Article(id=1322164743255737226, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322164546295410919, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1735574400000, receivedDateStr=2024-12-31, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793158239424, onlineDateStr=2026-10-28, pubDate=1764000000000, pubDateStr=2025-11-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793158239424, onlineIssueDateStr=2026-10-28, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793158239424, creator=13701087609, updateTime=1793158239424, updator=13701087609, issue=Issue{id=1322164546295410919, tenantId=1146029695717560320, journalId=1225396423026438145, year='2025', volume='45', issue='11', pageStart='1', pageEnd='284', issueExtLink='null', onlineDate='null', pubDate='1764000000000', pubDateStr='2025-11-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793158192465, creator='13701087609', updateTime=1793158905697, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1322167537857573862, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322164546295410919, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1322167537861768167, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322164546295410919, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=133, endPage=140, ext={EN=ArticleExt(id=1322164743415120779, articleId=1322164743255737226, tenantId=1146029695717560320, journalId=1225396423026438145, language=EN, title=Study on Bearing Capacity Effect of Variable Cross-Section Pillar in Goaf, columnId=null, journalTitle=Mining Research and Development, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Due to the influence of ore-rock endowment and blasting construction quality, variable cross-section pillars are commonly present in room-and-pillar underground mining mines. To study the bearing capacity effect of variable cross-section pillars, taking the variable cross-section pillar of a limestone mine as the research object, a mechanical model of the variable cross-section pillar was established, the expressions for its stress and safety factor were derived, the relationships between stress, safety factor and factors such as the diameter d of the variable cross-section pillar and the radius R of the variable cross-section area were studied respectively, and the stress distribution characteristic was analyzed. The results show that the stress of variable cross-section pillars changes gradually in the variable cross-section area, and the stress amplitude decreases with the increase of R or d. The safety factor increases with the increase of R, and the rate of change increases gradually. It also increases synchronously with the increase of d. Compared with constant cross-section pillars, variable cross-section pillars have a more uniform stress distribution, a better stress transfer effect at the junction with the roof, a higher safety factor, and better stability. Numerical simulation and engineering examples have verified the reliability of the theoretical calculation results.

, authors=Lichun JIANG, Liuting WEI, Junhao CHEN, authorsList=Lichun JIANG, Liuting WEI, Junhao CHEN, authorCompany=null, correspAuthors=Liuting WEI, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1322164748653806514, articleId=1322164743255737226, tenantId=1146029695717560320, journalId=1225396423026438145, language=CN, title=采空区变截面矿柱承载力学效应研究, columnId=1226462295417598973, journalTitle=矿业研究与开发, columnName=矿山安全与环保, runingTitle=null, highlight=null, articleAbstract=

受矿岩禀赋和爆破施工质量的影响,变截面矿柱普遍存在于房柱法地下开采矿山中。为研究变截面矿柱承载力学效应,以某石灰岩矿变截面矿柱为研究对象,构建变截面矿柱力学模型,推导其应力和安全系数表达式,分别研究应力及安全系数与变截面矿柱直径d、变截面区半径R等因素之间的关系,并分析应力分布特征。结果表明:变截面矿柱应力在变截面区域是逐渐变化的,应力幅值随着R或d的增大而减小;安全系数随着R的增大而增大,且变化速率逐渐增大,随着d的增大同步增大;与等截面矿柱相比,变截面矿柱应力分布更均匀,与顶板相接处应力传递效果更好,安全系数更高,稳定性更好。数值模拟和工程实例验证了理论计算结果的可靠性。

, authors=姜立春, 韦柳婷, 陈俊豪, authorsList=姜立春, 韦柳婷, 陈俊豪, authorCompany=null, correspAuthors=韦柳婷, authorNote=

姜立春(1968—),男,安徽滁州人,博士,教授,主要从事矿山岩土安全方面的研究。E-mail:

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韦柳婷(1998—),女,广西河池人,硕士研究生,主要从事矿山岩土安全方面的研究。E-mail:
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姜立春(1968—),男,安徽滁州人,博士,教授,主要从事矿山岩土安全方面的研究。E-mail:

