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In order to explore the blast-induced crack propagation behavior in rock mass with two vertical prefabricated defects, a series of blasting experiments of models with double vertical cracks were carried out based on digital laser caustics. The evolution process of blast-induced crack is shown and the effect of single-hole charge on the crack propagation behavior (crack propagation length, stress intensity factor, propagation velocity, and initiation time, et al) in rock mass with defects was explored. The results show that the crack propagation length, propagation velocity, crack initiation toughness and stress intensity factor at the end of the double vertical cracks increase with the increase of single-hole charge. For crack Ju, the effect of single-hole charge on crack propagation velocity is small, and the limit velocity of crack propagation is about 0.38 times of the shear wave velocity. For cracks Dl and Dr, the initiation time decreases, but the peak stress intensity factor increases with the increase of single hole charge. Besides, the stress intensity factor and propagation length of crack Dr increases significantly compared with crack Dl. The crack Dl starts to crack earlier than the crack Dr when the energy of the blasting stress wave acting on both ends of defect B is enough to cause the crack to propagate on both sides. The increase of charge in a single hole can increase the propagation velocity of crack Dr, but has little effect on the propagation velocity of crack Dl.

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为探究在爆炸载荷作用下含两条垂直预制缺陷岩体的爆生裂纹扩展行为，采用数字激光焦散线方法开展了一系列双垂直裂隙模型爆破实验，展现了爆生裂纹演化过程，揭示了单孔装药量对含缺陷岩体裂纹扩展行为（裂纹扩展长度、应力强度因子、扩展速度和起裂时间等）的影响规律。研究结果表明：随着单孔装药量增加，双垂直裂隙端部的裂纹扩展长度、裂纹扩展速度、裂纹起裂韧度和应力强度因子均呈增加趋势。对于裂纹Ju，单孔的药量对裂纹扩展速度影响较小，并且裂纹扩展极限速度约为横波速度的0.38倍；对于迎爆端裂纹Dl和背爆端裂纹Dr，随着单孔药量的增加，裂纹Dl和Dr的起裂时间减小，但裂纹Dl和裂纹Dr的峰值应力强度因子增大。相比于裂纹Dl，裂纹Dr的应力强度因子和扩展长度增加显著。当爆炸应力波作用于缺陷B两端部的能量足以使两侧裂纹扩展时，裂纹Dl比裂纹Dr先起裂。单孔药量的增加能够增大裂纹Dr的扩展速度，但是对裂纹Dl扩展速度影响较小。研究结果可为含缺陷岩体在爆破荷载作用下的断裂行为提供实验参考，有助于含缺陷岩体爆破安全设计工作。

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刘钊（1986-），男，讲师、硕士，从事安全科学与工程方面的研究，（E-mail）。

LIU Zhao (1986-), male, lecturer, master degree, engaged in research in safety science and engineering, (E-mail) .

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刘钊（1986-），男，讲师、硕士，从事安全科学与工程方面的研究，（E-mail）。

LIU Zhao (1986-), male, lecturer, master degree, engaged in research in safety science and engineering, (E-mail) .

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刘钊（1986-），男，讲师、硕士，从事安全科学与工程方面的研究，（E-mail）。

LIU Zhao (1986-), male, lecturer, master degree, engaged in research in safety science and engineering, (E-mail) .

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propagation velocity and stress intensity factor curve of Dr, figureFileSmall=k4GGR0LUnv1BvPqx0F45Tw==, figureFileBig=0cW2G9m6i7iWdJza1PlvKw==, tableContent=null), ArticleFig(id=1241769340207432341, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241769330183045430, language=CN, label=图7, caption=裂纹Dr的扩展速度及应力强度因子曲线, figureFileSmall=k4GGR0LUnv1BvPqx0F45Tw==, figureFileBig=0cW2G9m6i7iWdJza1PlvKw==, tableContent=null), ArticleFig(id=1241769340446507685, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241769330183045430, language=EN, label=Table 1, caption=

Crack propagation length of each model after blasting (unit: mm)

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药量80 mg100 mg120 mg145 mg
Ju30323542
Dl54825
Dr10112047
), ArticleFig(id=1241769340576531119, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241769330183045430, language=CN, label=表1, caption=

各模型爆后裂纹扩展长度（单位：mm）

, figureFileSmall=null, figureFileBig=null, tableContent=
药量80 mg100 mg120 mg145 mg
Ju30323542
Dl54825
Dr10112047
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含双垂直缺陷岩体爆生裂纹扩展行为试验研究
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刘钊 1 , 张树辉 2 , 臧小静 1
爆破 | 理论与技术探索 2024,41(1): 21-26
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爆破 | 理论与技术探索 2024, 41(1): 21-26
含双垂直缺陷岩体爆生裂纹扩展行为试验研究
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刘钊1 , 张树辉2, 臧小静1
作者信息
  • 1.黄河交通学院　交通工程学院，焦作　454950
  • 2.中冶建筑研究总院有限公司，北京　100088

    • 刘钊（1986-），男，讲师、硕士，从事安全科学与工程方面的研究，（E-mail）。

    LIU Zhao (1986-), male, lecturer, master degree, engaged in research in safety science and engineering, (E-mail) .

