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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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https://doi.org/10.5194/npg-2017-3
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
08 Feb 2017
Review status
A revision of this discussion paper was accepted for the journal Nonlinear Processes in Geophysics (NPG) and is expected to appear here in due course.
Continuum model of wave propagation in fragmented media: linear damping approximation
Maxim Khudyakov1, Arcady V. Dyskin1, and Elena Pasternak2 1School of Civil, Environment al and Mining Engineering, The University of Western Australia, Perth, 6009, Australia
2School of Mechanical and Chemical Engineering, The University of Western Australia, Perth, 6009, Australia
Abstract. Energy dissipation during wave propagation in fragmented geomaterials can be caused by independent movement of fragments leading to energy loss on their impact. By considering a pair of impacting fragments at times much greater than the period of their oscillations we show that at large time scale, the dynamics of the pair can be described by a linear viscous model with damping coefficient expressed through the restitution coefficient representing energy loss on impact. Wave propagation in fragmented geomaterials is also considered at the large time scale assuming that the wavelengths are much larger than the fragment sizes such that the attenuation associated with wave scattering on the fragment interfaces can be neglected. These assumptions lead to Kelvin-Voigt model of wave propagation, which allows the determination of dispersion relationship. As the attenuation and dispersion are not related to the rate dependence of rock deformation, but rather to the interaction of fragments the increasing damping and dispersion at low frequencies can be seen as an indication of fragmented nature of the geomaterial and the capacity of the fragments for independent movement.

Citation: Khudyakov, M., Dyskin, A. V., and Pasternak, E.: Continuum model of wave propagation in fragmented media: linear damping approximation, Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2017-3, in review, 2017.
Maxim Khudyakov et al.
Interactive discussionStatus: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
Printer-friendly Version - Printer-friendly version      Supplement - Supplement
 
RC1: 'Review', Anonymous Referee #1, 12 Mar 2017 Printer-friendly Version 
AC1: 'Answers on Review 1', Maxim Khudyakov, 18 May 2017 Printer-friendly Version Supplement 
 
RC2: 'Review of NPG-2017-3', Anonymous Referee #2, 17 Mar 2017 Printer-friendly Version Supplement 
AC2: 'Answers on Review 2', Maxim Khudyakov, 18 May 2017 Printer-friendly Version Supplement 
Maxim Khudyakov et al.
Maxim Khudyakov et al.

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Short summary
In order to assess energy loss during wave propagation in fragmented media, an impact model is proposed. The proposed model can be expressed by or used together with other linear damping models, which is important for the determination of mechanical characteristics of such media and mineral exploration.
In order to assess energy loss during wave propagation in fragmented media, an impact model is...
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