SUMMARYThe ultimate bearing capacity problem of a strip foundation resting on a soil reinforced by a group of regularly spaced columns is investigated in the situation when both the native soil and reinforcing material are purely cohesive. Making use of the yield design homogenization approach, it is shown that such a problem may be dealt with as a plane strain yield design problem, provided that the reinforced soil macroscopic strength condition has been previously determined. Lower and upper bound estimates for such a macroscopic criterion are obtained, thus giving evidence of the reinforced soil strong anisotropy. Performing the upper bound kinematic approach on the homogenized bearing capacity problem, by using the classical Prandtl's failure mechanism, makes it then possible to derive analytical upper bound estimates for the reinforced foundation bearing capacity, as a function of the reinforced soil parameters (volume fraction and cohesion ratio), as well as of the relative extension of the reinforced area. It is shown in particular that such an estimate is closer to the exact value of the ultimate bearing capacity, than that derived from a direct analysis which implicitly assumes that the reinforced soil is an isotropic material.
SUMMARYThe design against failure of an embankment resting upon a soft soil improved by a group of columns is investigated with the help of the yield design homogenization approach. Assuming that both constituents of the reinforced ground are purely cohesive materials ('lime column' technique), an upper bound estimate for the macroscopic strength condition of the reinforced soil as a homogenized medium is first obtained, providing definite evidence of a shear strength anisotropy associated with the reinforcement preferential orientation. The kinematic method of yield design is then performed on the basis of such a criterion, making use of rotational failure mechanisms involving slip circles in the reinforced ground. Upper bound estimates are finally obtained for the embankment stability factor, as functions of the degree of reinforcement and relative thickness of the soil layer. These results are compared with those derived from a simplified analysis, where the reinforced soil is assumed to exhibit an averaged isotropic cohesion. This comparison clearly indicates that the latter simplified analysis may produce quite unsafe estimates for the embankment stability, which can be attributed to the fact that it fails to capture the inherent strength anisotropy of the reinforced soil.
Dans le présent article, on étudie la détermination de la capacité portante ultime d'une fondation rigide posée sur un sol, de cohésion C 2 , de poids volumique J et d'angle de frottement I , renforcé par une tranchée constituée d'un matériau de caractéristiques C 1 , J et I Ces matériaux sont supposés homogènes, isotropes et leur résistance obéit au critère de Coulomb du type « courbe intrinsèque » en déformation plane. La mise en oeuvre de l'approche cinématique de la théorie du calcul à la rupture en considérant le mécanisme de ruine du type « Prandtl » conduit à l'expression d'une borne supérieure de la capacité portante ultime exprimée en termes de facteurs de portance. A partir de ce résultat établi analytiquement pour tous les cas de renforcement, on identifie les caractéristiques mécaniques du matériau constitutif de la tranchée permettant l'augmentation de la capacité portante ultime du sol à renforcer.ABSTRACT. This contribution deals with the ultimate bearing capacity determination for a rigid foundation resting on a soil reinforced by a trench. The soil and the reinforcing material, being homogeneous and isotropic, are characterized by a plane strain Coulomb's strength criterion with respective cohesion, friction angle and unit weight C 2 , J I and C 1 , J , I Based on the kinematic approach of yield design theory, using Prandtl's mechanism an upper bound of the ultimate bearing capacity is established analytically for all reinforcement cases. Therefore, the mechanical characteristics of the trench material are identified from which the reinforcement occurs.MOTS-CLÉS : déformation plane, approche cinématique, mécanisme, capacité portante, pesanteur, renforcement, tranchée, critère de résistance.
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