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tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, companyId=1322164750490911667, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=华南理工大学 土木与交通学院,广东 广州 510640)])], figs=[ArticleFig(id=1322164752747447247, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=EN, label=Fig.1, caption=Real scene diagram and mechanical model of variable cross-section pillar, figureFileSmall=nCl5qYQ6A01nbK/fyNkmPw==, figureFileBig=yV/SVwWI/p6Z7qhrwJ9brQ==, tableContent=null), ArticleFig(id=1322164752852304848, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=CN, label=图1, caption=变截面矿柱实景图及力学模型, figureFileSmall=nCl5qYQ6A01nbK/fyNkmPw==, figureFileBig=yV/SVwWI/p6Z7qhrwJ9brQ==, tableContent=null), ArticleFig(id=1322164753091380177, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=EN, label=Fig.2, caption=Calculation model of pillar bearing capacity, figureFileSmall=gLcGe0yI5XI1+aLi+jOCgg==, figureFileBig=yGHlNA2bvqrgWluYnO19bw==, tableContent=null), ArticleFig(id=1322164754832016338, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=CN, label=图2, caption=矿柱承载力计算模型, figureFileSmall=gLcGe0yI5XI1+aLi+jOCgg==, figureFileBig=yGHlNA2bvqrgWluYnO19bw==, tableContent=null), ArticleFig(id=1322164754932679635, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=EN, label=Fig.3, caption=Stress curves of variable cross-section pillars under different radiuses of variable cross-section area, figureFileSmall=aXFkrukYM2nDQahSd0P3Gw==, figureFileBig=7tPWTsbdXgbZvJHo3WX5WQ==, tableContent=null), ArticleFig(id=1322164755058508756, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=CN, label=图3, caption=不同变截面区半径下的变截面矿柱应力曲线, figureFileSmall=aXFkrukYM2nDQahSd0P3Gw==, figureFileBig=7tPWTsbdXgbZvJHo3WX5WQ==, tableContent=null), ArticleFig(id=1322164755138200533, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=EN, label=Fig.4, caption=Stress curves of variable cross-section pillars under different diameters of variable cross-section pillars, figureFileSmall=Kc8Ck85Yv3HEEMNMSA0zBA==, figureFileBig=DfE94/ucwZDxhTRKDOtH/A==, tableContent=null), ArticleFig(id=1322164755226280918, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=CN, label=图4, caption=不同变截面矿柱直径下的变截面矿柱应力曲线, figureFileSmall=Kc8Ck85Yv3HEEMNMSA0zBA==, figureFileBig=DfE94/ucwZDxhTRKDOtH/A==, tableContent=null), ArticleFig(id=1322164755293389783, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=EN, label=Fig.5, caption=Numerical model of variable cross-section 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tableContent=null), ArticleFig(id=1322164755603768283, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=EN, label=Fig.7, caption=Comparison of theoretical calculation results and numerical simulation results, figureFileSmall=ZpkeMpIkuybFa+7yt1pP6g==, figureFileBig=z2dYLa9pbSNdu8r2VtSsqA==, tableContent=null), ArticleFig(id=1322164755666682844, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=CN, label=图7, caption=理论计算结果与数值模拟结果对比, figureFileSmall=ZpkeMpIkuybFa+7yt1pP6g==, figureFileBig=z2dYLa9pbSNdu8r2VtSsqA==, tableContent=null), ArticleFig(id=1322164755733791709, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=EN, label=Fig.8, caption=Safety factor variation curves of variable cross-section pillars under different radiuses of variable cross-section area, figureFileSmall=wicVlrt9DaJkFxb1vkzZmQ==, figureFileBig=5fMGm4bNXm3RqWNlG9095g==, tableContent=null), ArticleFig(id=1322164755809289182, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=CN, label=图8, caption=不同变截面区半径下的安全系数变化曲线, figureFileSmall=wicVlrt9DaJkFxb1vkzZmQ==, figureFileBig=5fMGm4bNXm3RqWNlG9095g==, tableContent=null), ArticleFig(id=1322164755922535391, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=EN, label=Fig.9, caption=Real scene diagram of a variable cross-section pillar in goaf of case 2, figureFileSmall=nZnG1vxu7tjTaFyP72hLkA==, figureFileBig=CVQPlD+6D+9RYvuw38SkVQ==, tableContent=null), ArticleFig(id=1322164756035781600, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=CN, label=图9, caption=实例2采空区变截面矿柱实景图, figureFileSmall=nZnG1vxu7tjTaFyP72hLkA==, figureFileBig=CVQPlD+6D+9RYvuw38SkVQ==, tableContent=null), ArticleFig(id=1322164756220330977, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=EN, label=Table 1, caption=

