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Article(id=1241777707994906935, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241777699996368955, articleNumber=null, orderNo=null, doi=10.3963/j.issn.1001-487X.2024.02.016, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1691942400000, receivedDateStr=2023-08-14, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773992476699, onlineDateStr=2026-03-20, pubDate=1717171200000, pubDateStr=2024-06-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773992476699, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773992476699, creator=13701087609, updateTime=1773992476699, 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=127, endPage=135, ext={EN=ArticleExt(id=1241777709622296937, articleId=1241777707994906935, tenantId=1146029695717560320, journalId=1240670690148397066, language=EN, title=Study on the Influence of Different Charge Structures on Morphology of Explosion Pile based on GDEM-BlockDyna, columnId=1240702072862069231, journalTitle=Blasting, columnName=BLASTING IN ORE AND ROCK, runingTitle=null, highlight=null, articleAbstract=

This study focuses on the impact of charge structure on the distribution of blast pile morphology in a limestone mine. A combination of theoretical analysis, GDEM-BlockDyna numerical simulation, and on-site optimization tests were conducted to investigate the morphological distribution of step blasting and blast reactors. The change in blast pile morphology with different charge structures was analyzed. The results indicate that the looseness and throwing distance of the blast pile initially increase and then decrease with an increase in the upper charge proportion of the interval section. The height of the explosion pile generally decreases but shows an initial decrease followed by an increase when there is a large air interval proportion. Additionally, the slope angle of the blast pile increases with an increase in charge proportion in the upper section of the interval section but decreases when this proportion becomes too large. These findings demonstrate that explosive pile patterns vary according to charge structure. Furthermore, through numerical simulation methods, effective optimization can be achieved for charge structure, leading to improved on-site explosion patterns and economic benefits for mining operations.

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YU Yan (1981-), female, Qixia County, Yantai City, Shandong Province, bachelor's degree, resource development engineering, (E-mail) .
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论文以某石灰石矿山为背景，针对矿山开采过程中存在的问题，以装药结构对爆堆形态分布的影响为主线，采用理论分析、GDEM-BlockDyna数值模拟及现场优化试验相结合的方法，展开了台阶爆破爆堆形态分布研究，分析了爆堆形态随装药结构的变化规律。爆堆松散度和抛掷距离会随着间隔段上部装药比例的增加先上升后下降，而爆堆高度总体呈下降趋势，但在空气间隔比例较大时会先减小后增加，爆堆坡面角会随着间隔段上部装药比例的增加而增加，但比例过高时则会下降。研究成果表明：爆堆形态随装药结构呈现出一定的变化规律，通过数值模拟方法，有效优化了装药结构，改善了现场爆堆形态，提升了矿山经济效益，可以为类似矿山生产提供指导。

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于燕（1981-），女，山东省烟台市栖霞县，本科，资源开发工程，（E-mail）。
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张肯（1999-），男，江西省上饶市万年县，硕士，采矿工程专业研究生，（E-mail）。

ZHANG Ken (1999-), male, Wannian County, Shangrao City, Jiangxi Province, master's degree, graduate student in mining engineering, (E-mail) .

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张肯（1999-），男，江西省上饶市万年县，硕士，采矿工程专业研究生，（E-mail）。

ZHANG Ken (1999-), male, Wannian County, Shangrao City, Jiangxi Province, master's degree, graduate student in mining engineering, (E-mail) .

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张肯（1999-），男，江西省上饶市万年县，硕士，采矿工程专业研究生，（E-mail）。

ZHANG Ken (1999-), male, Wannian County, Shangrao City, Jiangxi Province, master's degree, graduate student in mining engineering, (E-mail) .

