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Article(id=1241355807430865515, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241355799189058005, articleNumber=null, orderNo=null, doi=10.3963/j.issn.1001-487X.2023.04.014, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1673539200000, receivedDateStr=2023-01-13, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773891887767, onlineDateStr=2026-03-19, pubDate=1701360000000, pubDateStr=2023-12-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773891887767, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773891887767, creator=13701087609, updateTime=1773891887767, updator=13701087609, issue=Issue{id=1241355799189058005, tenantId=1146029695717560320, journalId=1240670690148397066, year='2023', volume='40', issue='4', pageStart='1', pageEnd='229', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773891885801, creator=13701087609, updateTime=1773898068569, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241381731652129441, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241355799189058005, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241381731652129442, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241355799189058005, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=103, endPage=109, ext={EN=ArticleExt(id=1241355807720272505, articleId=1241355807430865515, tenantId=1146029695717560320, journalId=1240670690148397066, language=EN, title=Experimental Study on Delay Time of Hole-by-hole Initiation based on HHT Spectrum Analysis, columnId=1240702072862069231, journalTitle=Blasting, columnName=BLASTING IN ORE AND ROCK, runingTitle=null, highlight=null, articleAbstract=

In order to solve the problem that excessive blasting vibration affects the safety of village buildings (structures) on the earth's surface during the mining process of an underground orebody, the inter-hole delays of 8 ms, 10 ms, 12 ms, 14ms and 18ms and inter-row delay of 100 ms were selected for tests in the #63113 ore room of the orebody III in the mine. By combining the actual situation of the site and the empirical formula, the natural vibration frequency of the brick-concrete buildings with 1 to 2 floors in the village was 7.63~13.23 Hz. The blasting vibration data was collected on site and HHT transformation was applied on the measured blasting vibration signals by MATLAB. The characteristics of the signals were then analyzed from the perspectives of time domain, frequency domain and energy. The highly adaptive EMD decomposition was used to decompose the original vibration signal into the IMF components which were transformed by 10-layer db8 wavelet transform and the proportion of energy in the total energy of the frequency band 7.8~15.7 Hz of level 9 was summarized. The three-dimensional Hilbert spectrum and marginal spectrum were obtained by Hilbert transformation of the reconstructed signal with the IMF components. Through EMD decomposition and wavelet transform research on the blasting vibration signals, it is concluded that the three-direction energy ratio corresponding to the 12 ms delay time at No.3 measuring point is reduced by 14.07%, 24.89% and 6.26%, respectively. The experiments show that the problem that the problem that the low frequency energy takes a large proportion in the total energy can be improved by optimizing the inter-hole delay, and the resonance effect can be effectively avoided. By comparing the Hilbert marginal spectrum and the three-dimensional Hilbert spectrum with different delay times, the main vibration frequency and the maximum instantaneous energy of the blasting with an inter-hole delay of 12 ms appear 200 ms after the detonation, concentrated in the range of 30~40 Hz which is higher than the natural vibration band of the buildings, and thus have the least influence on the structures.

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为解决某矿山矿体回采时爆破振动过大影响地表村庄建（构）筑物安全的问题，通过结合现场实际情况与经验公式计算，选取8、10、12、14和18 ms的孔间微差时间和100 ms的排间微差时间作为在该矿Ⅲ矿体63113矿房试验的爆破参数，根据村庄多为1~2层砖混结构建筑计算得到其自振频率7.63~13.23 Hz。现场采集爆破振动数据并利用Matlab对测得的爆破振动信号做HHT变换并从时域、频域和能量的角度分析信号的特点。使用具有高度自适应性的EMD分解将原始振动信号分解为IMF分量，再对IMF分量做10层db8小波变换并总结level 9的频带7.8~15.7 Hz具有的能量在总能量中的占比规律，对用IMF分量重构后的信号做Hilbert变换得到三维希尔伯特谱及边际谱。通过对爆破振动信号做EMD分解和小波变换研究得出，12 ms的微差时间设计在3号测点的三向能量占比分别减小了14.07%、24.89%和6.26%，试验表明通过改进孔间微差时间可以改善低频能量在总能量中占比较多的问题，能有效避免共振效应。对比不同孔间微差时间的Hilbert边际谱和三维希尔伯特谱从频域和能量角度分析得出，孔间微差时间为12 ms的爆破的主振频率和最大瞬时能量出现在起爆后200 ms，集中在大于建筑固有自振频带的30~40 Hz间，对建（构）筑物产生的影响最小。试验通过HHT频谱分析为选择合理的逐孔微差起爆时间提供了有效的判断依据，为更多类似的研究提供了思路与方向。

