含孔多裂隙岩石力学特性与破裂分形维数相关性研究
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摘要
为研究含孔多裂隙岩石破裂及分形特征,制备含孔多裂隙岩石试件并对其进行单轴压缩试验,运用RFPA2D软件数值研究破裂过程,构建悬臂梁和结构面力学模型解释拉伸裂纹的形成机制以及裂隙倾角对试件抗压强度的影响效应。此外,引入盒维数法计算分形维数,以此定量表征最终破坏后的物理、数值模型试件裂纹的几何分布特征及其与破裂特性的相关性。研究结果表明:(1)试件破坏模式可划分为穿切裂隙剪切破坏(I型)和沿裂隙剪切破坏(II型)2类,试验与数值模拟结果吻合;(2)孔洞两侧的岩桥可简化为悬臂梁模型,由于非几何对称部位作用的弯矩较大,导致孔洞周边出现较多的拉伸裂纹;(3)预制多裂隙显著弱化了试件的抗压强度,随着裂隙倾角的增大,抗压强度呈先减小后增大的趋势,弱化系数W的变化规律与之相反,与结构面力学模型的解释一致;(4)最终破坏后的含孔多裂隙岩石新生裂纹几何分布的分形维数D与破坏特性密切相关;相比于II型破坏,发生I型破坏的试件抗压强度更大,受力过程中出现的宏观裂纹更多且扩展更充分,导致分形维数更大,数据拟合进一步证明抗压强度与分形维数近似服从正相关关系。
In order to study fracturing and fractal characteristics of rocks containing a hole and multi-flaws,model specimens containing a hole and multi-flaws were prepared and uniaxial compression tests were conducted. Failure process of rock specimens was numerically studied by RFPA2 D. Formation mechanism of tensile cracks and the effect of different flaw inclinations on the compression strength were explained by constructing an overhanging beam and structural plane mechanical model. Box-counting dimension method was introduced to quantify new cracks geometric distribution of physical and numerical model specimens after failure,and its correlation with fracture characteristics was investigated. Satisfactory agreement between numerical and test results indicate that the failure modes in the specimen can be classified into two modes,namely cutting through the flaw(mode I) and sliding along the flaw(mode II). The rock bridge near the pre-hole is considered as an overhanging beam model,and the generation of tensile cracks around the hole appears to be produced by the maximum bending moment acting at the non-symmetrical part of the overhanging beam. The compression strength of the specimens is weakened by pre-flaws,which can be explained by the structural plane mechanical model. With increasing the flaw inclination,the compression strength of the specimens decreases first and then increases,while the weakening factor shows a crosscurrent. The fractal dimension of new cracks geometric distribution of rock samples after failure is closely related to fracture characteristics. Compared with mode II,the specimen failing in mode I has a greater compression strength,leading to a higher fractal dimension. The results of data fitting show a positive correlation between the compression strength and the fractal dimension.
In order to study fracturing and fractal characteristics of rocks containing a hole and multi-flaws,model specimens containing a hole and multi-flaws were prepared and uniaxial compression tests were conducted. Failure process of rock specimens was numerically studied by RFPA2 D. Formation mechanism of tensile cracks and the effect of different flaw inclinations on the compression strength were explained by constructing an overhanging beam and structural plane mechanical model. Box-counting dimension method was introduced to quantify new cracks geometric distribution of physical and numerical model specimens after failure,and its correlation with fracture characteristics was investigated. Satisfactory agreement between numerical and test results indicate that the failure modes in the specimen can be classified into two modes,namely cutting through the flaw(mode I) and sliding along the flaw(mode II). The rock bridge near the pre-hole is considered as an overhanging beam model,and the generation of tensile cracks around the hole appears to be produced by the maximum bending moment acting at the non-symmetrical part of the overhanging beam. The compression strength of the specimens is weakened by pre-flaws,which can be explained by the structural plane mechanical model. With increasing the flaw inclination,the compression strength of the specimens decreases first and then increases,while the weakening factor shows a crosscurrent. The fractal dimension of new cracks geometric distribution of rock samples after failure is closely related to fracture characteristics. Compared with mode II,the specimen failing in mode I has a greater compression strength,leading to a higher fractal dimension. The results of data fitting show a positive correlation between the compression strength and the fractal dimension.
