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Article(id=1241777702852694038, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241777699996368955, articleNumber=null, orderNo=null, doi=10.3963/j.issn.1001-487X.2024.02.013, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1680624000000, receivedDateStr=2023-04-05, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773992475473, onlineDateStr=2026-03-20, pubDate=1717171200000, pubDateStr=2024-06-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773992475473, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773992475473, creator=13701087609, updateTime=1773992475473, updator=13701087609, issue=Issue{id=1241777699996368955, tenantId=1146029695717560320, journalId=1240670690148397066, year='2024', volume='41', issue='2', pageStart='1', pageEnd='252', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773992474792, creator=13701087609, updateTime=1773992784144, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241778997575619516, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241777699996368955, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241778997575619517, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241777699996368955, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=104, endPage=111, ext={EN=ArticleExt(id=1241777704547192863, articleId=1241777702852694038, tenantId=1146029695717560320, journalId=1240670690148397066, language=EN, title=Optimization and Application of Blasting Parameters of Deep Hole Bench Blasting in Open Pit Mine, columnId=1240702072862069231, journalTitle=Blasting, columnName=BLASTING IN ORE AND ROCK, runingTitle=null, highlight=null, articleAbstract=

In deep hole bench blasting in open-pit mines, several issues arise including high consumption of explosives per blast, large bulk and foundation ratio, increased overall cost, inadequate loose blasting pile for shovel loading, and excessive blasting vibrations that affect slope stability. This study focuses on the controlled blasting project of deep-hole benches in Duobaoshan open-pit mine. Theoretical analysis was conducted to establish an analytical formula for the stress field caused by hole-by-hole blasting. The parameters such as hole and row spacings, minimum bottom resistance line, and delay time between holes were determined based on this formula. The LS-DYNA software was utilized to analyze the blasting stress and crushing range under these parameters. Furthermore, six groups of industrial field tests were carried out at Duobaoshan open pit mine using different blasting parameters. These tests aimed to determine the variation patterns of powder factor, fragmentation size, and looseness characteristics among different explosives. The optimized parameters for controlled deep hole bench blasting in Duobaoshan open-pit mine were verified and determined through these experiments. The main research findings are as follows: (1) Under the coupling charge condition of Duobaoshan open-pit blasts and utilizing theoretical derivation and analysis of stress fields from hole-by-hole initiation method, it was found that the influence of stress field distribution is limited to front and rear holes with a delay time between holes set at 17 ms. (2) UAV tilt photography technology along with mobile phone photography can be employed to collect data on detonation piles' characteristics and lumpiness size at blast sites. Analysis based on collected data provides effective insights into looseness levels. (3) For the 178 mm of the hole diameter and 17 ms of the holes' delay time of the deep hole bench blasting in Duobaoshan open-pit mine, the powder factor is 0.60 kg/m3 and the hole row spacing is 7 m×5 m under the conditions that the blast lumpiness is less than 60 cm and the looseness is greater than 1.45 shovel loading.

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LOU Xiao-ming (1972-), male, doctor, professor, main research interests: Blasting Engineering and Mining Engineering, (E-mail) .
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露天矿深孔台阶爆破常存在炸药单耗和大块及根底率偏高增加综合成本、爆堆松散度过小不利于铲装、爆破振动过大影响边坡稳定等问题。以多宝山露天矿深孔台阶控制爆破为工程依托，从理论上建立了逐孔起爆爆破引起的应力场解析式，确定了逐孔起爆的孔排距、最小底抗线和孔间延期时间；采用LS-DYNA软件对此爆破参数建立的模型爆破应力大小和破碎范围进行了分析，并在多宝山露天矿进行了6组不同爆破参数条件下的现场工业试验，确定了不同炸药单耗等爆破参数与块度、松散度的变化规律，验证并确定了优化的多宝山露天矿深孔台阶控制爆破参数。主要研究成果为：（1）在多宝山露天矿爆破的耦合装药条件下，通过逐孔起爆应力场的理论推导和分析，应力场分布和应力大小的影响仅限于前后两孔之间，孔间延期时间17 ms是比较合理的。（2）爆破现场爆堆和块度大小数据的收集可以通过无人机倾斜摄影技术和手机拍照进行，由此收集的数据分析获得的松散度和块度是有效合理的。（3）多宝山露天矿深孔台阶爆破，当炮孔直径为178 mm和孔间延期时间17 ms时，满足爆堆块度小于60 cm、松散度大于1.45铲装条件下的炸药单耗为0.60 kg/m3、孔排距为7 m×5 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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张衍昊（1997-），男，硕士研究生，主要研究方向爆破工程及采矿工程，（E-mail）。