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褚夫蛟（1988-），男，讲师、博士（后），主要从事矿山安全及控制爆破研究，（E-mail）。

CHU Fu-jiao (1988-), male, lecturer, postdoc, mainly engaged in mine safety and controlled blasting, (E-mail) .

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褚夫蛟（1988-），男，讲师、博士（后），主要从事矿山安全及控制爆破研究，（E-mail）。

CHU Fu-jiao (1988-), male, lecturer, postdoc, mainly engaged in mine safety and controlled blasting, (E-mail) .

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褚夫蛟（1988-），男，讲师、博士（后），主要从事矿山安全及控制爆破研究，（E-mail）。

CHU Fu-jiao (1988-), male, lecturer, postdoc, mainly engaged in mine safety and controlled blasting, (E-mail) .

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journalId=1240670690148397066, articleId=1241355807430865515, language=EN, label=Table 1, caption=

Blasting vibration data when the delay time is 10 ms

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测点编号爆心距/m径向速度/（cm·s-1）径向频率/Hz切向速度/（cm·s-1）切向频率/Hz垂向速度/（cm·s-1）垂向频率/Hz
1396.330.0815.810.1022.100.1320.51
2463.240.0929.850.1721.280.4354.05
3553.340.0517.860.1120.620.2143.01
), ArticleFig(id=1241355818646434072, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355807430865515, language=CN, label=表1, caption=

微差时间为10 ms时的爆破振动数据

, figureFileSmall=null, figureFileBig=null, tableContent=
测点编号爆心距/m径向速度/（cm·s-1）径向频率/Hz切向速度/（cm·s-1）切向频率/Hz垂向速度/（cm·s-1）垂向频率/Hz
1396.330.0815.810.1022.100.1320.51
2463.240.0929.850.1721.280.4354.05
3553.340.0517.860.1120.620.2143.01
), ArticleFig(id=1241355818768068893, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355807430865515, language=EN, label=Table 2, caption=

EMD decomposition results of blasting vibration signal with a delay time of 14 ms

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sig14 ms径向切向垂向
Frequencies/HzRelative Energy/%Frequencies/HzRelative Energy/%Frequencies/HzRelative Energy/%
IMF1254~38100.02393~38100.01288~38300.03
IMF2152~16000.01307~15800.0018.8~850.66
IMF36~23.335.937.42~25.357.198.14~52.756.96
IMF40.659~22.238.114.27~1931.235.98~30.823.44
IMF51.74~13.110.533.25~10.27.373.35~15.915.99
IMF62.09~5.0213.313.39~7.283.812.89~10.41.07
IMF70.82~2.320.990.405~3.030.120.593~3.030.99
IMF80.481~3.130.570.276~0.7410.250.757~1.890.21
IMF90.28~3.620.53--0.251~0.7430.15
Residual0.0125~0.2380.010.0178~0.6960.010.0151~0.8760.51
), ArticleFig(id=1241355820269629730, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355807430865515, language=CN, label=表2, caption=

微差时间为14 ms时的爆破振动信号EMD分解结果

, figureFileSmall=null, figureFileBig=null, tableContent=
sig14 ms径向切向垂向
Frequencies/HzRelative Energy/%Frequencies/HzRelative Energy/%Frequencies/HzRelative Energy/%
IMF1254~38100.02393~38100.01288~38300.03
IMF2152~16000.01307~15800.0018.8~850.66
IMF36~23.335.937.42~25.357.198.14~52.756.96
IMF40.659~22.238.114.27~1931.235.98~30.823.44
IMF51.74~13.110.533.25~10.27.373.35~15.915.99
IMF62.09~5.0213.313.39~7.283.812.89~10.41.07
IMF70.82~2.320.990.405~3.030.120.593~3.030.99
IMF80.481~3.130.570.276~0.7410.250.757~1.890.21
IMF90.28~3.620.53--0.251~0.7430.15
Residual0.0125~0.2380.010.0178~0.6960.010.0151~0.8760.51
), ArticleFig(id=1241355820445790506, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355807430865515, language=EN, label=Table 3, caption=

