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 σ 2 and σ 3 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 σ 2 and σ 3 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.