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Article(id=1322164938815157082, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322164760943116291, 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=1736352000000, receivedDateStr=2025-01-09, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793158286049, onlineDateStr=2026-10-28, pubDate=1766592000000, pubDateStr=2025-12-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793158286049, onlineIssueDateStr=2026-10-28, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793158286049, creator=13701087609, updateTime=1793158286049, updator=13701087609, issue=Issue{id=1322164760943116291, tenantId=1146029695717560320, journalId=1225396423026438145, year='2025', volume='45', issue='12', pageStart='1', pageEnd='302', issueExtLink='null', onlineDate='null', pubDate='1766592000000', pubDateStr='2025-12-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793158243641, creator='13701087609', updateTime=1793158929367, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1322167637195477357, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322164760943116291, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1322167637199671662, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322164760943116291, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=98, endPage=105, ext={EN=ArticleExt(id=1322164939037455195, articleId=1322164938815157082, tenantId=1146029695717560320, journalId=1225396423026438145, language=EN, title=Stability Analysis of Jointed Rock Slopes with Different Protective Measures, columnId=null, journalTitle=Mining Research and Development, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to quantify the effects of different protective measures on the stability of jointed rock slopes, the Particle Flow Code in two-dimensions (PFC2D), strength reduction method and failure criterion characterized by a coherent fracture plane were used to reveal the failure characteristics of jointed rock slope when the parameters of contact model have been reduced until the critical rock failure state had occurred. Then the safety factor and microcrack evolution as well as energy dissipation law of jointed slopes under three working conditions including slope-cutting, anchor cable reinforcement and without any protective measures were comprehensively researched. Research shows that when the mechanical parameters have been reduced until the critical rock failure state has occurred, the main failure mode of jointed rock slope is tensile-sliding failure. The slope-cutting measure can partially improve the slope stability, and the anchor cables installed at a zone where is below the joint surface and close to the the intersection of the steeply inclined fracture and the gentle slip surface can significantly improve the slope stability. During the adjustment process to the stable state, the number of microcracks and dissipated energy generated in anchor cable-reinforced slopes are sequentially less than those in slope-cutting slopes and slopes without any protective measures. The research results can provide a reference for the slope engineering in similar open-pit mines.

, authors=Fan XIAO1, Qinwen XIAO1, Bin DAI1, Xiaoshuang LI2, Cheng HUANG1, authorsList=Fan XIAO, Qinwen XIAO, Bin DAI, Xiaoshuang LI, Cheng HUANG, authorCompany=null, correspAuthors=Cheng 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=1322164942745219950, articleId=1322164938815157082, tenantId=1146029695717560320, journalId=1225396423026438145, language=CN, title=不同治理措施条件下含节理岩体边坡稳定性分析, columnId=1226462295417598973, journalTitle=矿业研究与开发, columnName=矿山安全与环保, runingTitle=null, highlight=null, articleAbstract=

为了量化不同治理措施对含节理岩体边坡稳定性的提升效果，采用颗粒离散元软件PFC2D，结合强度折减法，并以贯通性破裂面为失稳判据，从细观力学角度揭示了接触参数折减至临界破坏状态边坡岩体的失稳破裂特征，并深入分析了实施削坡处理、锚索加固措施及未治理三种工况下含节理边坡安全系数、微裂纹演化与能量耗散规律。研究表明：当力学参数劣化至临界破坏状态时，含节理边坡的主要破坏模式为拉裂滑移破坏；采用分台阶削坡处理措施能在一定程度上增强边坡的稳定性能，而在陡倾破裂带和平缓滑移面拟交汇处布设锁定节理面下方岩体的锚索能显著提升边坡的稳定性；锚索加固边坡在调整至稳定状态过程产生的微裂纹数量和耗散能均少于削坡处理边坡和未治理的边坡，且微裂纹主要分布于锚头附近区域。研究结果可为类似不规范开采露天矿山边坡治理提供参考。

, authors=肖繁1, 肖钦文1, 戴斌1, 李小双2, 黄诚1, authorsList=肖繁, 肖钦文, 戴斌, 李小双, 黄诚, authorCompany=null, correspAuthors=黄诚, authorNote=