ZHANG Yan-hao (1997-), male, master degree candidate, main research interests: Blasting Engineering and Mining Engineering, (E-mail) .

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张衍昊（1997-），男，硕士研究生，主要研究方向爆破工程及采矿工程，（E-mail）。

ZHANG Yan-hao (1997-), male, master degree candidate, main research interests: Blasting Engineering and Mining Engineering, (E-mail) .

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张衍昊（1997-），男，硕士研究生，主要研究方向爆破工程及采矿工程，（E-mail）。

ZHANG Yan-hao (1997-), male, master degree candidate, main research interests: Blasting Engineering and Mining Engineering, (E-mail) .

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Method for mapping cast blasting stockpile morphology based on drone oblique photography[J]. Coal Engineering, 2021, 53(2): 99-105. (in Chinese), articleTitle=Method for mapping cast blasting stockpile morphology based on drone oblique photography, refAbstract=null)], funds=[Fund(id=1241777724310753378, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777702852694038, awardId=52109124, language=EN, fundingSource=National Natural Science Foundation of China(52109124), fundOrder=null, country=null), Fund(id=1241777724415610983, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777702852694038, awardId=52109124, language=CN, fundingSource=国家自然科学基金项目(52109124), fundOrder=null, country=null), Fund(id=1241777724507885677, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777702852694038, awardId=01612111, language=EN, fundingSource=Research on Controlled Blasting Technology of High and Steep Slope in Duobaoshan Open-pit Mine(01612111), fundOrder=null, country=null), Fund(id=1241777724625326195, tenantId=1146029695717560320, 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ArticleFig(id=1241777722884689936, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777702852694038, language=CN, label=图11, caption=松散系数随炸药单耗变化图, figureFileSmall=sDkLmRgr7+G3/tS5bN/knQ==, figureFileBig=14IzpNBaRlDW0i5whugmrg==, tableContent=null), ArticleFig(id=1241777722976964625, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777702852694038, language=EN, label=Table 1, caption=

Rock material parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
密度/（g·cm-3）弹性模量/GPa泊松比抗压强度/MPa切线模量/GPa抗拉强度/MPa
2.7623.020.2853.682.2010.57
), ArticleFig(id=1241777723115376670, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777702852694038, language=CN, label=表1, caption=

岩石力学参数

, figureFileSmall=null, figureFileBig=null, tableContent=
密度/（g·cm-3）弹性模量/GPa泊松比抗压强度/MPa切线模量/GPa抗拉强度/MPa
2.7623.020.2853.682.2010.57
), ArticleFig(id=1241777723241205797, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777702852694038, language=EN, label=Table 2, caption=

Rock material parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
密度/（g·cm-3）弹性模量/GPa泊松比屈服应力/MPa切线模量/GPa硬化系数
2.7623.020.2853.682.201.00
), ArticleFig(id=1241777723358646320, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777702852694038, language=CN, label=表2, caption=

岩石材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
密度/（g·cm-3）弹性模量/GPa泊松比屈服应力/MPa切线模量/GPa硬化系数
2.7623.020.2853.682.201.00
), ArticleFig(id=1241777723463503922, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777702852694038, language=EN, label=Table 3, caption=

