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Article(id=1322594561801695946, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322594503278580030, 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=1727625600000, receivedDateStr=2024-09-30, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793260716151, onlineDateStr=2026-10-29, pubDate=1737734400000, pubDateStr=2025-01-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793260716151, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793260716151, creator=13701087609, updateTime=1793260716151, updator=13701087609, issue=Issue{id=1322594503278580030, tenantId=1146029695717560320, journalId=1225396423026438145, year='2025', volume='45', issue='1', pageStart='1', pageEnd='276', issueExtLink='null', onlineDate='null', pubDate='1737734400000', pubDateStr='2025-01-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793260702199, creator='13701087609', updateTime=1793260702199, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=48, endPage=54, ext={EN=ArticleExt(id=1322594561977856715, articleId=1322594561801695946, tenantId=1146029695717560320, journalId=1225396423026438145, language=EN, title=Study on Optimization of Point Pillar Parameters Under Artificial Roof of a Copper Mine, columnId=null, journalTitle=Mining Research and Development, columnName=null, runingTitle=null, highlight=null, articleAbstract=

The stope structure parameters of the mine are important factors to ensuring safe and efficient mining. With the background of the No. I ore body of a copper mine in Yunnan Province, four different point pillar sizes were proposed by engineering analogy method. And the displacement and stress of the stope under different point pillar sizes were analyzed by FLAC3D numerical simulation software. The results show that when the excavation is to the fourth layer, the 4 m×6 m and 5 m×5 m point pillar size schemes can withstand the maximum tensile stress beyond the mining site, and the two schemes can be excluded. The tensile stress of mining sites with 5 m×6 m and 6 m×6 m point pillar size schemes has not reached the limit state, but the optimization effect of rectangular point pillar is obviously better than that of square point pillar. Finally, the reasonable size of point pillar has been determined to be 5 m×6 m, which can provide a reference for mine stope test.

, authors=Chenxin PENGI, Deyong HUANGI, Zefeng DUANI, Kaidong SHII, authorsList=Chenxin PENG, Deyong HUANG, Zefeng DUAN, Kaidong SHI, authorCompany=null, correspAuthors=Deyong HUANG, 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=1322594565249413847, articleId=1322594561801695946, tenantId=1146029695717560320, journalId=1225396423026438145, language=CN, title=某铜矿人工假顶条件下采场点柱参数优化研究, columnId=1226462294490657775, journalTitle=矿业研究与开发, columnName=采矿与矿山充填, runingTitle=null, highlight=null, articleAbstract=

矿山的采场结构参数是保证采场安全高效开采的重要因素。以云南省某铜矿Ⅰ号矿体为背景，通过工程类比法制定出4种不同的点柱尺寸，采用FLAC3D数值模拟软件对不同点柱尺寸下采场的位移、应力进行了分析。分析结果表明：开挖至第四分层时，4 m×6 m与5 m×5 m点柱方案超出采场所能承受最大拉应力，两方案排除；采用5 m×6 m与6 m×6 m采场所受拉应力均未达到极限状态，但长方形点柱优化效果明显好于正方形点柱优化效果，最终确定合理的点柱尺寸为5 m× 6 m，该参数可为矿山的采场试验提供参考。

, authors=彭晨鑫I, 黄德镛I, 段泽锋I, 史凯东I, authorsList=彭晨鑫, 黄德镛, 段泽锋, 史凯东, authorCompany=null, correspAuthors=黄德镛, authorNote=

彭晨鑫（1999—），男，山西忻州人，硕士，主要从事矿业工程等方面研究。E-mail:

, correspAuthorsNote=
黄徳镛（1966—），男，贵州遵义人，博士，副教授，主要从事岩土工程、采矿工程方面科研教学工作。E-mail:
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彭晨鑫（1999—），男，山西忻州人，硕士，主要从事矿业工程等方面研究。E-mail:

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彭晨鑫（1999—），男，山西忻州人，硕士，主要从事矿业工程等方面研究。E-mail:

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Study on point pillar parameters of upward horizontal slicing stoping filling method with point pillars in a mine[J]. Modern Mining, 2023, 39(3):47-50., articleTitle=Study on point pillar parameters of upward horizontal slicing stoping filling method with point pillars in a mine, refAbstract=null)], funds=[Fund(id=1322594575768728333, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, awardId=52174114, language=CN, fundingSource=国家自然科学基金项目(52174114), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1322594565685621464, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, xref=null, ext=[AuthorCompanyExt(id=1322594565694010073, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, companyId=1322594565685621464, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=Faculty of Land Resources Engineering, Kunming University of Science and Technology, Kunming, Yunnan 650093, China), AuthorCompanyExt(id=1322594565706592986, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, companyId=1322594565685621464, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=昆明理工大学 国土资源工程学院，云南　昆明　650093)])], figs=[ArticleFig(id=1322594570156749561, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=EN, label=Fig.1, caption=Longitudinal projection of current mining situation, figureFileSmall=Grk1gfmqt+g7yfMx/e9pPA==, figureFileBig=7CoaUlYy5X5oY4mneRfcrA==, tableContent=null), ArticleFig(id=1322594570219664122, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=CN, label=图1, caption=开采现状纵投影图, figureFileSmall=Grk1gfmqt+g7yfMx/e9pPA==, figureFileBig=7CoaUlYy5X5oY4mneRfcrA==, tableContent=null), ArticleFig(id=1322594570991416059, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=EN, label=Fig.2, caption=hierarchical diagram of the 3D model, figureFileSmall=z5UUkAX250jq/gMXY0e+EA==, figureFileBig=syJ3LLGnMV/C5WOEcqcgLw==, tableContent=null), ArticleFig(id=1322594571054330620, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=CN, label=图2, caption=三维模型分层, figureFileSmall=z5UUkAX250jq/gMXY0e+EA==, figureFileBig=syJ3LLGnMV/C5WOEcqcgLw==, tableContent=null), ArticleFig(id=1322594571402457853, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=EN, label=Fig.3, caption=Cloud maps of stope displacement in the fifth layer, figureFileSmall=u3f7Arfobt3reRcAD0OVpg==, figureFileBig=RJXMzvY9m+zG/q2CJex83Q==, tableContent=null), ArticleFig(id=1322594571490538238, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=CN, label=图3, caption=第五分层采场位移云图, figureFileSmall=u3f7Arfobt3reRcAD0OVpg==, figureFileBig=RJXMzvY9m+zG/q2CJex83Q==, tableContent=null), ArticleFig(id=1322594571557647103, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=EN, label=Fig.4, caption=Cloud maps of maximum principal stress in the fifth layer, figureFileSmall=rvN88JU6SVuF5kqUGahz1g==, figureFileBig=6x+giKabYAa+4/L1v62dlQ==, tableContent=null), ArticleFig(id=1322594571830276864, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=CN, label=图4, caption=第五分层最大主应力云图, figureFileSmall=rvN88JU6SVuF5kqUGahz1g==, figureFileBig=6x+giKabYAa+4/L1v62dlQ==, tableContent=null), ArticleFig(id=1322594571905774337, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=EN, label=Fig.5, caption=Cloud maps of minimum principal stress in the fifth layer, figureFileSmall=5clce0uJ+xULTGLzNNYRGw==, figureFileBig=d4GuSBuR+5nPSYyOijLv9A==, tableContent=null), ArticleFig(id=1322594572027409154, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=CN, label=图5, caption=第五分层最小主应力云图, figureFileSmall=5clce0uJ+xULTGLzNNYRGw==, figureFileBig=d4GuSBuR+5nPSYyOijLv9A==, tableContent=null), ArticleFig(id=1322594572300038915, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=EN, label=Table 1, caption=

Schemes of point pillar size

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方案跨度/m点柱中心距/m点柱尺寸/m分层高度/m
1713×114×64
2613×115×54
3613×115×64
4513×116×64
), ArticleFig(id=1322594574057452292, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=CN, label=表1, caption=

