【作者】 郭晓霞；

【导师】 林皋； 迟世春；

【作者基本信息】 大连理工大学 ， 结构工程， 2009， 博士

【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。更多还原

【Abstract】 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.更多还原