Abstract: The critical state model for sand is capable of describing the stress-strain relationships over a range of densities and stress levels, as well as the feature of dilatancy. Considering that the soil is generally under true triaxial stress condition in practical engineering problems, the extension of the state-dependent model in the multi-axial stress space will be taken into account in this paper. The iteration scheme for the implicit integration algorithm is formulated in the three-invariant plasticity model platform. With this algorithm programed into the user subroutines, Vumat, the constitutive model is implemented into the finite element analysis based on ABAQUS. Through the Explicit procedure, the sand element tests with different relative densities are simulated first. Then the bearing capacity of circle and strip foundation is analyzed subsequently. The calculated results show that this algorithm is converged and robust, as well as being potential to deal with large-scale boundary value problems.

Key words: fully implicit integration algorithm, state-dependent constitutive model, elasto-plastic theory