A Multi Plane Model for Natural Anisotropy of Sand

Anisotropy of sand is mainly due to the geometrical arrangement of particles that depends on the orientation of applied load respect to the bedding plane. It is geologically due to micro-fabric created by the arrangement of the particles configured during deposition. Most of the models develop using stress/strain invariants are not capable of identifying this kind of anisotropy. This is mainly because stress/strain invariants are quantities not capable of carrying directional information with them selves. The main objective of this paper is to outline a methodology for modeling the elastic-plastic behaviour of an inherently anisotropy arising from certain kind of plane of deposition. The constitutive equations of the model are derived within the context of elastic behaviour of the whole medium and plastic sliding of interfaces of predefined multi-planes, following the framework of working with six stress/strain components and not missing the directional effects. The formulation incorporates explicity the notion of the preferred direction, which defines the orientation of the material fabric. The proposed multi-plane based model is capable of predicting the behaviour of soils on the basis of plastic sliding mechanisms, elastic behaviour of particles and possibilities to see the micro-fabric effects as natural anisotropy as well as induced anisotropy in plasticity. The model is capable of predicting the behaviour of soil under different orientation of bedding plane, history of strain progression stress and strain axes and induced anisotropy are include in a rational way without any additional hypotheses. The spatial strength distribution at a an approximation of probable mobilized sliding mechanism is proposed as a ellipsoid function built up on bedding plane.