热力学方法在土体本构模型中的应用研究
|
摘要
传统岩土本构模型包括两类,一类是拟合试验数据得到的经验模型,这种模型以提高拟合精度为目标,缺乏对岩土材料应力应变本质特性的把握。另一类是理论模型,以德鲁克公设或伊留申公设以及塑性位势理论为基础推导得到。但德鲁克公设或伊留申公设实际上是区分硬化和软化材料,并不等价于热力学第二定律。经典弹塑性理论采用屈服函数、塑性势、硬化规律以及弹性常数来描述土的力学性质。但这些函数及其系数均独立选择,理论上不够严谨,且实际岩土材料的塑性势面并不总是存在的,这些都限制了传统模型的发展和应用。论文从热力学基本定律出发,以内部变量为基础,讨论了土体能量势函数和耗散函数的构造方法以及土的能量耗散特性等。研究了能量保守的邓肯—张E-B模型的卸荷再加荷性质,土体动力变形机理及其阈值应变,建立了考虑土体结构变化的本构模型。
在工程界广泛采用的邓肯—张E-B模型中,卸荷、再加荷模量及体积模量通常均表示为压力的幂次函数。但这种组合导致土体卸荷、再加荷过程中的能量非保守,也即在简单的应力循环内会产生能量的耗散;在反复加载作用下将产生残余变形的累积,这违背了弹性模型构造的基本要求。论文研究了弹性体积及剪切模量对Gibbs自由能函数的贡献,构造土体的Gibbs自由能函数,对柔度矩阵进行修正。修正的邓肯—张E-B卸荷再加荷模型的柔度矩阵中包含弹性体应力(或应变)与弹性剪应变(或应力)之间的耦合项。耦合的幅值反应了材料各向异性的程度,由应力比确定。此外柔度阵还反映了剪切引起的剪胀变形,因而能够更好地描述筑坝土石料的应力—应变特性,并保持能量守恒。
论文以Hardin-Drnevich模型和Ramberg-Osgood模型的骨架曲线为基础,采用Masing准则构造其滞回圈,对塑性中心移动为直线和骨架曲线两种情况,分别构造了土体动力耗散函数。然后从热力学基本定律出发,研究了土体动力耗散特性及动力变形机理。发现筑坝堆石料的动力特性存在2个阈值应变,分别定义为第1和第2阈值应变。2个阈值应变将土体动力特性分成3段。当土体的动应变小于第1阈值应变时,土体屈服为常摩擦系数的摩擦耗散控制;当土体动应变介于第1和第2阈值应变之间时,土体屈服为变摩擦系数的摩擦耗散控制;当土体动应变大于第2阈值应变时,土体屈服除摩擦机制外还存在剪胀等土体结构改变的效应。土体的2个阈值应变主要受最大动剪切模量系数及指数控制,无黏性土的摩擦角对其也有一定的影响。第2阈值应变与传统意义上以孔压升高或体积变化为标准定义的门槛应变相当。从工程应用的角度看,若土体动应变小于第1阈值应变,则可直接采用最大动剪模量及常阻尼比进行土体动力分析。
发展了一个能够考虑组构张量和它的发展模式影响的本构方程。将热力学方法与孔隙组构张量理论结合起来,从修正剑桥模型的各向同性模型自动演化到能考虑组构特性影响的各向异性模型的耗散增量函数。从孔隙组构发展的角度讨论了本构方程内部重要的独立变量与粒状材料状态之间的关系,结果表明了随着组构张量的演化,颗粒孔隙发生重新排列,各向异性程度也在发生改变。在真实应力空间中,组构张量除了影响屈服面的偏转外,也影响材料的硬化规律。
Traditional constitutive models of soils may be divided into two groups.One is experiential models obtained by fitting experimental data,which aim at improving fitting precision.The other is theoretic models,which can be obtained based on Drucker's Stability Postulate,Ilyushin's Postulate and plastic potential theory.However,in fact,Drucker's Stability Postulate or Ilyushin's Postulate only can be used to distinct between hardening and softening material,is not equivalent to the second law of thermodynamics.Classic elasto-plastic theory adopt several elementary factors including yield function,plastic potential,hardening rule and elastic law to describe mechanics behavior of soils.Generally speaking,these factors are determined independently and contradict each other sometimes, and the plastic potential surface does not always exist for geomaterials.To avoid these differences,starting from modern ideas of thermomechanics,this research discussed the construction of the free energy function and dissipation incremental function,and energy dissipative characteristics for soils.Energy conservative unloading and reloading part of Duncan-Chang E-B model,dynamic deformation mechanism and threshold shear strain for soils are studied.Besides,develop a constitutive model taking into account the fabric tensors and their evolution modes based on thermodynamics approach.
For the widely used Duncan-Chang E-B model in engieering,the unloading-reloading modulus and the bulk modulus are usually defined through the pressure-dependent expression. But such a model leads to a non-conservative elastic response during the unloading and reloading process,which means that(for instance) multiple cycles applied to such a material could lead to continuous production of energy.This research formulate elastic component of Gibbs free energy function for soils from the elastic component of Duncan-Chang E-B model based on contribution of elastic bulk modulus and elastic shear modulus to Gibbs free energy function,and modify the compliance matrix starting from elastic component of the Gibbs free energy function.A very important result of modified model is that leads to coupling between elastic volumetric stress(or strain) and elastic deviatoric strain(or stress) behavior.The magnitude of this coupling reflects a degree of material anisotropy,which is determined by the value of the stress ratio.Besides,the material behavior is modeled as elastic with additional dilatancy term in the bulk modulus due to shear modulus dependency on pressure. The appearance of these additional terms demonstrates that the modified model can accurately model elastic component of stress and strain relationship curves of undrained and drained triaxial tests for dam material of high rockfill dam under the different consolidation pressures, at the same time,it is energy conservative in closed stress cycles.
Starting from the skeleton curves of Hardin-Drnevich model and Ramberg-Osgood model and formulating the hysteresis loop by use of Masing's rule,the research construct dynamic dissipation function for soils using the assumptions of the beeline and the skeleton curve shift laws by use of thermodynamic approaches.Then discuss corresponding yield surface and energy dissipation mechanism of materials of two high core rockfill dams at different dynamic strain amplitudes.Two types of cyclic threshold shear strain,called the first threshold shear strain and the second threshold shear strain,are proposed for dynamic characteristics of rockfill non-cohesive materials.Two threshold shear strains represent boundaries between fundamentally different dynamic characteristics of cyclic soil behavior. For cyclic strains below the first threshold shear strain,soil behaves as a constant friction coefficient material.Between the first and the second threshold shear strain,the yield of soil is controlled by the variable friction coefficient.Above the second threshold shear strain,soil becomes increasingly nonlinear,with significant dilatancy-induced microstructural changes taking place under cyclic loading.Both the first and the second threshold shear strain do depend significantly on the maximum dynamic shear modulus coefficient and exponent.In addition,friction angle of cohesionless soil also influences them to some extent.The second threshold strain is equivalent to that defined by traditional pore pressure increasing and volume varying.From the engineering application aspect,if dynamic strain for soil is smaller than the first threshold strain,then maximum dynamic shear modulus and constant damping ratio can be used to analyze dynamic characteristics for soils.
Develop a constitutive equation taking into account the fabric tensors and their evolution modes.Link modern ideas of thermomechanics opinion to the theory of void fabric tensors. The dissipation incremental function of anisotropic model considering the effect of fabric characteristic can be obtained automatically from the modified Cam-clay constitutive model. After discussing the relationship between essential independent variables in constitutive equations and the state of granular materials from a viewpoint of the evolution mode of the void fabric tensors,the results show that with the development and change of void fabric,the pore of granular materials can rearrange and show less symmetry(more anisotropic).In the true stress space,fabric not only affects the deflection of the yield surface,but also affects the hardening rule.
在工程界广泛采用的邓肯—张E-B模型中,卸荷、再加荷模量及体积模量通常均表示为压力的幂次函数。但这种组合导致土体卸荷、再加荷过程中的能量非保守,也即在简单的应力循环内会产生能量的耗散;在反复加载作用下将产生残余变形的累积,这违背了弹性模型构造的基本要求。论文研究了弹性体积及剪切模量对Gibbs自由能函数的贡献,构造土体的Gibbs自由能函数,对柔度矩阵进行修正。修正的邓肯—张E-B卸荷再加荷模型的柔度矩阵中包含弹性体应力(或应变)与弹性剪应变(或应力)之间的耦合项。耦合的幅值反应了材料各向异性的程度,由应力比确定。此外柔度阵还反映了剪切引起的剪胀变形,因而能够更好地描述筑坝土石料的应力—应变特性,并保持能量守恒。
论文以Hardin-Drnevich模型和Ramberg-Osgood模型的骨架曲线为基础,采用Masing准则构造其滞回圈,对塑性中心移动为直线和骨架曲线两种情况,分别构造了土体动力耗散函数。然后从热力学基本定律出发,研究了土体动力耗散特性及动力变形机理。发现筑坝堆石料的动力特性存在2个阈值应变,分别定义为第1和第2阈值应变。2个阈值应变将土体动力特性分成3段。当土体的动应变小于第1阈值应变时,土体屈服为常摩擦系数的摩擦耗散控制;当土体动应变介于第1和第2阈值应变之间时,土体屈服为变摩擦系数的摩擦耗散控制;当土体动应变大于第2阈值应变时,土体屈服除摩擦机制外还存在剪胀等土体结构改变的效应。土体的2个阈值应变主要受最大动剪切模量系数及指数控制,无黏性土的摩擦角对其也有一定的影响。第2阈值应变与传统意义上以孔压升高或体积变化为标准定义的门槛应变相当。从工程应用的角度看,若土体动应变小于第1阈值应变,则可直接采用最大动剪模量及常阻尼比进行土体动力分析。
发展了一个能够考虑组构张量和它的发展模式影响的本构方程。将热力学方法与孔隙组构张量理论结合起来,从修正剑桥模型的各向同性模型自动演化到能考虑组构特性影响的各向异性模型的耗散增量函数。从孔隙组构发展的角度讨论了本构方程内部重要的独立变量与粒状材料状态之间的关系,结果表明了随着组构张量的演化,颗粒孔隙发生重新排列,各向异性程度也在发生改变。在真实应力空间中,组构张量除了影响屈服面的偏转外,也影响材料的硬化规律。
Traditional constitutive models of soils may be divided into two groups.One is experiential models obtained by fitting experimental data,which aim at improving fitting precision.The other is theoretic models,which can be obtained based on Drucker's Stability Postulate,Ilyushin's Postulate and plastic potential theory.However,in fact,Drucker's Stability Postulate or Ilyushin's Postulate only can be used to distinct between hardening and softening material,is not equivalent to the second law of thermodynamics.Classic elasto-plastic theory adopt several elementary factors including yield function,plastic potential,hardening rule and elastic law to describe mechanics behavior of soils.Generally speaking,these factors are determined independently and contradict each other sometimes, and the plastic potential surface does not always exist for geomaterials.To avoid these differences,starting from modern ideas of thermomechanics,this research discussed the construction of the free energy function and dissipation incremental function,and energy dissipative characteristics for soils.Energy conservative unloading and reloading part of Duncan-Chang E-B model,dynamic deformation mechanism and threshold shear strain for soils are studied.Besides,develop a constitutive model taking into account the fabric tensors and their evolution modes based on thermodynamics approach.
