Modeling of granular material's packing: Equivalence between vibrated solicitations and consolidation

Abstract

A granular material submitted to regular vertical vibrations such as those applied by a “tap-tap”, undergoes a progressive densification whose kinetic can be modelled by several empirical or heuristic models. These models, which correlate the experimental data of densification, use fitting parameters which are not related with a “local physics”. One of these famous models is the three parameters model of the James Frank Institute of Chicago [Knight et al., Phys. Rev. E 51, 3957 (1995)]. This relation makes it possible to highlight two stages: a short first stage during which the relaxation occurs quickly and a second stage during which the steady state is reached asymptotically for very long times. Boutreux and de Gennes [Boutreux and De Gennes, Physica 244, 59 (1997)] gave a theoretical justification of this equation by using an approach based on arguments of free volume and geometrical exclusion at the grain scale. On the other hand, on the basis of the works of Chicago's team, Lesaffre et al. [Lesaffre et al., C. R. Acad. Sci. Paris Série IV, 647 (2000)] developed a more general model that enables to describe the kinetics of relaxation of granular materials saturated with fluids of very different viscosities. This last work opens the field of saturated materials like soils. Nevertheless, these models require fitting parameters which are very dependent on the taps intensity and on the initial density. It has also been shown that these models did not succeed in describing with a good accuracy the final relaxation towards the steady state. The aim of this work is to develop a model describing the relaxation kinetic of a granular medium subjected to vertical vibrations. By using an approach of granular physics on one hand, and of soil mechanic on the other hand, the proposed model can be applied both to dry, saturated and unsaturated granular materials. The ability of this new model to describe the relaxation under taps for different granular materials and several water contents was successfully tested. A comparative study between this equation and other models of the literature makes it possible to compare the quality of the fitting with the experimental data.