Physical and mechanical parameters of rock

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类型容重/(kN/m3)抗压强度/MPa弹性模量/GPa泊松比黏聚力/MPa内摩擦角/(°)剪切模量/GPa
矿体26.344.268.200.2713.6439.213.23
围岩25.240.835.120.2910.4524.751.98
), ArticleFig(id=1322164756308411362, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164743255737226, language=CN, label=表1, caption=

岩石物理力学参数

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类型容重/(kN/m3)抗压强度/MPa弹性模量/GPa泊松比黏聚力/MPa内摩擦角/(°)剪切模量/GPa
矿体26.344.268.200.2713.6439.213.23
围岩25.240.835.120.2910.4524.751.98
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采空区变截面矿柱承载力学效应研究
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姜立春 , 韦柳婷 , 陈俊豪
矿业研究与开发 | 矿山安全与环保 2025,45(11): 133-140
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矿业研究与开发 |矿山安全与环保 2025 , 45 (11) : 133 -140
采空区变截面矿柱承载力学效应研究
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姜立春(1968—),男,安徽滁州人,博士,教授,主要从事矿山岩土安全方面的研究。E-mail:

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姜立春(1968—),男,安徽滁州人,博士,教授,主要从事矿山岩土安全方面的研究。E-mail:

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姜立春 , 韦柳婷 , 陈俊豪
作者信息
  • 华南理工大学 土木与交通学院,广东 广州 510640
通讯作者:
韦柳婷(1998—),女,广西河池人,硕士研究生,主要从事矿山岩土安全方面的研究。E-mail:
作者简介:

姜立春(1968—),男,安徽滁州人,博士,教授,主要从事矿山岩土安全方面的研究。E-mail:

Study on Bearing Capacity Effect of Variable Cross-Section Pillar in Goaf
Lichun JIANG , Liuting WEI , Junhao CHEN
Affiliations
  • School of Civil Engineering & Transportation, South China University of Technology, Guangzhou, Guangdong 510640, China
出版时间: 2025-11-25
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受矿岩禀赋和爆破施工质量的影响,变截面矿柱普遍存在于房柱法地下开采矿山中。为研究变截面矿柱承载力学效应,以某石灰岩矿变截面矿柱为研究对象,构建变截面矿柱力学模型,推导其应力和安全系数表达式,分别研究应力及安全系数与变截面矿柱直径d、变截面区半径R等因素之间的关系,并分析应力分布特征。结果表明:变截面矿柱应力在变截面区域是逐渐变化的,应力幅值随着R或d的增大而减小;安全系数随着R的增大而增大,且变化速率逐渐增大,随着d的增大同步增大;与等截面矿柱相比,变截面矿柱应力分布更均匀,与顶板相接处应力传递效果更好,安全系数更高,稳定性更好。数值模拟和工程实例验证了理论计算结果的可靠性。

变截面矿柱  /  承载力学效应  /  应力分布特征  /  安全系数  /  稳定性分析

Due to the influence of ore-rock endowment and blasting construction quality, variable cross-section pillars are commonly present in room-and-pillar underground mining mines. To study the bearing capacity effect of variable cross-section pillars, taking the variable cross-section pillar of a limestone mine as the research object, a mechanical model of the variable cross-section pillar was established, the expressions for its stress and safety factor were derived, the relationships between stress, safety factor and factors such as the diameter d of the variable cross-section pillar and the radius R of the variable cross-section area were studied respectively, and the stress distribution characteristic was analyzed. The results show that the stress of variable cross-section pillars changes gradually in the variable cross-section area, and the stress amplitude decreases with the increase of R or d. The safety factor increases with the increase of R, and the rate of change increases gradually. It also increases synchronously with the increase of d. Compared with constant cross-section pillars, variable cross-section pillars have a more uniform stress distribution, a better stress transfer effect at the junction with the roof, a higher safety factor, and better stability. Numerical simulation and engineering examples have verified the reliability of the theoretical calculation results.