点柱尺寸方案

, figureFileSmall=null, figureFileBig=null, tableContent=
方案跨度/m点柱中心距/m点柱尺寸/m分层高度/m
1713×114×64
2613×115×54
3613×115×64
4513×116×64
), ArticleFig(id=1322594574388802309, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=EN, label=Table 2, caption=

Mechanical parameters of ore bodies

, figureFileSmall=null, figureFileBig=null, tableContent=
取样位置容重/(kN/m3)抗拉强度/MPa弹性模量/GPa黏聚力/MPa内摩擦角/(°)泊松比μ体积模量/GPa剪切模量/GPa
上盘围岩27.540.4824.681.3835.200.2013.7110.28
矿体32.340.5222.761.1637.160.2515.179.10
下盘围岩28.710.5125.971.3936.210.2215.4610.64
人工假顶18.800.380.400.1432.000.390.260.21
), ArticleFig(id=1322594574749512454, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=CN, label=表2, caption=

岩体力学参数

, figureFileSmall=null, figureFileBig=null, tableContent=
取样位置容重/(kN/m3)抗拉强度/MPa弹性模量/GPa黏聚力/MPa内摩擦角/(°)泊松比μ体积模量/GPa剪切模量/GPa
上盘围岩27.540.4824.681.3835.200.2013.7110.28
矿体32.340.5222.761.1637.160.2515.179.10
下盘围岩28.710.5125.971.3936.210.2215.4610.64
人工假顶18.800.380.400.1432.000.390.260.21
), ArticleFig(id=1322594574837592839, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=EN, label=Table 3, caption=

The maximum displacement settlement for point pillars with different sizes

, figureFileSmall=null, figureFileBig=null, tableContent=
步骤不同点柱尺寸下最大沉降位移/ mm
4 m×6 m5 m×5 m5 m×6 m6 m×6 m
开挖第一分层10.6410.099.107.69
开挖第二分层13.9713.5211.9210.32
开挖第三分层16.0115.6114.1212.18
开挖第四分层17.5617.5915.7913.77
开挖第五分层18.6918.5816.6414.91
), ArticleFig(id=1322594574900507400, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=CN, label=表3, caption=

不同点柱尺寸下顶板最大沉降位移

, figureFileSmall=null, figureFileBig=null, tableContent=
步骤不同点柱尺寸下最大沉降位移/ mm
4 m×6 m5 m×5 m5 m×6 m6 m×6 m
开挖第一分层10.6410.099.107.69
开挖第二分层13.9713.5211.9210.32
开挖第三分层16.0115.6114.1212.18
开挖第四分层17.5617.5915.7913.77
开挖第五分层18.6918.5816.6414.91
), ArticleFig(id=1322594574976004873, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=EN, label=Table 4, caption=

The maximum principal stress for point pillars with different sizes

, figureFileSmall=null, figureFileBig=null, tableContent=
步骤不同点柱尺寸下最大主应力/MPa
4 m×6 m5 m×5 m5 m×6 m6 m×6 m
开挖第一分层66.6464.9560.1759.13
开挖第二分层67.9266.3662.4560.87
开挖第三分层68.0367.4164.1962.31
开挖第四分层69.8568.1565.4264.02
开挖第五分层72.8170.2866.2965.31
), ArticleFig(id=1322594575248634634, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=CN, label=表4, caption=

不同点柱尺寸下最大主应力

, figureFileSmall=null, figureFileBig=null, tableContent=
步骤不同点柱尺寸下最大主应力/MPa
4 m×6 m5 m×5 m5 m×6 m6 m×6 m
开挖第一分层66.6464.9560.1759.13
开挖第二分层67.9266.3662.4560.87
开挖第三分层68.0367.4164.1962.31
开挖第四分层69.8568.1565.4264.02
开挖第五分层72.8170.2866.2965.31
), ArticleFig(id=1322594575319937803, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=EN, label=Table 5, caption=

