Proposition of a general yield function in geomechanics

Siegfried Maïolino

doi:10.1016/j.crme.2004.11.008

Proposition of a general yield function in geomechanics
[Proposition d'une fonction de charge générale en géomécanique]

Présenté par : Jean Salençon

Siegfried Maïolino ^1,²

¹ École polytechnique, laboratoire de mécanique des solides, 91128 Palaiseau cedex, France
² Centre d'études techniques de l'équipement de Lyon, laboratoire régional de Lyon – mécanique des roches, 25, avenue François-Mitterrand, case numéro 1, 69674 Bron cedex, France

Comptes Rendus. Mécanique, Volume 333 (2005) no. 3, pp. 279-284.

Résumé
Abstract

Un critère général lisse et convexe est proposé pour modéliser le comportement particulier des géomatériaux, particulièrement les roches qui possèdent une enveloppe de Mohr linéaire ou parabolique et une forme particulière dans le plan déviatorique. Ces caractéristiques sont définies par deux fonctions : l'équation du critère dans le plan méridien principal et le ratio d'extension. Ces deux fonctions sont intégrées dans une équation garantissant le caractère régulier et convexe de la fonction de charge indépendamment des fonctions caractéristiques. Cette expression est intéressante car elle permet ainsi la constitution directe d'un modèle à partir de tests triaxiaux, en extension et compression. Elle permet également le développement des formes régularisées correspondant au critère de Mohr–Coulomb et au critère de Hœk–Brown ce dernier étant propre à la mécanique des roches.

A general smooth and convex yield function is proposed, able to model the particular behavior of geomaterials, particularly rock materials that are characterized by a linear or parabolic Mohr's envelope, and a particular shape in the deviatoric plane. These characteristics are defined by two functions: the equation of the criterion in the meridian plane and the extension ratio, which are integrated in a general equation ensuring convexity and smoothness of the yield function, whatever the characteristic functions. This expression is interesting, because it allows a straightforward development of a constitutive model based on triaxial tests, in extension and compression. It also allows the development of smooth criteria corresponding to the Mohr–Coulomb criterion and the Hœk–Brown criterion, the latter typical of rock mechanics.

Reçu le : 2004-11-03
Accepté le : 2004-11-09
Publié le : 2005-01-07

DOI : 10.1016/j.crme.2004.11.008

Keywords: Soils, Rocks, Yield function, Criterion, Constitutive model, Hœk–Brown, Mohr–Coulomb
Mots-clés : Sols, Roches, Fonction de charge, Critère, Loi de comportement, Hœk–Brown, Mohr–Coulomb

Affiliations des auteurs :

Siegfried Maïolino ^{1, 2}

¹ École polytechnique, laboratoire de mécanique des solides, 91128 Palaiseau cedex, France
² Centre d'études techniques de l'équipement de Lyon, laboratoire régional de Lyon – mécanique des roches, 25, avenue François-Mitterrand, case numéro 1, 69674 Bron cedex, France

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Siegfried Maïolino. Proposition of a general yield function in geomechanics. Comptes Rendus. Mécanique, Volume 333 (2005) no. 3, pp. 279-284. doi : 10.1016/j.crme.2004.11.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.11.008/

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