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

Article


Ali, Adham A. and Strunin, Dmitry V.. 2019. "The role of rheology in modelling elastic waves with gas bubbles in granular fluid-saturated media." Journal of Mechanics of Materials and Structures. 14 (1), pp. 1-24. https://doi.org/10.2140/jomms.2019.14.1
Article Title

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

ERA Journal ID36514
Article CategoryArticle
AuthorsAli, Adham A. (Author) and Strunin, Dmitry V. (Author)
Journal TitleJournal of Mechanics of Materials and Structures
Journal Citation14 (1), pp. 1-24
Number of Pages24
Year2019
Place of PublicationUnited States
ISSN1559-3959
Digital Object Identifier (DOI)https://doi.org/10.2140/jomms.2019.14.1
Web Address (URL)https://msp.org/jomms/2019/14-1/jomms-v14-n1-p01-p.pdf
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 lambda as a function of the wave number k. We compared the lambda(k)-dependence for the cases with and without the bubbles, using typical values of the input mechanical parameters. For the both cases, the lambda(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.

KeywordsFrenkel–Biot’s waves, bubbles, rheology, porous media
ANZSRC Field of Research 2020370609. Seismology and seismic exploration
490105. Dynamical systems in applications
490109. Theoretical and applied mechanics
Byline AffiliationsComputational Engineering and Science Research Centre
Institution of OriginUniversity of Southern Queensland
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