Parameters of explosive material equation of state

, figureFileSmall=null, figureFileBig=null, tableContent=
ρr/（g·cm-3） D/（m·s-1） PCJ/GPa A/GPa B/GPa R1 R2 ω E0/（kJ·m-3） V
1.2048005.802140.184.200.900.154.192×1061.0
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炸药材料状态方程参数

, figureFileSmall=null, figureFileBig=null, tableContent=
ρr/（g·cm-3） D/（m·s-1） PCJ/GPa A/GPa B/GPa R1 R2 ω E0/（kJ·m-3） V
1.2048005.802140.184.200.900.154.192×1061.0
), ArticleFig(id=1241777723652247614, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777702852694038, language=EN, label=Table 4, caption=

Parameters of field blasting test

, figureFileSmall=null, figureFileBig=null, tableContent=
 试验1试验2试验3试验4试验5试验6
台阶高度H/m13.014.215.313.213.415.4
单耗/（kg·m-3）0.470.530.600.670.740.80
炮孔直径D/mm178178178178178178
孔间/ms171717171717
排间/ms424242424242
孔距/m8.07.57.06.06.05.0
排距/m5.55.35.04.54.04.0
), ArticleFig(id=1241777723752910917, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777702852694038, language=CN, label=表4, caption=

场爆破试验参数

, figureFileSmall=null, figureFileBig=null, tableContent=
 试验1试验2试验3试验4试验5试验6
台阶高度H/m13.014.215.313.213.415.4
单耗/（kg·m-3）0.470.530.600.670.740.80
炮孔直径D/mm178178178178178178
孔间/ms171717171717
排间/ms424242424242
孔距/m8.07.57.06.06.05.0
排距/m5.55.35.04.54.04.0
), ArticleFig(id=1241777723857768523, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777702852694038, language=EN, label=Table 5, caption=

Statistics of the percentage of different blasting lumpiness (average value of three blasting data)

, figureFileSmall=null, figureFileBig=null, tableContent=
块度/cm不同块度所占百分比/%
试验1试验2试验3试验4试验5试验6
0~2045.5355.8157.9764.5471.3573.33
20~4024.3021.0627.5223.6819.9619.89
40~6018.1414.0710.298.785.865.16
60~Topsize12.039.064.223.002.831.62
), ArticleFig(id=1241777723971014733, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777702852694038, language=CN, label=表5, caption=

爆破不同块度所占百分比统计（三次爆破数据的平均值）

, figureFileSmall=null, figureFileBig=null, tableContent=
块度/cm不同块度所占百分比/%
试验1试验2试验3试验4试验5试验6
0~2045.5355.8157.9764.5471.3573.33
20~4024.3021.0627.5223.6819.9619.89
40~6018.1414.0710.298.785.865.16
60~Topsize12.039.064.223.002.831.62
), ArticleFig(id=1241777724063289426, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777702852694038, language=EN, label=Table 6, caption=

Statistics of variation of looseness coefficient with single explosive consumption (average value of data of three bursts)

, figureFileSmall=null, figureFileBig=null, tableContent=
 试验1试验2试验3试验4试验5试验6
松散系数1.3201.3901.4601.4901.5001.505
), ArticleFig(id=1241777724163952726, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777702852694038, language=CN, label=表6, caption=

松散系数随炸药单耗变化统计（三次爆破数据的平均值）

, figureFileSmall=null, figureFileBig=null, tableContent=
 试验1试验2试验3试验4试验5试验6
松散系数1.3201.3901.4601.4901.5001.505
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露天矿深孔台阶爆破逐孔起爆参数的优化研究与应用
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张衍昊 1a, 1b , 刘少光 2 , 楼晓明 1a, 1b
爆破 | 矿岩爆破 2024,41(2): 104-111
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爆破 | 矿岩爆破 2024, 41(2): 104-111
露天矿深孔台阶爆破逐孔起爆参数的优化研究与应用
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张衍昊1a, 1b , 刘少光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.宁德市公安局，宁德　352100

