Sound scattering in dense granular media

Goddard rattler-jamming mechanism for quantifying pressure dependence of elastic moduli of grain packs

“…Zimmer et al [17] measure an even steeper pressure dependence of roughly P 0.8 on their glass-bead samples at pressures from 0.1 to 0.4 MPa before the data trend off to the Hertzian dependence when P > 1 MPa. However, Jia and Mills [16] measure a pressure dependence for their glass-bead packs that is very close to the Hertzian prediction over the pressure range from 0.07 to 0.8 MPa.…”

“…For close packs, one has n 0 /n ∞ → 1 and a classic Hertzian dependence K ∝ 1/2 emerges at low strain, which corresponds to a pressure dependence of K ∝ P 1/3 . This dependence was observed in the low-strain experiments of Jia and Mills [16], who carefully compacted their random bead packs so that n 0 /n ∞ → 1 prior to their measurement of wave speeds. For random loose packs (or random very loose packs), we have n 0 /n ∞ → 0 at zero stress, which results in the non-Hertzian strain dependence K ∝ (1+2m/χ )/2 , corresponding to a pressure dependence of K ∝ P (1+2m/χ )/(3+2m/χ ) .…”

“…Similarly, the upper limit corresponds to grains so rough that no slip occurs, resulting in the maximum transmitted shear at a contact. Acoustic data collected on unconsolidated sand and glass bead packs as presented in numerous investigations [1,2,[13][14][15][16][17] demonstrate that over the approximate stress range of 10 −3 to 10 MPa (corresponding to sediment overburden depths ranging from 10 −1 to 10 3 m), elastic moduli of the dry frame vary more rapidly than the Hertzian prediction of P 1/3 . At lower levels of applied pressure (<10 MPa), power-law pressuredependence is generally observed to have an exponent larger than the Hertzian 1/3.…”

Multiple Scattering of Elastic Waves in Granular Media: Theory and Experiments

“…New tools such as pulsed ultrasound propagation through granular beds under stress have been recently developed to probe the elastic response of three-dimensional granular packings (Brunet et al (2008a;; Jia et al (1999); Jia (2004); Jia et al (2009) ;Johnson & Jia (2005); Khidas & Jia (2010)). In particular, by studying the 5 www.intechopen.com low-amplitude coherent wave propagation and multiple ultrasound scattering, it is possible to infer many fundamental properties of granular materials such as elastic constants and dissipation mechanisms (Brunet et al (2008a;; Jia et al (1999); Jia (2004) ;Jia et al (2009)). In soil mechanics and geophysics, the effective medium approach (a continuum mechanics, long wavelength description) has been commonly used to describe sound propagation in granular media (Duffy & Mindlin (1957); Goddard (1990)).…”

“…The authors interpreted this as being due to sound propagating within the granular medium predominantly along strong force chains. In recent years, our understanding of wave propagation in granular materials has advanced both experimentally and theoretically, covering topics such as surface elastic waves, booming avalanches (Bonneau et al (2007;2008)), earthquake triggering (Johnson & Jia (2005)), and coda-like scattered waves (Jia et al (1999); Jia (2004); Jia et al (2009)). The understanding of wave motion in granular media took a major step forward with the experimental observation of the coexistence of a coherent ballistic pulse travelling through an "effective contact medium" and a multiply scattered signal (Jia et al (1999)).…”