Experimental Study on Propagation Behavior of Blast-induced Crack in Rock Mass with Double Vertical Defects
Zhao LIU1 , Shu-hui ZHANG2, Xiao-jing ZANG1
Affiliations
  • 1.School of Traffic Engineering, Huanghe Jiaotong University, Jiaozuo 454950, China
  • 2.China Metallurgical Construction Research Institute, Beijing 100088, China
出版时间: 2024-03-01 doi: 10.3963/j.issn.1001-487X.2024.01.004
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摘要
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为探究在爆炸载荷作用下含两条垂直预制缺陷岩体的爆生裂纹扩展行为，采用数字激光焦散线方法开展了一系列双垂直裂隙模型爆破实验，展现了爆生裂纹演化过程，揭示了单孔装药量对含缺陷岩体裂纹扩展行为（裂纹扩展长度、应力强度因子、扩展速度和起裂时间等）的影响规律。研究结果表明：随着单孔装药量增加，双垂直裂隙端部的裂纹扩展长度、裂纹扩展速度、裂纹起裂韧度和应力强度因子均呈增加趋势。对于裂纹Ju，单孔的药量对裂纹扩展速度影响较小，并且裂纹扩展极限速度约为横波速度的0.38倍；对于迎爆端裂纹Dl和背爆端裂纹Dr，随着单孔药量的增加，裂纹Dl和Dr的起裂时间减小，但裂纹Dl和裂纹Dr的峰值应力强度因子增大。相比于裂纹Dl，裂纹Dr的应力强度因子和扩展长度增加显著。当爆炸应力波作用于缺陷B两端部的能量足以使两侧裂纹扩展时，裂纹Dl比裂纹Dr先起裂。单孔药量的增加能够增大裂纹Dr的扩展速度，但是对裂纹Dl扩展速度影响较小。研究结果可为含缺陷岩体在爆破荷载作用下的断裂行为提供实验参考，有助于含缺陷岩体爆破安全设计工作。

焦散线  /  缺陷岩体  /  爆破  /  装药量  /  裂纹扩展

In order to explore the blast-induced crack propagation behavior in rock mass with two vertical prefabricated defects, a series of blasting experiments of models with double vertical cracks were carried out based on digital laser caustics. The evolution process of blast-induced crack is shown and the effect of single-hole charge on the crack propagation behavior (crack propagation length, stress intensity factor, propagation velocity, and initiation time, et al) in rock mass with defects was explored. The results show that the crack propagation length, propagation velocity, crack initiation toughness and stress intensity factor at the end of the double vertical cracks increase with the increase of single-hole charge. For crack Ju, the effect of single-hole charge on crack propagation velocity is small, and the limit velocity of crack propagation is about 0.38 times of the shear wave velocity. For cracks Dl and Dr, the initiation time decreases, but the peak stress intensity factor increases with the increase of single hole charge. Besides, the stress intensity factor and propagation length of crack Dr increases significantly compared with crack Dl. The crack Dl starts to crack earlier than the crack Dr when the energy of the blasting stress wave acting on both ends of defect B is enough to cause the crack to propagate on both sides. The increase of charge in a single hole can increase the propagation velocity of crack Dr, but has little effect on the propagation velocity of crack Dl.

