基于三剪屈服准则的空间轴对称特征线场理论及其应用
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摘要
基于三剪屈服准则建立了有重材料的空间轴对称特征线场理论,其特点是:在描述空间轴对称三向应力作用下的材料屈服特性时,三剪屈服准则较Mohr-Coulomb屈服准则能反映中间主应力对材料屈服的影响,并且该准则还可用一个表达式来精确表达工程中常用的Mohr-Coulomb屈服准则、Tresca屈服准则和Mises屈服准则,从而提高准则对材料的适用范围;在描述材料塑性区内的应力状态时,摒弃了以往基于Mohr-Coulomb屈服准则必须采用的Haar-Von Karman完全塑性假设,通过引入中间主应力参数来表达不同材料可能具有的不同塑性区应力状态,并且Haar-Von Karman完全塑性假设仅为其特例。另外,利用该特征线场理论研究了竖井井壁压力的计算问题并与传统方法做了比较。结果表明:该方法能更好地反映井周岩土屈服特性及塑性区应力状态对井壁压力的影响。
The axisymmetric characteristics line theory for weight materials was established based on the triple shear unified yield criterion.The main features are as follows: in describing the yield properties for materials under axisymmetric three dimensional stress states,the triple shear unified yield criterion used here can reflect the intermediate principal stress effects on the yield characteristics for materials compared with the Mohr-Coulomb yield criterion used before,and can be suitable to more kinds of materials because the common used criteria such as the Mohr-Coulomb failure criterion,the Tresca yield criterion and the Von Mises yield criterion can be expressed accurately with its only one equation.In describing the stress states in plastic zone,the Haar-Von Karman plasticity hypothesis based on the Mohr-Coulomb yield criterion is neglected through introducing the intermediate principal stress parameter to express the different stress states in plastic zones for different materials.This method can also take the Haar-Von Karman plasticity hypothesis as one of its special cases.As an example,pressures acting on the shaft wall were researched using the new axisymmetric characteristics line theory and results were compared with the traditional method.The results show that the proposed method gives a better description to the pressures acting on shafts influenced by yield properties for rock and/or soil round the shafts and the stress states in plastic zones.
The axisymmetric characteristics line theory for weight materials was established based on the triple shear unified yield criterion.The main features are as follows: in describing the yield properties for materials under axisymmetric three dimensional stress states,the triple shear unified yield criterion used here can reflect the intermediate principal stress effects on the yield characteristics for materials compared with the Mohr-Coulomb yield criterion used before,and can be suitable to more kinds of materials because the common used criteria such as the Mohr-Coulomb failure criterion,the Tresca yield criterion and the Von Mises yield criterion can be expressed accurately with its only one equation.In describing the stress states in plastic zone,the Haar-Von Karman plasticity hypothesis based on the Mohr-Coulomb yield criterion is neglected through introducing the intermediate principal stress parameter to express the different stress states in plastic zones for different materials.This method can also take the Haar-Von Karman plasticity hypothesis as one of its special cases.As an example,pressures acting on the shaft wall were researched using the new axisymmetric characteristics line theory and results were compared with the traditional method.The results show that the proposed method gives a better description to the pressures acting on shafts influenced by yield properties for rock and/or soil round the shafts and the stress states in plastic zones.
引文
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[12]YU Mao-hong,LI Jiang-chun,ZHANG Yong-qiang.Unified characteristics line theory of spacial axisymmetric plastic problem[J].Science in China(series E),2001,44(2):207-215.
[13]胡小荣,魏雪英,俞茂宏.三轴压缩下岩石强度与破坏面角度的双剪理论分析[J].岩石力学与工程学报,2003,22(7):1093-1098.HU Xiao-rong,WEI Xue-ying,YU Mao-hong.Characteristics of rock strength and failure under triaxial compression analyzed by twin shear theory[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(7):1093-1098.
[14]胡小荣,俞茂宏.岩土类介质强度准则新探[J].岩石力学与工程学报,2004,23(18):3037-3043.HU Xiao-rong,YU Mao-hong.New research on failure criterion for geomaterial[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(18):3037-3043.
