Elastic moduli of cemented sphere packs

We present a method for estimating the effective elastic moduli of a dense random pack of identical elastic spheres with elastic binder (cement). The cement concentration in the pore space varies from a few percent (where it fills the space at grain contacts) to 100%. To construct the solution we st art at a small cement concentration value where the effective moduli of the pack are given by the contact cement theory (CCT). The next, and most impo rtant, step is to obtain the (unknown a priori) elastic moduli at 100% ceme nt concentration. To do so, we: (1) treat the starting cemented pack, that is a three-phase system of grains, cement, and voids, as an elastically equ ivalent two-phase system of voids in a homogeneous matrix; (2) apply an eff ective medium theory (EMT) to find the elastic moduli of this matrix; and ( 3) calculate the effective moduli of this matrix with the voids filled with cement. We treat these moduli as the desired moduli of the pack with 100% cement concentration. We interpolate between this point and the initial (sm all cement concentration) point by using the EMT to populate the no-void el astic body with voids. Using CCT as the initial construction point gives us control over the microstructure of the composite which proves to be crucia l in this modeling. The results predict the compressional elastic modulus ( that is the product of density and compressional-wave velocity squared) fro m wave-propagation experiments on epoxy-cemented glass beads, ice-cemented Ottawa sand, and in-situ acoustic data in natural sands cemented by gas hyd rate within experimental accuracy. (C) 1999 Elsevier Science Ltd. All right s reserved.