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Article(id=1241321694560842193, tenantId=1146029695717560320, journalId=1235980550691926019, issueId=1241321691524158287, articleNumber=null, orderNo=null, doi=10.3969/j.issn.0253-6099.2025.02.008, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1729958400000, receivedDateStr=2024-10-27, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773883754624, onlineDateStr=2026-03-19, pubDate=1743436800000, pubDateStr=2025-04-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773883754624, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773883754624, creator=13701087609, updateTime=1773883754624, updator=13701087609, issue=Issue{id=1241321691524158287, tenantId=1146029695717560320, journalId=1235980550691926019, year='2025', volume='45', issue='2', pageStart='1', pageEnd='204', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773883753901, creator=13701087609, updateTime=1773884632018, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241325374676726363, tenantId=1146029695717560320, journalId=1235980550691926019, issueId=1241321691524158287, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241325374676726364, tenantId=1146029695717560320, journalId=1235980550691926019, issueId=1241321691524158287, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=47, endPage=53, ext={EN=ArticleExt(id=1241321695030604245, articleId=1241321694560842193, tenantId=1146029695717560320, journalId=1235980550691926019, language=EN, title=Numerical Simulation of Blasting with Wedge Cut Based on LS-DYNA Software and Its Application, columnId=1236276106018484431, journalTitle=Mining and Metallurgical Engineering, columnName=MINING, runingTitle=null, highlight=null, articleAbstract=

The western No.2 mining area of a certain mine adopts the non-pillar sublevel caving in mining, and excessive wedge cut height in the 1 546 m sublevel leads to poor blasting effect. To address this problem, blasting with wedge cut was specially studied. Firstly, the rock parameters were calibrated based on the RHT constitutive model and the damage threshold of the rock was determined to be 0.4 by a fluid-structure interaction analysis with the LS-DYNA software. A comparative analysis of the cut blasting effects with different cut width shows that with the cut height fixed at 23 m, the effective damage rate of the rock presents a unimodal distribution with an increase in cut width. The optimal cut width is found to be 24 m, with which the effective damage rate of the rock can reach a peak value of 0.692 5. Based on these parameters, the on-site application of designed cutting scheme indicates that over 85% of blast-forming space can meet the requirement, presenting a reasonable fragment distribution of muck pile, with the angle of repose at approximately 40°.

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某矿西二采区采用无底柱分段崩落法开采，1 546 m分段楔形切割拉槽存在拉槽高度过大导致爆破效果不佳的问题。针对该问题进行了楔形切割拉槽爆破研究。基于RHT本构模型标定矿岩参数，采用LS-DYNA软件，运用流固耦合算法，确定矿岩损伤阈值为0.4；对比分析不同拉槽宽度方案的爆破成槽效果，结果表明：拉槽高度固定为23 m时，矿岩有效损伤率随着拉槽宽度增加呈单峰曲线变化；最佳拉槽宽度为24 m，此时矿岩有效损伤率达到峰值0.692 5。基于该参数设计拉槽方案，现场试验结果表明，爆破成形空间达标率超过85%，爆堆块度分布合理，安息角约40°。

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陈帮洪（1984—），男，四川乐山人，硕士，助理工程师，主要从事地下采矿及岩石力学方面的研究工作。E-mail：

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陈帮洪（1984—），男，四川乐山人，硕士，助理工程师，主要从事地下采矿及岩石力学方面的研究工作。E-mail：

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陈帮洪（1984—），男，四川乐山人，硕士，助理工程师，主要从事地下采矿及岩石力学方面的研究工作。E-mail：

