Spatial Vibration Characteristics and Damage Identification of Toppling Dangerous Rock Mass - Chen ZHAO; Mowen XIE; Yan DU; Zhengjun HUANG; Zheng HE; Guang LU (工程科学与技术)
Objective Currently, most studies on kinetic indices that reflect the damage of dangerous rock masses analyze the vibration characteristics in a single direction. Identifying the damage is challenging when the direction of structural plane evolution is difficult to determine or when the direction of evolution is multidirectional. This study aims to develop a high sensitivity index that can reflect the spatial three-dimensional damage evolution process of the dangerous rock mass. It investigates the spatial vibration characteristics of the damage evolution process, proposing a particle trajectory time-domain dynamics index with heightened sensitivity to the damage of the dangerous rock mass structural plane in various directions of damage evolution.Methods Dangerous rock mass is regarded as a three-dimensional entity. The vibration characteristics of the toppling dangerous rock mass are analyzed through numerical simulations, and formulas for calculating the amplitude and natural frequency of horizontal and vertical shimmy are derived based on the spring-proton shimmy model. The sensitivity of different vibration modes is related to the direction of structural plane evolution. The unidirectional dynamics index sensitivity is determined by the dominant vibration type in this direction, controlling the index sensitivity by the evolution direction of the structural plane. The index sensitivity is highest when the monitoring direction aligns with the normal and evolution directions of the structural plane, and it is lowest for the kinetic indices in the vertical direction to the structural plane evolution direction. Particle trajectory is applied to the damage identification of dangerous rock mass, and the spatial position during vibration is represented by a three-dimensional vector. The three-dimensional data are standardized and synthesized into one dimension, and the time-domain dynamic index algorithm of particle trajectory is defined. Finally, a collapse-similar model test is designed. Using a limestone dangerous rock mass sample, a rock similar material is configured and cast to form a toppling dangerous rock mass similar model. The damage evolution of the structural plane is simulated by deepening the trailing edge fissure through manual cutting, and the three-dimensional vibration data are recorded under two different cutting modes (vertical and oblique cutting). The change rule of the one-direction time-frequency kinetic index and particle trajectory time-domain kinetic index in the evolution process of dangerous rock mass is analyzed.Results and Discussions When comparing the vibration time course curves at the same scale, the X and Z-direction curves gradually thicken with increased cutting depth, indicating that the vibration amplitude of the dangerous rock mass increases. Conversely, the Y-direction curve does not exhibit any notable change. The standard deviation of the vibration amplitude and the kurtosis index increase significantly with the progression of damage in the dangerous rock mass, showing a strong correlation with this damage. During vertical cutting, the relative changes in the kurtosis indices for the X, Y, and Z-directions are 55.66, 2.34, and 8.63, respectively. The kurtosis indices in the X and Z-directions increase exponentially with the deepening of the cracks, whereas the Y-direction shows only a slight fluctuation. The relative changes in the indices for the X, Y, and Z-directions are 0.21, 0.02, and 0.21, respectively. The change in the main frequency in the Y-direction is much smaller than in the X and Z-directions, indicating a considerable difference in the sensitivity of the main frequency among the different directions. The sensitivity of different directions to the main frequency is much smaller than X and Z-directions. The unidirectional kinetic indices are strongly correlated with the damage evolution of the structural plane and show directional differences in the damage sensitivity of the dangerous rock mass. The maximum difference in the sensitivity of the indices across different directions can range from 2.50 to 23.79 times. When the structural plane evolves obliquely along the Y–Z direction, the relative changes in the standard deviation of the Y-direction amplitude and the kurtosis index are 0.57 and 6.45, respectively. The sensitivity of the Y-direction index increases due to the simultaneous decrease in the Y–Z direction constraints during oblique cutting. The time-domain indices of the particle trajectories of the dangerous rock mass under the two cutting methods have been calculated. In Test 1, the standard deviation of the particle trajectory and the kurtosis index shows a clear positive correlation with the damage of the structural plane, with the index increasing faster as the damage deepens. The relative changes in the standard deviation of the particle trajectory and the kurtosis index are 2.85 and 8.62, respectively, while in Test 2, these changes are 2.12 and 68.50.Conclusions The particle trajectory dynamics indices are highly sensitive to the damage of the structural plane of the dangerous rock mass when evolving in different directions. The sensitivity of the particle trajectory index is significantly higher than that of the non-sensitive direction time-domain index, effectively addressing the issue that the unidirectional dynamics index is only sensitive to a specific evolution direction of the structural plane. This characteristic makes it suitable for the damage identification of dangerous rock masses, especially when it is challenging to determine the evolution direction of the structural plane or when the direction is multidirectional.