Formulation and implementation of an isotropic plasticity model enriched with shift stress and fractional flow rule

Clay and sand were often treated as two different materials that required respective constitutive models to capture the state-dependent nonassociated responses. This study developed a three-dimensional isotropic plasticity model for clay with different over-consolidation ratios (OCRs) and sand with particle breakage, through adopting shift stress-enriched loading/bounding surface, fractional flow rule and flexible critical state line, in the transformed stress space. The model was implemented in Abaqus through UMAT subroutine with an explicit adaptive substepping integration algorithm. Validation against a series of element tests on clay and sand showed that the unified model can well reproduce the stress–strain and critical state behavior of clay and sand. To further demonstrate the capability of the model, two typical boundary value problems, i.e., shear band and ground settlement, were simulated. It was found that as the shear band initiated, higher shear strain and dilatancy were accumulated within the shear band, whereas dilatancy outside the shear band ceased soon with further shearing. Ground settlement and the associated excess pore water pressure at the same consolidation time decreased with the increasing OCR, which agreed well with other studies. The simulation performances verified the capability of the unified model in resolving practical engineering problems.