肖繁（1993—），男，江西吉安人，博士，主要从事矿山岩石力学与数值模拟研究。E-mail：

, correspAuthorsNote=
黄诚（1987—），男，江西吉安人，硕士，副教授，主要从事岩体工程数值模拟研究。E-mail：
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肖繁（1993—），男，江西吉安人，博士，主要从事矿山岩石力学与数值模拟研究。E-mail：

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肖繁（1993—），男，江西吉安人，博士，主要从事矿山岩石力学与数值模拟研究。E-mail：

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Physical and mechanical parameters of the rock and joint

, figureFileSmall=null, figureFileBig=null, tableContent=
类别单轴抗压强度/MPa弹性模量/GPa泊松比黏聚力/kPa内摩擦角/（°）
黑云母花岗岩99.8500.22——
节理———16032
), ArticleFig(id=1322164948248146855, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164938815157082, language=CN, label=表1, caption=

岩石与节理的物理力学参数

, figureFileSmall=null, figureFileBig=null, tableContent=
类别单轴抗压强度/MPa弹性模量/GPa泊松比黏聚力/kPa内摩擦角/（°）
黑云母花岗岩99.8500.22——
节理———16032
), ArticleFig(id=1322164948319450024, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164938815157082, language=EN, label=Table 2, caption=

Microscopic mechanical parameters of the slope particle flow model

, figureFileSmall=null, figureFileBig=null, tableContent=
类别抗拉强度/MPa黏聚力/MPa内摩擦角/（°）摩擦因数接触刚度比接触模量/GPa法向刚度/GPa切向刚度/GPa颗粒半径/m颗粒密度/（g•cm－3）
平行黏结模型2.02.5000.310.55.4————
光滑节理模型2.11.8600.38——22——
颗粒单元————————0.25~0.352.65
), ArticleFig(id=1322164948386558889, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164938815157082, language=CN, label=表2, caption=

边坡颗粒流模型细观力学参数

, figureFileSmall=null, figureFileBig=null, tableContent=
类别抗拉强度/MPa黏聚力/MPa内摩擦角/（°）摩擦因数接触刚度比接触模量/GPa法向刚度/GPa切向刚度/GPa颗粒半径/m颗粒密度/（g•cm－3）
平行黏结模型2.02.5000.310.55.4————
光滑节理模型2.11.8600.38——22——
颗粒单元————————0.25~0.352.65
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不同治理措施条件下含节理岩体边坡稳定性分析
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肖繁 1 , 肖钦文 1 , 戴斌 1 , 李小双 2 , 黄诚 1
矿业研究与开发 | 矿山安全与环保 2025,45(12): 98-105
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矿业研究与开发 |矿山安全与环保 2025 , 45 (12) : 98 -105
不同治理措施条件下含节理岩体边坡稳定性分析
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肖繁1 , 肖钦文1, 戴斌1, 李小双2, 黄诚1
作者信息
  • 1.吉安职业技术学院 智能建造学院，江西 吉安市　343000
  • 2.齐鲁理工学院 土木工程学院，山东 济南　250200
通讯作者:
黄诚（1987—），男，江西吉安人，硕士，副教授，主要从事岩体工程数值模拟研究。E-mail：
作者简介:

肖繁（1993—），男，江西吉安人，博士，主要从事矿山岩石力学与数值模拟研究。E-mail：

Stability Analysis of Jointed Rock Slopes with Different Protective Measures
Fan XIAO1 , Qinwen XIAO1, Bin DAI1, Xiaoshuang LI2, Cheng HUANG1
Affiliations
  • 1.School of Intelligent Construction, Ji'an College, Ji'an, Jiangxi 343000, China
  • 2.School of Civil Engineering, Qilu Institute of Technology, Jinan, Shandong 250200, China
出版时间: 2025-12-25
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摘要
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为了量化不同治理措施对含节理岩体边坡稳定性的提升效果，采用颗粒离散元软件PFC2D，结合强度折减法，并以贯通性破裂面为失稳判据，从细观力学角度揭示了接触参数折减至临界破坏状态边坡岩体的失稳破裂特征，并深入分析了实施削坡处理、锚索加固措施及未治理三种工况下含节理边坡安全系数、微裂纹演化与能量耗散规律。研究表明：当力学参数劣化至临界破坏状态时，含节理边坡的主要破坏模式为拉裂滑移破坏；采用分台阶削坡处理措施能在一定程度上增强边坡的稳定性能，而在陡倾破裂带和平缓滑移面拟交汇处布设锁定节理面下方岩体的锚索能显著提升边坡的稳定性；锚索加固边坡在调整至稳定状态过程产生的微裂纹数量和耗散能均少于削坡处理边坡和未治理的边坡，且微裂纹主要分布于锚头附近区域。研究结果可为类似不规范开采露天矿山边坡治理提供参考。

