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Article(id=1241442319614923256, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241442313185063097, articleNumber=null, orderNo=null, doi=10.3963/j.issn.1001-487X.2023.01.022, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1662825600000, receivedDateStr=2022-09-11, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773912513879, onlineDateStr=2026-03-19, pubDate=1677600000000, pubDateStr=2023-03-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773912513879, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773912513879, creator=13701087609, updateTime=1773912513879, updator=13701087609, issue=Issue{id=1241442313185063097, tenantId=1146029695717560320, journalId=1240670690148397066, year='2023', volume='40', 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=1773912512346, creator=13701087609, updateTime=1773912765519, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241443375145079400, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241442313185063097, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241443375145079401, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241442313185063097, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=160, endPage=169, ext={EN=ArticleExt(id=1241442319866581499, articleId=1241442319614923256, tenantId=1146029695717560320, journalId=1240670690148397066, language=EN, title=Correlation Study between Blasting Vibration and Surrounding Rock Damage Range of Hard Rock Underground Cavern Engineering, columnId=1240702076553065119, journalTitle=Blasting, columnName=BLASTING SAFETY, runingTitle=null, highlight=null, articleAbstract=

Field detection of surrounding rock damage range is cumbersome. In order to obtain the surrounding rock damage range simply and accurately, a major underground cavern project to be built is taken as the research background. Theoretical analysis and numerical simulation are adopted according to the blasting design scheme to establish the cumulative damage calculation model of multi-stage delay blasting with different charges. By using equivalent blasting load method and LS-DYNA complete restart technology, the blasting vibration data and the cumulative damage range of surrounding rock under multi-stage delay blasting loads are obtained. The cumulative damage effect of surrounding rock of the underground cavern is analyzed and the correlation between blasting vibrations and the cumulative damage range of surrounding rock is studied. The results show that the induced damage of surrounding rock of the underground cavern is mainly caused by blasting of the second circle holes and the surrounding hole, and the damage range of surrounding rock of the cavern vault (2.21 m) is significantly larger than that of the surrounding rock of the arch waist (2.05 m). The peak value of the blasting vibration curve is within the delay time range of cutting holes, which is not consistent with the blasting stage that causes the damage of surrounding rock. Therefore, the correlation between the peak particle vibration velocity and the damage range of the surrounding rock should be studied within the delay time which has great influence on the damage of surrounding rock. The quantitative relationship between the cumulative damage range of surrounding rock and blasting charge, blasting center distance and peak particle vibration velocity is established, and the functional relationship between the cumulative damage range of surrounding rock can be deduced from the peak particle vibration velocity at any blasting center distance. It provides a basis for controlling the blasting damage of surrounding rock and has practical significance for guiding the safety of blasting construction on site.

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为了简便而准确地获取爆破荷载下硬岩地下洞室围岩损伤范围，以某待建重要地下洞室工程为研究背景，采用理论分析和数值模拟的方法，根据爆破设计方案，建立不同药量条件下多段延时爆破累积损伤计算模型，利用等效爆破荷载的方法和LS-DYNA完全重启动技术，得到多段延时爆破荷载作用下的爆破振动数据和围岩累积损伤范围。分析地下洞室围岩累积损伤效应，研究爆破振动与围岩累积损伤范围之间的相关性。研究结果表明：诱导地下洞室周边围岩损伤的荷载主要来自于二圈孔和周边孔爆破，其中洞室拱顶围岩损伤范围（2.21 m）明显大于拱腰围岩损伤范围（2.05 m）；爆破全时程振动曲线的峰值处于掏槽孔延期时间范围内，与造成洞室周边围岩损伤的爆破段位不一致，应以对围岩损伤影响较大爆破段位的质点峰值振动速度研究与围岩损伤范围的相关性；建立了围岩累积损伤范围与爆破药量、爆心距和质点峰值振动速度之间的量化关系，得到了可通过任意爆心距处质点峰值振动速度推断围岩累积损伤范围的函数关系式，为控制围岩爆破损伤提供依据。

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仇安兵（1971-），男，高级工程师，主要从事基建工程管理工作，（E-mail）。
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吴志超（1995-），男，硕士研究生，主要从事地下洞室爆破方面的研究工作，（E-mail）。

