Theoretical Research on the Pendulum-type Wave in Nonlinear Block-rock Mass Based on Hyperbolic Elastic Model

Pendulum-type wave is a kind of sign-alternating wave with discontinuous and nonlinear characteristics found in deep rock mass, which is different from the traditional continuum elastic waves. The dynamic engineering disasters such as rockbrusts and anomalously low friction phenomenon occur frequently in surrounding deep level tunnels rock mass, and the study of pendulum-type wave is of great significance for explaining the mechanism and prevention of these engineering disasters. The presence of multiple fractures makes geomaterials nonlinear. Therefore, it is unreasonable to use linear model to study pendulum-type wave in block-rock mass. With the consideration of the nonlinear deformation characteristics of deep rock mass, a nonlinear dynamic model of pendulum-type wave in block-rock mass is established by introducing hyperbolic elastic model of interlayers of geoblocks, and the time-domain characteristics, frequency-domain characteristics and the law of energy transfer are studied. Furthermore, the influence of initial geostress on pendulum-type wave propagation in nonlinear block-rock mass is studied. The research shows that the improved nonlinear model can not only shows the nonlinear deformation of block-rock mass, but also limits the maximum compression deformation of cracks between rock blocks. Under the action of strong impact loading, the acceleration amplitude of blocks far away from the impact point increases significantly, and is the largest, which is not conducive to the structure safety of rock mass. With the increase of impact loading, the frequency response of blocks tends to move to high-frequency domain, and the frequency center increases continuously. Kinetic energy and potential energy are constantly transformed to each other in block-rock mass, and in the free vibration stage, they are in inverse phase, i.e. when the kinetic energy reaches the maximum, the elastic potential energy is the minimum, and vice versa. Relative to the initial geostress, the hyperbolic elastic model can be grouped into three categories: low stress state, high stress state and ultra-high stress state. Under different initial geostress states, the dynamic response of the block-rock mass is very different. With the increase of initial geostress, the displacement amplitude decrease approximately exponentially. In ultra-high stress state, the displacement amplitude of rock blocks decreases by more than 95% compared with that without initial geostress. Therefore, we conclude that in the ultra-high stress state, the pendulum-type wave phenomenon will not occur in block-rock mass, and the wave propagation is close to the longitudinal wave. This paper provides a reference for further study on nonlinear pendulum-type wave in block-rock mass under the conditions of strong impact and high initial geostress.