适用于砂土循环加载分析的边界面塑性模型
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摘要
基于临界状态土力学框架,建立了一个适用于砂土排水循环加载的边界面塑性模型。采用了考虑虚拟峰值应力比的偏应变硬化准则,初始加载阶段应力点位于边界面上,反向加载阶段以历史最大屈服面作为边界面,同时实现了对密砂软化现象的模拟和对历史所受最大应力的记忆。边界面采用修正的椭圆形,引入考虑密度与应力水平的状态相关剪胀函数,采用非相关联流动法则和以应力反向点作为映射中心的径向映射准则。模型仅有10个参数,通过常规三轴试验即可确定,并且使用一套参数可以模拟不同围压、密度的单调和循环加载情况。分别对饱和砂土的单调、循环排水三轴试验进行模拟,结果表明,该模型能够合理地反映饱和砂土排水条件下的应力-应变特性。
A bounding surface plasticity model for describing the stress-strain behavior of saturated sand subjected to drained cyclic loading is presented within a critical-state framework. A hardening rule depending on incremental deviatoric strain is adopted. During the initial loading, the stress state always locates on the bounding surface. During the unloading and reloading processes, the bounding surface is the historical maximum yielding surface. This hardening rule can describe the softening phenomena of dense sands and remember the stress history by the bounding surface. The shape of the bounding surface is a modified ellipse, which enables the model to describe the plastic strain during loading with constant stress ratio. This model incorporates state-dependent dilatancy and adopts the non-associated flow rule, so it can reasonably describe the volume change behavior of sandy soil. A mapping rule passing through stress reversal points is adopted. A single set of 10 model constants calibrated by conventional triaxial tests is needed for one type of sand under different initial void ratios and different confining pressures. The predicted results by the model for the monotonic and cyclic triaxial tests on Hostun sand, Nevada sand, Toyoura sand and Fuji River sand demonstrate that the model can reasonably describe the stress-strain characteristics of saturated sand.
A bounding surface plasticity model for describing the stress-strain behavior of saturated sand subjected to drained cyclic loading is presented within a critical-state framework. A hardening rule depending on incremental deviatoric strain is adopted. During the initial loading, the stress state always locates on the bounding surface. During the unloading and reloading processes, the bounding surface is the historical maximum yielding surface. This hardening rule can describe the softening phenomena of dense sands and remember the stress history by the bounding surface. The shape of the bounding surface is a modified ellipse, which enables the model to describe the plastic strain during loading with constant stress ratio. This model incorporates state-dependent dilatancy and adopts the non-associated flow rule, so it can reasonably describe the volume change behavior of sandy soil. A mapping rule passing through stress reversal points is adopted. A single set of 10 model constants calibrated by conventional triaxial tests is needed for one type of sand under different initial void ratios and different confining pressures. The predicted results by the model for the monotonic and cyclic triaxial tests on Hostun sand, Nevada sand, Toyoura sand and Fuji River sand demonstrate that the model can reasonably describe the stress-strain characteristics of saturated sand.
引文
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[2]PRASAD Y,RAO S N.Experimental studies on foundations of compliant structures-II.Under cyclic loading[J].Ocean Engineering,1994,21(1):15-27.
[3]BYRNE B W,HOULSBY G T.Experimental investigations of response of suction caissons to transient vertical loading[J].Journal of Geotechnical and Geoenvironmental Engineering,2002,128(11):926-939.
[4]SINGH S P,RAMASWAMY S V.Response of plate anchors to sustained-cyclic loading[J].Indian Geotechnical Journal,2002,32(2):161-172.
[5]胡存.适用于饱和黏土循环动力分析的边界面塑性模型及应用[D].天津:天津大学,2012.HU Cun.An isotropic bounding-surface plasticity model for cyclic behaviors of saturated clay and its application[D].Tianjin:Tianjin University,2012.
[6]DARVE F,LABANIEH S.Incremental constitutive law for sands and clays:Simulations of monotonic and cyclic tests[J].International Journal for Numerical and Analytical Methods in Geomechanics,1982,6(2):243-275.
