基于材料特性相关塑性位势理论的单剪试验数值模拟

发布时间：2018-04-22 06:31

本文选题：材料特性相关塑性位势理论 + 砂土　；参考：《宁夏大学》2017年硕士论文

【摘要】：土体在地震、交通及波浪荷载等复杂受力条件下,主应力轴相对土体会发生不同程度的旋转,该条件下土体应力应变关系描述始终是工程界、学术界研究的热点和难点问题。现有土体本构关系绝大部分都在连续介质力学的理论框架下建立,该理论框架采用了材料为各向同性的假设,当材料为各向同性时,主应力轴旋转对材料的本构关系无任何影响,这个假设对描述土体在主应力轴旋转条件下的应力应变关系带来了巨大挑战。砂土在自然形成过程中,颗粒会沿某一方向定向排列,表现出原生各向异性,在复杂应力条件下,颗粒空间排列会发生演化,表现出明显的应力诱发各向异性,这种条件下明显加剧了其应力应变关系描述的复杂性。为此,本文在课题组提出的材料特性相关塑性位势理论的基础上,考虑到砂土细观组构对其力学特性的影响,建立砂土的土体本构模型,根据现有单剪试验结果,从单剪的应力应变关系描述、剪胀方程和三维主空间考虑主应力旋转的应力应变关系描述开展研究,最后,又用PFC软件对单剪试验进行模拟。主要内容如下:1、针对单剪试验应力应变特点,推导了该应力条件下的砂土的本构描述方程,并进行了试验模拟。根据单剪试验主应力轴发生旋转的特点,将组构张量引入砂土屈服方程中,描述该应力条件下细观组构对砂土屈服函数的影响;根据材料状态砂土对临界状态线的影响规律,将新定义的各向异性状态变量引入临界状态方程,描述细观组构对其临界状态的影响;在基于材料特性相关塑性位势理论建立砂土的本构模型;最后,基于单剪试验结果,对给试验条件下的应力应变及应力与非共轴角之间的关系进行了模拟,并与实验结果进行了比较分析。2、基于材料特性相关塑性位势理论,结合单剪试验,采用能量转换原理推导了砂土的应力剪胀方程。根据单剪试验过程中的主应力轴旋转特点,通过材料特性相关塑性位势理论计算主应力轴旋转过程中主应变增量变化角的关系,用主应力旋转角和对应主应变旋转角的差值定义非共轴性参数c,用该参数描述主应力轴旋转条件下材料参数对砂土剪胀关系的影响;结合材料相关特性理论的剪账方程进行对比,分析单剪试验条件下将松砂、中密砂及密砂的主应力旋转角、非共轴参数与剪账性的特点。3、使用PFC商业程序,用离散元模拟单剪试验条件下应力应变关系和剪账关系。根据单剪试验条件确定离散元初始加载条件,分析球形颗粒在不同围压,不同孔隙率和不同颗粒半径等排列条件下应力应变关系,并且分析其力链分布规律。
[Abstract]:Under the complex loading conditions such as earthquake, traffic and wave loads, the principal stress axis rotates to different degrees relative to the soil mass. Under this condition, the stress-strain relationship description of soil is always a hot and difficult problem in engineering and academic circles. Most of the existing constitutive relations of soil are established under the theoretical framework of continuum mechanics, which adopts the assumption that the material is isotropic, when the material is isotropic. The rotation of the principal stress axis has no effect on the constitutive relationship of the material. This assumption poses a great challenge to describe the stress-strain relationship of soil under the rotation of the principal stress axis. In the process of natural formation of sand, particles will be arranged in a certain direction, showing primary anisotropy. Under complex stress conditions, particle space arrangement will evolve, showing obvious stress-induced anisotropy. Under this condition, the complexity of the stress-strain relationship is obviously increased. Therefore, on the basis of the theory of plastic potential related to material characteristics proposed by the research group, considering the influence of the meso-fabric of sand on its mechanical properties, the constitutive model of soil mass of sand is established, and according to the results of single shear test, the constitutive model of sandy soil is established. In this paper, the stress-strain relation of single shear is described, the expansion equation of shear and the stress-strain relation of three dimensional principal space considering the rotation of principal stress are studied. Finally, the single shear test is simulated by PFC software. The main contents are as follows: 1. According to the stress-strain characteristics of single shear test, the constitutive equation of sand under this stress condition is derived, and the experimental simulation is carried out. According to the characteristics of rotation of principal stress axis in single shear test, the fabric Zhang Liang is introduced into the yield equation of sandy soil to describe the effect of mesoscopic fabric on the yield function of sandy soil under the stress condition, and according to the influence law of sand and soil in material state on critical state line, The newly defined anisotropic state variable is introduced into the critical state equation to describe the influence of mesoscopic fabric on the critical state. The constitutive model of sand is established based on the plastic potential theory related to the material properties. Finally, based on the results of single shear test, The stress-strain and the relationship between stress and non-coaxial angle under experimental conditions are simulated and compared with the experimental results. Based on the theory of plastic potential related to the material properties and the single shear test, the stress strain and the relationship between the stress and the non-coaxial angle are simulated and compared with the experimental results. Based on the principle of energy conversion, the stress-shear expansion equation of sand is derived. According to the rotation characteristics of principal stress axis in the process of single shear test, the relationship between principal strain increment and variation angle during rotation of principal stress axis is calculated by the theory of material characteristic correlation plastic potential. The non-coaxial parameter c is defined by the difference between the rotation angle of principal stress and the rotation angle of corresponding principal strain, and the influence of material parameters on the shear expansion of sand under the rotating condition of principal stress axis is described. Comparing with the shearing equation of material related property theory, this paper analyzes the principal stress rotation angle of loose sand, middle dense sand and dense sand under the condition of single shear test, and the characteristics of non-coaxial parameters and shearing property. The commercial program of PFC is used to analyze the main stress rotation angle, non-coaxial parameter and shearing property of loose sand, middle dense sand and dense sand. The stress-strain relation and shear account relation under single shear test are simulated by discrete element method. The initial loading conditions of discrete elements are determined according to the single shear test conditions. The stress-strain relationships of spherical particles under different confining pressures, different porosity and different particle radius are analyzed, and the force chain distribution is analyzed.
【学位授予单位】：宁夏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU43

【参考文献】