边坡稳定性  /  强度折减  /  锚索加固  /  削坡  /  数值模拟

In order to quantify the effects of different protective measures on the stability of jointed rock slopes, the Particle Flow Code in two-dimensions (PFC2D), strength reduction method and failure criterion characterized by a coherent fracture plane were used to reveal the failure characteristics of jointed rock slope when the parameters of contact model have been reduced until the critical rock failure state had occurred. Then the safety factor and microcrack evolution as well as energy dissipation law of jointed slopes under three working conditions including slope-cutting, anchor cable reinforcement and without any protective measures were comprehensively researched. Research shows that when the mechanical parameters have been reduced until the critical rock failure state has occurred, the main failure mode of jointed rock slope is tensile-sliding failure. The slope-cutting measure can partially improve the slope stability, and the anchor cables installed at a zone where is below the joint surface and close to the the intersection of the steeply inclined fracture and the gentle slip surface can significantly improve the slope stability. During the adjustment process to the stable state, the number of microcracks and dissipated energy generated in anchor cable-reinforced slopes are sequentially less than those in slope-cutting slopes and slopes without any protective measures. The research results can provide a reference for the slope engineering in similar open-pit mines.

Slope stability  /  Strength reduction  /  Anchor cable reinforcement  /  Slope-cutting  /  Numerical simulation
肖繁, 肖钦文, 戴斌, 李小双, 黄诚. 不同治理措施条件下含节理岩体边坡稳定性分析. 矿业研究与开发, 2025 , 45 (12) : 98 -105 .
Fan XIAO, Qinwen XIAO, Bin DAI, Xiaoshuang LI, Cheng HUANG. Stability Analysis of Jointed Rock Slopes with Different Protective Measures[J]. Mining Research and Development, 2025 , 45 (12) : 98 -105 .
