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Article(id=1322594676742402451, 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=1722182400000, receivedDateStr=2024-07-29, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793260743555, onlineDateStr=2026-10-29, pubDate=1737734400000, pubDateStr=2025-01-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793260743555, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793260743555, creator=13701087609, updateTime=1793260743555, 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=71, endPage=78, ext={EN=ArticleExt(id=1322594678768251284, articleId=1322594676742402451, tenantId=1146029695717560320, journalId=1225396423026438145, language=EN, title=Study on Stope Stability in a Lead-Zinc Mine Mined by Sublevel Rock-Cutting Stage Room Method, columnId=null, journalTitle=Mining Research and Development, columnName=null, runingTitle=null, highlight=null, articleAbstract=

A lead-zinc mine adopts the sublevel rock-cutting stage room method to mine a sharply inclined medium-thickness ore body. On the basis of ensuring the stope stability, in order to further improve the benefits of mining, the Mathews stability diagram method was used to analyze the stope stability of the No.I ore body of the mine as the research object. By calculating the stability coefficient and hydraulic radius, the limit span of roof surrounding rock and side wall surrounding rock is 55.79 m and 44 m respectively, which shows that the current span of the mine of 50 m is reasonable. Combined with the calculation results, 9 schemes with different stage heights and roof thicknesses were formulated, and the numerical simulation studies on the stope stability under 9 schemes were carried out using FLAC3D to compare and analyze the maximum principal stresses, the minimum principal stresses, roof displacements, and plastic zone maps of the different schemes. Through the analysis of the simulation results, it is found that the optimization of the roof thickness from 8 m to 7 m and the stage height of 40 m are reasonable parameter combination, which can not only ensure the stope stability, but also improve the profitability of mining.

, authors=Zefeng DUAN1, Deyong HUANG1, Ziyue JIA1, Chenxin PENG1, Kaidong SHI1, Zhiyu CHEN2, authorsList=Zefeng DUAN, Deyong HUANG, Ziyue JIA, Chenxin PENG, Kaidong SHI, Zhiyu CHEN, 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=1322594687848919488, articleId=1322594676742402451, tenantId=1146029695717560320, journalId=1225396423026438145, language=CN, title=某铅锌矿分段凿岩阶段矿房法采场稳定性研究, columnId=1226462294490657775, journalTitle=矿业研究与开发, columnName=采矿与矿山充填, runingTitle=null, highlight=null, articleAbstract=

某铅锌矿采用分段凿岩阶段矿房法开采急倾斜中厚矿体，在保证采场稳定性的基础上，为进一步提高矿山开采的收益，以矿山的Ⅰ号矿体为研究对象，运用Mathews稳定图法对采场稳定性进行分析，通过计算稳定性系数、水力半径，得到顶板围岩和侧帮围岩的极限跨度分别为55.79 m和44 m，说明现在的矿房跨度为50 m是合理的。结合计算结果，制定了不同阶段高度、顶板厚度的9种方案，运用FLAC3D开展9种方案的采场稳定性数值模拟研究，对比分析不同方案的最大主应力、最小主应力、顶板位移和塑性区分布。通过分析模拟结果可知：顶板厚度由之前的8 m优化为7 m，阶段高度为40 m是最佳的参数配置，既可以保证采场稳定，又提高了矿山开采的收益。

, authors=段泽锋1, 黄德镛1, 贾子月1, 彭晨鑫1, 史凯东1, 陈治宇2, authorsList=段泽锋, 黄德镛, 贾子月, 彭晨鑫, 史凯东, 陈治宇, authorCompany=null, correspAuthors=黄德镛, authorNote=

段泽锋（1999—），男，山西朔州人，硕士研究生，主要研究方向为现代采矿理论与工艺。E-mail:

, correspAuthorsNote=
黄德镛（1966—），男，贵州遵义人，博士，副教授，主要从事矿山岩土工程和采矿工程方面的科研教学工作。E-mail:
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段泽锋（1999—），男，山西朔州人，硕士研究生，主要研究方向为现代采矿理论与工艺。E-mail:

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段泽锋（1999—），男，山西朔州人，硕士研究生，主要研究方向为现代采矿理论与工艺。E-mail:

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tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594676742402451, language=EN, label=Table 1, caption=

