Cosserat's theory for granular materials under plane strain conditions of deformation is presented. The constitutive equations discussed are a generalization of the j2 deformation theory of plasticity for frictional materials with internal constraint. Shear band formation is treated as a bifurcation problem and predictions about the state of bifurcation, the shear band orientation and the evolution of its thickness are made. The theoretical predictions are tested against experimental results from biaxial tests on sand specimens. Dans cet article on présente une théorie de Cosserat pour des matériaux pulvérulents soumis à des déformations planes. Les équations rhéologiques proposées représentent une généralization de la théorie de la deformation J2 pour les matériaux à frottement interne avec contraintes internes. La formation de bandes de cisaillement y est traitée comme étant un probléme de bifurcation et on y fait des prédictions à propos de l'état de bifurcation, de l'orientation de la bande de cisaillement et de l'évolution de son épaisseur. Les prédictions basées sur la théorie sont comparées à des résultats expérimentaux obtenus dans des essais biaxiaux avec des échantillons de sable.

[1] The catastrophic Vaiont landslide (Southern Alps, Italy) of 9 October 1963 moved 2.7 Â 10 8 m 3 of rock that collapsed in an artificial lake, causing a giant wave that killed 1917 people. The landslide was preceded by 2-3 years of creep that ended with the final collapse of the rock mass slipping at about 30 m s À1 . Assuming that creep was localized in a clay-rich water-saturated layer, in this study we propose shear heating as the primary mechanism for the long-term phase of accelerating creep. We study only the creeping phase of the slide, and we model this phase using a rigid block moving over a thin zone of high shear strain rates. Introducing a thermal softening and velocity strengthening law for the basal material, we reformulate the governing equations of a water-saturated porous material, obtaining an estimate for the collapse time of the slide. Our model is calibrated upon real velocity measurements from the Vaiont landslide and provides an estimation of the critical time of failure up to 169 days before the collapse. We also show that the slide became critical $21 days before the collapse, when shear heating started localizing in the clay-rich layer, inducing a tendency for slip localization and thermal runaway instability in a plane. The total loss of strength in the slipping zone during the last minutes prior to the slide is explained by the onset of thermal pressurization, triggered by the temperature rise within the clay-rich layer.

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SUMMARYThe spontaneous shear band formation in the biaxial test on dry sand samples with constant cell pressure is treated as a bifurcation problem. The constitutive response of sand is described in terms of mobilized friction and dilatancy. Dilatancy is looked upon as an internal constraint and the hardening rule is expressed in terms of an adequate dimensionless stress measure. Owing to fail of normality in sand, localization always occurs in the hardening regime. The theoretical solution of the shear band inclination is a geometrical mean of the classical Coulomb and Roscoe solutions and is in good agreement with the experimental data. The incipient shear modulus is proportional to the stress level and can be estimated to be also proportional to the secant modulus.

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