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Article(id=1241756505855283728, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241699613942543237, articleNumber=null, orderNo=null, doi=10.3963/j.issn.1001-487X.2024.03.007, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1692374400000, receivedDateStr=2023-08-19, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773987421716, onlineDateStr=2026-03-20, pubDate=1725120000000, pubDateStr=2024-09-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773987421716, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773987421716, creator=13701087609, updateTime=1773987421716, updator=13701087609, issue=Issue{id=1241699613942543237, tenantId=1146029695717560320, journalId=1240670690148397066, year='2024', volume='41', issue='3', pageStart='1', pageEnd='260', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773973857626, creator=13701087609, updateTime=1773992982583, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241779829880721843, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241699613942543237, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241779829880721844, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241699613942543237, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=51, endPage=59, ext={EN=ArticleExt(id=1241756506178245138, articleId=1241756505855283728, tenantId=1146029695717560320, journalId=1240670690148397066, language=EN, title=Study on Edge Hole Spacing based on Stress Field of Deep Hole Delay Blasting, columnId=1240702072862069231, journalTitle=Blasting, columnName=BLASTING IN ORE AND ROCK, runingTitle=null, highlight=null, articleAbstract=

To solve the problem of the filling bodies failure on both sides of the room caused by differential blasting of large diameter deep holes in underground mine, the stress field generated by differential blasting should be studied to determine a reasonable edge hole spacing and a delay time between the holes. According to the stress wave propagation and attenuation law, the front and rear detonation hole distance, delay time, and edge hole distance generated by complex stress field were determined. Furthermore, the superposition of the stress wave generated by the two-hole differential blasting in the blasted rock mass and the filling body was analyzed according to the wave theory. The stress field function analytical formula of the two-hole differential blasting was obtained. Meanwhile, the collapse range of the blasted rock mass and the failure range of the filled body under different side hole spacing conditions under the same hole spacing and delay time were determined. The LS-DYNA numerical simulation software established six numerical models, and the stress critical points were selected in the blasted rock mass and filling body for analysis after simulating the initiation of explosives under different schemes. The simulation results show that different edge hole distances had almost no effect on the collapse range of the exposed rock mass when the distance between edge holes was more significant than the range of the crack zone. Appropriately increasing the distance between edge holes can effectively reduce the damage caused by stress waves to the filling body. Finally, the field industrial test of four groups of blasting parameters was carried out, and the optimized blasting parameters were determined as the spacing between the two holes on the same side was 2.0 m, the delay time between the front and rear initiation holes was 9 ms, and the side hole spacing was 1.8 m.

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LOU Xiao-ming (1972-), male, Ph. D, Professor, Main research direction: Blasting engineering and mining engineering, (E-mail) .
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为解决地下矿房大直径深孔延期爆破导致矿房两侧充填体的破坏问题，需对延期爆破产生的应力场进行研究，以确定合理的边孔距与孔间延期时间。根据应力波传播和衰减规律，确定了产生复杂应力场的前后起爆孔距、延期时间和边孔距。基于矿山实际情况，根据波动学理论分析了两孔延期爆破产生的应力波在被爆岩体和充填体内的叠加，取得了两孔延期爆破的应力场函数解析式，结合Mises准则，确定了在相同孔间距、延期时间的情况下，不同边孔距离的情况下被爆岩体的崩落范围以及充填体的破坏范围。通过LS-DYNA数值模拟软件建立了6个数值模型，模拟不同方案下炸药起爆后，在被爆岩体和充填体内选取应力临界点进行分析，模拟结果表明：边孔距大于裂隙区范围时，不同边孔距对被爆岩体的崩落范围几乎无影响；适当的增大边孔距可以能够有效降低应力波对充填体造成的破坏。最后，对4组爆破参数进行了现场工业试验，得到了优化后的爆破参数为：同侧两孔间距2.0 m，前后起爆孔延期9 ms，边孔距1.8 m。

, correspAuthors=null, authorNote=null, correspAuthorsNote=
楼晓明（1972-），男，博士、教授，主要研究方向爆破工程及采矿工程，（E-mail）。
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姚炳金（1999-），男，硕士研究生，主要研究方向爆破工程及采矿工程，（E-mail）。

YAO Bing-jin (1999-), male, Master's student, Main research direction: Blasting engineering and mining engineering, (E-mail) .

