Dynamics of torsional waves in complex fractured poro-viscoelastic media with corrugated boundaries

Abstract

This paper aims to study the propagation of torsional surface waves in an anisotropic, pre-stressed, heterogeneous, fractured poro-viscoelastic layer resting on a similarly structured half-space, under the impact of corrugated boundaries. The corrugated boundaries are modeled in various forms, including triangular, rectangular, and parabolic shapes, to explore their impact on wave behavior. The heterogeneities of the media are represented using binomial functions with positive real exponents. By employing appropriate variable substitution and the separation of variables technique, the governing dynamic equations are transformed into the modified Bessel’s differential equations for the theoretical derivation. By using the asymptotic expansions of the modified Bessel’s functions, analytical solutions for the dispersion equation are derived. The derived dispersion equations are shown to perfectly match standard results in specific cases, validating the theoretical approach. Numerical analysis reveals that the group, damped, and phase velocities of the torsional surface waves are significantly influenced not only by the factors such as wavenumber, pre-stress, heterogeneity, and the depth of irregularities but also by the specific geometry of the corrugated boundaries. This work has potential applications in geophysics and structural engineering, particularly in the design and analysis of materials with complex boundary conditions and in understanding wave propagation in heterogeneous media. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.