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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 149
Surface Vibration of Porous Media: Wave Number and Spatial Results G. Lefeuve-Mesgouez, A. Mesgouez, H. Bolvin and A. Chambarel
Laboratory A1114 Climate Soil and Environment, University of Avignon, France Full Bibliographic Reference for this paper
G. Lefeuve-Mesgouez, A. Mesgouez, H. Bolvin, A. Chambarel, "Surface Vibration of Porous Media: Wave Number and Spatial Results", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 149, 2006. doi:10.4203/ccp.83.149
Keywords: wave propagation, porous media, Biot theory, surface vibration, Fourier transform, wave number.
Summary
The study of mechanical wave propagation in soils has received
considerable attention in the last decades. As a matter of fact, a
better understanding of propagation phenomena would allow a better
apprehension of problems in a large number of areas of applied
mechanics or geomechanics. In the 1990s, Jones et al. [1]
developed a semi-analytical approach to analyse displacements in
the wave number and spatial domains for an harmonic load acting on
a viscoelastic ground. Extensions of this work have been done for
the study of moving loads, Lefeuve-Mesgouez et al. [2]
and Sheng et al. [3]. All this research was
restricted to the case of viscoelastic soils. Degrande et al.
[4] also developed a similar approach for porous media.
The authors propose to develop such an approach in the case of porous media using the whole Biot theory [5], in order to analyse results obtained in the wave number domain and to understand dispersion and attenuation phenomena. In fact, the study of the displacements in the wave number domain allows localization and dissociation of body and surface waves and this can be useful in the interpretation of results in the spatial domain in which all waves are mixed.
An harmonic vertical load acts uniformly over a rectangle. It
rests on an homogeneous porous soil which is modelled as a
two-phase continuum composed of a porous deformable viscoelastic
solid skeleton and a fluid component corresponding to the viscous
fluid which saturates the porous space. The model is
three-dimensional but it can be easily restricted to
two-dimensional geometries. The equations field is
nondimensionalised to present the problem in a general and
meaningful manner. By introducing the Helmholtz decomposition for
the solid and relative displacements in the equations of motion
and in the stress-strain relations, one can obtain the wave
equations relative to the problem that underline the existence of
the body waves. As a matter of fact, in such a medium, three body
waves exist: the
Results presented in this paper are obtained for the case of a
two-dimensional problem involving a strip load over the surface of
the half-space. The analysis of the real part of the transformed
displacements dissociates the contribution of the different waves:
contribution of the body waves have opposite signs compared to the
contribution of the surface wave. The major features are peaks
located at corresponding wave numbers. The
The influence of the permeability has also been studied. It has
important consequences on the The main perspective of this work is to deal with transient regimes and multilayered soils. Such semi-analytical approaches can also been used as benchmarks to validate numerical tools. References
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