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Gold Science and Technology, 2022, 30(3): 414-426., articleTitle=Numerical simulation of homogeneous rock mass damage by double-hole simultaneous blasting based on RHT model, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1241327679190921650, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, xref=1., ext=[AuthorCompanyExt(id=1241327679199310259, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, companyId=1241327679190921650, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.Kunming Engineering & Research Institute of Nonferrous Metallurgy Co., Ltd., Kunming 650231, Yunnan, China), AuthorCompanyExt(id=1241327679207698869, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, companyId=1241327679190921650, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.昆明有色冶金设计研究院股份公司，云南　昆明　650231)]), AuthorCompany(id=1241327679304167877, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, xref=2., ext=[AuthorCompanyExt(id=1241327679312556485, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, companyId=1241327679304167877, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2.School of Environment and Resource, Southwest University of Science and Technology, Mianyang 621010, Sichuan, China), AuthorCompanyExt(id=1241327679316750790, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, companyId=1241327679304167877, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2.西南科技大学　环境与资源学院，四川　绵阳　621010)])], figs=[ArticleFig(id=1241327684555436820, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Fig.1, caption=Numerical simulation of blasting parameters by fluid-structure interaction analysis, figureFileSmall=jlWmljlw2GZ9UK5AafW3Ow==, figureFileBig=sWS7roDJmQXyJ2HvyuuLPw==, tableContent=null), ArticleFig(id=1241327684660294424, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=图1, caption=流固耦合算法爆炸数值模拟示意图, figureFileSmall=jlWmljlw2GZ9UK5AafW3Ow==, figureFileBig=sWS7roDJmQXyJ2HvyuuLPw==, tableContent=null), ArticleFig(id=1241327684790317858, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Fig.2, caption=Numerical model of wedge hole, figureFileSmall=aHDqFIbyW5TJG7Jg0TKhSw==, figureFileBig=KOjJyp/S07EFYrsy5/s+PQ==, tableContent=null), ArticleFig(id=1241327684899369770, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=图2, caption=楔形孔模型, figureFileSmall=aHDqFIbyW5TJG7Jg0TKhSw==, figureFileBig=KOjJyp/S07EFYrsy5/s+PQ==, tableContent=null), ArticleFig(id=1241327685050364722, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Fig.3, caption=Blasting damage distribution of wedge cut（0<D<1）, figureFileSmall=V61fjQSVW6SIxbHEpEYsiA==, figureFileBig=cH3GjSvaejEFmQ/sGuhXgA==, tableContent=null), ArticleFig(id=1241327686581285692, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=图3, caption=楔形孔爆破损伤分布（0<D<1）

（a）t=339 μs时损伤分布；（b）最终损伤分布

, figureFileSmall=V61fjQSVW6SIxbHEpEYsiA==, figureFileBig=cH3GjSvaejEFmQ/sGuhXgA==, tableContent=null), ArticleFig(id=1241327686711309126, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Fig.4, caption=Rock failure range in different damage value intervals, figureFileSmall=F0xHQT2DyVtcO2wOnLotsw==, figureFileBig=n6+NjtN88CACnq5pgNyTAA==, tableContent=null), ArticleFig(id=1241327686858109778, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=图4, caption=不同损伤值区间岩石破坏分布范围

（a）0.2<D<1；（b）0.3<D<1；（c）0.4<D<1；（d）0.5<D<1；（e）0.6<D<1；（f）0.7<D<1

, figureFileSmall=F0xHQT2DyVtcO2wOnLotsw==, figureFileBig=n6+NjtN88CACnq5pgNyTAA==, tableContent=null), ArticleFig(id=1241327687034270559, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Fig.5, caption=Changes in damage zone and fracture zone of wedge hole for rock with different damage values, figureFileSmall=/kvjDMYWfXdQiuctwxLlpQ==, figureFileBig=u55xNei0jXq4QSsqVfaCQA==, tableContent=null), ArticleFig(id=1241327687155905382, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=图5, caption=矿岩不同损伤范围楔形孔压碎区和裂隙区变化, figureFileSmall=/kvjDMYWfXdQiuctwxLlpQ==, figureFileBig=u55xNei0jXq4QSsqVfaCQA==, tableContent=null), ArticleFig(id=1241327687302706030, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Fig.6, caption=Cut blasting model, figureFileSmall=+BzrG+HRFmCmKeI+Gr5JXA==, figureFileBig=YXHyee983gUwwLuQyBkKQg==, tableContent=null), ArticleFig(id=1241327687445312377, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=图6, caption=切割拉槽爆破模型, figureFileSmall=+BzrG+HRFmCmKeI+Gr5JXA==, figureFileBig=YXHyee983gUwwLuQyBkKQg==, tableContent=null), ArticleFig(id=1241327687604695947, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Fig.7, caption=Evolution of original damage at different stages of blasting, figureFileSmall=S2OeT1AprGCvC6B5KF+nIg==, figureFileBig=vffxFKioAYMeBVTDCuo9JA==, tableContent=null), ArticleFig(id=1241327687717942163, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=图7, caption=各时段爆破原始损伤演化情况

（a）390 s；（b）990 s；（c）2 670 s；（d）5 609 s

, figureFileSmall=S2OeT1AprGCvC6B5KF+nIg==, figureFileBig=vffxFKioAYMeBVTDCuo9JA==, tableContent=null), ArticleFig(id=1241327687868937120, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Fig.8, caption=Final effective damage range under different cut designs, figureFileSmall=hFCUIltwE8I7bE570+gyDg==, figureFileBig=EQjz3O6Qx3PKTeScK9rYHg==, tableContent=null), ArticleFig(id=1241327687977989031, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=图8, caption=不同拉槽方案下最终有效损伤分布

