Uniaxial deformation of a random packing of particles

Summary Mechanical behavior of dense packing spheres with small irregularities is investigated in this paper. A generalization of the hertzian contact model for surfaces of the form x ^k yields a normal contact force F _n , which is proportional to ζ^{1+1/ k} , with the normal displacement ζ. For oblique forces, the frictional force can be calculated, 10]. Different load cases are explained in detail. It is shown that the stress-strain curve during initial loading of the packing is identical with the force-displacement relation at the contact point, using an appropriate constant. The results for uniaxial loading, unloading and reloading are illustrated. As experimentally observed, the axial pressure in unloading is smaller than during loading, while the lateral pressure increases. The stress-strain relation is compared with well-known empirical relations of rock and soil mechanics, and the wave velocity for spherical irregularities agrees with earlier geomechanical theories for random packing of smooth spheres. Received 19 July 1998; accepted for publication 19 October 1998