基于断裂力学的裂隙岩体强度分析初探
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摘要
基于断裂力学讨论裂隙岩体的强度一直是断裂力学与岩石力学等学科的重要课题。通过分析单个线性裂纹在压缩载荷作用下的剪切断裂条件,明确了压缩状态下张破裂剪切断裂韧性的物理意义及求解办法。使用复变函数和边界配置法求解了裂尖应力强度因子无量纲系数,进而对张破裂压剪准则进行了改进,使之更加便捷地进行有限裂纹体断裂的预测。基于修正的压剪判据推导了裂隙岩体试件的抗压强度求解公式,算例表明该文方法所建立的强度公式是准确、可靠的。最后,详细讨论了摩擦系数、裂隙倾角、裂隙长度、黏聚力以及围压对裂隙岩体试件抗压强度的影响机理。
The study on rock strength based on fracture mechanics is still a significant project in the field of fracture mechanics and rock mechanics.Through the analysis of shear failure mechanism of a single linear crack under compression,the physical mechanism of compression-shear fracture toughness for tensile failure was investigated,and the corresponding solving method was also presented.A set of complex stress functions is proposed and by using the boundary collocation method(BCM),the dimensionless coefficients of stress intensity factors(SIFs) for a cracked specimen under compression was obtained.By using the SIF dimensionless coefficients,the compression-shear fracture criteria for tensile failure was improved and the formula of compressive strength of fractured rock specimens was derived.An example was presented to demonstrate the reliability of the method introduced in this paper.Finally,the effects of friction coefficients,crack orientation,crack length,cohesion,and confining pressure on rock compressive strength were discussed.
The study on rock strength based on fracture mechanics is still a significant project in the field of fracture mechanics and rock mechanics.Through the analysis of shear failure mechanism of a single linear crack under compression,the physical mechanism of compression-shear fracture toughness for tensile failure was investigated,and the corresponding solving method was also presented.A set of complex stress functions is proposed and by using the boundary collocation method(BCM),the dimensionless coefficients of stress intensity factors(SIFs) for a cracked specimen under compression was obtained.By using the SIF dimensionless coefficients,the compression-shear fracture criteria for tensile failure was improved and the formula of compressive strength of fractured rock specimens was derived.An example was presented to demonstrate the reliability of the method introduced in this paper.Finally,the effects of friction coefficients,crack orientation,crack length,cohesion,and confining pressure on rock compressive strength were discussed.
引文
[1]成都地质学院工程地质教研室.岩石裂隙强度[M].北京:地质出版社,1982:1.Teaching and Research Section of Engineering Geologyof Chengdu Geology Institute.The strength of rock joints[M].Beijing:The Geological Publishing House,1982:1.(in Chinese)
[2]谢和平,陈忠辉.岩石力学[M].北京:科学出版社,2004:187.Xie Heping,Chen Zhonghui.Rock mechanics[M].Bejing:Science Press,2004:187.(in Chinese)
[3]裴建良.含多组自然裂隙岩石的力学行为[D].成都:四川大学,2011.Pei Jianliang.Research on mechanical behavior of rockwith multi-group nature cracks[D].Chengdu:SichuanUniversity,2011.(in Chinese)
[4]张志强,李宁,陈方方,张平.非贯通裂隙岩体破坏模式研究现状与思考[J].岩土力学,2009,30(增2):142―148.Zhang Zhiqiang,Li Ning,Chen Fangping,Zhang Ping.Review and status of research on failure mode ofnon-penetrative fractured rock mass[J].Rock and SoilMechanics,2009,30(Suppl 2):142―148.(in Chinese)
[5]李贺,尹光志,许江,张文卫.岩石断裂力学[M].重庆:重庆大学出版社,1988:83.Li He,Yin Guangzhi,Xu Jiang,Zhang Wenwei.Rockfracture mechanics[M].Chongqing:ChongqingUniversity Press,1988:83.(in Chinese)
[6]刘东燕,范景伟.二向应力作用下断续节理岩体的强度特性研究[J].贵州工学院学报,1991,20(4):92―98.Liu Dongyan,Fan Jingwei.Characteristics of rock masswith bidirectional intermittent cross joints[J].Journal ofGuizhou Institute of Technology,1991,20(4):92―98.(in Chinese)
[7]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―25.Li Zailiang,Wang Yuanhan,Li Tingjie.The methods ofboundary numerical calculation in fracture mechanics[M].Beijing:Seismological Press,1996:22―25.(inChinese)
[8]Zhu Z,Wang L G,Bibhu Mohanty,et al.Stress intensityfactor for a cracked specimen under compression[J].Engineering Fracture Mechanics,2006,73:482―489.
