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Article(id=1241409515720069469, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241409507583127593, articleNumber=null, orderNo=null, doi=10.3963/j.issn.1001-487X.2024.04.004, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1706025600000, receivedDateStr=2024-01-24, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773904692821, onlineDateStr=2026-03-19, pubDate=1732982400000, pubDateStr=2024-12-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773904692821, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773904692821, creator=13701087609, updateTime=1773904692821, updator=13701087609, issue=Issue{id=1241409507583127593, tenantId=1146029695717560320, journalId=1240670690148397066, year='2024', volume='41', issue='4', pageStart='1', pageEnd='204', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773904690881, creator=13701087609, updateTime=1773904736091, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241409697262137710, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241409507583127593, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241409697262137711, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241409507583127593, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=25, endPage=34, ext={EN=ArticleExt(id=1241409516080779621, articleId=1241409515720069469, tenantId=1146029695717560320, journalId=1240670690148397066, language=EN, title=Study on Fracture Characteristics and Crack Propagation Features of Fissured Rock Mass based on 3D Printed Samples, columnId=1240702071733801442, journalTitle=Blasting, columnName=THEORETICAL AND TECHNOLOGICAL EXPLORATION, runingTitle=null, highlight=null, articleAbstract=

To study the influence of rock fracture characteristics with different inclination angles, the notched semi-disk bending (NSCB) specimens were prepared based on the 3D printing technology for experiments on typeI static fracture characteristics of rock mass. Specifically, the straight-cut groove half-disc bending specimens (NSCB) with crack angles were prepared by 3D printing technology to investigate the influence of different pre-fabricated crack angles on rock fracture characteristics. Furthermore, the printed specimens were placed in dry ice and subjected to quasi-static three-point bending tests when their surface temperature reached-30℃ after the solidification and baking treatments. The experiment revealed the influence of pre-fabricated crack angles on fracture toughness, initiation angle, and fracture energy. The results show that the average fracture toughness of NSCB specimens containing fissures is smaller than that of standard NSCB specimens. The fracture toughness of specimens is positively correlated with the fissure inclination angle. For NSCB specimens containing fissures, the initiation angle increases with the increase of the fissure inclination angle when β is between 0° and 90°, and the crack propagation path shows a distinct ‘deflection’ phenomenon. The fissure inclination angle significantly impacts the complexity of the NSCB specimen propagation path. The crack propagation path becomes more complex when the fissure inclination angle and fractal dimension increase. From the perspective of fracture energy, the fracture energy increases with the increase of the fissure inclination angle.

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GE Jin-jin (1988-), male, lecturer, engaged in research on deep rock mechanics properties, (E-mail) .
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为探究不同倾角裂隙对岩石断裂特性的影响，本研究基于3D打印技术制备直切槽半圆盘弯曲（NSCB）试件，开展含裂隙岩体Ⅰ型静态断裂特性的试验研究。为探究不同的预制裂隙角度对于岩石断裂特性的影响，本研究基于3D打印技术制备含裂隙倾角的直切槽半圆盘弯曲试件（NSCB），打印好的试件经过固化，烘烤处理后，将其放置在干冰中，待其表面温度达到-30℃时进行准静态三点弯曲试验，该试验揭示了预制裂隙倾角对于断裂韧度、起裂角、断裂能的影响规律。结果表明：含裂隙NSCB试件平均断裂韧度均小于标准NSCB试件，且试件断裂韧度与裂隙倾角成正相关；对于含裂隙的NSCB试件，在β介于0°~90°之间时，起裂角随着裂隙倾角的增大而增大，裂纹拓展路径则表现出明显的“偏折”现象；从断裂破坏的能量角度分析，断裂能随着裂隙倾角的增大而增大。

, correspAuthors=null, authorNote=null, correspAuthorsNote=
葛进进（1988-），男，讲师，从事深部岩石力学特性研究，（E-mail）。
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余雷雷（1993-），男，硕士研究生，从事岩石断裂力学相关研究工作，（E-mail）。

YU Lei-lei (1993-), male, postgraduate student, engaged in research related to rock fracture mechanics, (E-mail) .