Variable cross-section pillar  /  Bearing capacity effect  /  Stress distribution characteristic  /  Safety factor  /  Stability analysis
姜立春, 韦柳婷, 陈俊豪. 采空区变截面矿柱承载力学效应研究. 矿业研究与开发, 2025 , 45 (11) : 133 -140 .
Lichun JIANG, Liuting WEI, Junhao CHEN. Study on Bearing Capacity Effect of Variable Cross-Section Pillar in Goaf[J]. Mining Research and Development, 2025 , 45 (11) : 133 -140 .
房柱法是金属和非金属矿床常用的采矿方法。该采矿法通过预留的点状、条状矿柱支撑顶板岩体,以维持矿房的稳定[1-4]。设计预留矿柱的横截面形状通常为规则圆形、方形或矩形。在实际施工过程中,受矿岩禀赋和凿岩爆破施工的影响,最终矿柱形状与设计形状存在出入,经常会出现不规则截面矿柱现象,以及沿纵向变截面矿柱问题。矿柱失稳破坏极易引发顶板冒落,甚至导致采空区垮塌灾害[5-7]。在重力荷载作用下,与等截面矿柱相比,变截面矿柱内部应力分布、应力传递效果明显不同,承载力学效应也不同,能否满足安全生产要求,是矿山关注的焦点。
目前,国内外学者对矿柱稳定性开展了大量研究,主要集中在规则矿柱方面[8-17]。陈顺满等[10]研究了深部回采矿柱承载机理及失稳形式,并对矿柱稳定性影响因素开展了敏感性分析。刘建等[11]基于损伤启裂板裂界限模型,利用FLAC3D模拟原位压缩和单轴压缩条件下硬岩矿柱脆性破坏过程,并分析其破坏特征。XU等[12]借助ABAQUS对圆形、方形和矩形截面岩石试件在单轴压缩下的变形响应进行了数值模拟试验,研究截面形状对岩石强度和变形特性的影响。LI等[13]基于数值模拟方法,研究了宽高比对岩石试样破坏模式的影响。朱德福等[14]基于离散元和机器学习的方法,建立了矿柱强度预测模型。姜立春等[15]综合考虑残矿开采环境下覆岩、采场内崩落体挤压和爆破震动等荷载作用,推导出矿柱的轴向应力及安全系数表达式。徐文彬等[16]基于Voronoi图法理论,分析了不规则矿柱的稳定性。何环莎等[17]利用数值模拟计算方法,分析了相同围岩条件下上大下小圆台矿柱、两端大中间小圆柱、圆形矿柱和方形矿柱等不同形状矿柱的稳定性。总体而言,相关研究大多将矿柱简化为规则矿柱,忽略了矿柱截面大小沿纵向变化对矿柱稳定性的影响,当矿柱截面变化较大时,将矿柱简化为规则形状难以反映其差异化特性。
本文在现场调研的基础上,以某石灰岩矿变截面矿柱为研究对象,建立其力学模型,并推导其应力和安全系数表达式,研究不同直径、不同变截面区半径条件下,变截面矿柱内部应力及安全系数的变化情况;结合数值模拟和对比分析方法,研究变截面矿柱应力分布特征和力学承载特性,通过工程实例验证理论分析结果的可靠性。
某地下房柱法开采的石灰岩矿山,岩体结构均匀致密,节理和裂隙不发育。变截面矿柱实景图及力学模型如图1所示。采矿设计预留矿柱为圆形,采空区形成后,矿柱沿垂直方向下部近似圆柱体,上部至顶部截面逐渐变大,外轮廓线近似弧线(见图1(a)),变截面起点介于矿柱中下部与上部之间。沿着垂直剖面方向看,近似花瓶形。
图1(b)为图1(a)的力学模型,图中A为变截面矿柱下部与底板相接点,B为横截面变化起始点,C为变截面矿柱顶部与顶板相接点,BD连线垂直于顶板,垂足为D。将变截面矿柱简化为顶、底部两端固定的变截面圆柱体,高度为h。其中,AB段为等截面圆柱,直径为d;BC段为变截面圆柱体,轮廓线BC为圆弧且与线AB、线CD相切,该圆弧半径为R。为简化描述,将变截面矿柱分为等截面区域和变截面区域两段,分别对应AB段和BC段,变截面矿柱直径用等截面区域的直径d来表示。P为上覆岩层对变截面矿柱的荷载,坐标原点位于变截面矿柱顶部中点,x轴沿变截面矿柱垂直向下为正,y轴沿水平方向向右为正。