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(in Chinese), articleTitle=Study on blasting crushing effect and vibration rule of rock foundation pit based on GDEM, refAbstract=null), Reference(id=1241777736201601504, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, doi=null, pmid=null, pmcid=null, year=2015, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[16], rfOrder=26, authorNames=王宇涛, journalName=null, refType=null, unstructuredReference=王宇涛. 基于RHT本构的岩体爆破破碎模型研究[D]. 北京: 中国矿业大学(北京), 2015., articleTitle=基于RHT本构的岩体爆破破碎模型研究, refAbstract=null), Reference(id=1241777736277098978, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, doi=null, pmid=null, pmcid=null, year=2015, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[16], rfOrder=27, authorNames=WANG Yu-tao, journalName=null, refType=null, unstructuredReference=WANG Yu-tao. Study on blasting fracture model based on RHT constitustructure[D]. Beijing: China University of Mining and Technology (Beijing), 2015. (in Chinese), articleTitle=Study on blasting fracture model based on RHT constitustructure, refAbstract=null)], funds=[Fund(id=1241777732686774660, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, awardId=42271296, language=EN, fundingSource=National Natural Science Foundation of China(42271296), fundOrder=null, country=null), Fund(id=1241777732770660743, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, awardId=42271296, language=CN, fundingSource=国家自然科学基金面上项目(42271296), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1241777720296801248, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, xref=1., ext=[AuthorCompanyExt(id=1241777720309384161, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, companyId=1241777720296801248, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, 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tableContent=null), ArticleFig(id=1241777728668631330, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=EN, label=Fig. 8, caption=Non-linear surface fitting diagram, figureFileSmall=xbAiatckt8G/u+s1S0PK3A==, figureFileBig=l8A5RAMTfpl5uZFkQbCu+A==, tableContent=null), ArticleFig(id=1241777728760906023, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=CN, label=图8, caption=爆堆抛掷距离非线性曲面拟合图, figureFileSmall=xbAiatckt8G/u+s1S0PK3A==, figureFileBig=l8A5RAMTfpl5uZFkQbCu+A==, tableContent=null), ArticleFig(id=1241777728878346538, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=EN, label=Fig. 9, caption=Fitting of nonlinear surface of blast heap height, figureFileSmall=VM6nbC/gzkerxcscvh5shQ==, figureFileBig=a1EZM2GEGcpI6EuwZypDeQ==, tableContent=null), ArticleFig(id=1241777728958038319, tenantId=1146029695717560320, 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tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=EN, label=Fig. 13, caption=Effect diagram after explosion, figureFileSmall=tFbIbZv7HU2eDqfEjNeHoQ==, figureFileBig=MSiOy9gPmTjVyhRy2qy63w==, tableContent=null), ArticleFig(id=1241777731181019473, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=CN, label=图13, caption=爆后效果图, figureFileSmall=tFbIbZv7HU2eDqfEjNeHoQ==, figureFileBig=MSiOy9gPmTjVyhRy2qy63w==, tableContent=null), ArticleFig(id=1241777731264905557, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=EN, label=Table 1, caption=

Model physical and mechanical parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
材料密度ρ/（kg·m-3）弹性模量E/GPa泊松比μ粘聚力C/MPa内摩擦角ϕ/°剪胀角ϕ/°
石灰岩28504.10.216.14010
), ArticleFig(id=1241777731344597337, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=CN, label=表1, caption=

模型物理力学参数

, figureFileSmall=null, figureFileBig=null, tableContent=
材料密度ρ/（kg·m-3）弹性模量E/GPa泊松比μ粘聚力C/MPa内摩擦角ϕ/°剪胀角ϕ/°
石灰岩28504.10.216.14010
), ArticleFig(id=1241777731453649245, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=EN, label=Table 2, caption=

Landau parameter table of explosives

, figureFileSmall=null, figureFileBig=null, tableContent=
密度/（kg·m-3）爆速/（m·s-1）爆热/（J·kg-1）爆生气体初始绝热指数爆生气体初始绝热指数爆压/GPa
110042003.4e631.3331
), ArticleFig(id=1241777731650781539, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=CN, label=表2, caption=

炸药朗道参数表

, figureFileSmall=null, figureFileBig=null, tableContent=
密度/（kg·m-3）爆速/（m·s-1）爆热/（J·kg-1）爆生气体初始绝热指数爆生气体初始绝热指数爆压/GPa
110042003.4e631.3331
), ArticleFig(id=1241777731738861926, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=EN, label=Table 3, caption=

Parameters of the JWL equation of state of explosives

, figureFileSmall=null, figureFileBig=null, tableContent=
A/GPa B/GPa R1 R2 ω E/GPa
49.461.893.91.20.32.48
), ArticleFig(id=1241777731814359403, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=CN, label=表3, caption=