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吴志超（1995-），男，硕士研究生，主要从事地下洞室爆破方面的研究工作，（E-mail）。

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吴志超（1995-），男，硕士研究生，主要从事地下洞室爆破方面的研究工作，（E-mail）。

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Environmental Earth Sciences, 2021, 80(11): 404-416., articleTitle=Forecasting discharge rate and chloride content of karstic spring water by applying the Levenberg Marquardt algorithm, refAbstract=null)], funds=[Fund(id=1241442345460224450, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442319614923256, awardId=51934001, language=CN, fundingSource=国家自然科学基金重点项目(51934001), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1241442333657453543, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442319614923256, xref=null, ext=[AuthorCompanyExt(id=1241442333661647848, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442319614923256, companyId=1241442333657453543, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China), 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Blasting design parameter

, figureFileSmall=null, figureFileBig=null, tableContent=
序号炮孔名称雷管段别孔数/个单孔药量/kg合计/kg
1掏槽孔MS1142.129.4
2辅助掏槽孔MS3121.821.6
3辅助孔MS5121.821.6
4MS7181.832.4
5MS9121.821.6
6二圈孔MS9101.818.0
7MS11261.846.8
8周边孔MS3560.950.4
9底板孔MS15151.827.0
 合计   268.8
), ArticleFig(id=1241442344935936430, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442319614923256, language=CN, label=表1, caption=

爆破设计参数

, figureFileSmall=null, figureFileBig=null, tableContent=
序号炮孔名称雷管段别孔数/个单孔药量/kg合计/kg
1掏槽孔MS1142.129.4
2辅助掏槽孔MS3121.821.6
3辅助孔MS5121.821.6
4MS7181.832.4
5MS9121.821.6
6二圈孔MS9101.818.0
7MS11261.846.8
8周边孔MS3560.950.4
9底板孔MS15151.827.0
 合计   268.8
), ArticleFig(id=1241442345057571250, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442319614923256, language=EN, label=Table 2, caption=

Physical and mechanical parameters of rock

, figureFileSmall=null, figureFileBig=null, tableContent=
岩石弹性模量/GPa泊松比密度/（kg·m-3）摩擦角/°黏聚力/MPa抗拉强度/MPa
微风化片麻状花岗岩51.890.19260253.19.186.4
), ArticleFig(id=1241442345166623158, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442319614923256, language=CN, label=表2, caption=

岩石物理力学参数

, figureFileSmall=null, figureFileBig=null, tableContent=
岩石弹性模量/GPa泊松比密度/（kg·m-3）摩擦角/°黏聚力/MPa抗拉强度/MPa
微风化片麻状花岗岩51.890.19260253.19.186.4
), ArticleFig(id=1241442345275675066, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442319614923256, language=EN, label=Table 3, caption=

Blasting charge and damage range of surrounding rock in each model

, figureFileSmall=null, figureFileBig=null, tableContent=
模型序号掏槽孔装药量/kgMS1掏槽孔单段总药量/kgMS11辅助孔单段总药量/kgMS13周边孔单段总药量/kg损伤范围/m
Ⅰ1.825.240.143.21.84
Ⅱ1.926.642.345.61.98
Ⅲ2.028.044.648.02.08
Ⅳ2.129.446.850.42.21
Ⅴ2.230.849.052.82.34
Ⅵ2.332.251.255.22.46
Ⅶ2.433.653.557.62.58
Ⅷ2.535.055.760.02.70
Ⅸ2.636.457.962.42.83
), ArticleFig(id=1241442345355366845, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442319614923256, language=CN, label=表3, caption=