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姚炳金（1999-），男，硕士研究生，主要研究方向爆破工程及采矿工程，（E-mail）。

YAO Bing-jin (1999-), male, Master's student, Main research direction: Blasting engineering and mining engineering, (E-mail) .

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姚炳金（1999-），男，硕士研究生，主要研究方向爆破工程及采矿工程，（E-mail）。

YAO Bing-jin (1999-), male, Master's student, Main research direction: Blasting engineering and mining engineering, (E-mail) .

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(in Chinese), articleTitle=null, refAbstract=null), Reference(id=1241756539183223459, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241756505855283728, doi=10.13827/j.cnki.kyyk.1997.02.016, pmid=null, pmcid=null, year=1997, volume=null, issue=2, pageStart=54, pageEnd=57, url=null, language=null, rfNumber=[13], rfOrder=23, authorNames=杨宏宝, 陈忠毅, journalName=矿业研究与开发, refType=null, unstructuredReference=杨宏宝, 陈忠毅. 异种介质界面爆破技术在廉江银矿的应用[J]. 矿业研究与开发, 1997(2): 54-57., articleTitle=异种介质界面爆破技术在廉江银矿的应用, refAbstract=null), Reference(id=1241756539325829800, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241756505855283728, doi=10.13827/j.cnki.kyyk.1997.02.016, pmid=null, pmcid=null, year=1997, volume=null, issue=2, pageStart=54, pageEnd=57, url=null, language=null, rfNumber=[13], rfOrder=24, authorNames=YANG Hong-bao, CHEN Zhong-yi, journalName=Mining Research and Development, refType=null, unstructuredReference=YANG Hong-bao, CHEN Zhong-yi. Application of heterogeneous medium interface blasting technology in Lianjiang silver mine[J]. 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ArticleFig(id=1241756529829925297, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241756505855283728, language=EN, label=Table 1, caption=

Rock material parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
密度ρ/（g·cm-3）弹性模量/GPa泊松比屈服强度/MPa抗拉强度/MPa切线模量/GPa
2.5116.200.2160.809.126.69
), ArticleFig(id=1241756529993503159, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241756505855283728, language=CN, label=表1, caption=

岩石力学参数

, figureFileSmall=null, figureFileBig=null, tableContent=
密度ρ/（g·cm-3）弹性模量/GPa泊松比屈服强度/MPa抗拉强度/MPa切线模量/GPa
2.5116.200.2160.809.126.69
), ArticleFig(id=1241756530110943679, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241756505855283728, language=EN, label=Table 2, caption=

Compressive dynamic load coefficient

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σc/MPa<6060~100100~150150~200>200
ξ1>75~74~53~4<3
), ArticleFig(id=1241756530219995593, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241756505855283728, language=CN, label=表2, caption=

抗压动荷载系数

, figureFileSmall=null, figureFileBig=null, tableContent=
σc/MPa<6060~100100~150150~200>200
ξ1>75~74~53~4<3
), ArticleFig(id=1241756530324853202, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241756505855283728, language=EN, label=Table 3, caption=

Coefficient of tensile load

, figureFileSmall=null, figureFileBig=null, tableContent=
σt/MPa<6060~100100~150150~200>200
ξ2<1.41.4~1.61.6~1.81.8~2.0>2.0
), ArticleFig(id=1241756530450682328, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241756505855283728, language=CN, label=表3, caption=

抗拉动荷载系数

, figureFileSmall=null, figureFileBig=null, tableContent=
σt/MPa<6060~100100~150150~200>200
ξ2<1.41.4~1.61.6~1.81.8~2.0>2.0
), ArticleFig(id=1241756530563928541, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241756505855283728, language=EN, label=Table 4, caption=

Filling body parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
密度ρ/（g·cm-3）弹性模量/GPa泊松比屈服强度/MPa抗拉强度/MPa切线模量/GPa
1.870.610.312.840.300.23
), ArticleFig(id=1241756530672980453, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241756505855283728, language=CN, label=表4, caption=

