Wave propagation in an unconsolidated granular material: A micro-mechanical approach |
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| Affiliation: | 1. School of Engineering and Computing Sciences, Durham University, DH1 3LE, UK;2. Department of Engineering, University of Cambridge, CB2 1PZ, UK;3. Department of Mechanics, KTH, Osquars Backe 18, Stockholm 10044, Sweden;1. Department of Mechanical Engineering, The University of Auckland, 20 Symonds Street, 1010, Auckland, New Zealand;2. Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, India;3. Advanced Materials, Callaghan Innovation, 24 Balfour Rd, Parnell, Auckland 1052, Auckland, New Zealand;4. Sir Lawrence Wackett Aerospace Research Centre, School of Engineering, RMIT University, GPO Box 2476, Melbourne, VIC 3001, Australia;1. Departamento de Física, CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58059-900, João Pessoa, Brazil;2. Department of Chemistry and Biochemistry and BioCircuits Institute, University of California San Diego, La Jolla, CA 92093-0340, USA |
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| Abstract: | We provide a theoretical analysis to support the presence of both slow and fast compression waves in an unconsolidated, fully saturated, granular material. We derive the constitutive relation for such an aggregate based upon a micro-mechanics analysis. In doing this, we take in account the coupling between the solid particles and fluid. As a consequence of this coupling, the lubrication layer provides a connection between particles, both when they are separating and when they are compressing. The predictions of the speed and attenuation of the fast compression waves compare well with experimental data over the range of frequencies for which the nonlinear dissipation associated with the relative velocities between solid and fluid is negligible. Slow waves are also predicted without comparison, because of the absence of clear experimental data. Predictions of the speed and attenuation for the shear wave are also provided and show a good agreement with experimental data when surface roughness is taken into account. |
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