为简化计算,作如下基本假设:
(1)变截面矿柱岩体为均匀、各向同性弹性体,不考虑节理裂隙的影响;
(2)只考虑上覆岩层自重作用且为均布荷载,变截面矿柱等间距均匀布置。
矿柱承载力计算模型如图2所示。根据面积承载理论,变截面矿柱受到的荷载为其所分摊的顶板面积对应的上覆岩层自重应力,与矿柱自身面积承受的上覆岩层自重应力总和[18],则变截面矿柱所受的荷载为:
式中:γ为上覆岩层平均容重,kN/m3;H为平均开采深度,m;Wa为除矿柱之外的矿房宽度,m。
由于截面变化,变截面矿柱应力分成AB段和BC段计算。AB段截面应力σx1为:
BC段截面应力σx2为:
式中:Ax为BC段任一位置处的截面面积,m2,Ax=πy2,且x和y满足关系式。因此,BC段截面应力σx2为:
在上覆荷载作用下,综合式(1)、式(2)和式(4),变截面矿柱应力σx的表达式为:
安全系数是评价矿柱稳定性最常用的指标之一,矿柱安全系数通常取1.2~1.4,既可保证矿柱稳定,又具有一定的安全冗余度[19]。考虑到截面变化的影响,定义变截面矿柱的安全系数K为矿柱强度与矿柱平均应力的比值,计算式为:
式中:σp为矿柱承载强度,MPa;σm为矿柱平均应力,MPa。
BIENIAWSKI矿柱强度公式考虑了矿柱形状的影响,其应用广泛、效果好[20]。根据BIENIAWSKI矿柱强度公式,估算变截面矿柱强度,具体计算公式如下:
式中:σc为岩石单轴抗压强度,MPa;w为变截面矿柱宽度,m,这里取矿柱宽度w=d;h为矿柱高度,m;η为形状效应指数,其取值通过矿柱的径高比来确定,当矿柱的径高比小于等于5.0时,η=1.0,当矿柱的径高比大于5.0时,η=1.4。
由式(5)积分求得变截面矿柱平均应力σm,见式(8)。将式(7)和式(8)代入式(6),可得变截面矿柱安全系数K,见式(9)。
某房柱法开采的地下石灰岩矿山所开采的矿层为栖霞组灰岩,地表覆土厚6.8~91.5 m,平均厚51.38 m。矿石为灰至灰黑色,隐晶或细晶结构,层理、节理和裂隙不发育,厚层状或块层状构造。
经多年开采,该矿山已形成+211 m、+196 m中段采空区,现回采+176 m中段。现场实地调研显示,矿房宽度为8.0~12.0 m,矿房高度为7.0~10.0 m,采区内变截面矿柱直径约为6.0~10.0 m。根据矿山地质资料及岩石力学试验结果,得出的岩石物理力学参数见表1。
根据采空区情况,选取+176 m水平中段作为研究对象,矿体埋深约为90 m,取矿房宽度为12.0 m,采空区高度为10.0 m,计算分析变截面矿柱应力分布特征和安全系数变化趋势。
由式(5)可知,变截面矿柱应力大小与变截面矿柱直径、变截面矿柱变截面区半径、矿房宽度、采空区埋深及岩体容重等因素相关。对某地下矿山采空区而言,当采空区埋深和岩体容重等数值一定时,变截面矿柱直径、变截面区半径是区别于等截面矿柱的关键参数。因此,结合式(5)计算不同变截面矿柱直径和变截面区半径条件下的矿柱应力。
(1)变截面区半径取值不同。当变截面矿柱直径d=8.0 m一定时,计算变截面区半径R分别为1.0 m、2.0 m、3.0 m、4.0 m、5.0 m的矿柱应力,如图3所示。
由图3可知,当变截面矿柱直径d一定时,沿着x轴方向,变截面矿柱应力先增大再保持不变,且增大速率逐渐减小,等截面区域应力为定值且为最大值。应力变化区域对应变截面矿柱截面变化区,随着变截面区半径R的增大,应力变化区域增大,变截面区域应力整体减小,且减小的速率逐渐降低,应力曲线逐渐平缓。
(2)变截面矿柱直径取值不同。当变截面区半径R=3.0 m一定时,计算变截面矿柱直径d分别为6.0 m、7.0 m、8.0 m、9.0 m、10.0 m的矿柱应力,如图4所示。