The minimum principal stress for point pillars with different sizes

, figureFileSmall=null, figureFileBig=null, tableContent=
步骤不同点柱尺寸下最小主应力/MPa
4 m×6 m5 m×5 m5 m×6 m6 m×6 m
开挖第一分层0.496 70.489 70.447 60.437 7
开挖第二分层0.509 10.493 50.466 70.441 1
开挖第三分层0.511 50.508 40.471 20.453 7
开挖第四分层0.520 00.511 80.480 60.461 6
开挖第五分层0.536 00.523 30.490 00.476 9
), ArticleFig(id=1322594575651287820, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594561801695946, language=CN, label=表5, caption=

不同点柱尺寸下最小主应力

, figureFileSmall=null, figureFileBig=null, tableContent=
步骤不同点柱尺寸下最小主应力/MPa
4 m×6 m5 m×5 m5 m×6 m6 m×6 m
开挖第一分层0.496 70.489 70.447 60.437 7
开挖第二分层0.509 10.493 50.466 70.441 1
开挖第三分层0.511 50.508 40.471 20.453 7
开挖第四分层0.520 00.511 80.480 60.461 6
开挖第五分层0.536 00.523 30.490 00.476 9
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某铜矿人工假顶条件下采场点柱参数优化研究
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彭晨鑫 I , 黄德镛 I , 段泽锋 I , 史凯东 I
矿业研究与开发 | 采矿与矿山充填 2025,45(1): 48-54
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矿业研究与开发 |采矿与矿山充填 2025 , 45 (1) : 48 -54
某铜矿人工假顶条件下采场点柱参数优化研究
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彭晨鑫I , 黄德镛I , 段泽锋I, 史凯东I
作者信息
  • 昆明理工大学 国土资源工程学院，云南　昆明　650093
通讯作者:
黄徳镛（1966—），男，贵州遵义人，博士，副教授，主要从事岩土工程、采矿工程方面科研教学工作。E-mail:
作者简介:

彭晨鑫（1999—），男，山西忻州人，硕士，主要从事矿业工程等方面研究。E-mail:

Study on Optimization of Point Pillar Parameters Under Artificial Roof of a Copper Mine
Chenxin PENGI , Deyong HUANGI , Zefeng DUANI, Kaidong SHII
Affiliations
  • Faculty of Land Resources Engineering, Kunming University of Science and Technology, Kunming, Yunnan 650093, China
出版时间: 2025-01-25
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摘要
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矿山的采场结构参数是保证采场安全高效开采的重要因素。以云南省某铜矿Ⅰ号矿体为背景，通过工程类比法制定出4种不同的点柱尺寸，采用FLAC3D数值模拟软件对不同点柱尺寸下采场的位移、应力进行了分析。分析结果表明：开挖至第四分层时，4 m×6 m与5 m×5 m点柱方案超出采场所能承受最大拉应力，两方案排除；采用5 m×6 m与6 m×6 m采场所受拉应力均未达到极限状态，但长方形点柱优化效果明显好于正方形点柱优化效果，最终确定合理的点柱尺寸为5 m× 6 m，该参数可为矿山的采场试验提供参考。

人工假顶  /  点柱尺寸  /  上向水平充填法  /  采场结构参数  /  数值模拟

The stope structure parameters of the mine are important factors to ensuring safe and efficient mining. With the background of the No. I ore body of a copper mine in Yunnan Province, four different point pillar sizes were proposed by engineering analogy method. And the displacement and stress of the stope under different point pillar sizes were analyzed by FLAC3D numerical simulation software. The results show that when the excavation is to the fourth layer, the 4 m×6 m and 5 m×5 m point pillar size schemes can withstand the maximum tensile stress beyond the mining site, and the two schemes can be excluded. The tensile stress of mining sites with 5 m×6 m and 6 m×6 m point pillar size schemes has not reached the limit state, but the optimization effect of rectangular point pillar is obviously better than that of square point pillar. Finally, the reasonable size of point pillar has been determined to be 5 m×6 m, which can provide a reference for mine stope test.

