Rayleigh Wave Propagation on the Partially Saturated Poro-Thermo-Viscoelastic Half-Space Based on Fractional Order Viscoelasticity

This paper investigates the propagation characteristics of Rayleigh wave in a partially saturated porous thermo-viscoelastic half-space based on considering fractional viscoelastic effects and thermal coupling effects. By establishing a set of governing equations including mass balance, generalized Darcy's law, momentum balance, and generalized heat conduction, a fractional Zener model is introduced to characterize the thermo-viscoelastic behavior of the solid skeleton. The field equations are derived using Helmholtz vector decomposition and combined with traction-free and adiabatic boundary conditions to obtain the dispersion equation and phase velocity expression of Rayleigh wave. The influences of material parameters such as medium saturation, intrinsic permeability, medium viscoelasticity, and thermal expansion coefficient on the phase velocity of Rayleigh wave are discussed. Numerical analysis indicates that an increase in the thermal expansion coefficient results in an elevation of the Rayleigh wave phase velocity, where the enhancement of the P1 compression wave velocity plays a dominant role in various wave velocities. The increase in medium elasticity leads to an elevation in the phase velocity of Rayleigh wave, with the velocity enhancement of P1 waves and S waves playing a dominant role. The research results reveal the influence laws of thermal expansion and viscoelasticity on Rayleigh wave propagation, providing theoretical support for the analysis of wave propagation characteristics in porous media within relevant engineering scenarios.