Investigation of the damping characteristics of grouted coal gangue with different particle gradations under multistage triaxial cyclic loading

Understanding and optimizing the damping behavior of grouted coal gangue under complex cyclic stress conditions is of significant importance for guiding grouting design, improving mine safety, and enhancing the long-term durability of engineering structures. Triaxial multistage cyclic tests were conducted on artificial specimens with varying confining pressures and particle gradations to elucidate the evolution of damping in grouted coal gangue under cyclic loading. The stress and strain response, as well as the variation of dynamic shear modulus, damping ratio, and damping coefficient with the number of loading cycles, were investigated. The results indicate that the grouted coal gangue exhibits a staged loading and steady cyclic response under multistage cyclic loading, with irrecoverable deformation accumulating progressively with increasing stress levels. Confining pressure enhances the cyclic stability and dynamic stiffness of the specimens by suppressing crack opening and particle slippage, thereby improving skeleton interlocking and load-bearing continuity. Within each stress level, the dynamic shear modulus demonstrates a rapid increase followed by fluctuating evolution trend with cycle number but decreases overall with rising stress. Elastic energy density and energy dissipation density evolve in stages, exhibiting an initial rapid decline followed by gradual attenuation during mid-cycles. The dissipation energy density fluctuating more intensely under high stress levels. The damping ratio and damping coefficient generally decay and converge with increasing cycles and display a negative correlation with the dynamic shear modulus. These findings reveal the coupled effects of confining pressure and particle gradation on the damping characteristics of grouted coal gangue, providing an experimental basis for assessing the stability and fatigue damage of grouted structures under cyclic loads.