[9]Zhu Z,Ji S,Xie H.An improved method of collocationfor the problem of crack surface subjected to uniformload[J].Engineering Fracture Mechanics,1996,54(5):731―741.
[10]Zhu Z,Xie H,Ji S.The mixed boundary problems for amixed mode crack in a finite plate[J].EngineeringFracture Mechanics,1997,56(5):647―655.
[11]朱哲明,谢和平.裂纹表面承受均布载荷时的应力强度因子及裂纹张开位移的边界配位法[J].计算结构力学与应用学报,1997,14(2):182―188.Zhu Zheming,Xie Heping.Collocation method of theSIF and COD for the crack surface subjected to uniformloading[J].Journal of Computational StructuralMechanics and Applications,1997,14(2):182―188.(inChinese)
[12]谢和平,朱哲明,范天佑.脆性岩石断裂破坏机理的边界配位法分析[J].力学学报,1998,30(2):238―246.Xie Heping,Zhu Zheming,Fan Tianyou.The analysis offracture of brittle rock material by using the boundarycollation method[J].Acta Mechanica Sinica,1998,30(2):238―246.(in Chinese)
[13]谢和平,朱哲明,田晓艳,崔希民.裂纹张开位移的边界配位法计算方法[J].机械强度,1997,19(2):63―67.Xie heping,Zhu Zheming,Tian xiaoyan,Cui ximin.Thecalculating method for crack opening displacements byusing the boundary collocation method[J].Journal ofMechanical Strength,1997,19(2):63―67.(in Chinese)
[14]易志坚.求解应力强度因子的一种新方法[J].重庆交通学院学报,1991,10(3):37―41.Yi Zhijian.A new method of determining the stressintensity factors[J].Journal of Chongqing JiaotongInstitute,1991,10(3):37―41.(in Chinese)
[15]Chen Y Z,Wang Z X.Solution of multiple crackproblem in a finite plate using coupled integral equations[J].International Journal of Solids and Structures,2012,49:87―94.
[16]周群力.混凝土重力坝与基岩胶结面用断裂力学方法进行计算的探讨[J].水文地质工程地质,1979(6):21―31.Zhou Qunli.Calculation using fracture mechanics forcement face between concrete gravity dam and thebedrock[J].Hydrogeology and Engineering Geology,1979(6):21―31.(in Chinese)
[17]Muskhelishvili N I.Some basic problems ofmathematical theory of elasticity[M].Translated byRadok J R M,Leyden:Noordhoff InternationalPublishing,1975:110―121.
[18]杨慧,曹平,江学良,等.双轴压缩下闭合裂纹应力强度因子的解析与数值方法[J].中南大学学报(自然科学版),2008,39(4):850―855.Yang Hui,Cao Ping,Jiang Xueliang,et al.Analyticaland numerical research of stress intensity factor with aclosed-crack in finite-rock-plates under biaxialcompression[J].Journal of Central South University(Science and Technology),2008,39(4):850―855.(inChinese)
[19]Byerlee J D.Friction of rocks[J].Pure and AppliedGeophysics,1978,116:615―626.
