Comptes Rendus
Quasi-static versus dynamic failure instabilities in fluid-saturated porous media
Comptes Rendus. Mécanique, Volume 330 (2002) no. 5, pp. 339-345.

Using a linear perturbation approach, we show that under quasi-static conditions, unbounded growth of perturbations coincides with localization under drained or undrained conditions. Under dynamic loadings, unbounded growth is related either to the emergence of stationary discontinuities (and these are set by drained conditions) or to the appearance of the flutter phenomenon (acceleration waves). For associative behaviour the inception of unbounded growth is always set (under both static and dynamic conditions) by the singularity of the drained acoustic tensor. It is only for non-associative flow that unbounded growth may correspond to undrained localization in quasi-static conditions and to flutter under dynamic conditions.

En utilisant une méthode de perturbation linéaire, on montre qu'en conditions quasi-statiques la croissance illimitée de perturbations correspond exactement aux conditions de localisation en conditions drainées ou non drainées. Lorsque l'on prend en compte les effets d'inertie, elle correspond soit à l'émergence de discontinuités stationnaires ou à l'apparition du phénomène de balancement (flutter) pour les ondes d'acceleration. Pour un écoulement associé, sa première apparition correspond toujours à la singularité du tenseur acoustique drainé. Un écoulement non-associé est nécessaire pour qu'elle apparaisse en premier à la singularité du tenseur acoustique non-drainé (quasi-statique) ou à l'apparition du balancement (dynamique).

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DOI: 10.1016/S1631-0721(02)01465-1
Keywords: porous media, plasticity, perturbation, localization, static, dynamic
Mot clés : milieux poreux, élasto-plasticité, perturbation, localisation, statique, dynamique

Ahmed Benallal 1; Claudia Comi 2

1 Laboratoire de mécanique et technologie, ENS de Cachan/CNRS/Université Paris 6, 61, avenue du Président Wilson, 94235 Cachan, France
2 Department of Structural Engineering, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy
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Ahmed Benallal; Claudia Comi. Quasi-static versus dynamic failure instabilities in fluid-saturated porous media. Comptes Rendus. Mécanique, Volume 330 (2002) no. 5, pp. 339-345. doi : 10.1016/S1631-0721(02)01465-1. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01465-1/

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