炸药JWL状态方程参数

, figureFileSmall=null, figureFileBig=null, tableContent=
A/GPa B/GPa R1 R2 ω E/GPa
49.461.893.91.20.32.48
), ArticleFig(id=1241777731902439791, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=EN, label=Table 4, caption=

Simulation tests with different proportions

, figureFileSmall=null, figureFileBig=null, tableContent=
装药结构空气间隔比例/%　　上段炮孔装药比例
中部空气间隔装药10.0----
中部空气分段间隔装药12.51∶42∶33∶24∶1
中部空气分段间隔装药15.01∶42∶33∶24∶1
中部空气分段间隔装药17.51∶42∶33∶24∶1
中部空气分段间隔装药20.01∶42∶33∶24∶1
), ArticleFig(id=1241777732003103091, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=CN, label=表4, caption=

不同比例间隔装药模拟试验方案

, figureFileSmall=null, figureFileBig=null, tableContent=
装药结构空气间隔比例/%　　上段炮孔装药比例
中部空气间隔装药10.0----
中部空气分段间隔装药12.51∶42∶33∶24∶1
中部空气分段间隔装药15.01∶42∶33∶24∶1
中部空气分段间隔装药17.51∶42∶33∶24∶1
中部空气分段间隔装药20.01∶42∶33∶24∶1
), ArticleFig(id=1241777732091183477, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=EN, label=Table 5, caption=

Parameters of different charging structures

, figureFileSmall=null, figureFileBig=null, tableContent=
自变量（装药结构）因变量（爆堆各参数）
间隔比例/%装药比例松散系数/η抛掷距离/m高度/m坡面角/°
001.4122.5612.0528
1001.4120.4312.3424
12.51∶41.3819.9112.3622
12.52∶31.3923.6212.7534
12.53∶21.4022.3612.6728
12.54∶11.4123.5512.2928
151∶41.3919.5812.9726
152∶31.4020.2312.5629
153∶21.4221.0811.4529
154∶11.3719.5911.9925
17.51∶41.3422.7813.5735
17.52∶31.3528.0912.6933
17.53∶21.3928.4712.3334
17.54∶11.3520.9212.0432
201∶41.3417.9812.9027
202∶31.4020.7012.3829
203∶21.4119.4812.1726
204∶11.3819.6112.6523
), ArticleFig(id=1241777732225401207, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=CN, label=表5, caption=

不同装药结构爆堆各项参数

, figureFileSmall=null, figureFileBig=null, tableContent=
自变量（装药结构）因变量（爆堆各参数）
间隔比例/%装药比例松散系数/η抛掷距离/m高度/m坡面角/°
001.4122.5612.0528
1001.4120.4312.3424
12.51∶41.3819.9112.3622
12.52∶31.3923.6212.7534
12.53∶21.4022.3612.6728
12.54∶11.4123.5512.2928
151∶41.3919.5812.9726
152∶31.4020.2312.5629
153∶21.4221.0811.4529
154∶11.3719.5911.9925
17.51∶41.3422.7813.5735
17.52∶31.3528.0912.6933
17.53∶21.3928.4712.3334
17.54∶11.3520.9212.0432
201∶41.3417.9812.9027
202∶31.4020.7012.3829
203∶21.4119.4812.1726
204∶11.3819.6112.6523
), ArticleFig(id=1241777732342841723, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=EN, label=Table 6, caption=

Breaking of test parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
最大孔距/m最小孔距/m最大排距/m最小排距/m钻孔孔深/m超深/m堵塞长度/m
8.16.25.694.6613.51.54.5
单孔装药量/kg平均孔距/m平均排距/m台阶高度/m前排孔至坡顶线平均距离/m单位消耗量/（kg·t-1） 
2087.815.3122.10.176 
), ArticleFig(id=1241777732426727806, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=CN, label=表6, caption=

破试验参数

, figureFileSmall=null, figureFileBig=null, tableContent=
最大孔距/m最小孔距/m最大排距/m最小排距/m钻孔孔深/m超深/m堵塞长度/m
8.16.25.694.6613.51.54.5
单孔装药量/kg平均孔距/m平均排距/m台阶高度/m前排孔至坡顶线平均距离/m单位消耗量/（kg·t-1） 
2087.815.3122.10.176 
), ArticleFig(id=1241777732506419583, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777707994906935, language=EN, label=Table 7, caption=