Q rock mass quality calculation results

, figureFileSmall=null, figureFileBig=null, tableContent=
岩性岩体质量指标RQD值节理组系数Jn节理表面粗糙度系数Jr节理的风化、破碎和胶结程度Ja节理含水状况折减系数Jω应力折减系数SfQ值分级
围岩57.2761.5112.55.7一般
矿体63.0061.5112.56.3一般
), ArticleFig(id=1322594700301808132, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594676742402451, language=CN, label=表1, caption=

Q 值岩体质量计算结果

, figureFileSmall=null, figureFileBig=null, tableContent=
岩性岩体质量指标RQD值节理组系数Jn节理表面粗糙度系数Jr节理的风化、破碎和胶结程度Ja节理含水状况折减系数Jω应力折减系数SfQ值分级
围岩57.2761.5112.55.7一般
矿体63.0061.5112.56.3一般
), ArticleFig(id=1322594700368916997, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594676742402451, language=EN, label=Table 2, caption=

Values of stability coefficient and allowable hydraulic radius

, figureFileSmall=null, figureFileBig=null, tableContent=
暴露面Q′ABCNS
顶板围岩14.317 510.21.002.863 54.24
侧帮围岩14.317 510.26.9619.930 012.25
), ArticleFig(id=1322594700461191686, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594676742402451, language=CN, label=表2, caption=

稳定性系数和允许水力半径的值

, figureFileSmall=null, figureFileBig=null, tableContent=
暴露面Q′ABCNS
顶板围岩14.317 510.21.002.863 54.24
侧帮围岩14.317 510.26.9619.930 012.25
), ArticleFig(id=1322594700536689159, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594676742402451, language=EN, label=Table 3, caption=

Values of mechanical parameters of rock mass

, figureFileSmall=null, figureFileBig=null, tableContent=
岩性密度/(g/cm3)泊松比抗拉强度/MPa变形模量/GPa黏聚力/MPa内摩擦角/(°)体积模量/GPa剪切模量/GPa
围岩2.800.210.279.720.6241.226.753.86
矿体3.520.230.408.100.6531.276.433.14
), ArticleFig(id=1322594700637352456, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594676742402451, language=CN, label=表3, caption=

岩体力学参数值

, figureFileSmall=null, figureFileBig=null, tableContent=
岩性密度/(g/cm3)泊松比抗拉强度/MPa变形模量/GPa黏聚力/MPa内摩擦角/(°)体积模量/GPa剪切模量/GPa
围岩2.800.210.279.720.6241.226.753.86
矿体3.520.230.408.100.6531.276.433.14
), ArticleFig(id=1322594700712849929, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594676742402451, language=EN, label=Table 4, caption=

Simulation schemes of stage height and top column thickness

, figureFileSmall=null, figureFileBig=null, tableContent=
模拟方案顶板厚度/m阶段高度/m
方案一630
方案二640
方案三650
方案四730
方案五740
方案六750
方案七830
方案八840
方案九850
), ArticleFig(id=1322594700779958794, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594676742402451, language=CN, label=表4, caption=

阶段高度以及顶板厚度模拟方案

, figureFileSmall=null, figureFileBig=null, tableContent=
模拟方案顶板厚度/m阶段高度/m
方案一630
方案二640
方案三650
方案四730
方案五740
方案六750
方案七830
方案八840
方案九850
), ArticleFig(id=1322594700868039179, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594676742402451, language=EN, label=Table 5, caption=

Simulation results of stope stability in each scheme

, figureFileSmall=null, figureFileBig=null, tableContent=
编号最大主应力/MPa最小主应力/MPa顶板下沉位移量/ mm顶板鼓起位移量/ mm稳定性
方案一13.680.2656.768.13稳定
方案二14.470.43711.6813.36破坏
方案三15.430.49616.4617.95破坏
方案四13.430.2495.396.56稳定
方案五14.060.3567.479.11稳定
方案六14.990.47313.5315.47破坏
方案七13.110.2274.185.27稳定
方案八13.850.3096.527.86稳定
方案九14.870.42111.7712.89破坏
), ArticleFig(id=1322594701006451212, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322594676742402451, language=CN, label=表5, caption=

