Experimental study on spatial vibration characteristics and early damage detection of unstable rock mass

Most studies on vibration-based inversion of unstable rock mass damage focus on unidirectional vibrations along the normal direction of crack degradation, while the three-dimensional vibration characteristics of unstable rock masses remain largely unexplored. To investigate the evolution of spatial vibration features during structural plane degradation and to identify highly sensitive indicators reflecting the spatial damage progression of unstable rock masses, this study takes toppling-type unstable rock masses as the research object. A simplified dynamic model is employed to derive the variation characteristics of dynamic indicators during the degradation of structural planes. It is found that unidirectional dynamic indicators—such as natural frequency and peak amplitude—exhibit strong directional dependence in their sensitivity to structural damage, limiting their effectiveness in identifying multidirectional deterioration. To address this issue, spatial motion trajectories are utilized for damage identification, and a three-dimensional approximate entropy (ApEn3D) algorithm is proposed to quantitatively characterize spatial motion states. A collapse-simulating experiment was conducted to compare the evolution of dominant frequency and ApEn3D during the progressive failure of unstable rock masses. The results reveal that ApEn3D is negatively correlated with structural plane damage. As cracks deepen, anisotropic vibration characteristics show varying degrees of dominant frequency reduction, amplitude amplification, and energy concentration. The sensitivity of the dominant frequency to structural damage varies significantly by direction, with up to a 10.5-fold difference observed. In contrast, ApEn3D decreases by 13% and is less influenced by the direction of crack evolution, making it more effective for identifying structural plane degradation in unstable rock masses..