[15]胡小荣,林太清.三剪屈服准则及其在极限内压计算中的应用[J].中国有色金属学报,2007,17(2):207-215.HU Xiao-rong,LIN Tai-qing.Triple-shear yield criterion and its application to limit pressures for thin and thick wall cylinders and thick wall spherical shells[J].The Chinese Journal of Nonferrous Metals,2007,17(2):207-215.
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[2]Hill R.The mathematical theory of plasticity[M].Oxford:Oxford University Press,1950.
[3]俞茂宏.双剪理论及其应用[M].北京:科学出版社,1998.YU Mao-hong.Twin shear theory and its applications[M].Beijing:Science Press,1998.
[4]Mogi K.Effect of intermediate principal stress on rock failure[J].J Geophys Res,1967,72:5117-5131.
[5]Mogi K.Failure and flow of rocks under high triaxial compression[J].J Geophys Res,1971,76:1255-1269.
[6]Michelis P.Polyaxial yielding of granular rock[J].J Eng Mech ASCE,1985,111(18):1049-1066.
[7]YU Mao-hong.Advances in strength theories for materials under complex stress state in the 20th century[J].Applied Mechanics Reviews,2002,55(3):169-218.
[8]张金涛,林天健.三轴实验中岩石的应力状态和破坏性质[J].力学学报,1979,2:99-105.ZHANG Jin-tao,Lin Tian-jian.Stress conditions and variations of rupture characteristics of a rock as shown by tri-axial test[J].Acta Mechica Sinica,1979,2:99-105.
[9]许东俊,耿乃光.岩石强度随中间主应力的变化规律[J].固体力学学报,1985,6(1):72-80.XU Dong-jun,GENG Nai-guang.The variation law of rock strength with increase of intermediate principal stress[J].Acta Mechanica Solida Sinica,1985,6(1):72-80.
[10]李小春,许东俊.双剪应力强度理论的试验验证—拉西瓦花岗岩强度特性的真三轴实验研究[R].岩土报告(90)52号,武汉:中科院武汉岩土所,1990.LI Xiao-chun,XU Dong-jun.Experimental verification of the twin shear theory-true triaxial test research of strength of Lawaxi Granite[R].Rock and Soil(90)52,Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Science,1990.
[11]俞茂宏,李建春,张永强.空间轴对称塑性问题的统一特征线理论[J].中国科学(E辑),2001,31(4):323-331.YU Mao-hong,LI Jian-chun,ZHANG Yong-qiang.Unified characteristics line theory of spacial axisymmetric plastic problem[J].Science in China(series E),2001,31(4):323-331.
[12]YU Mao-hong,LI Jiang-chun,ZHANG Yong-qiang.Unified characteristics line theory of spacial axisymmetric plastic problem[J].Science in China(series E),2001,44(2):207-215.
[13]胡小荣,魏雪英,俞茂宏.三轴压缩下岩石强度与破坏面角度的双剪理论分析[J].岩石力学与工程学报,2003,22(7):1093-1098.HU Xiao-rong,WEI Xue-ying,YU Mao-hong.Characteristics of rock strength and failure under triaxial compression analyzed by twin shear theory[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(7):1093-1098.
[14]胡小荣,俞茂宏.岩土类介质强度准则新探[J].岩石力学与工程学报,2004,23(18):3037-3043.HU Xiao-rong,YU Mao-hong.New research on failure criterion for geomaterial[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(18):3037-3043.
[15]胡小荣,林太清.三剪屈服准则及其在极限内压计算中的应用[J].中国有色金属学报,2007,17(2):207-215.HU Xiao-rong,LIN Tai-qing.Triple-shear yield criterion and its application to limit pressures for thin and thick wall cylinders and thick wall spherical shells[J].The Chinese Journal of Nonferrous Metals,2007,17(2):207-215.
[16]李广信.高等土力学[M].北京:清华大学出版社,2004.LI Guang-xin.Advanced soil mechanics[M].Beijing:Tsinghua University Press,2004.
[17]高磊.矿山岩石力学[M].北京:机械工业出版社,1987.GAO Lei.Rock mechanics for mine[M].Beijing:Mechanical Engineering Press,1987.
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