具有非线性强度包络线的双剪双参数统一强度准则改进式及其特征分析
|
摘要
通过应力莫尔圆分析证明现有的双剪双参数统一强度准则采用的强度包络线为线性包络线,在此基础上对原有准则作了改进,改进后的双剪双参数统一强度准则采用了抛物线和双曲线形强度包络线,能够更好地表征岩石的强度特性,特别是抗拉强度特性。对改进式所作的π平面极限线和子午线分析表明,采用抛物线和双曲线形强度包络线基本上不会改变原准则在π平面上的极限线形状,但子午线由直线改为曲线,极限面在主应力空间内分别为抛物面和双曲面,其锥顶距坐标原点也比采用线性强度包络线的要小。从锥形极限面的大小来看,具有双曲线形和抛物线形强度包络线的双剪双参数统一强度准则改进式要小于直线形的,且抛物线形的最小。
Analysis of the Mohr circles proves that the original two-parameter double shear unified failure criterion has the linear type failure envelope,and the improved failure criteria with parabolic and hyperbolic type failure envelopes are given out in order to describe the rock failure properties,especially the rock tensile property better than the original one. Analyses of loci in the π plane and meridian lines show that the parabolic and hyperbolic type failure envelopes have no influences on the shape of the loci in the π plane,but the shape of the meridian lines are changed from straight lines to curved lines. The limit surfaces of the improved criteria are paraboloid or hyperboloid in the principal stress coordinates. Distances from the conic points to the original coordinate point are smaller than those using the linear type failure envelope. Cone sizes among the criteria using three different envelopes are the criteria with parabolic type failure envelope being the smallest,with hyperbolic type failure envelope being the second,and with linear type failure envelope being the largest.
Analysis of the Mohr circles proves that the original two-parameter double shear unified failure criterion has the linear type failure envelope,and the improved failure criteria with parabolic and hyperbolic type failure envelopes are given out in order to describe the rock failure properties,especially the rock tensile property better than the original one. Analyses of loci in the π plane and meridian lines show that the parabolic and hyperbolic type failure envelopes have no influences on the shape of the loci in the π plane,but the shape of the meridian lines are changed from straight lines to curved lines. The limit surfaces of the improved criteria are paraboloid or hyperboloid in the principal stress coordinates. Distances from the conic points to the original coordinate point are smaller than those using the linear type failure envelope. Cone sizes among the criteria using three different envelopes are the criteria with parabolic type failure envelope being the smallest,with hyperbolic type failure envelope being the second,and with linear type failure envelope being the largest.
引文
[1]Mogi K.Effect of intermediate principal stress on rock failure[J].J.Geophys.Res.,1967,72:5117–5131.
[2]Mogi K.Failure and flow of rocks under high triaxial compression[J].J.Geophys.Res.,1971,76:1255–1269.
[3]Michelis P.Polyaxial yielding of granular rock[J].J.Eng.Mech.,ASCE,1985,111(18):1049–1066.
[4]张金涛,林天健.三轴试验中岩石的应力状态和破坏性质[J].力学学报,1979,(2):99–105.(Zhang Jintao,Lin Tianjian.Stress conditions and variations of rupture characteristics of a rock as shown by tri-axial test[J].Acta Mechanica Sinica,1979,(2):99–105.(in Chinese))
[5]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 Dongjun,Geng Naiguang.The variation law of rock strength with increase of intermediate principal stress[J].Acta Mechanica Solida Sinica,1985,6(1):72–80.(in Chinese))
[6]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试验研究[R].武汉:中国科学院武汉岩土力学研究所,1990.(Li Xiaochun,Xu Dongjun.Experimental verification of the twin shear theory—true triaxial test research of strength of Lawaxi granite[R].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,1990.(in Chinese))
[7]俞茂宏,何丽南,宋凌宇.双剪强度理论及其推广[J].中国科学(A辑),1985,28(12):1113–1120.(Yu Maohong,He Linan,Song Lingyu.Twin shear theory and its generalization[J].Science China(Series A),1985,28(12):1113–1120.(in Chinese))
[8]俞茂宏,刘凤羽.一个新的普遍形式的强度理论[J].土木工程学报,1990,23(1):34–40.(Yu Maohong,Liu Fengyu.A new general strength theory[J].China Civil Engineering Journal,1990,23(1):34–40.(in Chinese))
[9]俞茂宏.岩土类材料的统一强度理论及其应用[J].岩土工程学报,1994,16(2):1–10.(Yu Maohong.Unified strength and its application for rock and soil[J].Chinese Journal of Geotechnical Engineering,1994,16(2):1–10.(in Chinese))
[10]俞茂宏.双剪理论及其应用[M].北京:科学出版社,1998.(Yu Maohong.Twin Shear Theory and Its Application[M].Beijing:Science Press,1998.(in Chinese))
[11]胡小荣,俞茂宏.统一强度理论及其在巷道围岩弹塑性分析中的应用研究[J].中国有色金属学报,2002,12(5):1021–1026.(Hu Xiaorong,Yu Maohong.Unified strength theory and its application in elsto-plastic analysis of tunnel[J].The Chinese Journal of Nonferrous Metals,2002,12(5):1021–1026.(in Chinese))
[12]徐栓强,俞茂宏,胡小荣.基于双剪统一强度理论的地下圆形洞室稳定性的研究[J].煤炭学报,2003,28(5):522–526.(Xu Shuanqiang,Yu Maohong,Hu Xiaorong.The stability analysis of circular tunnel based on twin shear unified strength theory[J].Journal of China Coal Society,2003,28(5):522–526.(in Chinese))
[13]高江平,俞茂宏,李四平.太沙基地基极限承载力的双剪统一解[J].岩石力学与工程学报,2005,24(15):2736–2740.(Gao Jiangping,Yu Maohong,Li Siping.Double-shear unified solution of Terzaghi ultimate bearing capacity of foundation[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(15):2736–2740(in Chinese))
[14]蒋明镜,沈珠江.考虑剪胀的线性软化柱形孔扩张问题[J].岩石力学与工程学报,1997,16(6):550–557.(Jiang Mingjing,Shen Zhujiang.On expansion of cylindrical cavity with linear softening and shear dilatation behavior[J].Chinese Journal of Rock Mechanics and Engineering,1997,16(6):550–557.(in Chinese))
[15]赵彭年.松散介质力学[M].北京:地震出版社,1995.(Zhao Pengnian.Mechanics of Loose Medium[M].Beijing:Earthquake Press,1995.(in Chinese))
[2]Mogi K.Failure and flow of rocks under high triaxial compression[J].J.Geophys.Res.,1971,76:1255–1269.
