基于介观结构的饱和与非饱和多孔介质有效应力

李锡夔; 杜友耀; 段庆林

doi:10.6052/0459-1879-15-289

基于介观结构的饱和与非饱和多孔介质有效应力

doi: 10.6052/0459-1879-15-289

大连理工大学工业装备结构分析国家重点实验室, 大连 116024

基金项目: 国家自然科学基金(11372066),国家重点基础研究发展计划(2010CB731502)资助项目.

详细信息

通讯作者:
李锡夔,教授,主要研究方向:计算力学,颗粒材料力学,多孔介质力学.E-mail:xikuili@dlut.edu.cn

中图分类号: O354.4
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出版历程
- 收稿日期: 2015-07-30
- 修回日期: 2015-12-03
- 刊出日期: 2016-01-18

MESO-STRUCTURE INFORMED EFFECTIVE STRESSES IN SATURATED AND UNSATURATED POROUS MEDIA

The State key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116024, China

摘要

摘要: 基于描述含液颗粒材料介观结构的Voronoi 胞元模型和离散颗粒集合体与多孔连续体间的介-宏观均匀化过程, 定义饱和与非饱和多孔介质有效应力. 导出了计及孔隙液压引起之颗粒体积变形的饱和多孔介质广义有效应力. 用以定义广义有效应力的Biot 系数不仅依赖于颗粒材料的多孔连续体固体骨架及单个固体颗粒的体积模量(材料参数),同时与固体骨架当前平均广义有效应力及单个固体颗粒的体积应变(状态量) 有关. 提出了描述非饱和多孔介质中非混和固体颗粒、孔隙液体和气体等三相相互作用的具介观结构的Voronoi 胞元模型.具体考虑在低饱和度下双联(binary bond) 模式的摆动(pendular) 液桥系统介观结构. 导出了基于介观水力-力学模型的非饱和多孔介质的各向异性有效应力张量与有效压力张量. 考虑非饱和多孔介质Voronoi 胞元模型介观结构的各向同性情况,得到了与非饱和多孔连续体理论中唯象地假定的标量有效压力相同的有效压力形式.但本文定义的与确定非饱和多孔介质有效应力和有效压力相关联的Bishop 参数由基于三相介观水力-力学模型, 作为饱和度、孔隙度和介观结构参数的函数导出,而非唯象假定.
- 饱和与非饱和多孔连续体 /
- 含液离散颗粒集合体 /
- 介观结构的Voronoi 胞元模型 /
- 有效应力 /
- Biot 系数 /
- Bishop 参数
Abstract: Based on the meso-strucrured Voronoi cell model and the meso-macro homogenization procedure between the discrete particle assembly and the porous continuum for wet granular materials, the e ective stresses in saturated and unsaturated porous media are defined. The generalized e ective stress for saturated porous continua taking into account the volumetric deformation of solid grains due to pore liquid pressure are derived. The Biot coe cient introduced to define the generalized e ective stress depends on not only the bulk moduli of both the porous media and the solid grains (material parameters), but also the current mean stress of solid skeleton of porous media and the current volumetric strains of the individual grain due to the hydrostatic pressure (state variables). The wet meso-structured Voronoi cell model, consisting of three immiscible and interrelated (i.e., solid grains, interstitial liquid and gas) phases, is proposed. The meso-structural pattern with the binary bond mode of pendular liquid bridges valid at low bulk saturation is particularly assumed to derive the meso-hydro-mechanically informed anisotropic e ective pressure and e ective stress tensors for unsaturated porous media. As the isotropic case of the wet meso-structured Voronoi cell model is considered, the meso- hydro-mechanically informed e ective pressure tensor degrades to the scalar variable in the form as same as that given in the theory of unsaturated porous continua. The proposed meso-hydro-mechanically informed Bishop's parameter is derived and obtained as a function of the saturation, the porosity, meso-structural parameters, while without the need to introduce any phenomenological assumptions.
- saturated and partially saturated porous continua /
- wet discrete particle assembly /
- meso-structured Voronoi cell model /
- e ective stress /
- Biot coe cient /
- Bishop parameter

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参考文献(33)

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