Effect of flow-independent viscosity on the propagation behavior of Rayleigh wave in partially saturated soil based on the fractional standard linear solid model

Abstract

Based on the mixture theory, considering the flow-independent viscosity related to solid skeleton, the present work investigates the propagation characteristics of Rayleigh wave in partially saturated viscoelastic soil. Firstly, the complex history-dependent viscoelastic behavior of solid skeleton is characterized by the fractional standard linear solid constitutive model. The generalized governing equations of motion for the partially saturated viscoelastic soil are established theoretically. Secondly, the analytical solution of Rayleigh wave fields in the partially saturated viscoelastic soil is obtained using the wave function expansion method. Finally, the influences of flow-independent viscosity characterized by fractional viscoelastic parameter on the propagation behaviors of Rayleigh wave are implemented analytically and then discussed in detail. The results show that the fractional index, stress relaxation time and strain relaxation time in the fractional standard linear solid constitutive model have significant influence on the phase velocity and attenuation coefficient of Rayleigh wave. The fractional index, stress relaxation time and strain relaxation time have similar effects on the P1 and S waves included in body waves. Additionally, the influences of the fluid hydraulic conductivity and liquid saturation on the wave propagation cannot be ignored.