Transient solution for multilayered poroviscoelastic media obtained by an exact stiffness matrix formulation

The authors propose a semi‐analytical approach to studying wave propagation in multilayered poroviscoelastic grounds due to transient loads. The theoretical development is based on the exact stiffness matrix method for the Biot theory coupled with a matrix conditioning technique. It is developed in the wavenumber frequency domain after a Fourier transform on the surface space variables and the time variable. The usual methods yield a poorly conditioned numerical system. This is due in particular to the presence of mismatched exponential terms. In this article, increasing exponential terms are eliminated and only decreasing exponential terms remain. Consequently, the method can be applied to a large field of configurations without restriction concerning high frequencies, large Fourier transform parameters or large layer thicknesses. Validation and efficiency of the method are discussed. Effects of layering show that the layer impedance influence on solid and fluid displacements. Moreover, this approach can be of interest for the validation of numerical tools. Copyright © 2009 John Wiley & Sons, Ltd.     

Intrinsic poroelasticity constants and a semilinear model

This paper presents an intrinsic micromechanical model for poroelasticity that leads to an alternative set of material constants. In the intrinsic model, the deformations of the solid phase, the fluid phase, and the pore space are explicitly modeled, and porosity is considered as a primary variable. The averaging process distinguishes an external frame surface averaging and an internal phase volume averaging. The variational principle leads to a porosity equilibrium equation that defines the nonlinear deformation of pore volume. Three fundamental deformation modes with their intrinsic material constants are identified: the shape preserving volumetric deformation of the solid phase, the porosity change due to solid grain rearrangement, and the porosity change associated with the microanisotropy and microinhomogeneity of solid phase. The linearized model is fully consistent with the Biot theory of poroelasticity. A semilinear model considering only porosity deformation nonlinearity with linear material constant leads to a universal exponential strain hardening law. The theory is tested against laboratory data of sandstone. Copyright © 2007 John Wiley & Sons, Ltd.     

One‐dimensional analysis of a poroelastic medium during freezing

A solution to the problem of freezing of a poroelastic material is derived and analysed in the case of one‐dimensional deformation. The solution is sought within the framework of thermo‐poroelasticity, with specific account of the behaviour of freezing materials. The governing equations of the problem can be combined into a pair of coupled partial differential equations for the temperature and the fluid pressure, with particular forms in the freezing and the unfrozen regions. In the freezing region, the equations are highly non‐linear, partly due to the dependence of thermal and hydraulic properties on water saturation, which varies with temperature. Consequently, the solution is obtained through numerical methods, with special attention to the propagation of the freezing front boundary. The response to one‐dimensional freezing is illustrated for the case of cement paste. Finally, the influence on the solution of varying selected parameters is analysed, such as the temperature boundary conditions, the parameters characterizing the geometry of the porous system, the ratio of fluid and thermal diffusivities, and the rate of cooling applied at the freezing end. Copyright © 2008 John Wiley & Sons, Ltd.     

Polarisations of quasi-waves in a general anisotropic porous solid saturated with viscous fluid

Wave propagation is studied in a general anisotropic poroelastic solid saturated with a viscous fluid flowing through its pores of anisotropic permeability. The extended version of Biot’s theory is used to derive a system of modified Christoffel equations for the propagation of plane harmonic waves in such media. The non-trivial solution of this system is ensured by a biquadratic equation whose roots represent the complex velocities of four attenuating quasi-waves in the medium. These complex velocities define phase velocity and attenuation of each quasi-wave propagating along a given phase direction in three-dimensional space. The solution itself defines the polarisations of the quasi-waves along with phase shift. The variations of polarisations of quasi-waves with their phase direction, are computed for a realistic numerical model.