Optimized blasting effect analysis table

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试验方案炸药单耗/（kg·t-1）松散系数/η抛掷距离/m高度/m坡面角/°
优化后0.1691.4219.311.829
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化后爆破效果分析表

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试验方案炸药单耗/（kg·t-1）松散系数/η抛掷距离/m高度/m坡面角/°
优化后0.1691.4219.311.829
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基于GDEM-BlockDyna的不同装药结构对爆堆形态影响研究
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张肯 1 , 于燕 2 , 刘犇 3 , 张建华 1 , 黄刚 1 , 李江江 4 , Eric Munene Kinyua 1
爆破 | 矿岩爆破 2024,41(2): 127-135
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爆破 | 矿岩爆破 2024, 41(2): 127-135
基于GDEM-BlockDyna的不同装药结构对爆堆形态影响研究
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张肯1 , 于燕2 , 刘犇3, 张建华1, 黄刚1, 李江江4, Eric Munene Kinyua1
作者信息
  • 1.武汉理工大学　资源与环境工程学院，武汉　430070
  • 2.华新水泥股份有限公司，武汉　430073
  • 3.华新水泥（郴州）有限公司，郴州　423022
  • 4.武汉科技大学，武汉　430081

    • 张肯（1999-），男，江西省上饶市万年县，硕士，采矿工程专业研究生，（E-mail）。

    ZHANG Ken (1999-), male, Wannian County, Shangrao City, Jiangxi Province, master's degree, graduate student in mining engineering, (E-mail) .

通讯作者:

于燕（1981-），女，山东省烟台市栖霞县，本科，资源开发工程，（E-mail）。
Study on the Influence of Different Charge Structures on Morphology of Explosion Pile based on GDEM-BlockDyna
Ken ZHANG1 , Yan YU2 , Ben LIU3, Jian-hua ZHANG1, Gang HUANG1, Jiang-jiang LI4, Eric Munene Kinyua1
Affiliations
  • 1.School of Resources and Environmental Engineering, Wuhan University of Technology, Wuhan 430070, China
  • 2.Huaxin Cement Co., Ltd., Wuhan 430073, China
  • 3.Huaxin Cement (Chenzhou) Co., Ltd., Chenzhou 423022, China
  • 4.Wuhan University of Science and Technology, Wuhan 430081, China
出版时间: 2024-06-01 doi: 10.3963/j.issn.1001-487X.2024.02.016
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摘要
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论文以某石灰石矿山为背景，针对矿山开采过程中存在的问题，以装药结构对爆堆形态分布的影响为主线，采用理论分析、GDEM-BlockDyna数值模拟及现场优化试验相结合的方法，展开了台阶爆破爆堆形态分布研究，分析了爆堆形态随装药结构的变化规律。爆堆松散度和抛掷距离会随着间隔段上部装药比例的增加先上升后下降，而爆堆高度总体呈下降趋势，但在空气间隔比例较大时会先减小后增加，爆堆坡面角会随着间隔段上部装药比例的增加而增加，但比例过高时则会下降。研究成果表明：爆堆形态随装药结构呈现出一定的变化规律，通过数值模拟方法，有效优化了装药结构，改善了现场爆堆形态，提升了矿山经济效益，可以为类似矿山生产提供指导。

台阶爆破  /  数值模拟  /  装药结构  /  爆堆形态

This study focuses on the impact of charge structure on the distribution of blast pile morphology in a limestone mine. A combination of theoretical analysis, GDEM-BlockDyna numerical simulation, and on-site optimization tests were conducted to investigate the morphological distribution of step blasting and blast reactors. The change in blast pile morphology with different charge structures was analyzed. The results indicate that the looseness and throwing distance of the blast pile initially increase and then decrease with an increase in the upper charge proportion of the interval section. The height of the explosion pile generally decreases but shows an initial decrease followed by an increase when there is a large air interval proportion. Additionally, the slope angle of the blast pile increases with an increase in charge proportion in the upper section of the interval section but decreases when this proportion becomes too large. These findings demonstrate that explosive pile patterns vary according to charge structure. Furthermore, through numerical simulation methods, effective optimization can be achieved for charge structure, leading to improved on-site explosion patterns and economic benefits for mining operations.

