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Article(id=1241769330644422868, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241769329201578292, articleNumber=null, orderNo=null, doi=10.3963/j.issn.1001-487X.2024.01.006, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1671811200000, receivedDateStr=2022-12-24, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773990479383, onlineDateStr=2026-03-20, pubDate=1709222400000, pubDateStr=2024-03-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773990479383, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773990479383, creator=13701087609, updateTime=1773990479383, updator=13701087609, issue=Issue{id=1241769329201578292, tenantId=1146029695717560320, journalId=1240670690148397066, year='2024', volume='41', issue='1', pageStart='1', pageEnd='220', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773990479040, creator=13701087609, updateTime=1773992264087, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241776816298459159, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241769329201578292, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241776816298459160, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241769329201578292, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=37, endPage=43, ext={EN=ArticleExt(id=1241769330988355802, articleId=1241769330644422868, tenantId=1146029695717560320, journalId=1240670690148397066, language=EN, title=Dynamic Response Characteristics of Primary Tunnel Support under Blasting Excavation with Reserved Core Soil Method, columnId=1240702071733801442, journalTitle=Blasting, columnName=THEORETICAL AND TECHNOLOGICAL EXPLORATION, runingTitle=null, highlight=null, articleAbstract=

The primary support is the main load-bearing structure in the tunnel construction stage, the response rule and safety control of the primary support under dynamic disturbance are of great significance to ensure the safe and rapid construction. Figuring out the dynamic response characteristics and the safety control of the primary support is an important issue for the blasting excavation of a soft rock tunnel with reserved core soil. A three-dimensional finite-element numerical model was established by ANSYS/LSDYNA for the Linchang tunnel blasting excavation, and the reliability of the numerical model was verified by the field vibration monitoring data. The stress distribution characteristics of the primary tunnel support under the simultaneous action of two blast sources was studied combined with the construction characters of the reserved core soil method. The attenuation law of blasting vibration was obtained by using Sadovsky empirical formula. The safety criterion of blasting vibration velocity for the primary tunnel support under the simultaneous blasting excavation of both sides of the lower bench was proposed by taking stress as the control standard. The results show that the maximum vibration velocity appears at the arch foot of the primary support rather than at the tunnel floor or vault, which is different from the full section method and bench blasting method. Meanwhile, the propagation path of the blasting stress wave is dramatically affected at the un-backfilled area of the tunnel invert. The vibration velocity of the primary tunnel support is larger and attenuates faster on the left arch foot versus right arch foot. The maximum tensile stress and shear stress appear on the left arch foot of the tunnel under simultaneous blasting with 7.544 MPa and 2.78 MPa, respectively, which exceed the allowable value of the specification. According to the established linear stress-vibration velocity relationship, a blasting vibration safety criterion of primary tunnel support is proposed based on the ultimate strength. In addition, the safety vibration velocity threshold of the primary support in Linchang tunnel is 10 cm/s.

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HE Ru (1990-), Ph. D, lecturer, mainly engaged in engineering blasting, underground engineering and other aspects of teaching and research work, (E-mail) .
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初期支护是隧道施工阶段的主要承力结构，爆破施工动力扰动下初期支护的响应规律及安全控制对确保隧道安全快速施工有着重要意义。为研究预留核心土法爆破开挖影响下软岩隧道初期支护的动力响应特征及其安全控制，以林场隧道爆破施工为工程背景，依据隧道初期支护现场爆破振动监测结果，利用ANSYS/LSDYNA建立三维有限元数值计算模型，结合预留核心土法爆破作业特点，研究了两个不同距离爆源同时作用下隧道初期支护的应力分布特征，利用萨道夫斯基经验公式获得了预留核心土法爆破振动传播衰减规律，提出了以应力为控制标准的两侧下台阶同时起爆条件下隧道初期支护的爆破振动速度安全判据。结果表明：不同于全断面法和台阶法爆破，预留核心土法两侧下台阶同时起爆时，最大振动速度出现于隧道初期支护拱脚处，而非隧道底板或拱顶；仰拱未回填区域的存在显著影响爆破应力波传播路径，相较于右侧拱脚，隧道初期支护左侧拱脚处的振动速度更大，且随距离增加而衰减的更明显；初期支护结构稳定性受拉应力控制，最大拉应力及剪应力出现于隧道左侧拱脚处，最大拉应力为7.544 MPa，最大的剪应力为2.78 MPa，均超过规范允许值；根据建立的应力-振速线性关系，提出基于极限强度的隧道初期支护爆破振动安全判据；在林场隧道爆破条件下初期支护的爆破振速安全阈值为10 cm/s。研究成果为隧道爆破施工设计以及安全控制提供理论研究基础。