（a）方案1；（b）方案2；（c）方案3；（d）方案4；（e）方案5；（f）方案6

, figureFileSmall=hFCUIltwE8I7bE570+gyDg==, figureFileBig=EQjz3O6Qx3PKTeScK9rYHg==, tableContent=null), ArticleFig(id=1241327688070263729, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Fig.9, caption=Borehole arrangement for wedge cut, figureFileSmall=HDjKSbtAKKodX74btukdjw==, figureFileBig=GpPmAj00Oky9Py1RTJK2xw==, tableContent=null), ArticleFig(id=1241327688179315645, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=图9, caption=楔形拉槽炮孔布置, figureFileSmall=HDjKSbtAKKodX74btukdjw==, figureFileBig=GpPmAj00Oky9Py1RTJK2xw==, tableContent=null), ArticleFig(id=1241327688284173250, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Fig.10, caption=On-site space formed after blasting, figureFileSmall=BWzvl+29Rno14UTSLh3csQ==, figureFileBig=b2VyUeTdLS+jkkIjBI+3Lw==, tableContent=null), ArticleFig(id=1241327688426779595, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=图10, caption=爆破后现场空间形态, figureFileSmall=BWzvl+29Rno14UTSLh3csQ==, figureFileBig=b2VyUeTdLS+jkkIjBI+3Lw==, tableContent=null), ArticleFig(id=1241327688544220112, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Fig.11, caption=Statistical analysis of blasting fragmentation, figureFileSmall=flYnwh9sGFcMrxPOdlC/ew==, figureFileBig=0tPqrp0ccFEZXj12AI7Apw==, tableContent=null), ArticleFig(id=1241327688661660631, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=图11, caption=爆破块度统计分析

（a）块度圈定；（b）块度统计

, figureFileSmall=flYnwh9sGFcMrxPOdlC/ew==, figureFileBig=0tPqrp0ccFEZXj12AI7Apw==, tableContent=null), ArticleFig(id=1241327688787489759, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Table 1, caption=

Physico-mechanical properties of rock in western No.2 mining area of a mine

, figureFileSmall=null, figureFileBig=null, tableContent=
抗拉强度/MPa单轴抗压强度/MPa弹性模量/GPa泊松比抗剪强度剪切模量/GPa拉压强度比剪压强度比
C/MPaφ/（°）
12.9901150.251.0545460.1430.35
), ArticleFig(id=1241327688900735969, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=表1, caption=

某矿西二采区矿岩物理力学参数

, figureFileSmall=null, figureFileBig=null, tableContent=
抗拉强度/MPa单轴抗压强度/MPa弹性模量/GPa泊松比抗剪强度剪切模量/GPa拉压强度比剪压强度比
C/MPaφ/（°）
12.9901150.251.0545460.1430.35
), ArticleFig(id=1241327689064313834, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Table 2, caption=

Material parameters of rock in western No.2 mining area based on RHT constitutive model

, figureFileSmall=null, figureFileBig=null, tableContent=
参数符号参数取值参数符号参数取值参数符号参数取值
密度ρ0/（kg·m-3）2 700状态方程参数B01.68拉伸应变率指数βt0.018 2
初始孔隙度α01.014 9状态方程参数B11.68参考压缩应变率3.0×10-5
孔隙开始压碎时压力pel/MPa30状态方程参数T1/GPa27.648参考拉伸应变率3.0×10-6
孔隙压实时压力pcomp0.6状态方程参数T20失效压缩应变率3.0×1025
孔隙度指数np3.0压缩屈服面参数0.4失效拉伸应变率3.0×1025
多项式系数A1/GPa27.648拉伸屈服面参数0.7初始损伤参数D10.04
多项式系数A2/GPa46.449剪切模量缩减系数ζ0.48损伤参数D21.0
多项式系数A3/GPa28.389失效面参数A2.508 9最小破坏残余应变0.015
洛德角相关系数B0.067失效面指数N0.722 3最小失效应变Af1.62
压缩应变率指数βc0.013 8拉压子午比参数Q00.68残余应力强度指数nf0.6
), ArticleFig(id=1241327689227891696, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=表2, caption=

某矿西二采区矿岩RHT本构模型材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数符号参数取值参数符号参数取值参数符号参数取值
密度ρ0/（kg·m-3）2 700状态方程参数B01.68拉伸应变率指数βt0.018 2
初始孔隙度α01.014 9状态方程参数B11.68参考压缩应变率3.0×10-5
孔隙开始压碎时压力pel/MPa30状态方程参数T1/GPa27.648参考拉伸应变率3.0×10-6
孔隙压实时压力pcomp0.6状态方程参数T20失效压缩应变率3.0×1025
孔隙度指数np3.0压缩屈服面参数0.4失效拉伸应变率3.0×1025
多项式系数A1/GPa27.648拉伸屈服面参数0.7初始损伤参数D10.04
多项式系数A2/GPa46.449剪切模量缩减系数ζ0.48损伤参数D21.0
多项式系数A3/GPa28.389失效面参数A2.508 9最小破坏残余应变0.015
洛德角相关系数B0.067失效面指数N0.722 3最小失效应变Af1.62
压缩应变率指数βc0.013 8拉压子午比参数Q00.68残余应力强度指数nf0.6
), ArticleFig(id=1241327689345332215, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Table 3, caption=