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余雷雷（1993-），男，硕士研究生，从事岩石断裂力学相关研究工作，（E-mail）。

YU Lei-lei (1993-), male, postgraduate student, engaged in research related to rock fracture mechanics, (E-mail) .

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余雷雷（1993-），男，硕士研究生，从事岩石断裂力学相关研究工作，（E-mail）。

YU Lei-lei (1993-), male, postgraduate student, engaged in research related to rock fracture mechanics, (E-mail) .

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Static physical and mechanical properties of photosensitive resin

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波速/（m·s-1）密度/（g·cm-3）抗压强度/MPa弹性模量/GPa
1315.81.204751.353
), ArticleFig(id=1241409540390965416, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241409515720069469, language=CN, label=表1, caption=

固化光敏树脂静态物理力学性能

, figureFileSmall=null, figureFileBig=null, tableContent=
波速/（m·s-1）密度/（g·cm-3）抗压强度/MPa弹性模量/GPa
1315.81.204751.353
), ArticleFig(id=1241409541905109170, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241409515720069469, language=EN, label=Table 2, caption=

Calculation results of fracture toughness

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试件编号温度/℃ Pmax/kN KIC/（MPa·m1/2）平均KIC/（MPa·m1/2）
DL-S-1-31.15.022.42 
DL-S-2-30.54.862.322.36
DL-S-3-32.04.962.33 
DL-0°-1-30.53.821.84 
DL-0°-2-31.23.921.891.81
DL-0°-3-30.83.511.70 
DL-30°-1-31.33.961.90 
DL-30°-2-30.34.121.991.92
DL-30°-3-31.53.881.87 
DL-45°-1-31.04.422.13 
DL-45°-2-32.14.222.042.06
DL-45°-3-31.14.142.00 
DL-60°-1-30.14.322.09 
DL-60°-2-30.44.442.142.14
DL-60°-3-30.24.522.18 
DL-90°-1-30.44.762.30 
DL-90°-2-31.34.662.252.27
DL-90°-3-30.64.702.27 
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断裂韧度计算结果

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试件编号温度/℃ Pmax/kN KIC/（MPa·m1/2）平均KIC/（MPa·m1/2）
DL-S-1-31.15.022.42 
DL-S-2-30.54.862.322.36
DL-S-3-32.04.962.33 
DL-0°-1-30.53.821.84 
DL-0°-2-31.23.921.891.81
DL-0°-3-30.83.511.70 
DL-30°-1-31.33.961.90 
DL-30°-2-30.34.121.991.92
DL-30°-3-31.53.881.87 
DL-45°-1-31.04.422.13 
DL-45°-2-32.14.222.042.06
DL-45°-3-31.14.142.00 
DL-60°-1-30.14.322.09 
DL-60°-2-30.44.442.142.14
DL-60°-3-30.24.522.18 
DL-90°-1-30.44.762.30 
DL-90°-2-31.34.662.252.27
DL-90°-3-30.64.702.27 
), ArticleFig(id=1241409542135795901, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241409515720069469, language=EN, label=Table 3, caption=

Calculation of fracture energy

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试件编号宏观裂纹倾角/°断裂面面积/mm2断裂能/（J·mm-2）平均断裂能/（J·mm-2）
DL-S-1无406.6002.07 
DL-S-2无384.1252.142.11
DL-S-3无391.4502.12 
DL-0°-10°208.7501.27 
DL-0°-20°217.1001.221.24
DL-0°-30°208.1251.23 
DL-30°-130°264.5751.39 
DL-30°-230°253.0001.461.43
DL-30°-330°255.7901.44 
DL-45°-145°314.3751.58 
DL-45°-245°303.3201.631.60
DL-45°-345°326.8541.59 
DL-60°-160°327.3751.74 
DL-60°-260°320.5601.791.76
DL-60°-360°330.5501.75 
DL-90°-190°414.3251.98 
DL-90°-290°409.4542.032.01
DL-90°-290°410.2502.02 
), ArticleFig(id=1241409542278402243, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241409515720069469, language=CN, label=表3, caption=

