Influence of delay time between holes on the time-frequency characteristics of blast vibration propagation based on Monte Carlo method
-
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
-
[1] 李胜林, 梁书锋, 李晨, 等. 露天矿山深孔台阶爆破技术的现状与发展趋势 [J]. 矿业科学学报, 2021, 6(5): 598–605. DOI: 10.19606/j.cnki.jmst.2021.05.009.LI S L, LIANG S F, LI C, et al. Current status and development trend of deep hole bench blasting technology in open-pit mines [J]. Journal of Mining Science and Technology, 2021, 6(5): 598–605. DOI: 10.19606/j.cnki.jmst.2021.05.009. [2] 漆佳裕, 杨朝云, 周鹭, 等. 银山矿业露天采场生产爆破振动测试分析 [J]. 铜业工程, 2019(5): 45–50. DOI: 10.3969/j.issn.1009-3842.2019.05.012.QI J Y, YANG Z Y, ZHOU L, et al. Vibration testing and research analysis of production blasting in an open-pit mine [J]. Copper Engineering, 2019(5): 45–50. DOI: 10.3969/j.issn.1009-3842.2019.05.012. [3] 潘荣森, 陈浩, 杨砚, 等. 露天高陡型边坡爆破振动监测和稳定性分析 [J]. 铜业工程, 2023(2): 141–146. DOI: 10.3969/j.issn.1009-3842.2023.02.020.PAN R S, CHEN H, YANG Y, et al. Blasting vibration monitoring and stability of open high steep slope [J]. Copper Engineering, 2023(2): 141–146. DOI: 10.3969/j.issn.1009-3842.2023.02.020. [4] 赵凯, 赵丁凤, 张东, 等. 地铁隧道毫秒延时爆破环境振动特性研究 [J]. 爆炸与冲击, 2020, 40(10): 105201. DOI: 10.11883/bzycj-2019-0445.ZHAO K, ZHAO D F, ZHANG D, et al. Characteristics of environmental vibration induced by millisecond-delay blasting in metro tunnel excavation [J]. Explosion and Shock Waves, 2020, 40(10): 105201. DOI: 10.11883/bzycj-2019-0445. [5] 谢烽, 韩亮, 刘殿书, 等. 基于叠加原理的隧道爆破近区振动规律研究 [J]. 振动与冲击, 2018, 37(2): 182–188. DOI: 10.13465/j.cnki.jvs.2018.02.027.XIE F, HAN L, LIU D S, et al. Vibration law analysis for a tunnel's field near blasting based on waveform superposition theory [J]. Journal of Vibration and Shock, 2018, 37(2): 182–188. DOI: 10.13465/j.cnki.jvs.2018.02.027. [6] NORÉN-COSGRIFF K M, RAMSTAD N, NEBY A, et al. Building damage due to vibration from rock blasting [J]. Soil Dynamics and Earthquake Engineering, 2020, 138: 106331. DOI: 10.1016/j.soildyn.2020.106331. [7] YANG J H, LU W B, JIANG Q H, et al. A study on the vibration frequency of blasting excavation in highly stressed rock masses [J]. Rock Mechanics and Rock Engineering, 2016, 49(7): 2825–2843. DOI: 10.1007/s00603-016-0964-6. [8] 孙金山, 李正川, 刘贵应, 等. 爆破振动在边坡岩土介质中诱发的动应力与振动特征分析 [J]. 振动与冲击, 2018, 37(10): 141–148. DOI: 10.13465/j.cnki.jvs.2018.10.021.SUN J S, LI Z C, LIU G Y, et al. Dynamic stress and vibration characteristics of geomaterials in slopes induced by blasting vibration [J]. Journal of Vibration and Shock, 2018, 37(10): 141–148. DOI: 10.13465/j.cnki.jvs.2018.10.021. [9] HAO H, WU C Q. Numerical study of characteristics of underground blast induced surface ground motion and their effect on above-ground structures. Part II. Effects on structural responses [J]. Soil Dynamics and Earthquake Engineering, 2005, 25(1): 39–53. DOI: 10.1016/j.soildyn.2004.08.002. [10] SINGH T N, DONTHA L K, BHARDWAJ V. Study into blast vibration and frequency using ANFIS and MVRA [J]. Mining Technology: Transactions of the Institutions of Mining and Metallurgy, 2008, 117(3): 116–121. DOI: 10.1179/037178409x405741. [11] PARK D, JEON B, JEON S. A numerical study on the screening of blast-induced waves for reducing ground vibration [J]. Rock Mechanics and Rock Engineering, 2009, 42(3): 449–473. DOI: 10.1007/s00603-008-0016-y. [12] BLAIR D P. Blast vibration control in the presence of delay scatter and random fluctuations between blastholes [J]. International Journal for Numerical and Analytical Methods, 1993, 17(2): 95–118. DOI: 10.1002/nag.1610170203. [13] BLAIR D P, ARMSTRONG L W. The spectral control of ground vibration using electronic delay detonators [J]. Fragblast, 1999, 3(4): 303–334. DOI: 10.1080/13855149909408055. [14] 何理, 殷琳, 钟冬望, 等. 爆破振动强度、波形与频谱研究综述预测及主动控制 [J]. 