各模型爆破药量及围岩损伤范围

, figureFileSmall=null, figureFileBig=null, tableContent=
模型序号掏槽孔装药量/kgMS1掏槽孔单段总药量/kgMS11辅助孔单段总药量/kgMS13周边孔单段总药量/kg损伤范围/m
Ⅰ1.825.240.143.21.84
Ⅱ1.926.642.345.61.98
Ⅲ2.028.044.648.02.08
Ⅳ2.129.446.850.42.21
Ⅴ2.230.849.052.82.34
Ⅵ2.332.251.255.22.46
Ⅶ2.433.653.557.62.58
Ⅷ2.535.055.760.02.70
Ⅸ2.636.457.962.42.83
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硬岩地下洞室工程爆破振动与围岩损伤范围相关性研究
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吴志超 , 龚敏 , 仇安兵 , 吴晓东 , 刘翔宇 , 彭娇娇
爆破 | 安全与管理 2023,40(1): 160-169
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爆破 | 安全与管理 2023, 40(1): 160-169
硬岩地下洞室工程爆破振动与围岩损伤范围相关性研究
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吴志超 , 龚敏, 仇安兵 , 吴晓东, 刘翔宇, 彭娇娇
作者信息
  • 北京科技大学　土木与资源工程学院，北京　100083

    • 吴志超（1995-），男，硕士研究生，主要从事地下洞室爆破方面的研究工作，（E-mail）。

通讯作者:

仇安兵（1971-），男，高级工程师，主要从事基建工程管理工作，（E-mail）。
Correlation Study between Blasting Vibration and Surrounding Rock Damage Range of Hard Rock Underground Cavern Engineering
Zhi-chao WU , Min GONG, An-bing QIU , Xiao-dong WU, Xiang-Yu LIU, Jiao-Jiao PENG
Affiliations
  • School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China
出版时间: 2023-03-01 doi: 10.3963/j.issn.1001-487X.2023.01.022
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摘要
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为了简便而准确地获取爆破荷载下硬岩地下洞室围岩损伤范围，以某待建重要地下洞室工程为研究背景，采用理论分析和数值模拟的方法，根据爆破设计方案，建立不同药量条件下多段延时爆破累积损伤计算模型，利用等效爆破荷载的方法和LS-DYNA完全重启动技术，得到多段延时爆破荷载作用下的爆破振动数据和围岩累积损伤范围。分析地下洞室围岩累积损伤效应，研究爆破振动与围岩累积损伤范围之间的相关性。研究结果表明：诱导地下洞室周边围岩损伤的荷载主要来自于二圈孔和周边孔爆破，其中洞室拱顶围岩损伤范围（2.21 m）明显大于拱腰围岩损伤范围（2.05 m）；爆破全时程振动曲线的峰值处于掏槽孔延期时间范围内，与造成洞室周边围岩损伤的爆破段位不一致，应以对围岩损伤影响较大爆破段位的质点峰值振动速度研究与围岩损伤范围的相关性；建立了围岩累积损伤范围与爆破药量、爆心距和质点峰值振动速度之间的量化关系，得到了可通过任意爆心距处质点峰值振动速度推断围岩累积损伤范围的函数关系式，为控制围岩爆破损伤提供依据。

地下洞室  /  延时爆破  /  累积损伤  /  等效荷载  /  数值模拟

Field detection of surrounding rock damage range is cumbersome. In order to obtain the surrounding rock damage range simply and accurately, a major underground cavern project to be built is taken as the research background. Theoretical analysis and numerical simulation are adopted according to the blasting design scheme to establish the cumulative damage calculation model of multi-stage delay blasting with different charges. By using equivalent blasting load method and LS-DYNA complete restart technology, the blasting vibration data and the cumulative damage range of surrounding rock under multi-stage delay blasting loads are obtained. The cumulative damage effect of surrounding rock of the underground cavern is analyzed and the correlation between blasting vibrations and the cumulative damage range of surrounding rock is studied. The results show that the induced damage of surrounding rock of the underground cavern is mainly caused by blasting of the second circle holes and the surrounding hole, and the damage range of surrounding rock of the cavern vault (2.21 m) is significantly larger than that of the surrounding rock of the arch waist (2.05 m). The peak value of the blasting vibration curve is within the delay time range of cutting holes, which is not consistent with the blasting stage that causes the damage of surrounding rock. Therefore, the correlation between the peak particle vibration velocity and the damage range of the surrounding rock should be studied within the delay time which has great influence on the damage of surrounding rock. The quantitative relationship between the cumulative damage range of surrounding rock and blasting charge, blasting center distance and peak particle vibration velocity is established, and the functional relationship between the cumulative damage range of surrounding rock can be deduced from the peak particle vibration velocity at any blasting center distance. It provides a basis for controlling the blasting damage of surrounding rock and has practical significance for guiding the safety of blasting construction on site.