For the widely used Duncan-Chang E-B model in engieering,the unloading-reloading modulus and the bulk modulus are usually defined through the pressure-dependent expression. But such a model leads to a non-conservative elastic response during the unloading and reloading process,which means that(for instance) multiple cycles applied to such a material could lead to continuous production of energy.This research formulate elastic component of Gibbs free energy function for soils from the elastic component of Duncan-Chang E-B model based on contribution of elastic bulk modulus and elastic shear modulus to Gibbs free energy function,and modify the compliance matrix starting from elastic component of the Gibbs free energy function.A very important result of modified model is that leads to coupling between elastic volumetric stress(or strain) and elastic deviatoric strain(or stress) behavior.The magnitude of this coupling reflects a degree of material anisotropy,which is determined by the value of the stress ratio.Besides,the material behavior is modeled as elastic with additional dilatancy term in the bulk modulus due to shear modulus dependency on pressure. The appearance of these additional terms demonstrates that the modified model can accurately model elastic component of stress and strain relationship curves of undrained and drained triaxial tests for dam material of high rockfill dam under the different consolidation pressures, at the same time,it is energy conservative in closed stress cycles.
Starting from the skeleton curves of Hardin-Drnevich model and Ramberg-Osgood model and formulating the hysteresis loop by use of Masing's rule,the research construct dynamic dissipation function for soils using the assumptions of the beeline and the skeleton curve shift laws by use of thermodynamic approaches.Then discuss corresponding yield surface and energy dissipation mechanism of materials of two high core rockfill dams at different dynamic strain amplitudes.Two types of cyclic threshold shear strain,called the first threshold shear strain and the second threshold shear strain,are proposed for dynamic characteristics of rockfill non-cohesive materials.Two threshold shear strains represent boundaries between fundamentally different dynamic characteristics of cyclic soil behavior. For cyclic strains below the first threshold shear strain,soil behaves as a constant friction coefficient material.Between the first and the second threshold shear strain,the yield of soil is controlled by the variable friction coefficient.Above the second threshold shear strain,soil becomes increasingly nonlinear,with significant dilatancy-induced microstructural changes taking place under cyclic loading.Both the first and the second threshold shear strain do depend significantly on the maximum dynamic shear modulus coefficient and exponent.In addition,friction angle of cohesionless soil also influences them to some extent.The second threshold strain is equivalent to that defined by traditional pore pressure increasing and volume varying.From the engineering application aspect,if dynamic strain for soil is smaller than the first threshold strain,then maximum dynamic shear modulus and constant damping ratio can be used to analyze dynamic characteristics for soils.
Develop a constitutive equation taking into account the fabric tensors and their evolution modes.Link modern ideas of thermomechanics opinion to the theory of void fabric tensors. The dissipation incremental function of anisotropic model considering the effect of fabric characteristic can be obtained automatically from the modified Cam-clay constitutive model. After discussing the relationship between essential independent variables in constitutive equations and the state of granular materials from a viewpoint of the evolution mode of the void fabric tensors,the results show that with the development and change of void fabric,the pore of granular materials can rearrange and show less symmetry(more anisotropic).In the true stress space,fabric not only affects the deflection of the yield surface,but also affects the hardening rule.
引文
[1]钱家欢,殷宗泽.土工原理与计算(第2版)(精)[M].北京:中国水利水电出版社,2003.
[2]Robert D S,Lembit K.Threshold of dilation under cyclic loading[J].Journal of the Geotechnical Engineering Division,ASCE,1977,103(GT10):1174-1178.
[3]Richard P R,Richard D W.Modulus and damping due to uniform and variable cyclic loading[J].Journal of Geotechnical Engineering,1988,114(8):861-876.
[4]Vucetic M.Cyclic threshold shear strains in soils[J].Journal of Geotechnical Engineering,1994,120(12):2208-2229.
[5]Hsu C C,Vucetic M.Volume threshold shear strain for cyclic settlement[J].Journal of Geotechanical and Geoenvironiment Engineering,2004,130(1):58-70.
[6]Bjerrum L.Embankment on soft ground.In Performance of Earth and Earth supported Structures[C],1972,2:1-54.
[7]沈珠江.现代土力学的基本问题[J].力学与实践,1998,20(6):1-6.
[8]沈珠江.土体结构性的数学模型-21世纪土力学的核心问题[J].岩土工程学报,1996,18(1):95-97.
[9]谢定义,齐吉琳.土结构性及其定量化参数研究的新途径[J].岩土工程学报,1999,21(6):651-656.
[10]郑颖人,沈珠江,龚晓南.广义塑性力学—岩土塑性力学原理[M].北京:建筑工业出版社,2002.
[11]Houlsby G T,Puzrin A M.Principles of hyperplasticity:an approach to plasticity theory based on thermodynamic principles[M].London:Springer,2006.
[12]钱家欢,殷宗泽.土工原理与计算(第二版)[M].北京:中国水利水电出版社,1996.
[13]Duncan J M,Byrne P,Wong K S,et al.Strength,stress-strain and bulk modulus parameters for finite element analysis of stresses and movements in soil masses[J].Geotechnical Engineering,1980.
[14]徐舜华,徐光黎,程瑶.土的剑桥模型发展综述[J].长江科学院院报,2007,24(5):27-32.
[15]Roscoe K H,Schofield A N,Wroth C P.On yielding of soils[J].Geotechnique 1958,8:22-53.
[16]Roscoe K H,Burland J B.On the generalized stress-strain behaviour of "wet clay"[M].Cambridge:Cambridge University Press,1968.
[17]魏汝龙.正常压密粘土的塑性势[J].水利学报,1964,6.
[18]Sandler I S,Dimaggio F L,Baladi G Y.Generalized Cap Model for Geological Materials[J].Journal of Geotechnical Engineering Division,1976,102(7):683-699.
[19]章根德.土的本构关系及其工程应用[M].北京:科学出版社,1995.
[20]卢应发,刘德富,田斌,等.广义帽盖模型和数值模拟[J].工程力学,2006,23(11):9-13.
[21]Hsieh H S,E.K J.Double-Yield-Surface Cam-Clay Plasticity Model.Ⅰ:Theory[J].Journal of Geotechnical Engineering,1990,116:1381-1401.
[22]Borja R I,Hsieh H S,Kavazanjian J E.Double-Yield-Surface Model.Ⅱ:Implementation and Verification[J].Journal of Geotechnical Engineering,1990,116:1402-1421.
[23]Rouainia M,Wood D M.A kinematic hardening constitutive model for natural clays with loss of structure[J].Geotechnique,2000,50(2):153-164.
[24]李兴照,黄茂松,王录民.流变性软黏土的弹黏塑性边界面本构模型[J].岩石力学与工程学报,2007,26(7):1393-1401.
[25]Leoni M,Karstunen M,Vermeer P A.Anisotropic creep model for soft soils[J].Geotechnique,2008,58(3):215-226.
[26]Ohta H,Sekiguchi H.Constitutive equations considering anisotropy and stress reorientation in clay.In:Wittke W,editor.Proc of the 3nd Int Conference on Numerical in Geomechanics[C].Aachen:University of Aachen,1979:475-484.
[27]孙德安,姚仰平.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.
[28]Voyiadjis G Z,Song C R.Anisotropic Modified Cam Clay Model with Plastic Spin for Finite Strains[J].Journal of Engineering Mechanics 2000,126(10):1012-1019.
[29]Liu M D,Carter J P.A structured Cam Clay model[J].Canadian Geotechnical Journal,2002,39(6):1313-1332.
[30]Wheeler S J,Naatanen A,Karstunen M,et al.An anisotropic elastoplastic model for soft clays[J].Canadian Geotechnical Journal,2003,40(2):403-418.
[31]Wheeler S J,Cudny M,Neher H P,et al.Some developments in constitutive modelling of soft clays.In:Vermeer P A,editor.International Workshop on Geotechnics of Soft Soils-Theory and Practice[C],2003:1-20.
[32]刘元雪,施建勇.基于应力空间变换的修正剑桥模型改进[J].岩土力学,2003,24(1):1-7.
[33]刘元雪,施建勇.应力空间变换—岩土本构描述的一条新途径[J].岩石力学与工程学报,2003,22(2):217-222.
[34]刘元雪,施建勇,尹光志.基于应力空间变换的原状软土本构模型[J].水利学报,2004,(6):14-20.
[35]Mita K A,Dasari G R,Lo K W.Performance of a Three-Dimensional Hvorslev-Modified Cam Clay Model for Overconsolidated Clay[J].International Journal of Geomechanics,2004,4:296-309.
[36]Carter J P,Liu M D.Review of the Structured Cam Clay Model.Invited paper,Soil constitutive models:evaluation,selection,and calibration[J],ASCE,Geotechnical special publication,2005,128:99-132.
[37]魏星,黄茂松.黏土的各向异性边界面模型[J].水利学报,2006,37(7):831-837.
[38]姚仰平,孔玉侠,宋美娜.考虑原生各向异性土的统一硬化模型[J].工业建筑,2008,38(8):6-9.
[39]Been K,Jefferies M G.A state parameter for sands.Geotechnique,1985,35(2):99-112.
[40]Manzari M T,Dafalias Y F.A critical state two-surface plasticity model for sands[J].Geotechnique,1997,47(2):255-272.
[41]Yu H S.CASM:a unified state parameter model for clay and sand[J].International Journal for Numerical and Analytical Methods in Geomechanics,1998,22(8):621-653.
[42]Gajo A,Wood D M.A kinematic hardening constitutive model for sands:the multiaxial formulation[J].Int J Numer Anal Meth Geomech,1999,23:925-965.
[43]罗刚,张建民.考虑物理状态变化的砂土本构模型[J].水利学报,2004,(7):26-31.
[44]罗刚,张建民.考虑物态变化的六参数砂土本构模型[J].清华大学学报:自然科学版,2004,44(3):402-405.
[45]王刚,张建民.密度和压力对砂土变形特性影响的统一模拟[J].清华大学学报:自然科学版,2003,43(8):1100-1103.
[46]王国欣,肖树芳.土结构性本构模型研究现状综述[J].工程地质学报,2006,14(5):620-626.
[47]施斌.粘性土微观结构研究回顾与展望[J].工程地质学报,1996,4(1):39-44.
[48]苗天德,刘忠玉.湿陷性黄土的变形机理与本构关系[J].岩土工程学报,1999,21(4):383-387.
[49]王常明,夏玉斌.海积软土固结变形的结构性模型研究[J].长春科技大学学报,2001,31(4):363-367.
[50]宋章,程谦恭,张炜,等.原状黄土显微结构特征与湿陷性状分析[J].工程地质学报,2007,15(5):646-653.
[51]沈珠江.岩土破损力学与双重介质模型[J].水利水运工程学报,2002,(4):1-6.
[52]沈珠江.岩土破损力学—结构类型与荷载分担[J].岩石力学与工程学报,2004,23(13):2137-2142.
[53]刘恩龙,沈珠江.结构性土的强度准则[J].岩土工程学报,2006,28(10):1248-1252.
[54]李凡.岩土材料破损特性的颗粒流研究[J].土木工程学报,2007,40(9):78-81.
[55]何开胜,沈珠江.结构性粘土的弹粘塑损伤模型[J].水利水运工程学报,2002,(4):7-13.
[56]Desai C S,Ma Y.Modelling of joints and interfaces using the disturbed-state concept[J].International Journal for Numerical and Analytical Methods in Geomechanics,1992,16(9):623-653.