    • 张衍昊（1997-），男，硕士研究生，主要研究方向爆破工程及采矿工程，（E-mail）。

    ZHANG Yan-hao (1997-), male, master degree candidate, main research interests: 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）。
Optimization and Application of Blasting Parameters of Deep Hole Bench Blasting in Open Pit Mine
Yan-hao ZHANG1a, 1b , Shao-guang LIU2, 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.Ningde Public Security Bureau, Ningde 352100, China
出版时间: 2024-06-01 doi: 10.3963/j.issn.1001-487X.2024.02.013
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摘要
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露天矿深孔台阶爆破常存在炸药单耗和大块及根底率偏高增加综合成本、爆堆松散度过小不利于铲装、爆破振动过大影响边坡稳定等问题。以多宝山露天矿深孔台阶控制爆破为工程依托，从理论上建立了逐孔起爆爆破引起的应力场解析式，确定了逐孔起爆的孔排距、最小底抗线和孔间延期时间；采用LS-DYNA软件对此爆破参数建立的模型爆破应力大小和破碎范围进行了分析，并在多宝山露天矿进行了6组不同爆破参数条件下的现场工业试验，确定了不同炸药单耗等爆破参数与块度、松散度的变化规律，验证并确定了优化的多宝山露天矿深孔台阶控制爆破参数。主要研究成果为：（1）在多宝山露天矿爆破的耦合装药条件下，通过逐孔起爆应力场的理论推导和分析，应力场分布和应力大小的影响仅限于前后两孔之间，孔间延期时间17 ms是比较合理的。（2）爆破现场爆堆和块度大小数据的收集可以通过无人机倾斜摄影技术和手机拍照进行，由此收集的数据分析获得的松散度和块度是有效合理的。（3）多宝山露天矿深孔台阶爆破，当炮孔直径为178 mm和孔间延期时间17 ms时，满足爆堆块度小于60 cm、松散度大于1.45铲装条件下的炸药单耗为0.60 kg/m3、孔排距为7 m×5 m。

逐孔起爆爆破应力场  /  孔间延期时间  /  爆破块度  /  爆堆松散度  /  爆破参数优化

In deep hole bench blasting in open-pit mines, several issues arise including high consumption of explosives per blast, large bulk and foundation ratio, increased overall cost, inadequate loose blasting pile for shovel loading, and excessive blasting vibrations that affect slope stability. This study focuses on the controlled blasting project of deep-hole benches in Duobaoshan open-pit mine. Theoretical analysis was conducted to establish an analytical formula for the stress field caused by hole-by-hole blasting. The parameters such as hole and row spacings, minimum bottom resistance line, and delay time between holes were determined based on this formula. The LS-DYNA software was utilized to analyze the blasting stress and crushing range under these parameters. Furthermore, six groups of industrial field tests were carried out at Duobaoshan open pit mine using different blasting parameters. These tests aimed to determine the variation patterns of powder factor, fragmentation size, and looseness characteristics among different explosives. The optimized parameters for controlled deep hole bench blasting in Duobaoshan open-pit mine were verified and determined through these experiments. The main research findings are as follows: (1) Under the coupling charge condition of Duobaoshan open-pit blasts and utilizing theoretical derivation and analysis of stress fields from hole-by-hole initiation method, it was found that the influence of stress field distribution is limited to front and rear holes with a delay time between holes set at 17 ms. (2) UAV tilt photography technology along with mobile phone photography can be employed to collect data on detonation piles' characteristics and lumpiness size at blast sites. Analysis based on collected data provides effective insights into looseness levels. (3) For the 178 mm of the hole diameter and 17 ms of the holes' delay time of the deep hole bench blasting in Duobaoshan open-pit mine, the powder factor is 0.60 kg/m3 and the hole row spacing is 7 m×5 m under the conditions that the blast lumpiness is less than 60 cm and the looseness is greater than 1.45 shovel loading.