Parameters of equation of state for rock powder explosive No.2

, figureFileSmall=null, figureFileBig=null, tableContent=
爆轰压力P/GPaA/GPaGPaB/R1R2ω比内能E0/GPa初始相对体积V′
958621.65.811.770.287.381.0
), ArticleFig(id=1241327689445995516, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=表3, caption=

2#岩石粉状乳化炸药状态方程参数

, figureFileSmall=null, figureFileBig=null, tableContent=
爆轰压力P/GPaA/GPaGPaB/R1R2ω比内能E0/GPa初始相对体积V′
958621.65.811.770.287.381.0
), ArticleFig(id=1241327689613766661, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Table 4, caption=

Parameters of equation of state for air materials

, figureFileSmall=null, figureFileBig=null, tableContent=
空气密度ρair/（kg·m-3）C0C1C2C3C4C5C6E0/kPa
1.2900000.40.402.5
), ArticleFig(id=1241327691119521803, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=表4, caption=

空气材料状态方程参数

, figureFileSmall=null, figureFileBig=null, tableContent=
空气密度ρair/（kg·m-3）C0C1C2C3C4C5C6E0/kPa
1.2900000.40.402.5
), ArticleFig(id=1241327691253739540, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Table 5, caption=

Calculation parameters for radius of damage zone and fracture zone in wedge cut blast

, figureFileSmall=null, figureFileBig=null, tableContent=
岩石密度/（kg·m-3）岩石抗压强度/MPa岩石抗拉强度/MPa泊松比岩石波速/（m·s-1）初始裂纹密度岩石弹性模量/GPa炸药密度/（kg·m-3）炸药爆速/（m·s-1）
2 7009012.90.253 2000.061151 3004 000
), ArticleFig(id=1241327691350208537, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=表5, caption=

某矿楔形拉槽爆破压碎区和裂隙区半径计算参数

, figureFileSmall=null, figureFileBig=null, tableContent=
岩石密度/（kg·m-3）岩石抗压强度/MPa岩石抗拉强度/MPa泊松比岩石波速/（m·s-1）初始裂纹密度岩石弹性模量/GPa炸药密度/（kg·m-3）炸药爆速/（m·s-1）
2 7009012.90.253 2000.061151 3004 000
), ArticleFig(id=1241327691551535142, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Table 6, caption=

Radius of damage zone and fracture zone in wedge cut blast

, figureFileSmall=null, figureFileBig=null, tableContent=
冲击波初始压力Pc/GPa侧向应力系数b岩体初始损伤D0压碎区半径R1/m裂隙区半径R2/m
8.3770.250.150.143.08
), ArticleFig(id=1241327691656392752, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=表6, caption=

楔形拉槽爆破压碎区和裂隙区半径

, figureFileSmall=null, figureFileBig=null, tableContent=
冲击波初始压力Pc/GPa侧向应力系数b岩体初始损伤D0压碎区半径R1/m裂隙区半径R2/m
8.3770.250.150.143.08
), ArticleFig(id=1241327691811582013, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Table 7, caption=

Simulation scheme of wedge cut

, figureFileSmall=null, figureFileBig=null, tableContent=
方案拉槽高度H/m拉槽宽度d/m装药量Qw/kg装药长度L/m
123151 110.9221.3
223181 333.1265.6
323211 555.3309.8
423241 777.4354.1
523271 999.6398.3
623302 221.8442.6
), ArticleFig(id=1241327691899662403, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=表7, caption=

楔形切割拉槽模拟方案

, figureFileSmall=null, figureFileBig=null, tableContent=
方案拉槽高度H/m拉槽宽度d/m装药量Qw/kg装药长度L/m
123151 110.9221.3
223181 333.1265.6
323211 555.3309.8
423241 777.4354.1
523271 999.6398.3
623302 221.8442.6
), ArticleFig(id=1241327692004520011, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Table 8, caption=

Effective damage rate of each scheme

, figureFileSmall=null, figureFileBig=null, tableContent=
方案1方案2方案3方案4方案5方案6
0.603 50.632 60.671 30.692 50.674 60.640 0
), ArticleFig(id=1241327692092600402, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=表8, caption=