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0　引言
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露天矿山建设和生产过程中，边坡稳定性分析是一项至关重要的工作[1-2]。近年来，由于不规范开采和不良地质环境等因素影响，露天矿山边坡滑坡、垮塌等灾害事故时有发生，给人民群众生命财产安全造成重大损失[3]。为解决边坡灾害事故问题，许多学者对岩体边坡稳定性和破坏特征进行了深入研究。孙书伟等[4]采用底摩擦试验方法分析了不同岩土强度的露天矿山边坡稳定性和破坏机制。王恒恒等[5]对比分析了不同抗剪强度参数测定方法下的露天矿山边坡稳定性差异。赵黎等[6]依据CRITIC-GRA-AHP法的敏感性排序理论探究了某石灰石矿山边坡坡高、最终边坡角等参数对边坡稳定性的影响。刘杨等[7]以含缓倾软弱夹层的石灰石矿山高边坡为研究对象，运用有限元强度折减法深入分析了不同降雨条件下的边坡稳定性。孙东等[8]借助有限元软件PLAXIS2D模拟分析了不同含水量和不同降雨历时对风化砂岩边坡稳定性的影响。WANG J H等[9]通过引入MPM数值方法，建立了一种考虑降雨过程地表径流和渗流作用的边坡模型，并定量分析了边坡的稳定性和变形破坏特征。
为了进一步揭示岩体边坡裂纹扩展演化过程和破坏形式，众多学者将离散单元法应用于边坡工程的稳定性定量评价。周健等[10]以颗粒离散元软件PFC2D为平台，利用强度折减法和重力增加法分析了边坡的安全系数和滑移面，并与有限元和条分法计算结果进行对比，验证了模型的可靠性。王培涛等[11]对颗粒流的强度折减法进行了优化，定量研判了边坡在开挖扰动前后的安全系数和变形破坏特征。CHEN J等[12]通过颗粒离散元模拟和室内声发射试验，深入分析了含水岩质边坡的稳定性特征和阶梯式破坏机制。考虑到不良结构面可能是导致岩体边坡失稳的重要因素[13-15]，贺续文等[16]通过预设裂隙的方式建立了节理岩体边坡颗粒流模型，并分析了不同节理连通率对边坡稳定性和破坏形态的影响。岑夺丰等[17]基于PFC2D平行黏结模型构建块裂反倾巨厚层状岩质边坡模型，研究了岩层倾角、层间裂隙间距等参数对边坡破坏形态、能量耗散演化特征等的影响。
从以往的研究来看，颗粒离散元法在模拟岩体边坡裂纹扩展、变形破坏等方面呈现出显著的优势。然而，前人应用强度折减法来计算边坡安全系数时，大多采用模型颗粒位移的突变特征作为边坡失稳的判定依据，该方法在实际操作中难以精准掌控。此外，不同治理措施对边坡工程稳定性提升的定量评估研究目前鲜有报道。为此，本文借助颗粒离散元软件PFC2D建立含节理的露天矿山岩质边坡模型，运用强度折减法计算边坡安全系数，以模型开始出现贯通性破裂面作为边坡失稳的判据，对露天矿山中含节理边坡的安全系数进行了精确计算。同时，从细观力学角度探究了接触参数折减至临界破坏状态边坡岩体的失稳破裂特征。并以此为基础，对比分析了在削坡、锚索加固措施以及未治理条件下边坡的安全系数、微裂纹演化、能量耗散等特征。研究结果可为不规范开采露天矿山边坡治理提供参考。
1　边坡模型的建立
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广东省某露天开采的建筑用花岗岩矿，矿体主要为黑云母花岗岩，矿山因早期不规范开采，在中部区域形成高陡边坡。矿区内未见明显断裂构造，但节理裂隙较发育。以矿山中部区域坡角较大的边坡剖面作为稳定性分析剖面，在颗粒离散元软件PFC2D中建立边坡岩体数值计算模型，如图1所示。该模型长154 m，宽115 m，共有4个台阶，台阶高度6~34 m，平台宽度4.5~6.8 m，节理面倾角为25°。边坡岩体模型由颗粒单元和接触单元组成，总共生成31 223个颗粒。岩石颗粒的接触模型采用平行黏结模型，而节理面的接触模型选用光滑节理模型。模型只考虑重力作用，为了添加水平方向和竖直方向的位移约束，在模型两侧边界和底部分别设置了刚性墙体单元。根据颗粒离散元法理论，计算模型的细观力学参数与岩石材料的宏观力学参数并没有固定的函数关系，为了获得能够准确反映岩石宏观力学行为的细观力学参数，通常采用的方法是开展单轴、三轴压缩或巴西劈裂等数值模拟试验，不断调整细观力学参数来匹配岩石材料的宏观力学参数[18]。本文采用单轴压缩数值模拟试验来标定边坡岩体的细观力学参数，该过程不作为本文的研究重点，仅列出最终选定的边坡颗粒流模型细观力学参数和岩石与节理的物理力学参数，见表1和表2。