Energy Ratio between 7.8~15.7 Hz and total energy in three directions under different designs/%

, figureFileSmall=null, figureFileBig=null, tableContent=
 径向/%切向/%垂向/%
原设计34.8741.1323.78
8 ms设计23.2827.3012.31
10 ms设计28.8619.517.35
12 ms设计20.8016.2417.52
14 ms设计33.8631.6834.15
18 ms设计24.0632.539.65
), ArticleFig(id=1241355820559036719, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355807430865515, language=CN, label=表3, caption=

不同设计下7.8~15.7 Hz间能量分别占三向总能量比值/%

, figureFileSmall=null, figureFileBig=null, tableContent=
 径向/%切向/%垂向/%
原设计34.8741.1323.78
8 ms设计23.2827.3012.31
10 ms设计28.8619.517.35
12 ms设计20.8016.2417.52
14 ms设计33.8631.6834.15
18 ms设计24.0632.539.65
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基于HHT频谱分析逐孔起爆微差时间试验研究
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褚夫蛟 1 , 王作鹏 2 , 李铭涵 1 , 高智 1 , 丁明海 1 , 殷树海 1
爆破 | 矿岩爆破 2023,40(4): 103-109
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爆破 | 矿岩爆破 2023, 40(4): 103-109
基于HHT频谱分析逐孔起爆微差时间试验研究
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褚夫蛟1 , 王作鹏2, 李铭涵1, 高智1, 丁明海1, 殷树海1
作者信息
  • 1.山东理工大学　资源与环境工程学院，淄博　255000
  • 2.山东东平宏达矿业有限公司，泰安　271000

    • 褚夫蛟（1988-），男，讲师、博士（后），主要从事矿山安全及控制爆破研究，（E-mail）。

    CHU Fu-jiao (1988-), male, lecturer, postdoc, mainly engaged in mine safety and controlled blasting, (E-mail) .

Experimental Study on Delay Time of Hole-by-hole Initiation based on HHT Spectrum Analysis
Fu-jiao CHU1 , Zuo-peng WANG2, Ming-han LI1, Zhi GAO1, Ming-hai DING1, Shu-hai YIN1
Affiliations
  • 1.School of Resources and Environmental Engineering, Shandong University of Technology, Zibo 255000, China
  • 2.Shandong Dongping Hongda Mining Co., Ltd., Taian 271000, China
出版时间: 2023-12-01 doi: 10.3963/j.issn.1001-487X.2023.04.014
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摘要
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为解决某矿山矿体回采时爆破振动过大影响地表村庄建（构）筑物安全的问题，通过结合现场实际情况与经验公式计算，选取8、10、12、14和18 ms的孔间微差时间和100 ms的排间微差时间作为在该矿Ⅲ矿体63113矿房试验的爆破参数，根据村庄多为1~2层砖混结构建筑计算得到其自振频率7.63~13.23 Hz。现场采集爆破振动数据并利用Matlab对测得的爆破振动信号做HHT变换并从时域、频域和能量的角度分析信号的特点。使用具有高度自适应性的EMD分解将原始振动信号分解为IMF分量，再对IMF分量做10层db8小波变换并总结level 9的频带7.8~15.7 Hz具有的能量在总能量中的占比规律，对用IMF分量重构后的信号做Hilbert变换得到三维希尔伯特谱及边际谱。通过对爆破振动信号做EMD分解和小波变换研究得出，12 ms的微差时间设计在3号测点的三向能量占比分别减小了14.07%、24.89%和6.26%，试验表明通过改进孔间微差时间可以改善低频能量在总能量中占比较多的问题，能有效避免共振效应。对比不同孔间微差时间的Hilbert边际谱和三维希尔伯特谱从频域和能量角度分析得出，孔间微差时间为12 ms的爆破的主振频率和最大瞬时能量出现在起爆后200 ms，集中在大于建筑固有自振频带的30~40 Hz间，对建（构）筑物产生的影响最小。试验通过HHT频谱分析为选择合理的逐孔微差起爆时间提供了有效的判断依据，为更多类似的研究提供了思路与方向。

