 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13554 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8194
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| In English (Mech. Solids): | | 5360 |
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| Anil K. Vashishth, Vishakha Gupta, and Sourab Kamboj, "Binary Poroelastic Model with Duality in Porosity and Permeability: Wave Propagation and Reflection-Refraction Phenomena," Mech. Solids. 60 (7), 5737-5771 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
7 |
Pages |
5737-5771 |
| DOI |
10.1134/S0025654425603386 |
| Title |
Binary Poroelastic Model with Duality in Porosity and Permeability: Wave Propagation and Reflection-Refraction Phenomena |
| Author(s) |
Anil K. Vashishth (Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, 136119 India)
Vishakha Gupta (Department of Mathematics, Dyal Singh College, Karnal, Haryana, 132001 India)
Sourab Kamboj (Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, 136119 India, mathsourab11020@kuk.ac.in) |
| Abstract |
The propagation of harmonic plane waves in a fractured porous medium saturated with two
immiscible viscous fluids is important to be studied for modelling complex subsurface wave phenomena. Such multiphase fractured systems are commonly present in sedimentary rock formations, where
the coexistence of immiscible fluids and fractures challenges conventional modelling approaches.
Despite its relevance to geophysics, reservoir engineering, and environmental applications, studies in
this area are limited. Traditional single-porosity models often fail to capture the coupled fluid–solid
interactions and the added complexity introduced by fractures. The present study is motivated by the
need to develop a more comprehensive understanding of wave propagation under these realistic conditions. The volume average approach is used to model the poroelastic solid in this study. Double
porosity and double permeability are incorporated in the mathematical formulation. Analytical results
yield complex wave velocities for five types of waves in the fractured porous solid saturated with two
immiscible fluids. The interface between water and the fractured porous solid is considered as permeable, with both closed-pore and open-pore boundary conditions as particular cases of this realistic
interface. The amplitude and energy ratios of the reflected and refracted waves are derived by hybrid
numerical and analytical methods. Numerical computations are done to examine the phase velocity
and attenuation of plane waves as a function of frequency. The effects of volume fractions, matrix and
fracture permeabilities, and fluid saturation on phase velocities are also examined. The influence of
incidence angle, frequency, fracture volume fraction, and partially opened surface pores significantly
affects the energy partition. A comparison of Biot’s theory and volume average theory is also done to
assess their relative merits in simulating the behaviour of porous media. The outcomes of this study
provide useful insights into energy distribution in complex porous structures and have potential applications in subsurface imaging, reservoir characterisation, and underwater sound propagation. Further,
results from earlier studies are reached as limiting cases for model validation. |
| Keywords |
volume average theory, fractured porous solid, double porosity and permeability, immiscible fluids, wave propagation, reflection and refraction |
| Received |
24 June 2025 | Revised |
19 September 2025 | Accepted |
03 October 2025 |
| Link to Fulltext |
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