2　边坡稳定性分析
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2.1　边坡安全系数的确定
边坡工程稳定性分析的核心任务是确定边坡的安全系数。安全系数反映的是边坡当前状态相比失稳破坏的临界状态所拥有的安全储备裕量。强度折减法是一种评估边坡安全系数的重要方法，它依据的原理是逐步降低边坡岩体的强度参数，直至系统达到极限平衡状态[10]。该方法与有限元、离散元等数值模拟方法相结合时，能够迅速且直观地计算出边坡的安全系数。因此，本文采用强度折减法来计算边坡的安全系数。对于岩体颗粒流模型，平行黏结接触和光滑节理接触的抗拉强度、黏聚力以及摩擦因数均对岩体的强度有显著影响。这里假设当前状态边坡岩体模型的平行黏结接触抗拉强度σcb、黏聚力cb、内摩擦角θb和光滑节理接触的抗拉强度σcs、黏聚力cs、内摩擦角θs具有相同的安全储备，当逐步折减上述接触模型参数时，存在一组临界参数σ′cb，c′b，θ′b，σ′cs，c′s，θ′s，使得边坡发生失稳破坏，边坡的安全系数F可定义如下：
在评估边坡是否发生失稳破坏方面，前人大多以边坡特征部位颗粒体发生位移突变作为判定依据。然而颗粒位移发生突变的部位往往难以准确把握，且模型在短时间产生大变形后仍有可能维持静力平衡，因此，采用该判据很难精准得出边坡的安全系数。考虑到受结构面影响的岩质边坡破坏形式主要表现为沿特定滑移面发生的剪切破坏，或是结构面倾角过高导致的倾倒破坏，本文选用计算模型开始出现贯通性破裂面作为边坡失稳的判定依据。在建立边坡颗粒流模型以后，按照公式（1）逐步折减抗拉强度σcb等接触参数，随着接触参数的降低，边坡模型收敛速度逐渐放缓，在形成贯通的破裂面后，其失稳破坏程度持续加剧，数值计算再也无法达到收敛状态，进一步验证了将贯通性破裂面作为边坡失稳判定依据的合理性。经计算，得到边坡的安全系数为1.3。
2.2　边坡失稳破坏特征
为了揭示边坡在力学参数劣化后的失稳破坏特征及其控制因素，深入分析接触参数折减至临界破坏状态（即F＝1.3）所对应的边坡岩体细观力学特性，结果如图2所示。
图2（a）展示了边坡内部微裂纹在不同时刻的演变情况，其中红色线段代表拉伸微裂纹，绿色线段代表剪切微裂纹（颜色标识见电子版）。当时间t＝5×104时步时，坡脚和坡体中下部沿节理面每隔一段距离出现一团微裂纹簇，其中坡体中部聚集的微裂纹数量最多，且主要为拉伸微裂纹，该区域的微裂纹沿竖向延伸至坡面，形成第一条陡倾破裂带。随着时间的推移，节理面上微裂纹簇的数量逐渐增加并有相连的趋势，与此同时，延伸至坡面形成的陡倾破裂带数量也相应增加。当t＝2×105时步时，节理面上多个微裂纹簇相连形成平缓的滑移面，在紧邻坡肩的深部区域，出现一条呈圆弧状的陡倾破裂带，该破裂带上微裂纹尤为密集；当t＝4×105时步时，圆弧状陡倾破裂带与沿节理面的平缓滑移面相连接，形成贯通性的主破裂面，而在其左侧的陡倾破裂面以类似方式与平缓滑移面交汇形成多条贯通性的次级破裂面，这些破裂面的存在，使得坡体被切割成了多个条块结构。
图2（b）为边坡颗粒位移随时间的变化情况。当t＝5×104时步时，可观察到节理面以上的岩体颗粒位移明显大于节理面以下的岩体，同时从坡脚至坡顶呈现递减的趋势，说明坡体在沿着节理面缓慢滑移，并且越是接近坡底的岩体滑动速度越快，这可能与下方坡体所承受的重力更大有关。随着时间的推移，节理面上方岩体滑移速率的差异性变得显著，层间颗粒黏结被拉断形成张开的破裂面。随着张拉破裂面数量的增加，坡体被切割成了多个条块结构，这些条块在脱离母岩体的约束后，滑移速率会进一步加快。