各方案模拟结果

, figureFileSmall=null, figureFileBig=null, tableContent=
编号最大主应力/MPa最小主应力/MPa顶板下沉位移量/ mm顶板鼓起位移量/ mm稳定性
方案一13.680.2656.768.13稳定
方案二14.470.43711.6813.36破坏
方案三15.430.49616.4617.95破坏
方案四13.430.2495.396.56稳定
方案五14.060.3567.479.11稳定
方案六14.990.47313.5315.47破坏
方案七13.110.2274.185.27稳定
方案八13.850.3096.527.86稳定
方案九14.870.42111.7712.89破坏
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某铅锌矿分段凿岩阶段矿房法采场稳定性研究
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段泽锋 1 , 黄德镛 1 , 贾子月 1 , 彭晨鑫 1 , 史凯东 1 , 陈治宇 2
矿业研究与开发 | 采矿与矿山充填 2025,45(1): 71-78
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矿业研究与开发 |采矿与矿山充填 2025 , 45 (1) : 71 -78
某铅锌矿分段凿岩阶段矿房法采场稳定性研究
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段泽锋1 , 黄德镛1 , 贾子月1, 彭晨鑫1, 史凯东1, 陈治宇2
作者信息
  • 1.昆明理工大学 国土资源工程学院，云南　昆明　650093
  • 2.贵州能源集团有限公司，贵州　贵阳　550081
通讯作者:
黄德镛（1966—），男，贵州遵义人，博士，副教授，主要从事矿山岩土工程和采矿工程方面的科研教学工作。E-mail:
作者简介:

段泽锋（1999—），男，山西朔州人，硕士研究生，主要研究方向为现代采矿理论与工艺。E-mail:

Study on Stope Stability in a Lead-Zinc Mine Mined by Sublevel Rock-Cutting Stage Room Method
Zefeng DUAN1 , Deyong HUANG1 , Ziyue JIA1, Chenxin PENG1, Kaidong SHI1, Zhiyu CHEN2
Affiliations
  • 1.Faculty of Land Resources Engineering, Kunming University of Science and Technology, Kunming, Yunnan 650093, China
  • 2.Guizhou Energy Group Co., Ltd., Guiyang, Guizhou 550081, China
出版时间: 2025-01-25
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摘要
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某铅锌矿采用分段凿岩阶段矿房法开采急倾斜中厚矿体，在保证采场稳定性的基础上，为进一步提高矿山开采的收益，以矿山的Ⅰ号矿体为研究对象，运用Mathews稳定图法对采场稳定性进行分析，通过计算稳定性系数、水力半径，得到顶板围岩和侧帮围岩的极限跨度分别为55.79 m和44 m，说明现在的矿房跨度为50 m是合理的。结合计算结果，制定了不同阶段高度、顶板厚度的9种方案，运用FLAC3D开展9种方案的采场稳定性数值模拟研究，对比分析不同方案的最大主应力、最小主应力、顶板位移和塑性区分布。通过分析模拟结果可知：顶板厚度由之前的8 m优化为7 m，阶段高度为40 m是最佳的参数配置，既可以保证采场稳定，又提高了矿山开采的收益。

铅锌矿  /  分段凿岩阶段矿房法  /  Mathews稳定图法  /  数值模拟  /  采场稳定性

A lead-zinc mine adopts the sublevel rock-cutting stage room method to mine a sharply inclined medium-thickness ore body. On the basis of ensuring the stope stability, in order to further improve the benefits of mining, the Mathews stability diagram method was used to analyze the stope stability of the No.I ore body of the mine as the research object. By calculating the stability coefficient and hydraulic radius, the limit span of roof surrounding rock and side wall surrounding rock is 55.79 m and 44 m respectively, which shows that the current span of the mine of 50 m is reasonable. Combined with the calculation results, 9 schemes with different stage heights and roof thicknesses were formulated, and the numerical simulation studies on the stope stability under 9 schemes were carried out using FLAC3D to compare and analyze the maximum principal stresses, the minimum principal stresses, roof displacements, and plastic zone maps of the different schemes. Through the analysis of the simulation results, it is found that the optimization of the roof thickness from 8 m to 7 m and the stage height of 40 m are reasonable parameter combination, which can not only ensure the stope stability, but also improve the profitability of mining.