Artificial roof  /  Point pillar size  /  Upward horizontal filling method  /  Stope structure parameter  /  Numerical simulation
彭晨鑫, 黄德镛, 段泽锋, 史凯东. 某铜矿人工假顶条件下采场点柱参数优化研究. 矿业研究与开发, 2025 , 45 (1) : 48 -54 .
Chenxin PENG, Deyong HUANG, Zefeng DUAN, Kaidong SHI. Study on Optimization of Point Pillar Parameters Under Artificial Roof of a Copper Mine[J]. Mining Research and Development, 2025 , 45 (1) : 48 -54 .
正文
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0　引言
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与浅部开采相比，开采深部采场时面临着更多的困难，进一步增加了开采作业的难度[1-2]，采场结构参数对于矿山工作的稳定性与安全性有着至关重要的作用，因此选取合理的结构参数是矿体开采工作至关重要的一环。采场结构参数[3]数值模拟研究的内容主要包括采场尺寸与形状、支护方式、岩体性质等，主要是为了适应采场高效开采的要求，同时发挥设备的最大效率，提高矿石资源的回采率并获得最大效益[4-5]。
采场结构参数优化主要有以下三种模拟方法：有限元法[6]、离散元法、边界元法。张爱民等[7]以思山岭铁矿为研究对象，开展了大直径深孔空场嗣后充填法采场结构研究，对传统条形采场和方形采场进行模拟分析，最终得出最优的采场结构参数。张应平[8]以某磷矿典型层状节理岩体为研究对象，采用FLAC3D有限差分软件和UDEC离散元法对层状岩体中不同矿柱倾角对采场围岩稳定性的影响展开模拟分析，获得了采场矿柱的最优倾角和矿柱尺寸，实现了对采场冒落范围的预测分析。陈顺满等[9]为了研究破碎围岩下矿柱的应力规律和回采率的问题提出了响应面法，并结合有限元模拟软件建立了响应面回归模型，最后采用非线性多目标优化的方法得到最佳的采场结构参数。李俊平等[10]针对二里河铅锌矿1 100 m中段地压显现严重的问题，设计正交试验方案并运用FLAC3D软件分析不同采场结构参数下采场的稳定性，最终得到矿房长40 m、间柱厚10 m、顶柱厚12 m的最佳结构参数，成功解决了1 100 m中段地压严重的问题。安傲清[11]利用ANSYS有限元分析软件对玲珑金矿东风矿区8种不同采场结构参数方案进行模拟，从Mises等效应力和竖向位移沉降两个角度进行分析，得到最佳的采场结构参数。
云南省某铜矿Ⅰ号矿体现采用点柱式水平上向分层充填法进行开采，500 m中段首采分层结束后，采用水泥尾砂浆充填形成人工假底[12-13]，作为400 m中段最后一分段回采时的假顶。此条件下400 m中段最后一分段480 m分段若采用原点柱尺寸不能保障安全高效的采矿作业，因此，需对400 m中段人工假顶下的采场内点柱参数进行优化。本文通过工程类比法制定点柱尺寸参数，采用数值模拟分析的方法对Ⅰ号铜矿体点柱尺寸参数进行优化研究，确定最优的点柱尺寸参数，以期为矿山的采场试验提供借鉴。
1　工程背景
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1.1　矿山概况
本文研究矿山位置靠近哀牢山脉东侧的戛洒江东岸。矿带地处曼岗河组第三岩性段的中上部，主要矿化岩石包括变质的石榴黑云凝灰岩、片岩和含白云石的大理岩，Ⅰ号铜矿体平均倾角为37.5°，矿体平均厚度为7.16 m。矿山采用点柱式水平上向分层充填采矿法开采，采场内所遗留的点柱对维护采场稳定性起到一定作用，但随着开采深度的增加，点柱受到的应力不断增大，可能会导致冒顶事故。阶段高100 m，分段高20 m,400 m中段中最后一分段为480 m分段。现需要对该分段人工假顶下采场内的点柱尺寸进行优化研究。