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何如（1990-），博士、讲师，主要从事工程爆破、地下工程等方面的教学研究工作，（E-mail）。
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徐昊（1998-），男，硕士研究生，主要从事隧道与地下工程方面的研究工作，（E-mail）。

XU Hao (1998-), male, master degree, mainly engaged in tunnel and underground engineering research work, (E-mail) .

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徐昊（1998-），男，硕士研究生，主要从事隧道与地下工程方面的研究工作，（E-mail）。

XU Hao (1998-), male, master degree, mainly engaged in tunnel and underground engineering research work, (E-mail) .

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徐昊（1998-），男，硕士研究生，主要从事隧道与地下工程方面的研究工作，（E-mail）。

XU Hao (1998-), male, master degree, mainly engaged in tunnel and underground engineering research work, (E-mail) .

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Safety regulations for blasting[S]. Beijing: Standards Press of China, 2015. 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ArticleFig(id=1241769349095166023, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241769330644422868, language=EN, label=Fig. 8, caption=Distribution characteristics of peak stress at the characteristic positions of primary support, figureFileSmall=vIrxCyOkg32UTTmVPdGufw==, figureFileBig=9d35f2cvOwP9Sc3iAwcr3A==, tableContent=null), ArticleFig(id=1241769349179052111, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241769330644422868, language=CN, label=图8, caption=初期支护不同特征位置的峰值应力分布特征, figureFileSmall=vIrxCyOkg32UTTmVPdGufw==, figureFileBig=9d35f2cvOwP9Sc3iAwcr3A==, tableContent=null), ArticleFig(id=1241769349279715412, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241769330644422868, language=EN, label=Table 1, caption=

Parameters of surrounding rock material parameters

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围岩等级密度/（g·cm-2）弹性模量/GPa泊松比屈服强度/MPa
Ⅳ2.2445.20.3119
Ⅲ2.24813.20.2733
), ArticleFig(id=1241769349388767324, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241769330644422868, language=CN, label=表1, caption=

围岩材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
围岩等级密度/（g·cm-2）弹性模量/GPa泊松比屈服强度/MPa
Ⅳ2.2445.20.3119
Ⅲ2.24813.20.2733
), ArticleFig(id=1241769349497819237, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241769330644422868, language=EN, label=Table 2, caption=

Parameters of Initial lining material

, figureFileSmall=null, figureFileBig=null, tableContent=
材料名称密度/（g·cm3）弹性模量/GPa泊松比
喷射混凝土2.425.50.2
), ArticleFig(id=1241769349585899626, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241769330644422868, language=CN, label=表2, caption=

初期支护材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
材料名称密度/（g·cm3）弹性模量/GPa泊松比
喷射混凝土2.425.50.2
), ArticleFig(id=1241769349699145843, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241769330644422868, language=EN, label=Table 3, caption=

Parameters of explosive

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密度/（g·cm-2）爆速/（cm·μs-1） A B R1 R2 ω E0
0.9520.342.14184.20.90.154.19
), ArticleFig(id=1241769349959192699, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241769330644422868, language=CN, label=表3, caption=