由图4可知,当变截面区半径R一定时,沿着x轴方向,变截面矿柱应力逐渐增大,且变化速率逐渐减小,直到x等于R后保持不变。随着变截面矿柱直径d的增大,变截面矿柱应力整体减小,变化速率逐渐降低。
为进一步研究变截面矿柱的承载力学效应,基于理论计算分析工况,采用FLAC3D数值分析软件,构建172.0 m×172.0 m×150.0 m的采空区数值模型,如图5所示,取采空区总跨度为72.0 m,变截面矿柱直径d为8.0 m,变截面区半径R分别为0、1.0 m、2.0 m、3.0 m、4.0 m、5.0 m。在模型侧面及底部分别施加铰链约束和固定约束,岩体破坏服从摩尔库伦准则,计算矿柱应力。
限于篇幅,选取R为0、1.0 m、3.0 m、5.0 m的计算结果进行展示,不同变截面区半径下的矿柱应力云图如图6所示。
当R为0时,变截面矿柱退化为等截面矿柱。由图6可知,变截面矿柱应力变化趋势和等截面矿柱大体相似,矿柱中部应力较大,顶部和底部应力较小,呈现出由中部向两端逐渐减小的趋势,最大应力出现在矿柱边缘。
由图6(a)可知,在上覆荷载作用下,等截面矿柱中部应力较大值出现在矿柱边缘四个角及矿柱中心,连线呈“X”形;在矿柱顶部,应力从矿柱与顶板相接处向顶板深部逐渐减小,应力传递变化区主要集中在顶板。
由图6(b)至图6(d)可知,变截面矿柱中部应力呈现中心小、两边大的趋势,随着变截面区半径的逐渐增大,高应力区(蓝色区域,颜色标识见电子版)面积更窄且向矿柱下部移动。在矿柱上部,变截面区与顶板相接处的应力较小(图6(d)区域E),其值与该处顶板应力相近,从变截面区约二分之一处开始向顶板深处,矿柱应力逐渐减小,直到和深处岩体应力一致。和等截面矿柱相比,变截面矿柱上方的顶板,其应力变化过渡区域的高度更小。
综上所述,相比于等截面矿柱,变截面矿柱内部的应力分布更加均匀,应力集中区域变小,与顶板的应力过渡得更好,应力变化区域更小。
矿柱变截面区与顶板相接区域(图6(d)区域E)相对整个矿柱所占体积比很小,且该区域应力与矿柱整体应力相差较大,与理论计算结果对比分析时暂不考虑该区域的影响。理论计算和数值模拟得出的变截面矿柱最大应力和最小应力结果对比如图7所示。
由图7(a)可知,数值模拟计算的最大应力值整体小于理论计算值,且随着变截面区半径的变化而小幅度波动,但整体曲线仍趋于水平。究其原因,模拟计算时荷载的施加方式及数值模型网格划分的细小差异导致计算结果的误差和波动。
由图7(b)可知,随着变截面区半径R的增大,变截面矿柱最小应力逐渐减小。当变截面区半径R为2.0~5.0 m时,理论计算和数值模拟结果相近;当变截面区半径R为1.0 m时,理论计算结果与数值模拟结果存在一定的误差。究其原因,当变截面区半径较小时,变截面区主要起到应力传递的作用,使变截面矿柱与顶板相接处应力均匀变化。
两种方法计算的变截面矿柱最大应力和最小应力曲线变化趋势基本一致,验证了理论分析结果的可靠性。
以+176 m水平中段为研究对象,选取变截面矿柱直径d为6.0 m、7.0 m、8.0 m、9.0 m、10.0 m,变截面区半径R为1.0 m、2.0 m、3.0 m、4.0 m、5.0 m,结合式(9)计算不同变截面矿柱直径和变截面区半径组合下的矿柱安全系数,如图8所示。
由图8可知,当变截面矿柱直径d一定时,变截面矿柱安全系数K随着变截面区半径R的增大而增大,且变化速率逐渐增大。在相同的变截面区半径R下,随着变截面矿柱直径d的增大,安全系数K同步增大。
当变截面区半径R取0时,变截面矿柱即退化成等截面矿柱。限于篇幅,以直径为8.0 m的等截面矿柱为例,结合式(9)计算其安全系数,与变截面矿柱对比(见图8)。由图8可知,当变截面区半径R为1.0 m时,变截面矿柱和等截面矿柱安全系数相近;当变截面区半径R为2.0~5.0 m时,变截面矿柱的安全系数高于等截面矿柱,且随着变截面区半径的增大而增大。这说明变截面区半径的增大有利于提高矿柱的安全系数,使得变截面矿柱的安全性更好。
