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

This paper probes into the propagation characteristics of Rayleigh waves in a partially saturated, porous, thermo-viscoelastic half-space, with full consideration of the fractional viscoelastic effect and thermal coupling effect. A fractional Zener model is introduced to depict the thermo-viscoelastic mechanical behavior of the solid skeleton by constructing a complete set of governing equations that include mass balance, generalized Darcy’s law, momentum balance, and generalized heat conduction. Field equations are derived by means of Helmholtz vector decomposition, and the dispersion equation, and the phase velocity expression of Rayleigh waves are obtained by combining the traction-free and adiabatic boundary conditions of the medium. The impacts of key material properties, such as medium saturation, intrinsic permeability, medium viscoelasticity, and thermal expansion coefficient, on the dispersion feature of Rayleigh waves are discussed in detail. Numerical analysis results show that an increase in the thermal expansion coefficient will lead to a rise in Rayleigh wave phase velocity, in which the increase in P1 compressional wave velocity plays a dominant role among the velocities of various types of waves. Meanwhile, the attenuation coefficient of Rayleigh waves presents a decreasing trend and gradually tends to be stable with the growth of the thermal expansion coefficient. Similarly, the phase velocity of Rayleigh waves also increases with the rise in fractional order index, which is jointly dominated by the velocity enhancement of P1 waves and S waves. In addition, the attenuation coefficient of Rayleigh waves increases first and then decreases with the increase in fractional order index and reaches the peak value when the fractional order index is about 0.4. The research results reveal the influence of laws of thermal expansion characteristics and viscoelasticity on Rayleigh wave propagation and provide theoretical support for the analysis of wave propagation characteristics in porous media in relevant engineering applications.