A micromechanical μUNSAT effective stress expression for stress-strain behaviour of wet granular materials

The definition of an effective stress variable for idealized triphasic granular media as the contact stress arising from interparticle forces is examined through discrete element modelling computations in concert with appropriately derived analytical stress expressions based on homogenization. The latter take a more practical importance, in that they also circumvent the need for direct measurements of interparticle contact forces. Considering dry or pendular-regime conditions for slightly polydisperse dense and loose packings, the contact stress-strain behaviours in dry or wet conditions are compared along a variety of loading paths, depending on the level of plastic dissipation involved. The contact stress indeed emerges as an effective stress variable with a remarkable stress-strain character along contractant loading paths and for dense solid packings where the behaviour is close to be non-dissipative. Along more dilatant loading paths or for looser packings, plastic dissipation increases and the coincidence of the constitutive behaviour in both dry and triphasic conditions is restricted to the initial stages of the loading paths, limiting the applicability of the contact stress to the estimation of initial stiffnesses. The stark constitutive differences between the proposed effective stress and Bishop's stress are also highlighted.