Lead-zinc mine  /  Sublevel rock-cutting stage room method  /  Mathews stability diagram method  /  Numerical simulation  /  Stope stability
段泽锋, 黄德镛, 贾子月, 彭晨鑫, 史凯东, 陈治宇. 某铅锌矿分段凿岩阶段矿房法采场稳定性研究. 矿业研究与开发, 2025 , 45 (1) : 71 -78 .
Zefeng DUAN, Deyong HUANG, Ziyue JIA, Chenxin PENG, Kaidong SHI, Zhiyu CHEN. Study on Stope Stability in a Lead-Zinc Mine Mined by Sublevel Rock-Cutting Stage Room Method[J]. Mining Research and Development, 2025 , 45 (1) : 71 -78 .
正文
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0　引言
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采场稳定性研究涉及多个要素，包括阶段高度、分段高度、矿房跨度、间柱宽度及顶板厚度等[1-2]。在国内外采矿行业中，针对这些参数的优化设计，普遍采用了物理模型试验[3]、经验类比分析、理论解析计算[4]、数值模拟技术[5-9]以及综合评价体系[10-11]等多种方法。
随着计算机技术的发展，数值模拟分析在采场稳定性研究领域的应用越来越多。刘志义等[12]采用FLAC3D构建采场模型，优化某铁矿阶段空场嗣后充填采矿法的采场长度，最终得出在考虑经济效益和巷道未进行支护的情况下，采场长度不宜超过36 m。崔轩等[13]以哈拉孜铁矿为研究对象，采用理论分析与数值模拟相结合的方法，对采场宽度进行模拟分析，分析了不同采场宽度时采动过程的力学特征，最终确定哈拉孜铁矿采场最优宽度为8 m。郭沫川等[14]对分段空场嗣后充填采矿法的底部结构采用数值模拟方法研究，进行了稳定性分析和参数优化，最终推荐回采进路间距为9 m。赵康等[15]以江西某大型钨矿山为工程背景，分析矿柱连续回采胶结充填和矿房连续回采过程中矿岩的变形特征，得出矿房宽16 m、矿柱宽14 m的方案最为合适。
针对某铅锌矿使用的分段凿岩阶段矿房法，重新选取采场结构参数并进行采场稳定性分析，利用Mathews稳定图法计算顶板围岩和侧帮围岩的极限暴露跨度，验证现有设计的矿房跨度合理性，制定出9种不同阶段高度和不同顶板厚度的模拟方案，然后通过数值模拟对不同方案的采场稳定性进行分析，在采场稳定的基础上选择对矿山最经济的方案，确保采场的稳定性和矿山开采的经济性。
1　矿山现状及存在的问题
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1.1　开采技术条件
本文所研究的Ⅰ号铅锌矿床位于白河厂背斜轴部南翼的昆阳群黑山组(Pt1hs)内部，主要赋存在该地层间的裂隙及放射状裂隙系统中，其分布与所在岩层的产状保持一致。Ⅰ号矿体厚度为4.8~16 m，平均10 m左右，矿体倾角为75°~83°，平均80°，锌品位为8%~10%。
1.2　采矿方法
矿山目前采用分段凿岩阶段矿房法开采，如图1所示。
1.2.1　采场结构参数
阶段高度设定为30~60 m，矿房的跨度为50 m，在使用中深孔凿岩机时，通常将分段高度设定在10~15 m范围内。按垂直走向布置，间柱宽度设定为6 m，顶板厚度设定为8 m，以确保整个采场结构的稳定性和安全性。
1.2.2　采切工程
在脉外下盘开掘阶段运输巷道，采场矿块间柱内布置有2个人行材料通风天井，阶段运输巷道与人行材料通风天井之间采用穿脉巷道联通。在人行材料通风天井中每隔9 m垂高开凿分段凿平岩巷道。在阶段运输平巷紧邻矿体下盘的一侧开设漏斗颈状通道，在采场中心部位设立切割天井并使之与分段凿岩巷道相通，在切割天井底部由分段凿岩巷道向矿体上下盘开掘切割横巷，为爆破落矿提供补偿空间。采场底部采用平底式底部结构，沿矿体走向每间隔8 m挖掘装矿巷道连接阶段运输巷道和底部凿岩巷道，用于出矿。