[57]Armaleh S H,Desai C S.Modelling and testing of a cohesionless material using the disturbed state concept[J].Int J Mech Behavior Mater,1994,5:279-295.
[58]Geomech I.Disturbed state model for sand geosynthetic interfaces and application to pull-out tests[J].Int J Numer Anal Meth Geomech,1999,23:1873-1892.
[59]Fakharian K,Evgin E.Elasto-plastic modelling of stress-path-dependent behaviour of interfaces[J].International Journal for Numerical and Analytical Methods in Geomechanics,2000,24(2):183-199.
[60]谢定义,齐吉琳.考虑土结构性的本构关系[J].土木工程学报,2000,33(4):35-41.
[61]骆亚生,谢定义,邵生俊,等.复杂应力状态下的土结构性参数[J].岩石力学与工程学报,2004,23(24):4248-4251.
[62]雷华阳.结构性海积软土的弹塑性研究[J].岩土力学,2002,23(6):721-724.
[63]谢定义.土动力学[M].西安:西安交通大学出版社,1988.
[64]刘汉龙,余湘娟.土动力学和岩土地震工程.第九届土力学及岩土工程学术会议论文集[C].北京:清华大学出版社.2003:56-68.
[65]王志良,王余庆,韩清宇.不规则循环剪切荷载作用下土的粘弹性模型[J].岩土工程学报,1980,2(3):10-20.
[66]Pyke R.Nonlinear soil models for irregular cyclic loadings[J].Journal of the Geotechnical Engineering Division,1979,105(6):715-726.
[67]王志良,韩清宇.粘弹塑性土层地震反应的波动分析法[J].地震工程与工程振动,1981,1(1):117-137.
[68]Ishihara K,Yoshida N,Tsujino S.Modelling of stress-strain relations of soils in cyclic loading[C].In:Nagoya,editor.Proceedings of the Fifth International Conference on Numerical Methods in Geomechanics,1985.p.373-380.
[69]栾茂田.土动力非线性分析中的变参数Ramberg-Osgood本构模型[J].地震工程与工程振动,1992,12(2):69-78.
[70]Bardet J P.Scaled memory model for cyclic behavior of soils[J].Journal of Geotechnical Engineering,1995,121(11):766-775.
[71]张克绪,李明宰.基于非曼辛准则的土动弹塑性模型[J].地震工程与工程振动,1997,17(2):74-81.
[72]Puzrin A M,Shiran A.Effects of the constitutive relationship on seismic response of soils.Part Ⅰ.Constitutive modeling of cyclic behavior of soils[j].Soil Dynamics and Earthquake Engineering,2000,19(5):305-318.
[73]Fang H L.A state-dependent multi-mechanism model for sands[J].Geotechnique,2003,53(4):407-420.
[74]Iwan W D.On a class of models for the yielding behavior of continuous and composite system[J].ASME,1967,34(3):21-33
[75]Nossan A S.An overlay model for cyclic behaviour of sands[C].In:Zurich,editor.Proceedings of The International Symposium on Numerical Models in Geomechanics,1982:110-116.
[76]郑大同,王惠昌.循环荷载作用下土的非线性应力应变模型[J].岩土工程学报,1985,5(1):65-76.
[77]李小军,廖振鹏.土应力变关系的粘—弹—塑模型[J].地震工程与工程振动,1989,9(3):65-72.
[78]孔亮,王燕昌,郑颖人.土体动本构模型研究评述[J].宁夏大学学报:自然科学版,2001,22(1):17-22.
[79]Mroz Z.On the description of anisotropic work hardening[J].J Mech Phys Solids,1967,15(3):163-175.
[80]Prevost J H.Mathematical modelling of monotonic and cyclic undrained clay behaviour[J].International Journal for Numerical and Analytical Methods in Geomechanics,1977,1(2):195-216.
[81]Prevost J H.Anisotropic undrained stress-strain behavior of clays.Journal of the Geotechnical Engineering Division,1978,104(8):1075-1090.
[82]Prevost J H.A simple plasticity theory for frictional cohesionless soils[J].International journal of soil dynamics and eathquake engineering,1985,4(1):9-17.
[83]Zienkiewicz O C.广义塑性力学和地力学的一些模型[J].应用数学与力学,1982,3(3):267-267.
[84]Mroz Z,Zienkiewicz O C.Uniform formulation of constitutive equations for clays and sand[J].Mechanics of engineering materials,1984:415-450.
[85]Mroz Z,Norris V A,Zienkiewicz O C.An anisotropic hardening model for soils and its application to cyclic loading[J],International Journal for Numerical and Analytical Methods in Geomechanics,1978,2(3):203-221.
[86]Mroz Z,Pietruszczak S.A constitutive model for sand with anisotropic hardening rule[J].International Journal for Numerical and Analytical Methods in Geomechanics,1983,7(3):305-320.
[87]Zienkiewicz O C,Mroz Z.Generalized plasticity formulation and applications to geomechanics[J].Mechanics of engineering materials,1984:655-680.
[88]Elgamal A,Yang Z,Parra E.Computational modeling of cyclic mobility and post-liquefaction site response[J].Soil Dynamics and Earthquake Engineering,2002,22(4):259-271.
[89]Peng J,Lu J,Law K H,et al.ParCYCLIC:finite element modelling of earthquake liquefaction response on parallel computers[J].International Journal for Numerical and Analytical Methods in Geomechanics,2004,28(12):1207-1232.
[90]Dafalias Y F,Popov E P.A model of nonlinearly hardening materials for complex loading[J].Acta Mechanica,1975,21(3):173-192.
[91]Krieg R D.A practical two surface plasticity theory[J].J Appl Mech,1975,42(3):641-646.
[92]吴兴征.堆石料的静动力本构模型及其在混凝土面板堆石坝中的应用[D].大连:大连理工大学,2001.
[93]Dafalias Y F.A model for soil behavior under monotonic and cyclic loading conditions[C].Transactions of 5th international conference on Smirt.West Berlin,1979.
[94]Dafalias Y F,Herrmann L R.Bounding surface formulation of soil plasticity[C].In:Pande G N,Zienkiewicz O C,editors.Soil Mechanics-Transient and Cyclic Loads:Constitutive Relations and Numerical Treatment.New York:John Wiley and Sons,1982:253-282.
[95]Dafalias Y F.Bounding Surface Plasticity:Ⅰ:Mathematical Foundation and Hypoplasticity[J].Journal of Engineering Mechanics,1986,112(9):966-987.
[96]Dafalias Y F,Herrmann L R.Bounding surface plasticity Ⅱ:application to isotropic cohesive soils[J].Journal of Engineering Mechanics,1986,112(12):1263-1291.
[97]Anandarajah A,Dafalias Y F.Bounding surface plasticity Ⅲ:application to anisotropic cohesive soils[J].Journal of Engineering Mechanics,1986,112(12):1292-1318.
[98]Al-Tabbaa A,Wood D M.An experimentally based bubble model for clay[C].In:Pietruszczak S,Pande G N,editors.Numerical Models in Geomechanics:Elsevier Science Publishers Ltd,1989:91-99.
[99]Liang R Y,Ma F.Anisotropic plasticity model for undrained cyclic behavior of clays.Ⅰ:theory[J].Journal of Geotechnical Engineering,1992,118(2):229-245.
[100]Borja R I,Amies A P.Multiaxial cyclic plasticity model for clays[J].Journal of Geotechnical Engineering,1994,120(6):1051-1070.
[101]Pestana J M,Biscontin G,Nadim F,et al.Modeling cyclic behavior of lightly overconsolidated clays in simple shear[J].Soil Dynamics and Earthquake Engineering,2000,19(7):501-519.
[102]Li T.Two-surface plasticity model for cyclic undrained behavior of clays[J].Journal of Geotechnical and Geoenvironmental Engineering,2002,128:613-626.
[103]Bardet J P.Application of plasticity theory to soil behavior:a new sand model[D].Pasadena:California Institutive of Technology,1987.
[104]Nakai T,Fujii J,Taki H.Kinematic extension of anisotropic hardening model for sand[C].In:Pietruszczak S,Pande G N,editors.Numerical Models in Geomechanics:Elsevier Science Publishers Ltd,1989:36-45.
[105]Anandarajah A.Procedures for elastoplastic liquefaction modeling of sands[J].Journal of Engieering Mechanics,1994,120:1563-1563.
[106]Arulanandan K,Li X S,Sivathasan K.Numerical simulation of liquefaction-induced deformations[J].Journal of Geotechnical and Geoenvironmental Engineering,1999,126(7):657-666.
[107]Matsuoka H.Stress-strain relationships of sands based on the mobilized plane[J].Soils and Foundations,1974,14(2):47-61.
[108]Aubry D,Hujeux J C,Lassoudiere F,et al.A double memory model with multiple mechanisms for cyclic soil behaviour[C].Proceedings of the International Symposiumon Numerical Models in Geomechanics.Zurich,1982:3-13.
[109]Towhata I,Ishihara K.Modelling soil behavior under principal stress axes rotation[C].Proceedings of The Fifth International Conference on Numerical Methods in Geomechanics.Nagoya,1985:523-530.
[110]Kabilamany K,Ishihara K.Stress dilatancy and hardening laws for rigid granular model of sand[J].Soil dynamics and earthquake engineering,1990,9(2):66-77.
[111]Kabilamany K,Ishihara K.Cyclic behaviour of sand by the multiple shear mechanism model[J].Soil Dynamics and Earthquake Engineering,1991,10(2):74-83.
[112]Prevost J H,Keane C M.Multi-mechanism elasto-plastic model for soils[J].Journal of Engineering Mechanics,1990,116(9):1924-1944.
[113]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.
[114]Hashiguchi K,Chen Z P.Elastoplastic constitutive equation of soils with the subloading surface and the rotational hardening[J].International Journal for Numerical and Analytical Methods in Geomechanics,1998,22(3):197-227.
[115]Iai S,Matsunaga Y,Kameoka T.Strain space plasticity model for cyclic mobility[J].Soils and Foundations,1992,32(2):1-15.
[116]Iai S,Ozutsumi O.Yield and cyclic behaviour of a strain space multiple mechanism model for granular materials[J].International Journal for Numerical and Analytical Methods in Geomechanics,2005,29(4):417-442.
[117]Akiyoshi T,Matsumoto H,Fuchida K,et al.Cyclic mobility behaviour of sand by the three-dimensional strain space multimechanism model[J].International Journal for Numerical and Analytical Methods in Geomechanics,1994,18(6):397-415.
[118]Hamadi K,Modaressi-Farahmand Razavi A,Darve F.Bifurcation and instability modelling by a multimechanism elasto-plastic model[J].International Journal for Numerical and Analytical Methods in Geomechanics,2008,32(5):461-492.
[119]李亮,赵成刚.饱和土体动力本构模型研究进展[J].世界地震工程,2004,20(1):138-148.
[120]Shen Z J.A stress-strain model for sands under complex loading[C].In:FANG J H,Sumio M,editors.Advances in Constitutive Laws for Engineering Material,1989:303-308.
[121]沈珠江,栾茂田.复杂荷载下砂土液化变形的结构性模型[C].第五届全国土动力学学会会议论文集.大连:大连理工大学出版社,1998:1-10.
[122]沈珠江.砂土液化分析的散粒体模型[J].岩土工程学报,1999,21(6):742-748.
[123]谢定义,张建民.饱和砂土瞬态动力学特性与机理分析[M].西安:陕西科学技术出版社,1995.
