Intergranular squirt flow in sand: grains with viscous cement

Abstract

We offer an exact solution to the problem of deformation of two elastic spherical particles with viscous cement at their contact. This model is intended to mimic a granular geomaterial whose grains are covered with viscous fluid of geologic or biogenic nature (e.g., marine sediment, heavy-oil sand, asphalt concrete). The solution for the normal stiffness of a two-grain combination is reduced to an ordinary integro-differential equation that has to be solved numerically. We find two approximations for the rigorous numerical solution. The simplest one, based on the Maxwell viscoelastic model, cannot accurately reproduce the relaxational behavior of the system. The second one is based on the Cole–Cole model that allows one to introduce a spectrum of relaxation times. This expression is very accurate and can be used instead of the numerical solution. The complex effective elastic moduli of the aggregate are calculated from statistical averaging for a dense random pack of identical spheres. The theoretical results match well experimental data obtained on a glass bead pack with viscous epoxy cement.