Dynamic response analysis of coal rock system based on time varying principle

Coal mine rockburst is a rock dynamic disaster caused by instability of coal rock system. In order to further explore the mechanism of rockburst, based on the dynamic time-varying characteristics of rockburst, from the perspective of dynamic system, combined with the principle of time-varying mechanics, the parameters of the coal and rock specimen-testing machine system, roof-pillar system and roadway surrounding rock system were identified. The variation laws of system parameters under the influence of three different time-varying types of external disturbance, internal parameter and external load were obtained, and the dynamic equation of coal-rock time-varying system was established, which proved that the rockburst caused by instability of coal-rock system is a time-varying problem. The time-varying characteristics of different coal-rock systems were further analyzed, and the discriminant methods of time-varying system satisfying superposition, homogeneity, controllability and observability were obtained. The stability of coal-rock time-varying system was analyzed based on Lyapunov stability theory. The disturbed state of stable and unstable coal-rock time-varying system was analyzed by freezing coefficient method combined with engineering background. The results show that the displacement and velocity response of the system show a trend of attenuation vibration and finally reach a gradually stable state when simple harmonic disturbance is applied to a stable time-varying system. Because of the time-varying internal parameters, the stable coal-rock system can evolve from a stable system to an unstable coal-rock system. Under the simple harmonic disturbance, the system response enlarges continuously until the system destabilizes and causes rockburst. The problem of time-varying boundary of coal-rock system is further analyzed, and the time-varying law of system stability of three subsystems of the surrounding rock elastic zone, plastic zone and fracture zone under the boundary are obtained. The time-varying mechanics principle is applied to the field of rockburst, and a simple criterion of rock burst ground pressure caused by instability of coal-rock system is put forward.