[124]姚仰平,谢定义.土的动力本构关系的新探讨[J].西安建筑科技大学学报,1997,29(2):159-163.
[125]姚仰平,谢定义.饱和砂土动应力-应变关系的模拟[C].见:栾茂田,编.土动力学理论与实践—第五届全国土动力学学术会议.大连:大连理工大学出版社,1998:82-87.
[126]刘元雪,郑颖人.含主应力轴旋转的土一般应力应变关系[J].应用数学和力学,1998,19(5):407-413.
[127]刘元雪,郑颖人.含主应力轴旋转的土体本构关系研究进展[J].力学进展,2000,30(4):597-604.
[128]李小军.非线性场地地震反应分析方法的研究[D].国家地震局工程力学研究所,1993.
[129]徐干成.饱和砂土循环动应力应变特性的弹塑性模拟研究[J].岩土工程学报,1995,17(2):1-12.
[130]王建华,要明伦.循环应变下饱和砂(粉)土衰化动力特性研究[J].水利学报,1997,(7):24-30.
[131]李相崧,邹离湘.砂土材料模拟剪胀破坏的动力本构模型[C].见:栾茂田,编.第五届全国土动力学学术会议.大连:大连理工大学出版社,1998:47-52.
[132]丰土根,刘汉龙.砂土多机构边界面塑性模型初探[J].岩土工程学报,2002,24(3):382-385.
[133]迟世春,刘怀林.土工建筑物动力真非线性分析的量化记忆模型[J].水利学报,2003,10:51-59.
[134]迟世春,许艳林.多维量化记忆模型及其验证[J].岩土工程学报,2005,27(2):167-172.
[135]迟世春,宋振河.土的量化记忆模型及其参数确定[J].岩土力学,2004,25(1):77-81.
[136]李兴照,黄茂松.循环荷载作用下流变性软黏土的边界面模型[J].岩土工程学报,2007,29(2):249-254.
[137]曲圣年,殷有泉.塑性力学的Drucker公设和Ilyushin公设[J].力学学报,1981,5:47-55.
[138]殷有泉,曲圣年.弹塑性耦合和广义正交法则[J].力学学报,1982,1:63-70.
[139]郑颖人,孔亮.塑性力学中的分量理论—广义塑性力学[J].岩土工程学报,2000,22(3):269-274.
[140]郑颖人.广义塑性力学理论[J].岩土力学,2000,21(2):188-192.
[141]郑颖人.岩土塑性力学的新进展—广义塑性力学[J].岩土工程学报,2003,25(1):1-10.
[142]郑颖人.关于岩土塑性的几点认识[J].岩土工程界,2002,5(4):14-16.
[143]黄文彬.关于塑性力学两公设适用性的分析[J].力学与实践,1992,14(2):64-65.
[144]胡亚元.关于率无关塑性力学和广义塑性力学的评述[J].岩土工程学报,2005,27(1):128-131.
[145]黄速建.塑性力学的稳定性公设的热力学原理[J].固体力学学报,1988,9(2):95-101.
[146]刘元雪.岩土本构理论的几个基本问题研究[J].岩土工程学报,2001,23(1):45-48.
[147]Ziegler H.An introduction to thermomechanics[M].Amsterdam:North-Holland,1983.
[148]孔亮,Collins I F.模拟土体本构特性的热力学方法[J].岩土力学,2008,29(7):1732-1740.
[149]Ziegler H,Wehrli C.The derivation of constitutive relations from the free energy and the dissipation function[J].Advances Applied Mechanics,1987,25:183-238.
[150]赵成刚,张雪东,郭璇.土的本构方程与热力学[J].力学进展,2006,36(4):611-618.
[151]Houlsby G T.A study of plasticity theories and their applicability to soils[D].Cambridge UK:University of Cambridge,1981.
[152]Collins I F,Houlsby G T.Application of thermomechanical principles to the modeling of geomateriais[J].Proc Royal Society of London,,Series A,1997,453:1975-2001.
[153]Houlsby G T.The use of a variable shear modulus in elastic-plastic models for clays[J].Comput Geotech,1985,1:3-13.
[154]Houlsby G T,Amorosi A,Rojas E.Elastic moduli of soils dependent on pressure:a hyperelastic formulation[J].Geotechnique,2005,55(5):383-392.
[155]Graham J,Houlsby G T.Anisotropic elasticity of a natural clay[J].Geotechnique,1983,33:165-180.
[156]Borja R I,Tamagnini C,Amorosi A.Coupling plasticity and energy conserving elasticity models for clays[J].Journal of Geotechnical and Geoenviromental Engineering,1997,123(10):948-957.
[157]Einav I,Puzrin A M.Pressure-dependent elasticity and energy conservation in elastoplastic models for soils[J].Journal of Geotechnical and Geoenvironmental Engineering,2004,130(1):81-92.
[158]Einav I.Application of thermodynamical approaches to mechnics of soils[D].Technion-Israel Institute of Technology.Israel,2002.
[159]Houlsby G T,Puzrin A M.A thermomechanical framework for constitutive models for rate-independent dissipative materials[J].International Journal of Plasticity,2000,16(9):1017-1047.
[160]Houlsby G T,Puzrin A M.An approach to plasticity based on generalised thermodynamics[J].Constitutive Modelling of Granular Materials,2000:319-331.
[161]Collins I F,Hilder T.A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests[J].International Journal for Numerical and Analytical Methods in Geomechanics,2002,26(11):1313-1347.
[162]Puzrin A M,Houlsby G T.A thermomechanical framework for rate-independent dissipative materials with internal functions[J].International Journal of Plasticity,2001,17(8):1147-1165.
[163]Puzrin A M,Houlsby G T.Fundamentals of kinematic hardening hyperplasticity[J].International Journal of Solids and Structures,2001,38(21):3771-3794.
[164]Houlsby G T,Puzrin A M.Rate-dependent plasticity models derived from potential functions[J].Journal of Rheology,2002,46:113-126.
[165]Puzrin A M,Houlsby G T.Rate-dependent hyperplasticity with internal functions[J].Journal of Engineering Mechanics,2003,129(3):252-263.
[166]Likitlersuang S,Houlsby G T.Development of hyperplasticity models for soil mechanics[J].International Journal for Numerical and Analytical Methods in Geomechanics,2006,30(3):229-254.
[167]Collins I F,Tai A.What has thermo-mechanics to offer geo-mechanics[J].2005:281-288.
[168]Collins I F,Kelly P A.A thermomechanical analysis of a family of soil models[J].Geotechnique,2002,52(7):507-518.
[169]Collins I F.A systematic procedure for constructing critical state models in three dimensions[J].International Journal of Solids and Structures,2003,40(17):4379-4397.
[170]Likitlersuang S.A hyperplasticity model for clay behaviour:an application to Bangkok clay[D].Oxford University,2003.
[171]Collins I F,Muhunthan B.On the relationship between stress-dilatancy,anisotropy,and plastic dissipation for granular materials[J].Geotechnique,2003,53(7):611-618.
[172]Collins I F.The concept of stored plastic work or frozen elastic energy in soil mechanics[J].Geotechnique,2005,55(5):373-382.
[173]Collins I F.Elastic/plastic models for soils and sands[J].International Journal of Mechanical Sciences,2005,47(4):493-508.
[174]秦理曼,迟世春,林皋.基于热力学的砂土统一模型[J].水利学报,2006a,4:403-410.
[175]秦理曼,迟世春,林皋.基于热力学的砂土不排水统一模型[J].岩石力学与工程学报,2006b,7:1316-1322.
[176]王立忠,沈恺伦.K0固结结构性软黏土的本构模型[J].岩土工程学报,2007,29(4):496-504.
[177]Li X S.Thermodynamics-based constitutive framework for unsaturated soils.1:Theory[J].Geotechnique,2007,57(5):411-422.
[178]Li X S.Thermodynamics-based constitutive framework for unsaturated soils.2:A basic triaxial model[J].Geotechnique,2007,57(5):423-435.
[179]Buscarnera G,Nova R.An elastoplastic strainhardening model for soil allowing for hydraulic bonding-debonding effects[J].International Journal for Numerical and Analytical Methods in Geomechanics,2008.
[180]Einav I.Breakage mechanics-Part Ⅰ:Theory[J].Journal of the Mechanics and Physics of Solids,2007,55(6):1274-1297.
[181]Einav I.Breakage mechanics-Part Ⅱ:Modelling granular materials[J].Journal of the Mechanics and Physics of Solids,2007,55(6):1298-1320.
[182]Einav I.Soil mechanics:breaking ground[J].Philosophical Transactions of the Royal Society A:Mathematical,Physical and Engineering Sciences,2007,365(1861):2985-3002.
[183]Einav I.Fracture propagation in brittle granular matter[C].Proceedings of the Royal Society A:Mathematical,Physical and Engineering Sciences,2007,463(2087):3021-3035.
[184]Hardin B O.Crushing of soil particles[J].Journal of Geotechnical Engineering,1985,111(10):1177-1192.
[185]贾宇峰.考虑颗粒破碎的粗粒土本构关系研究[D].大连:大连理工大学,2008.
[186]王秋生.基于超塑性力学的软粘土本构理论研究[D].浙江:浙江大学,2007.
[187]Germain P,Suquet P,Nguyen Q S,et al.Continuum thermodynamics[J].ASME,Transactions,Journal of Applied Mechanics,1983,50(4b):1010-1020.
[188]Reddy B D,Martin J B.Internal variable formulations of problems in elastoplasticity:constitutive and algorithmic aspocts[J].Appl Mech Rev,1994,47(9):429-456.
[189]Maugin G A.Thermomechanics of nonliear irreversible behaviors[M].Singapore:World Scientific Press,1999.
[190]王竹溪.热力学(第二版)[M].北京:北京大学出版社,2005.
[191]Trusdell C A.Rational thermodynamics.2nd enlarged edition[M].New York:Springer verlag,1984.
[192]Collins I F,Muhunthan B,Tai A T T,et al.The concept of a'Reynolds-Taylor stare'and the mechanics of sands[J].Geotechnique,2007,57(5):437-447.
[193]Radjal F,Jean M,Moreau J J.Force distributions in dense two-dimensional granular systems[J].Phys Rev Lett,1996,77(2):274-277.
[194]秦理曼.基于能量耗散的土的本构关系研究[D].大连:大连理工大学,2006.
[195]Collins I F.Associated and non-associated aspects of the constitutive laws for coupled elastic/plastic materials[J].International Journal of Geomechanics,2002,2(2):259-267.
[196]Zytynski M,Randolph M F,Nova R,et al.On modelling the unloading-reloading behaviour of soils[J].International Journal for Numerical and Analytical Methods in Geomechanics,1978,2(1):87-93.
[197]Graham J,Houlsby G T.Elastic anisotropy of a natural clay[M].University of Oxford Department of Engineering Science,1982.
[198]Houlsby G T,Wroth C P.The variation of shear modulus of a clay with pressure and overconsolidation ratio[J].Soils and Foundations,1991,31(3):138-143.
[199]Einav I,Puzrin A M,Houlsby G T.Continuous Hyperplastic Models for Overconsolidated Clays[J].Mathematical and Computer Modelling,2003,37:515-523.
[200]Einav I,Puzrin A M.Continuous hyperplastic critical state(CHCS) model derivation[J].International Journal of Solids and Structures,2004,41:199-226.
[201]Ishihara K.Evaluation of soil properties for use in earthquake response analysis[C].Proceedings of the international symposium on numerical models in geomechanics.Zurich,1982:237-259.
