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Article(id=1149738720254935819, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149738718707237637, articleNumber=1003-3033(2024)08-0108-12, orderNo=null, doi=10.16265/j.cnki.issn1003-3033.2024.08.0597, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1708358400000, receivedDateStr=2024-02-20, revisedDate=1716220800000, revisedDateStr=2024-05-21, acceptedDate=null, acceptedDateStr=null, onlineDate=1752048672020, onlineDateStr=2025-07-09, pubDate=1724774400000, pubDateStr=2024-08-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1752048672020, onlineIssueDateStr=2025-07-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1752048672020, creator=13701087609, updateTime=1752048672020, updator=13701087609, issue=Issue{id=1149738718707237637, tenantId=1146029695717560320, journalId=1146031787341344770, year='2024', volume='34', issue='8', pageStart='1', pageEnd='252', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1752048671651, creator=13701087609, updateTime=1756376992009, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1167893010143519453, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149738718707237637, language=EN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1167893010143519454, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149738718707237637, language=CN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=108, endPage=119, ext={EN=ArticleExt(id=1149738720519176972, articleId=1149738720254935819, tenantId=1146029695717560320, journalId=1146031787341344770, language=EN, title=Experimental study on spalling failure of deep hard rock tunnels with different lithology and cross-section shapes, columnId=1149733269173878863, journalTitle=China Safety Science Journal, columnName=Safety engineering technology, runingTitle=null, highlight=null, articleAbstract=

To explore the influence of the lithology and cross-section shape on spalling failure properties of deep hard rock tunnels，indoor true triaxial tests on spalling failure were performed. Firstly，two types of rock samples (marble and granite) and two typical cross-section shapes (high side wall gate arch shape and horseshoe shape) samples in practical applications were selected. Then，the failure characteristics under the influence of different lithology and cross-section shapes were analyzed from the three aspects including spalling failure mode，spalling rock plate characteristics，and the characteristic stress during spalling. Finally，numerical simulation was conducted to explore the corresponding displacement and stress distribution characteristics during the development and propagation of the cracks. Furthermore，the spalling failure characteristics of deep hard rock tunnels were investigated. The results indicated that the slab peeling and opening failure phenomenon for the marble sample was more significant than the granite one in terms of spalling failure mode during the test process. Moreover，the cross-sectional contour range involved in spalling failure for the horseshoe shape sample was smaller than the high-side wall gate arch shape. Different lithologies presented different flaked rock slab shapes for different flaked rock slab characteristics. Compared with the high-side wall gate shape，the flaked rock slabs near the outer layer relevant to the curved wall arch sample were more slender. For the characteristic stress during spalling，the granite sample had a larger threshold at the beginning of the spalling and a faster rate for the evolution process of the spalling failure compared with the marble one. Furthermore，compared with the horseshoe shape sample，the characteristic stresses of the high-side wall gate arch sample were higher from the beginning of plate cracking to the occurrence of obvious plate cracking failure. The area with large displacement in the numerical simulation was mainly observed on the side wall of the hole. The farther away from the side wall，the smaller the displacement. Moreover，the major reason the spalling occurs can be attributed to the tangential stress concentration.

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为探究岩性与断面形状对深部硬岩隧洞板裂失稳特性的影响，开展板裂失稳室内真三轴试验。首先，选择以大理岩和花岗岩为主的2种硬岩试样以及高边墙城门洞形和曲墙拱形2种实际应用中的典型断面形状试样；然后，从板裂失稳形态、剥落岩板(片)特征及板裂特征应力3方面入手，对比分析不同岩性与断面形状影响下的不同破坏特征；最后，利用数值模拟探究围岩板裂裂纹发育扩展过程中相应的位移及应力分布特征，进一步揭示深部硬岩隧洞的板裂失稳特性。结果表明：试验过程中，对于板裂失稳形态，与花岗岩相比，大理岩试样岩板剥落及张开破坏现象更为显著；与高边墙城门洞形相比，曲墙拱形试样板裂破坏涉及的断面轮廓范围更小。对于剥落岩板(片)特征，不同岩性产生不同的剥落岩板形态；与高边墙城门洞形相比，曲墙拱形试样对应的近外层剥落岩板更趋细长。对于板裂特征应力，与大理岩相比，花岗岩试样在板裂开始时的应力门槛值更高，板裂失稳演化进程更快；与曲墙拱形相比，高边墙城门洞形试样从开始出现板裂直至发生明显板裂破坏的特征应力均更高。数值模拟中的位移较大区域集中在孔洞侧壁处，距离侧壁越远，位移相对越小；切向应力集中是导致板裂发生的主要原因。

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李翔 (1977—)，男，湖南沅江人，博士，副教授，主要从事地下工程安全可靠性及灾害风险防控、深部岩石力学与工程等方面的研究。E-mail：。

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李翔 (1977—)，男，湖南沅江人，博士，副教授，主要从事地下工程安全可靠性及灾害风险防控、深部岩石力学与工程等方面的研究。E-mail：。