1.2　采矿方法
（1）采场布置及结构参数。
根据Ⅰ号铜矿矿体赋存情况，盘区沿矿体走向布置，每300 m划分为一个盘区。阶段高100 m，分段高20 m,4 m一个分层，矿块长50 m，矿体的水平厚度为矿块宽，当存在多层矿体时宽度为多层矿体与夹石厚度的和。相邻矿块之间留4 m宽的间柱。采场内矿柱原始尺寸为5 m×5 m，跨度为7 m。
（2）采准、切割。
沿脉采准干线布置在矿带的下盘，距离最下层矿体60 m。回采联道垂直矿体走向布置在矿块中部，回采联道一端连通沿脉采准干线，另一端掘到要回采矿体的最上一个分层的上盘，回采联道在穿矿段水平布置，标高比采准干线低约8 m（为各分段首采分层底板标高），回采联道水平段与采准干线连接段的坡度控制在18%以内。沿要回采矿体最上层的上盘布置回风上山，连通上下两个分段的回采联道。切割横巷沿矿体走向布置。
（3）凿岩、爆破及出矿。
凿岩：脉外巷道及采场采用281凿岩台车，孔深3.5 m，炮眼排距0.7~0.9 m，孔距0.8~1.0 m；顶板控制爆破层炮眼间距0.5~0.8 m，控制爆破层厚度0.5~0.7 m。一次性将整条进路断面炮眼打好。
爆破：选用32 mm岩石乳化炸药，数码电子雷管起爆，排间进行微差爆破，间隔25~50 ms，控制爆破层采用导爆索起爆，后续一次齐发爆破。起爆方式为电子雷管起爆器起爆。
出矿：选用装载机，装入卡车倒入指定脉外溜井。
（4）通风及充填。
通风：采用局部机械通风方法或回风上山自然通风的方式，排出作业面污风，通风时间依通风难易而定。
充填：500 m中段分层开采完毕后，其首采分层充填高度为4 m，采用钢筋 + 水泥尾砂浆全胶结充填，灰砂比为1:4，首采分层充填后作为400 m中段最后一个分段的人工假顶。中段其余分层充填高度为4 m，底层采用废石 + 分级尾砂充填，厚度为3.2 m，面层全胶结充填，厚0.8 m，灰砂比为1:6，研究针对胶面层试块进行强度试验，其单轴抗压强度约0.38 MPa，满足强度要求，根据各中段采场调查，其胶面层平整性较好，满足大型设备运行要求。
1.3　开采现状
400 m中段开采到460 m分段第四分层，最上部采场距离500 m中段首采分层垂直高度不到35 m。目前500 m中段已开采到560 m分段第四分层，最上部采场距离500 m中段首采分层垂直高度不到40 m。图1为400 m中段开采现状。
2　方案建立与数值模拟
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基于FLAC3D数值模拟软件，针对Ⅰ号铜矿体400 m中段人工假顶下点柱尺寸参数进行优化模拟，得到最佳的点柱尺寸参数以保证人工假顶下的采场稳定生产。
2.1　方案建立及数值模拟
2.1.1　点柱尺寸优化方案
本文基于工程类比分析法[14-16]，总结分析了国内外采用点柱式上向分层充填法[17]的矿山案例，发现在开采过程中设计的点柱主要呈方形，而圆柱形点柱的应用相对较少。矿山的实际点柱在通常情况下为矩形，且在4 m×4 m至6 m× 6 m的范围内，因此本研究选择：4 m× 6 m、5 m× 5 m、5 m× 6 m、6 m× 6 m四种点柱尺寸方案开展数值模拟（见表1）。
2.1.2　模型的建立与单元划分
模型建立的过程如下。
（1）通过CAD绘图软件根据采场实际情况，绘制选定中段的平面图；完成绘图后，将二维平面图形导入到Rhino软件中，构建出人工假顶下480 m分段的3个采场的三维实体模型。
（2）利用其内置的Griddle插件进行网格划分，采用四边形渐变式网格对模型细节进行优化处理。模型中采场作为研究核心部分，采用精度为1 m的网格进行精细划分；矿体采用3 m的网格进行划分；上下盘围岩采用9 m的网格进行划分。最终所构建的模型共 317 402 个网格点，542 292 个单元。
（3）将构建完成的模型导入到FLAC3D软件中，对模型进行参数赋值、设置边界条件并对初始应力平衡求解。
（4）对模型进行开挖、充填的工程模拟，构建出的三维模型分层如图2所示。