[202]Hardin B O,Blandford G E.Elasticity of particulate materials[J].Journal of Geotechnical Engineering,1989,115(6):788-805.
[203]Jamiolkowski M,Lancellotta R,Lo Presti D C F.Remarks on the stiffness at small strains of six Italian clays[J].Pre-failure deformation of geomaterials,1994,2:817-836.
[204]Viggiani G,Atkinson J H.Stiffness of fine-grained soil at very small strains[J].Geotechnique,1995,45(2):249-265.
[205]Rampello S,Silvestri F,Viggiani G.The dependence of G_0 on stress state and history in cohesive soils[C].Proceeding 1st International Conference on pre-failure deformation characteristics of geomaterials,.Sapporo,1994:1155-1160.
[206]Rampello S,Viggiani G M B,Amorost A.Small-strain stiffness of reconstituted clay compressed along constant triaxial effective stress ratio paths[J].Geotechnique,1997,47(3):475-489.
[207]Apriadi D,Likitlersuang S,Pipatpongsa T,et al.Hyperplasticity modelling of normally consolidated clays in simple shear[C].Proceeding of theTenth International Summer Symposium.Tokyo,2008:1-4.
[208]Likitlersuang S,Houlsby G T.Development of hyperplasticity models for soil mechanics[J].International Journal for Numerical and Analytical Methods in Geomechanics,2006,30(3):229-254.
[209]陆万明,罗学富.弹性理论基础[M].北京:清华大学出版社,2001.
[210]Arthur J R F,Chua K S,Dunstan T.Induced anisotropy in a sand[J].Geotechnique,1977,27(1):13-30.
[211]张坤勇,殷宗泽,徐志伟.土体各向异性的再认识[J].岩土工程技术,2004,18(1):1-4.
[212]Love A E H.A treatise on the mathematical theory of elasticity[M].Cambridge:Cambridge University Press,1927.
[213]孙静,袁晓铭.DGZ-1多功能共振柱常规试验可靠性分析[J].地震工程与工程振动,2006,26(5):258-263.
[214]Lanzo G,Vucetic M,Doroudian M.Reduction of shear modulus at small strains in simple shear[J].Journal of Geotechnical and Geoenvironmental Engineering,1997,123:1035-1042.
[215]Vucetic M,Lanzo G,Doroudian M.Damping at small strains in cyclic simple shear test[J].Journal of Geotechnical and Geoenvironmental Engineering,1998,124:585-594.
[216]Vucetic M,Lanzo G,Doroudian M.Effect of the shape of cyclic loading on damping ratio at small strains[J].Journal of the Japanese Geotechnical Society:soils and foundation,1998,38(1):111-120.
[217]Lanzo G,Vucetic M.Effect of soil plasticity on damping ratio at small cyclic strains[J].Journal of the Japanese Geotechnical Society:soils and foundation,1999,39(4):131-141.
[218]Chu-Chung Hsu A M,Mladen Vucetic M.Volumetric threshold shear strain for cyclic settlement[J].Journal of Geotechnical and Geoenviroumental Engineering,2004,130:58-70.
[219]Hsu C C,Vucetic M.Threshold shear strain for cyclic pore-water pressure in cohesive soils[J].Journal of Geotechnical and Geoenvironmental Engineering,2006,132:1325-1335.
[220]Duku P M,Stewart J P,Whang D H,et al.Volumetric strains of clean sands subject to cyclic loads[J].Journal of Geotechnical and Geoenvironmental Engineering,2008,134:1073-1085.
[221]Drnevich V P.Long-tor resonant colomun apparatus operating manual[S].Ine USA,1984.
[222]祝龙根,吴晓峰.饱和砂和低塑粘土临界应变的研究[J].大坝观测与土工测试,1988,12(1):27-33.
[223]Dobry R,Swiger W F.Threshold strain and cyclic behavior of cohesionless soils[J].Austin TX,1979:521-525.
[224]Collins I F,Kelly P A.Discussion a thermomechanical analysis of a family of soil models[J].Geotechnique,2003,53(6):606-609.
[225]Hardin B O,Drnevich V P.Shear modulus and damping in soils:design equations and curves[J].Journal of the Soil Mechanics and Foundations Division,ASCE,1972,98(7):667-692.
[226]Idriss I M,Dobry R,Singh R D.Nonlinear behavior of soft clays during cyclic loading[J].Journal of the Geotechnical Engineering Division,1975,104(12):1427-1447.
[227]Masing G.Proceedings of the 2nd International Congress of Applied Mechanics[C].1926.
[225]Kong X J,Lou S L,Zou D G,et al.The equivalent dynamic shear modulus and equivalent damping ratio of rockf ill material for dam[J].Chinese Journal of hydrology,2001,8:20-25.
[229]Veletsos A S.Structural and Geotechnical Mechanics[M].New Jersey,Prentice-Hall Inc.,Englewood Cliffs,1977.
[230]Oda M,Nemat-Nasser S,Konishi J.Stress-induced anlsotropy in granular masses[J].Soils and Foundations,1985,25(3):85-97.
[231]Pietruszczak S,Krucinski S.Description of anisotropic response of clays using a tensorial measure of structural disorder[J].Mechanics of Materials,1989,8(2):237-249.
[232]Chang C S,Hicber P Y.An elasto-plastic model for granular materials with microstructural consideration[J].International Journal of Solids and Structures,2005,42(14):4258-4277.
[233]Kachaaov M,Sevostianov I.On quantitative characterization of microstroctures and effective properties[J].International Journal of Solids and Structures,2005,42(2):309-336.
[234]Mehrabadi M M,Nemat-Nasser S,Oda M.On statistical description of stress and fabric in granular materials[J].International Journal for Numerical and Analytical Methods in Geomechanics,1982,6(1).
[235]Tobita H,Hamielec A E.Modeling of network formation in free radical polymerization[J].Macromolecules,1989,22(7):3098-3105.
[236]Bathurst R J,Rothenburg L.Observations on stress-force-fabric relationships in idealized granular materials[J].Mech Mater,1990,9:65-80.
[237]Kruyt N P,Rothenburg L.Kinematic and static assumptions for homogenization in micromechanics of granular materials[J].Mechanics of Materials,2004,36(12):1157-1173.
[238]Kanatani K I.Distribution of directional data and fabric tensors[J].International journal of engineering science,1984,22(2):149-164.
[239]Muhunthan B.Micromechanics of Steady State,Collapse and Stress-Strain Modeling of Soils[D].Purdue University,Lafayette,Indiana,1991.
[240]Muhunthan B,Alwail T A.Use of Image Analysis in Mathematical Characterization of Orientation Data[J].Scanning-New York and Baden Then Mahwah,1992,14:291-291.
[241]顾成权,方云.黄土湿陷性的微观结构研究[J].西部探矿工程,2003,15(10):1-3.
[242]Cowin P.The complement of desmosomal plaque proteins in different cell types[J].Journal of Cell Biology,1985,101(4):1442-1454.
[243]Guo P J.Modelling granular materials with respect to stress-dilatancy and fabric:A fundamental approach[D].University of Calgary,2000.
[244]Sewell,M J.Legendre transformations and extremum Principle[C].In:HoPkins H G,Sewell M J,editors.Mechanics of solids,The Rodney Hill 60th anniversary volume.Oxford:Pergamon,1982:563-605.
[2]Robert D S,Lembit K.Threshold of dilation under cyclic loading[J].Journal of the Geotechnical Engineering Division,ASCE,1977,103(GT10):1174-1178.
[3]Richard P R,Richard D W.Modulus and damping due to uniform and variable cyclic loading[J].Journal of Geotechnical Engineering,1988,114(8):861-876.
[4]Vucetic M.Cyclic threshold shear strains in soils[J].Journal of Geotechnical Engineering,1994,120(12):2208-2229.
[5]Hsu C C,Vucetic M.Volume threshold shear strain for cyclic settlement[J].Journal of Geotechanical and Geoenvironiment Engineering,2004,130(1):58-70.
[6]Bjerrum L.Embankment on soft ground.In Performance of Earth and Earth supported Structures[C],1972,2:1-54.
[7]沈珠江.现代土力学的基本问题[J].力学与实践,1998,20(6):1-6.
[8]沈珠江.土体结构性的数学模型-21世纪土力学的核心问题[J].岩土工程学报,1996,18(1):95-97.
[9]谢定义,齐吉琳.土结构性及其定量化参数研究的新途径[J].岩土工程学报,1999,21(6):651-656.
[10]郑颖人,沈珠江,龚晓南.广义塑性力学—岩土塑性力学原理[M].北京:建筑工业出版社,2002.
[11]Houlsby G T,Puzrin A M.Principles of hyperplasticity:an approach to plasticity theory based on thermodynamic principles[M].London:Springer,2006.
[12]钱家欢,殷宗泽.土工原理与计算(第二版)[M].北京:中国水利水电出版社,1996.
[13]Duncan J M,Byrne P,Wong K S,et al.Strength,stress-strain and bulk modulus parameters for finite element analysis of stresses and movements in soil masses[J].Geotechnical Engineering,1980.
[14]徐舜华,徐光黎,程瑶.土的剑桥模型发展综述[J].长江科学院院报,2007,24(5):27-32.
[15]Roscoe K H,Schofield A N,Wroth C P.On yielding of soils[J].Geotechnique 1958,8:22-53.
[16]Roscoe K H,Burland J B.On the generalized stress-strain behaviour of "wet clay"[M].Cambridge:Cambridge University Press,1968.
[17]魏汝龙.正常压密粘土的塑性势[J].水利学报,1964,6.
[18]Sandler I S,Dimaggio F L,Baladi G Y.Generalized Cap Model for Geological Materials[J].Journal of Geotechnical Engineering Division,1976,102(7):683-699.
[19]章根德.土的本构关系及其工程应用[M].北京:科学出版社,1995.
[20]卢应发,刘德富,田斌,等.广义帽盖模型和数值模拟[J].工程力学,2006,23(11):9-13.
[21]Hsieh H S,E.K J.Double-Yield-Surface Cam-Clay Plasticity Model.Ⅰ:Theory[J].Journal of Geotechnical Engineering,1990,116:1381-1401.
[22]Borja R I,Hsieh H S,Kavazanjian J E.Double-Yield-Surface Model.Ⅱ:Implementation and Verification[J].Journal of Geotechnical Engineering,1990,116:1402-1421.
[23]Rouainia M,Wood D M.A kinematic hardening constitutive model for natural clays with loss of structure[J].Geotechnique,2000,50(2):153-164.
[24]李兴照,黄茂松,王录民.流变性软黏土的弹黏塑性边界面本构模型[J].岩石力学与工程学报,2007,26(7):1393-1401.
[25]Leoni M,Karstunen M,Vermeer P A.Anisotropic creep model for soft soils[J].Geotechnique,2008,58(3):215-226.
[26]Ohta H,Sekiguchi H.Constitutive equations considering anisotropy and stress reorientation in clay.In:Wittke W,editor.Proc of the 3nd Int Conference on Numerical in Geomechanics[C].Aachen:University of Aachen,1979:475-484.
[27]孙德安,姚仰平.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.
[28]Voyiadjis G Z,Song C R.Anisotropic Modified Cam Clay Model with Plastic Spin for Finite Strains[J].Journal of Engineering Mechanics 2000,126(10):1012-1019.
