Bettina Albers

Acoustic Waves in Porous Solid—Fluid Mixtures

In this article we consider two problems of propagation of weak discontinuity waves in porous materials. In the first part we present basic properties of bulk waves in fully saturated materials. These materials are modelled by a two-component immiscible mixture. We present general propagation conditions for such a model which yield three modes of propagation: P1-, S-, and P2-waves. Then we discuss the dispersion relation and show that results are strongly dependent on the way in which waves are excited. In the second part we present some properties of surface waves. We begin with the classical Rayleigh and Love problems and extend them on heterogeneous materials important in practical applications. Subsequently we proceed to surface waves in two-component porous materials on the contact surface with vacuum (impermeable boundary) and with a liquid (permeable boundary). We show the existence of different modes of surface waves in the high frequency limit as well as the degeneration of the problem in the low frequency limit.

Monochromatic surface waves at the interface between poroelastic and fluid halfspaces

The topic of the previous work of Albers and Wilmanski was the study of monochromatic surface waves at the boundary between a porous medium and a vacuum. This article is an extension of this research to the propagation of surface waves on the interface between a porous halfspace and a fluid halfspace. Results for phase and group velocities and attenuations are shown in dependence on both the frequency and the surface permeability. In contrast to classical papers on surface waves where only the limits of the frequency ω→0, ω→∞ and the limits of the surface permeability (fully sealed and fully open boundary) were studied, we investigate the problem in the full range of both parameters. For the analysis we use the ‘simple mixture model’ which is a simplification of the classical Biot model for poroelastic media. The construction of a solution is shown and the dispersion relation solved numerically. There exist three surface waves for this boundary: a leaky Rayleigh wave and both a true and a leaky Stoneley wave. The true Stoneley wave exists only in a limited range of the surface permeability.

BEM and FEM results of displacements in a poroelastic column

The dynamical investigation of two-component poroelastic media is important for practical applications. Analytic solution methods are often not available since they are too complicated for the complex governing sets of equations. For this reason, often some existing numerical methods are used. In this work results obtained with the finite element method are opposed to those obtained by Schanz using the boundary element method. Not only the influence of the number of elements and time steps on the simple example of a poroelastic column but also the impact of different values of the permeability coefficient is investigated.

Unsaturated porous media flow with thermomechanical interaction

We propose a model for unsaturated poro-plastic flow derived from the thermodynamic principles. For the isothermal case, the problem consists of a degenerate coupled system of two PDEs with two independent hysteresis operators describing hysteresis phenomena in both the solid and the pore fluids. Under natural hypotheses, we prove the existence of a global strong solution for this system. Copyright

Hysteresis in Unsaturated Porous Media—Two Models for Wave Propagation and Engineering Applications

Two models for the description of unsaturated porous media flow are revisited. The first is a continuum model suitable for the description of sound wave propagation in elastic media. Even if the model does not contain a hysteresis operator, the effect of hysteresis in the capillary pressure curve is accounted for. The two processes drainage and imbibition are investigated separately and the limit values of material parameters and acoustic properties are determined. The second model is a thermomechanical model capable for the description of flows in elastoplastic porous media. It contains two independent hysteresis operators describing hysteresis phenomena in both the solid and the pore fluids.

Linear Wave Propagation in Unsaturated Rocks and Soils

In this contribution an overview of the continuum mechanical modeling of linear elastic partially saturated porous media and the application of such a model to linear wave propagation is given. First the involved microstructural variables are discussed and the construction of the model is presented. The macroscopic parameters used in the model are obtained by micro-macro-transition procedure from the measurable microscopic quantities. The linear elastic wave propagation analysis is demonstrated exemplarily for sandstone, sand and clayey loam. The properties of the four appearing waves – three compressional and one shear wave – are compared. Phase speeds and attenuations of these waves depend both on the frequency and on the degree of saturation.

Propagation of Sound Waves in Poroelastic Media with Anisotropic Permeability

By means of a Biot-like model with isotropic stress-strain relations but anisotropic permeability monochromatic waves in a two-component poroelastic medium are analyzed. The anisotropy is induced by the anisotropy of the tortuosity which is introduced by a second order symmetric tensor. The model describes for a certain choice of orientation of the propagation direction four modes of propagation: a decoupled transversal S 1-wave, a pseudo transversal mode S 2 and two pseudo longitudinal modes P 1 and P 2. Phase speeds and attenuations of these waves are shown in dependence on the orientation of the principal directions of the tortuosity.

On The Influence of Saturation and Frequency on Monochromatic Plane Waves in Unsaturated Soils

The propagation of sound waves in partially saturated sandstone is investigated by use of a macroscopic linear model which is based on the two-component model of Biot and on the Simple Mixture Model by Wilmanski. The considered porous medium consists of a deformable skeleton and two compressible pore fluids (water and air). The wave analysis of the poroelastic model reveals the existence of four body waves: three longitudinal waves, P1, P2, P3, and one shear wave, S . The dependence of their phase velocities and attenuations on the saturation and on the frequency is studied and compared to experimental observations and the sound velocity of suspensions.