Time-disturbance failure behaviors and fractional-order deterioration constitutive model of rock under true triaxial stresses

Blasting excavation in three-dimensional (3D) high geo-stress underground engineering often induces time-delay catastrophes in the surrounding rock within a certain distance from the working face. While numerous studies explore failure mechanisms and analytical theories under two-dimensional (2D) stress, limited research addresses time-disturbance failures under 3D stress. To better simulate the damage caused by excavation and the subsequent failure triggered by frequent disturbances in deep underground environments, a time-dependent disturbance method under true triaxial conditions was proposed in this study. A series of true triaxial static compression and time-disturbance tests was conducted on gabbro to examine its strength, deformation, failure mechanisms, and precursory characteristics under varying loading scenarios. A novel energy calculation approach was introduced, grounded in the mechanical behavior of gabbro. The total strain energy ( U ) and the elastic strain energy ( U e ) increase with higher σ 2 and σ 3 . However, the dissipated strain energy ( U d ) decreases with increasing σ 2 but increases with σ 3 . Under true triaxial time-dependent disturbance, shear failure and rock fragmentation become more pronounced. As time-disturbance failure approaches, the fractal dimension generally first oscillates with a small amplitude, followed by larger-amplitude fluctuations. Utilizing the experimental findings and considering both the time-disturbance damage effect and the 3D stress effect, a fractional-order deterioration model was established to characterize the time-disturbance failure behaviors of rock. This model incorporates fractional-order switching elements reflecting both initial and accelerated deformation responses. This research provides a theoretical foundation for investigating time-disturbance disasters during deep engineering dynamic excavation.