Dynamic Stability and Fuzzy Reliability Analysis of Toppling Perilous Rock Under Seismic Excitation

To predict the occurrence of the collapse disaster in toppling perilous rock under the action of bidirectional earthquakes, the dynamic stability and fuzzy reliability calculation method of toppling perilous rock under the action of bidirectional earthquakes is proposed. First, the mass viscoelasticity model is used to simulate two main control surfaces of toppling perilous rock, the seismic dynamic response model and motion equation of toppling perilous rock are established based on the D’Alembert principle, and the Newmark-β method is used to solve the dynamic motion equation. Then, the instability event of toppling perilous rock is considered a fuzzy event, the membership function expression of the stability coefficient of toppling perilous rock is determined based on the fuzzy failure criterion, the calculation equations of the toppling perilous rock dynamic stability coefficient and fuzzy reliability are established, and the fuzzy reliability evaluation method based on the probability distribution of reliability is proposed. Finally, the influence of different superposition modes of seismic excitation on the fuzzy reliability of toppling perilous rock is analyzed. The calculation results of toppling perilous rock in the engineering case show that the fuzzy reliability calculated after considering the fuzzy failure criterion is reduced by 10.73% to 25.66% compared with the classical reliability. Considering the bidirectional seismic excitation, the fuzzy reliability of toppling perilous rock is reduced by 5.46% to 14.89%. Compared with using the acceleration peak time encounter mode to superpose the seismic excitation, the fuzzy reliability of toppling perilous rock is reduced by 3.4% when the maximum action effect time encounter mode is adopted.