充填体力学参数

, figureFileSmall=null, figureFileBig=null, tableContent=
密度ρ/（g·cm-3）弹性模量/GPa泊松比屈服强度/MPa抗拉强度/MPa切线模量/GPa
1.870.610.312.840.300.23
), ArticleFig(id=1241756530782032360, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241756505855283728, language=EN, label=Table 5, caption=

Explosive material parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
密度ρ/（g·cm-3）爆速D/（m·s-1）爆压/（1011 Pa） A/（1011 Pa） B/（1011 Pa） R1 R2 ω E0/（1011 Pa） V
0.903.00×1030.030.49460.0018913.9071.1180.3330.03871.00
), ArticleFig(id=1241756530886889967, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241756505855283728, language=CN, label=表5, caption=

炸药材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
密度ρ/（g·cm-3）爆速D/（m·s-1）爆压/（1011 Pa） A/（1011 Pa） B/（1011 Pa） R1 R2 ω E0/（1011 Pa） V
0.903.00×1030.030.49460.0018913.9071.1180.3330.03871.00
), ArticleFig(id=1241756530995941879, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241756505855283728, language=EN, label=Table 6, caption=

Field blasting test parameter table

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爆破参数试验1试验2试验3试验4
边孔距/m1.61.71.81.9
两孔间距/m2.02.02.02.0
首排距/m3.03.03.03.0
孔间延期/ms9.09.09.09.0
排间延期/ms42.042.042.042.0
), ArticleFig(id=1241756531138548221, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241756505855283728, language=CN, label=表6, caption=

现场爆破试验参数表

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爆破参数试验1试验2试验3试验4
边孔距/m1.61.71.81.9
两孔间距/m2.02.02.02.0
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基于深孔延期爆破应力场的边孔距的研究
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姚炳金 1a, 1b , 牛明远 2 , 曾令峰 2 , 郭文康 2 , 林日宗 2 , 楼晓明 1a, 1b
爆破 | 矿岩爆破 2024,41(3): 51-59
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爆破 | 矿岩爆破 2024, 41(3): 51-59
基于深孔延期爆破应力场的边孔距的研究
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姚炳金1a, 1b , 牛明远2, 曾令峰2, 郭文康2, 林日宗2, 楼晓明1a, 1b
作者信息
  • 1a.福州大学　紫金地质与矿业学院，福州　350116
  • 1b.福州大学　爆炸技术研究所，福州　350116
  • 2.紫金矿业建设有限公司，厦门　361026

    • 姚炳金（1999-），男，硕士研究生，主要研究方向爆破工程及采矿工程，（E-mail）。

    YAO Bing-jin (1999-), male, Master's student, Main research direction: Blasting engineering and mining engineering, (E-mail) .

通讯作者:

楼晓明（1972-），男，博士、教授，主要研究方向爆破工程及采矿工程，（E-mail）。
Study on Edge Hole Spacing based on Stress Field of Deep Hole Delay Blasting
Bing-jin YAO1a, 1b , Ming-yuan NIU2, Ling-feng ZENG2, Wen-kang GUO2, Ri-zong LIN2, Xiao-ming LOU1a, 1b
Affiliations
  • 1a.Zijin School of Geology and Mining, Fuzhou University, Fuzhou 350116, China
  • 1b.Institute of Explosion Technology, Fuzhou University, Fuzhou 350116, China
  • 2.Zijin Mining Construction Co., Ltd., Xiamen 361026, China
出版时间: 2024-09-01 doi: 10.3963/j.issn.1001-487X.2024.03.007
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摘要
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为解决地下矿房大直径深孔延期爆破导致矿房两侧充填体的破坏问题，需对延期爆破产生的应力场进行研究，以确定合理的边孔距与孔间延期时间。根据应力波传播和衰减规律，确定了产生复杂应力场的前后起爆孔距、延期时间和边孔距。基于矿山实际情况，根据波动学理论分析了两孔延期爆破产生的应力波在被爆岩体和充填体内的叠加，取得了两孔延期爆破的应力场函数解析式，结合Mises准则，确定了在相同孔间距、延期时间的情况下，不同边孔距离的情况下被爆岩体的崩落范围以及充填体的破坏范围。通过LS-DYNA数值模拟软件建立了6个数值模型，模拟不同方案下炸药起爆后，在被爆岩体和充填体内选取应力临界点进行分析，模拟结果表明：边孔距大于裂隙区范围时，不同边孔距对被爆岩体的崩落范围几乎无影响；适当的增大边孔距可以能够有效降低应力波对充填体造成的破坏。最后，对4组爆破参数进行了现场工业试验，得到了优化后的爆破参数为：同侧两孔间距2.0 m，前后起爆孔延期9 ms，边孔距1.8 m。

