Dynamic acoustoelastic testing of weakly pre-loaded unconsolidated water-saturated glass beads

Abstract

Dynamic acoustoelastic testing is applied to weakly pre-loaded unconsolidated water-saturated glass beads. The gravitational acceleration produces, on the probed beads, a static stress of order 130 Pa, thus the granular medium is close to the jamming transition. A low-frequency (LF) acoustic wave gently disturbs the medium, inducing successively slight expansion and compaction of the granular packing expected to modulate the number of contacts between beads. Ultrasound (US) pulses are emitted simultaneously to dynamically detect the induced modification of the granular skeleton. US propagation velocity and attenuation both increase when the LF pressure increases. The quadratic nonlinear elastic parameter β, related to the pressure dependence of US propagation velocity, was measured in the range 60-530 if water-saturated glass beads are considered as an effective medium. A dynamic modification of US scattering induced by beads is proposed to modulate US attenuation. Complex hysteretic behaviors and tension-compression asymmetry are also observed and analyzed by time-domain and spectral analyses. Furthermore acoustic nonlinearities are measured in cases of quasi-static and dynamic variations of the LF wave amplitude, providing quantitatively similar acoustic nonlinearities but qualitatively different.

Frequency, pressure, and strain dependence of nonlinear elasticity in Berea Sandstone

“…to determine max (t j ), the time at which the correlation function is maximum [Renaud et al, 2009[Renaud et al, , 2010. This time of flight shift can be converted into a relative velocity change using…”

“…The first step in analysis of s ( t − t j ) from the steady state time domain is to compare it to the reference pulse s ( t − t 0 ) by computing the cross correlation: to determine τ max ( t j ), the time τ at which the correlation function is maximum [ Renaud et al , , ]. This time of flight shift can be converted into a relative velocity change using where t 0 is the time of flight of the reference pulse.…”

“…The probe ( p ) is a HF pulse (of low strain amplitude, ε p ≃10 −7 ) that tests the state of the sample at all phases of the pump strain field, i.e., in both compression and tension. From the response of the probe to the pump modulation, a complete description of the rich nonlinear elastic properties of the sample is obtained, e.g., hysteresis, tension/compression asymmetry, and nonlinear elastic constants, providing a more complete picture on the nonlinear phenomena than static experiments [ Renaud et al , , , , , , ; Moreschi et al , ; Trarieux et al , ; Rivière et al , , ].…”

Modeling nonlinear viscoelasticity in dynamic acoustoelasticity

“…This method has already been demonstrated to be relevant and sensitive to nonlinear elastic and hysteretic responses, particularly when characterizing the aforementioned complex media: granular media, 13,14 ultrasound contrast agents, 15,16 and micro-damaged solids (rock samples, [17][18][19] bone tissues, 20 metals, 21 and concrete 22 ). The different nonlinear hysteretic shapes of the acoustoelastic responses ( Figure 2) motivate us to consider the nonlinear viscous effects in addition to more standard nonlinear elastic contributions.…”

Determination of the acoustoelastic coefficient for surface acoustic waves using dynamic acoustoelastography: An alternative to static strain

“…Renaud et al 20 used a similar dynamic method for parametric interaction of longitudinal waves, interacting in perpendicular directions, first in bone 20 and then in Pyrex 21 and glass beads. 22 This technique was presented improved in Renaud et al 23,24 by using a piezoelectric disk for the low frequency generation and a laser vibrometer for the low frequency detection.…”