underground cavities  /  delay blasting  /  accumulated damage  /  equivalent load  /  numerical simulation
吴志超, 龚敏, 仇安兵, 吴晓东, 刘翔宇, 彭娇娇. 硬岩地下洞室工程爆破振动与围岩损伤范围相关性研究. 爆破, 2023 , 40 (1) : 160 -169 . DOI: 10.3963/j.issn.1001-487X.2023.01.022
Zhi-chao WU, Min GONG, An-bing QIU, Xiao-dong WU, Xiang-Yu LIU, Jiao-Jiao PENG. Correlation Study between Blasting Vibration and Surrounding Rock Damage Range of Hard Rock Underground Cavern Engineering[J]. Blasting, 2023 , 40 (1) : 160 -169 . DOI: 10.3963/j.issn.1001-487X.2023.01.022
正文
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钻爆法是当前地下工程岩体开挖的主要方法，具有施工成本低和破岩效率高的优点。然而，爆破开挖产生的巨大瞬时能量若控制不当，将对围岩造成严重损伤，影响地下工程施工和结构的安全[1]。研究地下洞室的开挖爆破对围岩的损伤机理及作用规律，明确爆破荷载作用形成的围岩损伤范围，对于一些爆破损伤控制要求较高的地下工程如核废料贮存洞室、地下贮油库、水电工程等具有重要的研究价值。
国内外学者对爆破荷载作用下围岩损伤范围测定进行了大量现场实验研究和数值分析研究。唐忠义等对现有主要爆破损伤范围测定方法进行了总结[2]；吕国鹏等采用声波测试技术对现场围岩爆破损伤范围进行了检测[3]；潘强等运用爆炸动力学和应力衰减规律建立了理论公式[4]，以预估围岩损伤范围；满柯等研究了装药结构对围岩爆破损伤范围的影响[5]。基于爆破振动与围岩损伤的良好相关性，以爆破振动作为判断围岩损伤范围的依据是近年研究的热点。熊海华等通过岩体质点峰值振动速度安全判据[6]，得到了岩体爆破损伤范围计算公式；谢冰等结合现场声波测试和数值模型实验[7]，推导出了爆区损伤范围与距爆源30m处质点峰值振动速度之间的函数关系式；严鹏等基于现场振动监测和声波实测数据[8]，建立了多个爆心距处振速峰值与围岩损伤范围的指数关系。现有研究表明爆通过爆破振速判断围岩损伤范围是可行的，但并未考虑以下内容：一是现有研究采用全时程振动曲线的峰值作为围岩损伤的判断依据，而不是造成洞室周边围岩损伤的爆破分段振速峰值，可能出现爆破振速峰值所在段位时间与造成围岩损伤段位时间不一致的情况；二是采用固定监测距离的质点峰值振速作为损伤预测公式依据，测点位置不够灵活，一旦变更监测点爆心距，则无法利用该公式预测爆破围岩损伤范围。因此有必要将爆破损伤与振速峰值所在段位不一致、测点爆心距设置不灵活等问题纳入到振动峰值预测围岩损伤的研究中。
以某待建重要地下洞室工程为研究背景，结合LS-DYNA重启动技术，通过建立多段延时爆破累积损伤计算模型，研究不同延时段位爆破荷载对围岩的损伤机理，明确多段延时爆破对洞室轮廓周边围岩产生损伤的延时段位；构建围岩损伤范围与爆心距、爆破药量及振速峰值之间的量化关系，推导出采用现场实测爆破振动数据判断硬岩地下洞室围岩损伤的计算公式。以期为硬岩地下洞室控制围岩损伤提供理论依据，保障硬岩地下洞室的爆破安全施工。
1　工程概况