炸药参数

, figureFileSmall=null, figureFileBig=null, tableContent=
密度/（g·cm-2）爆速/（cm·μs-1） A B R1 R2 ω E0
0.9520.342.14184.20.90.154.19
), ArticleFig(id=1241769350089216132, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241769330644422868, language=EN, label=Table 4, caption=

Vibration velocity threshold of tunnel primary support at arch feet on both sides

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位置判断标准振速安全阈值/（cm·s-1）
右侧拱脚极限抗拉强度12.68
极限抗剪强度66.90
左侧拱脚极限抗拉强度19.13
极限抗剪强度31.02
), ArticleFig(id=1241769350206656653, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241769330644422868, language=CN, label=表4, caption=

初期支护两侧拱脚处振速阈值

, figureFileSmall=null, figureFileBig=null, tableContent=
位置判断标准振速安全阈值/（cm·s-1）
右侧拱脚极限抗拉强度12.68
极限抗剪强度66.90
左侧拱脚极限抗拉强度19.13
极限抗剪强度31.02
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预留核心土法爆破开挖下隧道初期支护动力响应特性
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徐昊 1 , 何如 1 , 李栋伟 1 , 季安 2 , 何锦 2 , 代四龙 1
爆破 | 理论与技术探索 2024,41(1): 37-43
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爆破 | 理论与技术探索 2024, 41(1): 37-43
预留核心土法爆破开挖下隧道初期支护动力响应特性
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徐昊1 , 何如1 , 李栋伟1, 季安2, 何锦2, 代四龙1
作者信息
  • 1.东华理工大学　土木与建筑工程学院，南昌　330013
  • 2.中核华泰建设有限公司，深圳　518055

    • 徐昊（1998-），男，硕士研究生，主要从事隧道与地下工程方面的研究工作，（E-mail）。

    XU Hao (1998-), male, master degree, mainly engaged in tunnel and underground engineering research work, (E-mail) .

通讯作者:

何如（1990-），博士、讲师，主要从事工程爆破、地下工程等方面的教学研究工作，（E-mail）。
Dynamic Response Characteristics of Primary Tunnel Support under Blasting Excavation with Reserved Core Soil Method
Hao XU1 , Ru HE1 , Dong-wei LI1, An JI2, Jin HE2, Si-long DAI1
Affiliations
  • 1.School of Civil and Architectural, East China University of Technology, Nanchang 330013, China
  • 2.China Nuclear Huatai Construction Co., Ltd., Shenzhen 518055, China
出版时间: 2024-03-01 doi: 10.3963/j.issn.1001-487X.2024.01.006
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摘要
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初期支护是隧道施工阶段的主要承力结构，爆破施工动力扰动下初期支护的响应规律及安全控制对确保隧道安全快速施工有着重要意义。为研究预留核心土法爆破开挖影响下软岩隧道初期支护的动力响应特征及其安全控制，以林场隧道爆破施工为工程背景，依据隧道初期支护现场爆破振动监测结果，利用ANSYS/LSDYNA建立三维有限元数值计算模型，结合预留核心土法爆破作业特点，研究了两个不同距离爆源同时作用下隧道初期支护的应力分布特征，利用萨道夫斯基经验公式获得了预留核心土法爆破振动传播衰减规律，提出了以应力为控制标准的两侧下台阶同时起爆条件下隧道初期支护的爆破振动速度安全判据。结果表明：不同于全断面法和台阶法爆破，预留核心土法两侧下台阶同时起爆时，最大振动速度出现于隧道初期支护拱脚处，而非隧道底板或拱顶；仰拱未回填区域的存在显著影响爆破应力波传播路径，相较于右侧拱脚，隧道初期支护左侧拱脚处的振动速度更大，且随距离增加而衰减的更明显；初期支护结构稳定性受拉应力控制，最大拉应力及剪应力出现于隧道左侧拱脚处，最大拉应力为7.544 MPa，最大的剪应力为2.78 MPa，均超过规范允许值；根据建立的应力-振速线性关系，提出基于极限强度的隧道初期支护爆破振动安全判据；在林场隧道爆破条件下初期支护的爆破振速安全阈值为10 cm/s。研究成果为隧道爆破施工设计以及安全控制提供理论研究基础。