断裂能计算

, figureFileSmall=null, figureFileBig=null, tableContent=
试件编号宏观裂纹倾角/°断裂面面积/mm2断裂能/（J·mm-2）平均断裂能/（J·mm-2）
DL-S-1无406.6002.07 
DL-S-2无384.1252.142.11
DL-S-3无391.4502.12 
DL-0°-10°208.7501.27 
DL-0°-20°217.1001.221.24
DL-0°-30°208.1251.23 
DL-30°-130°264.5751.39 
DL-30°-230°253.0001.461.43
DL-30°-330°255.7901.44 
DL-45°-145°314.3751.58 
DL-45°-245°303.3201.631.60
DL-45°-345°326.8541.59 
DL-60°-160°327.3751.74 
DL-60°-260°320.5601.791.76
DL-60°-360°330.5501.75 
DL-90°-190°414.3251.98 
DL-90°-290°409.4542.032.01
DL-90°-290°410.2502.02 
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基于3D打印试件的裂隙岩体断裂特性及裂纹扩展特征研究
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余雷雷 a , 徐颖 a, b , 葛进进 a , 李洪伟 a , 倪苏黔 a , 张仲一 a , 尚辉 a
爆破 | 理论与技术探索 2024,41(4): 25-34
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爆破 | 理论与技术探索 2024, 41(4): 25-34
基于3D打印试件的裂隙岩体断裂特性及裂纹扩展特征研究
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余雷雷a , 徐颖a, b, 葛进进a , 李洪伟a, 倪苏黔a, 张仲一a, 尚辉a
作者信息
  • a.安徽理工大学　土木建筑学院，淮南　232001
  • b.安徽理工大学　国家重点实验室，淮南　232001

    • 余雷雷（1993-），男，硕士研究生，从事岩石断裂力学相关研究工作，（E-mail）。

    YU Lei-lei (1993-), male, postgraduate student, engaged in research related to rock fracture mechanics, (E-mail) .

通讯作者:

葛进进（1988-），男，讲师，从事深部岩石力学特性研究，（E-mail）。
Study on Fracture Characteristics and Crack Propagation Features of Fissured Rock Mass based on 3D Printed Samples
Lei-lei YUa , Ying XUa, b, Jin-jin GEa , Hong-wei LIa, Su-qian NIa, Zhong-yi ZHANGa, Hui SHANGa
Affiliations
  • a.School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, China
  • b.State Key Laboratory, Anhui University of Science and Technology, Huainan 232001, China
出版时间: 2024-12-01 doi: 10.3963/j.issn.1001-487X.2024.04.004
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摘要
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为探究不同倾角裂隙对岩石断裂特性的影响，本研究基于3D打印技术制备直切槽半圆盘弯曲（NSCB）试件，开展含裂隙岩体Ⅰ型静态断裂特性的试验研究。为探究不同的预制裂隙角度对于岩石断裂特性的影响，本研究基于3D打印技术制备含裂隙倾角的直切槽半圆盘弯曲试件（NSCB），打印好的试件经过固化，烘烤处理后，将其放置在干冰中，待其表面温度达到-30℃时进行准静态三点弯曲试验，该试验揭示了预制裂隙倾角对于断裂韧度、起裂角、断裂能的影响规律。结果表明：含裂隙NSCB试件平均断裂韧度均小于标准NSCB试件，且试件断裂韧度与裂隙倾角成正相关；对于含裂隙的NSCB试件，在β介于0°~90°之间时，起裂角随着裂隙倾角的增大而增大，裂纹拓展路径则表现出明显的“偏折”现象；从断裂破坏的能量角度分析，断裂能随着裂隙倾角的增大而增大。

3D打印  /  NSCB  /  断裂韧度  /  起裂角  /  断裂能

To study the influence of rock fracture characteristics with different inclination angles, the notched semi-disk bending (NSCB) specimens were prepared based on the 3D printing technology for experiments on typeI static fracture characteristics of rock mass. Specifically, the straight-cut groove half-disc bending specimens (NSCB) with crack angles were prepared by 3D printing technology to investigate the influence of different pre-fabricated crack angles on rock fracture characteristics. Furthermore, the printed specimens were placed in dry ice and subjected to quasi-static three-point bending tests when their surface temperature reached-30℃ after the solidification and baking treatments. The experiment revealed the influence of pre-fabricated crack angles on fracture toughness, initiation angle, and fracture energy. The results show that the average fracture toughness of NSCB specimens containing fissures is smaller than that of standard NSCB specimens. The fracture toughness of specimens is positively correlated with the fissure inclination angle. For NSCB specimens containing fissures, the initiation angle increases with the increase of the fissure inclination angle when β is between 0° and 90°, and the crack propagation path shows a distinct ‘deflection’ phenomenon. The fissure inclination angle significantly impacts the complexity of the NSCB specimen propagation path. The crack propagation path becomes more complex when the fissure inclination angle and fractal dimension increase. From the perspective of fracture energy, the fracture energy increases with the increase of the fissure inclination angle.