各方案有效损伤率

, figureFileSmall=null, figureFileBig=null, tableContent=
方案1方案2方案3方案4方案5方案6
0.603 50.632 60.671 30.692 50.674 60.640 0
), ArticleFig(id=1241327692189069396, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=EN, label=Table 9, caption=

Statistics of fragmentation for muck pile block after wedge cut blast

, figureFileSmall=null, figureFileBig=null, tableContent=
分级/m所占面积/m2比例/%
>0.61.7221.16
0.3～0.61.2315.13
0.1～0.34.3353.25
<0.10.8510.46
合计8.13100.00
), ArticleFig(id=1241327692302315612, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321694560842193, language=CN, label=表9, caption=

楔形拉槽爆破后爆堆块度统计表

, figureFileSmall=null, figureFileBig=null, tableContent=
分级/m所占面积/m2比例/%
>0.61.7221.16
0.3～0.61.2315.13
0.1～0.34.3353.25
<0.10.8510.46
合计8.13100.00
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基于LS-DYNA的楔形切割拉槽爆破数值模拟研究及应用
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陈帮洪 1 , 陈星明 2 , 武尚荣 1 , 费志文 1
矿冶工程杂志 | 采矿 2025,45(2): 47-53
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矿冶工程杂志 | 采矿 2025, 45(2): 47-53
基于LS-DYNA的楔形切割拉槽爆破数值模拟研究及应用
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陈帮洪1 , 陈星明2, 武尚荣1, 费志文1
作者信息
  • 1.昆明有色冶金设计研究院股份公司，云南　昆明　650231
  • 2.西南科技大学　环境与资源学院，四川　绵阳　621010

    • 陈帮洪（1984—），男，四川乐山人，硕士，助理工程师，主要从事地下采矿及岩石力学方面的研究工作。E-mail：

Numerical Simulation of Blasting with Wedge Cut Based on LS-DYNA Software and Its Application
Banghong CHEN1 , Xingming CHEN2, Shangrong WU1, Zhiwen FEI1
Affiliations
  • 1.Kunming Engineering & Research Institute of Nonferrous Metallurgy Co., Ltd., Kunming 650231, Yunnan, China
  • 2.School of Environment and Resource, Southwest University of Science and Technology, Mianyang 621010, Sichuan, China
出版时间: 2025-04-01 doi: 10.3969/j.issn.0253-6099.2025.02.008
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摘要
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某矿西二采区采用无底柱分段崩落法开采，1 546 m分段楔形切割拉槽存在拉槽高度过大导致爆破效果不佳的问题。针对该问题进行了楔形切割拉槽爆破研究。基于RHT本构模型标定矿岩参数，采用LS-DYNA软件，运用流固耦合算法，确定矿岩损伤阈值为0.4；对比分析不同拉槽宽度方案的爆破成槽效果，结果表明：拉槽高度固定为23 m时，矿岩有效损伤率随着拉槽宽度增加呈单峰曲线变化；最佳拉槽宽度为24 m，此时矿岩有效损伤率达到峰值0.692 5。基于该参数设计拉槽方案，现场试验结果表明，爆破成形空间达标率超过85%，爆堆块度分布合理，安息角约40°。

无底柱分段崩落法  /  切割拉槽  /  RHT  /  本构模型  /  数值模拟  /  损伤  /  拉槽爆破

The western No.2 mining area of a certain mine adopts the non-pillar sublevel caving in mining, and excessive wedge cut height in the 1 546 m sublevel leads to poor blasting effect. To address this problem, blasting with wedge cut was specially studied. Firstly, the rock parameters were calibrated based on the RHT constitutive model and the damage threshold of the rock was determined to be 0.4 by a fluid-structure interaction analysis with the LS-DYNA software. A comparative analysis of the cut blasting effects with different cut width shows that with the cut height fixed at 23 m, the effective damage rate of the rock presents a unimodal distribution with an increase in cut width. The optimal cut width is found to be 24 m, with which the effective damage rate of the rock can reach a peak value of 0.692 5. Based on these parameters, the on-site application of designed cutting scheme indicates that over 85% of blast-forming space can meet the requirement, presenting a reasonable fragment distribution of muck pile, with the angle of repose at approximately 40°.