[3]Michelis P.Polyaxial yielding of granular rock[J].J.Eng.Mech.,ASCE,1985,111(18):1049–1066.
[4]张金涛,林天健.三轴试验中岩石的应力状态和破坏性质[J].力学学报,1979,(2):99–105.(Zhang Jintao,Lin Tianjian.Stress conditions and variations of rupture characteristics of a rock as shown by tri-axial test[J].Acta Mechanica Sinica,1979,(2):99–105.(in Chinese))
[5]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 Dongjun,Geng Naiguang.The variation law of rock strength with increase of intermediate principal stress[J].Acta Mechanica Solida Sinica,1985,6(1):72–80.(in Chinese))
[6]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试验研究[R].武汉:中国科学院武汉岩土力学研究所,1990.(Li Xiaochun,Xu Dongjun.Experimental verification of the twin shear theory—true triaxial test research of strength of Lawaxi granite[R].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,1990.(in Chinese))
[7]俞茂宏,何丽南,宋凌宇.双剪强度理论及其推广[J].中国科学(A辑),1985,28(12):1113–1120.(Yu Maohong,He Linan,Song Lingyu.Twin shear theory and its generalization[J].Science China(Series A),1985,28(12):1113–1120.(in Chinese))
[8]俞茂宏,刘凤羽.一个新的普遍形式的强度理论[J].土木工程学报,1990,23(1):34–40.(Yu Maohong,Liu Fengyu.A new general strength theory[J].China Civil Engineering Journal,1990,23(1):34–40.(in Chinese))
[9]俞茂宏.岩土类材料的统一强度理论及其应用[J].岩土工程学报,1994,16(2):1–10.(Yu Maohong.Unified strength and its application for rock and soil[J].Chinese Journal of Geotechnical Engineering,1994,16(2):1–10.(in Chinese))
[10]俞茂宏.双剪理论及其应用[M].北京:科学出版社,1998.(Yu Maohong.Twin Shear Theory and Its Application[M].Beijing:Science Press,1998.(in Chinese))
[11]胡小荣,俞茂宏.统一强度理论及其在巷道围岩弹塑性分析中的应用研究[J].中国有色金属学报,2002,12(5):1021–1026.(Hu Xiaorong,Yu Maohong.Unified strength theory and its application in elsto-plastic analysis of tunnel[J].The Chinese Journal of Nonferrous Metals,2002,12(5):1021–1026.(in Chinese))
[12]徐栓强,俞茂宏,胡小荣.基于双剪统一强度理论的地下圆形洞室稳定性的研究[J].煤炭学报,2003,28(5):522–526.(Xu Shuanqiang,Yu Maohong,Hu Xiaorong.The stability analysis of circular tunnel based on twin shear unified strength theory[J].Journal of China Coal Society,2003,28(5):522–526.(in Chinese))
[13]高江平,俞茂宏,李四平.太沙基地基极限承载力的双剪统一解[J].岩石力学与工程学报,2005,24(15):2736–2740.(Gao Jiangping,Yu Maohong,Li Siping.Double-shear unified solution of Terzaghi ultimate bearing capacity of foundation[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(15):2736–2740(in Chinese))
[14]蒋明镜,沈珠江.考虑剪胀的线性软化柱形孔扩张问题[J].岩石力学与工程学报,1997,16(6):550–557.(Jiang Mingjing,Shen Zhujiang.On expansion of cylindrical cavity with linear softening and shear dilatation behavior[J].Chinese Journal of Rock Mechanics and Engineering,1997,16(6):550–557.(in Chinese))
[15]赵彭年.松散介质力学[M].北京:地震出版社,1995.(Zhao Pengnian.Mechanics of Loose Medium[M].Beijing:Earthquake Press,1995.(in Chinese))
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心