Numerical Analysis of Sand Behavior based on Modified Multi-laminate Model

Farzad Peyman, Seyed Amirodin Sadrnejad

Generalized form of multi-laminate integration framework satisfying compatibility of strain/deformation and equilibrium of stress/forces at each material point was employed to sum up the plastic modulus matrices of integrated planes to build up the main modulus matrix. This has been conducted through defining on plane modulus behaviors for normal, tangent and their interactions for loading and unloading. This modulus formulation enables the analysis to include the role of some material behavior aspects in the overall internal plasticity mechanism flexibility for a more accurate description of mechanism behavior under any arbitrary loading conditions. Specification of stress/strain history on the sample planes in materials with the models developed using stress/strain invariants is not feasible. This is mainly because stress/strain invariants are quantities not capable of carrying directional information with themselves.

In this article, a constitutive model capable of predicting sand behavior under static and dynamic loading working with stress and strain invariants was modified and implemented in the multi-laminate framework to be capable of predicting any arbitrary stress path may take place on a sand element in soil structure. The proposed model is capable of presenting different stress/strain histories on the sample planes followed the applied load/deformation paths in soil materials. Model verification under different loading/unloading/reloading stress/strain paths has been examined and failure direction of sand samples was visualized upon the activities of on plane plastic strain values and then exceeding a certain limit, specified as failed plane. This constitutive model can be used to predict the sand behavior upon inherent/induced anisotropy, rotation of principal stress/strain axes, localization of stress/strain and even failure mechanism.