[2]谢和平,陈忠辉.岩石力学[M].北京:科学出版社,2004:187.Xie Heping,Chen Zhonghui.Rock mechanics[M].Bejing:Science Press,2004:187.(in Chinese)
[3]裴建良.含多组自然裂隙岩石的力学行为[D].成都:四川大学,2011.Pei Jianliang.Research on mechanical behavior of rockwith multi-group nature cracks[D].Chengdu:SichuanUniversity,2011.(in Chinese)
[4]张志强,李宁,陈方方,张平.非贯通裂隙岩体破坏模式研究现状与思考[J].岩土力学,2009,30(增2):142―148.Zhang Zhiqiang,Li Ning,Chen Fangping,Zhang Ping.Review and status of research on failure mode ofnon-penetrative fractured rock mass[J].Rock and SoilMechanics,2009,30(Suppl 2):142―148.(in Chinese)
[5]李贺,尹光志,许江,张文卫.岩石断裂力学[M].重庆:重庆大学出版社,1988:83.Li He,Yin Guangzhi,Xu Jiang,Zhang Wenwei.Rockfracture mechanics[M].Chongqing:ChongqingUniversity Press,1988:83.(in Chinese)
[6]刘东燕,范景伟.二向应力作用下断续节理岩体的强度特性研究[J].贵州工学院学报,1991,20(4):92―98.Liu Dongyan,Fan Jingwei.Characteristics of rock masswith bidirectional intermittent cross joints[J].Journal ofGuizhou Institute of Technology,1991,20(4):92―98.(in Chinese)
[7]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―25.Li Zailiang,Wang Yuanhan,Li Tingjie.The methods ofboundary numerical calculation in fracture mechanics[M].Beijing:Seismological Press,1996:22―25.(inChinese)
[8]Zhu Z,Wang L G,Bibhu Mohanty,et al.Stress intensityfactor for a cracked specimen under compression[J].Engineering Fracture Mechanics,2006,73:482―489.
[9]Zhu Z,Ji S,Xie H.An improved method of collocationfor the problem of crack surface subjected to uniformload[J].Engineering Fracture Mechanics,1996,54(5):731―741.
[10]Zhu Z,Xie H,Ji S.The mixed boundary problems for amixed mode crack in a finite plate[J].EngineeringFracture Mechanics,1997,56(5):647―655.
[11]朱哲明,谢和平.裂纹表面承受均布载荷时的应力强度因子及裂纹张开位移的边界配位法[J].计算结构力学与应用学报,1997,14(2):182―188.Zhu Zheming,Xie Heping.Collocation method of theSIF and COD for the crack surface subjected to uniformloading[J].Journal of Computational StructuralMechanics and Applications,1997,14(2):182―188.(inChinese)
[12]谢和平,朱哲明,范天佑.脆性岩石断裂破坏机理的边界配位法分析[J].力学学报,1998,30(2):238―246.Xie Heping,Zhu Zheming,Fan Tianyou.The analysis offracture of brittle rock material by using the boundarycollation method[J].Acta Mechanica Sinica,1998,30(2):238―246.(in Chinese)
[13]谢和平,朱哲明,田晓艳,崔希民.裂纹张开位移的边界配位法计算方法[J].机械强度,1997,19(2):63―67.Xie heping,Zhu Zheming,Tian xiaoyan,Cui ximin.Thecalculating method for crack opening displacements byusing the boundary collocation method[J].Journal ofMechanical Strength,1997,19(2):63―67.(in Chinese)
[14]易志坚.求解应力强度因子的一种新方法[J].重庆交通学院学报,1991,10(3):37―41.Yi Zhijian.A new method of determining the stressintensity factors[J].Journal of Chongqing JiaotongInstitute,1991,10(3):37―41.(in Chinese)
[15]Chen Y Z,Wang Z X.Solution of multiple crackproblem in a finite plate using coupled integral equations[J].International Journal of Solids and Structures,2012,49:87―94.
[16]周群力.混凝土重力坝与基岩胶结面用断裂力学方法进行计算的探讨[J].水文地质工程地质,1979(6):21―31.Zhou Qunli.Calculation using fracture mechanics forcement face between concrete gravity dam and thebedrock[J].Hydrogeology and Engineering Geology,1979(6):21―31.(in Chinese)
[17]Muskhelishvili N I.Some basic problems ofmathematical theory of elasticity[M].Translated byRadok J R M,Leyden:Noordhoff InternationalPublishing,1975:110―121.
[18]杨慧,曹平,江学良,等.双轴压缩下闭合裂纹应力强度因子的解析与数值方法[J].中南大学学报(自然科学版),2008,39(4):850―855.Yang Hui,Cao Ping,Jiang Xueliang,et al.Analyticaland numerical research of stress intensity factor with aclosed-crack in finite-rock-plates under biaxialcompression[J].Journal of Central South University(Science and Technology),2008,39(4):850―855.(inChinese)
[19]Byerlee J D.Friction of rocks[J].Pure and AppliedGeophysics,1978,116:615―626.
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