Probing Weak Forces in Granular Media through Nonlinear Dynamic Dilatancy: Clapping Contacts and Polarization Anisotropy

Abstract

Rectification (demodulation) of high-frequency shear acoustic bursts is applied to probe the distribution of contact forces in 3D granular media. Symmetry principles allow for rectification of the shear waves only with their conversion into longitudinal mode. The rectification is due to nonlinear dynamic dilatancy, which is found to follow a quadratic or Hertzian power law in the shear wave amplitude. Evidence is given that a significant portion of weak contact forces is localized below 10(-2) of the mean force-a range previously inaccessible by experiment. Strong anisotropy of nonlinearity for shear waves with different polarization is observed.

Sound wave propagation in weakly polydisperse granular materials

“…It has, according to, Ref. [25,16], its signature in the frequency content of the wave, closing contacts can generate high frequency signals, but opening contacts also interfere. In order to study the influence of the clapping contacts on the wave-propagation, in parallel to the polydisperse simulation from Figs.…”

Field observations of seismic velocity changes caused by shaking-induced damage and healing due to mesoscopic nonlinearity

“…This shows that similar to the stress-induced changes also changes induced by transient shaking occur in the medium at those contacts that are responsible for the nonlinear behaviour of the bulk. Considering a single Hertzian contact (Johnson 1985) between two beads which are subjected to a static and dynamic deformation, Tournat et al (2004) showed that the contact nonlinearity increases with decreasing contact strain. This means that the nonlinearity is generated by the weakest contacts of grains or cracks.…”

Reflection of Nonlinear Acoustic Waves from the Mechanically Free Surface of an Unconsolidated Granular Medium

“…In quadratic approximation of nonlinear acoustics the static stress/strain relationships proposed in [41,42] reproduce the nonlinear term in equation (11) and predict also an additional nonlinear term proportional to square of the shear strain, if the shear strain exists simultaneously with longitudinal one. The additional term describes the generation of longitudinal waves due to effect of dilatancy [24,41,42]. The static stress/strain relationship proposed in [41,42] does not reproduce hysteretic quadratic nonlinear term in equation (21), because hysteresis is a dynamic phenomenon.…”

“…Multiple experiments [14][15][16][17][18]24] demonstrate that in unconsolidated granular media the velocity of both longitudinal and shear acoustic waves is the power function of pressure (of normal stress) and, consequently, in accordance with equation (3), of depth coordinate theory [39,40] predicts α=1/6 both for longitudinal and shear acoustic waves [32,18]. The experimental observations of higher powers up to α=1/4 (both for longitudinal and shear waves) could be theoretically attributed to different factors [33,34,18], such as increasing with pressure number of contacts between a bead and its neighbors, i.e.…”

“…The observations in granular medium of higher harmonics generation [21] (including processes accompanied by acoustic wave mode conversion [22]), of acoustic wave packet demodulation [23][24][25], of subharmonics excitation [26], and of modulation transfer [27] have been reported. Nonlinear acoustic methods have been applied for the first time for characterization of the intergrain force statistical distribution [24] which is a fundamental property of granular materials.…”