考虑强度各向异性的黏性土应变局部化有限元分析
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摘要
针对黏性土的强度各向异性及应变局部化问题,将Pietruszczak微结构张量联合应力不变量的方法发展至分析黏性土的黏聚力各向异性,并将其引入Cosserat连续体理论下的Drucker-Prager本构模型中,实现黏聚力随应力状态变化而动态更新,推导有关公式并借助于有限元软件ABAQUS的二次开发功能进行数值实现,通过与试验结果的对比,验证所发展的数值方法的可靠性和有效性。对平面应变条件下的单轴压缩和挡土墙被动破坏算例进行分析,说明黏聚力的强度各向异性对承载力和变形有重要影响,并对不同工况下黏聚力的取值提供合理建议。经过与经典连续体模型的计算结果进行对比研究,证明文中所发展的Cosserat连续体理论下考虑强度各向异性的数值模型,能克服经典连续体模型病态的网格敏感性,保持应变局部化问题的适定性。
Aiming at the problems of strength anisotropy and strain localization of cohesive soils,Pietruszczak′s method considering microstructure tensor combined with stress invariance was developed to analyze the cohesion anisotropy of cohesive soils and introduced into Drucker-Prager constitutive model based on Cosserat continuum theory to realize dynamically updating of the cohesion with the change of the stress state. The relevant formulas were derived and the numerical implementation was carried out by means of the secondary development function of the finite element software-ABAQUS. The reliability and effectiveness of the numerical method developed in this paper were verified by comparison with the experimental results. Examples of uniaxial compression and passive failure of the retaining wall under plane strain condition were illustrated,and the reasonable values of the cohesion under different working conditions were proposed. It is shown that the cohesion anisotropy has an important influence on bearing capacity and deformation. Comparison with the calculation results by the classical continuum model indicates that the developed numerical model considering the strength anisotropy based on the Cosserat continuum theory can overcome the ill-posedness of mesh sensitivity and maintain the well-posedness of the strain localization problem.
Aiming at the problems of strength anisotropy and strain localization of cohesive soils,Pietruszczak′s method considering microstructure tensor combined with stress invariance was developed to analyze the cohesion anisotropy of cohesive soils and introduced into Drucker-Prager constitutive model based on Cosserat continuum theory to realize dynamically updating of the cohesion with the change of the stress state. The relevant formulas were derived and the numerical implementation was carried out by means of the secondary development function of the finite element software-ABAQUS. The reliability and effectiveness of the numerical method developed in this paper were verified by comparison with the experimental results. Examples of uniaxial compression and passive failure of the retaining wall under plane strain condition were illustrated,and the reasonable values of the cohesion under different working conditions were proposed. It is shown that the cohesion anisotropy has an important influence on bearing capacity and deformation. Comparison with the calculation results by the classical continuum model indicates that the developed numerical model considering the strength anisotropy based on the Cosserat continuum theory can overcome the ill-posedness of mesh sensitivity and maintain the well-posedness of the strain localization problem.
引文
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[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):5 146-5 162.
[21]CHANG J F,CHU X H,XU Y J.Finite-element analysis of failure in transversely isotropic geomaterials[J].International Journal of Geomechanics,2015,15(6):1 943-5 622.
[22]YAO Y,TIAN Y,GAO Z.Anisotropic UH model for soils based on a simple transformed stress method:Anisotropic UH Model[J].International Journal for Numerical and Analytical Methods in Geomechanics,2017,41(1):54-78.
[23]余天堂,卢应发,SHAO J F.沉积岩的一种时间效应模型[J].岩石力学与工程学报,2002,21(11):1 598-1 601.(YU Tiantang,LUYingfa,SHAO J F.A time-effect model of sedimentary rocks[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(11):1 598-1 601.(in Chinese))
[24]GAO Z W,ZHAO J D.Efficient approach to characterize strength anisotropy in soil[J].Journal of Engineering Mechanics,2012,138(12):1 447-1 456.
[25]SCHWEIGER H F,SCHARINGER F,WILTASKY C,et al.Amultilaminate framework for modelling induced and inherent anisotropy of soils[J].Geotechnique,2009,59(2):87-100.
