Vol. 14, No. 1, 2019

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The role of rheology in modelling elastic waves with gas bubbles in granular fluid-saturated media

Adham A. Ali and Dmitry V. Strunin

Vol. 14 (2019), No. 1, 1–24
Abstract

Elastic waves in fluid-saturated granular media depend on the rheology which includes elements representing the fluid and, if necessary, gas bubbles. We investigated the effect of different rheological schemes, including and excluding the bubbles, on the linear Frenkel–Biot waves of P1 type. For the wave with the bubbles the scheme consists of three segments representing the solid continuum, fluid continuum, and a bubble surrounded by the fluid. We derived the Nikolaevskiy-type equations describing the velocity of the solid matrix in the moving reference system. The equations are linearized to yield the decay rate λ as a function of the wave number k. We compared the λ(k)-dependence for the cases with and without the bubbles, using typical values of the input mechanical parameters. For the both cases, the λ(k)-curve lies entirely below zero, which is in line with the notion of the elastic wave being an essentially passive system. We found that the increase of the radius of the bubbles leads to faster decay, while the increase in the number of the bubbles leads to slower decay of the elastic wave.

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Keywords
Frenkel–Biot's waves, bubbles, rheology, porous media
Milestones
Received: 25 January 2018
Revised: 31 December 2018
Accepted: 7 January 2019
Published: 7 April 2019
Authors
Adham A. Ali
Department of Mathematics
Kirkuk University
Kirkuk
Iraqi
Computational Engineering and Science Research Centre
Faculty of Health, Engineering and Sciences
University of Southern Queensland
Toowoomba, Australia
Dmitry V. Strunin
Computational Engineering and Science Research Centre, Faculty of Health, Engineering and Sciences
University of Southern Queensland
Toowoomba
Australia