爆破振动  /  初期支护  /  质点峰值振速  /  动力响应  /  安全判据

The primary support is the main load-bearing structure in the tunnel construction stage, the response rule and safety control of the primary support under dynamic disturbance are of great significance to ensure the safe and rapid construction. Figuring out the dynamic response characteristics and the safety control of the primary support is an important issue for the blasting excavation of a soft rock tunnel with reserved core soil. A three-dimensional finite-element numerical model was established by ANSYS/LSDYNA for the Linchang tunnel blasting excavation, and the reliability of the numerical model was verified by the field vibration monitoring data. The stress distribution characteristics of the primary tunnel support under the simultaneous action of two blast sources was studied combined with the construction characters of the reserved core soil method. The attenuation law of blasting vibration was obtained by using Sadovsky empirical formula. The safety criterion of blasting vibration velocity for the primary tunnel support under the simultaneous blasting excavation of both sides of the lower bench was proposed by taking stress as the control standard. The results show that the maximum vibration velocity appears at the arch foot of the primary support rather than at the tunnel floor or vault, which is different from the full section method and bench blasting method. Meanwhile, the propagation path of the blasting stress wave is dramatically affected at the un-backfilled area of the tunnel invert. The vibration velocity of the primary tunnel support is larger and attenuates faster on the left arch foot versus right arch foot. The maximum tensile stress and shear stress appear on the left arch foot of the tunnel under simultaneous blasting with 7.544 MPa and 2.78 MPa, respectively, which exceed the allowable value of the specification. According to the established linear stress-vibration velocity relationship, a blasting vibration safety criterion of primary tunnel support is proposed based on the ultimate strength. In addition, the safety vibration velocity threshold of the primary support in Linchang tunnel is 10 cm/s.