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依托某待建重要地下洞室工程，工程岩体主要以燕山晚期岩浆侵入的二长花岗岩、辉长岩和前泥盆系片麻状花岗岩为主，三种岩体均较为完整，岩质坚硬，地表层为含碎石的残积土，地下空间局部存在节理密集带和断裂构造带，物理力学性质较差。图1为研究区段地质剖面图，图中包含中风化片麻状花岗岩及微风化片麻状花岗岩，地下洞室长为500 m，轴线方向为N45°W，底面标高为-92 m，埋深为157~203 m，洞室周边围岩主要为微风化片麻状花岗岩，RQD值为75%~100%，节理裂隙发育较少，根据Q系统法岩体分级，岩体Q值总体以10<Q<40为主，围岩质量较好。
研究区段断面结构设计见图2，洞室断面形式采用直墙三心拱结构，高度为9 m，宽度为10 m，拱高为3.3 m，三拱半径分别为2.6 m、7 m和2.6 m。
2　地下洞室爆破围岩累积损伤的数值模拟
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2.1　爆破设计方案
地下洞室全断面爆破设计方案如图3所示，采用分段延时爆破进行开挖，每循环爆破进尺为3 m。采用2#岩石乳化炸药，装药结构为不耦合装药，炮孔直径为45 mm，装药直径为32 mm。其中，掏槽孔布置为双排楔形结构，炮孔角度为65°，通过导爆管雷管MS1段位同时起爆。爆破过程中，导爆管雷管跳段使用，防止因雷管延时误差造成串段。因此，其他炮孔延时段位分别为MS3~MS15的奇数段位，其中，临近轮廓面的二圈孔设置为段位MS9和MS11，周边孔和底板孔的段位分别为MS13和MS15。具体爆破设计参数如表1所示。
2.2　计算模型
根据地下洞室实际尺寸，采用HYPERMESH和LS-DYNA程序联合建立三维计算模型，如图4所示。整体模型尺寸为70 m（长）×60 m（宽）×70 m（高），洞室尺寸为10 m×9 m，洞室距模型边界距离为30 m，符合圣维南原理。模型共划分网格单元约165万个，共有节点约170万个，网格尺寸最小值达到0.2 m。根据爆破设计方案，计算每段爆破荷载，确定各段等效弹性边界，以此将爆破工作面进行分区处理，数值模拟过程中，将各段爆破荷载分别施加在对应等效弹性边界上，以此实现更符合现场实际的分段延时爆破作用模拟，同时避免出现负体积导致计算中断。模型外边界采用无反射边界，以减小反射作用造成的影响。
2.3　岩石材料本构模型及参数
岩石材料采用*MAT_RHT本构模型，该模型定义了材料由等效塑性应变累积而成的损伤，当破坏面上的应力达到材料的极限强度时，损伤和破坏面在非弹性过程中进一步累积塑性应变。围岩破坏时的塑性应变为
式中：为最小失效应变；为失效截断压力，MPa；D为损伤变量；p*为归一化压力，MPa；D1，D2为损伤常数。
由塑性应变累积得到的损伤变量表示为
式中：Δεp为等效塑性应变增量；为破坏时的塑性应变。
根据工程地勘报告，地下洞室周边围岩主要为微风化片麻状花岗岩，其基本物理力学参数见表2。
2.4　爆破荷载的计算
目前，普遍采用*MAT_HIGH_EXPLOSIVE_BURN作为乳化炸药的本构模型，利用JWL状态方程描述爆轰产物的压力变化过程，在建模过程中，需建立炸药模型，对于隧道群孔爆破而言，计算模型中炮孔数量高达百余个，直接建立炸药单元，运行工作量巨大，采用共节点的计算方法需要通过设置质量缩放以解决模型负体积的问题，而采用流固耦合和设置质量缩放将导致计算结果的准确性无法得到保障。因此，本文采用施加等效爆破荷载的方法解决地下洞室全断面爆破数值模拟过程中遇到的问题。
全断面等效爆破荷载计算方法以单个炮孔柱状条形药包爆炸后作用于炮孔壁的爆破压力峰值为基础，利用爆破荷载静力等效简化理论，得到不同段位炮孔施加在相应等效弹性边界上的爆破压力峰值，结合爆破荷载作用时间，得到等效爆破荷载全时程曲线。
根据凝聚态炸药爆轰波理论[9]，径向不耦合装药装药条件下的炮孔爆破荷载峰值P0为
式中：ρ0为炸药密度，kg/m3；D为炸药爆轰速度，m/s；γ为等熵指数，在岩石爆破中一般取3；v为爆轰气体的膨胀绝热指数，在岩石爆破中一般取1.5；a为装药直径，m；b为炮孔直径，m。
