Semi-analytical solution for the transient response of saturated viscoelastic porous media based on fractional Poynting-Thomson model

Abstract

The vibration and deformation of subgrade soil under the dynamic load is the main research topic in transportation geotechnics, yet existing studies rarely provide analytical solutions for viscoelastic transient response problems. Building on the Biot wave equations and considering the material’s compressibility, this work introduces the fractional Poynting-Thomson viscoelastic model to establish a transient response model for a saturated viscoelastic single-layer porous medium under typical boundary conditions. By integrating the state-space method, Laplace transform, and the elasticity-viscoelasticity correspondence principle, an analytical solution in the Laplace domain is derived. Employing the inverse Laplace transform, the time-domain solution to the original problem is obtained. The correctness of the solution is verified through comparison with existing solutions. Analysis of numerical examples indicates that the fractional time parameter $\alpha f$ significantly influences the medium’s long-term response. The dash-pot viscosity coefficients have a pronounced effect on the hysteresis of $P_2$ wave.