HHT  /  微差时间  /  EMD  /  小波变换  /  自振频率

In order to solve the problem that excessive blasting vibration affects the safety of village buildings (structures) on the earth's surface during the mining process of an underground orebody, the inter-hole delays of 8 ms, 10 ms, 12 ms, 14ms and 18ms and inter-row delay of 100 ms were selected for tests in the #63113 ore room of the orebody III in the mine. By combining the actual situation of the site and the empirical formula, the natural vibration frequency of the brick-concrete buildings with 1 to 2 floors in the village was 7.63~13.23 Hz. The blasting vibration data was collected on site and HHT transformation was applied on the measured blasting vibration signals by MATLAB. The characteristics of the signals were then analyzed from the perspectives of time domain, frequency domain and energy. The highly adaptive EMD decomposition was used to decompose the original vibration signal into the IMF components which were transformed by 10-layer db8 wavelet transform and the proportion of energy in the total energy of the frequency band 7.8~15.7 Hz of level 9 was summarized. The three-dimensional Hilbert spectrum and marginal spectrum were obtained by Hilbert transformation of the reconstructed signal with the IMF components. Through EMD decomposition and wavelet transform research on the blasting vibration signals, it is concluded that the three-direction energy ratio corresponding to the 12 ms delay time at No.3 measuring point is reduced by 14.07%, 24.89% and 6.26%, respectively. The experiments show that the problem that the problem that the low frequency energy takes a large proportion in the total energy can be improved by optimizing the inter-hole delay, and the resonance effect can be effectively avoided. By comparing the Hilbert marginal spectrum and the three-dimensional Hilbert spectrum with different delay times, the main vibration frequency and the maximum instantaneous energy of the blasting with an inter-hole delay of 12 ms appear 200 ms after the detonation, concentrated in the range of 30~40 Hz which is higher than the natural vibration band of the buildings, and thus have the least influence on the structures.