采场深孔爆破  /  延期爆破  /  爆破应力场  /  边孔距  /  充填体

To solve the problem of the filling bodies failure on both sides of the room caused by differential blasting of large diameter deep holes in underground mine, the stress field generated by differential blasting should be studied to determine a reasonable edge hole spacing and a delay time between the holes. According to the stress wave propagation and attenuation law, the front and rear detonation hole distance, delay time, and edge hole distance generated by complex stress field were determined. Furthermore, the superposition of the stress wave generated by the two-hole differential blasting in the blasted rock mass and the filling body was analyzed according to the wave theory. The stress field function analytical formula of the two-hole differential blasting was obtained. Meanwhile, the collapse range of the blasted rock mass and the failure range of the filled body under different side hole spacing conditions under the same hole spacing and delay time were determined. The LS-DYNA numerical simulation software established six numerical models, and the stress critical points were selected in the blasted rock mass and filling body for analysis after simulating the initiation of explosives under different schemes. The simulation results show that different edge hole distances had almost no effect on the collapse range of the exposed rock mass when the distance between edge holes was more significant than the range of the crack zone. Appropriately increasing the distance between edge holes can effectively reduce the damage caused by stress waves to the filling body. Finally, the field industrial test of four groups of blasting parameters was carried out, and the optimized blasting parameters were determined as the spacing between the two holes on the same side was 2.0 m, the delay time between the front and rear initiation holes was 9 ms, and the side hole spacing was 1.8 m.