引文
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[12]李夕兵,翁磊,谢晓锋,等.动静载荷作用下含孔洞硬岩损伤演化的核磁共振特性试验研究[J].岩石力学与工程学报,2015,34(10):1 985-1 993.(LI Xibing,WENG Lei,XIE Xiaofeng,et al.Study on the degradation of hard rock with a pre-existing opening under static-dynamic loadings using nuclear magnetic resonance technique[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(10):1 985-1 993.(in Chinese))
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[14]宋义敏,潘一山,章梦涛,等.洞室围岩三种破坏形式的试验研究[J].岩石力学与工程学报,2010,29(增1):2 741-2 745.(SONG Yimin,PAN Yishan,ZHANG Mengtao,et al.Experimental investigation on fracture of three types of underground caverns[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(Supp.1):2 741-2 745.(in Chinese))
[15]张艳博,刘善军.含孔岩石加载过程的热辐射温度场变化特征[J].岩土力学,2011,32(4):1 013-1 017.(ZHANG Yanbo,LIU Shanjun.Thermal radiation temperature field variation of hole rock in loading process[J].Rock and Soil Mechanics,2011,32(4):1 013-1 017.(in Chinese))
[16]朱谭谭,靖洪文,苏海健,等.孔洞-裂隙组合型缺陷砂岩力学特性试验研究[J].煤炭学报,2015,40(7):1 518-1 525.(ZHU Tantan,JING Hongwen,SU Haijian,et al.Experimental investigation on mechanical behavior of sandstone with coupling effects under uniaxial compression[J].Journal of China Coal Society,2015,40(7):1 518-1 525.(in Chinese))
[17]腾俊洋,唐建新,李欣怡.含孔洞加锚岩石力学特性及裂纹扩展规律[J].岩石力学与工程学报,2018,37(1):87-103.(TENG Junyang,TANG Jiangxin,LI Xinyi.Mechanical property and fracture propagation rule of anchored rock with a hole under uniaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2018,37(1):87-103.(in Chinese))
[18]李术才,杨磊,李明田,等.三维内置裂隙倾角对类岩石材料拉伸力学性能和断裂特征的影响[J].岩石力学与工程学报,2009,28(2):281-289.(LI Shucai,YANG Lei,LI Mingtian,et al.Influence of 3D internal crack dip angle on tensile mechanical properties and fractural features of rock-like material[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(2):281-289.(in Chinese))
[19]黄彦华,杨圣奇,鞠杨,等.断续断续裂隙类岩石材料三轴压缩力学特性试验研究[J].岩土工程学报,2016,38(7):1 212-1 220.(HUANG Yanhua,YANG Shengqi,JU Yang,et al.Experimental study on mechanical behavior of rock-like material containing pre-exist[J].Chinese Journal of Geotechnical Engineering,2016,38(7):1 212-1 220.(in Chinese))
[20]李化敏,李回贵,宋桂军,等.神东矿区煤系地层岩石物理力学性质[J].煤炭学报,2016,41(11):2 661-2 671.(LI Huamin,LI Huigui,SONG Guijun,et al.Physical and mechanical properties of coal-bearing strata rock in Shendong Coalfield[J].Journal of China Coal Society,2016,41(11):2 661-2 671.(in Chinese))
[21]杜时贵,黄曼,罗战友,等.岩石结构面力学原型试验相似材料研究[J].岩石力学与工程学报,2010,29(11):2 263-2 270.(DUShigui,HUANG Man,LUO Zhanyou,et al.Similar material study of mechanical prototype test of rock structural plane[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(11):2 263-2 270.(in Chinese))
[22]蔡美峰,何满潮,刘东燕.岩石力学与工程[M].北京:科学出版社,2013:100-104.(CAI Meifeng,HE Manchao,LIU Dongyan.Rock mechanics and engineering[M].Beijing:Science Press,2013:100-104.(in Chinese))
[23]谢和平.分形-岩石力学导论[M].2版.北京:科学出版社,2005:228-234.(XIE Heping.Fractal-rock mechanics induction[M].2nd ed.Beijing:Science Press,2005:228-234.(in Chinese))
[24]陈新,王仕志,李磊.节理岩体模型单轴压缩破碎规律研究[J].岩石力学与工程学报,2012,31(5):898-907.(CHEN Xin,WANGShizhi,LI Lei.Characteristics of fragments of jointed rock mass model under uniaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(5):898-907.(in Chinese))
[25]邓涛,杨林德,韩文峰.加载方式对大理岩碎块分布影响的试验研究[J].同济大学学报:自然科学版,2007,35(1):10-14.(DENGTao,YANG Linde,HAN Wenfeng.Influence of loading form on distribution of marble fragments[J].Journal of Tongji University:Natural Science,2007,35(1):10-14.(in Chinese))
[26]ZHANG K,CAO P,MA G,et al.Strength,fragmentation and fractal properties of mixed flaws[J].Acta Geotechnica,2016,11(4):901-912.
