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A mathematical model for wave propagation in a composite solid matrix containing two immiscible fluids

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Abstract

Constitutive relations and field equations have been extended for a porous medium composed of two solids and containing two chemically non-reactive immiscible fluids. By generalizing the closure relation of porosity change and employing this into the mass balance equations, the stress–strain relations have been developed. The idea of generalized compressibility tests is invoked to find the value of dimensionless parameters appearing in the closure relation of porosity change. By generalizing momentum balance equations of Lo et al. (Water Resour Res 41:1–20, 2005), the propagation of dilatational and rotational waves is explored. It is found that four dilatational and two rotational waves exist in the porous medium. In contrast to Biot’s theory, the presence of the second fluid and second solid in the porous medium gives rise to additional P- and S-waves. Variation of phase speeds and corresponding attenuation coefficients of existing waves versus frequency, saturation of the fluid phases and solid fraction are computed numerically and depicted graphically.

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Authors and Affiliations

  1. Department of Mathematics, I.K. Gujral Punjab Technical University, Jalandhar, Punjab, 144 603, India

    Ashish Arora

  2. Department of Mathematics, DAV Institute of Engineering and Technology, Jalandhar, 144 008, India

    Neeru Bala

  3. I.K. Gujral Punjab Technical University, Jalandhar, Punjab, 144 603, India

    Neeru Bala

  4. Department of Mathematics, Panjab University, Chandigarh, 160 014, India

    S. K. Tomar

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  1. Ashish Arora
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  2. Neeru Bala
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  3. S. K. Tomar
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Correspondence to S. K. Tomar.

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Arora, A., Bala, N. & Tomar, S.K. A mathematical model for wave propagation in a composite solid matrix containing two immiscible fluids. Acta Mech 227, 1453–1467 (2016). https://doi.org/10.1007/s00707-016-1571-z

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  • DOI: https://doi.org/10.1007/s00707-016-1571-z

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