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[27]王建锋,陈祖煜,张基泰.各向异性非线性强度条件下的边坡稳定性[J].力学与实践,2004,26(5):22-25.(WANG Jianfeng,CHENZuyu,ZHANG Jitai.Slope stability under anisotropic nonlinear strength conditions[J].Mechanics in Engineering,2004,26(5):22-25.(in Chinese))
[28]LO K Y.Stability of slopes in anisotropic soils[J].Journal of the Soil Mechanics and Foundations Division,ASCE,1965,91(SM4):85-106.
[29]张坤勇,殷宗泽.复杂应力条件下土体各向异性及其建模思路[J].岩土力学,2007,28(增1):149-154.(ZHANG Kunyong,YIN Zongze.Discussion on soil′s anisotropy under complicated stress state and the study method[J].Rock and Soil Mechanics,2007,28(Supp.1):149-154.(in Chinese))
[30]KULHAWY F H,MAYNE P W.Manual on estimating soil properties for foundation design[R].Ithaca,NY:Cornell University,1990.
[31]高彦斌,楼康明.上海软粘土强度固有各向异性[J].同济大学学报:自然科学版,2013,41(11):1 658-1 663.(GAO Yanbin,LOUKangming.Strength anisotropy of Shanghai soft clay induced by inherent fabric[J].Journal of Tongji University:Natural Science,2013,41(11):1 658-1 663.(in Chinese))
[32]TANG H X,DU T,ZHANG L J,et al.A plane strain testing apparatus characterized by flexible loading and non-contact deformation measurement and its application to the study of shear band failure of sand[J].International Journal of Distributed Sensor Networks,2018,14(9):1-16.
[2]BARDEN L,SIDES G.Engineering behavior and structure of compacted clays[J].Journal of the Soil Mechanics and Foundations Division,ASCE,1970,96(SM4):171-200.
[3]BARDEN L.The influence of structure on deformation and failure in clay soil[J].Geotechnique,1972,22(1):159-163.
[4]QUIGLEY R M,THOMPSON C D.The fabric of anisotropically consolidated sensitive marine clay[J].Canadian Geotechnical Journal,1966,3(2):61-73.
[5]ALKARNI A A,ALSHAMRANI M A.Study of the effect of soil anisotropy on slope stability using method of slices[J].Computers and Geotechnics,2000,26(2):83-103.
[6]VAID Y P,SIVAYHAYALAN S.Static and cyclic liquefaction potential of Fraser Delta sand in simple shear and triaxial tests[J].Canadian Geotechnical Journal,1996,33(2):281-289.
[7]ARTHUR J R F,AMENZIES B.Inherent anisotropy in a sand[J].Geotechnique,1972,22(1):115-128.
[8]ARTHUR J R F,CHUA K S,DUNSTAN T.Induced anisotropy in a sand[J].Geotechnique,1979,27(1):13-30.
[9]PIETRUSZCZAK S,MROZ Z.On failure criteria for anisotropic cohesive-frictional materials[J].International Journal for Numerical and Analytical Methods in Geomechanics,2001,25(5):509-524.
[10]SEKIGUCHI H,OHTA H.induced anisotropy and time dependency in clays[C]//Proceedings of 9th ICSMFE.[S.l.]:[s.n.],1977:229-238.
[11]MATSUOKA H,YAO Y P,SUN D A.The Cam-clay models reviesed by the SMP criterion[J].Soils and Foundations,1999,39(1):81-95.
[12]YAO Y P,SUN D A.Application of lade′s criterion to cam-clay model[J].Journal of Engineering Mechanics,2000,127(6):112-119.