blast vibration  /  primary support  /  peak particle velocity  /  dynamic response  /  safety criterion
徐昊, 何如, 李栋伟, 季安, 何锦, 代四龙. 预留核心土法爆破开挖下隧道初期支护动力响应特性. 爆破, 2024 , 41 (1) : 37 -43 . DOI: 10.3963/j.issn.1001-487X.2024.01.006
Hao XU, Ru HE, Dong-wei LI, An JI, Jin HE, Si-long DAI. Dynamic Response Characteristics of Primary Tunnel Support under Blasting Excavation with Reserved Core Soil Method[J]. Blasting, 2024 , 41 (1) : 37 -43 . DOI: 10.3963/j.issn.1001-487X.2024.01.006
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钻爆法因其工序简单、成本低、工程环境适应性强等优点，已被广泛应用于各类山岭隧道的建设中。然而，爆破产生的振动对于隧道支护结构和周边围岩为不利外部荷载[1]。由于软岩隧道围岩承载能力较差，其隧道结构和周边围岩受到爆破地震波作用产生的动力响应更为明显。初期支护作为隧道施工和运营阶段保持围岩稳定性的主要承力结构，研究隧道初期支护的爆破震动响应规律及对其进行安全控制对保障隧道安全快速建设有着重要意义。
国内外学者对隧道支护结构的爆破动力响应已有了较为深入的研究，主要通过数值模拟、现场监测、现场试验等方法进行研究。运用数值模拟软件，斯朗拥宗研究了单一爆源振动下不同龄期的初期支护混凝土喷层的动态响应[2]。Dai基于MIDAS/GTSNS研究了在有、无衬砌两种工况下隧道爆破影响下围岩的位移情况[3]，发现围岩在有支护情况下比无支护情况下的位移量减少50%。采用数值模拟和现场监测相结合的手段，Zhang Zhen等研究了下方新建隧道爆破开挖影响下上部既有隧道的振速与应力分布[4]，建立了质点峰值振速与应力之间的关系，提出了上方既有隧道底板的振速安全阈值。吴忠仕等考虑隧道扩建对周边既有隧道复合衬砌的影响[5]，建立了最大拉应力与峰值振速安全准则，提出了既有隧道衬砌的安全振速判据。肖可等针对穿越断层破碎带隧道二衬的应力和振速进行研究[6]，获得了断层带影响下隧道二衬结构的安全振速阈值。Huang Haibin等针对在小净距隧道爆破开挖影响下既有隧道二衬结构的振速与应力分布进行研究[7]，提出既有隧道二衬砌的拱顶处受爆破扰动影响最大。杨建华等研究了在隧道内部存在空洞情况下喷射混凝土层的振速规律[8]，结果表明：空洞存在会对喷射混凝土层的振速产生放大作用，且使得振动频率变缓、振动时间延长。综合采用试验、现场监测、数值模拟方法，Jiang Nan等学者针对水下新建隧道爆破对既有隧道二衬结构的影响进行研究[9]，建立了海底爆破引起的水下声压衰减规律数学模型，Yu Jianxin等通过现场爆破试验[10]，研究了新建隧道爆破振动对既有隧道衬砌结构振速分布规律，认为增加自由面数量可有效减小爆破振动。Wang Haibo等学者基于现场爆破试验结果和振动监测数据[11]，利用Flac3D软件建立数值模型，研究了基坑爆破对下方既有地铁隧道二衬影响，建立了二衬振速、应力和位移之间的关系式。贺泳超等基于不同龄期混凝土动态响应特性试验[12]，研究了爆破振动对隧道二衬新浇混凝土的影响，提出了不同龄期混凝土试块与爆源之间最短的安全距离。唐先习等基于现场混凝土试块爆破振动损伤试验并且结合数值模拟研究了单一爆源作用下不同龄期下初期支护混凝土层损伤进行研究[13]，提出了不同龄期混凝土试块的安全振速阈值。
综上所述，已有研究大多是针对全断面法、台阶法等可概化为单一爆源的爆破开挖方法，且研究对象多为二次衬砌或复合式衬砌，而对于施作时间更早、围岩压力承受比例更高的初期支护的爆破动力响应研究较少，对于采用预留核心土法两侧下台阶同时爆破开挖影响下初期支护结构动力响应特性及安全判据的研究更为鲜见。为此，本文结合林场隧道软岩段爆破工程实际，采用现场监测和动力有限元数值模拟相结合的研究方法，研究隧道两侧下台阶同时爆破影响下初期支护的振动特性，得到初期支护的爆破振速衰减规律和应力分布特征，获得针对预留核心土法两侧下台阶同时起爆条件下隧道拱脚处的萨道夫斯基经验公式，结合应力与质点峰值振速的关系，建立下台阶爆破振动影响下初期支护的安全判据，以期为同类隧道工程的爆破设计和安全控制提供参考。
