横观各向同性土的三维强度准则
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摘要
横观各向同性土体的强度规律包括两个方面:偏平面上的强度曲线畸变和大主应力作用面与沉积面相对夹角?方向上的强度参数变化。当前对横观各向同性材料强度准则的研究主要集中在反映主应力与沉积面垂直条件下偏平面上的强度规律,对方向角?方向上的强度规律研究还不完善。基于微观结构张量法,通过引入滑动面的概念,以大主应力垂直作用于水平沉积面时应力空间与物理空间重合为基准,利用三维滑动面与沉积面之间的相对位置关系,并综合方向角?方向上的强度变化规律,提出了三维横观各向同性强度参数ηn。将其与M-N强度准则相结合,得到了横观各向同性土的三维强度准则。所得强度准则考虑了主应力与沉积面绕某一主应力轴旋转过程中偏平面强度曲线的变化,综合地反映了横观各向同性土体的强度规律。
The strength characteristic of the transverse isotropic soil include two aspects. On one hand, the strength curves are not symmetric around the three principal stress axes on deviatoric plane. On the other hand, the strength parameter varies with the included angle d between the acting plane of the major principal stress and the depositional plane. The existing studies about the strength of transverse isotropic materials are immature, especially the strength description of the included angle ddirection. The concept of mobilized plane is introduced into a method that considers the microstructural tensor. Based on the coincidence of the stress space with the physical space, the relative position between the 3D mobilized plane and the depositional plane is analyzed. Then a 3D strength parameter η n is proposed by considering the change rules of included angle d direction. The transverse isotropic strength criterion is proposed by marrying the 3D strength parameter to the Matsuoka-Nakai strength criterion. The proposed transverse isotropic strength criterion is able to describe the distortion of the strength curves on deviatoric plane and the non-monotonic rule with respect to the included angle d comprehensively.
The strength characteristic of the transverse isotropic soil include two aspects. On one hand, the strength curves are not symmetric around the three principal stress axes on deviatoric plane. On the other hand, the strength parameter varies with the included angle d between the acting plane of the major principal stress and the depositional plane. The existing studies about the strength of transverse isotropic materials are immature, especially the strength description of the included angle ddirection. The concept of mobilized plane is introduced into a method that considers the microstructural tensor. Based on the coincidence of the stress space with the physical space, the relative position between the 3D mobilized plane and the depositional plane is analyzed. Then a 3D strength parameter η n is proposed by considering the change rules of included angle d direction. The transverse isotropic strength criterion is proposed by marrying the 3D strength parameter to the Matsuoka-Nakai strength criterion. The proposed transverse isotropic strength criterion is able to describe the distortion of the strength curves on deviatoric plane and the non-monotonic rule with respect to the included angle d comprehensively.
引文
[1]LAM W,TATSUOKA F.Effects of initial anisotropic fabric and 2?on strength and deformation characteristics of sand[J].Soils and Foundations,1988,28(1):89–106.
[2]KIRKGARD M M,LADE P V.Anisotropic three-dimensional behavior of a normally consolidated clay[J].Canadian Geotechnical Journal,1993,30(5):848–858.
[3]王洪瑾,张国平,周克骥.固有和诱发各向异性对击实粘性土强度和变形特性的影响[J].岩土工程学报,1996,18(3):1–10.(WANG Hong-jin,ZHANG Guo-ping,ZHOU Ke-ji.Effects of inherent and induced anisotropy on strength and deformation characteristics of compacted cohesive soil[J].Chinese Journal of Geotechnical Engineering,1996,18(3):1–10.(in Chinese))
[4]LADE P V,RODRIGUEZ N M,VAN DYCK E J.Effects of principal stress directions on 3D failure conditions in crossanisotropic sand[J].Journal of Geotechnical and Geoenvironmental Engineering,2014,140(2):1–12.
[5]ODA M,KOISHIKAWA I,HIGUCHI T.Experimental study of anisotropic shear strength of sand by plane strain test[J].Soils and Foundations,1978,18(1):25–38.
