基于介观结构的饱和与非饱和多孔介质有效应力

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

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.

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 effective stresses in saturated and unsaturated porous media are defined. The generalized effective stress for saturated porous continua taking into account the volumetric deformation of solid grains due to pore liquid pressure are derived. The Biot coefficient introduced to define the generalized effective 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 effective pressure and effective stress tensors for unsaturated porous media. As the isotropic case of the wet meso-structured Voronoi cell model is considered, the mesohydro-mechanically informed effective 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.