step blasting  /  numerical simulation  /  charge structure  /  burst pattern
张肯, 于燕, 刘犇, 张建华, 黄刚, 李江江, Eric Munene Kinyua. 基于GDEM-BlockDyna的不同装药结构对爆堆形态影响研究. 爆破, 2024 , 41 (2) : 127 -135 . DOI: 10.3963/j.issn.1001-487X.2024.02.016
Ken ZHANG, Yan YU, Ben LIU, Jian-hua ZHANG, Gang HUANG, Jiang-jiang LI, Eric Munene Kinyua. Study on the Influence of Different Charge Structures on Morphology of Explosion Pile based on GDEM-BlockDyna[J]. Blasting, 2024 , 41 (2) : 127 -135 . DOI: 10.3963/j.issn.1001-487X.2024.02.016
正文
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矿山台阶爆破后的爆堆形态往往是验证爆破设计合理性直观体现，爆堆形态的好坏对爆后的铲装作业有着直接的影响，岩石性质、爆破参数、炸药性能以及装药结构的变化，都能使爆堆的形态产生不同的变化。因此，近年来诸多学者就爆堆形态的预测和控制这个课题开展研究，并取得了许多成果。
在算法预测方面，王昱琛等基于海洋捕食者算法（MPV）对支持向量机（SVM）进行了优化提出了MPA-SVM算法[1]，通过选取基本爆破参数作为输入变量，松散系数和Weibull函数的控制变量作为输出变量，以工程数据为基础，对爆堆形态进行了预测，取得了良好的效果。温廷新等基于“试错法”提出了一种GA-ELM模型[2]，通过将遗传算法（GA）和极限学习机（ELM）确定了其最优节点参数，预测的爆堆形态有着贴合真实爆堆曲线的预测效果。黄永辉等基于极限学习机（ELM）神经网络[3]，建立了一种适用于预测高台阶爆破情况下爆堆形态的模型，模型精准度优于BP神经网络。Yu等针对露天矿山爆破过程中岩石运动信息难以准确获取的问题[4]，选取核函数建立支持向量机（SVM）模型，通过型参数，得到了最优爆破岩石轨迹预测模型。Murthy等将多层神经网络的表示能力与各种机器学习技术结合起来[5]，利用位于现场矿山的数据来预测爆堆形态，并使用图像分析技术，调整了训练参数，以减少交叉验证误差并提高准确性。程鹏等提出了爆堆形态估值算法的计算步骤为“数据采样—融合精度判别—数据融合最优权值计算—获得数据融合结果”，并制定了数据采样规则、推导了精度判别方法与最优权值确定方法[6]。
在数值模拟方面，冷振东基于3DEC模拟软件开展了三维台阶爆破模拟[7]，通过将起爆点设置在药柱上、中、下等不同位置分析了其对爆堆形态分布的影响。冯春等采用基于连续-非连续方法的GDEM软件模拟了69 m×35 m×20 m尺寸下的全台阶爆破模拟[8]，证明了GDEM方法在破岩抛掷模拟方面的可靠性。王金绪通过将LS-DYNA与DDA软件相结合[9]，提出了基于应变率-块度筛分拟合的模拟方法，对不同块度级配下的台阶爆破爆堆进行了预测模拟，分析了爆堆的形成过程，取得了较好的效果。Zou等基于位置的动力学（PBD）方法[10]，通过使用Voronoi算法将整个岩体体积离散为不规则形状的小块，来模拟生产爆破后的岩石运动，再现并分析了岩石碎裂运动，形成了最终的爆堆。
在现场研究方面，李胜林等基于无人机航拍扫描技术[11]，通过对爆堆进行三维建模，研究了不同起爆延期间隔与爆堆形态的关系。王浩等分析了含水炮孔下的爆破优化[12]，通过改变孔排距有效提高了爆堆的松散度。夏岸雄等研究了层状岩体台阶爆破的岩石抛掷问题[12]，通过优化现场参数确定了岩石的最佳抛掷方向。Zhang等利用数据分类和多元统计分析的方法[14]，建立了矿山爆破爆堆特征参数数据库并采用局部加权线性回归作为拟合方法，实现了不同台阶抛掷高度下的形状拟合，采用区间估计作为拟合结果检验方法，对获得的爆堆形态进行了验证。