[6]ZDRAVKOVIC L,POTTS D M,HIGHT D W.The effect of strength anisotropy on the behaviour of embankments on soft ground[J].Géotechnique,2002,52(6):447–457.
[7]殷宗泽,张坤勇,朱俊高.面板堆石坝应力变形计算中考虑土的各向异性[J].水利学报,2004,35(11):22–26.(YIN Zong-ze,ZHANG Kun-yong,ZHU Jun-gao.Considering soil’s anisotropy in the calculation of stress deformation of concret-faced rockfill dam[J].Journal of Hydraulic Engineering,2012,43(1):43–50.(in Chinese))
[8]陈越.粒状材料强度异向性的物理实质和数学表现形式[J].岩土工程学报,1992,14(1):1–13.(CHEN Yue.Physical essence and mechanical expressions of strength-anisotropy for granular materials[J].Chinese Journal of Geotechnical Engineering,1992,14(1):1–13.(in Chinese))
[9]姚仰平,祝恩阳.横观各向同性土的简明破坏机制解释[J].岩土力学,2014,35(2):328–333.(YAO Yang-ping,ZHU En-yang.Concise interpretation of damage mechanism for cross-anisotropic soil[J].Rock and Soil Mechanics,2014,35(2):328–333.(in Chinese))
[10]ABELEV A V,LADE P V.Characterization of failure in cross-anisotropic soils[J].Journal of Engineering Mechanics.2004,130(5):599–606.
[11]MORTARA G.A yield criterion for isotropic and crossanisotropic cohesive-frictional materials[J].International Journal for Numerical and Analytical Methods in Geomechanics,2010,34(10):953–977.
[12]LüX L,HUANG M S,QIAN J G.The onset of strain localization in cross-anisotropic soils under true triaxial condition[J].Soils and Foundations,2011,51(4):693–700.
[13]GAO Z W,ZHAO J D,YAO Y P.A generalized anisotropic failure criterion for geomaterials[J].International Journal of Solids and Structures,2010,47(22/23):3166–3185.
[14]GAO Z W,ZHAO J D.Efficient approach to characterize strength anisotropy in soils[J].Journal of Engineering Mechanics,2012,138(12):1447–1456.
[15]李学丰,黄茂松,钱建固.宏细观结合的砂土各向异性破坏准则[J].岩石力学与工程学报,2010,29(9):1885–1892.(LI Xue-feng,HUANG Mao-song,QIAN Jian-gu.Failure criterion of anisotropic sand with method of macro-meso incorporation[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(9):1885–1892.(in Chinese))
[16]刘洋.砂土的各向异性强度准则:原生各向异性[J].岩土工程学报,2013,35(8):1526–1534.(LIU Yang.Anisotropic strength criteria of sand:inherent anisotropy[J].Chinese Journal of Geotechnical Engineering,2013,35(8):1526–1534.(in Chinese))
[17]TOBITA Y,YANAGISAWA E.Modified stress tensors for anisotropic behavior of granular materials[J].Soils and Foundations,1992,32(1):85–99.
[18]YAO Y P,TIAN Y,GAO Z W.Anisotropic UH model for soils based on a simple transformed stress method[J].International Journal for Numerical and Analytical Methods in Geomechanics,2017,41(1):54–78.
[19]PIETRUSZCZAK S,MROZ Z.Formulation of anisotropic failure criteria incorporating a microstructure tensor[J].Computers and Geotechnics,2000,26(2):105–112.
[20]LADE P V.Modeling failure in cross-anisotropic frictional materials[J].International Journal of Solids and Structures,2007,44(16):5146–5162.
[21]KONG Y X,ZHAO J D,YAO Y P.A failure criterion for cross-anisotropic soils considering microstructure[J].Acta Geotechnica,2013,8(6):665–673.
[22]罗汀,李萌,孔玉侠,等.基于SMP的岩土各向异性强度准则[J].岩土力学,2009,30(增刊2):127–131.(LUO Ting,LI Meng,KONG Yu-xia,et al.Failure criterion based on SMP for anisotropic geomaterials[J].Rock and Soil Mechanics,2009,30(S2):127–131.(in Chinese))
[23]LIU M D,INDRARATNA B N.General strength criterion for geomaterials including anisotropic effect[J].International Journal of Geomechanics,2011,11(3):251–261.