caustic  /  defective rock mass  /  blasting  /  charge quantity  /  crack propagation
刘钊, 张树辉, 臧小静. 含双垂直缺陷岩体爆生裂纹扩展行为试验研究. 爆破, 2024 , 41 (1) : 21 -26 . DOI: 10.3963/j.issn.1001-487X.2024.01.004
Zhao LIU, Shu-hui ZHANG, Xiao-jing ZANG. Experimental Study on Propagation Behavior of Blast-induced Crack in Rock Mass with Double Vertical Defects[J]. Blasting, 2024 , 41 (1) : 21 -26 . DOI: 10.3963/j.issn.1001-487X.2024.01.004
正文
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爆破作为一种常用的破岩方法，在许多工程中得到广泛的应用[1,2]。天然岩体中经常存在不同尺度的缺陷，如节理、孔洞或微裂纹等。在岩石爆破过程中，这些缺陷在爆破作用下会对应力波的传播衰减产生重大影响[3]，进而改变裂纹的扩展规律和爆破效果[4]；同时，装药量不同也会影响岩体的最终爆破效果[5,6]。因此，探究在爆破荷载作用下装药量对含缺陷岩体的应力分布和裂纹扩展规律具有重要意义，对煤矿及巷道安全十分重要。
国内外学者对含缺陷岩体展开了大量研究，主要探究了缺陷的几何尺寸，倾角，力学性质，数量以及炮孔与缺陷的距离等因素对岩体爆生裂纹和损伤的影响。例如，李继业等采用采水泥石膏材料制作岩石相似模型试件[7]，开展不同节理数量和节理倾角的爆破模型实验，结果表明爆破振速衰减随着节理数量的增大而增大但是增幅较小，爆破振速衰减随着节理倾角的增大而减小且变化幅度显著。周文海等对研究了含节理岩体的爆生裂纹扩展与爆炸应力波传播规律[8]，通过建立含节理岩体的爆炸数值模型得到节理两侧岩体的有效应力和振动速度，并利用应力波的波动理论与能量密度理论计算出节理的透反射系数和透反射能量比。Chen等采用三维离散元程序（3DEC）对节理隧道爆破开挖的损伤进行了数值模拟[9]，分析了节理几何和力学性质、隧道深度和推进长度对损伤深度的影响。Wang等采用分离式Hopkinson压杆对不同节理介质试件进行了动态单轴压缩试验[10]，结果表明随着充填介质厚度和含水率的增加，节理对应力波的阻隔作用明显增强。Yang等以有机玻璃为实验材料[11]，对不同充填材料下预制裂隙的扩展行为展开研究，发现空气作为充填材料时翼裂纹扩展长度最大。Huang等探究了结构面对爆破裂纹扩展的影响[12]，基于切槽钻孔和时序控制断裂爆破方法，研究了不同炮孔形状对围岩损伤程度的影响以及不同充填节理特征对爆破裂纹扩展规律的影响，发现充填节理强度较大、孔间夹角较大时，有利于裂缝沿孔间连线扩展。Tian等通过数值和室内实验[13]，提出了地应力和节理共同作用下的爆破应力波衰减方程和周边孔距计算方法。
近年来，动态焦散法被广泛应用于裂纹扩展规律的研究和裂纹尖端动态力学参数的测量，是研究含裂隙岩体实验的重要光测方法。例如，杨仁树等探究了预裂爆破形成的预裂缝对爆生裂纹和原生裂纹动态断裂特性的影响[14]，获得了裂纹扩展的时实动力学参数。Li等研究了炮孔与节理的距离对岩体的损伤效应[15]，研究发现，爆生裂纹在节理中的扩展能力受裂纹角度的影响很大。随后，Li等研究了张开节理和缺陷曲率半径对爆生裂纹和岩体损伤的影响[16,17]。肖同社等研究了初始爆炸裂纹与节理面夹角和间距不同时[18]，裂纹尖端动应力强度因子的变化规律以及裂纹通过节理面的扩展规律。Zhang等研究了条形药包爆破作用下含裂隙岩体爆生裂纹扩展规律和孔洞所在岩层的损伤演化规律[19]。岳中文等研究了含预制不同形状空孔对岩石定向断裂控制爆破的影响规律[20]。Xu等采用动态焦散线方法研究了爆破作用下含未充填节理介质中裂纹的扩展规律，发现斜节理较垂直节理更容易产生翼面裂纹[21]。
以上研究大部分是针对缺陷尺寸或位置对岩体破碎和裂纹扩展行为的影响，但对于含两条垂直预制缺陷岩体相互影响时裂纹扩展行为的研究相对较少，且单孔装药量对含缺陷岩体爆生裂纹扩展行为影响规律需进一步探索。不仅可以探索在爆炸应力波作用下缺陷端部裂纹扩展行为，而且能够研究在绕射应力波作用下裂纹的扩展行为规律。因此，本文采用焦散线的方法探究不同装药量对含两条预制缺陷模型的裂纹动态扩展行为影响规律，研究结果可为含缺陷岩体在爆破荷载作用下的断裂行为提供实验参考。
