Bulk and Rayleigh Waves Propagation in Three-Phase Soil with Flow-Independent Viscosity

The flow-independent viscosity of the soil skeleton has significant influence on the elastic wave propagation in soils. This work studied the bulk and Rayleigh waves propagation in three-phase viscoelastic soil by considering the contribution of the flow-independent viscosity from the soil skeleton. Firstly, the viscoelastic dynamic equations of three-phase unsaturated soil are developed with theoretical derivation. Secondly, the explicit characteristic equations of bulk and Rayleigh waves in three-phase viscoelastic soil are yielded theoretically by implementing Helmholtz resolution for the displacement vectors. Finally, the variations of the motion behavior for bulk and Rayleigh waves with physical parameters such as relaxation time, saturation, frequency, and intrinsic permeability are discussed by utilizing calculation examples and parametric analysis. The results reveal that the influence of soil flow-independent viscosity on the wave speed and attenuation coefficient of bulk and Rayleigh waves is significantly related to physical parameters such as saturation, intrinsic permeability, and frequency.