[24]姚仰平,孔玉侠.横观各向同性土强度与破坏准则的研究[J].水利学报,2012,39(1):43–50.(YAO Yang-ping,KONG Yu-xia.Research on the cross-anisotropic soil’s strength and failure criterion[J].Journal of Hydraulic Engineering,2012,39(1):43–50.(in Chinese))
[25]YAO Y P,KONG Y X.Extended UH model:threedimensional unified hardening model for anisotropic clays[J].Journal of Engineering Mechanics,2012,138(7):853–866.
[26]张连卫,张建民,张嘎.基于SMP的粒状材料各向异性强度准则[J].岩土工程学报,2008,30(8):1107–1111.(ZHANG Lian-wei,ZHANG Jian-min,ZHANG Ga.SMP-based anisotropic strength criteria of granular materials[J].Chinese Journal of Rock Mechanics and Engineering,2008,30(8):1107–1111.(in Chinese))
[27]MATSUOKA H.Stress-strain relationships of sands based on the mobilized plane[J].Soils and Foundations,1974,14(2):47–61.
[28]路德春,杜修力.岩石材料的非线性强度与破坏准则研究[J].岩石力学与工程学报.2013,32(12):2394–2408.(LU De-chun,DU Xiu-li.Research on nonlinear strength and failure criterion of rock material[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(12):2394–2408.(in Chinese))
[29]路德春,姚仰平,邹博.广义非线性强度理论体系[J].岩土力学,2007,28(10):2009–2016.(LU De-chun,YAO Yang-ping,ZOU Bo.System of generalized nonlinear strength theory[J].Rock and Soil Mechanics,2007,28(10):2009–2016.(in Chinese))
[30]LADE P V,RODRIGUEZ N M,VAN DYCK E J.Effects of principal stress directions on 3D failure conditions in cross-anisotropic sand[J].Journal of Geotechnical and Geoenvironmental Engineering,2014,140(2):1–12.
[31]MATSUOKA H,JUN-ICHI H,KIYOSHI H.Deformation and failure of anisotropic sand deposits[J].Soil Mechanics and Foundation Engineering,1984,32(11):31–36.
[32]LüX L,HUANG M S,ANDRADE J E.Strength criterion for cross-anisotropic sand under general stress conditions[J].Acta Geotechnica.2016,11(6):1339–1350.
[33]LU D C,MA C,DU X L,et al.Development of a new nonlinear unified strength theory for geomaterials based on the characteristic stress concept[J].International Journal of Geomechanics,2017,17(2):1–11.
[34]杜修力,马超,路德春.岩土材料的非线性统一强度模型[J].力学学报,2014,46(3):389–397.(DU Xiu-li,MA Chao,LU De-chun.Nonlinear unified strength model of geomaterials[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(3):389–397.(in Chinese))
[35]杜修力,马超,路德春.岩土类材料的静水压力效应[J].岩石力学与工程学报,2015,34(3):572–582.(DU Xiu-li,MA Chao,LU De-chun.Effect of hydrostatic pressure on geomaterials[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(3):572–582.(in Chinese))
[36]LADE P V,NAM J,HONG W P.Shear banding and cross-anisotropic behavior observed in laboratiory sand tests with stress rotation[J].Canadian Geotechnical Journal,2008,45(1):74–84.
[2]KIRKGARD M M,LADE P V.Anisotropic three-dimensional behavior of a normally consolidated clay[J].Canadian Geotechnical Journal,1993,30(5):848–858.
[3]王洪瑾,张国平,周克骥.固有和诱发各向异性对击实粘性土强度和变形特性的影响[J].岩土工程学报,1996,18(3):1–10.(WANG Hong-jin,ZHANG Guo-ping,ZHOU Ke-ji.Effects of inherent and induced anisotropy on strength and deformation characteristics of compacted cohesive soil[J].Chinese Journal of Geotechnical Engineering,1996,18(3):1–10.(in Chinese))
[4]LADE P V,RODRIGUEZ N M,VAN DYCK E J.Effects of principal stress directions on 3D failure conditions in crossanisotropic sand[J].Journal of Geotechnical and Geoenvironmental Engineering,2014,140(2):1–12.
