The total stress tensor as the average stress within a triphasic granular medium is formally derived from micromechanics where internal forces associated with the solid phase, the two immiscible fluid phases and the associated three interfaces are explicitly accounted for. It is demonstrated that for rigid solid particles, the contributions of all local solid-fluid surface tensions to the total stress are eventually zero. The present work gives the total stress expression as a function of a solid-phase specific stress tensor and a fluid mixture stress contribution that is related to the material's microstructure. A generally non-spherical fluid mixture stress is obtained in contrast to an averaged hydrostatic fluid pressure usually associated with standard thermodynamics. The tensorial nature of this fluid mixture stress contribution is highlighted through numerical experiments pertaining to an idealized granular material in the pendular regime at low wetting saturations. Numerical simulations providing full access to microstructural information are conducted using the Discrete Element Method (DEM), which describes internal forces using resultant forces that clearly deviate from the distributed nature of internal forces in triphasic granular media, e.g., fluid pressures. Nevertheless, this micro-scale representation is demonstrated to be indeed valid for macro-scale stress description in the pendular regime.

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Summary A detailed multiscale analysis is presented of the swelling phenomenon in unsaturated clay‐rich materials in the linear regime through homogenization. Herein, the structural complexity of the material is formulated as a three‐scale, triple porosity medium within which microstructural information is transmitted across the various scales, leading ultimately to an enriched stress‐deformation relation at the macroscopic scale. As a side note, such derived relationship leads to a tensorial stress partitioning that is reminiscent of a Terzaghi‐like effective stress measure. Otherwise, a major result that stands out from previous works is the explicit expression of swelling stress and capillary stress in terms of micromechanical interactions at the very fine scale down to the clay platelet level, along with capillary stress emerging due to interactions between fluid phases at the different scales, including surface tension, pore size, and morphology. More importantly, the swelling stress is correlated with the disjoining forces due to electrochemical effects of charged ions on clay minerals and van der Waals forces at the nanoscale. The resulting analytical expressions also elucidate the role of the various physics in the deformational behavior of clayey material. Finally, the capability of the proposed formulation in capturing salient behaviors of unsaturated expansive clays is illustrated through some numerical examples.