[7]INEL S,LADE P V.Rotational kinematic hardening model for sand.Part II Characteristic work hardening law and predictions[J].Computers and Geotechnics,1997,21(3):217-234.
[8]LADE P V,INEL S.Rotational kinematic hardening model for sand.Part I concept of rotating yield and plastic potential surfaces[J].Computers and Geotechnics,1997,21(3):183-216.
[9]PASTOR M,ZIENKIEWICZ O C,CHAN A H C.Generalized plasticity and the modelling of soil behaviour[J].International Journal for Numerical and Analytical Methods in Geomechanics,1990,14(3):151-190.
[10]IWAN D W.On a class of models for the yielding behavior of continuous and composite systems[J].Journal of Applied Mechanics,1967,34:612-617.
[11]MROZ Z.On the description of anisotropic workhardening[J].Journal of the Mechanics and Physics of Solids,1967,15(3):163-175.
[12]DAFALIAS Y F.Bounding surface plasticity.I:Mathematical foundation and hypoplasticity[J].Journal of Engineering Mechanics,1986,112(9):966-987.
[13]徐舜华,郑刚,徐光黎.循环荷载下砂土的剪切硬化边界面本构模型[J].岩土力学,2010,31(1):1-8.XU Shun-hua,ZHENG Gang,XU Guang-li.A bounding surface constitutive model of sands with shear hardening[J].Rock and Soil Mechanics,2010,31(1):1-8.
[14]WANG Z L,DAFALIAS Y F,SHEN C K.Bounding surface hypoplasticity model for sand[J].Journal of Engineering Mechanics,1990,116(5):983-1001.
[15]胡存,刘海笑.适用于饱和黏土循环动力分析的新型边界面塑性模型[J].水利学报,2011,42(10):1192-1200.HU Cun,LIU Hai-xiao.A new type of bounding surface plasticity model for cyclic behavior of saturated clay[J].Journal of Hydraulic Engineering,2011,42(10):1192-1200.
[16]DAFALIAS Y F,POPOV E P.A model of nonlinearly hardening materials for complex loading[J].Acta Mechanica,1975,21(3):173-192.
[17]BARDET J P.Bounding surface plasticity model for sands[J].Journal of Engineering Mechanics,1986,112(11):1198-1217.
[18]CROUCH R S,WOLF J P,DAFALIAS Y F.Unified critical-state bounding-surface plasticity model for soil[J].Journal of Engineering Mechanics,1994,120(11):2251-2270.
[19]MANZARI M T,DAFALIAS Y F.A critical state two-surface plasticity model for sands[J].Geotechnique,1997,47(2):255-272.
[20]DAFALIAS Y F,MANZARI M T.Simple plasticity sand model accounting for fabric change effects[J].Journal of Engineering Mechanics,2004,130(6):622-634.
[21]LI X S,DAFALIAS Y F.Dilatancy for cohesionless soils[J].Geotechnique,2000,50(4):449-460.
[22]LI X S.A sand model with state-dependent dilatancy[J].Géotechnique,2002,52(3):173-186.
[23]KHALILI N,HABTE M A,VALLIAPPAN S.Abounding surface plasticity model for cyclic loading of granular soils[J].International Journal for Numerical Methods in Engineering,2005,63(14):1939-1960.
[24]KAN M E,TAIEBAT H A,KHALILI N.Simplified mapping rule for bounding surface simulation of complex loading paths in granular materials[J].International Journal of Geomechanics,2013,14(2):239-253.
[25]WANG G,XIE Y.Modified bounding surface hypoplasticity model for sands under cyclic loading[J].Journal of Engineering Mechanics,2013,140(1):91-101.
[26]BEARD R M.Holding capacity of plate anchors[M].California:Naval Construction Battalion Center,1980.
[27]ALLERSMA H G B,KIERSTEIN A A,MAES D.Centrifuge modelling on suction piles under cyclic and long term vertical loading[C]//The Tenth International Offshore and Polar Engineering Conference.Washington:International Society of Offshore and Polar Engineers,2000.
