Inter-granular friction and the mechanical and acoustical properties of granular media

The macroscopic mechanical and acoustical properties of a dense granular medium are dependent upon the form of the inter-granular contact. Our particular interest here is that of frictional contact. We take as our mathematical model a random packing of like elastic spheres, sufficiently densely packed, and our aim is the theoretical calculation of the effective elastic moduli of the medium and the speeds of propagation of elastic waves through the medium. To avoid separation a confining force is imposed. This gives rise to an initial equilibrium state, with finite contact areas between initially touching grains. The elastic moduli and the acoustical properties are determined by considering a further deformation and will be dependent on this initial state. Standard averaging techniques may be used once the behaviour at a single contact is known and this will be strongly dependent on whether inter-granular slip has taken place or not.