非饱和颗粒材料水力-力学耦合过程两尺度分析的二阶计算均匀化方法

A second-order computational homogenization method of granular materials with unsaturated discrete particle assembly - porous gradient Cosserat continuum modeling for the two scale analysis of coupled hydro-mechanical process is presented. The mathematical model and corresponding numerical method GCFD to determine the flow fields of pore fluids and the fluid drags on particles are developed with consideration of the liquid bridge effect and different flow modes depending on the saturation degree distribution within the representative volume element (RVE) of discrete particle assembly. In combination with the discrete element method (DEM) applied to the RVE taking into account the effect of liquid bridges and flowing pore fluids, the numerical method DEM-GCFD for coupled hydro-mechanical process is constructed.The Voronoi cell model is developed in the meso-scale to define locally averaged hydro-mechanical measures in unsaturated porous Cosserat continuum in terms of the microscopically based information. The generalized Hill's lemma for coupled hydro-mechanical process is presented. The microscopically informed macroscopic hydro-mechanical constitutive relations for unsaturated porous gradient Cosserat continuum are formulated. The global-local FEM-(DEM-GCFD) nested algorithm is developed and implemented. That is the finite element method for unsaturated porous gradient Cosserat continuum model with the nested DEM-GCFD for unsaturated RVE of discrete particle assembly model. The performance of the proposed second-order computational homogenization method along with the developed algorithm and its capability in detecting the microscopic mechanisms of macroscopic response are demonstrated.

提出基于非饱和离散颗粒集合体-多孔梯度Cosserat连续体模型的颗粒材料水力-力学耦合过程两尺度分析二阶计算均匀化方法。对非饱和离散颗粒集合体表征元发展依赖于饱和度、计及颗粒间液桥效应和不同孔隙水流动模式的确定孔隙流场及其作用于颗粒拖曳力的计算模型和数值方法。与计及液桥与流动孔隙流体作用的颗粒离散元法相结合，构造水力-力学耦合数值方法DEM-GCFD。发展介观尺度Voronoi cell模型，定义基于细观信息的非饱和多孔Cosserat连续体的局部平均水力-力学量。提出水力-力学耦合过程的广义Hill定理。导出基于细观信息的非饱和梯度多孔Cosserat连续体水力-力学本构关系。发展和实现全局-局部嵌套算法：非饱和多孔梯度Cosserat连续体模型的有限元法和与之嵌套的非饱和离散颗粒集合体表征元模型的DEM-GCFD。验证所提出二阶均匀化方法及其算法的有效性和揭示宏观响应细观机理的能力。

颗粒材料结构中由干化到湿化的发展过程是导致地质灾害和重大基础工程破坏的关键环境荷载和诱发因素。需要研究与此过程相关联的水力-力学耦合作用及介观机理。考虑到颗粒材料的非均质性、各向异性、间断性及水力-力学耦合行为的非线性与复杂性，需要求助于计算多尺度方法。颗粒材料在宏观和介观尺度分别模型化为非饱和多孔连续体和含液离散颗粒集合体。.本项目致力于发展模拟湿颗粒材料水力-力学耦合过程的协同计算多尺度方法。建立描述过程的介观模型；基于湿离散颗粒表征元中材料和响应信息，建立饱和/非饱和多孔梯度Cosserat连续体的本构关系；发展湿离散颗粒集合体-多孔多相Cosserat连续体的协同计算多尺度方法。.基于描述含液颗粒材料介观结构的Voronoi胞元模型和平均场理论,定义了基于颗粒材料介观结构的饱和与非饱和多孔连续体有效应力。表征了依赖于离散颗粒介观信息的用以定义饱和多孔介质广义有效应力的Biot系数合用以定义非饱和多孔介质有效应力与有效压力的Bishop参数张量。提出了依赖液桥介观结构的双联模式液桥失效临界距离公式与液桥力计算方法。发展了计及颗粒破碎的可破碎离散元模型。建立了计及液桥效应的湿颗粒离散元模型。.提出了非饱和颗粒材料水力-力学耦合问题协同多尺度模拟的连接尺度方法与二阶计算均匀化方法。导出了饱和-非饱和多孔介质二阶计算均匀化方法的Hill定理以制定下传规则和定义表征元的边值问题。建立了基于介观信息的达西定律及定义渗透系数和其它相关参数。在二阶计算均匀化方法框架内发展了饱和与非饱和多孔梯度Cosserat连续体的混合有限元过程。提出了基于Hu-Washizu三变量变分原理的高效高精度的一致性无网格法。在热动力学框架内，提出了基于二阶计算均匀化模拟的颗粒材料塑性、损伤-愈合的宏观表征方法。应变软化与局部化问题的多尺度模拟与表征结果表明了所提出表征方法的可应用性。