[28]ROWE P W.The stress-dilatancy relation for static equilibrium of an assembly of particles in contact[C]//Proceedings of the Royal Society A Mathematical,Physical and Engineering Sciences.London:The Royal Society,1962.
[29]ISHIHARA K,TATSUOKA F,YASUDA S.Undrained deformation and liquefaction of sand under cyclic stresses[J].Soils and Foundations,1975,15(1):29-44.
[30]WOOD D M,BELKHEIR K,LIU D F.Strain softening and state parameter for sand modelling[J].Geotechnique,1994,44(2):335-339.
[31]POOROOSHASB H B,HOLUBEC I,SHERBOURNE AN.Yielding and flow of sand in triaxial compression:Part I[J].Canadian Geotechnical Journal,1966,3(4):179-190.
[32]PRADHAN T B S,TATSUOKA F,SATO Y.Experimental stress-dilatancy relations of sand subjected to cyclic loading[J].Soils and Foundations,1989,29(1):45-64.
[33]GAJO A,WOOD M.Severn-trent sand:A kinematichardening constitutive model:The q-p formulation[J].Géotechnique,1999,49(5):595-614.
[34]ARULMOLI K,MURALEETHARAN K K,HOSSAINM M,et al.VELACS:Verification of liquefaction analyses by centrifuge studies[M].California:Earth Technology Corporation,1992.
[35]TATSUOKA F,ISHIHARA K.Drained deformation of sand under cyclic stresses reversing direction[J].Soils and Foundations,1974,14(3):51-65.
[2]PRASAD Y,RAO S N.Experimental studies on foundations of compliant structures-II.Under cyclic loading[J].Ocean Engineering,1994,21(1):15-27.
[3]BYRNE B W,HOULSBY G T.Experimental investigations of response of suction caissons to transient vertical loading[J].Journal of Geotechnical and Geoenvironmental Engineering,2002,128(11):926-939.
[4]SINGH S P,RAMASWAMY S V.Response of plate anchors to sustained-cyclic loading[J].Indian Geotechnical Journal,2002,32(2):161-172.
[5]胡存.适用于饱和黏土循环动力分析的边界面塑性模型及应用[D].天津:天津大学,2012.HU Cun.An isotropic bounding-surface plasticity model for cyclic behaviors of saturated clay and its application[D].Tianjin:Tianjin University,2012.
[6]DARVE F,LABANIEH S.Incremental constitutive law for sands and clays:Simulations of monotonic and cyclic tests[J].International Journal for Numerical and Analytical Methods in Geomechanics,1982,6(2):243-275.
[7]INEL S,LADE P V.Rotational kinematic hardening model for sand.Part II Characteristic work hardening law and predictions[J].Computers and Geotechnics,1997,21(3):217-234.
[8]LADE P V,INEL S.Rotational kinematic hardening model for sand.Part I concept of rotating yield and plastic potential surfaces[J].Computers and Geotechnics,1997,21(3):183-216.
[9]PASTOR M,ZIENKIEWICZ O C,CHAN A H C.Generalized plasticity and the modelling of soil behaviour[J].International Journal for Numerical and Analytical Methods in Geomechanics,1990,14(3):151-190.
[10]IWAN D W.On a class of models for the yielding behavior of continuous and composite systems[J].Journal of Applied Mechanics,1967,34:612-617.
[11]MROZ Z.On the description of anisotropic workhardening[J].Journal of the Mechanics and Physics of Solids,1967,15(3):163-175.
[12]DAFALIAS Y F.Bounding surface plasticity.I:Mathematical foundation and hypoplasticity[J].Journal of Engineering Mechanics,1986,112(9):966-987.
[13]徐舜华,郑刚,徐光黎.循环荷载下砂土的剪切硬化边界面本构模型[J].岩土力学,2010,31(1):1-8.XU Shun-hua,ZHENG Gang,XU Guang-li.A bounding surface constitutive model of sands with shear hardening[J].Rock and Soil Mechanics,2010,31(1):1-8.