HHT  /  millisecond time  /  EMD  /  wavelet transform  /  natural frequency
褚夫蛟, 王作鹏, 李铭涵, 高智, 丁明海, 殷树海. 基于HHT频谱分析逐孔起爆微差时间试验研究. 爆破, 2023 , 40 (4) : 103 -109 . DOI: 10.3963/j.issn.1001-487X.2023.04.014
Fu-jiao CHU, Zuo-peng WANG, Ming-han LI, Zhi GAO, Ming-hai DING, Shu-hai YIN. Experimental Study on Delay Time of Hole-by-hole Initiation based on HHT Spectrum Analysis[J]. Blasting, 2023 , 40 (4) : 103 -109 . DOI: 10.3963/j.issn.1001-487X.2023.04.014
正文
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现阶段金属矿山的爆破向着大直径、大孔深的方向发展，单孔爆破的药量也超过150 kg，同时越来越多的矿山分布在村庄以下或村庄附近，地下爆破作用引起的弹性震动会一直传递至地表村庄，对村庄建（构）筑物的安全稳定造成一定影响。为减小爆破振动对村庄的影响，通过选取合理的微差间隔时间减小爆破振动强度，改善爆破振动频率分布，达到爆破减振，维护地表建构筑物安全稳定的目标。
目前，国内外学者在爆破振动信号分析领域都有大量研究，其中的希尔伯特黄变换（Hilbert-Huang Transform，HHT）主要内容包含两部分，第一部分为经验模态分解（Empirical Mode Decomposition，EMD），第二部分为Hilbert谱分析（Hilbert Spectrum Analysis，HSA）。利用EMD方法将给定的信号分解结果为若干固有模态函数（Intrinsic Mode Function，IMF），也称作本征模态函数。李祥龙等基于EMD-HHT和小波理论研究了地下浅孔爆破振动规律[1]，得到了爆破振动信号的主要优势能量频带和能量分布时间主要集中在50 Hz、0.65 s以内的结论。Battista等将HHT应用于地震信号反馈中[2,3]，对评价EMD在时域和频域中的量化有意义。张智宇等基于HHT频谱分析研究了断层对地震波传播的影响[4]，研究发现低频作用对地震波传播影响更加明显。李建军利用HHT分析法对岩墙浅孔爆破开挖在既有铁路接触网铁塔基础处产生的振动波进行了处理和分析[5]。宋肖龙等研究了爆破振动对隧道围岩累积损伤效应的影响[6]，基于瞬时振幅的差异将损伤区域分为了微损伤和严重损伤区域。通过小波理论和HHT变换对爆破振动信号分析已经成为成熟的分析方法，正广泛应用于爆破工程实践的诸多领域。
基于以上研究，设计合理爆破试验方案，通过公式计算选取合适的孔间微差间隔时间区间和建（构）筑物的自振频率，做现场爆破试验并记录不同孔间微差时间爆破产生的振动信号，并对信号依次做HHT变换，振动信号经过EMD分解、小波包分析和Hilbert变换后，从时域、频域和能量的角度分析评价某矿山因回采产生的爆破振动对地表村庄建（构）筑物安全构成影响的因素，并选取最优的孔间微差时间。
1　项目概况及爆破试验
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1.1　项目概况
某铁矿山地处冲积平原，矿山周围有数个村庄，矿体从部分村庄下穿过。矿区内有多条矿体，其中的Ⅱ矿体和Ⅲ矿体从村庄下穿过，Ⅱ矿体为本生产阶段主要出矿矿体，主要开采水平在-260 m和-320 m，测试矿房选择较为方便、距离村庄较近的63113矿房。测试矿房与最近村庄村口（3号测点处）的水平标高分别为-320 m和44 m，二者水平距离约350 m，村庄与矿体位置关系及测点布置如图1所示。
矿山采用沿走向阶段空场嗣后充填采矿法，阶段高度60 m，爆破方式分为上向扇形中深孔爆破和下向平行深孔爆破，矿体爆破结构如图2所示。下向孔孔径140 mm，孔深35 m，孔排间距2.5 m×2.5 m，采用岩渣炸药间隔装药，单孔装药量160 kg，方形布孔，采用岩石粉状乳化炸药，使用数码电子雷管导爆索联合逐孔微差起爆。上向扇形中深孔爆破炮孔孔径小，一次爆破方量小，爆炸能量释放少，产生的爆破振动效应不显著，下向平行深孔爆破一次所耗药量更大，爆破释放的能量更多，产生的爆破振动效应更明显，故选下向平行深孔爆破时的爆破振动信号做HHT变换并分析。
1.2　爆破试验
为实现既能减小爆破振动，又能保持良好爆破效果的目的，设计先采用经验公式求出合理微差时间区间，再从合理区间内优选数组微差时间做爆破试验，爆破试验在原爆破方案的基础上只对爆破微差时间做了修改，其余参数不变。求合理微差时间区间采用我国长沙矿冶研究院对大冶铁矿进行逐孔起爆实验得到的孔间延期时间的经验公式[7]
