RAPID COMMUNICATIONS PHYSICAL REVIEW E 84, 020301(R) (2011) Elastic weakening of a dense granular pack by acoustic fluidization: Slipping, compaction, and aging X. Jia, * Th. Brunet, † and J. Laurent Universit´ e Paris-Est, Laboratoire de Physique des Milieux Divis´ es et Interfaces, CNRS FRE 3300, 5 Boulevard Descartes, F-77454 Marne-la-Vall´ ee, France (Received 25 January 2011; revised manuscript received 23 July 2011; published 23 August 2011) Sound velocity measurements in dense glass bead packs reveal significant softening effect at large amplitudes, due to the frictional nonlinearity at the grain contacts. Beyond a certain amplitude, the sound-matter interaction becomes irreversible, leaving the medium in a weakened and slightly compacted state. A slow recovery of the initial elastic modulus is observed after acoustic perturbation, revealing the plastic creep growth of microcontacts. The cross-correlation function of configuration-specific acoustic speckles highlights the relationship between the macroscopic elastic weakening and the local change of the contact networks, induced by strong sound vibration, in the absence of appreciable grain motion. DOI: 10.1103/PhysRevE.84.020301 PACS number(s): 45.70.−n, 43.35.+d, 91.30.−f I. INTRODUCTION A granular medium is an assembly of discrete macroscopic solid grains that interact with each other by dissipative contact forces. Unlike the ordinary solids and liquids, a dense granular medium exhibits multiple metastable configurations and may undergo a transition between solid state to liquid state when a large enough mechanical force is applied by shear or vibration [1–4]. A shaking experiment allows investigation of the com- plex behavior of driven, athermal granular systems such as compaction, segregation, and pattern formation [1]. In a granular system fluidized by continuous strong vibration where collisions dominate (acceleration normalized with the gravity Ŵ>1), it has been shown [3] that an effective viscosity and effective temperature can be defined in such a granular liquid. By decreasing the amplitude of vibration Ŵ< 1, the driven granular medium evolves into an amorphous state [3]. On the opposite side of the liquid-to-solid transition, the jammed granular state is determined by the inhomogeneous contact force networks [1]. A granular solid exhibits very nonlinear dynamics during shearing, accompanied by strong spatial and temporal variations in the contact distribution. In a weakly vibrated granular column, large force variations have been observed on the bottom boundary in the absence of appreciable grain motion, indicating a strong nonlinear and glassy dynamics of the force network [4]. Sound waves propagating through the contact force network provide a natural way to probe accurately and nondestructively the viscoelastic properties of a jammed granular state [5–10]. At large amplitude of vibration, sound waves may serve as controlled perturbation to explore the glassy dynamics of a granular solid [6,7]. Liu and Nagel found previously that sound transmission at Ŵ ∼ 1 in a glass bead pack under gravity exhibits large temporal fluctuations [6]. Unlike the shaking experiment, such structural relaxation, referred to here as “acoustic fluidization [11],” occurs nevertheless surprisingly where no visible rearrangement of the beads was observed. At * Corresponding author: jia@univ-mlv.fr † Present address: Universit´ e Bordeaux 1, CNRS UMR 5295, F-33405 Talence cedex, France. moderate vibration (Ŵ< 0.1), both a strong hysteretic behavior on the amplitude measurement [6] and a significant modulus softening in the resonance experiment [12] were also observed, but the underlying physics responsible for these nonlinear dynamics still remains unclear on the level of the contacts. In this paper, we examine quantitatively the hysteretic characteristics of the sound velocity in jammed granular media via pulsed ultrasonic waves. We focus our attention on the irreversible sound-matter interaction in a regime where the grain motion is visibly absent. The resultant rearrangement of the force network is, however, evidenced by the configuration- specific scattered waves. Compared to the previous resonance method (∼150 s), the velocity measurement reported here (∼10 s) is much faster, thus providing an adequate method for highlighting the slow dynamic behavior. All combined measurements, including the packing density, reveal the crucial role of frictional nonlinearity at the grain contact in the elastic weakening and the structural change induced by the acoustic fluidization, and would be helpful for understanding the unjamming or landsliding triggering process [12]. II. EXPERIMENTS Our granular materials consist of dry polydisperse glass beads of diameter d = 0.6–0.8 mm confined in a oedometer cell of 60 mm diam which is filled to a height H = 20 mm, with a packing density ≈ 0.61. This type of apparatus allows us to apply a constant uniaxial load P 0 on the bead pack from 85 to 340 kPa. A large longitudinal transducer of 30 mm diam is used as a plane-wave source, transmitting a ten-cycle tone burst centered at low frequency, 50 kHz. The corresponding wavelength λ is ≈ 15 mm, which is much larger than the bead size d, and the coherent wave propagation is detected by another large transducer at the bottom (inset of Fig. 1). To examine the nonlinear response, we vary the input voltage V input from 10 to 250 V, corresponding to a vibration displacement U ≈ 2–50 nm. Figure 1(a) shows typical ultrasound transmissions through the bead pack under P 0 = 340 kPa for increasing input amplitudes. The absolute value of sound speed c 0 can be measured by the time-of-flight T 0 as c 0 ≈ 770 m/s. As the input amplitude is increased, we observe that the total transmitted ultrasound is delayed progressively up to ∼2% 020301-1 1539-3755/2011/84(2)/020301(4) ©2011 American Physical Society