Analytical Study of Torsional Wave Behavior in Graded Poroelastic Layer Bonded to Viscoelastic Foundation

This study presents a theoretical investigation of torsional wave propagation in a graded, fluid-saturated porous layer perfectly bonded to a Kelvin–Voigt viscoelastic half-space. The porous layer exhibits anisotropic behavior with spatially varying rigidity and density, capturing material gradation effects. A complex dispersion relation governing wave propagation is derived using the method of separation of variables, and the real and imaginary components are used to characterize phase velocity and attenuation, respectively. The influence of porosity, gradation, and viscoelastic damping on the dispersion characteristics is examined through numerical analysis. Results indicate that porosity enhances both phase and damping velocities due to fluid–solid coupling, while increasing material gradation leads to stiffer response and stronger attenuation. The model reduces to classical cases under specific parameter limits, providing a basis for validation and comparative assessment. The findings contribute to a deeper understanding of wave dynamics in heterogeneous and dissipative media, with implications for subsurface characterization, seismic analysis, and the design of functionally graded composites.