目前，对于爆堆形态的研究仍较少，普遍都停留在传统装药的基础之上，缺少不同装药结构对爆堆形态的影响研究，因此，引入GDEM-BlockDyna软件，建立台阶爆破的间隔装药模型，以数值模拟、理论分析不同装药结构对爆堆松散度、爆堆抛掷距离、爆堆高度以及爆堆坡面角的影响，开展不同装药结构对爆堆形态的研究工作[15]。
1　台阶爆破空气间隔装药数值模型
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1.1　数值模拟方法
GDEM软件是由北京极道成然有限公司与中科院力学研究所联合研发的基于CDEM（Continuum Discontinuum Element Method）连续-非连续介质单元法的力学分析系列软件，采用CPU/GPU并行加速，有效提升了其在材料渐进破坏模拟方面的计算速度和计算规模，在矿山开采和岩石爆破等领域有着独特的模拟优势。该软件以GDEM-Env为平台，结构为1+N，集成了DAS、BlockDyna、PDyna、Gava等自主研发软件，以及返场动力学分析软件、SPH分析系统和地质体网格剖分系统等第三方软件。本文采用其中的BlockDyna软件进行模拟研究。
BlockDyna软件采用质点运动方程作为节点的控制方程，其表达式如下
式中：为节点惯性力；为节点质量阻尼力；为节点外力；为块体变形力；为块体刚度阻尼力；为界面变形力；为界面阻尼力。
节点运动计算表达式如下
式中：a为加速度；v为节点速度；u为节点位移全量；m为节点质量；Δu为计算时步。
1.2　基于GDEM-BlockDyna数值计算模型
1.2.1　数值模型尺寸及参数
计算模型包括台阶岩体、炸药、堵塞段以及空气，选用中部空气间隔来进行模拟，所选用的排距为5.25 m，孔距为7.65 m，排间延期时间为57.75 ms。
1.2.2　状态方程及边界条件
模拟采用文献[16]测定的岩体物理力学参数见表1，采用GDEM-BlockDyna软件中的自带的朗道爆源模型进行爆破模拟，炸药为乳化炸药，炸药朗道参数及JWL状态方程如表2和表3所示。
1.2.3　间隔装药模拟方案
间隔装药结构又称轴向不耦合装药结构，指的是在装药时利用间隔器将炸药分隔两段或多段，间隔介质一般包括水、岩屑、空气等，间隔器常采用竹筒、PVC管等材料。
此次模拟采用中部空气间隔装药，空气占比分别为装药长度的10%、12.5%、15%、17.5%、20%，每孔的堵塞长度相同，相同间隔比例的情况下装药量相同；与此同时，对10%以上的空气间隔进行分段间隔，固定中部空气间隔占比为10%，10%的空气间隔将炮孔分成了上端炮孔和下端炮孔，然后在上端炮孔1∶4、2∶3、3∶2和4∶1装药比例处设置余下空气间隔柱，装药示意图如图1所示，模拟试验方案如表4所示。为此建立17个数值计算模型，模型的结构及网格划分如图2所示，空气间隔装药模型中，采用SetAirMat接口函数将指定的材料和空气材料号进行关联，设置空气的密度为1.29 kg/m3，初始气压为1 MPa，绝热指数为1.33，其余材料参数模型与上节相同，设置起爆点在各装药段的底部，起爆方式均为底部起爆。
设置四排炮孔，单位制为m-kg-s。由于模拟的研究对象为台阶爆破爆破后爆堆的块度和尺寸，为保证模拟的可靠性，计算所划分的网格在厘米量级。
2　装药结构对爆堆形态影响数值模拟结果分析
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2.1　数值模拟结果统计
对不同装药结构下的台阶爆破模型进行模拟计算，爆破后爆堆的各项参数如表5所示。
2.2　爆堆形态随装药结构的变化规律分析
2.2.1　爆堆松散度随装药结构变化规律
爆堆松散度随装药结构的变化规律如图3所示，由图3分析可知在不同空气间隔比例下，在空气间隔比例大于10%的情况下，随着上段炮孔上部的装药比例增加，爆堆的松散度均呈现出先上升后下降趋势，除空气间隔比例为12.5%的情况外，当装药比例为3∶2时，爆堆的松散度最大。因此，可以看出装药比例和空气间隔比例对爆堆的松散度都有着显著的影响，而当空气间隔比例为15%，装药比例为3∶2时，爆堆的整体松散度最大，为1.42。