3D printing  /  NSCB  /  fracture toughness  /  crack initiation angle  /  fracture energy
余雷雷, 徐颖, 葛进进, 李洪伟, 倪苏黔, 张仲一, 尚辉. 基于3D打印试件的裂隙岩体断裂特性及裂纹扩展特征研究. 爆破, 2024 , 41 (4) : 25 -34 . DOI: 10.3963/j.issn.1001-487X.2024.04.004
Lei-lei YU, Ying XU, Jin-jin GE, Hong-wei LI, Su-qian NI, Zhong-yi ZHANG, Hui SHANG. Study on Fracture Characteristics and Crack Propagation Features of Fissured Rock Mass based on 3D Printed Samples[J]. Blasting, 2024 , 41 (4) : 25 -34 . DOI: 10.3963/j.issn.1001-487X.2024.04.004
正文
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在外部荷载下岩体断裂实际上是一个复杂的物理过程[1]。断裂力学被广泛地应用在爆破、边坡、地震等岩石工程问题研究中[2]，现已发展成为研究岩石断裂问题的有效方法。岩石断裂问题中，常用断裂韧性表征岩体阻止裂缝扩展的能力，其值越小裂缝越容易产生延伸[3]。
目前已有不少学者开展了岩体断裂韧性测试方面的研究。如：赵子江等分别采用NSCB试样和CCNBD试样进行了三点弯曲试验[4,5]，测定了层状页岩和大理岩的Ι型断裂韧度；Q Z Wang等利用试验对多种岩石弹性模量及断裂韧度等力学参数进行了测试与修正[6]；G Gao等结合数字图像相关（DIC）方法和高速摄影技术[7]，利用SHPB实验装置对NSCB花岗岩进行了动态断裂韧度研究；赵毅鑫等采用三点弯曲试验法对SCB煤样进行了Ι、II型断裂韧度测试[8]，并分析了2种断裂韧度的关系。
天然岩体是一种由不同节理、裂隙、夹层等组成的各向异性的非连续介质[9]。许多岩土工程的失稳和破坏都是由岩体内部裂隙的扩展和贯通诱发而造成[10]，节理裂隙的力学性质和破裂特征通常决定了整个岩体的承载能力与断裂模式[11]。因此，掌握裂隙岩石的断裂参数，获得断裂韧性、断裂能、起裂角等是明确岩体破裂机制，同时也是爆破，边坡支护等工程施工的关键。
由于天然岩体内部微裂隙错综复杂，既使得获取具有相同内部结构的同批次岩石试样难度较高，又导致试验结果离散性较大。近年来，随着3D打印技术的快速发展，其在复杂结构上突出的优势，具备几何适应性好、可个性化定制、天然模型还原度高、离散性小、高效便捷等优势，能克服传统制样方法的诸多不足[12]，目前越来越多学者运用3D打印技术解决岩石力学中传统方法无法解决的困难，如：Zhou等以陶瓷等5种原材料制备了3D打印岩体试样并开展了单轴压缩试验和直接拉伸试验[13]，结果表明光敏树脂是模拟岩石的最佳原材料；Aliabadian等对3D打印裂隙岩体开展了巴西劈裂抗拉、单轴压缩和直口半圆弯拉试验并结合DIC技术研究了裂纹萌生过程[14]。以上研究成果表明3D打印技术可以重构复杂实体，为制备裂隙岩体提供有效途径。
基于裂隙对岩体断裂韧性的影响尚不清晰，本文采用高分子光敏树脂材料打印含不同预制裂隙角度的直切槽半圆盘弯曲（notched semi-circlebend，NSCB）试件，对其开展静载三点弯曲试验，研究不同倾角裂隙岩体断裂参数（断裂韧性、断裂能、起裂角）与裂纹扩展特征，揭示外荷载作用下裂隙岩体断裂机制，研究成果对于防止外荷载作用下岩体失稳破坏导致灾难事件的发生具有重要理论与实践意义。
1　试验
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1.1　3D打印原理与设置
