Implementation of Bounding Surface Model into ABAQUS and Its Application to Wellbore Stability Analysis

Abstract:

The critical state concept based bounding surface model is one of the most widely used elastoplastic constitutive models for geomaterials, attributed mainly to its essential feature of allowing plastic deformation to occur for stress points within the bounding surface and thus the capability to represent the realistic non-recoverable behaviour of soils and rocks observed under the cyclic loading. This paper develops an implicit integration algorithm for the bounding surface model, using the standard return mapping approach (elastic predictor-plastic corrector), to obtain the updated stresses for the given strain increments. The formulation of the constitutive integration requires the derivation of a supplementary differential equation to describe the evolution of a key variable, i.e., the ratio between the image stress and the current stress quantities. It is essentially an extension of the integration scheme presented in an earlier work used for the simple bounding surface version of modified Cam Clay associated with a substantially simplified hardening rule. The integration algorithm for the bounding surface model is implemented into the finite element analysis commercial program, ABAQUS, through the material interface of UMAT (user defined material subroutine), and then used for the analysis of wellbore stability problem. The predictions from the ABAQUS simulations are generally in excellent agreement with the available analytical solutions, thus demonstrating the accuracy and robustness of the proposed integration scheme.