Variability of the stress field on intermediate length scales during the triaxial compression of granular materials

Defining a continuum stress field in a granular medium involves an approximation, as the underlying contact force network between particles is inhomogeneous and random. The continuum approximation introduces some baseline noise or variability in stress, which becomes more significant as the length scale of interest approaches the typical size of the grains. In this study we evaluate how the stress variability resulting from the homogenization of intergranular forces changes as the homogenization scale is increased. This is done by obtaining the probability distribution function of stresses from a large number of repeated discrete element method based simulations of the triaxial compression of granular samples. The numerical experiments share sample dimensions, generation protocols and imposed stresses, but involve randomly generated sets of granular packings made of different numbers of particles. The results from this study are used to propose and develop a consistent general framework to rigorously describe mesoscale stress fields and hence fill the gap between existing micro and macro mechanical approaches. A backbone curve is obtained expressing the change in stress variability as the mesoscale is traversed. The results deduced from the backbone curve are in good agreement with those of independent numerical and physical experiments on granular soils.