2.1.3　模拟参数选取以及边界条件
通过查阅资料以及矿山企业提供的人工假顶相关参数，计算体积模量与剪切模量，所需的矿岩体力学参数见表2。根据矿山实际情况建立真实边界模型，从X、Y、Z三个方向对位移进行控制，模型位移所施加的约束条件中Z方向约束为0，模型顶部不做任何约束使其为自由边界。
2.2　模拟结果分析
选取480 m分段采用点柱式水平上向分层充填法对开采区域进行模拟。根据矿山提供的采场剖面图可知，480 m分段上部存在前一分段首采分层后遗留的4 m厚的人工假顶，为简化模拟过程，对人工假顶上层的充填体进行简化。中段之间自下而上开采，按分层逐一开挖，每次开采为一个分层高度4 m，采后即充，共模拟5个分层。模型最大主应力为23.025 MPa，最小主应力为13.562 5 MPa，垂直应力为17.42 MPa。
2.2.1　模拟结果
开挖第一分层至第五分层最大沉降位移、最大主应力和最小主应力模拟结果分别见表3至表5。
2.2.2　开挖第五分层稳定性分析
选择开挖第五分层时，不同点柱尺寸下的采场位移、最大主应力、最小主应力云图（见图3至图5）进行稳定性分析。
（1）位移分析。根据图3可知，开挖第五分层时，4种方案采场的顶板均会受到上覆岩体的重力作用发生沉降位移，随着点柱尺寸的增大，位移逐渐减小，沉降位移分别为18.69 mm、18.58 mm、16.64 mm和14.91 mm。
（2）最大主应力分析。由图4可知，在开挖第五分层时，采场中的点柱受压应力作用效果明显，并且点柱中部存在显著的压应力集中，尤其是位于采场中部的点柱受到应力集中的效果更为明显，随着矿柱尺寸增大采场中点柱受应力集中影响越小。4种方案下点柱所受最大压应力分别为72.81 MPa、70.28 MPa、66.29 MPa和65.31 MPa，采场中部采空区受上覆岩体及人工假顶的影响，所受拉应力最大值分别为0.29 MPa、0.23 MPa、0.25 MPa和0.25 MPa, 其中6 m×6 m点柱尺寸方案点柱所受压应力最小，采场相较于其他 3 个方案更为稳固。
（3）最小主应力分析。由图5可知，开挖第五分层时，采场顶板、底板以拉应力为主，随着矿柱尺寸增大受应力集中影响越小。4种方案下采场最大拉应力分别为0.526 0 MPa、0.523 3 MPa、0.493 0 MPa和0.476 9 MPa。
3　点柱尺寸优选
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3.1　判断采场失稳的方法
当岩石受到超出其极限的压力时，会发生破裂，丧失其原有的承载能力，地下工程进行施工时，面临多重不确定性因素，特别是在复杂地压环境中，仅依据岩石强度准则判断岩体稳定性并不完全可靠。为提升判断准确性，需根据岩石强度破坏准则结合其他方法进行综合评估。
采场内顶底板的自然沉降与鼓起量，对于评判采场稳定性至关重要。长期矿山开采经验表明，位移量与采场稳定性紧密相关：当位移量控制在2 cm 以内时，采场稳定性基本不受影响；若位移量达到2~10 cm，采场则可能出现失稳迹象；一旦位移量超过10 cm，岩体将遭受严重破坏，导致采场垮塌。这些经验性的判断依据可为采场稳定性的评估提供重要参考。
3.2　方案对比
根据表3可知，4种点柱尺寸方案在开挖前四个分层时的最大位移量均小于2 cm，因此在开挖前四个分层的情况下，采场不会发生失稳。但4 m×6 m与5 m×5 m两方案开挖第五分层时最大位移量均接近采场失稳前所能承受的极限位移量，因此这两个方案不能很好地保障采场稳定。5 m×6 m与6 m×6 m两种点柱尺寸方案，采场顶板最大位移量均在采场所能承受的极限位移量之内，可保障采场安全生产。
根据表4可知，点柱尺寸越大，采场所受压应力越小，随着分层逐步开挖，充填采场所受压应力不断减小，其中4 m×6 m点柱与5 m×5 m点柱尺寸方案下采场所受压应力相差不大，5 m×6 m点柱尺寸方案下的压应力随分层的逐步开采再充填不断减小，其压应力最大值为66.29 MPa。6 m×6 m点柱尺寸方案所受压应力最小。综合考虑，5 m×6 m点柱方案和6 m×6 m点柱方案均处于稳定状态，可保障采场安全生产。
