On modeling acoustic waves in saturated poroelastic media

In this paper we present a comparison of the linear wave analysis for four models of poroelastic materials. As shown in a paper by Wilmanski (Arch. Mech. 2002) a nonlinear thermodynamical construction of a two-component model of such materials requires a dependence on the porosity gradient. In the linear version this dependence may or may not be present (WIAS-Preprint No. 868). Consequently, we may work with the model without a dependence on this gradient which is identical with Biot's model or we can use the so-called full model. In both cases we can construct simplified models without a coupling between partial stresses introduced by Biot. These simplified models have the advantage that their application to, for instance, surface wave analysis yields much simpler mathematical problems.
In the present work we show that such a simplification for granular materials leads to a good qualitative agreement of all four models in ranges of porosity and Poisson's ratio commonly appearing in geotechnical applications. Quantitative differences depend on the mode of propagation and vary between 10% and 20%. We illustrate the analysis with a numerical example corresponding to data for sands.
Simultaneously we demonstrate severe limitations of the applicability of Gassmann relations which yield an instability of models in a wide range of practically important values of parameters.

Appeared in

• J. Statist. Phys., 131 (2005), pp.873-996.

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