[5]ODA M,KOISHIKAWA I,HIGUCHI T.Experimental study of anisotropic shear strength of sand by plane strain test[J].Soils and Foundations,1978,18(1):25–38.
[6]ZDRAVKOVIC L,POTTS D M,HIGHT D W.The effect of strength anisotropy on the behaviour of embankments on soft ground[J].Géotechnique,2002,52(6):447–457.
[7]殷宗泽,张坤勇,朱俊高.面板堆石坝应力变形计算中考虑土的各向异性[J].水利学报,2004,35(11):22–26.(YIN Zong-ze,ZHANG Kun-yong,ZHU Jun-gao.Considering soil’s anisotropy in the calculation of stress deformation of concret-faced rockfill dam[J].Journal of Hydraulic Engineering,2012,43(1):43–50.(in Chinese))
[8]陈越.粒状材料强度异向性的物理实质和数学表现形式[J].岩土工程学报,1992,14(1):1–13.(CHEN Yue.Physical essence and mechanical expressions of strength-anisotropy for granular materials[J].Chinese Journal of Geotechnical Engineering,1992,14(1):1–13.(in Chinese))
[9]姚仰平,祝恩阳.横观各向同性土的简明破坏机制解释[J].岩土力学,2014,35(2):328–333.(YAO Yang-ping,ZHU En-yang.Concise interpretation of damage mechanism for cross-anisotropic soil[J].Rock and Soil Mechanics,2014,35(2):328–333.(in Chinese))
[10]ABELEV A V,LADE P V.Characterization of failure in cross-anisotropic soils[J].Journal of Engineering Mechanics.2004,130(5):599–606.
[11]MORTARA G.A yield criterion for isotropic and crossanisotropic cohesive-frictional materials[J].International Journal for Numerical and Analytical Methods in Geomechanics,2010,34(10):953–977.
[12]LüX L,HUANG M S,QIAN J G.The onset of strain localization in cross-anisotropic soils under true triaxial condition[J].Soils and Foundations,2011,51(4):693–700.
[13]GAO Z W,ZHAO J D,YAO Y P.A generalized anisotropic failure criterion for geomaterials[J].International Journal of Solids and Structures,2010,47(22/23):3166–3185.
[14]GAO Z W,ZHAO J D.Efficient approach to characterize strength anisotropy in soils[J].Journal of Engineering Mechanics,2012,138(12):1447–1456.
[15]李学丰,黄茂松,钱建固.宏细观结合的砂土各向异性破坏准则[J].岩石力学与工程学报,2010,29(9):1885–1892.(LI Xue-feng,HUANG Mao-song,QIAN Jian-gu.Failure criterion of anisotropic sand with method of macro-meso incorporation[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(9):1885–1892.(in Chinese))
[16]刘洋.砂土的各向异性强度准则:原生各向异性[J].岩土工程学报,2013,35(8):1526–1534.(LIU Yang.Anisotropic strength criteria of sand:inherent anisotropy[J].Chinese Journal of Geotechnical Engineering,2013,35(8):1526–1534.(in Chinese))
[17]TOBITA Y,YANAGISAWA E.Modified stress tensors for anisotropic behavior of granular materials[J].Soils and Foundations,1992,32(1):85–99.
[18]YAO Y P,TIAN Y,GAO Z W.Anisotropic UH model for soils based on a simple transformed stress method[J].International Journal for Numerical and Analytical Methods in Geomechanics,2017,41(1):54–78.
[19]PIETRUSZCZAK S,MROZ Z.Formulation of anisotropic failure criteria incorporating a microstructure tensor[J].Computers and Geotechnics,2000,26(2):105–112.
[20]LADE P V.Modeling failure in cross-anisotropic frictional materials[J].International Journal of Solids and Structures,2007,44(16):5146–5162.
