Influence of Delay Time Between Holes on the Time-Frequency Characteristics of Blast Vibration Propagation Based on Monte Carlo Methods

To investigate the influence of inter-hole delay on the intensity and frequency characteristics of blasting vibrations, an effective simulation of single-hole blasting vibration waveforms was achieved based on a single-hole blasting vibration prediction model. Subsequently, incorporating Blair's nonlinear superposition theory, a group-hole blasting vibration prediction model capable of reflecting the nonlinear vibration relationship between holes was constructed. Using a copper mine in Jiangxi Province as the engineering context, the constrained-traversal algorithm was employed to optimize the parameters of the single-hole prediction model. The simulated waveform output by this model exhibits a peak velocity error of 0.7% compared to the measured single-hole waveform, with identical predictions for the dominant frequency. The peak velocity error between the simulated waveform output by the group-hole blast vibration prediction model and the measured group-hole waveform is 3.9%, with the main frequency prediction being completely consistent. This fully validates the effectiveness of both the single-hole and group-hole blast vibration prediction models. Based on dual-hole blasting vibration experiments, employing Monte Carlo methodology, the model generated 1000 sets of single-hole simulated waveforms. From these, 500 sets of dual-hole blasting vibration waveform characteristics (peak velocity, dominant frequency, and energy distribution across frequency bands) were extracted to construct a sample set. Subsequently, statistical analysis was conducted on the damping rate, dominant frequency, and energy distribution across frequency bands for the superimposed vibration waves of dual-hole blasts at different delay times and blast center distances, using the upper limit of the 95% confidence interval and the mean value. Results indicate that at the same blast center distance, as the delay time increases, the damping rate first increases and then stabilizes, while the dominant frequency gradually decreases, with high-frequency energy progressively shifting toward low-frequency energy. At different blast centers, as the blast center distance increases, the damping rate generally decreases across various delay times, the dominant frequency shifts toward lower frequencies, low-frequency energy shows an overall increase, and high-frequency energy exhibits an overall decrease. The Monte Carlo method, based on extensive simulations and statistical analysis, not only reveals the random characteristics of blasting vibration signals but also enables quantitative analysis of their time-domain and frequency-domain features, holding significant theoretical and engineering value.