Rayleigh Wave Analysis in Fractional-Order Fluid-Saturated Porous Viscoelastic BISQ Half-Space Using the Surface Stiffness Matrix Method

The propagation of Rayleigh waves on the liquid-saturated poroviscoelastic half-space, considering fractional viscoelasticity and squirt-flow (BISQ) effects, is investigated using the surface stiffness matrix method. First, the state transfer equation of a Rayleigh wave on the fractional liquid-saturated poroviscoelastic material is derived from the governing equations and constitutive relations that account for fractional viscoelasticity and squirt-flow effects. Then, the transfer matrix with fractional and squirt-flow factors and the stiffness matrix of the state vector are obtained by solving the state transfer equation of a Rayleigh wave, and, subsequently, the surface stiffness matrix of a Rayleigh wave on the fractional BISQ poroviscoelastic half-space is derived. Finally, the application of mechanically traction-free conditions, as well as permeable and impermeable conditions, yields the frequency dispersive relation of the Rayleigh wave. The dependences of the Rayleigh wave speeds on the characteristic squirt-flow length and the fractional viscoelasticity of the solid and liquid phases are numerically discussed. It is observed that the Rayleigh wave speed is influenced not only by the viscoelasticity but also by the squirt-flow length. This work provides a stable numerical implementation for fractional BISQ Rayleigh wave problems, which suffer from high-frequency instability when solved by conventional transfer matrix approaches.