图2（c）为边坡颗粒间接触力链随时间的变化情况，接触力的量值可直接反映应力的大小。当t＝5×104时步时，沿节理面每隔一段距离的区域出现应力集中，其中坡体中下部的应力集中程度最为显著，说明在该边坡发生破坏的初始阶段，坡体中下部沿节理面的岩体在抵抗边坡下滑过程起了主要作用。随着时间的延长，应力最为集中的区域逐渐转移到右上方节理面，该区域最大接触力也呈现上涨的趋势。当t＝1×105时步时，最大接触力达到1.2×107 N，而后又随时间的推移逐渐回落。值得注意的是，应力集中转移至坡体中上部的同时，会沿竖向形成“山脊”状的应力高位延展区，当“山脊”内颗粒黏结被拉断，应力随即释放，该区域又转变为接触力缺失区。图2（c）中A点所对应的接触力出现了历史数据的最大值，后期因为颗粒黏结被拉断转变为接触力缺失区，该点恰好位于上述圆弧状陡倾破裂带与平缓滑移面相交汇的位置，这揭示了边坡即将发生贯通破坏之前，A点周边岩体在抵抗边坡失稳破坏过程中起到了至关重要的作用。当t＝4×105时步时，可观察到沿着节理面自上而下，应力集中区域最大接触力呈现由强到弱的趋势，节理面以上岩体由于受到“山脊”状应力高位扩展区域以及接触力缺失区域的影响，整体呈现出一种应力非均匀分布的状态。
由上述分析可知，节理影响下的边坡，在力学参数劣化到临界破坏状态后，会沿着节理面形成平缓滑移面，同时由于坡体滑移速率的差异，出现张拉性的陡倾破裂带，陡倾破裂带和平缓滑移面在克服二者拟交汇区域的最大黏结阻力后，最终形成贯通性的主破裂面。因此，本文的岩质边坡破坏模式为拉裂滑移破坏。
3　边坡安全治理措施研究
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3.1　安全治理措施与安全系数分析
根据《有色金属采矿设计规范》（GB 50771—2012）[19]，对于服务期超过20 a的露天矿山非工作帮边坡，安全系数应达到1.3~1.4，以确保边坡的安全稳定。文中所述高陡边坡在重力作用下基本处于稳定状态，但考虑到矿山爆破产生的振动效应及强降雨天气的潜在威胁，有必要对边坡施加安全治理措施，进一步提升其整体稳定性能。本文依据颗粒流程序PFC2D研究了两种边坡安全治理措施：一是按照矿山开采设计规范，对高陡边坡进行分台阶削坡处理（台阶高度不超过15 m，安全平台和清扫平台分别设置为5 m和7 m），以缓解早期不规范开采引起的边坡角过高问题；二是针对边坡节理面应力集中的问题，采取在坡面布设锚索的加固优化措施，将锚索下端固定在节理面以下的稳定岩层内，从而增强边坡的抗滑能力。如图3所示，边坡计算模型的削坡处理是在原边坡的基础上删除被削岩体范围内的颗粒。对于锚索加固处理的边坡模型，首先需要删除锚索范围内的岩石颗粒，然后生成锚索颗粒，锚索由锚固段、自由段以及锚头三部分组合而成，每部分均由单排颗粒黏结而成。为了确保锚索深入并锚固在节理面以下稳定岩体，设计锚索总长为43 m，其中锚固段5 m，锚索倾角为30°，锚索内部颗粒及锚固段与岩石颗粒间的接触模型均采用平行黏结模型，而自由段与岩石颗粒间的接触模型采用线性模型。从前述边坡破坏过程来看，陡倾破裂带和平缓滑移面相交的区域出现了接触力历史数据的最大值，该区域岩体性质的强弱对能否形成贯通性的主破裂面起到了至关重要的作用。因此，重点选择在该区域范围布设锚索。
在建立削坡处理和锚索加固的边坡模型后，分别按照公式（1）逐步折减岩体和节理的接触参数，直到形成贯通的破裂面且计算无法收敛，最终得到不同治理措施条件下的边坡安全系数，如图4所示。
由图4可知，削坡处理后的边坡安全系数从1.3增加至1.33，而锚索加固后的边坡安全系数却达到了2.8，说明削坡处理能在一定程度上增强边坡的稳定性能，但相比于削坡处理措施，锚索加固在提升边坡稳定性方面展现出更为显著的效果，可能因为其直接作用于节理面上，从而大大降低了节理对边坡岩体的弱化作用。
3.2　不同治理措施条件下边坡微裂纹和能量演化特征
为了进一步掌握边坡在不同治理措施下调整至稳定状态过程累积的损伤与破裂程度，分析了接触参数折减比率为1.29（该条件下边坡最终能达到稳定状态）的边坡模型微裂纹和耗散能特征。假设边坡系统与外界不存在热交换过程，耗散能Ed可通过以下公式进行计算：
式中：Eμ表示模型所有颗粒的滑动摩擦耗能；Eβ表示所有接触阻尼耗能；Eα表示模型局部阻尼耗能。
