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

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.