Frequency response characteristics and failure model of single-layered thin plate rock mass under dynamic loading

In underground engineering, disturbance of dynamic load can change layered rock mass stress state and induce accidents. Traditional elastic mechanics can’t effectively solve the complex deformation problem. However, Hamiltonian mechanics system can overcome this problem. Dual variables are introduced in symplectic space to solve the deflection equations of single-layered thin plate rock mass. Comparing vibration parameters, it’s found the 1st, 5th and 6th order are effective vibration modes. The resonance characteristics of thin plate are obtained with three dynamic loads. It’s found the thin plate is most likely to resonate and damage due to the smallest resonance frequency interval and the largest vibration amplitude by impact wave and rectangular wave respectively. Then, the vibration mode of multi-layered rock mass is analyzed through Multiple Reference Impact Testing. The failure of fine sandstone is caused by the resonance of effective vibration modes by hammer excitation. Finally, the failure mechanism of thin plate is obtained by the failure theory and LS-DYNA. It’s found the four sides and corners suffer tensile shear failure and shear failure respectively. When tensile failure occurs in central, the main crack and secondary crack propagate along long axis and short axis to form “O- 十 ” failure mode.