Scaling of the electrical conductivity of granular media

We derive the scaling properties of the dependence of the macroscopic electrical conductivity of granular media (e.g., sands) with a surface mechanism of electrical conduction on the grain size, when the medium is subjected to a given mechanical stress. In order to eliminate the influence of the inter-grain junction capacity, the direct electrical current is considered. We determine the applicability restrictions on the theory which disregards the ultimate crushing compression strength, adhesion, and the effect of charge carrier tunneling at grain junctions beyond the contact surface area. Solutions for several regular packings of grains are obtained as well.