2.2.2　爆堆抛掷距离随装药结构变化规律
爆堆抛掷距离随装药结构的变化规律如图4示，由图4分析可知在空气间隔比例为17.5%时的情况下，爆堆的块体岩石最远抛掷距离远远超过其他空气间隔比例下的抛掷距离。在其它空气间隔比例下，随着间隔比例的增加，爆堆的最远抛掷距离呈现出逐渐下降的趋势，此外，随着上段炮孔上部装药比例的增加，爆堆的最远抛掷距离呈现先上升后下降的趋势，根据现场铲装设备的型号可知，抛掷距离为20 m左右时比较适合现场设备的工况需求。因此，在空气间隔比例为10%时，爆堆的抛掷距离为20.43 m，图中在虚线附近的工况都比较符合现场需求。
2.2.3　爆堆高度随装药结构变化规律
爆堆高度随装药结构的变化规律如图5所示，由图5分析可知爆堆的整体高度总体呈现出下降的趋势。在空气间隔比例较小的情况下，随着上段炮孔上部装药比例的增加，爆堆高度随着装药比例的增加后减小，但是在空气间隔比例较大的情况下，爆堆高度则会先减小后增加，但由于装药量的减少，爆堆的整体高度大都高于12 m，而在空气间隔比例为15%，装药比例为3∶2的工况下，爆堆的高度最低为11.45 m，较符合现场铲装设备的生产需求。
2.2.4　爆堆坡面角随装药结构变化规律
爆堆坡面角随装药结构的变化规律如图6所示，由图6分析可知当空气间隔比例为17.5%时，爆堆的坡面角较大，均在30°以上，结合前述规律，在其它空气间隔比例下，当上段炮孔的上部装药比例增加时，爆堆坡面角也会相应增加。但是，当上部装药比例过高时，爆堆坡面角反而会下降。这是因为过高的上部装药比例会使得块体岩石在爆破过程中受到更充分的破碎，同时获得较大的抛掷速度，从而导致爆堆的坡面角度减小。
从模拟结果的分析结构可以看出，空气间隔比例为15%下装药比例为3∶2时，爆堆有着较好的松散度，同时爆堆的高度和抛掷距离也更加适合现场生产设备工作需求，因此可以选定其为优化后的空气间隔装药结构。
2.3　装药结构与爆堆形态规律综合分析
根据爆堆形态随装药结构的变化图，初步得到最佳的空气间隔比例和装药比例，对相关的爆破工作可进行指导和参考；但为验证爆堆形态与装药结构的相关性，进一步地对装药结构与爆堆各形态参数之间的规律进行探究，结合模拟所得数据，利用Origin软件对数据进行处理；将空气间隔比例与装药比例设置为自变量，爆堆松散系数、最大抛掷距离、高度及坡面角设置为因变量，爆堆参数随装药结构变化如表5所示。
在对单个因变量和多个自变量的回归分析中，常采用多项式回归分析的方法，其最大的优点在于可以通过增加自变量的高次项，从而对所输入的数据进行逼近，直到拟合的公式达到满意程度，因此可以采用此公式对数据进行拟合分析，下式为二元m次多项式回归方程
式中：z为因变量；x1、x2为自变量；z0、A、B为拟合参数。
将装药结构和不同参数的数据导入Origin软件中，绘制出各自的3D填充面图，通过非线性拟合方法中的Polynomial2D多项式回归方程对数据进行拟合分析，则可以得到爆堆参数与装药结构之间的拟合方程公式。
2.3.1　爆堆松散度随装药结构的变化规律
爆堆松散度与间隔比例、装药比例的三维拟合曲线图如图7所示，拟合后的R平方为0.79225，方程的相关性较好，根据拟合数据得出的爆堆松散度拟合方程为
式中：s为爆堆松散度；x、y为空气间隔比例、装药比例；z0、A、B为拟合参数，详见拟合图。
2.3.2　爆堆抛掷距离随装药结构的变化规律
爆堆抛掷距离与间隔比例、装药比例的三维拟合曲线图如图8所示，拟合后的R平方为0.78936，方程的相关性较好，根据拟合数据得出的爆堆抛掷距离拟合方程为
式中，l为爆堆抛掷距离，m。
2.3.3　爆堆高度随装药结构的变化规律
对于爆堆高度，在拟合中发现采用Polynomial2D多项式回归方程效果较差，故改用Gauss2D高斯模糊函数进行拟合，爆堆高度与间隔比例、装药比例的三维拟合曲线图如图9所示，拟合后的R平方为0.768，根据拟合数据得出的爆堆高度拟合方程为
式中：h为爆堆高度，m；x、y为空气间隔比例、装药比例；xc、yc、W1、W2、A为拟合参数，详见拟合图。
2.3.4　爆堆坡面角随装药结构的变化规律
爆堆坡面角与间隔比例、装药比例的三维拟合曲线图如图10所示，拟合后的R平方为0.75152，方程的相关性较好，根据拟合数据得出的爆堆坡面角拟合方程为
