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Article(id=1241355800166323195, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241355799189058005, articleNumber=null, orderNo=null, doi=10.3963/j.issn.1001-487X.2023.04.011, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1668268800000, receivedDateStr=2022-11-13, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773891886035, onlineDateStr=2026-03-19, pubDate=1701360000000, pubDateStr=2023-12-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773891886035, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773891886035, creator=13701087609, updateTime=1773891886035, 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=82, endPage=88, ext={EN=ArticleExt(id=1241355800438952957, articleId=1241355800166323195, tenantId=1146029695717560320, journalId=1240670690148397066, language=EN, title=Research on Blasting Vibration Propagation Law and Vibration Reduction Technology for Tunnel Excavation, columnId=1240702072862069231, journalTitle=Blasting, columnName=BLASTING IN ORE AND ROCK, runingTitle=null, highlight=null, articleAbstract=

At present, mining method is widely used in tunnel construction. The influence of blasting vibration on surrounding rock and supporting structure in tunnel and its disaster control are always hot issues. In order to study the propagation law of blasting vibration inside a tunnel, the vibration signals of simultaneous detonation and detonation at three benches were monitored on site based on the engineering background of a tunnel with soft surrounding rock. The nonlinear regression of Sadovski formula and Fourier transform method were used to analyze and study the test data. The results show that for the same section of the tunnel, the vault has the characteristics of large vibration velocity, high vibration frequency and slow attenuation rate. When 100 ms delay blasting is used between the three steps, the blasting energy can be discretely distributed in time and space, and the vibration superposition effect can be significantly weakened. A single hole blasting test was set in the middle of the cut area, and the single hole vibration waveform was obtained by setting the delay between the test hole and the entire blast as 100 ms. Based on the principle of linear superposition, the delay time was optimized by investigating vibration waveforms synthesized by cut blasting. The results show that when the delay time between holes is 4~7 ms, the peak vibration velocity caused by cut blasting decreases sharply, and the effect of interference is obvious. After the delay time exceeds 7 ms, the peak vibration velocity has no significant difference.

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LIU Chuan-peng (1995-), male, mainly engaged in traffic civil engineering, (E-mail) .
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目前隧道施工普遍应用矿山法，爆破振动对隧道内围岩、支护结构的影响及其灾害控制一直是热点问题。为研究爆破振动在隧道内部的传播规律，以某软弱围岩隧道为工程背景，分别对错距三台阶齐爆和分爆的振动信号进行现场监测。采用萨道夫斯基公式非线性回归、Fourier变换方法对测试数据进行分析和研究。结果表明：对于隧道同一断面，拱顶具有振动速度大、振动主频高、衰减速度慢的特点；三台阶间采用100 ms延时爆破时，可以实现爆破能量在时空分布上的离散，振动叠加效应明显减弱。设计单孔爆破试验，掏槽区域中间设置试验孔，试验孔与整个爆破网络的延期设置为100 ms获取单孔振动波形，基于线性叠加原理，计算不同延期时间下掏槽爆破合成振动波形来优选微差延期时间。结果表明：孔间延期时间在4~7 ms时，掏槽爆破引起的峰值振速急剧下降，干扰降振的效果明显，延时超过7 ms后，峰值振速无显著差异；掏槽孔延期时间取7 ms时减振效果最佳，将最佳延期时间应用于现场爆破，取得了良好的降振效果。

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刘传鹏（1995-），男，主要研究方向为交通土建，（E-mail）。
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项荣军（1989-），男，主要研究方向为交通土建，（E-mail）。

XIANG Rong-jun (1989-), male, mainly engaged in traffic civil engineering, (E-mail) .

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项荣军（1989-），男，主要研究方向为交通土建，（E-mail）。

XIANG Rong-jun (1989-), male, mainly engaged in traffic civil engineering, (E-mail) .

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项荣军（1989-），男，主要研究方向为交通土建，（E-mail）。

XIANG Rong-jun (1989-), male, mainly engaged in traffic civil engineering, (E-mail) .