试验采用Ray shape系列Shape 1 HD 3D打印机，该打印机采用DLP面曝光UV固化3D打印技术。光固化3D打印技术的核心机理是光固化化学反应，光敏树脂遇405 nm蓝光会发生光固化反应，由液态瞬间变成固态。Shape Ware 3D打印软件会将需要打印的*. STL文件处理成片层文件，然后DLP UV光机再逐层投影该文件。
由于打印机通过分层、层层堆叠的方式制作样本，层厚过薄会导致打印时长增加，而过厚会影响到模型精度，因而需对打印的层厚进行设定。通过测试，本试验设置打印层厚0.025 mm，以减小层厚对于试验结果的影响，具体打印原理如图1所示。
依图1所示3D打印原理示意图，首先在树脂槽内盛放一定量的光敏树脂，点击开始打印后，打印平台降至树脂槽底部，然后DLP UV光机用405 nm蓝光投射出待打印文件的片层影像，该影像在树脂槽的底部成像并粘结在打印平台上；完成一层的固化后打印平台向上抬升固定高度，紧接着DLP UV光机投影固化下一层，如此循环往复将试件完整打印出来。在进行3D打印试件时需要注意：
（1）倒入树脂前，需要检查离型膜是否有破损，槽内若有异物，及时清理。
（2）在实际打印过程中，通常由于机器的原因造成第一层打印厚度高于其它层面，即底层Z轴的拉伸，从而引起整个模型变形。通过Z轴补偿可以消除这种影响。本次打印设置Z轴补偿为0.4 mm。
（3）打印平台通过树状支撑将试件连接起来。支撑过粗，导致支撑与试件难以分开，在清除支撑的过程中可能会损坏试件；支撑过细，会导致难以拉起整个试件，打印过程中试件脱落，从而导致打印失败。经过打印测试后，最终设置打印顶宽度0.6 mm，顶球直径0.6 mm（图2为树状支撑图，并标注出了顶球与顶宽位置）。
1.2　试件制备
试样制备过程如图3所示：（1）利用sketch up软件建立几何模型并导出*. STL格式文件（2）在打印机自带软件Shape Ware输入*. STL格式文件，进行支撑编辑、切片处理，并导出打印机可以识别的*. RS文件。（3）选用PJHC-10透明色刚性树脂（用于模拟岩石脆性材料）加入料槽，插入U盘，启动打印机。（4）将打印完成的试件放入酒精中清理残留在表面的树脂，然后转入强紫外线光固化箱中旋转照射20 min，最后用电动砂盘打磨机将试件支撑连接面打磨平整。（5）为提高试件透明度，磨平后的试件，最后放入烘箱进行烘焙（设定温度70℃），烘烤24 h后试件由深棕色转变为透明色。
1.3　试件后处理
基于1.2小节试件制备方法及流程，打印立方体（50 mm×50 mm×50 mm）试件进行单轴抗压试验，测试其应力-应变曲线如图4（a）所示。通过图4（a）可以看出，应力-应变曲线分为3个阶段：压密（OA）、弹性变形（AB）、塑性变形（BC），且塑性变形阶段的应变远大于压密与弹性变形阶段；在塑性变形（BC）段，试件逐渐趋于扁平状，内部储存能量急剧增大，但试件仍未产生裂隙。为防止试件突然爆裂飞出，在应力-应变曲线C点处对其进行卸载，卸载后试件仍能恢复部分变形。由此可见，压缩荷载下打印试件呈塑性变形，和岩石的脆性破坏特征不符，不能直接用于裂隙岩体断裂特性的试验研究。
由文献[15]可知，高分子材料在低温环境下会发生“脆化”现象，当温度降低到一定程度时，此时高分子材料由常规状态转变为玻璃化状态，发生转变的温度称为Tg。研究发现，玻璃材料的黏度可在相对较窄的温度范围内变化超过15个数量级。针对这一现象，Angell引入了“脆性”指数M来表征材料动力学对温度依赖性的强弱[16]
式中：τ是结构松弛时间；T为绝对温度。因此，在采用低温“增脆”方法时，需要找到该高分子打印原料的转变温度Tg。