stope deep hole blasting  /  differential blasting  /  blasting stress field  /  edge hole spacing  /  filling body protection
姚炳金, 牛明远, 曾令峰, 郭文康, 林日宗, 楼晓明. 基于深孔延期爆破应力场的边孔距的研究. 爆破, 2024 , 41 (3) : 51 -59 . DOI: 10.3963/j.issn.1001-487X.2024.03.007
Bing-jin YAO, Ming-yuan NIU, Ling-feng ZENG, Wen-kang GUO, Ri-zong LIN, Xiao-ming LOU. Study on Edge Hole Spacing based on Stress Field of Deep Hole Delay Blasting[J]. Blasting, 2024 , 41 (3) : 51 -59 . DOI: 10.3963/j.issn.1001-487X.2024.03.007
正文
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在二步骤回采过程中，采场两侧的充填体不仅受到上覆围岩的静载荷压力，还会受到二步骤矿柱回采时爆破产生的动载荷影响，造成充填不同程度的垮塌、出矿品位降低。因此，有必要对二步骤回采时的矿体（岩）边孔距进行研究，尽量减少二步骤回采造成的充填体的破坏。
国内外学者在理论分析、数值模拟、工业实验等不同角度，进行了二步骤回采对充填体影响的相关研究。刘优平等采用LS-DYN分析凡口铅锌矿间柱采场近充填体炮孔的爆炸应力[1]，对比分析充填体内一系列节点的振动速度，以优化炮孔装药结构，从而控制爆破对充填体的影响。薛田喜等人结合萨道夫斯基公式研究充填体内爆破振动波的传播规律[2]。秦梨等人研究了不同灰砂比的充填体在冲击载荷下的力学特性[3]。张金等通过分离式霍普金森压杆，试验获得矿石和充填体的动力学参数[4]，并以此利用LS-DYNA对不同孔底距、排间距等多种方案的充填体响应进行模拟分析，得到了能够对应满足充填体稳定性且爆破效果最佳的方案。姜明归等从能耗角度得出充填体断裂韧度的计算公式[5]，朱瑞鹏等通过分析爆炸应力波在胶结充填体内部空隙中的透反射规[6]，建立了充填体张拉破坏理论模型，为胶结充填体在二步回采中稳定性分析提供了新的参考依据。胡建华等人[7]，分析了爆破作用对充-岩界面耦合体结构的力学影响，获取了不同界面粗糙度、充填体养护龄期和起爆方式等因素对爆破裂隙扩展及应力波峰值应力的影响。甘德清等人从宏-细-微三个尺度探讨充填体早期损伤对后期力学性能影响机制[8]。但对爆破条件下的应力波在充填体内的叠加以及其对充填体的影响研究较少。
在上述研究成果基础上，为减小爆破振动对采场顶板和采场侧帮充填体的振动影响，考虑具体矿山的岩石和充填体的力学性质，利用爆破引起的岩石和充填体中任一点爆破应力随距离和持续时间的函数关系式，确定前后起爆炮孔合理的延期时间，并在延期时间的基础上，研究不同边孔距条件下充填体的破坏范围。然后，采用显式动力有限元分析软件LS-DYNA，建立多个岩石-充填体耦合动力仿真模型，模拟不同边孔距下充填体的破坏范围与理论分析进行相互验证，以确定合理的边孔距。
1　工程概况
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山西紫金矿业有限公司旗下义兴寨地下金矿采用大直径深孔阶段空场嗣后充填采矿法，以隔一采一的顺序进行回采，矿房平均宽度14 m，长50 m，中段高度60 m。随着开采的进行，部分采场已经完成一步骤回采并充填完毕，而因为二步骤的回采孔网参数与一步骤回采的孔网参数有所差异，且由于充填体强度远低于岩体强度，一旦受到过大破坏将产生整体垮塌的风险，因此有必要对二步骤回采炮孔的布置进行研究。
由于矿房跨度较大，为确保安全，需在矿房正中央沿凿岩硐室长轴方向布置宽为3.6 m的安全间柱，一步骤回采时，一排布置6个炮孔，间柱两侧各3个炮孔，若以此布置炮孔，在二步骤回采时，由于边孔距离充填体过近，必然会引起充填体严重垮塌，因此在设计二步骤回采的炮孔布置时，一排布置4个炮孔，间柱两侧各2个孔，如图1所示。
2　理论分析
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2.1　孔间延期时间的选取
对于岩石中的爆破，单炮孔内炸药爆炸所产生的爆轰波作用于孔壁，透射入岩石中的冲击波在炮孔附近形成粉碎区，伴随着能量迅速衰减，冲击波随之转化为应力波，在岩石中任一点的爆破应力是关于该点与炮孔距离r和应力在该点的持续时间ts的函数[9]