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(in Chinese), articleTitle=Determination of tunnel electronic detonator blasting parameters under the condition of free surface change, refAbstract=null), Reference(id=1241355818520597409, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355800166323195, doi=null, pmid=null, pmcid=null, year=2012, volume=32, issue=1, pageStart=84, pageEnd=90, url=null, language=null, rfNumber=[19], rfOrder=36, authorNames=杨年华, 张乐, journalName=爆炸与冲击, refType=null, unstructuredReference=杨年华, 张乐. 爆破振动波叠加数值预测方法[J]. 爆炸与冲击, 2012, 32(1): 84-90., articleTitle=爆破振动波叠加数值预测方法, refAbstract=null), Reference(id=1241355818625455019, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355800166323195, doi=null, pmid=null, pmcid=null, year=2012, volume=32, issue=1, pageStart=84, pageEnd=90, url=null, language=null, rfNumber=[19], rfOrder=37, authorNames=YANG Nian-hua, ZHANG Le, journalName=Explosion and Shock Waves, refType=null, unstructuredReference=YANG Nian-hua, ZHANG Le. Blasting vibration waveform prediction method based on superposition principle[J]. Explosion and Shock Waves, 2012, 32(1): 84-90. (in Chinese), articleTitle=Blasting vibration waveform prediction method based on superposition principle, refAbstract=null), Reference(id=1241355818776449969, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355800166323195, doi=null, pmid=null, pmcid=null, year=2009, volume=15, issue=3, pageStart=17, pageEnd=21, url=null, language=null, rfNumber=[20], rfOrder=38, authorNames=张光雄, 杨军, 卢红卫, journalName=工程爆破, refType=null, unstructuredReference=张光雄, 杨军, 卢红卫. 毫秒延时爆破干扰降振作用研究[J]. 工程爆破, 2009, 15(3): 17-21., articleTitle=毫秒延时爆破干扰降振作用研究, refAbstract=null), Reference(id=1241355820328342455, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355800166323195, doi=null, pmid=null, pmcid=null, year=2009, volume=15, issue=3, pageStart=17, pageEnd=21, url=null, language=null, rfNumber=[20], rfOrder=39, authorNames=ZHANG Guang-xiong, YANG Jun, LU Hong-wei, journalName=Engineering Blasting, refType=null, unstructuredReference=ZHANG Guang-xiong, YANG Jun, LU Hong-wei. Research on seismic waveinterference effect of millisecond blasting[J]. Engineering Blasting, 2009, 15(3): 17-21. 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label=Fig. 8, caption=Statistical graph of peak vibration velocity under different delay times, figureFileSmall=PetmcO1oOvCW24Cj95uMEg==, figureFileBig=BMtg2/tVZEb3b0Nu8/7R/A==, tableContent=null), ArticleFig(id=1241355811415445975, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355800166323195, language=CN, label=图8, caption=不同延期时间下的峰值振速统计图, figureFileSmall=PetmcO1oOvCW24Cj95uMEg==, figureFileBig=BMtg2/tVZEb3b0Nu8/7R/A==, tableContent=null), ArticleFig(id=1241355811524497891, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355800166323195, language=EN, label=Table 1, caption=

Blasting parameters of upper bench

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炮孔分类炮孔数/个延期设置/ms炮孔长度/m炮孔装药量
孔药卷数/（卷/孔）单孔装药量/kg合计药量/kg
掏槽孔6503.082.414.4
扩槽孔61003.061.810.8
辅助孔      
周边孔243502.541.228.8
底板孔104002.661.818.0
合计77    116.7
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上台阶爆破参数表

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炮孔分类炮孔数/个延期设置/ms炮孔长度/m炮孔装药量
孔药卷数/（卷/孔）单孔装药量/kg合计药量/kg
掏槽孔6503.082.414.4
扩槽孔61003.061.810.8
辅助孔      
周边孔243502.541.228.8
底板孔104002.661.818.0
合计77    116.7
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Comparison of K and α values of the fitting curve