[27]彭瑞东,谢和平,鞠杨.二维数字图像分形维数的计算方法[J].中国矿业大学学报,2004,33(1):19-24.(PENG Ruidong,XIEHeping,JU Yang.Computation method of fractal dimension for 2Ddigital image[J].Journal of China University of Mining and Technology,2004,33(1):19-24.(in Chinese))
[2]DZIK E J,LAJTAI E Z.Primary fracture propagation from circular cavities loaded in compression[J].International Journal of Fracture,1996,79(1):49-64.
[3]李地元,李夕兵,李春林,等.单轴压缩下含预制孔洞板状花岗岩试样力学响应的试验和数值研究[J].岩石力学与工程学报,2011,30(6):1 198-1 206.(LI Diyuan,LI Xibing,LI Chunlin,et al.Experimental and numerical studies of mechanical response of plate-shape granite samples containing prefabricated holes under uniaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(6):1 198-1 206.(in Chinese))
[4]黎崇金,李夕兵,李地元.含孔洞大理岩破坏特性的颗粒流分析[J].工程科学学报,2017,39(12):1 791-1 801.(LI Chongjin,LI Xibing,LI Diyuan.Particle flow analysis of fracture characteristics of marble with a single hole[J].Chinese Journal of Engineering,2017,39(12):1 791-1 801.(in Chinese))
[5]杜明瑞,靖洪文,苏海健,等.含预制椭圆形孔洞砂岩强度及坏特征试验研究[J].中国矿业大学学报,2016,45(6):1 164-1 171.(DUMingrui,JING Hongwen,SU Haijian,et al.Experimental study of strength and failure characteristics of sandstone containing prefabricated elliptical hole[J].Journal of China University of Mining and Technology,2016,45(6):1 164-1 171.(in Chinese))
[6]杜明瑞,靖洪文,苏海健,等.孔洞形状对砂岩强度及破坏特征的影响[J].工程力学,2016,33(7):190-196.(DU Mingrui,JINGHongwen,SU Haijian,et al.Effects of holes-geometrical shape on strength and failure characteristics of sandstone sample containing a single hole[J].Engineering Mechanics,2016,33(7):190-196.(in Chinese))
[7]ZHU W C,LIU J,TANG C A,et al.Simulation of progressive fracturing processes around underground excavations under biaxial compression[J].Tunnelling and Underground Space Technology,2005,20(3):231-247.
[8]TANG C A,WONG R H C,CHAU K T,et al.Modeling of compression-induced splitting failure in heterogeneous brittle porous solids[J].Engineering Fracture Mechanics,2005,72(4):597-615.
[9]张后全,唐春安,宋力,等.布孔方式对孔洞材料宏观力学性能影响的研究[J].应用力学学报,2006,23(1):62-67.(ZHANGHouquan,TANG Chun′an,SONG Li,et al.Influence of hole distribution on macroscopic mechanical behavior of perforated materials[J].Chinese Journal of Applied Mechanics,2006,23(1):62-67.(in Chinese))
[10]段进超,唐春安,常旭,等.单轴压缩下含孔脆性材料的力学行为研究[J].岩土力学,2006,27(8):1 416-1 420.(DUAN Jinchao,TANG Chun′an,CHANG Xu,et al.Study on mechanics behavior of containing holes in brittle material subjected to uniaxial compression[J].Rock and Soil Mechanics,2006,27(8):1 416-1 420.(in Chinese))
[11]段进超,唐春安,常旭.脆性基多孔材料孔洞的尺寸效应及其破坏模式研究[J].岩土力学,2007,28(3):631-634.(DUAN Jinchao,TANG Chun′an,CHANG Xu.A study on hole size effects and failure mode of brittle materials containing multiple holes[J].Rock and Soil Mechanics,2007,28(3):631-634.(in Chinese))
[12]李夕兵,翁磊,谢晓锋,等.动静载荷作用下含孔洞硬岩损伤演化的核磁共振特性试验研究[J].岩石力学与工程学报,2015,34(10):1 985-1 993.(LI Xibing,WENG Lei,XIE Xiaofeng,et al.Study on the degradation of hard rock with a pre-existing opening under static-dynamic loadings using nuclear magnetic resonance technique[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(10):1 985-1 993.(in Chinese))
[13]杨圣奇,刘相如,李玉寿.单轴压缩下含孔洞裂隙砂岩力学特性试验分析[J].岩石力学与工程学报,2012,31(增2):3 539-3 546.(YANG Shengqi,LIU Xiangru,LI Yushou.Experimental analysis of mechanical behavior of sandstone containing hole and fissure under uniaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(Supp.2):3 539-3 546.(in Chinese))
