Dynamic wave propagation in infinite saturated porous media half spaces

Abstract

From a macroscopic perspective, saturated porous materials like soils represent volumetrically interacting solid-fluid aggregates. They can be properly modelled using continuum porous media theories accounting for both solidmatrix deformation and pore-fluid flow. The dynamic excitation of such multi-phase materials gives rise to different types of travelling waves, where it is of common interest to adequately describe their propagation through unbounded domains. This poses challenges for the numerical treatment and demands special solution strategies that avoid artificial and numerically-induced perturbations or interferences. The present paper is concerned with the accurate and stable numerical solution of dynamic wave propagation problems in infinite half spaces. Proceeding from an isothermal, biphasic, linear poroelasticity model with incompressible constituents, finite elements are used to discretise the near field and infinite elements to approximate the far field. The transient propagation of the poroacoustic body waves to the infinity is thereby modelled by a viscous damping boundary, which, for stability reasons, necessitates an appropriate treatment of the included velocity-dependent damping forces.

Simulation of Soils Under Rapid Cyclic Loading Conditions

“…They depend on the compression-and shearwave velocities, c p = √ (2μ S + λ S )/ρ and c s = √ μ S /ρ (cf. [19]), and on the dimensionless compression-and shear-wave damping coefficients a and b.…”

“…This procedure is often referred to as visco-damped boundaries (VDB) and originates from [24]. According to [19], the governing weak form, composed of a quasi-static and a viscous damped part, is given by…”

“…In general, they can be classified into so-called coupling methods, such as, for instance, the combined finite-element-infinite-element-method (FEM-IEM), and so-called absorbing-boundary-condition (ABC) methods. The present contributions proceeds from the approach proposed in [19]. Therein, the near and the far field are spatially discretised by mixed Taylor-Hood finite elements (FE) and infinite elements (IE), respectively, and, additionally, an energy-absorbing layer at the FE-IE interface has been introduced.…”

Nonlinear vibrations and mode interactions for a continuous rod with microstructure

“…By homogenization over a representative volume element, an averaged continuum model is obtained, in which every spatial point is simultaneously occupied by all the components in the sense of superimposed continua. This approach allowed to obtain a number of important results for the dynamic properties of fluid-saturated porous materials [30,31]. A comparison of different numerical schemes for the solution of multi-field coupled problems arising in the dynamics of porous media was presented by Markert et al [32].…”

FDM solutions to linear dynamics of porous media: Efficiency, stability, and parallel solution strategy

“…The TPM can be consistently derived from continuum mechanics, thermodynamics, the theory of mixtures, and the concept of volume fractions . For the static and dynamic behaviour of porous media, simulations based on the TPM (and Biot theory) have generated a great deal of advances; see, eg, previous studies …”