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测点位置径向切向竖向
KαKαKα
拱顶213.941.70169.591.65313.901.75
拱腰182.031.83130.001.78283.201.87
边墙162.501.86124.891.89263.171.91
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拱部测点拟合曲线K、α值比较

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测点位置径向切向竖向
KαKαKα
拱顶213.941.70169.591.65313.901.75
拱腰182.031.83130.001.78283.201.87
边墙162.501.86124.891.89263.171.91
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Main frequency of blasting vibration under different charge

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总药量/kg单段最大药量/kg爆心距/m峰值振速/（cm·s-1）主频/Hz
15636.278.70.3119.53
17446.878.70.3915.63
18856.278.70.4212.32
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不同药量下的爆破振动主频

, figureFileSmall=null, figureFileBig=null, tableContent=
总药量/kg单段最大药量/kg爆心距/m峰值振速/（cm·s-1）主频/Hz
15636.278.70.3119.53
17446.878.70.3915.63
18856.278.70.4212.32
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Peak particle velocity induced by cut blasting

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延期时间/ms034567
峰值振速/（cm·s-1）2.080.740.670.560.420.30
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掏槽试验峰值振速

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延期时间/ms034567
峰值振速/（cm·s-1）2.080.740.670.560.420.30
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隧道内部爆破振动传播规律与降振技术研究
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项荣军 1 , 刘传鹏 2 , 李胜林 2 , 凌天龙 3
爆破 | 矿岩爆破 2023,40(4): 82-88
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爆破 | 矿岩爆破 2023, 40(4): 82-88
隧道内部爆破振动传播规律与降振技术研究
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项荣军1 , 刘传鹏2 , 李胜林2, 凌天龙3
作者信息
  • 1.中铁十六局集团　路桥工程有限公司，北京　101500
  • 2.中国矿业大学（北京）　力学与建筑工程学院，北京　100083
  • 3.泰山学院　机械与建筑工程学院，泰安　271000

    • 项荣军（1989-），男，主要研究方向为交通土建，（E-mail）。

    XIANG Rong-jun (1989-), male, mainly engaged in traffic civil engineering, (E-mail) .

通讯作者:

刘传鹏（1995-），男，主要研究方向为交通土建，（E-mail）。
Research on Blasting Vibration Propagation Law and Vibration Reduction Technology for Tunnel Excavation
Rong-jun XIANG1 , Chuan-peng LIU2 , Sheng-lin LI2, Tian-long LING3
Affiliations
  • 1.China Railway 16th Bureau Group Road and Bridge Engineering Co., Ltd., Beijing 101500, China
  • 2.School of Mechanics and Civil Engineering, China University of Mining and Technology-Beijing, Beijing 100083, China
  • 3.College of Mechanical and Architectural Engineering, TaiShan University, Taian 271000, China
出版时间: 2023-12-01 doi: 10.3963/j.issn.1001-487X.2023.04.011
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摘要
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目前隧道施工普遍应用矿山法，爆破振动对隧道内围岩、支护结构的影响及其灾害控制一直是热点问题。为研究爆破振动在隧道内部的传播规律，以某软弱围岩隧道为工程背景，分别对错距三台阶齐爆和分爆的振动信号进行现场监测。采用萨道夫斯基公式非线性回归、Fourier变换方法对测试数据进行分析和研究。结果表明：对于隧道同一断面，拱顶具有振动速度大、振动主频高、衰减速度慢的特点；三台阶间采用100 ms延时爆破时，可以实现爆破能量在时空分布上的离散，振动叠加效应明显减弱。设计单孔爆破试验，掏槽区域中间设置试验孔，试验孔与整个爆破网络的延期设置为100 ms获取单孔振动波形，基于线性叠加原理，计算不同延期时间下掏槽爆破合成振动波形来优选微差延期时间。结果表明：孔间延期时间在4~7 ms时，掏槽爆破引起的峰值振速急剧下降，干扰降振的效果明显，延时超过7 ms后，峰值振速无显著差异；掏槽孔延期时间取7 ms时减振效果最佳，将最佳延期时间应用于现场爆破，取得了良好的降振效果。