式中，α为爆堆坡面角，°。
本节利用Origin软件对数据进行结果处理，采用多项式回归分析的方法，对装药结构与爆堆各形态参数之间的规律进行探究，拟合后得到的R平方都接近0.8，方程具有较好的相关性。
3　改进后装药结构爆破效果现场试验
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3.1　爆破试验方案
根据优化后的方案，选定空气间隔比例为15%下装药比例为3∶2时，进行优化后的现场试验。对各个炮孔进行调查，爆区的布孔图如图11所示，所选用的爆破参数如表6所示。
3.2　试验过程及结果分析
台阶起爆过程如图12所示，依次为起爆前台阶形态—起爆瞬间—爆堆抛掷—爆堆最终形态，从图中可以看出，爆破开始后自由面岩石在反射应力波作用下首先开始破坏，随后开始出现鼓包运动，岩石裂纹扩展过程明显，破碎完全，有着较好的抛掷效果，被破碎的岩块在重力作用下堆积成爆堆。
爆破后爆堆的效果图如图13所示，可以看出，爆破后爆堆沟槽明显，且对后平台的冲击较小，平台没有明显裂缝，爆堆块度较为均匀，坡面平整，堆料较为松散；爆破后数据见表7，爆破后的爆堆有着较好的松散度，同时爆堆的高度和抛掷距离也更加适合现场生产设备工作需求。
4　结论
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基于中部间隔装药方法，固定药柱中部空气间隔比例，对上部进行分段间隔，本文通过GDEM-BlockDyna软件模拟了不同空气间隔及装药比例下的17种台阶爆破模型，分析了不同装药结构对爆堆形态影响，得到了一些结论：
（1）爆堆松散度、抛掷距离、高度以及坡面角等形态参数随着空气间隔比例和上部药柱装药比例的变化呈现出了一定的变化规律，研究有助于矿山的生产管理，指导矿山爆破工作，并且对后续研究者具有参考性。
（2）当空气间隔比例为15%，上段药柱装药比例为3∶2时，爆堆松散度最大，同时爆堆的抛掷距离和高度也更加符合现场铲装设备需求。
（3）利用Origin软件，结合多项式回归分析方法，对不同爆堆参数与装药结构参数进行拟合分析得到拟合方程公式；结果表明，所得到的拟合方程R平方基本接近0.8，有着较好的相关性。
基金
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  • 国家自然科学基金面上项目(42271296)
文献
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2024年第41卷第2期
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doi: 10.3963/j.issn.1001-487X.2024.02.016
  • 接收时间：2023-08-14
  • 首发时间：2026-03-20
  • 出版时间：2024-06-01
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  • 收稿日期：2023-08-14
基金
National Natural Science Foundation of China(42271296)
国家自然科学基金面上项目(42271296)
作者信息
    1.武汉理工大学　资源与环境工程学院，武汉　430070
    2.华新水泥股份有限公司，武汉　430073
    3.华新水泥（郴州）有限公司，郴州　423022
    4.武汉科技大学，武汉　430081

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于燕（1981-），女，山东省烟台市栖霞县，本科，资源开发工程，（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
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
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