Effective properties of cemented granular materials

An analytical model is developed to describe the effective elastic properties of a cemented granular material that is modeled as a random packing of identical spheres. The elastic moduli of grains may differ from those of cement. The effective bulk and shear moduli of the packing are calculated from geometrical parameters (the average number of contacts per sphere and porosity), and from the normal and tangential stiffnesses of a two-grain combination. The latter are found by solving the problems of normal and tangential deformation of two elastic spherical grains cemented at their contact. A thin cement layer is approximated by an elastic foundation, and the grain-cement interaction problems are reduced to linear integral equations. The solution reveals a peculiar distribution pattern of normal and shear stresses at the cemented grain contacts: the stresses are maximum at the center of the contact region when the cement is soft relative to the grain, and are maximum at the periphery of the contact region when the cement is stiff. Stress distribution shape gradually varies between these two extremes as the cement's stiffness increases. The solution shows that it is mainly the amount of cement that influences the effective elastic properties of cemented granular materials. The radius of the cement layer affects the stiffness of a granular assembly much more strongly than the stiffness of the cement does. This theoretical model is supported by experimental results.