砂土的宏细观试验与材料特性相关位势理论及其各向异性本构模型研究

Because of the contradictions between continuity isotropy assumption of traditional plastic potential theory and discrete anisotropic properties of soil, leading to some shortages and limitations of the traditional elastoplastic constitutive model for geomaterials, so it need to improve the traditional potential theory and establish constitutive model based on it. The sand tests with the method of macro-micro incorporation is first carried out in this Fund, with micro observation on fabric characteristics of sand and macro observation on deformation and failure in different water content under complex loading conditions, the inherent relationship between macro and micro can be summarized. Aimed on the limitation of traditional theory-based assumption of isotropy, with strain distribution rules of material and its micro properties considered together, property-dependent potential theory can be established in continuum mechanics system. Based on mechanical characteristics dependent on sand state, the introduction of micro properties to expand the concept of state-dependent and to establish anisotropic yield and hardening law. Dilatancy equation of property-dependent is derived from energy conversion theorem and property-dependent potential theory, and the variation of dilatancy can be analyze under the conditions of principal stress relative to the fabric rotation. Finally, anisotropic constitutive model which describe the anisotropic deformation and failure mechanism with the influence of microscopic fabric can be established. The purpose of this study is to improve the traditional plastic potential theory by inherent laws of test results with the method of macro-micro incorporation,whith not only can promote the development of the constitutive theory for geomaterials, but also can establish a realistic constitutive model of sand.

基于连续性、各向同性假设的传统塑性位势理论与土体离散性和各向异性存在矛盾，导致传统岩土弹塑性本构模型的不足与局限，急需对传统位势理论进行改进并建立相应的本构模型。本项目首先开展宏细观结合的砂土试验，细观获取其组构信息，宏观观测其不同含水量、复杂加载条件下变形破坏试验规律，归纳宏细观特性的试验联系；针对传统位势理论各向同性假设的限制，将材料应变分配法则和砂土细观特性相关联，在连续介质力学体系下建立材料特性相关位势理论；引入细观特性扩展材料状态相关的概念，建立各向异性屈服、硬化规律与砂土细观特性的关系，推导基于能量转换定理和材料特性相关位势理论的剪胀方程，探讨主应力方向发生旋转条件下材料特性相关剪胀性的变化规律，最终建立一个能考虑细观组构影响的砂土各向异性本构模型。本研究旨在根据砂土宏细观试验特性的内在联系改进土体传统位势理论，既可促进岩土本构理论的发展，又有望建立更符合实际的砂土本构模型。

本项目以宁夏沿黄城市带大型工程建设所面临的砂土强度变形控制及防灾减灾等关键科学问题，进行了砂土宏细观试验特性、变形破坏、强度准则、材料特性相关位势理论及本构模型等方面的研究。重要结论为：（1）首次系统研发了砂土三个组构成因的定量测定技术，形成了砂土组构测定新体系，研发了岩石裂隙组构定量测定技术，解决了岩土材料细观机理无法直接用于宏观力学现象描述的问题。通过SEM细观试验，借助体视学和形态学图像处理分析技术、多学科交叉等优势提出了砂土组构理论新定义，推导了砂土三种组构成因细观平面幅值参量定量测定公式和三维正交空间的组构表达式，基于数学概率统计的方法，幅值计算公式转化为组构特性在平面上的可测参量，三个幅值参量中独立变化量只有两个，用任意两个幅值可以推导出三维空间组构的正交各向异性表达式。随细观颗粒几何物理特性的变化，该组构三维表达式可以自然描述材料的各向同性、横观各向同性和正交各向异性；（2）原创性提出了岩土材料特性相关塑性位势理论。针对传统塑性位势理论因采用连续性、均匀性与各向同性等基本假定导致其应用于岩土材料导致的局限性，根据砂土细观物理特性可以用宏观组构张量来描述的特点，把应变分配法则和材料特性联系起来，揭示了岩土塑性变形与其细观特性的内在联系，创立了考虑主应力轴旋转的新位势本构理论框架，实现了天然土体在复杂受力条件下变形及其非共轴特性描述；（3）系统建立了天然砂土的破坏准则、本构模型，实现了其强度、变形和渐进破坏宏细观机理的理论描述。采用宏细观结合的方法建立了砂土的各向异性破坏准则，既实现了三维空间描述砂土强度随细观组构变化规律，也实现了主应力轴固定、旋转等复杂条件下描述细观组构演化对强度的影响。基于材料特性相关塑性位势理论建立了本构模型，模型能够描述砂土的单调加载、纯主应力轴旋转和混合加载条件下砂土表现的非共轴变形特性，揭示了岩土材料宏观破坏特性的细观组构特性机理。