隧道工程  /  爆破振动  /  传播规律  /  线性叠加  /  最优延期时间

At present, mining method is widely used in tunnel construction. The influence of blasting vibration on surrounding rock and supporting structure in tunnel and its disaster control are always hot issues. In order to study the propagation law of blasting vibration inside a tunnel, the vibration signals of simultaneous detonation and detonation at three benches were monitored on site based on the engineering background of a tunnel with soft surrounding rock. The nonlinear regression of Sadovski formula and Fourier transform method were used to analyze and study the test data. The results show that for the same section of the tunnel, the vault has the characteristics of large vibration velocity, high vibration frequency and slow attenuation rate. When 100 ms delay blasting is used between the three steps, the blasting energy can be discretely distributed in time and space, and the vibration superposition effect can be significantly weakened. A single hole blasting test was set in the middle of the cut area, and the single hole vibration waveform was obtained by setting the delay between the test hole and the entire blast as 100 ms. Based on the principle of linear superposition, the delay time was optimized by investigating vibration waveforms synthesized by cut blasting. The results show that when the delay time between holes is 4~7 ms, the peak vibration velocity caused by cut blasting decreases sharply, and the effect of interference is obvious. After the delay time exceeds 7 ms, the peak vibration velocity has no significant difference.

tunnel engineering  /  blasting vibration  /  propagation law  /  linear superposition  /  optimal delay time
项荣军, 刘传鹏, 李胜林, 凌天龙. 隧道内部爆破振动传播规律与降振技术研究. 爆破, 2023 , 40 (4) : 82 -88 . DOI: 10.3963/j.issn.1001-487X.2023.04.011
Rong-jun XIANG, Chuan-peng LIU, Sheng-lin LI, Tian-long LING. Research on Blasting Vibration Propagation Law and Vibration Reduction Technology for Tunnel Excavation[J]. Blasting, 2023 , 40 (4) : 82 -88 . DOI: 10.3963/j.issn.1001-487X.2023.04.011