1.2.3　矿块回采
自切割天井开始沿走向分段回采。矿体为中厚矿体，全厚一次性自上而下分段回采，上一分段超前下一分段2~3排炮孔。分段内炮孔采用扇形孔布置方式。
1.2.4　护顶及地压管理
采场爆破后，应首先进行分段凿岩巷道的检查与支护，做好凿岩巷道的支护及管理工作后，再从事回采作业。分段凿岩巷道的支护可采取喷浆支护或锚杆支护方式。
1.3　目前存在问题
矿山现在采用分段凿岩阶段矿房法，初期基于矿山安全及采场稳定性的考量，原设计采用了矿房跨度为50 m，顶板厚度为8 m，阶段高度为40 m的采场结构参数。然而，在实际的生产运营过程中，经过一段时间的监测，发现开挖后的矿房表现出良好的稳固性，这说明原有的采场结构参数可能超出了保障矿房稳定性的最低要求。为了进一步提升矿山的经济效益，确保资源最大化利用，需要对I号矿体的采场结构参数进行优化。
2　基于Mathews稳定图法的极限暴露跨度研究
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2.1　Mathews 稳定图法简介
Mathews图表法是一种源自实践且便于操作的岩石分类体系，能有效展现岩体采场暴露面积形状系数S（水力半径）与稳定性系数N之间的关联性[16-17]。该方法由多位专家共同研究，构建出稳定性图，后经POTVIN等对若干系数进行校准与改进，形成了如今的稳定性图解法[18]。如图2所示，岩石状态被划分为稳定区、不稳定区以及崩落区三大类别。这种方法在采矿行业得到了广泛应用，特别是在地下开掘工程、空场采矿法的设计以及研究崩落法适用性的场合中。通过运用Mathews方法对无支护情况下采场所能承受的最大暴露面积进行了详细的计算和解析，从而为合理优化采场结构参数提供数据支持和理论基础。
2.2　基于Mathews稳定图法的计算
根据现场调查结果，计算得到某铅锌矿围岩和矿体的Q系统分级评分结果见表1。
（1）水力半径。水力半径S的计算公式表述如下：
式中：L1为矿房宽度；L2为矿房长度。
（2）稳定性系数N。稳定性系数N的计算公式为：
式中：Q′代表经过修正后的NGI岩体质量指数；A为岩石应力系数；B为节理产状调整系数；C为重力调整系数。其中Q′的计算公式为：
（3）岩石应力系数A。岩石应力系数通过将岩石的单轴抗压强度Rc除以采场中心线上产生的诱导应力σ1来计算得出的。该系数的取值范围遵循以下规律：
岩石应力系数A的图解如图3所示。
在该矿山中，由于缺乏实地地应力测量数据，只能依据地形地貌特征来进行天然应力的估算。由于该区域的地貌为山岭地形，可以初步假定天然主应力的方向大致遵循山体的自然结构，即接近垂直于地面的应力为主应力，反映山体的重力分量，同时考虑水平应力。
式中：γ为岩体容重；H为岩层厚度；σ1为自重应力；ρ为岩体密度；g为重力加速度。
由矿山提供的相关地质资料可知，1 590 m阶段矿体距离地表140 m，上覆岩层密度取2 900 kg/m3，则计算得出主应力σ1=3.98 MPa,Rc/σ1=20.74>10。
由此得：A=1。
（4）节理产状调整系数 B。节理产状调整系数B是通过对比采矿工作面的倾斜角度与主要节理组的倾斜角度差异来量化评估分析的，具体图解如图4所示。
（5）重力调整系数 C。重力调整系数 C 值可通过公式(6)计算：
式中，α为采场暴露面与水平面之间的角度，(°)。重力调整系数 C 值与采场倾角 α 的图解如图5所示。
2.3　计算结果及分析
冯兴隆等[19]建立了稳定性系数 N 与水力半径 S 之间的函数关系模型。式(7)为描述崩落现象与水力半径之间联系的数学表达式，当获取到某一特定的稳定性系数 N 时，可以通过该公式反推出相应的水力半径 S 值。式(8)则定义了稳定状态转变为破坏状态时的临界条件，借助这个公式，能够准确预测工程结构从稳定状态转变为破坏状态时所需的最小水力半径值。
结合矿山的现场情况，计算得出矿岩稳定性系数与允许水力半径的值见表2。
已知矿房的宽度为矿体的平均厚度(10 m)，根据水力半径计算顶板围岩矿房极限跨度L2:
由式(9)计算得出，顶板围岩矿房极限跨度L2≤55.79 m。
将极限矿房跨度55 m代入式（10），计算侧帮围岩极限矿房跨度L1：