hole by hole blasting stress field  /  hole delay time  /  blasting fragmentation  /  explosion looseness  /  blasting parameter optimization
张衍昊, 刘少光, 楼晓明. 露天矿深孔台阶爆破逐孔起爆参数的优化研究与应用. 爆破, 2024 , 41 (2) : 104 -111 . DOI: 10.3963/j.issn.1001-487X.2024.02.013
Yan-hao ZHANG, Shao-guang LIU, Xiao-ming LOU. Optimization and Application of Blasting Parameters of Deep Hole Bench Blasting in Open Pit Mine[J]. Blasting, 2024 , 41 (2) : 104 -111 . DOI: 10.3963/j.issn.1001-487X.2024.02.013
正文
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露天矿深孔台阶爆破常存在炸药单耗和大块及根底率偏高增加综合成本、爆堆松散度过小不利于铲装、爆破振动过大影响边坡稳定等问题。其中主要的原因，除施工人员和机械设备导致的炮孔精确度、装药和堵塞精细化等之外，爆破参数和工艺的设计优化程度也是关键因素。
目前，已有诸多学者开展了针对高陡边坡稳定性的深孔台阶爆破参数优化研究。尹岳降在长九神山灰岩矿进行了现场实验[1]，通过不同的单耗下爆破试验所得的爆破块度分布曲线，分析筛选出合适的单耗；郑炳旭通过在CDEM计算软件中引入朗道点火爆炸模型及岩体塑性-损伤-断裂模型[2]，实现了露天铁矿深孔爆破过程的模拟，得出了随着炸药单耗的增大，块体系统的不均匀系数，系统破裂度都随之增大，大块率随之减小和的结论；刘慧基于爆破块度分布的分形特征[3]，从理论上推导了炸药单耗与爆破块度分布均匀性指数的关系，对爆破块度分布的预测具有重要的指导意义；陈运轩通过对岩石爆破破碎过程的分析推出了炸药单耗与各种爆破块度之间的定量关系式并由此得出了平均块度增大一倍炸药单耗减少一倍的结论[4]；谭臻根据爆破块度预测模型存在的问题[5]，结合一组爆破试验，提出炸药单耗对块度分布的均匀性指数起主要作用，增加炸药单耗可增加细粒颗粒的产率；于永江运用分形理论导出了爆堆煤体块度分布与爆炸后碎石的分维数的关系[6]，提出了煤体爆破块度的分形维数的计算方法，通过线性回归，得出炸药单耗与块煤的分维数的关系，从而可以根据炸药单耗来预测爆堆块度的分布；王国标基于现场[7]，在紫金山金铜矿进行现场试验，在不同矿、岩条件下确定了合适的炸药单耗；耿威、郭明、张阳光等采用灰色关联分析的方法对影响爆破块度的主要因素进行分析[8-10]，提出影响爆破效果的主要因素是炸药单耗。
以上对于深孔台阶爆破的理论与实验等研究，主要通过现场实验数据，对爆破块度与炸药单耗等进行合理分析，从而优化爆破参数达到爆破效果较好的目的，但基于逐孔微差爆破分析爆破应力场分布和应力大小再优化爆破参数的较少。本文首先针对多宝山露天矿爆破耦合装药条件下，对逐孔起爆引起的应力大小及破碎范围进行了理论推导并用数值模拟进行分析验证，围绕推导出的孔网参数，在现场进行了6组共18次爆破实验，通过无人机对爆堆拍摄以及手机拍摄块度等数据的收集与分析，确定了合理的孔排距及炸药单耗，为高陡边坡深孔台阶控制爆破提供了一定的指导及参考。
1　工程概况
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多宝山高陡边坡铜矿采用露天台阶深孔松动爆破，矿区内岩石完整程度较好，致密坚硬，除地表少数强风化岩石抗压强度低于30 MPa，大多数岩石抗压、抗拉、抗剪强度大，内摩擦角大，试验台阶岩石普氏系数f在10~14之间。基于露天爆破回采矿量的需求，要求爆破块度控制在60 cm及以下，基本无根底产生，爆堆松散度1.45以上，从而达到利于钻孔、装药、铲装和运输等的目的。
