Critical state model for structured soil

Structure is an evident determinant for macroscopic behaviors of soils.However,this is not taken into account in most constitutive models,as structure is a rather complex issue in models.For this,it is important to develop and implement simple models that can reflect this important aspect of soil behavior.This paper tried to model structured soils based on well-established concepts,such as critical state and sub-loading.Critical state is the core of the classic Cam Clay model.The sub-loading concept implies adoption of an inner(sub-loading)yield surface,according to specific hardening rules for some internal strain-like state variables.Nakai and co-workers proposed such internal variables for controlling density(p)and structure(ω),using a modified stress space,called tij.Herein,similar variables are used in the context of the better-known invariants(p and q)of the Cam Clay model.This change requires explicit adoption of a non-associated flow rule for the sub-loading surface.This is accomplished by modifying the dilatancy ratio of the Cam Clay model,as a function of the new internal variables.These modifications are described and implemented under three-dimensional(3D)conditions.The model is then applied to simulating laboratory tests under different stress paths and the results are compared to experiments reported for different types of structured soils.The good agreements show the capacity and potential of the proposed model.