式中：σi为岩石中任一点的应力强度，Pa；σ0为初始波阵面径向应力，Pa；r0为初始波阵面半径，m；α为衰减系数，对于冲击波取α1=2+μ/（1-μ），对于应力波取a2=2-μ/（1-μ），其中μ为岩石的动态泊松比，通常μ=0.8μ0，μ0为岩石的静态泊松比；A为应力随时间变化的衰减系数，β=Cp（1-μ）/[α（1-μ）k]，其中Cp为岩石纵波速度，m/s；α和k为与岩石和炸药性质有关的常数[10,11]。A=[（1+λ）2-2μ（1-μ）（1-λ）2+（1+λ2）]1/2，λ为侧向压力系数[12]，λ=μ/（1-μ）。
结合义兴寨地下矿的岩石力学相关参数表1，可得出单炮孔产生的应力随距离、时间衰减曲线如图2和图3所示。
由图2图3可以看出，在距离爆源6m处和持续时间15 ms后，爆炸应力已大幅度衰减。由于现场情况有间柱的存在，中间两孔孔间大于3.6 m，其中一侧的中间孔，距离另一侧的充填体的距离大于6 m，故可忽略其应力叠加，因此只研究同一侧两孔的应力叠加对充填体的影响。
当孔间延期小于5 ms，应力场会充分叠加，容易导致矿房顶板的垮塌，以及矿房两侧充填体的大范围垮落。当同侧炮孔之间的延期时间大于15 ms，可能会出现第一个爆破孔已经完成爆破，而第二个爆破孔尚未起爆，未能达到能量密度的合理利用，孔间应力波叠加不合理，导致孔间延期爆破失去意义，不利于爆破中岩石的二次破碎，可能直接导致后续大块体增多，影响爆破效果。因此前后起爆的炮孔之间延期时间在5~15 ms之间选择。
2.2　双孔柱状药包延期起爆应力叠加破坏范围理论计算
2.2.1　双孔柱状药包延期起爆应力叠加及保护矿柱破坏范围理论计算
两孔先后起爆时应力波作用复杂，且纵波作用较强，因此计算两孔爆炸应力波刚相遇时的应力场大小，此时孔2反射纵波还未出现，为便于分析，只考虑孔1入射纵波和反射纵波以及孔2入射纵波的情况，结合式（1）其叠加公式如下
式中：t为延期爆破孔间延期时间，s；Δt为第二个药包产生的应力波到叠加点的时间，s。见图4。
为求得孔2与充填体间裂隙区范围，取σA值的大小为矿体的动态抗拉强度σtd。根据上式可以求得孔二与充填体之间矿石的最大破坏范围
式中：rl为孔2与充填体之间矿体的裂隙区范围，m；σcd为矿石的动态抗压强度，Pa。
式中，ξ1、ξ2分别为岩石的抗压、抗拉动载荷系数，见表2、表3。
结合义兴寨地下矿岩石力学相关参数表1，计算得出岩石动态抗压强度σcd=425.6 MPa，动态抗拉强度σtd=12.8 MPa。根据计算可知，两孔延期叠加条件下，孔一起爆后产生的应力场与孔二起爆后产生的应力场有叠加效果。
根据图2和图3，在保证两孔应力叠加且不会造成过大振动的情况下，选取延期时间为9 ms，同侧孔间距为2 m。根据计算，在此条件下，边孔起爆后造成的破坏范围为1.2 m左右，但不同的边孔距对实际破坏范围影响不大。随着边孔距的增加，爆破后剩余保护矿柱厚度会逐渐增加，但在不同边孔距情况下充填体的破坏不同，也需要理论计算。
2.2.2　双孔柱状药包延期起爆应力叠加及充填体破坏范围理论计算
应力波在经过岩体中的节理裂隙或是经过异质界面等情况下，会有部分波界面反射回来，产生反射的纵波和横波，另一部分会透过交界面，产生透射的纵波和横波，由于在交界面处倾斜入射的应力波情况十分复杂，因此设应力波垂直于交界面入射。
对计算矿岩中爆破应力波的传播参数虽然还没有精确的理论方法，但就最简单的纵波由一种介质垂直界面入射另一种介质而言，其透射的情况已有下面的数学解[13]
式中，Rr、Rt分别为应力波的垂直反射系数，透射系数。可用下式计算
式中：ρi（i=1，2）为介质i的密度，kg/m3；Ci（i=1，2）为介质i中纵波的速度，m/s；ρiCi为介质的波阻抗。
对于透射入充填体内的应力波叠加，如图5，药包1的应力波先传播一段时间，药包2才起爆，所以，此时应力波叠加位置和同时起爆就有所不同，位于中垂线靠近药包2的位置。C点为此时的应力波叠加点，θ、β分别为1、2炮孔的斜交角度。
这里将C点取出单元进行受力分析，结合式（9）利用三角形内外角关系和正交分解的原理，在二力方向上进行求和，可以求得两中深孔逐孔起爆时，其应力在充岩界面的透射，叠加规律。
结合式（1）、（12）、（13），充填体内与炮孔连线垂直与充-岩界面上任意一点的有效应力为
式中：lc为垂线上任意一点到充-岩边界的距离。
以边孔距1.5 m为例，根据上文选取的孔间距2 m，延期时间9 ms的情况下，可以求得充-岩界面充填体侧一点的有效应力如图6所示。