式中：Δt1为孔间延期时间，ms；Q为炮孔的平均装药量，kg；γe为炸药容重，5 kN/m3；γr为矿石容重，kN/m3；D为炸药爆速，m/s；Cr为矿石纵波波速，m/s；S为矿石移动距离，mm；V为矿块平均移动速度，mm/s。
由式（1）结合现场施工的实际数据计算得出孔间微差时间区间为8.176~17.314 ms，选取8、10、12、14和18 ms设置为每次爆破时的孔间微差间隔时间。通常认为两孔间隔100 ms起爆时，两孔产生的爆破振动波将不会互相影响，爆破效果与自由面的数量存在正相关的关系，合理选择最小抵抗线的距离也具有减振的效果[8]，为保证前排炮孔爆破后为后排炮孔的自由面形成留出充分的反应时间并便于观察孔间爆破振动波的波形叠加情况，检验设置不同孔间微差时间下的爆破效果。故参考预裂爆破的排间微差间隔时间，设置排间微差时间为100 ms。进行5次爆破试验并采集三个测点的每次爆破振动信号，其中孔间微差时间为10 ms的爆破振动信号数据整理见表1，爆破信号振动图像如图3所示。对每次实测的爆破振动信号做HHT变换并分析。
2　爆破振动信号HHT频谱分析
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2.1　EMD分解与小波包分析
对三个测点采集到的所有爆破振动信号做HHT变换后分析发现，各测点间的爆破振动波的传播规律相近，故只对村口的3号测点的爆破振动信号做详细的时频分析[8]。
基于Matlab对采集到的原爆破设计和孔间微差时间为8、10、12、14和18 ms的爆破振动信号做EMD分解后，剔除属于噪音的IMF分量并对剩余的IMF分量选用db8小波做10层小波包变换。EMD分解设置根据爆破振动监测仪TC-4850的采样频率设置为16 000 Hz，由Shannon采样定理可知，其Nyquist频率为8000 Hz。进行EMD分解和小波包变换得到，不同微差间隔时间下各测点信号的IMF分量的频率分布和相对能量大小。以微差时间为12 ms的垂向爆破振动信号经过9次EMD分解为例得到的各阶本征模态函数和残差如图4所示。
为减小爆破振动与建（构）筑物产生的共振效应[9]，先求出建构筑物的自振频率，矿山附近村庄的民房多为1~2层的自建砖混结构，建筑高度在3.3~6.6 m之间。中国科学院工程力学研究所按等截面悬臂梁的推导以及多层砖石建筑物动力特性的测定，自振周期与建（构）筑物高度最为密切，提出建（构）筑物的基本自振周期估算式如式（2）所示[10]
式中：fs为一般砌体建筑固有频率；H为建筑高度，带入村庄建筑高度3.3~6.6 m。计算得村庄建筑固有频率为7.63~13.23 Hz。为尽可能减少爆破地震与建筑物的共振，分析爆破振动信号中频率在7.63~13.23 Hz的能量占该段信号总能量的比重，并以该频带能量占比较小的设计作为合理设计。爆破振动产生能量的频率可以高达200 Hz，称频率在7.63~13.23 Hz之间及以下的能量为低频能量[11,12]。
通过分析所有IMF分量发现，无论是原爆破微差时间设计还是新微差时间设计，三向的爆破振动能量都在7.63~13.23 Hz之间有着分布，其中分布特征最显著的是3号测点孔间微差时间为14 ms时的EMD分解结果，EMD分解结果见表2。以孔间微差时间为14 ms时为例，径向相对能量占比较大的频带主要为6~23.3 Hz和0.659~22.2 Hz，两频带相对能量占比达到74.04%，切向的优势频带为7.42~25.3 Hz和4.27~19 Hz，此时两频带相对能量占比高达88.42%，相比之下垂向相对能量占比较大的频带整体上移为8.14~52.7 Hz和5.98~30.8 Hz，两频带相对能量占比达到80.4%。新旧爆破方案在实际爆破过程中都会出现爆破地震与建筑物产生共振的能量。
对IMF分量选用db8小波做10层小波包变换，得到频带7.8~15.7 Hz产生的能量在单个方向总能量中的占比。具体能量占比见表3，表3中“原设计”为经小波分解后原爆破设计下频带为7.8~15.7 Hz产生的能量占比的平均值。相比于原起爆参数设计，新设计的微差爆破产生的7.8~15.7 Hz的能量在三向总能量占比都有明显减小，其中以12 ms的设计效果最好，3号测点的径向、切向和垂向能量占比分别减小了14.07%、24.89%和6.26%。1号测点的三向能量占比分别减小了23.25%、31.21%和11.67%，2号测点的三向能量占比分别减小了7.31%、10.65%和12.51%。共振频率在径向和切向产生的能量占比大于垂向能量占比，这种情况不会随着微差时间的改变而有明显的改变。
综上所述，地下矿山爆破产生的爆破地震波传至地表时，具有低频能量多的特点，且低频能量的频率范围与地表建（构）筑物的自振频率相近，二者易产生共振。通过改变微差时间可以减小7.8~15.7 Hz的能量在总能量中的占比，能减小产生共振的概率，孔间微差时间设置为12 ms能取得最好的效果。修改后的微差起爆时间间隔较短，爆破作用时间也较短，更不易产生共振效应。
2.2　Hilbert变换与分析
经EMD分解后，原始信号分为多个IMF分量及其残差的组合，舍弃能量占比小且频率过大和过小的IMF分量以及残差，并对信号进行重构，即可得到重构信号的Hilbert谱，再Hilbert谱加入能量域的方向向量就得到三维希尔伯特谱。