试验深孔台阶高度15 m，坡面角75°，孔径178 mm，孔深17 m，孔距5~6 m，排距4 m，炸药单耗0.74~0.8 kg/m3；现场采用连续装药结构，逐孔微差起爆技术（图1）。采用以上爆破参数与工艺发现，存在后冲严重导致部分大块、炸药单耗虚高影响爆破成本等问题。
2　爆破应力场分布及单孔破碎范围的计算
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对于逐孔起爆，当采用耦合装药结构时，在爆炸源近区，单个炮孔起爆后所产生的冲击波作用于周围岩体并衰减为应力波，其衰减规律如下式所示[11]
式中：σr为径向应力；σθ为切向应力；为比例距离，且，r为计算点到装药中心的距离，rb为炮孔半径；α为应力波衰减指数，，其中μd为岩石的动态泊松比，通常μd=0.8μ，μ为岩石的静态泊松比；b为侧向应力系数，且b=μd/（1-μd）；p为孔壁受到的冲击波压力；p0为炸药的爆轰压力；ρ、ρ0分别为岩石和炸药的密度；CP，D分别为岩石中的声速和炸药爆速；γ为爆轰产物的绝热指数，一般取值为3。
接着由于应力波随时间衰减的过程是个复杂的过程，因此为了便于分析，认为应力波是通过负指数方式随时间进行衰减，并取衰减函数为[12]
式中：e为自然常数；β为应力波随时间变化的衰减系数；t为时间；
结合多宝山岩石力学等相关参数表1，在多宝山露天矿爆破的耦合装药条件下，利用式（1）、（5）得出单孔应力分别随距离、时间衰减图2和图3所示。
由图2可知，在距离爆源约12 m和延期时间20 ms处，爆破应力波已基本衰减完成，考虑多宝山露天矿爆破孔距5~6 m，且炸药单耗虚高等情况，逐孔起爆对爆破应力场和高陡边坡的稳定性影响考虑2孔的应力叠加和孔间延期时间17 ms是比较合理的，2孔应力场的叠加如图3所示。
由图3，两孔先后起爆时应力波作用复杂，且纵波作用较强，考虑两孔爆炸应力刚相遇时计算合力破岩，此时N孔反射纵波还未出现，为便于分析，只考虑M孔入射纵波和反射纵波以及N孔入射纵波的情况，M炮孔起爆t1ms后N炮孔起爆，由式1、5可得在任意点内引起的应力情况如下[13]
式中：σiM、σiQ、σiN、σiE分别为M炮孔的入射纵波、反射纵波和N炮孔的入射纵波以及在任意一点E的叠加应力；Rρ为反射纵波的反射系数。
假定孔间距7 m，延期时间17 ms，取两孔连线中点的应力进行计算，取Pρ为1，因上式没有涉及爆炸冲击波传播过程及爆炸应力波到达阶段，所以不考虑爆炸冲击波传播过程，爆炸应力到达阶段用红色虚线表示，该阶段时间很短且用Δt表示，应力大小随时间变化如图4所示。
岩石初始裂隙圈半径R1和爆生气体作用下的扩展长度R2分别为[14,15]
式中：σR为压碎圈和裂隙圈分界面上的应力；ρ0为炸药密度；D为炸药爆速；；B与侧向应力系数相关；γ为爆轰产物的膨胀绝热指数；σcd单轴抗压强度；σtd单轴抗拉强度；σc为微裂痕发生扩展的临界应力。
最后将初始裂隙区半径R1与爆生气体作用下的扩展长度R2相加，可求得整个裂隙区半径R3为
在裂隙区半径得出后，可认为裂隙区半径为最小抵抗线长度W，进而得到孔间距a和排间距b为[16]
式中，m为炮孔密集系数，m=1.0~1.3。
结合表1相关数据，将上面所得σiE代入到式10中取代σR，取炸药的密度ρ0=1.20 g/cm3；炸药爆速D=4800 m/s；γ取值为3。可得孔距a=7.15 m，排距b=4.96 m。
3　孔网参数数值模拟
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3.1　模拟方案