正文
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近二十年来，我国稳步推进交通运输体系建设，公路隧道和铁路隧道随之迎来建设高峰期。目前钻爆法依然是我国山岭隧道开挖的主要方法。与机械法相比，钻爆法经济、适应能力强。然而，隧道爆破开挖诱发的振动效应对隧道内支护结构的稳定性和周围建筑物的安全性都构成了影响。为减少此危害，学者们一方面对爆破振动的安全判据进行了大量研究，另一方面对降振措施进行了研究。
国内外学者普遍认为地震波影响下结构的动能和应力与振动速度密不可分，振动速度作为衡量爆破地震影响的一个重要指标而被广泛用于爆破安全判据的建立[1,2]，杨建华采用质点峰值振速（PPV）作为喷射混凝土的爆破振动安全判据[3]；于崇提出爆破振速控制是爆破安全的重要内容[4]，并进一步研究了爆破振动的可靠度问题。在爆破峰值振动速度评价指标的基础上，一些学者引入振动频率及持续时间综合评价结构的爆破振动响应特征[5,6]，何理提出爆破振动能量的大小主要取决于爆破振动速度、振动频率及振动持续时间三个影响因素[7]；于建新研究了振动信号能量在不同频段下的衰减规律[8]。现行《爆破安全规程》综合考虑峰值振动速度和振动频率两个指标建立了各类结构的爆破安全判据[9]，因此，研究爆破振动速度分布特征和主频特性并对隧道内结构进行安全性评价，具有重要意义[10]。
为了有效控制爆破地震波危害，国内外学者对控制爆破技术做了大量研究，取得了卓有成效的成果。传统隧道爆破降振措施包括：缩小循环进尺、减少单段最大装药量或总装药量、微差爆破技术、非爆破开挖技术等[11]。这些降振措施在一定程度上起到了积极的作用。然而，在复杂城市环境或特殊地层条件下，这些措施取得的降振效果仍是有限的。尤其是毫秒延期雷管误差达到10~120 ms，无法达到理想的微差干扰降振效果，限制了微差爆破技术的发展。高精度延时数码电子雷管的使用对改善爆破效果、降低振动效应具有重要意义。目前，数码电子雷管在露天矿山已有广泛应用，且有大量研究成果讨论了台阶爆破微差延期时间的设置[12-15]。数码电子雷管在隧道爆破中的应用尚处于初步推广阶段，关于合理的孔间延期时间还没有形成统一的认识[16]。
以北京密云西统路小西库隧道爆破施工为背景，通过现场振动监测，研究爆破地震波在隧道内部的传播规律及同一断面上振动特征，讨论了三台阶爆破降振措施。结合线性叠加原理和单孔爆破振动试验，给出了应用数码电子雷管时掏槽孔的最优延时间隔。本文的研究成果与方法可为钻爆法施工软弱围岩隧道提供参考。
1　隧道爆破振动测试
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1.1　工程背景
小西库隧道位于北京市密云区，地属低山地貌，岩体主要为碎石土、强风化白云岩。岩体破碎~极破碎，多以Ⅴ级围岩为主。拱顶岩体松散，围岩稳定性差，若不及时并加强支护，极易出现顶板坍塌、侧壁失稳等问题。
1.2　隧道施工爆破方案
小西库隧道净宽12 m，行车道净高4 m，开挖净面积129.1 m2。隧道施工揭露V级围岩时采用三台阶法施工，其中上台阶开挖高度为4 m，开挖面积约为36 m2。该隧道爆破施工采用高精度电子雷管，其上台阶采用逐圈（排）起爆方式，排间延时取50 ms，上台阶炮孔布置如图1所示，上台阶的爆破参数如表1所示。二台阶距离上台阶掌子面10~15 m不等，三台阶为左右交错开挖，距离二台阶20~30 m不等。
1.3　爆破振动测试方案
此次测试主要获取隧道喷锚支护断面各部位爆破振动速度，进而分析爆破振动在隧道内的传播规律。采用TC-50爆破测振仪，在隧道内同一断面的拱部（包括拱顶、拱腰、边墙）布置3个测点，使用卡扣使其与隧道刚性连接，如图2所示。振动传感器的x方向指向隧道轴线，y方向垂直于隧道轴线，z方向竖直向上。
2　隧道结构爆破振动特性
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2.1　爆破爆破振动传播规律
采用钻爆法开挖岩体时，炸药能量以应力波的形式在岩体内传播。受爆破参数、传播介质力学性质、地形地貌等影响，不同工况下爆破振动的衰减规律存在显著差异[10]。爆破振动大小与装药量、爆心距、传播介质的特性参数、局部地质条件、爆破形式等密切相关。目前，我国现行《爆破安全规程》采用萨道夫斯基公式拟合爆破峰值振动速度