[14]WANG Z L,DAFALIAS Y F,SHEN C K.Bounding surface hypoplasticity model for sand[J].Journal of Engineering Mechanics,1990,116(5):983-1001.
[15]胡存,刘海笑.适用于饱和黏土循环动力分析的新型边界面塑性模型[J].水利学报,2011,42(10):1192-1200.HU Cun,LIU Hai-xiao.A new type of bounding surface plasticity model for cyclic behavior of saturated clay[J].Journal of Hydraulic Engineering,2011,42(10):1192-1200.
[16]DAFALIAS Y F,POPOV E P.A model of nonlinearly hardening materials for complex loading[J].Acta Mechanica,1975,21(3):173-192.
[17]BARDET J P.Bounding surface plasticity model for sands[J].Journal of Engineering Mechanics,1986,112(11):1198-1217.
[18]CROUCH R S,WOLF J P,DAFALIAS Y F.Unified critical-state bounding-surface plasticity model for soil[J].Journal of Engineering Mechanics,1994,120(11):2251-2270.
[19]MANZARI M T,DAFALIAS Y F.A critical state two-surface plasticity model for sands[J].Geotechnique,1997,47(2):255-272.
[20]DAFALIAS Y F,MANZARI M T.Simple plasticity sand model accounting for fabric change effects[J].Journal of Engineering Mechanics,2004,130(6):622-634.
[21]LI X S,DAFALIAS Y F.Dilatancy for cohesionless soils[J].Geotechnique,2000,50(4):449-460.
[22]LI X S.A sand model with state-dependent dilatancy[J].Géotechnique,2002,52(3):173-186.
[23]KHALILI N,HABTE M A,VALLIAPPAN S.Abounding surface plasticity model for cyclic loading of granular soils[J].International Journal for Numerical Methods in Engineering,2005,63(14):1939-1960.
[24]KAN M E,TAIEBAT H A,KHALILI N.Simplified mapping rule for bounding surface simulation of complex loading paths in granular materials[J].International Journal of Geomechanics,2013,14(2):239-253.
[25]WANG G,XIE Y.Modified bounding surface hypoplasticity model for sands under cyclic loading[J].Journal of Engineering Mechanics,2013,140(1):91-101.
[26]BEARD R M.Holding capacity of plate anchors[M].California:Naval Construction Battalion Center,1980.
[27]ALLERSMA H G B,KIERSTEIN A A,MAES D.Centrifuge modelling on suction piles under cyclic and long term vertical loading[C]//The Tenth International Offshore and Polar Engineering Conference.Washington:International Society of Offshore and Polar Engineers,2000.
[28]ROWE P W.The stress-dilatancy relation for static equilibrium of an assembly of particles in contact[C]//Proceedings of the Royal Society A Mathematical,Physical and Engineering Sciences.London:The Royal Society,1962.
[29]ISHIHARA K,TATSUOKA F,YASUDA S.Undrained deformation and liquefaction of sand under cyclic stresses[J].Soils and Foundations,1975,15(1):29-44.
[30]WOOD D M,BELKHEIR K,LIU D F.Strain softening and state parameter for sand modelling[J].Geotechnique,1994,44(2):335-339.
[31]POOROOSHASB H B,HOLUBEC I,SHERBOURNE AN.Yielding and flow of sand in triaxial compression:Part I[J].Canadian Geotechnical Journal,1966,3(4):179-190.
[32]PRADHAN T B S,TATSUOKA F,SATO Y.Experimental stress-dilatancy relations of sand subjected to cyclic loading[J].Soils and Foundations,1989,29(1):45-64.
[33]GAJO A,WOOD M.Severn-trent sand:A kinematichardening constitutive model:The q-p formulation[J].Géotechnique,1999,49(5):595-614.
[34]ARULMOLI K,MURALEETHARAN K K,HOSSAINM M,et al.VELACS:Verification of liquefaction analyses by centrifuge studies[M].California:Earth Technology Corporation,1992.
[35]TATSUOKA F,ISHIHARA K.Drained deformation of sand under cyclic stresses reversing direction[J].Soils and Foundations,1974,14(3):51-65.