A thermodynamic damage model for 3D stress-induced mechanical characteristics and brittle–ductile transition of rock

Due to the existence of true three-dimensional high-geostress in deep underground engineering, rock shows different mechanical properties and brittle–ductile behaviours from conventional triaxial stress states, however, the different characteristics of rock are not clear. Therefore, a series of true triaxial tests were performed on deeply buried marble to investigate the effects of σ2 and σ3 on the characteristic strength (peak strength, yield strength and residual strength), post-peak deformation and brittle–ductile behaviour. Based on test results, a three-dimensional elastoplastic damage constitutive model that describes plastic hardening and damage softening of rock was established within the framework of irreversible thermodynamics, and a sensitivity analysis of key parameters (η and ζ) was performed. A method that controls the brittle–ductile behaviour of rock through key parameters η and ζ was studied, and functions of these two parameters with σ2 and σ3 were proposed. The proposed model was implemented numerically with the cutting-plane algorithm in a finite element program. A series of numerical simulation experiments were performed, and numerical simulation and experimental results are consistent. In addition, brittle–ductile transition of marble under untested true triaxial stress levels were reasonably predicted.