【作者】 路德春；

【导师】 姚仰平；

【作者基本信息】 北京航空航天大学 ， 道路与铁道工程， 2006， 博士

【摘要】 复杂应力状态在自然界和工程中普遍存在,材料在复杂应力状态下的变形和强度特性是一个基本问题。基于各国学者已取得的多种材料的强度试验结果,系统研究了各种材料强度的基本特性,提出了广义非线性强度理论,并给出变换应力的应用方法。研究土在复杂加载条件下的变形问题时,提出土在充分接近的两条加载应力路径下所产生的变形基本相等的观点,以此为基础建立了土的应力路径本构模型,通过定义一个新的加卸载准则将模型扩展用于循环加载条件,并且模型可较合理地模拟试验结果。论文的主要成果是:提出一个理论,即广义非线性强度理论(GNST);建立一个模型,即土的应力路径本构模型(SSPM)。广义非线性强度理论:基本特点是:(1)GNST具有统一的表达式,较少的参数(4个),并且参数都具有明确的物理意义。(2)GNST可反映土、岩石和混凝土等材料的基本强度特性。如,不同的抗拉、抗压强度;静水压力效应;中主应力效应;内聚力效应等。(3)GNST能将著名的强度理论(如,SMP准则、Mises准则等)作为特例包含在内。(4)GNST能合理描述各国学者得出的多种材料的强度试验结果。(5)GNST在主应力空间能形成连续光滑的破坏面,采用变换应力方法可方便地与弹塑性本构模型结合用于数值计算。广义非线性强度理论不是一个单一的非线性强度理论,而是一个理论体系,是一系列连续变化的强度理论,在π平面上涵盖了从下限SMP准则到上限扩展的Mises准则范围内的所有区域;在子午面上为幂函数形式,通过四个相互独立的材料强度参数的变化实现统一。广义非线性强度理论因其具有较强的功能和重要的理论意义,将具有广泛的应用前景。土的应力路径本构模型:以砂土为研究对象,以简单实用为出发点,建立一个可以考虑应力路径影响的土的本构模型,主要目的是把它作为解决实际工程问题的工具,因此简单是首要的;第二个主要要求是它能反映土的基本物理力学特性,特别是描述土性状的参数应具有明确的物理意义。土的应力路径本构模型的特点是:(1)模型简单,共有8个材料参数。对于正常固结土,只需5个参数,参数均具有明确的物理意义,利用常规试验即可确定。(2)模型可反映土的主要变形特性。如,应力-应变曲线的非线性、压硬性、剪胀性、中主应力对强度和变形的影响等。(3)模型可较合理地考虑应力路径对变形的影响。(4)模型不仅适用于单次加载条件,通过定义的两个应力状态参量给出的加卸载准则,模型也可用于循环加载应力路径。(5)模型可简化用于粘土,并将修正剑桥模型作为特例包含在内,进而反映土的临界状态。(6)在已建立的广义非线性强度理论的框架内,采用变换应力三维化方法,模型可合理地用于三维应力路径。应力路径相关性是土的重要力学特性,本文对应力路径影响土的变形机理和变形规律有一个比较明确的认识,提出的土的应力路径本构模型可较好地模拟土的应力路径相关性,并得到试验结果的证实。进一步深化了人们对土的基本特性和基本理论的认识。附录为土体平面应变条件下的主应力关系。更多还原

【Abstract】 Complex stress states widely exist both in nature and in engineering. Recently, the stress-strain relationship and the strength of materials under complex stress states have been pushed into spotlight. Based on the test data of various materials obtained by many scholars in their researches, a Generalized Non-linear Strength Theory (GNST) is proposed; meanwhile, the application of GNST into the transformed stress spaces is also given. A viewpoint that the stress-strain relationship of soils under two sufficiently close loading stress paths are approximately same with each other is proposed during the research of soil under complex loading conditions. Based on the above ideas, a constitutive model for soils which takes complex stress paths into account is established and this model can be used successfully into cyclic loading condition by defining a new loading/unloading criterion.The main achievement in this dissertation: (1) A theory, namely the Generalized Non-linear Strength Theory (GNST). (2) A model, namely the constitutive model for soils considering complex stress paths.Generalized Non-linear Strength Theory (GNST): The basic properties of GNST are listed as follows. (1) GNST has a unified mathematical form and relevantly fewer material parameters (only four parameters are needed in above theory), all of which have obvious physic significance. (2) GNST can be applied to describe the general strength behavior of materials like soils, concrete and rocks, including different extended and compressive strength and effect of hydrostatic pressure, intermediate principal stress and cohesion. (3) GNST could evolve back to some famous failure criteria and strength theories, such as SMP and Mises criterion which can be regarded as special cases of GNST. (4) Its validity can be confirmed by some existing well-known experimental data. (5) GNST owns continuous smooth failure plane in the principal stress space and can be conveniently applied into numerical analysis when it is combined with the transformed stress method.GNST should have a broad perspective for application, compared with other present criteria, because of its powerful function and theoretical significance. On the one hand, GNST could describe the failure behavior of materials like soils, rocks, concrete and metal as a failure criterion; on the other hand, GNST could be used to research the behavior of deformation for soils and concrete as a yield criterion. GNST has a continuous and smooth failure plane in the principal stress space, which results in a better convergence in numericalsolution.Constitutive model for soils considering complex stress paths: According to the mechanics behavior of sands, a constitutive model is established, which takes the following points into consideration. The first, this model, as a tool for solving engineering problems, is assumed that the principal purpose is to model the basic constitutive behavior of soils. So, simplicity will be of overriding importance. The second, the major requirement of the model is that it should, to large extent, reflect the underlying physical processes of the mechanics of soils. In particular, the parameters describing the soil should have an identifiable physical significance.The main features of this model are shown as follows. (1) This model has eight conventional material parameters in the general cases; especially, to normal consolidated clay, has only five material parameters, which can be defined by some ordinary experiments. (2) This model can reflect the general stress-strain behavior of sands including the non-linear stress-strain relationship, hardening behavior, positive/negative dilatancy, influence of intermediate principal stress on the deformation and strength, and the plastic strain coupled with hydrostatic and shear stress. (3) The stress-strain behavior influenced by complex stress paths can be well predicted. (4) This model can be used in simple loading as well as in cyclic loading. (5) This model can be simplified and used for clays, of which the Modified Cam-Clay (MCC) model can be viewed as a special case. (6) This model can be used to describe three-dimensional stress-strain behavior by combining transformed stress space in the framework of GNST.The stress-strain behavior influenced by complex stress paths is one aspect of compressive hardening features, which can be reckoned as the basic mechanics characteristic of soils. Based on test data, the presented model considering complex stress paths can well predict the stress-strain behavior depended on different stress paths.The relationship among principal stresses of soil under plane strain condition is proposed in appendix.更多还原