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1

Influence of inertia forces on soil settlement under harmonic loading

Wrana B., Pietrzak N.

Studia Geotechnica et Mechanica

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2013

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Vol. 35, nr 1

245--258

EN

The paper deals with the comparison of Biot’s model for saturated, porous soils with other simplified models used in dynamic analysis. The purpose of this paper is to determine some limits of validity of the various models. In order to do this a full set of governing, dynamic equations of Biot model and a series of simplifying models such as u-p simplification and quasi-static consolidation models are considered. These formulations are applied to a simple soil layer under periodic surface loading. A displacement of skeleton and a displacement of fluid are shown and compared with each model for various formulations.

2

Influence of coupling through porosity changes on the propagation of acoustic waves in linear poroelastic materials

Albers B., Wilmanski K.

Archives of Mechanics

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2006

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Vol. 58, nr 4-5

313-325

EN

In earlier works it has been shown that linearization of thermodynamical models of poroelastic materials yields a contribution to stresses in the form ......., where ... is the current porosity, ... denotes its value in the thermodynamical equilibrium and ... is a material parameter. It has been also claimed on the basis of rough estimates that this parameter gives only negligible contributions to the properties of acoustic waves. The purpose of this work is twofold. We investigate the influence of ß on the propagation of acoustic waves in more details. We use the full linear model of saturated poroelastic materials in which an additional coupling to porosity changes appears. This results from the presence of a term with the porosity gradient in the momentum sources. Such a model becomes identical with Biot's model without any added mass contribution in the limit if infinite relaxation time of porosity ... and for the parameters ß=0, and N=0, where the latter is describing the above mentioned influence of porosity gradient on the momentum sources. The analysis of influence of the parameter N, i.e. the influence of the porosity gradient on properties of acoustic waves, is the second purpose of this work. We also indicate a correction of the permeability contribution to the momentum source. The permeability coefficient ... is assumed in Biot's model to be dependent on the frequency. This is inconsistent with other temporal contributions to field equations. In order to obtain such a dependence in the Fourier space, one has to assume a viscous effect to enter the momentum source and we do so in the general equations. However, we do not use this general relation in the analysis of monochromatic waves.

3

Thermodynamical admissibility of Biot's model of poroelastic saturated materials

Wilmański K.

Archives of Mechanics

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2002

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Vol. 54, nr 5-6

709-736

EN

The paper is devoted to the analysis of nonlinear elastic two-component models of saturated porous media, which in a linear form, reproduce as closely as possible the classical Biot's model. We present a full evaluation of the second law of thermodynamics for four classes of nonlinear models. It is proven that two of them in which there is no dependence on higher gradients cannot lead to the Biot's model. On the other hand, two other models in which a dependence on the gradient of porosity is introduced, yield linear constitutive relations but not the field equations appearing in the Biot's model. However, a recombination of partial stresses and momentum sources leads to Biot's equations. This analysis together with earlier publications on the subject exhausts the discussion of the question of thermodynamical admissibility of the Biot's model.