Modeling true three-dimensional creep responses of hard rocks considering the time-dependent damage: A constitutive relationship study

In underground rock engineering, the three-dimensional (3D) stress state governs the time-dependent behavior of surrounding rocks, thereby directly affecting the long-term safety and stability of engineering structures. This study presents a novel true triaxial time-dependent constitutive model that characterizes nonlinear creep behavior governed by coupling of viscoplastic deformation and time-dependent damage. The model advances the 3D Hoek-Brown yield function by incorporating the azimuthal orientation of cracks. The coupled model is implemented using a numerical procedure that features an explicit nonlinear integration algorithm for updating the time-dependent damage factor. The model's effectiveness is validated by its accurate prediction of true triaxial creep test results for Jinping marble. The comprehensive constitutive model advances continuum damage mechanics, providing a scientific basis for analyzing and evaluating the long-term safety and stability of deep hard rock engineering.