A finite element implementation of the strain-softening model based on the Hoek-Brown criterion

A finite element method to model the Hoek-Brown (H-B) criterion with the strain-softening behavior is presented. Firstly, the reasonability of the current brittle-plastic calculation methods is analyzed. It is found that the plastic potential theory based on the Il'yushin's postulation can correctly capture different types of rock failure, while the methods based on the deviator stress dropping or the constant minor principal stress in the brittle-plastic process both have shortcomings. Then, with respect to the H-B criterion, the brittle-plastic implicit constitutive integration algorithm based on the plastic potential theory is deduced, while the elastic-perfectly plastic implicit constitutive integration algorithm is also presented. With a series of stress dropping and perfectly plastic flow, the strain-softening model is embedded in the program ABAQUS. It is validated by comparing the finite element calculations of the displacement curve and the stress distribution in the surrounding rock mass with strain-softening behavior of a circular tunnel with analytical solutions, showing good agreement between them. Finally, the calculation results of a diversion tunnel with thin rock overburden under high internal water pressure show that the proposed model has great advantages over the elastic-perfectly plastic model in predicting the instability failure caused by plastic run-through on the top of the tunnel, providing a reference for further lining design. © 2020, Engineering Mechanics Press. All right reserved.