1　工程背景
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林场隧道位于湖南省安化县古楼镇林场，起讫桩号为K43+060~K43+505，隧道全长445 m，下穿山体，地势起伏较大，相对高差约为103.5 m。其地质剖面图所图1所示。本文研究段里程桩号为K43+84~K43+189。该段主要由Ⅲ、Ⅳ级围岩组成，其中Ⅳ级围岩为中风化板岩，节理裂隙发育，岩体破碎，其抗压强度Rc=19 MPa，岩石自稳能力较差属于软岩。Ⅲ级围岩为微风化板岩。
该隧道采用预留核心土法开挖，开挖方向由出口端向进口端开挖，爆破位置为左下台阶和右下台阶。爆破采用2号岩石乳化炸药，炮孔直径为4 cm，每个下台阶共布置六个掏槽孔，炮孔深度1.5 m，每个炮孔装药量为1.8 kg，具体炮孔布置如图2所示。
2　数值模型及其验证
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2.1　数值计算模型的建立
结合现场实际工程情况，利用ANSYS/LS-DYNA动力有限元数值模拟软件建立三维数值模型，如图3所示。根据圣维南原理，模型周边尺寸选取3~5倍洞径，模型整体尺寸为40 m×40 m×105 m（x×y×z）。模型上边界为自由边界节，其余边界设置为无反射边界[14-16]。模型围岩、初期支护、炸药均采用8节点SOLID164实体单元，其中，围岩和初期支护单元采用Lagrange网格划分，炸药单元采用Ale网格划分，炸药材料与岩石、混凝土材料之间采用流-固耦合算法。
2.2　材料本构模型及参数选取
合理选取材料模型以确保数值模拟计算结果准确。模型材料包括不同级别围岩、初期支护、炸药。其中，结合工程实际，围岩、初期支护可概化为弹性均匀等效介质。根据弹塑性力学理论，可采取双向随动硬化弹塑性本构模型（*MAT_PLASTIC_KINEMATIC）[17-20]对上述材料的力学关系特征进行描述。围岩和初期支护的具体参数见表1和表2所示。
炸药采用*EOS_JWL状态方程，以模拟炸药轰爆过程中比热容和压力关系
式中：A、B、R1、R2、ω为材料参数；p为压力，Pa；V为相对体积；E0为初始比内能。模型中所有用的炸药材料模型（*MAT_HIGH_EXPLOSIVE_BURN）与现场采用的岩石2号岩石乳化炸药一致，主要输入参数如表3所示。
2.3　数值模型的可靠性验证
为验证数值模型的可靠性，采用TC-4850爆破测振仪对隧道初期支护进行现场爆破监测。分别将两台仪器布置于Ⅲ级和Ⅳ级围岩交界处和Ⅲ级围岩段的初期支护拱脚处，以收集不同围岩段初期支护的爆破振动数据。两台仪器间隔5 m，具体布置如图4所示。
选取现场1#监测点的数据进行模型验证，对比结果如图5所示。可知，数值模拟的振速合速度在约0.11 s处达到最大峰值约为0.334 cm/s，现场爆破振动数据在0.16 s处达到最大峰值约为0.318 cm/s。模拟波形与实际波形相似，最大值误差仅为5%，现场监测数据达到峰值时间与数值模型相比滞后了约0.05 s，误差位于允许范围内，故该模型可靠，可利用此数值模型进行后续研究。
3　隧道初期支护爆破动力特征分析及安全控制
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3.1　初期支护振动速度分析
通常使用萨道夫斯基公式来描述于质点振速与爆心距、最大装药量以及场地系数之间的关系，即
式中：v为质点峰值振速，cm/s；Q为最大单段装药量，kg；K为场地系数；α为衰减系数；R为监测点距离爆破位置的水平距离，m。
为方便分析，在初期支护横截面上选取5个关键特征位置，以右下台阶为原点，间隔5 m，沿隧道轴向对两侧初期支护的拱脚、拱腰和拱顶的合振速进行提取，如图6所示。可获得沿隧道纵向的5类关键特征位置的爆破振动质点合振速分布规律，如图7。
