A Study on Modelling the Plane Strain Behaviour of Sand and its Stability

The plane strain behaviour of sand is studied using, previously proposed, incremental model describing its pre-failure deformations. Original model has been formulated for the tri-axial configuration, and then generalized for 3D conditions. This 3D model was subsequently adapted to study deformations of sand in the plane strain conditions, in the x1, x3 plane. There are three unknowns in such a configuration, namely the principal strains ε1 , ε3 and the principal stress σ2. Respective equations were derived, and then applied to study deformations of sand for chosen stress paths. The governing incremental equations were integrated numerically, and it was shown, for some loading paths, that σ2 depends linearly on the other principal stresses, so introduction of apparent Poisson's ratio is justified, as a kind of approximation. Subsequent analysis of deformations of sand was performed using this concept, as well as using full system of governing equations.