A novel implementation method of GZZ-based constitutive model into FLAC3D

The Generalized Zhang and Zhu (GZZ) strength criterion is one of the three-dimensional criteria suggested by the International Society for Rock Mechanics and Rock Engineering (ISRM), and it has been widely used and validated. However, the shape of GZZ criterion is non-convex and non-smooth on the π-plane, limiting its implementation into the numerical software. To overcome this limitation, many modified GZZ criteria were proposed to improve the smoothness. Alternatively, a novel approximate numerical implementation method is performed in the mean stress-shear stress–Lode angle space (σm-J2-θσ) in this paper. It avoids the restriction of yield surface/criterion convexity and smoothness in the principal stress space. Then, a new GZZ-based constitutive model is proposed and implemented into FLAC3D. Moreover, the linearization of the nonlinear GZZ criterion according to the current stress level is used, and this can avoid iteration and greatly improve the computational efficiency. The proposed model is subsequently validated via experimental data, analytical solutions and field data. All results reveal that the proposed model can reproduce various mechanical behaviors of rocks, including nonlinear strength characteristics, dilation behavior and strain-softening behavior. Furthermore, the model can effectively capture the stress redistribution and deformation of rocks induced by tunneling. Therefore, the proposed implementation method of non-convex yield surface/criterion is feasible and able to achieve sufficient calculation accuracy, which provides another possible implementation choice for other yield surfaces/criteria.