由式(10)计算得出，侧帮极限矿房跨度L1≤44 m。
3　阶段高度的验证与顶板厚度的确定
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3.1　模型构建及模拟方案
采用了FLAC3D软件进行数值模拟分析，基于对岩体的分类，将矿体及其上下盘围岩统一视为坚硬岩体。本研究遵循摩尔-库仑屈服准则。建立的三维模型长460 m、宽80 m、高260 m，设定模型的X轴方向与矿体走向保持垂直，以此为基础，构建一个与矿山真实情况相吻合的三维有限元模型，如图6所示。
结合室内岩石力学试验计算所得的数据，再经过Hoek-Brown强度准则折减成岩体力学参数，具体数值见表3。
为了更有效地优化阶段矿房法下的阶段高度和顶板厚度，采用FLAC3D软件进行数值研究与分析，矿房跨度设定为50 m，间柱跨度设定为6 m。结合分段凿岩阶段矿房法顶板厚度和阶段高度的一般性取值，组合出9种模拟方案（见表4）。
3.2　数值模拟计算结果分析
由于篇幅限制无法展示全部方案的云图，这里仅以方案五（阶段高度40 m，顶板厚度7 m）为例进行最小主应力云图、最大主应力云图、位移云图和塑性区分布云图的分析。
3.2.1　最小主应力
根据图7(a)中垂直矿体走向的最小主应力分布图，可以明显看出矿房区域存在显著的拉应力集中现象，拉应力值在0~0.349 MPa之间，拉应力最大值低于矿体本身的抗拉强度极限，说明采场开挖后能保持稳定。而在图7(b)所示的沿矿体走向的最小主应力云图中可以看出，矿房的顶板、底板以及上下相邻开采阶段间均出现明显的拉应力峰值，其中最大拉应力值约为0.356 MPa。
3.2.2　最大主应力
根据图8(a)中垂直矿体走向的最大主应力分布情况，可以看出开挖后矿房的顶板、底板区域的压应力集中现象十分突出，特别是在底板区域，压应力集中程度更为显著。随着开采深度的增加，下一开采阶段相较于上一阶段的压应力集中现象更为明显。在上一阶段，顶板的最大压应力大约为6 MPa，底板的压应力最大值接近9 MPa；而到了下一阶段，顶板处的压应力增大到9 MPa左右，底板处的最大压应力也提高至13.94 MPa。在图8(b)沿矿体走向的最大主应力云图可进一步验证矿房顶部和底部存在显著的压应力集中现象。在上一阶段，顶板部位的压应力在1~4 MPa范围内变化，底板部位的压应力则在2~5 MPa之间；进入下一阶段后，顶板和底板的压应力范围分别为2~5 MPa和4~6 MPa。就局部压力集中点来看，在上一阶段矿房右上角顶板位置的压应力集中区间为5~8 MPa，左下角底板处的压应力集中范围是7~10 MPa；而到了下一阶段，矿房右上角顶板处的压应力集中值上升至7~10 MPa，而左下角底板处的压应力集中值增大至9~14.06 MPa。
3.2.3　垂直位移
图9(a)沿矿体走向的垂直位移云图研究表明，矿房的顶板、底板以及间柱内部均产生了位移，具体表现为顶板下沉和底板鼓起位置上呈对称分布。其中顶板的最大下沉位移量大约为7.43 mm，底板的最大鼓起位移量则接近9.09 mm。在两个矿房的中间位置，顶板和底板内部也有轻微的位移发生，其范围在3~6 mm之间。由图9(b)垂直矿体走向的垂直位移云图分析可以看出，顶板临近右上方区域和底板接近左下方区域的位移量较为显著，这些位置的位移量表现出一种对称性。顶板的下沉位移在6~7.47 mm之间，底板的鼓起位移则在7~9.11 mm之间。
3.2.4　塑性区分布
如图10(a)所示，通过沿矿体走向的塑性区分布云图可以发现，矿房的顶板和底板出现了拉伸破坏，形成了拉伸塑性区。在两个矿房的顶板和底板之间也出现拉伸破坏现象，但是未出现大面积的贯通破坏。除此之外，矿房底部两端也有局部拉伸破坏的迹象。从图10(b)垂直矿体走向的塑性区分布图中可以发现，两个开采阶段的矿房周围存在大面积拉伸破坏，然而塑性区之间未发生贯通，这表明从塑性变形的角度来看，采场结构仍然处于稳定状态。
3.2.5　综合对比
综合上述各方案的模拟结果，汇总至表5。
从表5中可以得出以下结论。
