On the mechanics of meso-scale structures in two-dimensional granular materials

Macroscopic behaviours of granular materials derive from the fabric distribution and evolution. Two kinds of fabric in the meso-scale can be distinguished: column-like clusters, called force-chains, which carry a majority of the external loading; and the loop-like clusters, called meso-loops, cells enclosed inside by contact branches. Some significant features in themeso-scale and how they influence themacroscopic behaviour of granular materials are investigated under the drained biaxial loading path. Results show that: (1) the macroscopic mechanical performance of the granular material can be associated to the evolution of the proportions of L3 (meso-loops with 3 sides) and L6+ (meso-loops of number of side no less than 6); (2) there exists a single mesoscopic topology as the signature of the critical state of granular materials; (3) the force-chains adjacent area is the main source and contributor of the global dilatancy of the granular material.Moreover, the instability of the idealised hexagonal loop, as the representation of L6+, is analysed. It is shown that under a loading path with a constant confinement, it is possible to proceed an elastic buckling, if there is a sufficient high confining stress or a sufficient low α0 (the initial opening angle of the hexagon, initially controlling the elongation of it along the axial direction). α0 and the stiffness ratio kt /kn (the tangential stiffness over the normal stiffness) are found to be greatly influential to the instability of the hexagon, through influencing the Mohr–Coulomb line of the hexagon.