Plastic compaction of cemented granular materials

We analytically relate hydrostatic stress to strain in a random dense pack of identical spheres cemented at their contacts. The spheres are elastic and the cement is perfectly plastic. This solution for the sphere pack is based on a solution for the normal interaction of two cemented spheres. Initially, the two spheres touch each other at a point. We show that, as loading increases and cement becomes plastic, a finite (Hertzian) direct-contact area between the spheres necessarily has to develop and progress. The stress-strain behavior of the pack depends on the cement's yield limit and on the amount of cement. At the same hydrostatic stress, the deformation of the cemented aggregate is smaller than that of the uncemented one. This difference becomes large as the yield limit increases. We calculate the bulk modulus of an aggregate from the stress-strain curve. In the plasticity domain, the bulk modulus of the cemented aggregate is smaller than that of the uncemented one. The difference between the two may easily reach 50%. Of course, as the cement's yield limit decreases, the aggregate's stress-strain curve and the bulk modulus approach those of the uncemented sphere pack. This theoretical conclusion is qualitatively supported by experiments on epoxy-cemented glass beads. The maximum contact stress in the cemented aggregate may be less than a half of that in the uncemented one. This result explains an experiment where an uncemented glass bead sample failed at a hydrostatic stress of 50 MPa, whereas an epoxy-cemented sample stayed intact.