参考田威等研究结果[17]，利用干冰对打印试件进行“增脆”处理。将试件用保鲜膜包裹后放入防爆干冰桶中，待其表面温度降至-20℃、-30℃和-40℃时分别开展单轴静态压缩试验。低温下试件应力-应变曲线如图4（b）所示。试件处于-20℃时，其压缩破裂形态相较于常温下的有所变化，虽然竖向压缩变形量依然较大，但此时试件表面开始出现压裂裂隙，由此表明温度降低可以使打印试件脆性增强；在-30℃时，试件出现明显的脆裂裂纹，应力-应变曲线出现“塔尖”形状，这与齐振武等基于3D打印试件模拟岩石压缩破裂的结果较为接近[18]；当温度降至-40℃时，此时打印试件内部因冰冻开始产生损伤，试件会发出噼里啪啦“响声”，并在压力机预加载阶段发生碎裂。
经过试验验证，最终确定打印试件的最佳冷冻温度为-30℃，其相应的物理力学参数如表1所示。
1.4　NSCB试验方案
采用如图5所示的试验装置，对NSCB模型试件进行静载三点弯曲试验。该试验装置包含：加载系统、摄像系统和数据记录系统，其中加载系统为中科院武汉岩土所研制的RMT-150B岩石压力机，试验采用负荷控制的加压方式，设置加载速率为0.1 kN/s；摄像系统由分辨率为5000万像素的Canon 5Dsr型相机，2台高功率LED灯构成，用来采集NSCB模型试件断裂过程图像。
依据国际岩石力学学会（ISRM）要求设计直切槽半圆盘弯曲试件（NSCB）的几何尺寸[19]，其中预制切缝宽度c为1 mm，长度a为10 mm，支座距离S为27.5 mm，试件直径D为50 mm，厚度B为25 mm。
为探究不同倾角裂隙对岩石断裂特性的影响，现设置NSCB试件上裂隙倾角β分别为0°、30°、45°、60°、90°。裂隙位于预制切缝与半圆盘顶点的中心点处，长度为7.5 mm，宽度为1 mm。如图6所示。
2　断裂特性分析
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图7为不同倾角裂隙NSCB试件的荷载-位移曲线。
从图7可知，NSCB试件在达到断裂荷载后，曲线垂直跌落，并在试验中伴随着清脆的断裂声，材料表现出脆性破坏特征。含不同倾角裂隙NSCB试件的平均断裂荷载分别是3750 N、3987 N、4260 N、4427 N、4707 N，平均峰值位移分别是0.09 mm、0.11 mm、0.175 mm、0.19 mm、0.23 mm，显然断裂荷载与峰值位移均随着裂隙倾角的增大呈现出逐渐增大的趋势，此外，标准NSCB试件的平均断裂荷载为4947 N，平均峰值位移为0.32mm。NSCB试件受载力学性能与其完整度、裂隙倾角密切相关，裂隙会降低NSCB试件的承载能力，且随着裂隙角度的减小削弱整体力学性能越多。
在岩石断裂力学中[20]，由Griffith理论可知，当预制裂纹尖端应力强度因子达到极限值时，裂纹将会快速扩展，直至扩展到加载端，此时临界应力强度因子即为断裂韧度。断裂韧度是表征裂纹抵抗扩展能力的物理量，断裂韧度越大，试件抵抗开裂的能力越强。根据ISRM建议的方法[21]，NSCB试样的断裂韧度KIC计算公式为
式中：P为试样破坏时的峰值加载值；Y′为无量纲应力强度因子，与无量纲支撑间距有关；aa为无量纲的预制裂纹长度，aa=0.4；其它符号意义同前。
将NSCB试件的断裂荷载数据代入式3进行计算，得到NSCB试件断裂韧度如表2所示。
从表2中可以看出，标准NSCB试件平均断裂韧度为2.36 MPa·m1/2；而含有裂隙NSCB试件平均断裂韧度均小于标准NSCB试件，且随着裂隙倾角的增大，平均断裂韧度不断增加，其中平均断裂韧度最大值为2.27 MPa.m1/2（β=90°）、最小值1.81 MPa·m1/2（β=0°），由此可见裂隙倾角角度对于试件抵抗裂纹拓展的能力影响显著。
为进一步表征断裂韧度随裂隙倾角的变化规律，以表2中裂隙倾角为横坐标、平均断裂韧度值为纵坐标，将两者关系绘制于图8中。
从图8可以看出，含裂隙NSCB试件断裂韧度随裂隙倾角呈线性增大关系。通过对断裂韧度与裂隙倾角之间的关系进行拟合得到
式中：KIC表示断裂韧度；β表示裂隙倾角。
3　裂纹扩展特征分析
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3.1　裂纹尖端起裂角
