## 2 Vibration Control Methods  
The vibration curve obtained from multi-hole blasting monitoring is the superposition of single-hole vibration waves generated by each blast hole, based on their respective arrival times at the monitoring point. This section first introduces the computational principles for wave arrival times, followed by an analysis of how variations in the spatial positions of monitoring points and blast holes influence the arrival sequence. Subsequently, a method is established to identify time windows with a high number of concurrent wave arrivals (referred to as clustering arrival periods) and their corresponding holes at a single monitoring point. A strategy is proposed to adjust the delay time for vibration control by reducing the number of concurrent wave arrivals during these clustering periods. A dense array of monitoring points is deployed around the blasting area to identify the maximum number of concurrent wave arrivals during clustering periods at each location, thereby pinpointing high-probability vibration hazard locations. These locations are systematically addressed to eliminate potential hazards. Finally, the reconstructed single-hole vibration curves are superimposed using [PERSON]'s principle to generate predicted vibration curves, enabling the evaluation of vibration reduction effectiveness. Principle for Calculating the Vibration Wave Arrival Time at the Monitoring Point (Wave Arrival Time)  
In bench blasting operations, each blast hole is initiated according to a predefined delay scheme, which determines the actual initiation time \(t_{1}\). The vibration waves generated after blasting require a specific time \(t_{2}\) to propagate to the monitoring point. The initiation time \(t_{1}\) is determined by the inter-hole delay \(\Delta t_{\rm H}\) and the inter-row delay \(\Delta t_{\rm R}\), while the propagation time \(t_{2}\) depends on the propagation distance \(R\) and the average propagation velocity \(c\). Consequently, the wave arrival time at the monitoring point is calculated using Equation (1). Blast holes are typically charged with columnar explosives, with charge lengths generally within 10 m, whereas the distance from the blast hole to the monitoring point often exceeds 150 m. The duration of the single-hole vibration wave actually includes the blast vibrations produced by the explosive from initiation to the end of the blast. Therefore, a single blast hole can be treated as a point source, and the propagation time of the detonation wave within the explosive column can be neglected. \[t=t_{1}+t_{2}=f(\Delta t_{\rm H},\Delta t_{\rm R})+g(R,c) \tag{1}\]  
where \(t\) represents the arrival time of the vibration wave; \(t_{1}\) is the detonation time; \(t_{2}\) is the wave propagation time; \(\Delta t_{\rm H}\) is the inter-hole delay time; \(\Delta t_{\rm R}\) is the row-to-row delay time; \(R\) is the propagation distance; and \(c\) is the average propagation velocity. The inter-hole delay time \(\Delta t_{\rm H}\) and row-to-row delay time \(\Delta t_{\rm R}\) are determined based on site-specific conditions such as the type of rock mass and the development of joint and fissure systems. By considering the position \(H(i)\) of each hole, the designed detonation sequence \(t_{1}(i)\) can be determined. The propagation distance \(R\) of the vibration wave is defined as the distance between the blast hole \(H(i)\) and the monitoring point \(M\), which corresponds to the magnitude of the displacement vector \(\mathbf{H}\mathbf{M}\) connecting these two points. The propagation velocity \(c\) is calculated as the ratio of the propagation distance \(R\) to the propagation time \(t_{\rm T}\). In practice, a field test method can be employed, in which a single blast source and two monitoring points are used. By calculating the ratio of the difference in propagation distance \(\Delta R\) to the difference in propagation time \(\Delta t_{\rm T}\), the average propagation velocity \(c\) can be obtained.