裂隙岩石拉伸断裂破坏理论分析试探
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摘要
利用边界配置法对最大周向应力理论、有效应力理论进行了修正,建立了实验室尺度下拉剪裂纹的两种破坏准则,并通过相应的破坏准则建立起了岩石单轴拉伸强度与断裂韧度之间的关系,给出了量化裂隙岩石试件抗拉强度的无量纲量,分析了裂纹倾角、裂纹长度对裂纹尖端开裂角及裂隙岩石试件的抗拉断能力的影响。结果表明,开裂角以及裂隙岩石的抗拉断裂能力(抗拉强度)均随裂纹倾角的增大而增大;对于具有宏观裂隙的试件,开裂角及抗拉断能力随裂隙长度的增加而递减;试件的尺度对裂隙岩石的强度影响不容忽视。
The maximum circumferential stress theory and the effective stress theory were improved based on the boundary collocation method,and then two kinds of failure criterion in the laboratory-scale were established.Moreover,the relationships between rock uniaxial tensile strength and fracture toughness were also developed through the corresponding criteria.Finally,the dimensionless variable which could quantify the uniaxial tensile strength was proposed;meanwhile the influences of crack inclination and crack length on the initial failure angle and the tensile strength of cracked rock mass were analyzed.The results show that both the initial failure angle and the tensile strength increase with the increase of crack inclination,and for specimens containing macroscopic cracks,both the initial failure angle and the tensile strength decrease as the crack length increases which indicates that the specimen scale has a great impact on rock fracture strength.
The maximum circumferential stress theory and the effective stress theory were improved based on the boundary collocation method,and then two kinds of failure criterion in the laboratory-scale were established.Moreover,the relationships between rock uniaxial tensile strength and fracture toughness were also developed through the corresponding criteria.Finally,the dimensionless variable which could quantify the uniaxial tensile strength was proposed;meanwhile the influences of crack inclination and crack length on the initial failure angle and the tensile strength of cracked rock mass were analyzed.The results show that both the initial failure angle and the tensile strength increase with the increase of crack inclination,and for specimens containing macroscopic cracks,both the initial failure angle and the tensile strength decrease as the crack length increases which indicates that the specimen scale has a great impact on rock fracture strength.
引文
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[2]Zhu Z M,Wang L G,Bibhu Mohanty,et al.Stress intensity factor fora cracked specimen under compression[J].Engineering FractureMechanics,2006,73(4):482-489.
[3]Zhu Z M,Ji S,Xie H.An improved method of collocation for theproblem of crack surface subjected to uniform load[J].EngineeringFracture Mechanics,1996,54(5):731-741.
[4]Zhu Z M,Xie H,Ji S.The mixed boundary problems for a mixedmode crack in a finite plate[J].Engineering Fracture Mechanics,1997,56(5):647-655.
[5]Zhu Z M.An alternative form of propagation criterion for two colline-ar cracks under compression[J].Mathematics and Mechanics of Sol-ids,2009,14:727-746.
[6]Zhu Z M.New biaxial failure criterion for brittle materials in com-pression[J].Journal of Engineering Mechanics,1999,125(11):1251-1258.
[7]Xie H,Zhu Z M,Fan T.The analysis of rock fracture characteristicsby using boundary collocation method[J].Acta Mech Sinica,1998,30:238-246.
[8]李碧勇,朱哲明,王蒙,等.有限板内偏心裂纹应力强度因子的边界配置法分析[J].四川大学学报(工程科学版),2010,42(9):59-63.Li Biyong,Zhu Zheming,Wang Meng,et al.Analysis of the stress in-tensity factor of a finite plate with an eccentric crack by boundarycollocation method[J].Journal of Sichuan University(EngineeringScience Edition),2010,42(9):59-63.
[9]王元汉,徐钺,谭国焕,等.岩体断裂的破坏机理与计算模拟[J].岩石力学与工程学报,2000,19(4):449-452.Wang Yuanhan,Xu Yue,Tan Guohuan,et al.Fracture mechanismand calculation of rock fracture[J].Chinese Journal of Rock Me-chanics and Engineering,2000,19(4):449-452.
[10]赵诒枢.复合型裂纹扩展的有效应力准则[J].机械强度,1992,11(2):51-53.Zhao Yishu.The effective stress criteria for mixed crack’s exten-sion[J].Journal of Mechanical Strength,1992,11(2):51-53.
[11]李世愚,和泰名,尹祥础.岩石断裂力学导论[M].合肥:中国科学技术大学出版社,2010:176-178.Li Shiyu,He Taiming,Yin Xiangchu.Introduction of rock fracturemechanics[M].Hefei:University of Science and Technology ofChina Press,2010:176-178.
[12]黎在良,王元汉,李廷芥.断裂力学中的边界数值方法[M].北京:地震出版社,1996:22-39.Li Zailiang,Wang Yuanhan,Li Tingjie.The methods of boundarynumerical calculation in fracture mechanics[M].Beijing:Seismo-logical Press,1996:22-39.
[13]Muskelishvih N I.Some basic problems of mathematical theory ofelasticity[M].Leyden:Noordhoff International Publishing,1975.
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