当考虑炮孔的装药系数时[10]，爆破荷载峰值Pb1有以下公式
式中：le为轴向装药系数。
文献[11]中将爆炸粉碎区和破碎区等效为爆炸源，得到等效爆破荷载作用的等效弹性边界，如图5为等效弹性边界示意图。
掏槽孔爆破为单自由面爆破，其等效弹性边界的爆破荷载Pe为
式中：k为群孔起爆时的荷载影响系数，其取值与掏槽孔个数及布置形式有关，本文取10 m；r0为炮孔半径；r1粉碎区半径，m；r2破碎区半径，m；μ为泊松比。
对于非掏槽孔爆破而言，等效弹性边界的爆破荷载Pe则表示为
式中，S为炮孔间距，m。
采用三角形荷载形式的爆破荷载时程曲线。爆破荷载上升段时间和下降段时间如下
式中：K为体积模量，105 Pa；Q为单段药量，kg；r为对比距离。
本文采用的乳化炸药爆速D=4500 m/s，炸药密度ρ0=1100 kg/m3，炮孔长度L1=3 m，如图6为按照爆破方案计算得到的全时程等效爆破荷载曲线。
3　硬岩地下洞室多段延时爆破荷载作用下围岩累积损伤效应
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3.1　围岩损伤判定条件
根据岩石的本构模型特征，引入损伤变量D。爆破前初始损伤D设置为0，若损伤值达到一定值，则该损伤对岩体力学性质造成一定影响，工程中普遍采用的损伤阈值为0.19，即D>0.19，判定围岩损伤[12]。
3.2　围岩爆破累积损伤效应研究
利用LS-DYNA程序完全重启动功能，运行计算模型的k文件。首先，得到掏槽爆破荷载（MS1段）作用于等效弹性边界的计算结果，通过设置关键词*STRESS_INITIALIZATION将MS1段爆破荷载产生的应力、应变、损伤等计算结果初始化，作为MS3段爆破荷载计算模型的初始条件。以此类推，计算得到多段位延时爆破荷载作用于洞室围岩的累积损伤结果如图7所示[13]。
图7描绘了MS1~MS15各段位爆破荷载作用于围岩的损伤情况，计算结果表明：掏槽区起到开创自由面的功能，因此单孔装药量大、炮孔间距小，MS1段爆破荷载超过围岩抗压强度，对掏槽区外部围岩造成压剪破坏，使围岩性质劣化，水平方向和垂直方向的损伤范围均达到1.9 m，然而未超过洞室轮廓范围，并未对围岩造成损伤。由于掏槽爆破荷载的影响，MS3段、MS5段和MS7段所处围岩性质出现劣化，岩石性能下降，爆破荷载作用下进一步扩大了围岩损伤范围。其中，MS3段、MS5段爆破荷载对围岩的损伤区域主要位于水平方向，水平方向损伤范围分别增大了0.37 m及0.49 m；MS7段爆破荷载对围岩水平、垂直方向均造成损伤，拱顶部位损伤范围增大了0.90 m，拱腰部位损伤范围增大了0.67 m。以上段位均未对洞室轮廓周边围岩造成损伤。
由图7可知，MS9段、MS11段和MS13段爆破作用对洞室周边围岩均造成损伤，其中，MS9段爆破荷载主要对洞室拱腰部位的水平方向造成损伤，MS11段爆破荷载主要对竖直方向的拱顶部位造成损伤，MS13段爆破在前两段爆破基础上，进一步扩大了拱顶及拱腰部位损伤范围。MS15段爆破主要损伤了洞室底板及拱脚部位，拱底部位主要为垂直方向损伤，拱脚部位因同时受到水平方向和垂直方向爆破荷载，主要为倾斜角45°的拉损伤。
图8描绘了多段延时爆破荷载作用下的洞室拱顶围岩与拱腰围岩损伤范围变化规律，图9表明了拱顶与拱腰同一深度处围岩累积损伤程度。由图可知，造成围岩拱顶损伤主要为MS9、MS11段和MS13段，MS9段爆破荷载作用下，拱腰部位围岩损伤变量首次超过损伤阈值0.19，使损伤范围达到1.09 m；MS11段爆破荷载作用下，拱顶部位围岩损伤变量达到0.24，损伤范围达到1.24 m，围岩性质明显下降；MS13段爆破荷载作用下，拱顶部位及拱腰部位围岩损伤变量及损伤范围均出现明显增大，拱顶损伤范围增长为2.21 m，拱腰损伤范围增长为2.05 m，MS13段爆破荷载对围岩损伤影响较大。