式中：v为质点峰值振动速度，cm/s；Q为单段最大起爆药量，kg；K为场地系数，α为衰减指数。
2.2　隧道拱部振动速度分布特征
为了分析爆破地震波在隧道内部的衰减特性，在距上台阶掌子面40 m处布置3个速度传感器，保持3个传感器位置固定并监测开挖掌子面推进过程中的振动速度。在隧道拱顶、拱腰和边墙分别获取有效数据18组。利用最小二乘法分别确定隧道拱部3个振动方向的K和α，得到用萨道夫斯基公式描述的爆破振动衰减规律，振动数据及拟合曲线如图3所示。
由图3（a）~（c）可以看出：同一断面上各测点竖向振速明显大于水平振速，水平径向与切向的振速相差不大；随着比例距离的增大，竖向振速逐渐接近水平向振速。图3（d）给出了拱顶、拱腰、边墙竖向峰值振动速度的衰减规律。对比3个部位竖向峰值振动速度可知：拱顶的竖向峰值振动速度最大，拱腰次之，边墙最小；3个部位峰值振动速度的差值随比例距离的增加而减小。综上所述，在隧道同一断面中，拱顶的竖向峰值振动速度数值最大。因此，在工程实际中，可以利用隧道拱顶竖向振动速度综合反映爆破地震波在隧道内的传播规律。
表2为振动数据拟合曲线的拟合参数K和α的值。对比表中结果可知：竖向峰值振速拟合曲线的K和α的值最大，表明爆破振动速度在竖直方向的衰减速度最快。
2.3　隧道拱部振动主频变化规律
提取拱顶、拱腰和边墙的振动数据，利用傅里叶变换计算得到竖向振动信号的主频。隧道不同部位竖向爆破振动的主频如图4所示。由图4可以看出：拱顶、拱腰、边墙测点处的主频均随比例距离增大逐渐变小；同一测试断面内，拱顶的爆破振动主频最大，拱腰次之，边墙最小。因此，隧道拱顶具有振动速度大，振动主频高的特点。
研究表明：单段最大药量、爆心距、传播介质性质等因素会对爆破振动频谱造成较大影响[17]。为了分析单段起爆药量对爆破振动主频的影响，在爆心距相同、地质条件相近的情况下，进行了3次爆破振动测试实验，实验数据如表3所示。
由表3可知：单段最大药量由36.2 kg增加至56.2 kg时，爆破振动主频降低36.9%；在其他参数基本相同的条件下，随着单段最大药量的增大，爆破振动信号中低频成分的占比逐渐增加，爆破振动信号的主振频率有向低频发展的趋势。由于工程结构体的自振频率往往较低，采用较大的单段药量不利于隧道结构的安全。
3　隧道爆破降振技术
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3.1　台阶法施工爆破降振技术
小西库隧道揭露Ⅴ级围岩时采用三台阶法施工，掘进初期三个台阶掌子面采用齐发爆破方式，爆破作业的总装药量为204 kg。为了确保隧道施工安全，在距上台阶掌子面75 m处隧道底板布设1台速度传感器，监测底板质点的爆破振动波形。三个台阶同时起爆时，隧道底板测点的振动速度时程曲线图5所示。由图5可以看出：爆破地震波具有9个幅值较大的峰值，相邻波峰的时差约为50 ms，与爆破网路的时差相对应；上台阶起爆时，掏槽孔的夹制作用较大，振动波形出现第一个较大的幅值；由于三台阶爆破区域距离较近，爆破振动叠加效应明显，导致下台阶起爆后，振动波形出现最大幅值，峰值振动速度为0.55 cm/s，爆破振动强度明显增强。由此可见，如果延时时间设置不合理，不仅不会降低爆破振动影响，有时还会增大地震效应[18]。
为降低爆破振动对隧道结构的不利影响，将施工方法调整为三台阶先后起爆，将爆炸能量在时空上进行分散。现场测试获得Ⅴ级围岩场地声波波速约为800 m/s，掌子面与三台阶最大距离为45 m，振动传播用时约56 ms。为便于现场实施，将各台阶起爆的间隔时间取为100 ms，并按此延期时间对爆破振动进行试验。距上台阶掌子面75 m处底板的振动曲线如图6所示。由图6可以看出：爆破振动持时明显增长，各台阶爆破的振动波形实现分离，无振动叠加现象；与三台阶同时爆破相比，在其他爆破参数相近的情况下，峰值振速由0.55 cm/s降至0.31 cm/s，降振率达44%，降振效果明显。
3.2　掏槽孔延期时间优化设计
毫秒爆破的振动是由各炮孔产生的振动叠加而成的。当药量相差不大、地质条件基本相同时，可认为每个炮孔产生的爆破振动波是相同的，此时爆破振动的叠加过程可看作是线性系统[19]。因此，根据延期时间计算群孔爆破不同相位，并基于线性系统中振动信号的叠加性模拟逐孔爆破振动信号，即
式中：F（t）为预测爆破振动信号；fi（t）为单个炮孔爆破振动信号；Ti为当前炮孔爆破振动信号传播至测点相比上一炮孔的延迟时间。