non-pillar sublevel caving method  /  cut  /  RHT  /  constitutive model  /  numerical simulation  /  damage  /  cut blasting
陈帮洪, 陈星明, 武尚荣, 费志文. 基于LS-DYNA的楔形切割拉槽爆破数值模拟研究及应用. 矿冶工程杂志, 2025 , 45 (2) : 47 -53 . DOI: 10.3969/j.issn.0253-6099.2025.02.008
Banghong CHEN, Xingming CHEN, Shangrong WU, Zhiwen FEI. Numerical Simulation of Blasting with Wedge Cut Based on LS-DYNA Software and Its Application[J]. Mining and Metallurgical Engineering, 2025 , 45 (2) : 47 -53 . DOI: 10.3969/j.issn.0253-6099.2025.02.008
正文
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切割拉槽作为无底柱分段崩落法开采的核心环节，直接影响矿石回采率与开采安全性。矿山一般采用切割平巷+天井的施工方式形成切割拉槽，但该方法工程量大、施工复杂，尤其在软破碎矿体中易引发安全事故[1-2]。此外，工作面浮石堆积、通风不良等问题进一步威胁作业安全。楔形切割拉槽法采用多进路开挖同步形成大型切割槽，可有效克服以上问题，显著提升施工效率并简化流程。然而，楔形切割拉槽法受爆破夹制效应制约，对布孔参数与起爆精度要求严苛，需通过优化孔网布置和爆破参数改善岩体破碎形态，为后续爆破创造有效自由面，才能提升整体爆破效果。
为提高切割拉槽效率与爆破效果，众多学者系统探究了炮孔对称性、掏槽方式、节理特征等对爆破效果的影响[3-7]，并进行了现场验证，在动力学分析、裂纹扩展机理等方面取得显著进展，但仍存在以下不足：试验验证与工程应用转化不足，理论体系尚未完善；多样化的切割拉槽布置方式缺乏普适性验证与推广；数值模拟多直接引用标准材料参数，未充分考虑实际岩体特性对爆破过程的动态影响。
基于此，本文以某矿西二采区为工程背景，采用LS-DYNA软件，运用流固耦合算法，对不同楔形拉槽布置方式的爆破损伤范围进行数值模拟，通过标定合理材料模型参数，结合数值模拟与现场试验，优化布孔方案，为选取高效、安全的楔形切割拉槽布置方式提供依据。
1　材料本构参数确定及验证
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1.1　流固耦合算法
采用流固耦合（ALE）算法对爆破进行数值模拟，该方法能有效解决大变形条件下爆破损伤问题。首先构建炸药与空气域的耦合体系，其中空气域被定义为ALE多物质空间，以模拟动态流动；其次，建立炸药单元与岩石单元之间的动态相互作用，通过共节点连接方式实现炸药与空气域单元的界面耦合。流固耦合算法爆炸数值模拟如图1所示。
1.2　材料模型参数确定
1.2.1　岩石材料模型
采用RHT（Riedel-Hiermaier-Thoma）本构模型为材料模型，该模型考虑了爆破动荷载作用下岩石材料的破坏强度对冲击压力、应变速率、应变硬化和损伤软化的影响，适用于岩体爆破损伤演化数值模拟[8]。根据相关研究[9]理论计算得到某矿西二采区矿岩物理力学参数以及RHT本构模型材料参数见表1～2。
1.2.2　炸药及空气材料模型
炸药爆破时会生成高温、高压气体。本文采用JWL EOS模型预测爆轰压力，其计算公式如下[10]：
式中：P为爆轰压力；V为爆轰产物相对体积；E0为爆轰产物比内能；A、B、R1、R2、ω均为JWL参数。矿山楔形拉槽采用2#岩石粉状乳化炸药，状态方程参数如表3所示。
ALE算法采用*MAT_NULL空气材料作为空物质材料模型，使用*EOS_LINEAR_POLYNOMIAL状态方程表征材料热动力学性质，状态方程为：
式中：P1为气体膨胀压强，kPa；μ为空气材料比体积；C0～C6均为空气材料状态方程参数，取值如表4所示。
1.3　矿岩参数验证及损伤阈值确定
1.3.1　矿岩压碎区与裂隙区半径计算
为验证数值模拟中材料参数与建模方法的合理性，基于某矿无底柱分段崩落法实际工程参数（2#岩石粉状乳化炸药、孔径80 mm，参数详见表5），进行楔形拉槽爆破压碎区与裂隙区半径数值模拟结果与理论值的对比。
损伤岩体耦合装药条件下，柱状药包爆炸冲击波造成的压碎区半径R1计算公式[11]为：
