https://doi.org/10.1140/epjp/s13360-025-06681-7
Regular Article
Dispersion analysis of Rayleigh waves in stratified anisotropic porous heterogeneous systems with irregular boundaries and interfacial slip dynamics
Department of Mathematics and Computing, Indian Institute of Technology, ISM, 826004, Dhanbad, Jharkhand, India
Received:
12
April
2025
Accepted:
22
July
2025
Published online:
8
August
2025
This research work investigates the dispersion characteristics of Rayleigh waves in an anisotropic porous layer subjected to initial stress that rests on an incompressible heterogeneous half-space with an irregular surface and a sliding contact interface. Using Biot’s poroelastic theory, the governing equations are formulated to account for anisotropy, initial stress, and porosity, while the heterogeneous half-space is characterized by depth-dependent material properties. The surface irregularity is modeled as a periodic corrugation, and the sliding interface condition is incorporated to account for imperfect bonding, allowing for a more accurate representation of composite structures. A parameter is introduced to characterize sliding contact interfaces. The solutions are derived using a harmonic wave analysis approach combined with the method of separation of variables, leading to analytical expressions for the displacement fields in both media. The dispersion relation for Rayleigh waves is obtained as a 6 
6 determinant matrix by using the appropriate conditions at the boundaries and interface. The effects of material heterogeneity, corrugation, initial stress, anisotropy, porosity, and sliding parameter on the propagation velocity and decay characteristics of Rayleigh waves are analyzed. MATHEMATICA software is utilized to perform numerical simulations and generate graphical outputs. The results, illustrated through graphs, offer a detailed understanding of the dynamics of Rayleigh waves in this intricate system. The findings demonstrate that surface corrugation enhances Rayleigh wave velocity at lower wavenumbers, while interfacial sliding reduces it due to diminished stiffness, together inducing significant dispersion effects. This study provides a refined framework for understanding wave propagation in porous heterogeneous media by incorporating surface and interface imperfections, contributing to more reliable analyses in geophysics, seismology, and subsurface exploration.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
