1D wave propagation in saturated viscous geomaterials: Improvement and validation of a fractional step Taylor–Galerkin finite element algorithm

Abstract

This paper tackles the numerical simulation of 1D wave propagation in saturated viscous porous media, and especially in soil-like geomaterials. For this purpose, an improved fractional step Taylor–Galerkin algorithm is first formulated and then validated on the basis of a new analytical solution. The algorithm, based on a stress–velocity–pressure formulation of the hydro-mechanical problem, combines an explicit Taylor–Galerkin method with a fractional time-stepping, while an accurate Runge–Kutta-type integrator is introduced to treat the viscosity of the porous skeleton. The overall algorithm results in an efficient stabilized scheme allowing for linear equal interpolation of field variables, even when the so-called “undrained incompressible limit” is approached. The accuracy and stability of the method are verified with reference to a 1D benchmark problem, concerning the propagation of P waves along a saturated viscoelastic soil stratum. For this problem, a frequency-domain analytical solution is derived, assuming incompressible interstitial fluid and soil grains. The assumption of Maxwell viscoelastic soil skeleton is analytically convenient to preserve the linearity of the problem, while the same rheology of a more realistic elasto-viscoplastic non-linear behaviour is maintained. The performance of the fractional step Taylor–Galerkin algorithm is explored simulating the dynamic response of the stratum to harmonic, impulsive and seismic input excitations. In particular, parametric analyses are performed to confirm the effectiveness of the method in reproducing fully undrained responses, as well as in dealing with weakly viscous materials.