Meso-hydro-mechanically informed effective stresses and effective pressures for saturated and unsaturated porous media

• A meso-structural Voronoi cell model for wet granular materials is proposed.
• The generalized effective stress for saturated porous media is re-defined.
• Tensorial and scalar Biot coefficients for saturated porous media are formulated.
• Effective stress and effective pressure for unsaturated porous media are redefined.
• The Bishop parameter for unsaturated porous media is formulated.

Based on the meso-structured Voronoi cell model and the meso-macro homogenization procedure between the discrete particle assembly and the porous continuum for wet granular materials, meso-hydro-mechanically informed effective pressure and effective stress measures for saturated and unsaturated porous media are defined.The meso-hydro-mechanically informed generalized effective stress for saturated porous continua taking into account the volumetric deformation of solid grains due to pore liquid pressure is derived. The Biot coefficient associated to the meso-hydro- mechanically informed generalized effective stress for saturated porous media is formulated. The differences of the definitions for proposed generalized effective stress and Biot coefficient compared with those defined in the generalized Biot theory of saturated porous continua and in averaging theories are discussed. The wet meso-structured Voronoi cell model, consisting of three immiscible and interrelated (i.e. solid grains, interstitial liquid and gas) phases, at low bulk saturation (below about 30%) is proposed. A meso-structural pattern with the binary bond mode of pendular liquid bridges is assumed in particular to derive the meso-hydro- mechanically informed macroscopic 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 meso-hydro-mechanically informed effective pressure tensor degrades to the scalar variable in the same form as in the theory of macroscopic unsaturated porous continua. The proposed meso-hydro-mechanically informed Bishop's parameter is derived and obtained as a function of saturation, porosity, and meso-structural parameters, without need to introduce any macroscopic phenomenological assumptions for the description of hydro-mechanical constitutive behavior.