A tensorial description of stresses in triphasic granular materials with interfaces

International audienceThe description of stress transmission in an unsaturated granular material in the low water saturation range (pendular regime) is studied within the micromechan-ics of a three-phase medium. Considering an REV (Representative Element Volume) comprised of solid grains and isolated inviscid water menisci whose statistical distributions are known, micro-and macro-relationships can be derived using a volume-averaging of stress for each one of the phases in a manner analogous to the derivation of Love-Weber equation defining stress in a dry granular medium. The main difference with respect to previous works in the literature lies in the homogenization technique whereby singular surfaces such as an air-water interface exhibiting surface tension are treated as an additional phase for which a so-called membrane stress is defined. Well-known contractile skin effects and the anisotropy of capillary stresses in unsaturated soils can be formally identified in the proposed tensorial expression that encompasses the statistics of not only grain contact normals, but also that of menisci spatial orientations and their surfaces, including water saturation. Solid grains are considered strictly incompressible with water being also an incompressible and inviscid liquid. An effective stress tensor that controls the strength of unsaturated granular media is hence proposed and verified based on discrete element modelling (DEM) numerical simulations of triaxial compression and simple shear tests on pendular-state granular soils at different confining pressures and matric suctions. The non-sphericity of the so-called capillary stress is also numerically demonstrated