The Pressure Dependence of Elastic Stiffness of Granular Materials: A Binary Model in Effective Medium Theory

Granular media have many interesting and unusual properties, different from those of either solids or liquids. The study of sound propagation and nonlinear elasticity in unconsolidated granular matter is an interest topic. In the simplest experiments, a packing of spherical glass beads is confined under hydrostatic conditions and the compression and shear sound speeds p V and s V are measured as functions of static confining pressure P. Experimentally it is exhibit that the bulk modulus K and shear modulusG of a granular assembly of elastic spheres increase with pressure p faster than the p1 3 . This result is law predicted by effective medium theory (EMT) based on Hertz-Mindlin contact forces. To understand the origin of these discrepancies, we treating contact stiffness as a variable, extend the effective medium approximation used to obtain elastic stiffness of a random pack of spherical grains. More specifically, we show that EMT can describe the moduli pressure dependence if introducing a binary model for grain contacts and a parameter t f , which represents the amount of non-slipping contacts in the mixture. The simple extension of the theory provides a better fit for many laboratory test result.