Discrete Element Modeling of Acoustic Wave Propagation in Granular Media: Nonlinearity and Material Softening

Granular media is one of the most common form of material which exists in many geophysical phenomena such as landslides and earthquakes. It is also present in the industry for transport, storage, and for mixing processes. Constitutive equations are essential to predict and control granular media behavior, but they are not fully developed yet. In particular, the history of a granular packing has a determinant influence on the arrangement of its particles and the organization and nature of inter-particle contacts. The arrangement of particles and contacts in turn affects the material response to external perturbations such as compression, shear and wave propagation. This thesis studies the propagation of acoustic waves through the contact network. The Effective Medium Theory and continuum descriptions partially solve the constitutive equations of dense packings of granular media but cannot fully describe the phenomenon as the Effective Medium Theory models ensembles and continuum descriptions neglect particle rearrangements. Dynamic testing has shown a dependency of resonance frequency on strain at low strains in confined granular packings (Johnson and Jia 2005; Inserra et al. 2008) but this study has not been extended to high strains. We present a detailed study of dynamic testing in confined random packings of weakly polydisperse glass beads using the Discrete Element Method to measure the resonance frequency over a range of strains. We find a decrease in resonance frequency at high strain, called softening, that only depends on the normal component of the contact force, the coordination number and the average inter-particle overlap. The mean-field assumption of the Effective Medium Theory successfully predicts the dependency of softening on confining stress. The Effective Contact Theory is a model developed in this thesis to relate the breaking of contacts and decrease in coordination number to softening by defining a granular temperature based on kinetic energy. For the first time, granular temperature is used to model contact evolution rather than particle motion. The Effective Contact Theory successfully relate the probability of a contact breaking to softening in granular media. Simulations of wave propagation in static packings show an excellent agreement between wave velocity measured from direct wave propagation, dynamic testing and bulk and shear compression tests. Wave damping and distortion increases with amplitude and frequency and, at high frequency, waves are propagated through scattering and rapidly damped