{i},R_{i})=V_{i}/V_{0}=(Q_{i}/Q_{0})^{\alpha}/(R_{0}/R_{i})^{\beta} \tag{5}\]  
where \(A(Q_{0},R_{0},Q_{i},R_{i})\) represents the proportional coefficient for the \(i\)-th blast hole, where \(i\) is the hole blasting sequence number; \(Q_{0}\) and \(R_{0}\) are the charge weight and spatial distance from the monitoring point for the test hole, respectively; and \(Q_{i}\) and \(R_{i}\) are the charge weight and spatial distance from the monitoring point for the \(i\)-th hole, respectively. (2) _Reconstruction method for the single-shot vibration curve at arbitrary locations._  
Based on the measured single-hole vibration curves, the single-hole vibration curves of the holes at any position are reconstructed by using the scaling factor and are extended to be valid in the whole time domain. Equation (6) is the reconstruction function of the single-hole vibration curve of any position of the hole. \[