Dispersion Relation and Dynamic Properties of Pendulum-Type Waves Caused by Low-Frequency Vibrations in Blocky Rock Masses with Complex Block-Hierarchical Structures.

Purpose: This article concentrates on the block-hierarchical structures of rock masses and investigates the dynamic problem and dispersion relation of pendulum-type waves caused by the low-frequency vibrations of rock blocks in blocky rock masses, and determines the effect of block-hierarchical structures. Methods: The blocky rock masses composed of granite blocks and rubber interlayers are simplified into the block–spring model and the wave motion model. Based on Bloch theorem and d'Alembert's principle, the dispersion relation and equations of motion of blocky rock masses with complex block-hierarchical structures are determined, respectively. Conclusion: With the increase of the rock size and geomechanical invariant, the initial frequency of the first attenuation zone gradually decreases, and only the low-frequency waves lower than that frequency can propagate in the blocky rock masses, which reveals the mechanism of low-frequency characteristics of pendulum-type waves theoretically. Research on the two models with different block-hierarchical structures indicates that the equivalent substitution of the two models is not universal and unconditional. The larger the stiffness ratio, or the higher the order of block-hierarchical structures, the smaller is the effect of ignoring the high-order hierarchical structures. Applications: The research will be of interest to a wide range of experts in the fields of stress wave propagation, earthquake engineering and rock bursts, as well as those working to reduce the engineering vibrations of underground structures and process monitored wave packet data for structures. [ABSTRACT FROM AUTHOR]