1　模型实验
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1.1　实验原理和系统
焦散线方法是记录裂纹扩展数据（长度、速度和应力强度因子）的一种光测实验技术[14-17]。对于含裂纹的板，在应力作用下裂纹尖端产生焦散斑。裂纹尖端的应力强度因子可以表示为
式中：KId是I型应力强度因子；Dmax是焦散斑的最大直径；z0是试件与参考平面之间的距离；g是焦散线数值因子[15-17]；deff为样品的厚度；c是样品的光学常数。
本实验采用的是数字激光焦散线实验系统，如图1所示。激光发射器发出的激光依次经过扩束镜、场镜1、试件和场镜2，最终汇聚到高速数码相机。高速数码相机能够记录和保存试件断裂的整个过程，本实验中高速数码相机的拍摄帧率为87 500。
1.2　模型设计
有机玻璃（PMMA）材料具有力学各向同性、高透光性，满足动焦散线法的试验要求，其裂纹尖端动态断裂扩展规律同脆性岩石材料相似，故选用有机玻璃为试验材料[14-21]。模型具体尺寸如图2所示，其中试件尺寸为300 mm×400 mm×5 mm，炮孔位于试件正中心，半径为3 mm；前置缺陷距离炮孔中心25 mm，其长度为60 mm，称为缺陷A，填充胶泥材料；后置缺陷长度30 mm，宽约0.2 mm，距离炮孔中心50 mm，称为缺陷B。
炸药选用叠氮化铅，单孔药量分别为145 mg、120 mg、100 mg、80 mg；采用耦合装药方式，炸药均匀分布在炮孔内，确保装药密度均匀；起爆方式为中心点起爆，每组模型各试验三次。
2　实验结果分析
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2.1　试件破坏形态
图3为各模型爆炸后效果图。为便于作图及分析描述，将缺陷A两端裂纹称为Ju，将缺陷B迎爆端扩展裂纹称为Dl，背爆端扩展裂纹称为Dr。随着爆炸应力波传播，缺陷A和缺陷B两端部共产生四条翼裂纹，随着装药量的增加，炮孔至缺陷A之间破碎越来越严重，炮孔周边爆生裂纹均无法穿过缺陷A继续扩展。统计各裂纹最终扩展长度，汇总如表1所示。对比裂纹Dl实验数据发现，当装药量为100 mg时，裂纹Dl扩展长度数据存在偏差，属于爆破实验误差。因此，当不考虑实验误差数据时，随装药量的增加，各裂纹扩展长度均逐渐增加。当药量小于120 mg时，其增加幅度比较缓慢，尤其对于裂纹Ju和裂纹Dl，可见端部裂纹Ju最终扩展长度受到药量变化影响并不显著。当装药量为145 mg时，各裂纹扩展长度均急剧增加，尤其对于缺陷B两端裂纹，更是成倍数增加，且此时裂纹Dl已经扩展至缺陷A表面，与爆生主裂纹相遇，形成一种“贯穿”。
2.2　焦散斑扩展过程
图4为在爆炸载荷作用下裂纹扩展时的焦散线图片。焦散斑能够反映出扩展裂纹尖端的应力集中情况，由图可知，在爆炸载荷作用下，缺陷A和B的两端均产生焦散斑；随着应力波和爆生气体的传播，裂纹尖端产生应力集中，焦散斑向前扩展，最终裂纹止裂。根据焦散斑的大小和位置，可以计算出在爆炸载荷作用下裂纹尖端的应力强度因子、扩展速度和长度等数据。
2.3　缺陷端部裂纹扩展行为分析
图5~7分别为裂纹Ju、裂纹Dl、裂纹Dr的扩展速度及应力强度因子曲线图。由图可知，随着药量增加，爆炸应力场增强，整体上，裂纹Ju、裂纹Dl、裂纹Dr的峰值应力强度因子随着装药量的增加而增加。当药量为145 mg时，各裂纹的动态扩展力学参数开始发生了明显的变化，呈现跳跃性增加。各曲线均呈现震荡变化趋势，表明裂纹扩展行为是一个裂纹尖端能量不断吸收及释放的动态变化过程。
对于裂纹Ju，随着药量增加，应力场较强，因此应力强度因子曲线变化规律较为明显，尤其在100 μs，即边界反射拉伸波作用之前，曲线整体上移，结果表明随着单孔药量的增加，裂纹Ju应力强度因子增大。应力强度因子与裂纹的扩展速度、扩展长度等关系密切，但仅从裂纹扩展速度曲线看，似乎并未呈现特别明显的相似规律，扩展速度曲线交叉变化，但统计平均扩展速度，也是与药量呈现正相关变化。研究表明，裂纹扩展极限速度约为横波速度的0.38倍，裂纹尖端能量不断积累、释放，导致裂纹扩展速度波动变化，但最终波动范围有限，不如应力强度因子变化明显，可见裂纹尖端的应力强度因子变化曲线更能反映应力场强度的变化规律。由图可以看出，随着药量的增加，裂纹Ju断裂韧度增加。因此，爆破载荷下试件的断裂韧度不只是取决于材料本身性质，还与加载速度、裂纹扩展速度等因素有关。在研究爆炸荷载作用下材料断裂问题时不能仅以静态断裂力学中的断裂韧性作为判据。