式中：D0为岩石初始损伤值；μc为岩石损伤后的泊松比，μc=μa（1-16Cd/9），μa为岩石损伤前的泊松比；Cd为损伤引起的裂纹密度；α为岩体应力波衰减指数，取2.25；ρ为岩石密度，kg/m3；C为岩石中冲击波传播速度，m/s；V0为炸药爆速，m/s；ρ0为炸药密度，kg/m3；k为等熵指数，取2.1；B0为某点应力状态相关系数；σcd为岩石单轴动态抗压强度，MPa。
爆生气体对岩体的作用是一个准静态过程。忽略裂隙体积，根据爆轰热力学理论以及裂隙区岩体应力状态和损伤定义，柱状耦合装药条件下爆生气体静态作用下的裂隙区半径计算公式[12]为：
式中：R2为爆生气体与冲击波作用下裂隙区半径，m；Py为裂隙区岩石内气体压力，取0.6Pc，Pc为透射入岩石的冲击波初始压力，MPa；D′为岩石二次损伤因子，取0.3；β为裂隙岩体应力波衰减指数，β=2-bD0，b为侧向应力系数；σtd为岩石动态单轴抗拉强度，MPa。
根据表5和公式（3）～（5），计算得到楔形拉槽爆破压碎区和裂隙区半径如表6所示。
1.3.2　参数验证模型建立
为了分析楔形孔爆破过程中爆生气体和爆炸应力波共同作用过程，采用LS-DYNA软件建立楔形孔二维准平面应变模型，见图2，模型尺寸长17.5 m，宽11.2 m；楔形孔排距1.2 m，间距7.5 m，耦合装药直径8 cm，空气域直径取5倍装药直径，为40 cm。边界条件为透射边界。
1.3.3　模拟结果及分析
楔形孔同步起爆时的爆破损伤演化特征如图3所示。相邻炮孔因间距较小产生贯穿效应，孔壁周围形成高损伤区（损伤值D=1）；压碎区表现为冲击波引发的径向塑性压缩损伤，裂隙区表现为由应力波衰减与爆生气体“气楔作用”共同诱导的放射状裂纹网络[13]。模拟结果中损伤分区的力学机制与实际爆破理论高度吻合，验证了RHT岩石本构模型参数的可靠性。
为确定岩石爆破损伤的有效阈值，结合压碎区与裂隙区动态响应特征进行分析。根据爆炸能量衰减规律，裂隙区因应力波与爆生气体作用形成贯通裂纹，但损伤程度随能量耗散逐步降低；弹性振动区仅引发岩石力学参数弱化，无宏观破坏。这表明当损伤值超过临界阈值时，岩石才会发生不可逆破坏。
LS-PREPOST软件后处理损伤分布范围如图4所示。由图4可得，0.7<D<1时，损伤区完全缺失裂隙带且压碎区半径为0.11 m（<0.14 m），显著偏离理论值，表明该阈值过大；0.4<D<1时，损伤分布呈现完整的径向裂隙网络（位于裂隙区理论半径内），压碎区半径为0.13 m，虽略大于计算值（虚线圆域），但考虑网格尺寸限制导致的微裂隙模拟偏差，该阈值下损伤分区与表6数据吻合度高。
矿岩不同损伤范围楔形孔压碎区和裂隙区变化如图5所示。0.4<D<1时，压碎区与裂隙区半径值与理论预测较为一致，进一步验证其作为有效损伤阈值的合理性。损伤阈值D=0.4可定义为矿岩爆破损伤的临界阈值。
2　楔形切割拉槽爆破方案
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2.1　孔底距确定
扇形炮孔单孔破岩面积最大时，孔底距a与裂隙区半径R2的关系[11]为：
按照某矿西二采区楔形切割拉槽参数布置，炮孔倾角大于45°时，根据式（6），取实际孔底距为3.7 m布孔，炮孔密集系数为1.559。
2.2　切割拉槽爆破方案建立
炸药单耗2.8 kg/m3，反向起爆，连续耦合装药，长短交错的“W”形堵塞方式，拉槽高度固定为23 m，拉槽宽度15～30 m，每隔3 m建立一个模型，共计6个模型，每个模型总装药量Qw和装药长度L见表7。
2.3　数值模型建立
切割拉槽爆破模型如图6所示，模型由切割平巷顶板、两侧垂直孔及顶部楔形孔所组成。楔形炮孔的布孔中心位于切割平巷中心线和进路中心线交点。模型计算采用g-cm-μs单位制，设定岩石、炸药、空气域网格单元尺寸分别为6、3、4 cm。
3　楔形切割拉槽爆破数值模拟
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3.1　爆破原始损伤演化情况
各时段爆破原始损伤演化情况如图7所示，炸药从掏槽底部起爆，爆炸后应力波以锥形体形式向自由面传播，由于楔形掏槽底部炮孔距离比较近，990 s时应力波阵面发生叠加，叠加后的波阵面以弧形形式向自由面传播，炮孔底部附近岩石受到的压应力大于其抗压强度，呈现压缩破坏形态。反向起爆应力波从顶部向自由面附近发生反射、叠加，使得拉槽顶部区域岩石破坏更显著。
3.2　有效损伤率变化规律
不同拉槽方案下最终有效损伤分布如图8所示。
由图8可知，岩石有效损伤区形状大体一致。受布孔方式的限制，靠近自由面炮孔有效损伤区分布更为密集（楔形拉槽模型两侧），导致爆破能量在炮孔间产生叠加效应，自由面应力波产生反射拉伸破坏，使得模型在靠近自由面区域以及炮孔间有效损伤区范围显著增大。