根据表5可知，随着点柱尺寸的增大，采场所受拉应力影响减少。通过模拟结果可知，开挖第一分层至第五分层时，采用4 m×6 m与5 m×6 m两种长方形的点柱尺寸方案时采场所受最大拉应力变化程度小于采用5 m×5 m与6 m×6 m两种正方形点柱尺寸方案。随着开挖分层数的增加，同一种点柱尺寸下拉应力作用效果不断增加，点柱尺寸4 m×6 m与点柱尺寸5 m×5 m两方案采场开挖第五分层所受最大拉应力相较于开挖第四分层分别增加了0.016 MPa、0.011 5 MPa。点柱尺寸5 m×6 m与点柱尺寸6 m×6 m两方案采场开挖第五分层所受最大拉应力相较于开挖第四分层分别增加0.009 4 MPa、0.015 3 MPa。根据采场失稳判据可知，开挖至第四分层时，4 m×6 m与5 m×5 m点柱方案超出采场所能承受最大拉应力。5 m×6 m与6 m×6 m采场所受拉应力均未达到极限状态，两种方案下的采场均为稳定状态。
综合上述模拟结果分析，首先排除4 m×6 m与5 m×5 m两种点柱尺寸方案。同时，考虑到长方形点柱的优化效果明显好于正方形点柱的优化效果，在5 m×6 m与6 m×6 m两种点柱方案中进一步优选5 m×6 m的点柱方案。采用此方案既能保障开采工作的安全进行，又能减少资源损失量。
4　结论
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本文以云南省某铜矿Ⅰ号铜矿体400 m中段的最后一个分段为研究对象，针对现采用点柱式水平上向分层充填法开采，分段的顶部存在500 m中段首采分层结束后充填形成的人工假顶的问题，基于FLAC3D模拟软件，通过工程类比法，制定出四种人工假顶下的点柱尺寸方案，构建相应的采场模型进行模拟分析，得出如下结论。
（1）通过对最大、最小主应力模拟结果进行分析可知，点柱尺寸越大，采场所受力的作用越小；通过对比开挖第一分层至第五分层各方案所受最大拉应力增加量可知长方形点柱的优化效果明显好于正方形点柱的优化效果。
（2）根据采场失稳判据可知，开挖至第四分层时，4 m×6 m与5 m×5 m点柱方案所受最大主应力为：69.85 MPa、68.15 MPa，超出采场所能承受的最大拉应力，因此两方案排除。采用5 m×6 m与6 m×6 m采场所受拉应力均未达到极限状态，两种方案下的采场均为稳定状态，其中6 m×6 m点柱拉应力最小，5 m×6 m点柱方案也处于稳定状态，可保障采场安全生产，但考虑到矿柱尺寸越大，采场的损失率越高，为提高资源回采率，决定选用点柱尺寸为5 m×6 m的方案，该参数为矿山的采场试验提供了参考借鉴。
基金
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  • 国家自然科学基金项目(52174114)
文献
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2025年第45卷第1期
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  • 接收时间：2024-09-30
  • 首发时间：2026-10-29
  • 出版时间：2025-01-25
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  • 收稿日期：2024-09-30
基金
国家自然科学基金项目(52174114)
作者信息
    昆明理工大学 国土资源工程学院，云南　昆明　650093

通讯作者:

黄徳镛（1966—），男，贵州遵义人，博士，副教授，主要从事岩土工程、采矿工程方面科研教学工作。E-mail:
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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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