Interaction Model for “Shelled Particles” and Small-Strain Modulus of Granular Materials

The elastic modulus of a granular assembly composed of spherical particles in Hertzian contact usually has a scaling law with the mean effective pressure p as $K∼G∼p1/3$⁠. Laboratory test results, however, reveal that the value of the exponent is generally around 1/2 for most sands and gravels, but it is much higher for reclaimed asphalt concrete composed of particles coated by a thin layer of asphalt binder and even approaching unity for aggregates consisting of crushed stone. By assuming that a particle is coated with a thin soft deteriorated layer, an energy-based simple approach is proposed for thin-coating contact problems. Based on the features of the surface layer, the normal contact stiffness between two spheres varies with the contact force following $kn∼Fnm$ and $m∈[1/3, 1]$⁠, with $m=1/3$ for Hertzian contact, $m=1/2$ soft thin-coating contact, $m=2/3$ for incompressible soft thin-coating, and $m=1$ for spheres with rough surfaces. Correspondingly, the elastic modulus of a random granular packing is proportional to $pm$ with $m∈[1/3, 1]$⁠.