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李翔 (1977—)，男，湖南沅江人，博士，副教授，主要从事地下工程安全可靠性及灾害风险防控、深部岩石力学与工程等方面的研究。E-mail：。

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Analysis of coal and gas outburst process considering effective stress[J]. 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Physical and mechanical parameters of rock samples

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硬岩种类 单轴抗压强度/MPa 弹性模量/GPa 泊松比 密度/(g·cm-3) 纵波波速/(m·s-1)
大理岩 55.8 91.7 0.21 2.80 4 485
花岗岩 63.7 88.4 0.30 2.61 3 472
), ArticleFig(id=1167877912448479874, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149738720254935819, language=CN, label=表1, caption=

试样材料物理力学参数

, figureFileSmall=null, figureFileBig=null, tableContent=
硬岩种类 单轴抗压强度/MPa 弹性模量/GPa 泊松比 密度/(g·cm-3) 纵波波速/(m·s-1)
大理岩 55.8 91.7 0.21 2.80 4 485
花岗岩 63.7 88.4 0.30 2.61 3 472
), ArticleFig(id=1167877912532365955, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149738720254935819, language=EN, label=Table 2, caption=

l/w ratio of peeled rock plate for various samples

, figureFileSmall=null, figureFileBig=null, tableContent=
试样①:
大理岩+
高边墙城
门洞形		 试样②:
大理岩+
曲墙拱形		 试样③:
花岗岩+
高边墙城
门洞形		 试样④:
花岗岩+
曲墙拱形
2.27 4.09 2.45 3.91
2.50 1.10 1.86 4.60
2.00 1.40 1.73 3.25
1.15 — 1.16 1.55
), ArticleFig(id=1167877912599474820, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149738720254935819, language=CN, label=表2, caption=

不同试样剥落岩板的长宽比(l/w)值

, figureFileSmall=null, figureFileBig=null, tableContent=
试样①:
大理岩+
高边墙城
门洞形		 试样②:
大理岩+
曲墙拱形		 试样③:
花岗岩+
高边墙城
门洞形		 试样④:
花岗岩+
曲墙拱形
2.27 4.09 2.45 3.91
2.50 1.10 1.86 4.60
2.00 1.40 1.73 3.25
1.15 — 1.16 1.55
), ArticleFig(id=1167877912674972293, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149738720254935819, language=EN, label=Table 3, caption=

Comparison of characteristic stress during spalling for various samples

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试样种类 σs /MPa σr /MPa (σr-σs)/MPa σr/UCS
试样①:大理岩+高边墙城门洞形 26.0 41.2 15.2 0.74
试样②:大理岩+曲墙拱形 23.8 32.0 8.2 0.57
试样③:花岗岩+高边墙城门洞形 45.5 47.0 1.5 0.74
试样④:花岗岩+曲墙拱形 43.0 45.7 2.7 0.72
), ArticleFig(id=1167877912733692550, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149738720254935819, language=CN, label=表3, caption=

不同试样板裂特征应力对比

, figureFileSmall=null, figureFileBig=null, tableContent=
试样种类 σs /MPa σr /MPa (σr-σs)/MPa σr/UCS
试样①:大理岩+高边墙城门洞形 26.0 41.2 15.2 0.74
试样②:大理岩+曲墙拱形 23.8 32.0 8.2 0.57
试样③:花岗岩+高边墙城门洞形 45.5 47.0 1.5 0.74
试样④:花岗岩+曲墙拱形 43.0 45.7 2.7 0.72
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不同岩性与断面形状的深部硬岩隧洞板裂失稳试验
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李翔 , 苗森 , 杨博
中国安全科学学报 | 安全工程技术 2024,34(8): 108-119
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中国安全科学学报 | 安全工程技术 2024, 34(8): 108-119
不同岩性与断面形状的深部硬岩隧洞板裂失稳试验
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李翔 , 苗森, 杨博
作者信息
  • 中南大学 资源与安全工程学院，湖南 长沙 410083