（1）采场稳定性可以反映出随着阶段高度的增加，顶板厚度对采场稳定性的影响逐渐增大。在阶段高度为30 m的情况下，无论顶板的厚度是6 m、7 m还是8 m，采场均能保持在稳定的工作状态，未出现明显的结构破坏现象。当阶段高度增大至40 m时，当顶板厚度为6 m时，由于受到阶段高度增大的应力影响，采场的稳定性被打破，开始出现破坏迹象；但当顶板厚度增大至7 m或8 m时，采场能够维持其稳定性。进一步将阶段高度提升至50 m后，所有不同顶板厚度条件下的采场均出现了不同程度的破坏，这充分说明在极端条件下，仅依赖增加顶板厚度不足以保障采场的整体稳定性。
（2）从最大主应力分析可以得出，在同一顶板厚度下，随着阶段高度的增加，最大主应力也逐渐增加，这说明阶段高度越高，其对采场地压强度的影响越大；在同一阶段高度下，随着顶板厚度的增加，最大主应力逐渐降低，这表明顶板可以有效减小地压强度的影响。
（3）分析最小主应力数值可以得出，在同一顶板厚度下，随着阶段高度的增加，最小主应力也逐渐增加，直至超过矿体的抗拉强度，造成破坏；在同一阶段高度下，随着顶板厚度的增加，最小主应力逐渐降低，这表明顶板可以有效地减小两个中段间的影响。
（4）分析各个方案的顶板下沉位移量可以发现，在同一顶板厚度下，随着阶段高度的增加，顶板下沉位移量也逐渐增加；在同一阶段高度下，随着顶板厚度的增加，最大主应力逐渐降低，这表明更厚的顶板可以更有效地抵抗下沉。
（5）分析表中各个方案顶板鼓起位移量可以得到，在同一阶段高度下，随着顶板厚度的增加，鼓起位移量减小，这表明厚的顶板可以有效地限制底板鼓起；在同一顶板厚度下，随着阶段高度的增加，鼓起位移量也增加。
因此，为了保证采场的稳定性，结合具体的地质条件和开采工艺等因素，并确保矿山开采的安全性和经济性，最终确定方案五为最佳方案，即顶板厚度为7 m，阶段高度为40 m。阶段高度也与矿山现用的阶段高度相同，模拟结果能够得到验证。
4　结论
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（1）本文首先利用Mathews稳定图法对某铅锌矿的极限暴露跨度进行分析，通过计算稳定性系数N和形状系数S（水力半径HR)，在确保采场开挖后稳定的情况下，计算得到顶板和侧帮的极限跨度分别为55.79 m和44 m，确定了现在采用的矿房跨度为50 m是合理的。
（2）结合Mathews稳定图法计算结果以及阶段高度和顶板厚度的一般性取值，制定9种不同结构参数的模拟方案，采用FLAC3D软件进行数值模拟。分析了在不同的阶段高度与顶板厚度情况下，采场的应力、位移以及塑性区的变化情况，从而评估各方案下采场的稳定性。
（3）通过对模拟结果分析得出，阶段高度越高，越容易导致采场失稳，增加顶板厚度可以加强采场的稳定性。综合考虑最终确定方案五为最佳方案，即顶板厚度为7 m，阶段高度为40 m。该方案既能保证采场的稳定性，又能保证矿山开采的经济性。
基金
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  • 国家自然科学基金资助项目(52174114)
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2025年第45卷第1期
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  • 接收时间：2024-07-29
  • 首发时间：2026-10-29
  • 出版时间：2025-01-25
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  • 收稿日期：2024-07-29
基金
国家自然科学基金资助项目(52174114)
作者信息
    1.昆明理工大学 国土资源工程学院，云南　昆明　650093
    2.贵州能源集团有限公司，贵州　贵阳　550081

通讯作者:

黄德镛（1966—），男，贵州遵义人，博士，副教授，主要从事矿山岩土工程和采矿工程方面的科研教学工作。E-mail:
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
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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