综上所述，多段延时爆破荷载作用下，MS1~MS7段未对洞室周边围岩产生损伤，拱顶围岩损伤主要来源于MS11段和MS13段爆破，拱腰损伤主要来源于MS9段和MS13段，MS15段只对洞室底板部位造成损伤；且拱顶损伤范围明显大于拱腰损伤范围，因此主要分析MS11段及MS13段爆破荷载与围岩拱顶损伤之间的量化关系。
3.3　累积损伤范围与振速峰值的函数关系分析
保持累积损伤计算模型的炮孔分布及其他参数不变，将掏槽孔单孔装药量以0.1 kg为增量，由1.8 kg增长到2.6 kg，按掏槽孔装药量从小到大分别设为Ⅰ号~Ⅸ号模型。其他炮孔装药量与掏槽孔装药量保持同比例变化，基于此，得到不同药量的计算模型。
统计了9个计算模型MS1段、MS11段和MS13段的单段总药量及拱顶损伤范围。由表3可知，掏槽孔（MS1）单孔装药量最大，但炮孔数量较少，单段总装药量较少；辅助孔（MS11）单孔装药量略小于掏槽，炮孔数量为26个，单段总药量较大；周边孔（MS13）决定着洞室轮廓面成形质量，因此单孔装药量最小，但周边孔作用面广，炮孔数量最多，单段总装药量较大；爆破荷载作用下形成的爆破损伤范围随炮孔装药量的增大明显增大。
为获取不同药量计算模型的爆破振动数据，在洞室底板中间区域布置7个测点，相邻测点间隔为5 m，距工作面最近点为1#测点，爆心距为10 m，最远测点为7#测点，爆心距为40 m，测点位置分布如图10所示。
读取测点处振动数据，获得各测点振动曲线及各段振速峰值，如图11为Ⅳ号模型3#、5#、7#测点位置垂向振动波形图，图12为各模型不同爆心距处MS11段和MS13段垂直方向质点峰值振动速度。
由图11可知，全断面多段延时爆破荷载作用下，发现掏槽爆破振速峰值明显最大，辅助孔（MS11）爆破振速峰值略大于周边孔（MS13）爆破振速峰值，结合上节分析掏槽爆破并未对洞室周边围岩产生损伤，因此以全段振速峰值预测损伤范围不够合理。由图12可知，多段延时爆破荷载作用下，爆破振速峰值随爆破药量的增大而增大，随爆心距的增大而减小，且减小幅度也随爆心距的增大而减小。
国内普遍采用萨道夫斯基公式表示爆破振动衰减规律，萨道夫斯基公式形式为
式中：V为质点峰值振动速度，cm/s；Q为单段药量，kg；k、α分别为与爆破点地形、地质等条件有关的系数及衰减指数；R为爆心距，m；ρ=Q1/3/R为比例药量。
岩体损伤范围与质点峰值振动速度存在指数关系[14]，即相同爆心距处，岩体损伤范围与质点峰值振动速度关系有如下表达式
式中：Dp为损伤范围，m；C、ω为拟合系数。
结合公式，进行多元线性回归分析，得到爆破峰值振动速度与爆心距、损伤范围和药量的关系。以下为回归过程：
将公式（9）的方程两边同时取自然对数，得到下式
令z=ln V，x=ln ρ，β=ln k，由公式（11）得到
根据公式（10），方程两边同时取自然对数，可得
令λ=ln C，y=Dp，则式（13）可表示为
将公式（12）和（14）合并，可获得z关于x和y的新的多元线性公式
式中：a、b、c为回归系数。
对Ⅰ~Ⅸ号模型的损伤范围、振速峰值、爆心距和药量等参数进行Levenberg-Marquardt迭代计算[15]，得到采用MS11段爆破振速获得的回归公式中a=1.4022，b=0.22074，c=3.24023，采用MS13段爆破振速获得的回归公式中a=1.42758，b=0.24189，c=3.12624。MS11段与MS13段回归公式的相关性系数R平方分别为0.9742，0.96044，均明显大于0.8，相关性较好，具有一定可靠性。如图13为利用MS11段与MS13段爆破数据及参数得到的回归曲面图。
根据以上回归分析，可得辅助孔（MS11）爆破的振速峰值与损伤范围、爆心距及药量回归函数关系式为
周边孔（MS13）爆破的振速峰值与损伤范围、爆心距及药量回归函数关系式为
根据上述累积损伤范围与药量、爆心距及振动峰值的函数关系，在实际施工中，代入相应的爆破设计参数及现场振动监测数据，即可预测循环爆破荷载作用下，硬岩地下洞室围岩累积损伤范围，指导现场爆破方案设计，具有实际工程意义和实用价值。