    • 李翔 (1977—)，男，湖南沅江人，博士，副教授，主要从事地下工程安全可靠性及灾害风险防控、深部岩石力学与工程等方面的研究。E-mail：。

Experimental study on spalling failure of deep hard rock tunnels with different lithology and cross-section shapes
Xiang LI , Sen MIAO, Bo YANG
Affiliations
  • School of Resources and Safety Engineering，Central South University，Changsha Hunan 410083，China
出版时间: 2024-08-28 doi: 10.16265/j.cnki.issn1003-3033.2024.08.0597
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摘要
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为探究岩性与断面形状对深部硬岩隧洞板裂失稳特性的影响，开展板裂失稳室内真三轴试验。首先，选择以大理岩和花岗岩为主的2种硬岩试样以及高边墙城门洞形和曲墙拱形2种实际应用中的典型断面形状试样；然后，从板裂失稳形态、剥落岩板(片)特征及板裂特征应力3方面入手，对比分析不同岩性与断面形状影响下的不同破坏特征；最后，利用数值模拟探究围岩板裂裂纹发育扩展过程中相应的位移及应力分布特征，进一步揭示深部硬岩隧洞的板裂失稳特性。结果表明：试验过程中，对于板裂失稳形态，与花岗岩相比，大理岩试样岩板剥落及张开破坏现象更为显著；与高边墙城门洞形相比，曲墙拱形试样板裂破坏涉及的断面轮廓范围更小。对于剥落岩板(片)特征，不同岩性产生不同的剥落岩板形态；与高边墙城门洞形相比，曲墙拱形试样对应的近外层剥落岩板更趋细长。对于板裂特征应力，与大理岩相比，花岗岩试样在板裂开始时的应力门槛值更高，板裂失稳演化进程更快；与曲墙拱形相比，高边墙城门洞形试样从开始出现板裂直至发生明显板裂破坏的特征应力均更高。数值模拟中的位移较大区域集中在孔洞侧壁处，距离侧壁越远，位移相对越小；切向应力集中是导致板裂发生的主要原因。

岩性  /  断面形状  /  深部硬岩隧洞  /  板裂失稳  /  真三轴试验

To explore the influence of the lithology and cross-section shape on spalling failure properties of deep hard rock tunnels，indoor true triaxial tests on spalling failure were performed. Firstly，two types of rock samples (marble and granite) and two typical cross-section shapes (high side wall gate arch shape and horseshoe shape) samples in practical applications were selected. Then，the failure characteristics under the influence of different lithology and cross-section shapes were analyzed from the three aspects including spalling failure mode，spalling rock plate characteristics，and the characteristic stress during spalling. Finally，numerical simulation was conducted to explore the corresponding displacement and stress distribution characteristics during the development and propagation of the cracks. Furthermore，the spalling failure characteristics of deep hard rock tunnels were investigated. The results indicated that the slab peeling and opening failure phenomenon for the marble sample was more significant than the granite one in terms of spalling failure mode during the test process. Moreover，the cross-sectional contour range involved in spalling failure for the horseshoe shape sample was smaller than the high-side wall gate arch shape. Different lithologies presented different flaked rock slab shapes for different flaked rock slab characteristics. Compared with the high-side wall gate shape，the flaked rock slabs near the outer layer relevant to the curved wall arch sample were more slender. For the characteristic stress during spalling，the granite sample had a larger threshold at the beginning of the spalling and a faster rate for the evolution process of the spalling failure compared with the marble one. Furthermore，compared with the horseshoe shape sample，the characteristic stresses of the high-side wall gate arch sample were higher from the beginning of plate cracking to the occurrence of obvious plate cracking failure. The area with large displacement in the numerical simulation was mainly observed on the side wall of the hole. The farther away from the side wall，the smaller the displacement. Moreover，the major reason the spalling occurs can be attributed to the tangential stress concentration.