一般情况下，掏槽孔引起的爆破振动速度最大。为了降低掏槽孔爆破对隧道结构的影响，将小西库隧道掏槽爆破形式改为逐孔起爆，并对孔间延期时间设置进行试验研究。在掏槽孔中间位置额外钻凿1个炮孔，装药量与掏槽孔药量一致。首先起爆试验孔并采集单孔爆破振动信号。距上台阶掌子面40 m处拱顶爆破振动波形如图7所示。由图7可以看出：单孔爆破振动信号经历1~2个波峰波谷后迅速衰减，振动持时约为65 ms；振动波形的主波周期为12.1 ms，峰值振动速度为-0.354 cm/s。
由于掏槽孔之间的距离较小，各炮孔爆破振动信号传播至测点的时间间隔可近似看作是相等的。将各炮孔间延期时间按1 ms逐渐递增，应用MATLAB软件对单孔波形进行线性叠加计算。统计叠加振动信号的正向和负向波峰，如图8所示。由图8可以看出：延期时间为1~7 ms时，峰值振动速度随延期时间的增加而逐渐减小，尤其当延期时间为5~7 ms时，峰值振动速度骤降，降振效果最好；当延期时间超过7 ms后，先行波和后行波的主振相无法实现错峰干扰，叠加后的峰值振动速度趋近于单孔试验结果。因此，掏槽孔的最优延期时间可取7 ms，这与文献[20]建议的延期时间取T/3~2T/3的结论一致。
在小西库隧道开展延期时间验证试验，分别设置掏槽孔间延期时间0 ms、3 ms、4 ms、5 ms、6 ms、7 ms共计6组爆破试验。试验中测点与掏槽区域的距离为40 m，统计掏槽孔爆破引起的峰值振动速度，如表4所示。由表4可知：峰值振动速度随孔间延期时间的增加而降低；延期时间为6 ms和7 ms时的实测峰值振速与线性叠加结果较为吻合；与掏槽孔同时起爆方案相比，延期时间为7 ms时，峰值振动速度降低了85.6%，甚至小于单孔爆破时的峰值振速（0.354 cm/s）。
综上所述，应用数码电子雷管可以实现逐孔爆破时振动波形的干扰叠加，大幅度降低振动强度。对于小西库隧道，将掏槽孔延期时间取为7 ms，能够较好地控制爆破振动效应。利用此方法对掏槽孔延期时间进行优化设计具有重要的实际意义。
4　结论
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（1）运用萨道夫斯基公式对隧道内部测点振动速度进行拟合，得出了隧道测点各向振速衰减规律，根据拱顶测点在振速值及衰减规律方面的特点，可将拱顶测点作为隧道爆破振动监测的特征点。
（2）Ⅴ级围岩隧道开挖过程中，将错距三台阶同时起爆调整为各台阶间隔100 ms先后起爆，各台阶的爆破振动波形相互分离，爆破能量在时空中得以分散，峰值振动速度降低率达44%，表明错分台阶后设置合理的延时可有效切分最大单响药量，实现降振的目的。
（3）利用线性叠加原理实现了掏槽爆破振动参数的预报和优化设计，预测结果与现场实测值较为吻合；综合考虑预测值和试验结果，确定掏槽孔最优延期时间为7 ms，降振效果良好。该方法可操作性较强，适于在实际工程中应用推广。
基金
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  • 国家自然科学基金资助项目(51374210; 51574247)
  • 山东省自然科学基金(ZR2020QE266)
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.2023.04.011
  • 接收时间：2022-11-13
  • 首发时间：2026-03-19
  • 出版时间：2023-12-01
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  • 收稿日期：2022-11-13
基金
The National Natural Science Foundation of China(51374210; 51574247)
国家自然科学基金资助项目(51374210; 51574247)
Shandong Natural Science Foundation(ZR2020QE266)
山东省自然科学基金(ZR2020QE266)
作者信息
    1.中铁十六局集团　路桥工程有限公司，北京　101500
    2.中国矿业大学（北京）　力学与建筑工程学院，北京　100083
    3.泰山学院　机械与建筑工程学院，泰安　271000

通讯作者:

刘传鹏（1995-），男，主要研究方向为交通土建，（E-mail）。
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2种不同金属材料的力学参数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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