各模型有效损伤区分布存在一定差异，主要是模型宽度不同导致炮孔倾角变化。随着拉槽宽度的增加，炮孔倾角逐渐变小，能量叠加区域发生相应变化，具体表现为各模型顶部及中心处有效损伤区随着拉槽宽度增大先增大后减小。如图8（e）、（f）所示，模型中部和顶部的部分区域损伤值低于0.4，可视为未发生有效损伤，可推断这些区域未发生岩石破坏。
采用有效损伤率表征不同拉槽宽度条件下的拉槽爆破效果。有效损伤率是指拉槽爆破平面模型中有效损伤（0.4<D<1）区域面积与整个拉槽爆破模型区域面积的比值。根据图8，计算得到各方案有效损伤率如表8所示。
表8表明，拉槽高度23 m条件下，楔形拉槽区域有效损伤率随着拉槽宽度增加呈先升后降趋势。这主要是拉槽宽度变化导致楔形孔布置角度调整，进而改变爆破应力波的传播导向特性，不同宽度下爆生气体的压力分布差异引发岩石破碎与抛掷空间不均衡。基于ORIGIN软件GaussAmp模型对有效损伤率-拉槽宽度数据进行拟合，建立有效损伤率Q与拉槽宽度d的定量关系方程，具体表达式为：
4　现场试验验证
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4.1　切割拉槽方案
某矿山1 546 m分段首次楔形切割拉槽位于4#～8#进路端部的矿岩交界面。该拉槽净高度23 m，拉槽宽度24 m，炮孔布置如图9所示，炮孔直径80 mm，以6#进路中心为界，右侧为1～10排炮孔，左侧为1′～10′排炮孔，每排布置4个中深孔。
4.2　拉槽空间质量
拉槽爆破后，观测楔形拉槽成槽的空间形态，实测底部宽度约25 m，高度约20 m，如图10所示。计算得出爆破形成空间面积535 m2，体积2 675 m3，超过设计拉槽空间的85%。假设矿岩松散系数为1.23，推算出本次爆破的爆堆体积约为3 291 m3。现场统计拉槽后累计出矿量580铲，铲运机斗容为6 m3，折合爆堆体积约3 480 m3，与推测的爆堆体积相差不大，从侧面表明推测的拉槽空间形态与实际形成空间相差不大。
4.3　爆堆形态及块度大小分析
在切割平巷中观测爆破后爆堆形态，爆堆自然安息角约40°。对6#进路拉槽爆破爆堆照片进行处理，并分析爆堆块度，如图11所示。由图11可知，爆破大块主要分布在爆堆中下区域，爆破块度面积范围为0～0.68 m2，主要分布在0～0.2 m2；等效尺寸范围为0～0.93 m，主要分布在0～0.3 m。对爆破块度尺寸分布进行分级，结果如表9所示。由表9可知，块度大于0.3 m的矿石仅占36.29%，而块度小于0.3 m的小块和粉状矿石占63.71%，小型块度矿石居多，表明切割拉槽爆破效果较好，达到了预期目标。
5　结论
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1）基于理论分析与经验参数标定，确定采区矿岩RHT本构模型参数，采用LS-DYNA软件，运用流固耦合算法进行数值模拟，对比压碎区/裂隙区理论半径与损伤分布特征，最终确定该矿区爆破有效损伤阈值为0.4<D<1。
2）楔形切割拉槽爆破数值模拟揭示了不同拉槽宽度下爆破损伤演化规律，有效损伤率随着拉槽宽度增加呈单峰曲线变化，即拉槽高度一定时，随着拉槽宽度增大，楔形拉槽区域有效损伤率呈现先增大后减小的变化特性。
3）拉槽宽度24 m时矿岩有效损伤率达到峰值0.692 5，现场试验结果表明该方案爆破成形空间达标率超85%，爆堆块度分布合理，安息角约40°，验证了RHT本构模型参数体系与损伤阈值选取的可靠性。
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2025年第45卷第2期
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doi: 10.3969/j.issn.0253-6099.2025.02.008
  • 接收时间：2024-10-27
  • 首发时间：2026-03-19
  • 出版时间：2025-04-01
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  • 收稿日期：2024-10-27
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    1.昆明有色冶金设计研究院股份公司，云南　昆明　650231
    2.西南科技大学　环境与资源学院，四川　绵阳　621010
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