[29]Liu M D,Carter J P.A structured Cam Clay model[J].Canadian Geotechnical Journal,2002,39(6):1313-1332.
[30]Wheeler S J,Naatanen A,Karstunen M,et al.An anisotropic elastoplastic model for soft clays[J].Canadian Geotechnical Journal,2003,40(2):403-418.
[31]Wheeler S J,Cudny M,Neher H P,et al.Some developments in constitutive modelling of soft clays.In:Vermeer P A,editor.International Workshop on Geotechnics of Soft Soils-Theory and Practice[C],2003:1-20.
[32]刘元雪,施建勇.基于应力空间变换的修正剑桥模型改进[J].岩土力学,2003,24(1):1-7.
[33]刘元雪,施建勇.应力空间变换—岩土本构描述的一条新途径[J].岩石力学与工程学报,2003,22(2):217-222.
[34]刘元雪,施建勇,尹光志.基于应力空间变换的原状软土本构模型[J].水利学报,2004,(6):14-20.
[35]Mita K A,Dasari G R,Lo K W.Performance of a Three-Dimensional Hvorslev-Modified Cam Clay Model for Overconsolidated Clay[J].International Journal of Geomechanics,2004,4:296-309.
[36]Carter J P,Liu M D.Review of the Structured Cam Clay Model.Invited paper,Soil constitutive models:evaluation,selection,and calibration[J],ASCE,Geotechnical special publication,2005,128:99-132.
[37]魏星,黄茂松.黏土的各向异性边界面模型[J].水利学报,2006,37(7):831-837.
[38]姚仰平,孔玉侠,宋美娜.考虑原生各向异性土的统一硬化模型[J].工业建筑,2008,38(8):6-9.
[39]Been K,Jefferies M G.A state parameter for sands.Geotechnique,1985,35(2):99-112.
[40]Manzari M T,Dafalias Y F.A critical state two-surface plasticity model for sands[J].Geotechnique,1997,47(2):255-272.
[41]Yu H S.CASM:a unified state parameter model for clay and sand[J].International Journal for Numerical and Analytical Methods in Geomechanics,1998,22(8):621-653.
[42]Gajo A,Wood D M.A kinematic hardening constitutive model for sands:the multiaxial formulation[J].Int J Numer Anal Meth Geomech,1999,23:925-965.
[43]罗刚,张建民.考虑物理状态变化的砂土本构模型[J].水利学报,2004,(7):26-31.
[44]罗刚,张建民.考虑物态变化的六参数砂土本构模型[J].清华大学学报:自然科学版,2004,44(3):402-405.
[45]王刚,张建民.密度和压力对砂土变形特性影响的统一模拟[J].清华大学学报:自然科学版,2003,43(8):1100-1103.
[46]王国欣,肖树芳.土结构性本构模型研究现状综述[J].工程地质学报,2006,14(5):620-626.
[47]施斌.粘性土微观结构研究回顾与展望[J].工程地质学报,1996,4(1):39-44.
[48]苗天德,刘忠玉.湿陷性黄土的变形机理与本构关系[J].岩土工程学报,1999,21(4):383-387.
[49]王常明,夏玉斌.海积软土固结变形的结构性模型研究[J].长春科技大学学报,2001,31(4):363-367.
[50]宋章,程谦恭,张炜,等.原状黄土显微结构特征与湿陷性状分析[J].工程地质学报,2007,15(5):646-653.
[51]沈珠江.岩土破损力学与双重介质模型[J].水利水运工程学报,2002,(4):1-6.
[52]沈珠江.岩土破损力学—结构类型与荷载分担[J].岩石力学与工程学报,2004,23(13):2137-2142.
[53]刘恩龙,沈珠江.结构性土的强度准则[J].岩土工程学报,2006,28(10):1248-1252.
[54]李凡.岩土材料破损特性的颗粒流研究[J].土木工程学报,2007,40(9):78-81.
[55]何开胜,沈珠江.结构性粘土的弹粘塑损伤模型[J].水利水运工程学报,2002,(4):7-13.
[56]Desai C S,Ma Y.Modelling of joints and interfaces using the disturbed-state concept[J].International Journal for Numerical and Analytical Methods in Geomechanics,1992,16(9):623-653.
[57]Armaleh S H,Desai C S.Modelling and testing of a cohesionless material using the disturbed state concept[J].Int J Mech Behavior Mater,1994,5:279-295.
[58]Geomech I.Disturbed state model for sand geosynthetic interfaces and application to pull-out tests[J].Int J Numer Anal Meth Geomech,1999,23:1873-1892.
[59]Fakharian K,Evgin E.Elasto-plastic modelling of stress-path-dependent behaviour of interfaces[J].International Journal for Numerical and Analytical Methods in Geomechanics,2000,24(2):183-199.
[60]谢定义,齐吉琳.考虑土结构性的本构关系[J].土木工程学报,2000,33(4):35-41.
[61]骆亚生,谢定义,邵生俊,等.复杂应力状态下的土结构性参数[J].岩石力学与工程学报,2004,23(24):4248-4251.
[62]雷华阳.结构性海积软土的弹塑性研究[J].岩土力学,2002,23(6):721-724.
[63]谢定义.土动力学[M].西安:西安交通大学出版社,1988.
[64]刘汉龙,余湘娟.土动力学和岩土地震工程.第九届土力学及岩土工程学术会议论文集[C].北京:清华大学出版社.2003:56-68.
[65]王志良,王余庆,韩清宇.不规则循环剪切荷载作用下土的粘弹性模型[J].岩土工程学报,1980,2(3):10-20.
[66]Pyke R.Nonlinear soil models for irregular cyclic loadings[J].Journal of the Geotechnical Engineering Division,1979,105(6):715-726.
[67]王志良,韩清宇.粘弹塑性土层地震反应的波动分析法[J].地震工程与工程振动,1981,1(1):117-137.
[68]Ishihara K,Yoshida N,Tsujino S.Modelling of stress-strain relations of soils in cyclic loading[C].In:Nagoya,editor.Proceedings of the Fifth International Conference on Numerical Methods in Geomechanics,1985.p.373-380.
[69]栾茂田.土动力非线性分析中的变参数Ramberg-Osgood本构模型[J].地震工程与工程振动,1992,12(2):69-78.
[70]Bardet J P.Scaled memory model for cyclic behavior of soils[J].Journal of Geotechnical Engineering,1995,121(11):766-775.
[71]张克绪,李明宰.基于非曼辛准则的土动弹塑性模型[J].地震工程与工程振动,1997,17(2):74-81.
[72]Puzrin A M,Shiran A.Effects of the constitutive relationship on seismic response of soils.Part Ⅰ.Constitutive modeling of cyclic behavior of soils[j].Soil Dynamics and Earthquake Engineering,2000,19(5):305-318.
[73]Fang H L.A state-dependent multi-mechanism model for sands[J].Geotechnique,2003,53(4):407-420.
[74]Iwan W D.On a class of models for the yielding behavior of continuous and composite system[J].ASME,1967,34(3):21-33
[75]Nossan A S.An overlay model for cyclic behaviour of sands[C].In:Zurich,editor.Proceedings of The International Symposium on Numerical Models in Geomechanics,1982:110-116.
[76]郑大同,王惠昌.循环荷载作用下土的非线性应力应变模型[J].岩土工程学报,1985,5(1):65-76.
[77]李小军,廖振鹏.土应力变关系的粘—弹—塑模型[J].地震工程与工程振动,1989,9(3):65-72.
[78]孔亮,王燕昌,郑颖人.土体动本构模型研究评述[J].宁夏大学学报:自然科学版,2001,22(1):17-22.
[79]Mroz Z.On the description of anisotropic work hardening[J].J Mech Phys Solids,1967,15(3):163-175.
[80]Prevost J H.Mathematical modelling of monotonic and cyclic undrained clay behaviour[J].International Journal for Numerical and Analytical Methods in Geomechanics,1977,1(2):195-216.
[81]Prevost J H.Anisotropic undrained stress-strain behavior of clays.Journal of the Geotechnical Engineering Division,1978,104(8):1075-1090.
[82]Prevost J H.A simple plasticity theory for frictional cohesionless soils[J].International journal of soil dynamics and eathquake engineering,1985,4(1):9-17.
[83]Zienkiewicz O C.广义塑性力学和地力学的一些模型[J].应用数学与力学,1982,3(3):267-267.
[84]Mroz Z,Zienkiewicz O C.Uniform formulation of constitutive equations for clays and sand[J].Mechanics of engineering materials,1984:415-450.
[85]Mroz Z,Norris V A,Zienkiewicz O C.An anisotropic hardening model for soils and its application to cyclic loading[J],International Journal for Numerical and Analytical Methods in Geomechanics,1978,2(3):203-221.
[86]Mroz Z,Pietruszczak S.A constitutive model for sand with anisotropic hardening rule[J].International Journal for Numerical and Analytical Methods in Geomechanics,1983,7(3):305-320.
[87]Zienkiewicz O C,Mroz Z.Generalized plasticity formulation and applications to geomechanics[J].Mechanics of engineering materials,1984:655-680.
[88]Elgamal A,Yang Z,Parra E.Computational modeling of cyclic mobility and post-liquefaction site response[J].Soil Dynamics and Earthquake Engineering,2002,22(4):259-271.
[89]Peng J,Lu J,Law K H,et al.ParCYCLIC:finite element modelling of earthquake liquefaction response on parallel computers[J].International Journal for Numerical and Analytical Methods in Geomechanics,2004,28(12):1207-1232.
[90]Dafalias Y F,Popov E P.A model of nonlinearly hardening materials for complex loading[J].Acta Mechanica,1975,21(3):173-192.
[91]Krieg R D.A practical two surface plasticity theory[J].J Appl Mech,1975,42(3):641-646.
[92]吴兴征.堆石料的静动力本构模型及其在混凝土面板堆石坝中的应用[D].大连:大连理工大学,2001.
[93]Dafalias Y F.A model for soil behavior under monotonic and cyclic loading conditions[C].Transactions of 5th international conference on Smirt.West Berlin,1979.
[94]Dafalias Y F,Herrmann L R.Bounding surface formulation of soil plasticity[C].In:Pande G N,Zienkiewicz O C,editors.Soil Mechanics-Transient and Cyclic Loads:Constitutive Relations and Numerical Treatment.New York:John Wiley and Sons,1982:253-282.
[95]Dafalias Y F.Bounding Surface Plasticity:Ⅰ:Mathematical Foundation and Hypoplasticity[J].Journal of Engineering Mechanics,1986,112(9):966-987.
[96]Dafalias Y F,Herrmann L R.Bounding surface plasticity Ⅱ:application to isotropic cohesive soils[J].Journal of Engineering Mechanics,1986,112(12):1263-1291.
[97]Anandarajah A,Dafalias Y F.Bounding surface plasticity Ⅲ:application to anisotropic cohesive soils[J].Journal of Engineering Mechanics,1986,112(12):1292-1318.
[98]Al-Tabbaa A,Wood D M.An experimentally based bubble model for clay[C].In:Pietruszczak S,Pande G N,editors.Numerical Models in Geomechanics:Elsevier Science Publishers Ltd,1989:91-99.
[99]Liang R Y,Ma F.Anisotropic plasticity model for undrained cyclic behavior of clays.Ⅰ:theory[J].Journal of Geotechnical Engineering,1992,118(2):229-245.
[100]Borja R I,Amies A P.Multiaxial cyclic plasticity model for clays[J].Journal of Geotechnical Engineering,1994,120(6):1051-1070.