lithology  /  cross-section shape  /  deep hard rock tunnel  /  spalling failure  /  true triaxial test
李翔, 苗森, 杨博. 不同岩性与断面形状的深部硬岩隧洞板裂失稳试验. 中国安全科学学报, 2024 , 34 (8) : 108 -119 . DOI: 10.16265/j.cnki.issn1003-3033.2024.08.0597
Xiang LI, Sen MIAO, Bo YANG. Experimental study on spalling failure of deep hard rock tunnels with different lithology and cross-section shapes[J]. China Safety Science Journal, 2024 , 34 (8) : 108 -119 . DOI: 10.16265/j.cnki.issn1003-3033.2024.08.0597
正文
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0 引言
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目前我国地下空间开发蓬勃发展，与之相关的基础交通、水利水电和矿山能源等多类隧洞工程正逐步向深部推进，进而呈现高应力、大埋深、地质复杂、灾害频发等特点[1-2]。其中，深部硬岩隧洞围岩的脆性板裂破坏是这类工程失稳的重要形式之一[3]，严重阻碍其掘进及后续支护施作的实施，且随埋深的增加极易导致岩爆等安全事故，造成重大人员伤亡和经济损失。因此，深入开展深部硬岩隧洞板裂失稳特性研究具有重要意义。
近些年来，针对深部硬岩板裂失稳问题，学者们从不同途径开展了大量研究，其中，从室内试验模拟这一途径来看，存在2类研究方法： ①针对硬质类实心完整岩块(或相似材料)，开展单轴[4]、双轴[5]及三轴[6]试验，此类试验采用的完整岩块尺寸相对较小，易造成突发性破坏，不利于充分认知板裂失稳的渐进演化全过程，且其主要体现材料自身的破坏，难以反映空间效应对隧洞围岩板裂失稳的影响。 ②为考虑隧洞空间整体特征，针对含孔洞硬岩试样(或相似模型)开展单轴[7]、双轴[8]等形式的先开孔、后加载试验，以及体现卸荷效应的先加载、后开孔试验(如双轴条件下的孔内卸压[9]、孔洞内充填物挖出[10]及配备挖掘[11]或钻孔[12]装置等不同手段)。而针对第 ②类的室内试验研究，为反映深部硬岩隧洞赋存环境下的三维应力状态，在上述单、双轴试验加载形式分别体现一、二维应力状态基础上，须进一步考虑沿隧洞轴向的主应力作用，因此，这类室内试验模拟需从现有单、双轴加载形式逐步拓展至真三轴加载形式。需要指出，在此过程中如能实现模拟开挖卸荷的先加载、后开孔方式，无疑是最具工程合理性的一种理想试验手段，但该方式目前尚很难具备可操作性[13]。为此，现阶段硬岩试样真三轴加载试验研究仍主要借鉴先开孔、后加载的方式。总体而言，近年来有关这方面的研究正处于起步发展阶段，虽已取得长足进步，但仍存在2个方面的不足： ①断面形状作为显著影响隧洞围岩破坏模式的重要因素之一[14]，已有研究着重考虑圆形[15]、椭圆形[16]及矩形[17]等简单常规断面形状，这与工程实际应用中相对复杂的高边墙城门洞形和曲墙拱形等典型断面形状并不完全相符。工程实践表明[18]:对于高边墙和不同曲率拱形区段等关键不利部位，其所在断面轮廓位置应力分布的明显变化将导致裂纹孕育、发展及由此形成的板裂失稳模式与已有试验结果存在较大差异，而当前针对含预制孔洞硬岩试样，尚未见这2种断面形状的真三轴试验研究。 ②岩性作为围岩产生变形破坏的另一主控因素，不同岩性之间物理力学性质存在差异，导致其具有不同的破坏机制[19]，而现有真三轴试验，多采用单一岩性的含预制孔洞硬岩试样，有关不同岩性对深部硬岩隧洞板裂失稳影响程度差异性的研究亦很少涉及。
鉴于此，笔者拟综合考虑岩性与断面形状这2类显著影响深部硬岩隧洞板裂失稳模式的重要因素，针对不同岩性与断面形状相互组合形成的不同试样，开展室内真三轴试验模拟，分析试验过程及各自呈现的不同破坏特征，进而探究围岩板裂裂纹发育扩展过程中相应的位移及应力分布特征，以期深化对深部硬岩隧洞板裂失稳特征的研究。
1 板裂失稳试验方案设计
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1.1 不同岩性与断面形状的试样制作
在试样制作过程中，选用质地均匀、完整性好的硬岩材料，遵照国际岩石力学与工程学会有关规定[20]加工预制开孔的立方体试样(100 mm×100 mm×100 mm，标准公差≤0.017 5 mm，垂直公差≤0.025 mm)。其中，岩性分别采用大理岩和花岗岩；断面形状分别加工制作成高边墙城门洞形和曲墙拱形的贯穿孔洞。据此针对同种岩性、2种断面以及同种断面、2种岩性的情况，通过岩性与断面形状的相互组合可获得以下4种不同试样。试样 ①:大理岩+高边墙城门洞形；试样 ②:大理岩+曲墙拱形；试样 ③:花岗岩+高边墙城门洞形；试样 ④:花岗岩+曲墙拱形，其断面形状尺寸及试样实物如图1所示。