由图7可知，在预留核心土法两侧下台阶同时爆破时，最大合振速均出现在隧道初期支护的左右两侧拱脚处，其次为拱腰处，而隧道拱顶的合振速最小；隧道左侧各特征位置的爆破振动合速度的峰值均出现于相对位置-15 m处，即左侧下台阶前方1.5 m处，而隧道右侧各特征位置的爆破振动合速度的峰值均出现于相对位置0 m处，即右侧下台阶侧爆源处；无论是在初期支护的拱脚还是拱腰，隧道左侧的振动合速度均大于隧道右侧；随着距离的增大，拱脚处振速衰减最为明显。
对比现有研究可知，采用全断面爆破时，振速峰值多出现在底板中部[21,22]；常规台阶法爆破时，峰值振速多出现在隧道底板和拱顶处[6]。相较于全断面和台阶法，预留核心土法两侧下台阶同时爆破开挖时，更需关注初期支护拱脚处的振动响应和损伤。
提取图7中各点的合振速，以研究隧道初期支护拱脚处的振动速度衰减规律。基于萨道夫斯基公式，运用多重线性函数对初期支护左右两侧拱脚合振速进行回归分析，得到两侧拱脚处的合振速回归经验公式
由式（3）和式（4）可知，左右两侧拱脚的场地系数差距较大，且相较于右侧拱脚的合速度，左侧拱脚合速度衰减系数更大、衰减更快。与全断面法和台阶法爆破开挖时的拱脚振动速度衰减规律相比[6,21,22]，预留核心土法两侧下台阶同时爆破开挖时，拱脚处的振速衰减系数更大，振速衰减更为明显。
3.2　初期支护结构应力分析
基于数值计算模型对隧道初期支护的应力分布进行分析。设右侧下台阶为原点，下台阶已开挖段为正方向，待开挖段为负方向。沿着隧道轴向间隔5 m对隧道两侧拱脚、拱腰和拱顶处的剪应力和拉应力进行提取。
提取研究区域段内初期支护的剪应力和拉应力如图8所示。可知，初期支护的峰值应力分布规律与峰值振动速度分布规律相一致；在预留核心土法两侧下台阶同时爆破作用下，初期支护所受到的最大剪应力和最大拉应力均出现在左右两侧下台阶前后5 m范围内；在同一高度位置上，初期支护结构各特征截面应力分布均呈现：拉应力>剪应力；在同一侧，初期支护结构拉应力及剪应力存在拱脚>拱腰>拱顶的趋势，拉应力及剪应力的最大值均出现在左侧拱脚处。
左侧拱脚处剪应力和拉应力的最大值分别为τmax=2.78 MPa和σmax=7.54 MPa
右侧拱脚处剪应力和拉应力的最大值分别为τmax=1.39 MPa和σmax=5.64 MPa
可发现，初期支护左侧拱脚处的应力峰值明显大于右侧拱脚。由于仰拱未回填段的存在影响了爆破应力波传播路径，左下台阶产生的爆破应力波向前方右下台阶传播较为困难，而右下台阶进行爆破时，应力波沿着后方待开挖岩石区域向左下台阶处传播，可实现两侧台阶爆破应力波的相互叠加，由此导致了左侧拱脚的应力峰值上升。
据《公路隧道设计规范》可知[23]，喷射混凝土的极限抗拉强度和抗剪强度为1.1 MPa和1.5 MPa。如图8所示，此次下台阶爆破位置前后10 m范围内的初期支护两侧拱脚和拱腰处的应力均超出规范安全允许值，初期支护处于不利状态。
4　隧道初期支护结构爆破振动安全控制
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隧道初期支护在爆破动力作用下的动力响应是一个从初始静力平衡状态到动力峰值再趋于平衡状态的过程。根据弹性动力学可知，针对确定的介质，其受到激励产生振动，波通过介质振动辐射能量，基于波前动量守恒原理建立应力与振速之间的关系[24]。取时间dt内沿着波阵面dA方向传播的波扰动范围内的质量M为
式中：ρ为介质密度；c为波速。
当介质M以速度v振动时，此时动量为
定义冲量为
基于动量守恒原理化简可知
由上式可知，应力与爆破振动速度之间存在着一定的对应关系，振速越大，应力越大。通过第3节分析可知，隧道初期支护两侧的最大剪应力和拉应力均出现在拱脚处。为了研究初期支护两侧拱脚的应力分布规律，分别提取对应位置处的振速进行线性拟合。
右侧拱脚
左侧拱脚
为获得两侧下台阶同时爆破时隧道初期支护的安全振速阈值，将《公路隧道设计规范》[23]中喷射混凝土的抗剪强度和抗拉强度τ=1.5 MPa和σ=1.1 MPa作为初期支护的动态极限抗剪强度和抗拉强度。将数值代入式（5）~（8）中，计算可得初期支护的爆破振速安全阈值，如表4所示。
可知，相对于剪切破坏，林场隧道初期支护更容易受到拉伸破坏；隧道初期支护的安全振速阈值达到12.68 cm/s。根据中华人民共和国国家标准《爆破安全规程》[25]中所规定：龄期为28 d的新浇混凝土振动安全允许值为10~12 cm/s。通过《爆破安全规程》[25]和上文所得的振速-应力拟合关系式，即公式（6），可知林场隧道初期支护安全控制标准式