对于缺陷B两侧裂纹Dl和Dr，其扩展力学参数曲线随着药量的变化表现出较大的差异，应力强度因子曲线中表现出随药量增加的正相关性，但裂纹扩展速度并非如此，这主要是边界反射波作用导致。可以看出，当药量低于145 mg时，左端裂纹的起裂均在100 μs之后，这是因为Dl和Dr裂纹的起裂是由边界反射拉伸波作用所导致的。因此在小药量的模型中，尽管应力场较弱，但其裂纹起裂时间较晚，直到反射拉伸波作用时，尖端积攒能量达到起裂韧度，裂纹开始起裂，较长时间的能量积攒转为能量的迅速释放导致其初期扩展速度甚至超过大药量模型中的裂纹扩展速度。裂纹Dl和Dr的起裂时间分别为：137 μs，137 μs（80 mg）、125 μs，125 μs（100 mg）、137 μs，102 μs（120 mg）和57.15 μs，68.58 μs（145 mg）。可见，当爆炸应力波作用于缺陷B两端部的能量足以使两侧裂纹扩展时，迎爆侧要高于背爆侧先行扩展。当药量减少时，初次到达的爆炸透射应力波及绕射波强度不足以引起缺陷B两端裂纹扩展。此时，裂纹在反射波叠加作用下发生扩展，缺陷B两端裂纹起裂时间较一致，甚至右侧先行扩展。结果表明，药量的增加能够降低裂纹Dl和Dr的起裂时间。
由图6（b）和7（b）可知，随着药量的增加，各模型中裂纹Dl和裂纹Dr的峰值应力强度因子分别为0.58 MN/m3/2、0.66 MN/m3/2；0.65 MN/m3/2、0.93 MN/m3/2；0.83MN/m3/2、0.83MN/m3/2；0.79 MN/m3/2、1.79 MN/m3/2。背爆侧应力强度因子峰值高于迎爆侧，说明背爆侧裂纹端部应力场较强，这和背爆侧裂纹扩展长度较长相一致。结果表明：随着药量的增加，裂纹Dl和裂纹Dr的峰值应力强度因子增大；对于裂纹Dr，应力强度因子增加显著。
3　结论
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采用数字激光焦散线的方法研究了在爆炸载荷下含两条垂直预制缺陷岩体的裂纹扩展行为，表征了爆生裂纹演化过程，探寻了单孔装药量对含缺陷岩体裂纹扩展行为的影响规律。主要结论如下所示：
（1）在爆炸应力波的作用下，缺陷A的尖端产生应力集中，并产生一定角度的爆生裂纹。随着单孔药量的增加，爆生裂纹的扩展长度，速度和裂纹尖端的应力强度因子均轻微增大，即单孔药量的增加能促进缺陷端部爆生裂纹的扩展。
（2）由于缺陷A对爆炸应力波的阻碍，缺陷B尖端的应力集中和裂纹扩展主要由于绕射应力波的作用。随着单孔装药量的增加，缺陷B尖端的扩展长度，速度和应力强度因子均增大。但相比于迎爆端裂纹Dl，单孔药量的增加对背爆端裂纹Dr的促进作用更加显著。药量的增加能够促进裂纹Dl和Dr的起裂更早，这是缺陷B扩展长度增加的最主要原因。当爆炸应力波作用于缺陷B两端部的能量足以使两侧裂纹扩展时，裂纹Dl比裂纹Dr先起裂。
（3）与缺陷A和缺陷B的迎爆端相比，单孔药量的增加对缺陷B的背爆端影响更加显著。此外，只有当药量达到一定量级时，药量增加才能更加显著促进缺陷端部爆生裂纹扩展。在工程爆破中，如果缺陷B是保留岩体时，应该注意绕射应力波对缺陷B的影响。
基金
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  • 国家自然科学基金(52064025)
文献
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2024年第41卷第1期
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doi: 10.3963/j.issn.1001-487X.2024.01.004
  • 接收时间：2023-03-11
  • 首发时间：2026-03-20
  • 出版时间：2024-03-01
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  • 收稿日期：2023-03-11
基金
National Natural Science Foundation of China(52064025)
国家自然科学基金(52064025)
作者信息
    1.黄河交通学院　交通工程学院，焦作　454950
    2.中冶建筑研究总院有限公司，北京　100088
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2种不同金属材料的力学参数
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