[14]宋义敏,潘一山,章梦涛,等.洞室围岩三种破坏形式的试验研究[J].岩石力学与工程学报,2010,29(增1):2 741-2 745.(SONG Yimin,PAN Yishan,ZHANG Mengtao,et al.Experimental investigation on fracture of three types of underground caverns[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(Supp.1):2 741-2 745.(in Chinese))
[15]张艳博,刘善军.含孔岩石加载过程的热辐射温度场变化特征[J].岩土力学,2011,32(4):1 013-1 017.(ZHANG Yanbo,LIU Shanjun.Thermal radiation temperature field variation of hole rock in loading process[J].Rock and Soil Mechanics,2011,32(4):1 013-1 017.(in Chinese))
[16]朱谭谭,靖洪文,苏海健,等.孔洞-裂隙组合型缺陷砂岩力学特性试验研究[J].煤炭学报,2015,40(7):1 518-1 525.(ZHU Tantan,JING Hongwen,SU Haijian,et al.Experimental investigation on mechanical behavior of sandstone with coupling effects under uniaxial compression[J].Journal of China Coal Society,2015,40(7):1 518-1 525.(in Chinese))
[17]腾俊洋,唐建新,李欣怡.含孔洞加锚岩石力学特性及裂纹扩展规律[J].岩石力学与工程学报,2018,37(1):87-103.(TENG Junyang,TANG Jiangxin,LI Xinyi.Mechanical property and fracture propagation rule of anchored rock with a hole under uniaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2018,37(1):87-103.(in Chinese))
[18]李术才,杨磊,李明田,等.三维内置裂隙倾角对类岩石材料拉伸力学性能和断裂特征的影响[J].岩石力学与工程学报,2009,28(2):281-289.(LI Shucai,YANG Lei,LI Mingtian,et al.Influence of 3D internal crack dip angle on tensile mechanical properties and fractural features of rock-like material[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(2):281-289.(in Chinese))
[19]黄彦华,杨圣奇,鞠杨,等.断续断续裂隙类岩石材料三轴压缩力学特性试验研究[J].岩土工程学报,2016,38(7):1 212-1 220.(HUANG Yanhua,YANG Shengqi,JU Yang,et al.Experimental study on mechanical behavior of rock-like material containing pre-exist[J].Chinese Journal of Geotechnical Engineering,2016,38(7):1 212-1 220.(in Chinese))
[20]李化敏,李回贵,宋桂军,等.神东矿区煤系地层岩石物理力学性质[J].煤炭学报,2016,41(11):2 661-2 671.(LI Huamin,LI Huigui,SONG Guijun,et al.Physical and mechanical properties of coal-bearing strata rock in Shendong Coalfield[J].Journal of China Coal Society,2016,41(11):2 661-2 671.(in Chinese))
[21]杜时贵,黄曼,罗战友,等.岩石结构面力学原型试验相似材料研究[J].岩石力学与工程学报,2010,29(11):2 263-2 270.(DUShigui,HUANG Man,LUO Zhanyou,et al.Similar material study of mechanical prototype test of rock structural plane[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(11):2 263-2 270.(in Chinese))
[22]蔡美峰,何满潮,刘东燕.岩石力学与工程[M].北京:科学出版社,2013:100-104.(CAI Meifeng,HE Manchao,LIU Dongyan.Rock mechanics and engineering[M].Beijing:Science Press,2013:100-104.(in Chinese))
[23]谢和平.分形-岩石力学导论[M].2版.北京:科学出版社,2005:228-234.(XIE Heping.Fractal-rock mechanics induction[M].2nd ed.Beijing:Science Press,2005:228-234.(in Chinese))
[24]陈新,王仕志,李磊.节理岩体模型单轴压缩破碎规律研究[J].岩石力学与工程学报,2012,31(5):898-907.(CHEN Xin,WANGShizhi,LI Lei.Characteristics of fragments of jointed rock mass model under uniaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(5):898-907.(in Chinese))
[25]邓涛,杨林德,韩文峰.加载方式对大理岩碎块分布影响的试验研究[J].同济大学学报:自然科学版,2007,35(1):10-14.(DENGTao,YANG Linde,HAN Wenfeng.Influence of loading form on distribution of marble fragments[J].Journal of Tongji University:Natural Science,2007,35(1):10-14.(in Chinese))
[26]ZHANG K,CAO P,MA G,et al.Strength,fragmentation and fractal properties of mixed flaws[J].Acta Geotechnica,2016,11(4):901-912.
[27]彭瑞东,谢和平,鞠杨.二维数字图像分形维数的计算方法[J].中国矿业大学学报,2004,33(1):19-24.(PENG Ruidong,XIEHeping,JU Yang.Computation method of fractal dimension for 2Ddigital image[J].Journal of China University of Mining and Technology,2004,33(1):19-24.(in Chinese))