Statistical analysis of stress transmission in wet granular materials

The micromechanics of wet granular materials encompasses complex microstructural and capillary interconnects that can be readily described through a formal derivation of stress transmission in such a 3-phase medium. In the quest for defining an appropriate stress measure, the stress tensor expression that results from homogenization[Duriez et al. J Mech Phys Solids 99 (2017): 495-511] of such a medium provides theoretical insights necessary to extract useful information on the relationship between capillary effects and microforce interactions via several small-scale parameters whose evaluation can be challenging. Using instead a statistical approach where microvariable distributions are described by probability density functions, the current study provides simple estimates of stress components in terms of only a few tractable microvariables such as coordination number and fabric anisotropy. In particular, the latter recognizes details of contacts such as force interactions being either mechanical or capillary, including interactions with and without mechanical contact. The developed expressions are in a good agreement with discrete element method simulation results of the triaxial loading of a wet granular assembly, notably for hydrostatic (mean) pressure. A new set of dimensionless groups is also identified to characterize the significance of mechanical and capillary physics, which facilitates a better understanding of the contribution of dominating elements to stress, while also providing the opportunity to incorporate important capillary effects in micromechanically based constitutive formulations.