We investigate the elastic behavior and damage of weakly cemented granular media under external load with ultrasound. The cementation controlled experiments are performed by freezing the capillary liquid at the bead contact in a dense glass or polymeric [poly(methyl methacrylate)] bead pack wet by tetradecane of volume fraction ϕ = 0.1%-4%. When the pendular rings are solidified, an abrupt increase by a factor of 2 in the compressional wave velocity is observed. We interpret the data in terms of effective medium models in which the contact stiffnesses are derived by either a bonded contact model [P. J. Digby, J. Appl. Mech. 48, 803 (1981)] or a cemented contact model [J. Dvorkin, A. Nur, and H. Yin, Mech. Mater. 18, 351 (1994)]. The former fails to quantitatively account for the results with a soft cement relative to the grain, whereas the latter considering the mechanical properties of the cement does apply. Moreover, we monitor the irreversible behavior of the cemented granular packs under moderate uniaxial loading (1.3 MPa) with the correlation method of ultrasound scattering. The damage of the cemented materials is accompanied by a compressional wave velocity decrease up to 60%, likely due to the fractures induced at the grain-cement interfaces.

The pulse broadening and decay of coherent sound waves propagating in disordered granular media are investigated. We find that the pulse width of these compressional waves is broadened when the disorder is increased by mixing the beads made of different materials. To identify the responsible mechanism for the pulse broadening, we also perform the acoustic attenuation measurement by spectral analysis and the numerical simulation of pulsed sound wave propagation along one-dimensional disordered elastic chains. The qualitative agreement between experiment and simulation reveals a dominant mechanism by scattering attenuation at the high-frequency range, which is consistent with theoretical models of sound wave scattering in strongly random media via a correlation length.

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In this paper, we study how the permeability of solid foam is modified by the presence of membranes that close partially or totally the cell windows connecting neighboring pores. The finite element method (FEM) simulations computing the Stokes problem are performed at both pore and macroscopic scales. For foam with fully interconnected pores, we obtain a robust power-law relationship between permeability and aperture size. This result is due to the local pressure drop mechanism through the aperture as described by Sampson for fluid flow through a circular orifice in a thin plate. Based on this local law, pore-network simulation of simple flow is used and is shown to reproduce FEM results. Then this low computational cost method is used to study in detail the effect of an open window fraction on the percolation properties of the foam pore space. The results clarify the effect of membranes on foam permeability. Finally, Kirkpatrick's model is adapted to provide analytical expressions that allow for our simulation results to be successfully reproduced.

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