选取2.1节某水泥用石灰岩矿山+176 m中段采空区为研究对象,该中段开采结束后留下矿柱支撑采空区,维持采空区的稳定。现场调研发现,某一变截面矿柱直径为7.0 m,变截面区半径为4.8 m,矿房宽度为12.0 m,矿房高度为9.0 m。已知该中段埋深约为90.0 m,其余参数见表1。由式(9)计算出该矿柱安全系数为2.45,安全系数较大,矿柱稳定。
现场勘察发现,该矿柱侧壁未见剥落和裂纹扩展现象,矿柱安全性良好。理论计算结果和现场实际情况基本一致,验证了理论计算的可靠性。
选取2.1节某水泥用石灰岩矿山+211 m中段采空区为研究对象,现场调研发现,该区域采空区矿柱尺寸通常较大,在采空区西侧存在一个较小的变截面矿柱,其直径约为2.9 m,高度约为10.0 m,变截面区半径约为3.6 m,矿房宽度约为10.5 m。实例2采空区变截面矿柱实景图如图9所示。经计算,该中段埋深约为55.0 m,其余参数见表1。由式(9)计算出该矿柱安全系数为1.05,小于最低安全系数允许值,此时矿柱处于危险状态。
现场勘察发现,该矿柱在上覆荷载作用下已出现部分裂纹扩展现象,采场底板可见散落碎石,矿柱处于不稳定状态。理论计算结果和现场实际情况基本一致,验证了理论计算的可靠性。
在某石灰岩矿采空区调研的基础上,构建变截面矿柱力学模型,推导出变截面矿柱应力及安全系数表达式,研究其应力及安全系数与直径d、变截面区半径R等因素之间的关系,结合数值模拟分析变截面矿柱应力分布特征,研究变截面矿柱力学承载效应。得出的主要结论如下。
(1)变截面矿柱应力沿着垂直方向在变截面区域是逐渐变化的,在等截面区域较稳定且出现最大值。受变截面矿柱直径d和变截面区半径R的影响,变截面区域应力幅值随着R或d的增大而减小,且减小速率逐渐降低。变截面矿柱安全系数随着R的增大而增大,且变化速率逐渐增大,随着d的增大同步增大。
(2)与等截面矿柱相比,变截面矿柱应力分布更均匀,与顶板相接处应力渐变区面积更小,应力传递更好;变截面矿柱安全系数更高,稳定性更好。
(3)矿山实例验证结果表明,实例1变截面矿柱安全系数为2.45,安全系数较大,矿柱保持稳定;实例2变截面矿柱安全系数为1.05,小于最低安全系数允许值,矿柱不稳定,部分节理已出现裂纹扩展现象,采场底板可见散落碎石。理论计算结果与现场实际情况基本一致,验证了理论计算结果的可靠性。
  • 国家重点研发计划项目(2022YFC2903802)
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  • 接收时间:2024-12-31
  • 首发时间:2026-10-28
  • 出版时间:2025-11-25
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  • 收稿日期:2024-12-31
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国家重点研发计划项目(2022YFC2903802)
作者信息
    华南理工大学 土木与交通学院,广东 广州 510640

通讯作者:

韦柳婷(1998—),女,广西河池人,硕士研究生,主要从事矿山岩土安全方面的研究。E-mail:
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2种不同金属材料的力学参数
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Percentage of
total species (%)
属
Genus
种数
Number of
species
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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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