三维希尔伯特谱是HHT变换得到的最直观结果，其反映的是信号时间、瞬时频率和幅值之间的关系。该图谱可以用于分析包含混合分量信号中各分量随时间变化的规律，以识别局部特征，3号测点的三维希尔伯特谱如图5所示。Hilbert边际谱就是在三维希尔伯特谱的时频平面上，各频率点振幅在时间总体上的累积，也就是频率相同、总时长上所有振幅的叠加，从统计意义上表征了整组数据每个频率点的累积幅值分布，3号测点的Hilbert边际谱如图6所示。
从图5（a）、图6（a）可以看出，当微差时间为8 ms时主振频率集中在15~30 Hz，瞬时能量较高的信号频率集中在5~15 Hz中间，此时振动频率过于向低频段集中，与当地建（构）筑物的自振频率7.63~13.23 Hz相近，不利于建（构）筑物的安全稳定。从图5（b）、图6（b）可以看出，当微差时间为10 ms时，主振频率在30 Hz左右，瞬时能量峰值较大处集中在350 ms时的10~15 Hz。从图5（c）、图6（c）可以看出，当微差时间为12 ms时，信号的主振频率在30~40 Hz之间，相比之下瞬时能量相差不大，该微差时间比较能符合减振设计。从图5（d）、图6（d）可以看出，当微差间隔时间为14 ms时，信号的主振频率集中在12~17 Hz，并且振动的幅值相比于其他微差间隔时间高出一个量级，故较接近于低频能量的瞬时能量若作用强度过大、作用时间过长时也会对建（构）筑物造成不利影响。从图5（e）、图6（e）可以看出，当微差间隔时间为18 ms时，重构信号主频在30 Hz，此时瞬时能量也集中于30 Hz，开始作用时间为200 ms，第二段较大的瞬时能量发生在700 ms，虽然瞬时能量峰值有所下降但是振动频率却下降到10 Hz左右，属于会危害到地表建（构）筑物的低频能量。
综上所述，选择主振频率大于7.63~13.23 Hz频带的微差时间设计更有利于地表建（构）筑物安全，从主振频率和瞬时能量的角度看选择12 ms作为微差时间可以最大程度地降低共振对建（构）筑物结构造成的不利影响。
3　结论
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（1）通过结合施工现场数据和经验公式计算得出8.176~17.314 ms的孔间微差时间区间，确定了孔间微差时间8、10、12、14、18 ms，排间微差时间100 ms作为现场爆破试验参数。
（2）结合中国科学院工程力学研究所提出的建筑物固有自振频率计算式计算得出的建筑自振频率为7.63~13.23 Hz。
（3）通过对各测点爆破震动信号做EMD分解和小波包分解后分析得出，爆破振动波在低频能量上对总能量有较多贡献，通过改变微差起爆时间可以减少低频能量在总能量中的占比，其中微差时间为12 ms的设计的效果最佳。低频能量在径向和切向上的占比大于垂向上低频能量的占比大于垂向上的能量占比，这种情况不随着微差时间的改变而改变。
（4）通过对爆破振动信号进行HHT变换后，综合分析了边际谱和三维希尔伯特谱，当微差间隔时间为12 ms时，爆破振动信号主振频率和瞬时最大能量分布在30~40 Hz，不与建构筑物的自振频率相交，地表建（构）筑物所受瞬时能量影响较小，相比于原爆破设计，爆破振动作用时间短，建构筑物受扰动小，由此可知12 ms为最优孔间微差时间。
基金
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  • 国家自然科学基金(51904177)
文献
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参考文献 引证文献
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2023年第40卷第4期
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doi: 10.3963/j.issn.1001-487X.2023.04.014
  • 接收时间：2023-01-13
  • 首发时间：2026-03-19
  • 出版时间：2023-12-01
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  • 收稿日期：2023-01-13
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Project supported by the National Natural Science Foundation of China(51904177)
国家自然科学基金(51904177)
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    1.山东理工大学　资源与环境工程学院，淄博　255000
    2.山东东平宏达矿业有限公司，泰安　271000
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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