Influence of delay time between holes on the time-frequency characteristics of blast vibration propagation based on Monte Carlo method
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摘要: 为探究孔间延时对爆破振动强度和频率特征的影响，基于单孔爆破振动预测模型和Blair非线性叠加理论，构建群孔爆破振动预测模型。并在江西某铜矿中验证其有效性：单孔、群孔爆破模拟波形与实测波形的峰值振速和主频误差均低于3.9%。基于该模型进行双孔爆破振动试验，利用蒙特卡罗思想，提取出500组双孔爆破振动波形特征（峰值振速、主频以各频带能量占比）构建样本集合。之后，选取出95%置信区间上限值和均值对不同延期时间及爆心距下的双孔叠加振动波的降振率、主频及各频带能量占比进行统计分析。结果表明，在同一爆心距下，随着延期时间的增加，降振率呈先增加后稳定的趋势，而主频呈逐渐减小的趋势，其高频带能量逐渐向低频带能量偏移；在同一延期时间下，随着爆心距的增加降振率整体逐渐减小，主频整体向低频偏移，其低频能量呈整体增大趋势，高频能量呈整体减小趋势。Abstract: 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 was constructed that can reflect the nonlinear vibration relationship between holes. 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 dominant 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. At the same time 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, resulting in an overall increase in low-frequency energy and an overall decrease in high-frequency energy. 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. -
图 8 单孔爆破振动模拟波形验证
Figure 8. Verification of single-hole blasting vibration simulation waveform
图 9 单孔爆破振动模拟波形频谱验证
Figure 9. Verification of single-hole blasting vibration simulation waveform spectrum
图 10 群孔爆破振动模拟波形的验证
Figure 10. Verification of multiple-hole blasting vibration simulation waveform
图 11 群孔爆破振动模拟波形的频谱验证
Figure 11. Verification of multiple-hole blasting vibration simulation waveform spectrum
图 13 峰值振速样本集合的分布情况
Figure 13. Distribution of the sample set of peak vibration velocity
图 14 0 ms延期时间下对数峰值振速的样本集合
Figure 14. Sample set of logarithmic peak velocity at 0 ms delay time
图 15 0 ms下对数峰值振速Q-Q图
Figure 15. Q-Q plot of logarithmic peak vibration velocity at 0 ms delay time
图 16 95%单侧置信区间上限示意图
Figure 16. Illustration of the upper limit of 95% one-sided confidence interval
图 17 0 ms延期时间下对数峰值振速的频率直方图及95%单侧置信区间上限值
Figure 17. Frequency histogram of logarithmic peak velocity at 0 ms delay time and upper bound of 95% one-sided confidence interval
图 18 不同延期时间下的爆破降振率
Figure 18. Vibration reduction rate of blasting under different delay times
图 19 不同回归算法下的R2、RMSE对比结果
Figure 19. Comparison of R2 and RMSE under different regression algorithms
图 21 降振率随爆心距的变化
Figure 21. Variation of vibration reduction ratio with detonation distance
图 25 不同孔间延时的主频变化
Figure 25. Changes of the dominant frequency with different inter-hole delays
图 26 不同回归算法下的R2、RMSE对比结果
Figure 26. Comparison of R2 and RMSE under dfferent regression algorithms
图 28 主频随爆心距的变化情况
Figure 28. Variation of dominant frequency with detonation center distance
图 33 不同孔间延时的低频能量变化
Figure 33. Variation of low-frequency energy with different inter-hole delay times
图 34 不同孔间延时的高频能量变化
Figure 34. Variation of high-frequency energy with different inter-hole delays
图 35 不同回归算法下的R2、RMSE对比结果
Figure 35. Comparison of R2 and RMSE under different regression algorithms
图 38 低频能量随爆心距的变化情况
Figure 38. Variation of low-frequency energy with detonation center distance
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