起裂角可以反映裂纹扩展方向，预测裂纹扩展路径，是揭示起裂机制的关键因素[22]。现定义裂纹与预制裂隙延长线夹角为起裂角（如图9所示），笔者在使用IMAGE J测量裂纹长度时已经对裂纹进行里提取，现测定起裂角度与预制裂隙β的关系及其拟合曲线如图10所示。
起裂角随着预制裂隙倾角的增加而增加，β=0°时，起裂角趋于0°，介于3°~6°之间，当β=90°时，起裂角在115°~120°之间，拟合曲线决定系数为R2=0.988，可以较准确地表征起裂角变化规律。β介于0°~90°之间时，起裂角随着预制裂隙倾角的增大而增大，将预制裂隙倾角作为横轴，起裂角作为纵轴进行拟合后可以得到
式中：σ表示起裂角；β表示预制裂隙倾角角度。
3.2　裂纹拓展路径
就均质材料而言，NSCB试样的裂纹扩展过程受预制裂纹方向控制，扩展路径基本为直线，方向由裂尖指向加载点[23]。对于含预制裂隙的NSCB试件，受裂隙角度的影响，裂纹拓展路径表现出明显的“偏折”现象。图11罗列了试件的最终破坏照片，并画出了受力模式，可以看出，当β=0°时，裂纹从预制裂隙尖端处断裂，笔直通过预制裂纹，到达顶部加载点。当β=30°、45°、60°、90°时，试件均从预制裂隙尖端起裂，直线状态到达预制裂隙中点后，“绕过”预制裂隙，沿曲线向加载点拓展。
分析断裂后试件可知，之所以裂纹拓展至预制裂隙时发生“偏转”现象，是由于预制裂隙尖端处处于高应力集中区，新的裂纹拓展一般都会发生在该区域[20]，而裂纹扩展过程是由无数新裂尖的起裂组成的，根据最大周向拉应力理论，脆性断裂裂纹在垂直于该力的平面内扩展，受预制裂隙角度影响，试样弹性对称轴发生变化，不同时刻新裂纹尖端的应力状态不同，使得最大周向拉应力发生改变，进而影响了裂纹的扩展方向。
基于断裂力学理论、裂隙倾角对起裂角的影响规律以及试件破坏模式受力图，尝试解释2.2小节中断裂韧度随裂隙倾角增大的原因：NSCB试件在三点压缩荷载作用下，其内部产生横向拉伸应力，并在切缝尖端处形成应力集中，当应力超过材料所承受极限时，NSCB试件内部开始产生Ⅰ型拉伸断裂，裂纹沿着切缝开始拓展一直延伸到预制裂隙中点处，此过程中裂纹始终呈Ⅰ型扩展。在横向拉伸应力的持续作用下，新生裂纹开始沿预制裂隙的应力集中点（距离顶点较近的一端）开始拓展，此时受预制裂隙角度的影响，作用在裂纹尖端处的拉伸应力随着裂隙角度的增大而减小，导致试件越不容易发生断裂，也即断裂韧度就会增大。
4　断裂能分析
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试样承受拉伸载荷，裂缝扩展单位面积所需要的能量，即断裂能，系统弹性应变能的释放是促使裂纹扩展的动力，假设外部载荷所做的功全部用于形成新的断裂面，基于试验中记录加载点的荷载-位移曲线求解断裂能。断裂能计算公式如下
式中：Gf为断裂能；W为外荷载所做的功；m为试件质量；g为重力加速度；δ为试样断裂破坏位移；P为荷载；A为断裂面面积；B为试样厚度。
计算断裂面面积A时，可用IMAGE J图像分析软件对长度L进行测量，A=L×B。外荷载所做的功W为荷载-位移曲线（图7）下方阴影面积，可以通过对其积分得到。mgδ是断裂过程中试样自重做的功，这里直切槽半圆盘弯曲试件质量较小，自重做功可以不予考虑。
依据公式9计算得到三点弯曲试验中NSCB试件扩展裂纹所需断裂能，如表3所示。
由表3可知，标准NSCB试件断裂能最大，由于其无预制裂隙，断裂韧度较大，试件抵抗开裂破坏能力较强，裂纹拓展阻力较大，因此断裂破坏过程中所消耗的断裂能也相对较大。对于含裂隙NSCB试件，断裂能随着预制裂隙角度的增大而增大。
根据龚江宏的研究裂纹的拓展应导致系统的总能量最低[24]，为了使系统的总能量最低，裂纹在材料中倾向于沿能量释放率G最大方向扩展。能量释放率与裂纹起裂角度θ或φ的关系可以用下图12描述。可以发现在起裂角度为0°时，能量释放率最大，裂纹沿偏离原平面的任何方向扩展都会导致能量释放率的降低。