由于应力波在充填体内产生的有效应力远小于充填体的动态抗压强度，根据Von Mises屈服准则，当时判充填体产生拉破坏。结合充填体力学相关参数，充填体的动态抗拉强度为0.7 MPa。上文计算得出，在孔间延期9 ms，孔距2 m的情况下，边孔起爆后被爆岩体破坏范围为1.2 m，因此计算整理边孔距大于1.2 m时的充填体内破坏范围变化趋势与保护矿柱剩余厚度的关系，如图7所示。
由图7分析可知，充填体的破坏范围随着边孔距的增大而减小，相应剩余的保护矿柱也随之增多，而在边孔距为1.8 m时充填体内几乎没有破坏，结合上文可知边孔爆破作用宽度1.2 m爆破后，剩余部分的保护矿柱会由其自重影响而掉落，不会影响矿石产量，因此边孔距取1.8 m更为合理。
3　数值模拟计算
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3.1　模型建立及材料参数选取
采场爆破采用垂直布孔的方式，孔间平行，为提高计算效率，将采场三维模型简化成垂直于炮孔的平面模型。确定孔距为2 m，延期时间9 ms，边孔距充填体距离分别为1.5 m、1.6 m、1.7 m、1.8 m、1.9 m、2.0 m。被爆岩体和充填体宽度都设为7 m，如图8所示。
本次模型炸药采用LS-DYNA常用的炸药材料模型HIGH_EXPLOSIVE_BURN模型以及*EOS_JWL状态方程用来描述炸药的爆炸过程。
空气材料模型及状态方程分别用关键字*MAT_NULL、*EOS_GRUNEISEN定义。岩石和充填体材料模型用关键字*MAT_PLASTIC_KINEMATIC定义。材料参数见表1、表4、表5。为减小误差，除充填体与岩石接触部分，皆设为无反射边界。数值模型采用cm-g-μs。
3.2　结果分析
由于篇幅限制，且因为爆炸过程矿体部分的应力残留很大，影响充填体部分的应力云图的显示，因此仅展示边孔距lm=1.5 m时充填体内的应力云图。
由图9可以看出，在t=2700 μs时第一只孔的应力波已经在充填体内传播了一段距离，且到了t=5000 μs可以明显看出应力波的衰减残留。而在t=11 000 μs时，相同位置第二只的应力云图与第一只孔的明显不同，说明两孔延期起爆应力场在刚进入充填体的一定距离内有所叠加，而随着距离的增大应力的持续衰减，叠加效应不再明显。
3.2.1　保护矿柱破坏范围验证
为验证式（7）的合理性，分别取6个数值模型中距边孔1.2 m的网格，如图10。图11为以边孔距1.5 m为例情况下，测点H41553的有效应力随时间衰减曲线。
将6个模型得到的破坏范围与理论计算所得的破坏范围对比，并汇总处理，得到图12。
由图12可以看出，由于数值模拟中反射的存在，不能忽视，因此不同边孔距下边孔起爆后在距边孔1.2 m处的有效应力并不相同，并且随着边孔距的增大，有效应力随之减小。但是与理论计算所得的有效应力相比，其误差均控制在正负1%以内。纵向比较不同边孔距情况下应力叠加最大相差仅为0.15 MPa，远小于岩石的动态抗拉强度。
总体来看，在两孔延期爆破时，数值模拟计算拟合曲线与理论计算拟合曲线基本一致。根据Mises准则判断，不同边孔距情况下，岩石破坏范围在1.2m左右。
3.2.2　充填体破坏范围验证
在每个模型中分别设置一条检测线，该检测线位于炮孔与充-岩界面的垂线上。根据理论计算，边孔距1.5 m时充填体内破坏范围为0.4 m，由于存在误差的可能性，因此选取充填体内，测线上0.5 m内的所有网格作为测点，网格编号存在重叠，因此仅每5个网格给出一个测点编号如图13所示。
以边孔距为1.5 m时为例，充-岩界面充填体一侧，给出图13中测点H116386的有效应力随时间衰减曲线如图14所示。
将每个模型的测点的有效应力曲线的峰值整理可以分别得到其应力衰减曲线，如图15所示。由图15纵向对比可以看出，随着边孔距的增大由岩石入射进充填体的应力，随着边孔距的增大而减小；初始应力越大，其在充填体内的衰减更快，而初始应力越小其衰减越慢，应力波在充填体内的衰减规律符合岩石的衰减规律；以充填体的动态抗拉强度0.7 MPa为限，可以看出，边孔距1.5 m时充填体破坏范围为0.42 m，而边孔距1.8 m时，应力波对充填体近乎无影响。总体来看，在两孔延期爆破时，数值模拟计算拟合曲线与理论计算拟合曲线基本一致，为使得爆破过程中充填体的破坏降到最小，且爆破效果良好，建议在孔间距为2 m，孔间延期9 ms时，边孔距取1.8 m。
4　现场工业试验
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4.1　现场工业试验方案