[13]孙德安,姚仰平,殷宗泽.初始应力各向异性土的弹塑性模型[J].岩土力学,2000,21(3):222-226.(SUN Dean,YAO Yangping,YIN Zongze.An elasto-plastic model for soil with initially stressinduced anisotropy[J].Rock and Soil Mechanics,2000,21(3):222-226.(in Chinese))
[14]王乃东,姚仰平.基于变换应力方法的各向异性模型三维化[J].岩土工程学报,2011,33(1):50-56.(WANG Naidong,YAO Yangping.Generalization of anisotropic constitutive models using transformed stress method[J].Chinese Journal of Geotechnical Engineering,2011,33(1):50-56.(in Chinese))
[15]姚仰平,田雨,刘林.三维各向异性砂土UH模型[J].工程力学,2018,35(3):49-55.(YAO Yangping,TIAN Yu,LIU Lin.Three-dimensional anisotropic UH model for sands[J].Engineering Mechanics,2018,35(3):49-55.(in Chinese))
[16]王栋,金霞.考虑强度各向异性的边坡稳定有限元分析[J].岩土力学,2008,29(3):667-672.(WANG Dong,JIN Xia.Slope stability analysis by finite elements considering strength anisotropy[J].Rock and Soil Mechanics,2008,29(3):667-672.(in Chinese))
[17]CASAGRANDE A,CARILLO N.Shear failure of anisotropic materials[J].Journal of the Boston Society of Civil Engineers,1944,31(4):1 941-1 953.
[18]范庆来,栾茂田.各向异性软粘土地基上浅基础破坏包络面研究[J].岩石力学与工程学报,2010,29(11):2 362-2 369.(FAN Qinglai,LUAN Maotian.Study of failure envelope of shallow foundation on anisotropic soft clay[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(11):2 362-2 369.(in Chinese))
[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):5 146-5 162.
[21]CHANG J F,CHU X H,XU Y J.Finite-element analysis of failure in transversely isotropic geomaterials[J].International Journal of Geomechanics,2015,15(6):1 943-5 622.
[22]YAO Y,TIAN Y,GAO Z.Anisotropic UH model for soils based on a simple transformed stress method:Anisotropic UH Model[J].International Journal for Numerical and Analytical Methods in Geomechanics,2017,41(1):54-78.
[23]余天堂,卢应发,SHAO J F.沉积岩的一种时间效应模型[J].岩石力学与工程学报,2002,21(11):1 598-1 601.(YU Tiantang,LUYingfa,SHAO J F.A time-effect model of sedimentary rocks[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(11):1 598-1 601.(in Chinese))
[24]GAO Z W,ZHAO J D.Efficient approach to characterize strength anisotropy in soil[J].Journal of Engineering Mechanics,2012,138(12):1 447-1 456.
[25]SCHWEIGER H F,SCHARINGER F,WILTASKY C,et al.Amultilaminate framework for modelling induced and inherent anisotropy of soils[J].Geotechnique,2009,59(2):87-100.
[26]唐洪祥,李锡夔.岩土体应变局部化的Cosserat连续体理论与数值分析[M].北京:科学出版社,2018:13-85.(TANG Hongxiang,LI Xikui.Theory and numerical analysis of cosine serat continuum for geotechnical strain localization[M].Beijing:Science Press,2018:13-85.(in Chinese))
[27]王建锋,陈祖煜,张基泰.各向异性非线性强度条件下的边坡稳定性[J].力学与实践,2004,26(5):22-25.(WANG Jianfeng,CHENZuyu,ZHANG Jitai.Slope stability under anisotropic nonlinear strength conditions[J].Mechanics in Engineering,2004,26(5):22-25.(in Chinese))
[28]LO K Y.Stability of slopes in anisotropic soils[J].Journal of the Soil Mechanics and Foundations Division,ASCE,1965,91(SM4):85-106.
[29]张坤勇,殷宗泽.复杂应力条件下土体各向异性及其建模思路[J].岩土力学,2007,28(增1):149-154.(ZHANG Kunyong,YIN Zongze.Discussion on soil′s anisotropy under complicated stress state and the study method[J].Rock and Soil Mechanics,2007,28(Supp.1):149-154.(in Chinese))
[30]KULHAWY F H,MAYNE P W.Manual on estimating soil properties for foundation design[R].Ithaca,NY:Cornell University,1990.
[31]高彦斌,楼康明.上海软粘土强度固有各向异性[J].同济大学学报:自然科学版,2013,41(11):1 658-1 663.(GAO Yanbin,LOUKangming.Strength anisotropy of Shanghai soft clay induced by inherent fabric[J].Journal of Tongji University:Natural Science,2013,41(11):1 658-1 663.(in Chinese))
[32]TANG H X,DU T,ZHANG L J,et al.A plane strain testing apparatus characterized by flexible loading and non-contact deformation measurement and its application to the study of shear band failure of sand[J].International Journal of Distributed Sensor Networks,2018,14(9):1-16.