3.4　回归公式在隧道临近断裂构造带区域工况中的应用
如图14为现场某段含有断裂构造带的工况，地下洞室与断裂构造带出现在同一片区域，二者最小距离仅为5 m。在多段延时爆破荷载作用下，若围岩损伤范围超过5 m，则损伤区会与断裂构造带贯通，对围岩稳定性存在极大的安全隐患，因此需要确保爆破围岩损伤范围小于5 m。
根据式（17），代入损伤范围Dp=5 m、爆心距R=25 m和爆破药量Q=50.4 kg等参数，得到对应安全振速阈值v=4.98 cm/s。在现场爆破施工过程中，在距爆源25 m区域设置振动监测点，若能确保测点振速峰值小于4.98 cm/s，则可保证围岩爆破损伤处于安全范围内，不会与断裂构造段贯通，保障施工安全。
4　结论
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以某待建重要地下洞室工程为依托，采用理论分析和数值模拟的方法，分析了围岩爆破累积损伤规律，研究了围岩损伤范围与爆心距、爆破药量、爆破振动之间的关系，得到以下结论：
（1）分段延时爆破荷载作用下，洞室周边围岩损伤主要来自位于二圈孔（MS9段、MS11段）和周边孔（MS13段）爆破荷载，最终使地下洞室拱顶区域损伤范围达到2.21 m，拱腰区域损伤范围达到2.05 m。
（2）爆破全时程振动曲线的峰值处于掏槽孔延期时间范围内，与造成围岩损伤的爆破段位不一致，应以对围岩损伤影响较大爆破段位的质点峰值振动速度研究与围岩损伤范围的相关性。
（3）根据爆破振动与围岩损伤范围的良好相关性，建立了围岩损伤范围与爆破药量、爆心距及质点峰值振速的函数关系。在实际工程应用中，可通过任意爆心距的质点峰值振动速度推断围岩损伤范围，减少了现场检测工作量，解决了振动监测点不灵活的问题。
（4）利用基于振速峰值的围岩损伤范围预测公式，可得到爆破振动安全阈值。当安全损伤范围为5 m时，距爆源25m处的振动安全阈值为4.98 cm/s，对指导现场爆破施工安全具有实际意义。
基金
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  • 国家自然科学基金重点项目(51934001)
文献
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2023年第40卷第1期
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doi: 10.3963/j.issn.1001-487X.2023.01.022
  • 接收时间：2022-09-11
  • 首发时间：2026-03-19
  • 出版时间：2023-03-01
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  • 收稿日期：2022-09-11
基金
国家自然科学基金重点项目(51934001)
作者信息
    北京科技大学　土木与资源工程学院，北京　100083

通讯作者:

仇安兵（1971-），男，高级工程师，主要从事基建工程管理工作，（E-mail）。
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https://castjournals.cast.org.cn/joweb/bp/CN/10.3963/j.issn.1001-487X.2023.01.022
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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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