试验开始前须将以上试样对应的硬岩材料加工制作成尺寸ϕ50 mm×100 mm的圆柱体试件，利用岩石测试系统开展单轴压缩试验。大理岩与花岗岩材料的基本物理力学参数取值(表中数值为同种岩性加工获得若干试样后，取其算术平均值)见表1。
1.2 板裂失稳试验设备与装置
试验加载仪器采用自行研制的岩石真三轴电液伺服试验系统，如图2所示。主要技术参数为：前、后和左、右2个水平方向(X、Y方向)可施加最大荷载2 000 kN，竖直方向(Z方向)可施加最大荷载3 000 kN，这3个方向加载速率为10 N/s~10 kN/s。
在三向应力加载作用下，为便于实时观察、记录试验过程中试样板裂失稳全过程，须配合使用在特殊加工的开孔加载块内安装微型摄像头的视频监控系统，具体设计布置如图3所示。
1.3 具体加载方案
试验加载模拟的初始应力状态参照埋深H为500 m的地应力环境[12，16]，以该埋深为例，依据中国地应力测量结果计算地应力[21]，并设σx、σy、σz分别对应图2b真三轴试验系统中X、Y、Z方向上的应力，且选取X方向为最大水平主应力方向，则分别有σx=17.7 MPa、σy=9.9 MPa、σz=13.5 MPa，将其视为初始应力值。相应地，断面形状分别为高边墙城门洞形和曲墙拱形时的初始应力状态如图4所示(图中箭头表示三向初始应力值对应的作用方向，三向初始应力的具体加载方式如图2b、图3b所示)。
考虑到深部硬岩隧洞围岩受到开挖掘进的影响，原岩应力初始状态被打破，围岩径向应力等迅速卸荷至较低水平，而竖向洞顶部位不断下沉，对围岩具有明显的分级加载作用[22];且为防止试样在持续加载过程中出现整体破坏，故试验加载路径借鉴已有试验[12，17]采用的三向同时加载至初始应力，竖直方向继续加大荷载至某一水平后，实施分级加载并保载的加载路径，如图5所示。其中，当试样加载达到三向初始应力状态后，将X方向由负荷控制(力控制)调整为位移控制，通过限制试样孔洞沿该方向的变形，以模拟平面应变状态。
2 板裂失稳试验过程及结果
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通过视频监控系统实时观察、记录板裂全过程，以下结合时间及应力状态，通过裂纹出现、扩展及贯通，直至岩板(片)发生屈曲张开、剥落等典型监控画面，分别展示前述4种试样的板裂失稳渐进过程，如图6—图9所示。
考虑到论文篇幅限制，以下仅针对图6简要描述试样 ①:大理岩+高边墙城门洞形的板裂失稳渐进过程。从图中可以看出，在初始地应力状态(图6a)下，洞壁完好，初始破坏发生在σz达到20.0 MPa的应力状态(图6b)，此时右下拱脚处后端出现微小岩片的剥落，右侧壁有隆起。当σz=25.0 ~32.5 MPa(图6c—图6e)，右下拱脚处后端出现沿X方向的裂纹，并扩展至中部，导致在此处有小型岩片屈曲张开(图6d)，板裂开始形成，岩片发生剥落；左侧竖直侧壁后端出现竖向裂纹，并伴随左上拱肩、侧壁中部的颗粒弹射，左上拱肩处还出现了小型岩片张开。当σz=35.5 ~39.5 MPa(图6f—图6g)，洞壁破坏主要集中在其左侧，主要形式为裂纹扩展、部分岩板张开及小型岩片剥落；左上拱肩处有裂纹沿X方向从前端延伸至中部(图6f)，同时后端竖向裂纹向上发展，并在左侧壁形成了贯穿前后的裂纹(图6g)，进而导致左侧拱肩处发生岩片屈曲张开。当σz=40.5 ~41.2 MPa(图6h—图6p)，左侧壁整体张开，并在σz=41.0 MPa时整体剥落(图6j)，可观察到洞壁左侧的岩片剥落后，其原位置处仍有薄岩板张开，并发生岩屑与颗粒的滑落、岩板(片)的剥落(图6k—图6m)，其内部甚至还有新发育的薄岩板在层层张开(图6n—图6p)，且在σz=41.2 MPa的保载阶段，这些层层张开的薄岩板之间的间距越来越大，直至发生剥落。从图6p可以看出，左侧壁若干层薄岩板层层剥落；在图6r中还可看到右侧竖直侧壁岩板发生屈曲张开；在图6s中更是进一步出现右上拱肩岩片及碎屑颗粒的滑落，右侧竖直侧壁又有薄岩板张开，此时试样板裂现象十分显著，图6s为试样最终破坏形态。
3 板裂失稳试验结果及对比分析
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3.1 不同岩性与断面形状的板裂失稳形态对比
针对上述4种试样对应的试验前后情形，分别从岩性与断面形状2方面入手，进一步对比分析试验揭示的板裂失稳具体形态。试样左、右侧壁破坏前后、试样整体破坏前及其破坏清理后的对比如图10所示。
3.1.1 同断面不同岩性影响下的板裂失稳形态