[101]Pestana J M,Biscontin G,Nadim F,et al.Modeling cyclic behavior of lightly overconsolidated clays in simple shear[J].Soil Dynamics and Earthquake Engineering,2000,19(7):501-519.
[102]Li T.Two-surface plasticity model for cyclic undrained behavior of clays[J].Journal of Geotechnical and Geoenvironmental Engineering,2002,128:613-626.
[103]Bardet J P.Application of plasticity theory to soil behavior:a new sand model[D].Pasadena:California Institutive of Technology,1987.
[104]Nakai T,Fujii J,Taki H.Kinematic extension of anisotropic hardening model for sand[C].In:Pietruszczak S,Pande G N,editors.Numerical Models in Geomechanics:Elsevier Science Publishers Ltd,1989:36-45.
[105]Anandarajah A.Procedures for elastoplastic liquefaction modeling of sands[J].Journal of Engieering Mechanics,1994,120:1563-1563.
[106]Arulanandan K,Li X S,Sivathasan K.Numerical simulation of liquefaction-induced deformations[J].Journal of Geotechnical and Geoenvironmental Engineering,1999,126(7):657-666.
[107]Matsuoka H.Stress-strain relationships of sands based on the mobilized plane[J].Soils and Foundations,1974,14(2):47-61.
[108]Aubry D,Hujeux J C,Lassoudiere F,et al.A double memory model with multiple mechanisms for cyclic soil behaviour[C].Proceedings of the International Symposiumon Numerical Models in Geomechanics.Zurich,1982:3-13.
[109]Towhata I,Ishihara K.Modelling soil behavior under principal stress axes rotation[C].Proceedings of The Fifth International Conference on Numerical Methods in Geomechanics.Nagoya,1985:523-530.
[110]Kabilamany K,Ishihara K.Stress dilatancy and hardening laws for rigid granular model of sand[J].Soil dynamics and earthquake engineering,1990,9(2):66-77.
[111]Kabilamany K,Ishihara K.Cyclic behaviour of sand by the multiple shear mechanism model[J].Soil Dynamics and Earthquake Engineering,1991,10(2):74-83.
[112]Prevost J H,Keane C M.Multi-mechanism elasto-plastic model for soils[J].Journal of Engineering Mechanics,1990,116(9):1924-1944.
[113]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.
[114]Hashiguchi K,Chen Z P.Elastoplastic constitutive equation of soils with the subloading surface and the rotational hardening[J].International Journal for Numerical and Analytical Methods in Geomechanics,1998,22(3):197-227.
[115]Iai S,Matsunaga Y,Kameoka T.Strain space plasticity model for cyclic mobility[J].Soils and Foundations,1992,32(2):1-15.
[116]Iai S,Ozutsumi O.Yield and cyclic behaviour of a strain space multiple mechanism model for granular materials[J].International Journal for Numerical and Analytical Methods in Geomechanics,2005,29(4):417-442.
[117]Akiyoshi T,Matsumoto H,Fuchida K,et al.Cyclic mobility behaviour of sand by the three-dimensional strain space multimechanism model[J].International Journal for Numerical and Analytical Methods in Geomechanics,1994,18(6):397-415.
[118]Hamadi K,Modaressi-Farahmand Razavi A,Darve F.Bifurcation and instability modelling by a multimechanism elasto-plastic model[J].International Journal for Numerical and Analytical Methods in Geomechanics,2008,32(5):461-492.
[119]李亮,赵成刚.饱和土体动力本构模型研究进展[J].世界地震工程,2004,20(1):138-148.
[120]Shen Z J.A stress-strain model for sands under complex loading[C].In:FANG J H,Sumio M,editors.Advances in Constitutive Laws for Engineering Material,1989:303-308.
[121]沈珠江,栾茂田.复杂荷载下砂土液化变形的结构性模型[C].第五届全国土动力学学会会议论文集.大连:大连理工大学出版社,1998:1-10.
[122]沈珠江.砂土液化分析的散粒体模型[J].岩土工程学报,1999,21(6):742-748.
[123]谢定义,张建民.饱和砂土瞬态动力学特性与机理分析[M].西安:陕西科学技术出版社,1995.
[124]姚仰平,谢定义.土的动力本构关系的新探讨[J].西安建筑科技大学学报,1997,29(2):159-163.
[125]姚仰平,谢定义.饱和砂土动应力-应变关系的模拟[C].见:栾茂田,编.土动力学理论与实践—第五届全国土动力学学术会议.大连:大连理工大学出版社,1998:82-87.
[126]刘元雪,郑颖人.含主应力轴旋转的土一般应力应变关系[J].应用数学和力学,1998,19(5):407-413.
[127]刘元雪,郑颖人.含主应力轴旋转的土体本构关系研究进展[J].力学进展,2000,30(4):597-604.
[128]李小军.非线性场地地震反应分析方法的研究[D].国家地震局工程力学研究所,1993.
[129]徐干成.饱和砂土循环动应力应变特性的弹塑性模拟研究[J].岩土工程学报,1995,17(2):1-12.
[130]王建华,要明伦.循环应变下饱和砂(粉)土衰化动力特性研究[J].水利学报,1997,(7):24-30.
[131]李相崧,邹离湘.砂土材料模拟剪胀破坏的动力本构模型[C].见:栾茂田,编.第五届全国土动力学学术会议.大连:大连理工大学出版社,1998:47-52.
[132]丰土根,刘汉龙.砂土多机构边界面塑性模型初探[J].岩土工程学报,2002,24(3):382-385.
[133]迟世春,刘怀林.土工建筑物动力真非线性分析的量化记忆模型[J].水利学报,2003,10:51-59.
[134]迟世春,许艳林.多维量化记忆模型及其验证[J].岩土工程学报,2005,27(2):167-172.
[135]迟世春,宋振河.土的量化记忆模型及其参数确定[J].岩土力学,2004,25(1):77-81.
[136]李兴照,黄茂松.循环荷载作用下流变性软黏土的边界面模型[J].岩土工程学报,2007,29(2):249-254.
[137]曲圣年,殷有泉.塑性力学的Drucker公设和Ilyushin公设[J].力学学报,1981,5:47-55.
[138]殷有泉,曲圣年.弹塑性耦合和广义正交法则[J].力学学报,1982,1:63-70.
[139]郑颖人,孔亮.塑性力学中的分量理论—广义塑性力学[J].岩土工程学报,2000,22(3):269-274.
[140]郑颖人.广义塑性力学理论[J].岩土力学,2000,21(2):188-192.
[141]郑颖人.岩土塑性力学的新进展—广义塑性力学[J].岩土工程学报,2003,25(1):1-10.
[142]郑颖人.关于岩土塑性的几点认识[J].岩土工程界,2002,5(4):14-16.
[143]黄文彬.关于塑性力学两公设适用性的分析[J].力学与实践,1992,14(2):64-65.
[144]胡亚元.关于率无关塑性力学和广义塑性力学的评述[J].岩土工程学报,2005,27(1):128-131.
[145]黄速建.塑性力学的稳定性公设的热力学原理[J].固体力学学报,1988,9(2):95-101.
[146]刘元雪.岩土本构理论的几个基本问题研究[J].岩土工程学报,2001,23(1):45-48.
[147]Ziegler H.An introduction to thermomechanics[M].Amsterdam:North-Holland,1983.
[148]孔亮,Collins I F.模拟土体本构特性的热力学方法[J].岩土力学,2008,29(7):1732-1740.
[149]Ziegler H,Wehrli C.The derivation of constitutive relations from the free energy and the dissipation function[J].Advances Applied Mechanics,1987,25:183-238.
[150]赵成刚,张雪东,郭璇.土的本构方程与热力学[J].力学进展,2006,36(4):611-618.
[151]Houlsby G T.A study of plasticity theories and their applicability to soils[D].Cambridge UK:University of Cambridge,1981.
[152]Collins I F,Houlsby G T.Application of thermomechanical principles to the modeling of geomateriais[J].Proc Royal Society of London,,Series A,1997,453:1975-2001.
[153]Houlsby G T.The use of a variable shear modulus in elastic-plastic models for clays[J].Comput Geotech,1985,1:3-13.
[154]Houlsby G T,Amorosi A,Rojas E.Elastic moduli of soils dependent on pressure:a hyperelastic formulation[J].Geotechnique,2005,55(5):383-392.
[155]Graham J,Houlsby G T.Anisotropic elasticity of a natural clay[J].Geotechnique,1983,33:165-180.
[156]Borja R I,Tamagnini C,Amorosi A.Coupling plasticity and energy conserving elasticity models for clays[J].Journal of Geotechnical and Geoenviromental Engineering,1997,123(10):948-957.
[157]Einav I,Puzrin A M.Pressure-dependent elasticity and energy conservation in elastoplastic models for soils[J].Journal of Geotechnical and Geoenvironmental Engineering,2004,130(1):81-92.
[158]Einav I.Application of thermodynamical approaches to mechnics of soils[D].Technion-Israel Institute of Technology.Israel,2002.
[159]Houlsby G T,Puzrin A M.A thermomechanical framework for constitutive models for rate-independent dissipative materials[J].International Journal of Plasticity,2000,16(9):1017-1047.
[160]Houlsby G T,Puzrin A M.An approach to plasticity based on generalised thermodynamics[J].Constitutive Modelling of Granular Materials,2000:319-331.
[161]Collins I F,Hilder T.A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests[J].International Journal for Numerical and Analytical Methods in Geomechanics,2002,26(11):1313-1347.
[162]Puzrin A M,Houlsby G T.A thermomechanical framework for rate-independent dissipative materials with internal functions[J].International Journal of Plasticity,2001,17(8):1147-1165.
[163]Puzrin A M,Houlsby G T.Fundamentals of kinematic hardening hyperplasticity[J].International Journal of Solids and Structures,2001,38(21):3771-3794.
[164]Houlsby G T,Puzrin A M.Rate-dependent plasticity models derived from potential functions[J].Journal of Rheology,2002,46:113-126.
[165]Puzrin A M,Houlsby G T.Rate-dependent hyperplasticity with internal functions[J].Journal of Engineering Mechanics,2003,129(3):252-263.
[166]Likitlersuang S,Houlsby G T.Development of hyperplasticity models for soil mechanics[J].International Journal for Numerical and Analytical Methods in Geomechanics,2006,30(3):229-254.
[167]Collins I F,Tai A.What has thermo-mechanics to offer geo-mechanics[J].2005:281-288.
[168]Collins I F,Kelly P A.A thermomechanical analysis of a family of soil models[J].Geotechnique,2002,52(7):507-518.
[169]Collins I F.A systematic procedure for constructing critical state models in three dimensions[J].International Journal of Solids and Structures,2003,40(17):4379-4397.
[170]Likitlersuang S.A hyperplasticity model for clay behaviour:an application to Bangkok clay[D].Oxford University,2003.
[171]Collins I F,Muhunthan B.On the relationship between stress-dilatancy,anisotropy,and plastic dissipation for granular materials[J].Geotechnique,2003,53(7):611-618.
[172]Collins I F.The concept of stored plastic work or frozen elastic energy in soil mechanics[J].Geotechnique,2005,55(5):373-382.
[173]Collins I F.Elastic/plastic models for soils and sands[J].International Journal of Mechanical Sciences,2005,47(4):493-508.
[174]秦理曼,迟世春,林皋.基于热力学的砂土统一模型[J].水利学报,2006a,4:403-410.
