This article presents an overview on poroelastodynamic models and some analytical solutions. A brief summary of Biot’s theory and on other poroelastic dynamic governing equations is given. There is a focus on dynamic formulations and the quasi-static case is not considered at all. Some analytical solutions for special problems, fundamental solutions, and Green’s functions are discussed. The numerical realization with two different methodologies, namely the Finite Element Method and the Boundary Element Method, is reviewed. Preprint No 3/2008 Institute of Applied Mechanics

Poroelastodynamics: Linear Models, Analytical Solutions, and Numerical Methods

https://hal.archives-ouvertes.fr/hal-00504035/document

Boundary Conditions at Fluid-Permeable Interfaces in Porous Media: a Variational Approach

A nonlinear viscoelastoplastic theory is developed for porous rate-dependent materials filled with a fluid in the presence of gravity. The theory is based on a rigorous thermodynamic formalism suitable for path-dependent and irreversible processes. Incremental evolution equations for porosity, Darcy's flux, and volumetric deformation of the matrix represent the simplest generalization of Biot's equations. Expressions for pore compressibility and effective bulk viscosity are given for idealized cylindrical and spherical pore geometries in an elastic-viscoplastic material with low pore concentration. We show that plastic yielding around pores leads to decompaction weakening and an exponential creep law. Viscous and plastic end-members of our model are consistent with experimentally verified models. In the poroelastic limit, our constitutive equations reproduce the exact Gassmann's relations, Biot's theory, and Terzaghi's effective stress law. The nature of the discrepancy between Biot's model and the True Porous Media theory is clarified. Our model provides a unified and consistent formulation for the elastic, viscous, and plastic cases that have previously been described by separate “end-member” models.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2014JB011258

(De)compaction of porous viscoelastoplastic media: Model formulation

Propagation and attenuation of Rayleigh waves in a semi-infinite unsaturated poroelastic medium

A general approach is proposed for defining the macroscopic free-energy function of a saturated porous medium subjected to finite deformations, under isothermal conditions, in the case of compressible fluid and solid constituents. Reference is made to an elementary volume treated as an ‘open system’, moving with the solid skeleton. The strain-like variables are characterized by a suitable strain measure and the variation of fluid-mass content. Although the free energy is obtained by assembling the contributions of the single constituents, the resulting free energy is not the simple sum of the free energies of the single constituents. It is shown that the simplified approaches previously proposed in the literature are recovered as particular cases of the more general framework proposed in the present article and, in addition, new simplified constitutive frameworks are investigated. The proposed approach paves the way to the consistent hyperelastic–plastic and thermo-elastic modelling of saturated porous media with compressible fluid and solid constituents.

K. Wilmanski

Papers

A few remarks on Biot's model and linear acoustics of poroelastic saturated materials