在理论和数值模拟的基础上，结合工程背景进行爆破试验，采用数码电子雷管进行延期爆破，设计现场工业试验方案4组，炮孔直径120 mm，炸药采用粒状铵油炸药，其相关参数与数值模拟中炸药参数相同参考表5，采用数码电子雷管起爆。考虑到边孔距离充填体更近，边孔采用“2 m装药1 m间隔”，中间孔采用“3 m装药1 m间隔”，上下堵塞各1.5 m，孔长49 m，其余爆破参数见表6。每次实验起爆两排，每组试验2次。以边孔距1.8 m为例，具体起爆网路如图16所示。
4.2　试验结果分析
由于篇幅有限，在此仅展示边孔距为1.8 m爆破试验后的三维扫描图如图17所示。
根据现场观测结合扫描图可以发现，边孔距为1.6 m时两帮爆破应力过大导致充填体破坏严重，壁面存在凹陷，片落，顶板也由于充填体的破坏出现大面积垮塌。边孔距为1.7 m时充填体存很小部分的片落，但采场的顶板无垮塌。边孔距为1.8 m时，采场侧帮充填体裸露，壁面平整光滑，整体完好无明显破坏，空区形态与设计采场形态基本吻合，而崩落的矿石块度较为均匀，大块较少，爆破效果良好。而边孔距为1.9m的试验，被爆岩体还有一部分与充填体粘接悬在采场侧帮，一方面影响回采进程的安全，同时造成了矿石的浪费。
综上可知，在固定间柱一侧两孔间距为2 m，孔间延期为9 ms时，边孔距选择1.8 m时充填体基本无破坏，同时保证被爆岩体全部崩落，爆破效果良好。
5　结论
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在延期爆破条件下，对炮孔爆炸产生的应力波在岩石和充填体中的传播、叠加等变化过程及应力作用下的破坏范围进行了理论、数值模拟和工业试验研究，获得结论如下：
（1）基于柱状装药的应力传播理论及其叠加规律，结合义兴寨地下矿的岩石和充填体的力学参数以及炸药相关参数得知，当前后起爆孔的延期时间在5~15 ms之间，孔距小于6 m时，仍需要考虑延期爆破应力场的叠加效应。
（2）通过建立多个数值模型，将不同边孔距条件下，理论计算得出被爆岩体和充填体的破坏范围与数值模拟拟合出的相比较，两者得到的结果吻合度较高，证明理论结果的正确性。
（3）爆破网路中边孔距不同，引起的爆破应力场大小也不同，相对应的爆破孔网参数取值也不同。义兴寨地下矿现场较优化的孔网参数取值，孔间距为2 m，孔间延期为9 ms时，边孔距选择1.8 m，可以保证充填体基本无破坏且爆破效果良好。
基金
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  • 国家自然科学基金(52109124)
  • 义兴寨金矿河湾斑岩型金矿深孔控制爆破技术研究(01612118)
文献
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2024年第41卷第3期
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doi: 10.3963/j.issn.1001-487X.2024.03.007
  • 接收时间：2023-08-19
  • 首发时间：2026-03-20
  • 出版时间：2024-09-01
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  • 收稿日期：2023-08-19
基金
National Natural Science Foundation of China(52109124)
国家自然科学基金(52109124)
Research on Deep Hole Controlled Blasting Technology for Hewan Porphyry Gold Mine(01612118)
义兴寨金矿河湾斑岩型金矿深孔控制爆破技术研究(01612118)
作者信息
    1a.福州大学　紫金地质与矿业学院，福州　350116
    1b.福州大学　爆炸技术研究所，福州　350116
    2.紫金矿业建设有限公司，厦门　361026

通讯作者:

楼晓明（1972-），男，博士、教授，主要研究方向爆破工程及采矿工程，（E-mail）。
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https://castjournals.cast.org.cn/joweb/bp/CN/10.3963/j.issn.1001-487X.2024.03.007
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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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