[175]秦理曼,迟世春,林皋.基于热力学的砂土不排水统一模型[J].岩石力学与工程学报,2006b,7:1316-1322.
[176]王立忠,沈恺伦.K0固结结构性软黏土的本构模型[J].岩土工程学报,2007,29(4):496-504.
[177]Li X S.Thermodynamics-based constitutive framework for unsaturated soils.1:Theory[J].Geotechnique,2007,57(5):411-422.
[178]Li X S.Thermodynamics-based constitutive framework for unsaturated soils.2:A basic triaxial model[J].Geotechnique,2007,57(5):423-435.
[179]Buscarnera G,Nova R.An elastoplastic strainhardening model for soil allowing for hydraulic bonding-debonding effects[J].International Journal for Numerical and Analytical Methods in Geomechanics,2008.
[180]Einav I.Breakage mechanics-Part Ⅰ:Theory[J].Journal of the Mechanics and Physics of Solids,2007,55(6):1274-1297.
[181]Einav I.Breakage mechanics-Part Ⅱ:Modelling granular materials[J].Journal of the Mechanics and Physics of Solids,2007,55(6):1298-1320.
[182]Einav I.Soil mechanics:breaking ground[J].Philosophical Transactions of the Royal Society A:Mathematical,Physical and Engineering Sciences,2007,365(1861):2985-3002.
[183]Einav I.Fracture propagation in brittle granular matter[C].Proceedings of the Royal Society A:Mathematical,Physical and Engineering Sciences,2007,463(2087):3021-3035.
[184]Hardin B O.Crushing of soil particles[J].Journal of Geotechnical Engineering,1985,111(10):1177-1192.
[185]贾宇峰.考虑颗粒破碎的粗粒土本构关系研究[D].大连:大连理工大学,2008.
[186]王秋生.基于超塑性力学的软粘土本构理论研究[D].浙江:浙江大学,2007.
[187]Germain P,Suquet P,Nguyen Q S,et al.Continuum thermodynamics[J].ASME,Transactions,Journal of Applied Mechanics,1983,50(4b):1010-1020.
[188]Reddy B D,Martin J B.Internal variable formulations of problems in elastoplasticity:constitutive and algorithmic aspocts[J].Appl Mech Rev,1994,47(9):429-456.
[189]Maugin G A.Thermomechanics of nonliear irreversible behaviors[M].Singapore:World Scientific Press,1999.
[190]王竹溪.热力学(第二版)[M].北京:北京大学出版社,2005.
[191]Trusdell C A.Rational thermodynamics.2nd enlarged edition[M].New York:Springer verlag,1984.
[192]Collins I F,Muhunthan B,Tai A T T,et al.The concept of a'Reynolds-Taylor stare'and the mechanics of sands[J].Geotechnique,2007,57(5):437-447.
[193]Radjal F,Jean M,Moreau J J.Force distributions in dense two-dimensional granular systems[J].Phys Rev Lett,1996,77(2):274-277.
[194]秦理曼.基于能量耗散的土的本构关系研究[D].大连:大连理工大学,2006.
[195]Collins I F.Associated and non-associated aspects of the constitutive laws for coupled elastic/plastic materials[J].International Journal of Geomechanics,2002,2(2):259-267.
[196]Zytynski M,Randolph M F,Nova R,et al.On modelling the unloading-reloading behaviour of soils[J].International Journal for Numerical and Analytical Methods in Geomechanics,1978,2(1):87-93.
[197]Graham J,Houlsby G T.Elastic anisotropy of a natural clay[M].University of Oxford Department of Engineering Science,1982.
[198]Houlsby G T,Wroth C P.The variation of shear modulus of a clay with pressure and overconsolidation ratio[J].Soils and Foundations,1991,31(3):138-143.
[199]Einav I,Puzrin A M,Houlsby G T.Continuous Hyperplastic Models for Overconsolidated Clays[J].Mathematical and Computer Modelling,2003,37:515-523.
[200]Einav I,Puzrin A M.Continuous hyperplastic critical state(CHCS) model derivation[J].International Journal of Solids and Structures,2004,41:199-226.
[201]Ishihara K.Evaluation of soil properties for use in earthquake response analysis[C].Proceedings of the international symposium on numerical models in geomechanics.Zurich,1982:237-259.
[202]Hardin B O,Blandford G E.Elasticity of particulate materials[J].Journal of Geotechnical Engineering,1989,115(6):788-805.
[203]Jamiolkowski M,Lancellotta R,Lo Presti D C F.Remarks on the stiffness at small strains of six Italian clays[J].Pre-failure deformation of geomaterials,1994,2:817-836.
[204]Viggiani G,Atkinson J H.Stiffness of fine-grained soil at very small strains[J].Geotechnique,1995,45(2):249-265.
[205]Rampello S,Silvestri F,Viggiani G.The dependence of G_0 on stress state and history in cohesive soils[C].Proceeding 1st International Conference on pre-failure deformation characteristics of geomaterials,.Sapporo,1994:1155-1160.
[206]Rampello S,Viggiani G M B,Amorost A.Small-strain stiffness of reconstituted clay compressed along constant triaxial effective stress ratio paths[J].Geotechnique,1997,47(3):475-489.
[207]Apriadi D,Likitlersuang S,Pipatpongsa T,et al.Hyperplasticity modelling of normally consolidated clays in simple shear[C].Proceeding of theTenth International Summer Symposium.Tokyo,2008:1-4.
[208]Likitlersuang S,Houlsby G T.Development of hyperplasticity models for soil mechanics[J].International Journal for Numerical and Analytical Methods in Geomechanics,2006,30(3):229-254.
[209]陆万明,罗学富.弹性理论基础[M].北京:清华大学出版社,2001.
[210]Arthur J R F,Chua K S,Dunstan T.Induced anisotropy in a sand[J].Geotechnique,1977,27(1):13-30.
[211]张坤勇,殷宗泽,徐志伟.土体各向异性的再认识[J].岩土工程技术,2004,18(1):1-4.
[212]Love A E H.A treatise on the mathematical theory of elasticity[M].Cambridge:Cambridge University Press,1927.
[213]孙静,袁晓铭.DGZ-1多功能共振柱常规试验可靠性分析[J].地震工程与工程振动,2006,26(5):258-263.
[214]Lanzo G,Vucetic M,Doroudian M.Reduction of shear modulus at small strains in simple shear[J].Journal of Geotechnical and Geoenvironmental Engineering,1997,123:1035-1042.
[215]Vucetic M,Lanzo G,Doroudian M.Damping at small strains in cyclic simple shear test[J].Journal of Geotechnical and Geoenvironmental Engineering,1998,124:585-594.
[216]Vucetic M,Lanzo G,Doroudian M.Effect of the shape of cyclic loading on damping ratio at small strains[J].Journal of the Japanese Geotechnical Society:soils and foundation,1998,38(1):111-120.
[217]Lanzo G,Vucetic M.Effect of soil plasticity on damping ratio at small cyclic strains[J].Journal of the Japanese Geotechnical Society:soils and foundation,1999,39(4):131-141.
[218]Chu-Chung Hsu A M,Mladen Vucetic M.Volumetric threshold shear strain for cyclic settlement[J].Journal of Geotechnical and Geoenviroumental Engineering,2004,130:58-70.
[219]Hsu C C,Vucetic M.Threshold shear strain for cyclic pore-water pressure in cohesive soils[J].Journal of Geotechnical and Geoenvironmental Engineering,2006,132:1325-1335.
[220]Duku P M,Stewart J P,Whang D H,et al.Volumetric strains of clean sands subject to cyclic loads[J].Journal of Geotechnical and Geoenvironmental Engineering,2008,134:1073-1085.
[221]Drnevich V P.Long-tor resonant colomun apparatus operating manual[S].Ine USA,1984.
[222]祝龙根,吴晓峰.饱和砂和低塑粘土临界应变的研究[J].大坝观测与土工测试,1988,12(1):27-33.
[223]Dobry R,Swiger W F.Threshold strain and cyclic behavior of cohesionless soils[J].Austin TX,1979:521-525.
[224]Collins I F,Kelly P A.Discussion a thermomechanical analysis of a family of soil models[J].Geotechnique,2003,53(6):606-609.
[225]Hardin B O,Drnevich V P.Shear modulus and damping in soils:design equations and curves[J].Journal of the Soil Mechanics and Foundations Division,ASCE,1972,98(7):667-692.
[226]Idriss I M,Dobry R,Singh R D.Nonlinear behavior of soft clays during cyclic loading[J].Journal of the Geotechnical Engineering Division,1975,104(12):1427-1447.
[227]Masing G.Proceedings of the 2nd International Congress of Applied Mechanics[C].1926.
[225]Kong X J,Lou S L,Zou D G,et al.The equivalent dynamic shear modulus and equivalent damping ratio of rockf ill material for dam[J].Chinese Journal of hydrology,2001,8:20-25.
[229]Veletsos A S.Structural and Geotechnical Mechanics[M].New Jersey,Prentice-Hall Inc.,Englewood Cliffs,1977.
[230]Oda M,Nemat-Nasser S,Konishi J.Stress-induced anlsotropy in granular masses[J].Soils and Foundations,1985,25(3):85-97.
[231]Pietruszczak S,Krucinski S.Description of anisotropic response of clays using a tensorial measure of structural disorder[J].Mechanics of Materials,1989,8(2):237-249.
[232]Chang C S,Hicber P Y.An elasto-plastic model for granular materials with microstructural consideration[J].International Journal of Solids and Structures,2005,42(14):4258-4277.
[233]Kachaaov M,Sevostianov I.On quantitative characterization of microstroctures and effective properties[J].International Journal of Solids and Structures,2005,42(2):309-336.
[234]Mehrabadi M M,Nemat-Nasser S,Oda M.On statistical description of stress and fabric in granular materials[J].International Journal for Numerical and Analytical Methods in Geomechanics,1982,6(1).
[235]Tobita H,Hamielec A E.Modeling of network formation in free radical polymerization[J].Macromolecules,1989,22(7):3098-3105.
[236]Bathurst R J,Rothenburg L.Observations on stress-force-fabric relationships in idealized granular materials[J].Mech Mater,1990,9:65-80.
[237]Kruyt N P,Rothenburg L.Kinematic and static assumptions for homogenization in micromechanics of granular materials[J].Mechanics of Materials,2004,36(12):1157-1173.
[238]Kanatani K I.Distribution of directional data and fabric tensors[J].International journal of engineering science,1984,22(2):149-164.
[239]Muhunthan B.Micromechanics of Steady State,Collapse and Stress-Strain Modeling of Soils[D].Purdue University,Lafayette,Indiana,1991.
[240]Muhunthan B,Alwail T A.Use of Image Analysis in Mathematical Characterization of Orientation Data[J].Scanning-New York and Baden Then Mahwah,1992,14:291-291.
[241]顾成权,方云.黄土湿陷性的微观结构研究[J].西部探矿工程,2003,15(10):1-3.
[242]Cowin P.The complement of desmosomal plaque proteins in different cell types[J].Journal of Cell Biology,1985,101(4):1442-1454.
[243]Guo P J.Modelling granular materials with respect to stress-dilatancy and fabric:A fundamental approach[D].University of Calgary,2000.
[244]Sewell,M J.Legendre transformations and extremum Principle[C].In:HoPkins H G,Sewell M J,editors.Mechanics of solids,The Rodney Hill 60th anniversary volume.Oxford:Pergamon,1982:563-605.