[21]KONG Y X,ZHAO J D,YAO Y P.A failure criterion for cross-anisotropic soils considering microstructure[J].Acta Geotechnica,2013,8(6):665–673.
[22]罗汀,李萌,孔玉侠,等.基于SMP的岩土各向异性强度准则[J].岩土力学,2009,30(增刊2):127–131.(LUO Ting,LI Meng,KONG Yu-xia,et al.Failure criterion based on SMP for anisotropic geomaterials[J].Rock and Soil Mechanics,2009,30(S2):127–131.(in Chinese))
[23]LIU M D,INDRARATNA B N.General strength criterion for geomaterials including anisotropic effect[J].International Journal of Geomechanics,2011,11(3):251–261.
[24]姚仰平,孔玉侠.横观各向同性土强度与破坏准则的研究[J].水利学报,2012,39(1):43–50.(YAO Yang-ping,KONG Yu-xia.Research on the cross-anisotropic soil’s strength and failure criterion[J].Journal of Hydraulic Engineering,2012,39(1):43–50.(in Chinese))
[25]YAO Y P,KONG Y X.Extended UH model:threedimensional unified hardening model for anisotropic clays[J].Journal of Engineering Mechanics,2012,138(7):853–866.
[26]张连卫,张建民,张嘎.基于SMP的粒状材料各向异性强度准则[J].岩土工程学报,2008,30(8):1107–1111.(ZHANG Lian-wei,ZHANG Jian-min,ZHANG Ga.SMP-based anisotropic strength criteria of granular materials[J].Chinese Journal of Rock Mechanics and Engineering,2008,30(8):1107–1111.(in Chinese))
[27]MATSUOKA H.Stress-strain relationships of sands based on the mobilized plane[J].Soils and Foundations,1974,14(2):47–61.
[28]路德春,杜修力.岩石材料的非线性强度与破坏准则研究[J].岩石力学与工程学报.2013,32(12):2394–2408.(LU De-chun,DU Xiu-li.Research on nonlinear strength and failure criterion of rock material[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(12):2394–2408.(in Chinese))
[29]路德春,姚仰平,邹博.广义非线性强度理论体系[J].岩土力学,2007,28(10):2009–2016.(LU De-chun,YAO Yang-ping,ZOU Bo.System of generalized nonlinear strength theory[J].Rock and Soil Mechanics,2007,28(10):2009–2016.(in Chinese))
[30]LADE P V,RODRIGUEZ N M,VAN DYCK E J.Effects of principal stress directions on 3D failure conditions in cross-anisotropic sand[J].Journal of Geotechnical and Geoenvironmental Engineering,2014,140(2):1–12.
[31]MATSUOKA H,JUN-ICHI H,KIYOSHI H.Deformation and failure of anisotropic sand deposits[J].Soil Mechanics and Foundation Engineering,1984,32(11):31–36.
[32]LüX L,HUANG M S,ANDRADE J E.Strength criterion for cross-anisotropic sand under general stress conditions[J].Acta Geotechnica.2016,11(6):1339–1350.
[33]LU D C,MA C,DU X L,et al.Development of a new nonlinear unified strength theory for geomaterials based on the characteristic stress concept[J].International Journal of Geomechanics,2017,17(2):1–11.
[34]杜修力,马超,路德春.岩土材料的非线性统一强度模型[J].力学学报,2014,46(3):389–397.(DU Xiu-li,MA Chao,LU De-chun.Nonlinear unified strength model of geomaterials[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(3):389–397.(in Chinese))
[35]杜修力,马超,路德春.岩土类材料的静水压力效应[J].岩石力学与工程学报,2015,34(3):572–582.(DU Xiu-li,MA Chao,LU De-chun.Effect of hydrostatic pressure on geomaterials[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(3):572–582.(in Chinese))
[36]LADE P V,NAM J,HONG W P.Shear banding and cross-anisotropic behavior observed in laboratiory sand tests with stress rotation[J].Canadian Geotechnical Journal,2008,45(1):74–84.