Return mapping scheme for the Hoek-Brown model with tension cut-off

Abstract

The present paper revisits a stress update procedure for the Hoek-Brown plasticity model enhanced by a Rankine type of tension cut-off failure criterion. Limiting tensile stresses not only supports the behavior of weak rock masses with a very low tensile strength but in combination with the original Hoek-Brown model improves robustness of the stress update procedure, i.e. the stress return mapping algorithm. Herein, the primary focus is on the stress return from a space of inadmissible trial stresses for which neither the Hoek-Brown yield surface nor its derivative can be evaluated. All potential scenarios are thoroughly discussed both in the framework of single- and multi-surface plasticity. The presented procedures were implemented and verified with the help of the Geo5 FEM software.

Keywords

• Hoek-Brown criterion
• Rankine criterion
• nonlinear yield function
• rock mechanics
• finite element method
• tension cut-off