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Reflection and Refraction of Attenuated Waves at the Interface Between Cracked Poroelastic Medium and Porous Solid Saturated with Two Immiscible Fluids

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Abstract

The present study is mainly focused on understanding the effect of cracks on the energy share of an incident wave at the interface between a cracked poroelastic solid containing single fluid and a porous solid containing two immiscible viscous fluids. We assume that both the media are dissipative due to presence of viscosity in pore fluids. The analysis is based on Snell’s law for the reflection and refraction of an incident wave from the common boundary of these two media. The proposed model is solved for the propagation of harmonic plane waves with the help of the Helmholtz technique. After solving the elastodynamical equations, we find three attenuated reflected waves and four attenuated refracted waves. The propagation of an attenuated wave in the respective dissipative medium defined as an inhomogeneous propagation of a wave, is represented through the propagation and the attenuation directions. These inhomogeneous waves propagate through the cracked poroelastic solid and are incident at a point on the interface. The phase velocities and attenuation coefficients are calculated for the propagation of each inhomogeneous wave. The expressions of reflection and refraction coefficients and energy share of each of the reflected and refracted waves for a given incident wave are obtained in closed form and computed numerically in the present study. Numerical examples are considered for the partition of incident energy in which we have studied the presence and absence of cracks in poroelastic solid with single fluid, effect of crack density, saturation parameter and Poisson’s ratio for the cracked poroelastic solid.

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Acknowledgments

The authors convey their sincere thanks to Council of Scientific and industrial research (CSIR), New Delhi, for providing SRF to Mr. Sushant Shekhar and also thanks to Scientist in-charge CSIR-4PI, Bangalore for providing all facilities related to this research work.

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Authors and Affiliations

  1. Academy of Scientific and Innovative Research, New Delhi, 110 001, India

    Sushant Shekhar & Imtiyaz A. Parvez

  2. CSIR-Fourth Paradigm Institute, Bangalore, 560037, India

    Sushant Shekhar & Imtiyaz A. Parvez

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  1. Sushant Shekhar
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  2. Imtiyaz A. Parvez
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Correspondence to Sushant Shekhar.

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Shekhar, S., Parvez, I.A. Reflection and Refraction of Attenuated Waves at the Interface Between Cracked Poroelastic Medium and Porous Solid Saturated with Two Immiscible Fluids. Transp Porous Med 113, 405–430 (2016). https://doi.org/10.1007/s11242-016-0704-0

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