在3.1小节的分析已经得出：预制裂隙角度的增大会导致裂纹拓展路径起裂角度的增大。在0°~90°范围内，裂纹扩展偏离原扩展平面的角度（起裂角度）越大，能量释放率越低，这一现象在断裂试验中表现为表观断裂能的增加。
5　结论
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本研究基于DLP面曝光UV固化3D打印技术制备NSCB试件，同时利用干冰对打印试件进行“增脆”处理用于裂隙岩体断裂特性的试验，探究不同倾角裂隙对岩石断裂特性的影响，研究结论如下：
（1）由断裂荷载-位移曲线和断韧度计算结果得到，NSCB试件受载力学性能与其完整度、裂隙倾角密切相关，裂隙会降低NSCB试件的承载能力，且随着裂隙角度的减小削弱整体力学性能越多，其中承载力最大值（β=90°）是最小值（β=0°）的1.26倍；含有裂隙NSCB试件平均断裂韧度均小于标准NSCB试件，断裂韧度与裂隙倾角之间的拟合呈线性函数关系。
（2）基于NSCB试件裂纹尖端起裂角、拓展路径以及裂纹分形维数对其扩展特征分析，宏观预制裂隙角度对于NSCB试件拓展路径复杂程度存在显著影响。在β介于0°~90°之间时，起裂角随着预制裂隙角度的增大而增大；标准NSCB试样的裂纹扩展路径基本为直线，方向由裂尖指向加载点；对于带宏观裂纹的NSCB试件，裂纹拓展路径则表现出明显的“偏折”现象。
（3）从断裂破坏的能量角度分析，标准NSCB试件断裂能最大，而对于含裂隙NSCB试件，断裂能随着预制裂隙角度的增大而增大。预制裂隙角度的增大会导致裂纹拓展路径起裂角度的增大，而在0°~90°范围内，裂纹扩展偏离原扩展平面的角度（起裂角度）越大，能量释放率越低，这一现象在断裂试验中表现为表观断裂能的增加。
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  • 国家自然科学基金面上项目(52074009)
  • 国家自然科学基金青年项目(52104116)
文献
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2024年第41卷第4期
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doi: 10.3963/j.issn.1001-487X.2024.04.004
  • 接收时间：2024-01-24
  • 首发时间：2026-03-19
  • 出版时间：2024-12-01
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  • 收稿日期：2024-01-24
基金
National Natural Science Foundation General Project(52074009)
国家自然科学基金面上项目(52074009)
National Natural Science Foundation Youth Program(52104116)
国家自然科学基金青年项目(52104116)
作者信息
    a.安徽理工大学　土木建筑学院，淮南　232001
    b.安徽理工大学　国家重点实验室，淮南　232001

通讯作者:

葛进进（1988-），男，讲师，从事深部岩石力学特性研究，（E-mail）。
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https://castjournals.cast.org.cn/joweb/bp/CN/10.3963/j.issn.1001-487X.2024.04.004
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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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