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

Vertical dynamic response of pipe pile embedded in unsaturated soil based on fractional‐order standard linear solid model and Rayleigh‐Love rod model

“…Employing the mixture theory and considering the FSLS model, the generalized governing equations for elastic waves propagation in three‐phase porous media are described as 36 $$$$\begin{equation}\bar \mu \left( \omega \right){u_{i,jj}} + \left[ {{C_{11}}\left( \omega \right) + \bar \mu \left( \omega \right)} \right]{u_{j,ji}} + {C_{12}}\left( \omega \right){w_{j,ji}} + {C_{13}}\left( \omega \right){v_{j,ji}} = \rho {\ddot u_i} + {\rho _w}{\ddot w_i} + {\rho _g}{\ddot v_i}\end{equation}$$$$ $$$$\begin{equation}{C_{21}}\left( \omega \right){u_{j,ji}} + {C_{22}}\left( \omega \right){w_{j,ji}} + {C_{23}}\left( \omega \right){v_{j,ji}} = {\rho _w}{\ddot u_i} ...$$…”

“…The Kelvin-Voigt model has been reported to be weak in describing the instantaneous deformation of the soil skeleton and thus has some restrictions in the study on soil dynamic behaviors. 36 In light of the above, Liu et al 36 constructed a new viscoelastic dynamic governing equations for unsaturated soils utilizing the fractional-order standard linear solid (FSLS) model and studied the influence of model parameters on elastic wave propagation. Naturally, the utilization of more refined soil models for the study of pile-soil interactions is of great significance for practical engineering applications.…”

“…In view of the above reasons, this work establishes an interaction model between the large-diameter pipe pile and the unsaturated soil on the basis of the Rayleigh-Love rod model and the fractional-order viscoelastic dynamic governing equations of unsaturated soils developed by Liu et al 36 Further, the analytical solution of the pipe pile complex impedance is deduced through a rigorous theoretical derivation. Finally, numerical results with known analytical solution are finally presented to discuss the influence of the model parameters for the FSLS model, lateral inertia effect and geometrical characteristic for the pipe pile, and saturation degree and intrinsic permeability for the unsaturated soil on the vertical complex impedance of the pipe pile.…”

“…In most of the current studies, the soil skeleton is limited to the simple Kelvin‐Voigt linear viscoelastic model. The Kelvin‐Voigt model has been reported to be weak in describing the instantaneous deformation of the soil skeleton and thus has some restrictions in the study on soil dynamic behaviors 36 . In light of the above, Liu et al 36 .…”

“…In view of the above reasons, this work establishes an interaction model between the large‐diameter pipe pile and the unsaturated soil on the basis of the Rayleigh‐Love rod model and the fractional‐order viscoelastic dynamic governing equations of unsaturated soils developed by Liu et al 36 . Further, the analytical solution of the pipe pile complex impedance is deduced through a rigorous theoretical derivation.…”