Keywords: reinforced soils, plasticity, multiphase model, finite element method, micropolar continuum, piled raft foundation.

The use of reinforcing inclusions in order to enhance the stability or improve the performance of geotechnical structures under working conditions, has been widely developed for several decades in the field of geotechnical engineering: soils reinforced by continuous threads, reinforced earth, soil nailing or piled raft foundations may be quoted among the most popular techniques. In most cases, the reinforcing inclusions take the form of linear structural elements (polymeric or metal strips, steel bars, metal or concrete piles) placed into the soil mass following a regular distribution and one or several preferential orientations. The so-obtained composite soil structure exhibits a strong heterogeneity, which leads to intractable, or at least computational time-consuming difficulties, when trying to simulate the response of this kind of structure numerically, by means for instance of finite element techniques.

As an alternative approach, a so-called multiphase description of reinforced soil structures has been recently proposed, in which the soil mass and reinforcement network are treated as mutually interacting superposed homogeneous continua [1]. The numerical implementation of such a multiphase model leads to a considerably shorter computational time than the use of a direct simulation. Indeed, the latter requires a highly refined mesh discretization of the structure, due to the small spacing between two neighboring inclusions as compared with the overall dimensions of the problem, in conjunction with the sharp contrast between the soil and reinforcing material in terms of stiffness and strength properties.

As regards some applications, such as reinforced earth or even soil nailing, in which "flexible" inclusions are used, a simplified version of this multiphase model, where only axial forces in the reinforcements are taken into account, remains sufficient [1]. On the contrary in the case of a reinforcement by "rigid" inclusions, which is for instance the case of piled raft foundations, a more elaborate version of this model should be proposed, where shear and bending effects are accounted for, through an idealization of the inclusions as 1D-beams continuously distributed throughout the matrix [2].

The present contribution is devoted to the extension of the latter model to the context of elastoplasticity, the behavior of each phase being characterized by its elastic and plastic properties. Thus, the matrix phase is given the same elastic (Young's modulus and Poisson's ratio) and yield (cohesion and internal friction angle) characteristics as the soil, with a corresponding associated plastic flow rule. As concerns the reinforcement phase, described as an oriented micropolar continuum, it appears that the elastic parameters to be introduced in the model may be interpreted as the axial, shear and bending stiffnesses of the reinforcements, considered as beams, per unit transverse area. Likewise, the yield criterion is formulated as a condition involving both the axial force and bending moment densities of the reinforcements.

A variational formulation and related finite element implementation of the model has been performed in the particular case when a perfect bonding condition between matrix and reinforcement phases may be assumed so that, restricting for instance the analysis to plane strain problems, three independent kinematic variables (two displacements and one rotation) are attached to each node of the finite element mesh [3].

Several results of the numerical implementation of the model in a finite element code are presented. A comparison between structural stiffnesses is performed on the illustrative example of a piled raft foundation, with a particular emphasis on assessing the influence of shear and bending rigidities on the global response of the structure.

The elastoplasticity of each phase is then treated separately by means of the classical iterative procedure. The numerical tool so obtained is first validated on the illustrative example of a shear loaded layer of reinforced soil, for which an analytical solution is available.

1

Sudret B. "Modélisation multiphasique des ouvrages renforcés par inclusions", PhD thesis, ENPC, Paris, 1999.

2

de Buhan P., Sudret B. "Micropolar multiphase model for materials reinforced by linear inclusions", Eur. J. Mech. A /Solids 19, p. 669-687, 2000. doi:10.1016/S0997-7538(00)00181-9

3

Hassen G. "Mise en oeuvre numérique d'un modèle multiphasique pour le calcul des ouvrages renforcés par inclusions avec prise en compte des effets dus à la flexion et au cisaillement", Master thesis, Paris, 2002.

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