A Modified Critical State Two-surface Plasticity Model for Sand: Theory and Implementation

This paper provides background information and documentation for the implementation of a robust plasticity model as a user-subroutine in the commercial finite difference code, FLAC3D by Itasca. The plasticity model presented is equal to the 3 dimensional critical state two-surface plasticity model for sands by Manzari et al., but uses a modified multi-axial surface formulation based on a versatile shape function prescribing a family of smooth and convex contours in the π-plane. The model is formulated within the framework of critical state soil mechanics and is capable of accurately simulating volumetric and stress-strain behaviour under monotonic and cyclic loading and thereby related observations like accumulation of pore pressure, cyclic mobility and cyclic liquefaction. The plasticity model is implemented with an integration scheme based on the general return mapping algorithm. The integration scheme faces convergence difficulties, primarily at very low mean effective stresses. The convergence problems are addressed by suitable correction strategies designed to add robustness, stability and efficiency to the integration scheme. An outline of all model parameters is given with suggestions for parameter reductions.