Transition from high-porosity to filled particulates: Effective medium modeling

We give a method for calculating the elastic constants of a close random pack of identical elastic spherical particles where the pore space is completely filled with elastic cement (for example, a glass bead pack filled with epoxy). The solution partly answers a general and as yet unresolved effective medium problem of contacting elastic inclusions embedded in an elastic matrix. The method is a combination of our theory of contact cementation (appropriate only for high-porosity particulates where small amounts of elastic cement are present at the grain contacts) with the self-consistent effective medium model. The case of a medium-to-small porosity aggregate where large portions of the pore space are filled with cement is addressed as well. In other words, we show how to make a transition from high-porosity cemented to completely filled granular materials. The theoretical results are confirmed by experiments.