图5为不同治理措施条件下边坡模型达到稳定时的微裂纹分布情况。从图5可以看出，未治理的原边坡模型在计算收敛前产生了较多微裂纹，主要集中于节理面和连通坡面的陡倾破裂带区域，但未形成贯通性的破裂面。经过削坡处理的边坡产生的微裂纹主要集中于陡倾破裂带上，且此类破裂带的数量较未治理原边坡有所减少，说明削坡处理延缓了微裂纹在节理面上的扩展。值得注意的是，锚索加固的边坡产生的微裂纹数量很少，且主要分布于锚头附近区域，这可能是因为靠近锚头一端的自由段在受到坡体重力作用后首先发生下弯拉伸，导致周边岩体随即产生少量塑性变形，并伴生微破裂，同时将拉力传递至锚固段以下的稳固岩体，从而抵消了坡体重力引起的下滑作用，边坡得以迅速调整至稳定状态。相比于未治理原边坡和削坡处理边坡，锚索加固后的边坡在节理面上几乎很难观察到微裂纹，说明锚索加固技术能够有效防止边坡发生滑移。
图6为不同治理措施条件下边坡模型累计微裂纹数随时间的变化情况。当时间t<3×104时步时，未治理原边坡和削坡处理边坡微裂纹数量的增长十分缓慢，当t>3×104时步后，进入急剧增长阶段，在经历一段时间的快速增长以后，微裂纹的增长速率呈下降趋势。与未治理原边坡相比，削坡处理后的边坡产生微裂纹的持续时间更短，且数量也相对较少，而锚索加固的边坡在系统稳定前产生的微裂纹数量极少，且持续的时间最短。
图7为不同治理措施条件下边坡模型耗散能随时间的变化情况。当时间t<3×104时步时，未治理原边坡和削坡处理边坡耗散能呈现出显著增长趋势，随后增长速率减缓。与累计微裂纹特征相类似，原边坡能量耗散所持续的时间和耗散能总量依次超过削坡处理的边坡和锚索加固边坡。但与之不同的是，耗散能在模型计算的初期阶段已进入快速增长状态，该阶段微裂纹数量仍处于极低水平。这表明，前期耗散能的增长并非主要由微裂纹的萌生扩展所引起的，而可能与岩石内部颗粒间的摩擦作用等因素有关。
4　结论
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（1）对于含节理的露天矿山岩质边坡，采用颗粒离散元软件PFC2D，并结合强度折减法和以贯通性破裂面为标志的判定依据，能够高效且精准地确定边坡的安全系数。
（2）对于含节理的露天矿山岩质边坡，当力学参数劣化到临界破坏状态时的主要破坏模式为拉裂滑移破坏。这种破坏模式涉及沿节理面的平缓滑移面与因坡体滑移速率差异而产生的张拉性陡倾破裂带，两者最终交汇形成贯通性的主破裂面。
（3）对于含节理的露天矿山岩质边坡，采用分台阶削坡处理措施能在一定程度上增强边坡的稳定性能，而在陡倾破裂带和平缓滑移面拟交汇处布设锁定节理面下方岩体的锚索却能显著提升边坡的稳定性。
（4）锚索加固边坡在力学参数劣化后调整至稳定状态过程产生的微裂纹数量和耗散能均少于削坡处理边坡和未治理的边坡，且微裂纹主要分布于锚头附近区域。
基金
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  • 山东省高等学校“青创人才引育计划”项目(鲁教科函〔2021〕51号)
  • 山东省自然科学基金资助项目(ZR2022ME188)
  • 济南市“新高校20条”科研带头人工作室项目(20228108)
  • 吉安职业技术学院高层次人才科研经费项目(25GCC-002)
文献
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2025年第45卷第12期
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  • 接收时间：2025-01-09
  • 首发时间：2026-10-28
  • 出版时间：2025-12-25
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  • 收稿日期：2025-01-09
基金
山东省高等学校“青创人才引育计划”项目(鲁教科函〔2021〕51号)
山东省自然科学基金资助项目(ZR2022ME188)
济南市“新高校20条”科研带头人工作室项目(20228108)
吉安职业技术学院高层次人才科研经费项目(25GCC-002)
作者信息
    1.吉安职业技术学院 智能建造学院，江西 吉安市　343000
    2.齐鲁理工学院 土木工程学院，山东 济南　250200

通讯作者:

黄诚（1987—），男，江西吉安人，硕士，副教授，主要从事岩体工程数值模拟研究。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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