爆破, 2024, 41(3): 189–204,262. DOI: 10.3963/j.issn.1001-487x.2024.03.023.HE L, YIN L, ZHONG D W, et al. Research review on blast vibration intensity, waveform and spectrum: prediction and active control [J]. Blasting, 2024, 41(3): 189–204,262. DOI: 10.3963/j.issn.1001-487x.2024.03.023. [15] LIU J, ZHANG Y, YUN B. A new method for predicting nonlinear structural vibrations induced by ground impact loading [J]. Journal of Sound and Vibration, 2012, 331(9): 2129–2140. DOI: 10.1016/j.jsv.2011.12.029. [16] ANDERSON D A, RITTER A P, WINZER S R, et al. A method for site-specific prediction and control of ground vibration from blasting [C]//Proceedings of the 1st Minisymposium on Explosives and Blasting Research. San Diego, 1985: 28–42. [17] BLAIR D P. The measurement, modelling and control of ground vibrations due to blasting [C]//Proceedings of the 2nd International Symposium Rock Fragmentation by Blasting. Colorado, 1987. [18] BOLOTIN V V. Statistical theory of the aseismic design of structures[C]//Proceedings of the 2nd World Conference on Earthquake Engineering. Tokyo, 1960: 1365–1374. [19] HOUSNER G W, JENNINGS P C. Generation of artificial earthquakes [J]. Journal of the Engineering Mechanics Division, 1964, 90(1): 113–150. DOI: 10.1061/JMCEA3.0000448. [20] 李洪超, 韩昊轩, 李胜林, 等. 台阶单孔爆破振动预测模型的构建与参数确定 [J]. 岩土工程学报, 2025, 47(12): 2652–2662.LI H C, HAN H X, LI S L, et al. Construction and parameter determination of bench blasting vibration prediction model [J]. Chinese Journal of Geotechnical Engineering, 2025, 47(12): 2652–2662. [21] 刘翔宇, 龚敏, 杨仁树, 等. 基于蒙特卡洛的电子雷管延期误差对隧道爆破振动影响研究 [J]. 振动与冲击, 2023, 42(23): 192–198. DOI: 10.13465/j.cnki.jvs.2023.23.023.LIU X Y, GONG M, YANG R S, et al. Effects of delay error of electronic detonator on tunnel blasting vibration based on Monte Carlo method [J]. Journal of Vibration and Shock, 2023, 42(23): 192–198. DOI: 10.13465/j.cnki.jvs.2023.23.023. [22] ZHANG X Y, YAN P, LU W B, et al. Frequency spectrum characteristics of blast-induced vibration with electronic detonators in ground blasting [J]. Journal of Building Engineering, 2023, 74: 106892. DOI: 10.1016/j.jobe.2023.106892. [23] 凌同华, 李夕兵, 王桂尧. 爆破震动灾害主动控制方法研究 [J]. 岩土力学, 2007, 28(7): 1439–1442. DOI: 10.16285/j.rsm.2007.07.029.LING T H, LI X B, WANG G Y. A study on initiative control of blast vibration damages [J]. Rock and Soil Mechanics, 2007, 28(7): 1439–1442. DOI: 10.16285/j.rsm.2007.07.029. [24] 贾小勇, 徐传胜, 白欣. 最小二乘法的创立及其思想方法 [J]. 西北大学学报(自然科学版), 2006, 36(3): 507–511. DOI: 10.3321/j.issn:1000-274X.2006.03.040.JIA X Y, XU C S, BAI X. The invention and way of thinking on least squares [J]. Journal of Northwest University (Natural Science Edition), 2006, 36(3): 507–511. DOI: 10.3321/j.issn:1000-274X.2006.03.040. [25] MARQUARDT D W. An algorithm for least-squares estimation of nonlinear parameters [J]. Journal of the Society for Industrial and Applied Mathematics, 1963, 11(2): 431–441. DOI: 10.1137/0111030. [26] SEN P K. Estimates of the regression coefficient based on Kendall's tau [J]. Journal of the American Statistical Association, 1968, 63(324): 1379–1389. DOI: 10.1080/01621459.1968.10480934. [27] 王珺, 宋琼雅, 许岳培, 等. 效应量置信区间的原理及其实现 [J]. 心理技术与应用, 2019, 7(5): 284–296. DOI: 10.16842/j.cnki.issn2095-5588.2019.05.003.WANG J, SONG Q Y, XU Y P, et al. Calculating confidence intervals of Cohen's d and eta-squared: a practical primer [J]. Psychology: Techniques and Applications, 2019, 7(5): 284–296. DOI: 10.16842/j.cnki.issn2095-5588.2019.05.003. [28] 韩亮. 深孔台阶爆破近区振动效应的试验研究 [D]. 北京: 中国矿业大学(北京), 2016.HAN L. Experimental study on vibration effect of deep Hole bench blasting in near field [D]. Beijing: China University of Mining and Technology (Beijing), 2016. [29] HUANG D, CUI S, LI X Q. Wavelet packet analysis of blasting vibration signal of mountain tunnel [J]. Soil Dynamics and Earthquake Engineering, 2019, 117: 72–80. DOI: 10.1016/j.soildyn.2018.11.025. [30] AMIRI G G, ASADI A. Comparison of different methods of wavelet and wavelet packet transform in processing ground motion records [J]. International Journal of Civil Engineering, 2009, 7(4): 248–257. [31] LING T H, LI X B, DAI T G, et al. Features of energy distribution for blast vibration signals based on wavelet packet decomposition [J]. Journal of Central South University of Technology, 2005, 12(S1): 135–140. DOI: 10.1007/s11771-005-0387-0. -
下载:
计量
- 文章访问数: 325
- HTML全文浏览量: 50
- PDF下载量: 60
- 被引次数: 0