为验证理论计算孔排距的合理性，采用ANSYS/LS-DYNA软件，建立台阶模型，模型的各类参数为孔径178 mm，台阶高15 m，堵塞长度5 m，孔距7 m，排距5 m，孔间延期时间17 ms，具体如图5所示。
假定岩体为各向同性的弹塑性材料，用MAT-PLASTIC-KINEMATIC定义其材料类型；考虑到球状药包选取2#岩石乳化炸药，材料类型MAT-HIGH-EXPLOSIVE-BURN，炸药状态方程关键字EOS-JWL[17]；岩石材料和炸药材料的具体参数如表2和3所示
式中：P为爆轰产物压力；E0、V和分别为初始比内能和相对比容；D为炸药爆速；A、B、R1、R2、ω为与材料性质相关的常数。
3.2　模拟结果分析
将模型从炮孔中心剖开，选取两炮孔中心监测点H3308920得有效应力随时间变化图。
将图6（b）与图4进行对比，由于简化了计算模型，理论计算与数值模拟应力随时间变化图数值上存在差异，但大体趋势相同。炮孔起爆后应力衰减迅速，并在第二只炮孔起爆后形成叠加，使整体有效应力比单只炮孔起爆时更大。
由图7可知，在两孔中心处单孔爆炸应力相比较于双孔爆炸叠加后的应力损伤范围较小，这是由于第二只孔爆炸后形成的应力与第一只孔所产生的应力发生叠加，导致应力损伤范围更广。从损伤范围来看，孔距7 m，排距5 m，孔间延期时间17 ms，能达到理想的爆破破坏效果。
4　现场爆破工业试验
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4.1　现场工业试验方案
每个露天矿对深孔爆破引起的爆破块度、爆堆松散度等要求各不相同，在理论和数值模拟确定的基本值基础上，采用现场工业实验并收集相关数据的方法，以取得炸药单耗等相关爆破参数与块度、松散度的关系，以取得较优化的爆破参数，现场工业实验方案6组，每组实验3次，取平均数据进行分析，具体爆破参数如表4所示。
4.2　数据收集方法
爆堆松散度的确定：基于现场条件，试验选取大疆精灵Phantom 4 RTK无人机。根据现场爆破区域的大小，设置无人机飞行范围，将飞行高度设置为30 m，拍摄相片重复率为80%，采用井字飞行倾斜摄影技术。将拍摄下来的爆堆图像在ContextCapture中处理，形成三维模型，根据三维模型的体积大小，并对比未爆前的体积大小，计算得爆堆松散度。
爆堆块度的确定：整个爆堆分为5次手机拍照，第一次为刚完成爆破岩块未铲装前的爆堆；第二次至第五次分别为铲装大约20%、40%、60%和80%后的爆堆。这样能保证整个爆堆真实块度的分布而不是仅仅表面块度的分布。拍照使用篮球作为参照物，且所有的图像都应对焦，并取每个爆堆至少50张以上、照片拍照面积3~7 m2的照片，放入爆破块度分析软件进行其块度分析，获得爆堆中不同块度的比例和大小。
4.3　爆破块度分析
鉴于人工筛分块度分析法的劳动强度大、费工费时等的诸多弊端[18]，为掌握现场试验爆破效果，采用图像分析法开展了18次矿山爆破块度对比分析。现场爆破块度照片和图像法识别效果见图8。根据爆破块度图像识别结果，得到爆破块度统计参数见表5，进而得到爆破块度分布情况图9所示。
由表5可知，6组实验方案取得的块度数据，即块度尺寸大于60 cm的粒度占整个爆堆的10%左右，理解其为非正常炸药爆破破碎，即节理裂隙发育、前次爆破时最后一排对下次爆破的前排（即抵抗线）产生的裂隙等产生的大块，故不列入炸药单耗与块度规律之间的变化范围。
由图9可知，所有实验平台的块度大小，随炸药单耗的增大，小块度级配百分比逐渐变大，这是由于随着单耗的增大，炮孔孔距和排距变小，导致粉碎区和邻近炮孔的小块度增多造成的。另外，随着单耗的增加，块度尺寸增大的速率减小。随着单耗的增加整体趋势是0~20 cm的块度所占比例增幅最大，而20~40 cm、40~60 cm、60~Topsize cm这三个区域所占的比例逐渐减小。
