FINITE ELEMENT LIMIT ANALYSIS OF REINFORCED SOILS BY THE STATIC THEOREM

Resumo

Two finite element formulations for the lower bound limit analysis of reinforced soil structures in plane strain are described. The material idealization is based on the idea that,from a macroscopic point of view, reinforced soil can be treated as a homogeneous material with anisotropic properties. The overall behavior of the reinforced soil is controlled by the mechanical properties of the soil and the reinforcement, as well as their relative proportions and geometrical arrangement. One element satisfies the equilibrium equation, for a constant body force, and the mechanical boundary condition, for prescribed traction with linearly distributed components, in a strict pointwise sense. The other element satisfies the equilibrium equation and the mechanical boundary condition only in a weak sense. The equilibrium equation, the mechanical boundary condition and the linearized yield criterion, expressed in terms of nodal stresses, are dealt with as constraints of a linear optimization problem whose objective function is defined by the loading. Examples are given to illustrate the effectiveness of the proposed procedures for computing lower bounds on the collapse load of reinforced soil structures.