由图10可知：对于大理岩和花岗岩2种岩性，当断面形状相同且固定为高边墙城门洞形时，大理岩试样出现8层(图10a中第Ⅳ、Ⅵ图)剥落或张开岩板，而花岗岩试样仅出现3层(图10c中第Ⅳ、Ⅵ图)剥落或张开岩板；当断面形状相同且固定为曲墙拱形时，大理岩试样出现4层(图10b中第Ⅳ、Ⅵ图)剥落或张开岩板，而花岗岩试样同样出现3层(图10d中第Ⅳ、Ⅵ图)剥落或张开岩板。由此可以看出，与花岗岩试样相比，大理岩试样板裂过程中产生的剥落或张开岩板层数相对更多，岩板的剥落及张开破坏现象更为显著，而这一差异在断面形状相同且固定为高边墙城门洞形的试样中体现得更趋明显。
另外，与大理岩试样板裂过程基本呈准静态的破坏现象不同，花岗岩试样在板裂过程中表现出一定的岩爆等动力破坏特征，如图8h、图9d所示岩片及碎屑颗粒出现较为剧烈的喷射，这一现象表明板裂与岩爆等动力破坏特征之间存在相关性。
为进一步阐释大理岩和花岗岩这2种岩性对板裂失稳形态的影响，以下引入弹性应变势能指标[23]，其对应的表达式为：
U = σ 2 c / 2 E
式中：U为弹性应变能，kJ/m3;σc为单轴抗压强度，MPa;E为弹性模量，GPa。
现以岩爆倾向性分类标准[24]为例，判别分析岩爆倾向性，具体如下：
U < 40 k J / m 3 弱 岩 爆 40 k J / m 3 < U ≤ 100 k J / m 3 中 等 岩 爆 100 k J / m 3 < U ≤ 200 k J / m 3 强 烈 岩 爆 U > 200 k J / m 3 极 强 烈 岩 爆
将表1中大理岩试样对应的σc=55.8 MPa、E=91.7 GPa，花岗岩试样对应的σc=63.7 MPa、E=88.4 GPa，代入式(1)，可得试验所用大理岩和花岗岩的弹性应变能U分别为17、23 kJ/m3。与式(2)对比可知：二者对应的U小于40 kJ/m3，虽都对应弱岩爆，但大理岩试样对应的弹性应变能(17 kJ/m3)小于花岗岩试样对应的弹性应变能(23 kJ/m3)，表明大理岩试样的岩爆倾向性程度相对低于花岗岩试样，这与图6—图9所示大理岩板裂过程中基本呈准静态破坏，而花岗岩试样则表现为岩片及碎屑颗粒较剧烈喷射等动力破坏特征(图8h和图9d)的弱岩爆试验现象相符，表明岩性是影响板裂失稳形态的重要因素。
3.1.2 同岩性不同断面影响下的板裂失稳形态
在同种岩性条件下，从2种断面形状方面来看，曲墙拱形试样板裂破坏涉及断面轮廓范围较为有限，因应力集中在拱脚或拱肩弧度变化处产生V型槽(图10b、图10d中第V图)。与之相比，高边墙城门洞形试样对应的V型(或弧形)槽(图10a、图10c中第V图)涉及断面轮廓范围更广。从板裂破坏几乎覆盖整个侧壁的角度看，根据图1所示试样断面形状尺寸数据，高边墙城门洞形、曲墙拱形断面形状轮廓周长分别为147、162 mm，侧壁长度分别为70、42 mm，这2种断面形状对应的试样侧壁占其断面周长的比例分别为48%、26%，与曲墙拱形相比，高边墙城门洞形在这方面的占比明显更高，这在一定程度上可视为板裂破坏所涉断面轮廓范围大小的影响原因。
另外，当岩性相同且固定为大理岩时，高边墙城门洞形试样在左右两侧直壁产生约8层剥落或张开岩板(图10a中第Ⅳ、Ⅵ图)，而曲墙拱形试样产生约4层剥落或张开岩板(图10b中第Ⅳ、Ⅵ图)，表现为高边墙城门洞形试样的剥落及张开破坏现象更趋显著。
3.2 不同岩性与断面形状的剥落岩板特征对比
试验完成后，对4种试样板裂过程中剥落的岩板(片)及碎屑分别进行整理归类，标注出整体性较好的部分岩板(片)尺寸，如图11所示。其中，l为长度(X方向长度)，w为宽度(Z方向高度)。相应地，4种试样各自标注尺寸岩板(片)的长宽比(l/w)值见表2。
3.2.1 同断面不同岩性影响下的剥落岩板特征
当断面形状相同且固定为高边墙城门洞形时，对于大理岩试样(图11a)，其侧壁外层剥落的岩板尺寸大、整体性好，沿X方向长度约为10 cm，为侧壁整体剥落，呈楔形状；对于花岗岩试样(图11c)，剥落的外层岩板X方向长度减小为7.6 cm，呈几何不规则形状，剥落的外层岩板在Z方向上的最大宽度也由大理岩中的4.4 cm减小为3.1 cm，尺寸明显缩小，但由表2可以看出，二者的(l/w)值较接近，分别为2.27、2.45。当断面形状相同且固定为曲墙拱形时，对于大理岩试样(图11b)，侧壁外层岩板剥落形状为纺锤形，而对于花岗岩试样(图11d)，则呈现为楔形，但这二者对应l和w的量测值几乎一致，其(l/w)值同样较接近，分别为4.09、3.91。
由图11还可看出，4种试样对应的剥落岩板(片)与孔端侧壁距离(Y方向)越远，板裂剥落岩板(片)尺寸相对越小，表明在远离孔端侧壁方向上，剥落岩板(片)尺寸渐趋变小，再结合表2数据，可观察到形状也更趋粗短。另外，试验过程中板裂剥落的岩板(片)形态主要有直板状、楔形板状、“中间厚、边缘薄”的岩板、弧形片状及不规则的薄片状结构，并出现由裂纹分割成多层薄片但相互间并未分离的组合岩板，剥落岩板表面均较光滑。剥落岩板(片)的部分典型形态如图12所示。由图12可知：典型形态可分为“中间厚、边缘薄”的大理岩岩板、大理岩组合岩板、花岗岩组合岩板及花岗岩弧形岩板。该试验结果与现场若干深部隧洞岩板(片)的实际主要形态符合较好。
3.2.2 同岩性不同断面影响下的剥落岩板特征