由图9和表5可知，随着单耗的增大，小于某一尺寸的百分比的块度尺寸呈整体趋势减小，即在多宝山露天矿，60 cm以上的石头被归结为大块，随着单耗增加大块率也逐渐变小。从表5可以看出，单耗0.60 kg/m3为优化成本的界点，单耗大于0.60 kg/m3时，95%的块度小于60 cm，随着单耗增大块度变化趋于缓和；单耗小于0.60 kg/m3时，非后面台阶坡面裂隙引起的大块，即因炸药单耗变小从而导致孔排距不合理引起的大块的增加。综合，实验三的爆破参数较合理。
4.4　爆堆松散度分析
将无人机所拍摄的三维爆堆模型如图10所示，利用ContextCapture软件计算爆破前后方量，得出松散系数随单耗变化的折线如图11所示。见表6。
松散度在单耗增大到一定值后，基本上保持不变。从上图中松散度与单耗之间的关系可以看出，在炸药单耗超过0.67 kg/m3后，松散度增加趋势变平缓。根据经验，一般松散系数在超过1.45后，铲装则影响不大。由图11可以看出，在单耗0.60 kg/m3左右即对铲装影响不大。
5　结论
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本次通过理论、数值模拟以及现场工业试验，得到了以下结论：
（1）在多宝山露天矿爆破的耦合装药条件下，通过逐孔起爆应力场的理论推导和分析，应力场分布和应力大小的影响仅限于前后两孔之间，孔间延期时间17 ms是比较合理的。
（2）爆破现场爆堆和块度大小数据的收集可以通过无人机倾斜摄影技术和手机拍照进行，由此收集的数据分析获得的松散度和块度是有效合理的。
（3）多宝山露天矿深孔台阶爆破，当炮孔直径为178 mm和孔间延期时间17 ms时，满足块度小于60 cm、松散度达到1.45铲装条件下的炸药单耗为0.60 kg/m3、孔排距为7 m×5 m。
基金
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  • 国家自然科学基金项目(52109124)
  • 多宝山露天矿高陡边坡控制爆破技术研究(01612111)
文献
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2024年第41卷第2期
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文章信息
doi: 10.3963/j.issn.1001-487X.2024.02.013
  • 接收时间：2023-04-05
  • 首发时间：2026-03-20
  • 出版时间：2024-06-01
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作者
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  • 收稿日期：2023-04-05
基金
National Natural Science Foundation of China(52109124)
国家自然科学基金项目(52109124)
Research on Controlled Blasting Technology of High and Steep Slope in Duobaoshan Open-pit Mine(01612111)
多宝山露天矿高陡边坡控制爆破技术研究(01612111)
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.宁德市公安局，宁德　352100

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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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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