Elastic wave propagation in dry granular media: Effects of probing characteristics and stress history

Elastic wave propagation provides a noninvasive way to examine polydisperse, frictional granular materials. The discrete element method (DEM) allows for a micromechanical interpretation of the acoustic response. Using experimentally measured granular microstructures as input, after straining them to various cyclic, oedometric compression states, we numerically perform both static and dynamic probing to deduce elastic moduli/wave velocities from small-strain modulus degradation and time/frequency-domain signals. Static probing allows to understand the path dependency of the elastic moduli, i.e., the stress response to small strain increments, as well as their degradation behavior, for medium-to-large probing strains. Complementarily, dynamic probing provides insights into the acoustic properties (dispersion relations) at different wavelengths, for various probing characteristics. The wave velocities extracted from the space-time evolution of particle motion are sensitive to travel distance and input waveform, but converge to the same long-wavelength velocities far away from the source, where short wavelengths are dispersed and attenuated. Analyzing the same space-time data in the frequency domain leads to the same results, much less dependent on the probing characteristics than in the time domain, and much faster than static probing. Concerning the dependence on the stress history, as expected, the moduli (and wave velocities) increase under initial oedometric compression. First unloading reveals a significant plastic, irreversible decrease of the moduli, whereas reloading along the oedometric path leads to a reduced degradation. The elastic regime, i.e., the probing strain at which the moduli begin to degrade, gradually decays, as the change of the deviatoric to mean stress ratio increases towards its maximum where plasticity/irreversibility is strongest. Interestingly, the moduli from static probing show that the degradation curves immediately before and after a load reversal are almost identical, suggesting that the elastoplastic behavior is symmetric around the turning point for tiny strains, as also confirmed by identical vibrational densities of states at reversal. Remarkably, the moduli, their degradation behavior and the shapes of the dispersion relations (normalized by their large wavelength limits), are all very similar during unloading and reloading, whereas they reflect a strongly different material behavior under initial loading.