  We study the effect of polydispersity on the macroscopic physical properties
of granular packings in two and three dimensions. A mean-field approach is
developed to approximate the macroscale quantities as functions of the
microscopic ones. We show that the trace of the fabric and stress tensors are
proportional to the mean packing properties (e.g. packing fraction, average
coordination number, and average normal force) and dimensionless correction
factors, which depend only on the moments of the particle-size distribution.
Similar results are obtained for the elements of the stiffness tensor of
isotropic packings in the linear affine response regime. Our theoretical
predictions are in good agreement with the simulation results.