在同种岩性条件下(大理岩试样)，当断面形状为高边墙城门洞形时(图11a)，剥落岩板中有2片长度分别为10、9 cm的楔形薄岩板，它们是在前后贯通的裂纹作用下侧壁整体屈曲张开后发生的剥落；与之相比，断面形状为曲墙拱形(图11b)时对应的剥落岩板(片)尺寸稍小，形态也有明显不同。在同种岩性条件下(花岗岩试样)，以上2种断面形状(图11c—图11d)各自对应的剥落岩板(片)长度、形态等亦存在明显差异。
对比表2中不同断面形状对应剥落岩板(片)的长宽比(l/w)，并结合图11可看出，对于尺寸较大、整体性较好的剥落岩板(取l≥4 cm)，(l/w)值在曲墙拱形中要显著大于高边墙城门洞形，前者取值为3.25~4.60，后者取值为1.73~2.50，这表明与高边墙城门洞形相比，曲墙拱形试样剥落的近外层岩板更趋细长(图11b、图11d)。
3.3 不同岩性与断面形状的板裂特征应力对比
在上述试验过程中，板裂开始及明显板裂破坏等现象的出现是板裂渐进演化的关键阶段，针对此类关键阶段，通过视频监控系统开展实时观测，可将获取的竖向应力视为特征应力[8]。基于此，现将试样板裂开始出现及形成明显板裂破坏时对应的应力水平视为特征应力，分别记作σs和σr，其取值可由图6—图9中的相应阶段确定。其中，σs取为岩板(片)发生屈曲张开时的应力值[8]，又因试验通常加载至试样发生显著板裂破坏时即开始卸载，故σr取为最大加载应力值，它们各自具体的取值情况见表3。在此基础上，参照远场最大主应力与岩石单轴抗压强度(Uniaxial Compression Strength，UCS)的比值(即脆性破坏评价指标)[25]判别硬岩隧洞围岩的脆性破坏程度(如少量片帮或岩板剥落、严重片帮及中等岩爆、剧烈岩爆)，文中采用σr与试验所用大理岩试样和花岗岩试样UCS(表1)的比值(σr/UCS)这一类似形式，见表3。
3.3.1 同断面不同岩性影响下的板裂特征应力
对于花岗岩和大理岩2种岩性，从表3可知：花岗岩试样板裂开始的特征应力σs分别为45.5 MPa(高边墙城门洞形)和43.0 MPa(曲墙拱形)，均显著大于同等条件下大理岩试样σs对应的26.0 MPa和23.8 MPa，说明岩性对板裂开始出现时的σs有较大影响，表现为大理岩试样在σs相对较低时即可出现板裂，其应力门槛明显低于花岗岩试样；进一步对比表3中花岗岩试样和大理岩试样这二者出现明显板裂破坏时的特征应力σr，以及特征应力差(σr-σs)，其中，大理岩试样对应的(σr-σs)分别为15.2(高边墙城门洞形)和8.2 MPa(曲墙拱形)，均显著大于同等条件下花岗岩试样对应的1.5和2.7 MPa，表明从板裂开始出现直至发生明显板裂破坏，花岗岩试样的板裂失稳进程显著快于大理岩试样；且从表3中的比值(σr/UCS)可看出，当断面形状相同且固定为曲墙拱形时，与大理岩试样对应的比值(=0.57)相比，花岗岩试样对应的比值(=0.72)相对偏大，表明花岗岩试样的脆性破坏程度更为显著，可能出现更趋剧烈的动力破坏特征(如图9d中岩片及碎屑颗粒的喷射)，这与围岩脆性破坏程度随该比值的增大而逐渐加剧的趋势[25]是一致的。
3.3.2 同岩性不同断面影响下的板裂特征应力
在同种岩性条件下，从断面形状这方面看，由表3可知：相较于曲墙拱形试样，高边墙城门洞形试样(无论是大理岩还是花岗岩)从板裂开始出现对应的σs至发生明显板裂破坏对应的σr均相对较大，其中，σr的差异在岩性相同且固定为大理岩时更为显著，其对应试样发生明显板裂破坏的σr差值达到最大(即有41.2-32.0=9.2 MPa)，表明高边墙城门洞形试样从开始出现板裂直至发生明显板裂破坏的门槛要求均高于曲墙拱形试样；对比表3中的比值(σr/UCS)可以看出，与曲墙拱形试样相比(无论是大理岩还是花岗岩)，高边墙城门洞形试样对应的比值均相对更大，其中，当岩性相同且固定为大理岩时，以上2种断面形状对应(σr/UCS)的差值达到最大(即为0.74-0.57=0.17)，表明相较于曲墙拱形试样，高边墙城门洞形试样的脆性破坏程度更趋剧烈，这与图10a—图10b中的高边墙城门洞形与曲墙拱形试样之间呈现出的破坏对比状况一致。
4 板裂失稳数值模拟结果及分析
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在探究板裂失稳的力学原理或内在机制方面，特别是针对以圆形或椭圆形隧洞为代表的简单常规断面轮廓，现有研究可基于经典弹塑性理论方法构建圆形[8]或椭圆形[16]孔洞的位移及应力解析解模型。但对于高边墙城门洞形与曲墙拱形等具有不同曲率区段的不规则断面轮廓，因其孔洞周边围岩位移、应力等分布情况的复杂性，导致当前应用于圆形或椭圆形孔洞的这类理想解析解模型不再适用，因此，从数值模拟方法入手寻求该问题的解决方式是现阶段致力研究的方向。
考虑到基于颗粒流分析程序(Particle Flow Code，PFC)的离散元数值模拟在探究岩石类材料变形破裂的细观演化方面具备较好适用性[28]，因此，在以上基于宏观现象的板裂失稳试验基础上，进一步通过PFC数值模拟从细观尺度开展初步研究。注意到在前述试验研究中，将图1中4种不同试样加载至初始应力水平后，沿孔洞断面轴线方向(即X方向)由负荷控制调整为位移控制(图5)，通过约束该方向变形，以模拟平面应变状态。相应地，文中PFC数值模拟同样以这4种不同试样为研究模型开展分析。限于论文篇幅，在此仅展示部分数值模拟结果并作简要分析。
