非均匀颗粒材料的特征长度与相关力学行为的多尺度研究

This research project focuses on the effects of heterogeneity of granular materials such as the natural gravel and artificial rockfill materials, on its deformation and failure at different scales. On microscopic level, Discrete Element Method will be used to investigate systematically the effects of particle size distribution (PSD) and local void distribution on deformation patterns, the existence and size of representative volume element (RVE) of different macro phyical properties. The objective of microscopic numerical investigation is to establish the link between PSD, local void distribution and the intrinsic length such as thickness of shear band, size of RVE, of granular materials. In addition, other important issues, such as the dilatancy and vortex structure in shear band related to non-uniform deformations phenomena for granular materials, will be addressed. In the macroscopic framework, gradient enhanced cosserat model which can reflect the micromechanically heterogeneous characters and size effects, and the corresponding numerical scheme based on finite element method (FEM) will be developed. The link between the characteristic length, size of RVE of proposed model and PSD, local void distribution of granular materials will be addressed from theoretical approach. Based on the aforementioned microscopic and macroscopic study work. Two-scale (micro-macro) model based on discrete particle model and the gradient enhanced cosserat model and DEM-FEM two-scale numerical solution will be developed. The results of the proposed project will provide a guide to choice the size of RVE in two-scale simulation, and improve the understanding on size effects of granular materials.

针对天然砂砾料及人工堆石料等非均匀颗粒材料，系统研究非均匀性对其不同尺度上变形模式与破坏等力学行为的影响。细观上基于离散颗粒模型调查颗粒级配、孔隙分布等对颗粒材料的变形模式、弹性模量及剪切强度的表征元存在性与尺寸的影响，建立剪切带宽度、表征元尺寸等特征长度与平均颗粒直径、颗粒级配及孔隙分布非均匀性之间的联系。宏观上应用均匀化方法发展包含颗粒级配及孔隙分布信息的梯度增强Cosserat连续体模型及有限元数值方案。建立模型中特征长度、表征元尺寸与平均颗粒直径、非均匀度等量的联系，并数值调查特征长度对强度与变形模式的影响。在上述基础上发展基于离散颗粒模型-梯度增强Cosserat连续体模型的两尺度模型及离散元-有限元两尺度数值求解系统。研究结果一方面对颗粒材料多尺度模拟时表征元尺寸的选择提供依据，一方面可加深对尺寸效应机理的认识，为堆石料缩尺条件下实验结果分析和应用提供借鉴。

以天然砂砾料及人工堆石料等非均质颗粒材料为背景，开展了非均质颗粒材料的变形模式及破坏行为的宏细观数值研究。其主要研究内容和成果可归结为三个方面：（1）基于离散颗粒模型考虑几何分布的非均性，以六方排列集合为参照定义了颗粒的径向和环向非均匀度，分析了非均匀度与应变分布、局部化模式的关联，并给出了非均匀度与首次屈服应力的关系；调查了非均质夹杂对残余位移场漩涡结构的影响，表明漩涡结构与非均匀应变场及非均值性密切相关；调查了缺陷/夹杂对剪切带的形成和发展的影响；调查了中主应力对颗粒材料破碎行为的影响，表明真三轴试验中,试样偏应力比峰值均随中主应力参数b值增大而减小。由于破碎随b值增加而明显增大,试样剪胀性随b值增大而逐渐减弱等。（2）基于颗粒材料Cosserat连续体探讨了有限元模拟时特征长度，单元尺寸及结构尺寸的关系，分析调查了非共轴性对剪切带形成及偶应力分布的影响。发展了一个基于细观力学的颗粒材料的微形态连续体模型，该模型考虑了细观变形的非均匀特性，给出了宏观量的细观表达。（3）两尺度模拟方面基于细观热力学途径，发展了一个考虑颗粒材料非均质特征的梯度模型，其宏-细观变量通过一个非仿射方案建立联系，数值算例表明了考虑滚动时高阶项对应变局部化的影响更为显著；建立了一个宏观Cosserat连续体-细观离散单元的两尺度框架，调查了表征元的存在性、尺寸以及颗粒粒径对表征元尺寸的影响。此外针对非均质材料的动力问题和多场耦合问题发展了多尺度有限元方案。本项目共培养了4名硕士研究生和5名博士生，项目的研究结果可促进对非均质颗粒材料相关力学行为的理解和认识，为解决岩土等领域的诸如尺寸效应等工程应用问题积累一定的基础。