式中：vk为规范中爆破安全振动允许值。根据前文振速及应力特征分析，结合林场隧道实际，林场隧道爆破振动安全控制值vk取为10 cm/s。
5　结论
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以林场隧道软岩段为研究对象，使用有限元模拟和现场监测分析了预留核心土法爆破施工下隧道初期支护的爆破动力响应特征，得出以下结论：
1）与全断面法和台阶法爆破法相比，在预留核心土法两侧下台阶同时爆破时，最大合振速均出现在隧道初期支护结构的左右两侧拱脚处；随着距离的增大，拱脚处的振速衰减最为明显。
2）仰拱未回填区域对爆破应力波的传播路径产生显著影响，同一横断面上，初期支护左侧拱脚合速度大于右侧拱脚；初期支护的峰值合振速出现于左侧下台阶前方1.5 m处，而隧道右侧初期支护结构的峰值合振速均出现于右侧下台阶侧位置处。
3）两侧下台阶同时爆破施工作用下，初期支护的峰值应力分布规律与峰值合振速分布规律相一致，初期支护结构稳定受拉应力控制，初期支护结构最大应力峰值出现在拱脚处，拉应力峰值大于剪应力峰值。
4）林场隧道两侧下台阶同时起爆的初期支护爆破振速安全阈值为10 cm/s，最危险截面为左侧拱脚。
基金
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  • 江西省地质环境与地下空间工程研究中心开放基金项目(JXDHJJ2022-005)
  • 国家自然科学基金项目(42061011)
  • 东华理工大学博士科研启动基金项目(DHBK2019236)
  • 东华理工大学研究生创新基金(YC2022-s611)
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2024年第41卷第1期
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文章信息
doi: 10.3963/j.issn.1001-487X.2024.01.006
  • 接收时间：2022-12-24
  • 首发时间：2026-03-20
  • 出版时间：2024-03-01
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  • 收稿日期：2022-12-24
基金
Jiangxi Geological Environment and Underground Space Engineering Research Center Open Fund Project(JXDHJJ2022-005)
江西省地质环境与地下空间工程研究中心开放基金项目(JXDHJJ2022-005)
National Natural Science Foundation of China(42061011)
国家自然科学基金项目(42061011)
Doctoral Research Foundation of East China University of Technology(DHBK2019236)
东华理工大学博士科研启动基金项目(DHBK2019236)
The Graduate Innovation Fund of East China University of Technology(YC2022-s611)
东华理工大学研究生创新基金(YC2022-s611)
作者信息
    1.东华理工大学　土木与建筑工程学院，南昌　330013
    2.中核华泰建设有限公司，深圳　518055

通讯作者:

何如（1990-），博士、讲师，主要从事工程爆破、地下工程等方面的教学研究工作，（E-mail）。
参考文献
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https://castjournals.cast.org.cn/joweb/bp/CN/10.3963/j.issn.1001-487X.2024.01.006
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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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