4种不同模型在板裂失稳过程中裂纹发展呈“V型”或弧形分布时的位移云图与切向应力云图如图13和图14所示。由图13可以看出，一是位移较大的黑色区域均集中在模型孔洞侧壁处，其边界与“V型”(或弧形)裂纹发育带基本重合，表明该区域围岩已发生板裂，正逐渐剥离直至张开，最终形成“V型”(或弧形)槽；二是在模型水平方向(即Y方向)距离侧壁越远，颜色从黑色渐趋转为灰色，直至变成白色，表明其位移越小。进一步观察图13可知：在同种断面条件下，与大理岩对应模型相比(图13a、图13b)，花岗岩对应模型(图13c、图13d)白色及浅灰色区域的面积均相对较小，表明在裂纹呈“V型”(或弧形)分布、围岩发生板裂失稳破坏时，花岗岩对应模型的位移要大于大理岩对应模型的位移；另一方面，在同种岩性条件下，与曲墙拱形对应模型相比(图13b、图13d)，高边墙城门洞形对应模型(图13a、图13c)的黑色区域面积明显更大、破坏涉及的断面轮廓范围更广，该特征与前述室内试验模拟现象总体上是相符的(图10)。由图14可知：切向应力相对集中区域(黑色部分)在孔洞侧壁水平方向上均呈多个“V型”条带分布，其范围由贴合裂纹发育带与张开岩板轮廓到围岩深处均有分布，条带之间存在一定的间距，表明侧壁发生板裂出现张开后，板裂失稳仍沿水平方向逐步向侧壁深处扩展，在应力的持续作用下，最终能够形成与试验结果相符的岩板层层张开及剥落现象，同时亦进一步印证了切向应力集中是板裂发生的主要原因[8]。
5 结论
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1) 不同岩性与断面形状的板裂失稳形态对比表明：在同断面不同岩性影响下，与花岗岩相比，大理岩试样板裂过程中产生的剥落或张开岩板层数更多，岩板剥落及张开破坏现象更趋显著；在同岩性不同断面影响下，与曲墙拱形相比，高边墙城门洞形试样板裂破坏涉及的断面轮廓范围更大。
2) 不同岩性与断面形状的剥落岩板特征对比表明：在同断面条件下，不同岩性对剥落岩板形态的影响不同，但对尺寸较大、整体性较好的剥落岩板的长宽比影响不明显；在同岩性条件下，不同断面形状显著影响近外层剥落岩板的长宽比，其比值在曲墙拱形试样中明显大于高边墙城门洞形试样。
3) 不同岩性与断面形状的板裂特征应力对比表明：在同断面不同岩性影响下，与大理岩相比，花岗岩试样在板裂开始时的应力门槛值更高，板裂失稳演化进程更快；在同岩性不同断面影响下，与曲墙拱形相比，高边墙城门洞形试样从开始出现板裂直至发生明显板裂破坏时的特征应力均更高。
4) 数值模拟结果对应的位移云图表明：在同断面不同岩性影响下，与大理岩相比，花岗岩模型发生板裂失稳破坏时的围岩位移更大；在同岩性不同断面形状影响下，与曲墙拱形相比，高边墙城门洞形模型产生较大位移的面积更大且涉及的断面轮廓范围更广。应力云图表明：板裂失稳沿模型侧壁水平方向逐步向围岩深处扩展，直至形成与试验结果相符的岩板层层张开及剥落现象。
基金
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  • 国家自然科学基金(51874354)
  • 国家自然科学基金(52074350)
文献
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2024年第34卷第8期
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doi: 10.16265/j.cnki.issn1003-3033.2024.08.0597
  • 接收时间：2024-02-20
  • 首发时间：2025-07-09
  • 出版时间：2024-08-28
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  • 收稿日期：2024-02-20
  • 修回日期：2024-05-21
基金
国家自然科学基金(51874354)
国家自然科学基金(52074350)
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    中南大学 资源与安全工程学院，湖南 长沙 410083
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2种不同金属材料的力学参数
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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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