Abstract
Unstable rock masses are highly prone to collapse disasters under seismic action. To calculate the stability of toppling-type unstable rocks under bidirectional seismic action and investigate the influence of ground motion randomness on their dynamic fuzzy reliability, this study analyzes the dynamic response of toppling-type unstable rocks through structural dynamics and random process theory. First, based on structural dynamics theory, a mechanical model for seismic dynamic response of toppling-type unstable rocks and its motion equations on two main controlling surfaces are established. The Wilson-q method and pseudo-excitation method are respectively employed to solve these motion equations, establishing calculation methods for dynamic response under deterministic seismic waves and random seismic excitations. Then, based on limit equilibrium theory, the calculation formula for dynamic stability coefficient under deterministic seismic action is derived. Random earthquakes are regarded as stationary random processes, and based on the first-passage failure criterion, the mean and variance of peak seismic force response under random seismic excitation are solved, thereby establishing a calculation method for random dynamic stability. Finally, the instability event of toppling-type unstable rocks is treated as a fuzzy event. A fuzzy failure criterion is introduced and an improved Monte-Carlo method is adopted to calculate the fuzzy reliability of unstable rock masses, establishing a rapid calculation method for dynamic fuzzy reliability and analyzing the influence of ground motion randomness on fuzzy reliability. The proposed method is applied to an engineering case study, with results showing that considering ground motion randomness increases the dynamic stability coefficient and fuzzy reliability of toppling-type unstable rocks by 6.34% and 22.83%, respectively, reducing the failure probability of unstable rock masses. Moreover, the fuzzy reliability calculated using the fuzzy failure criterion is more conservative for engineering safety. Considering the bidirectionality and randomness of ground motion provides a better assessment of the dynamic stability of toppling-type unstable rocks, offering a reference for evaluation of random seismic dynamic stability of unstable rock masses.
Full Text
Preamble
Title: Effects of Randomness of Bidirectional Ground Motion on the Fuzzy Reliability of Toppling Perilous Rock Mass
Authors: Jixu Zhang 1,2,3, Xiaodong Fu 1,2, Linfeng Wang 3,*
Affiliations:
1. State Key Laboratory of Geomechanics and Geotechnical Engineering Safety, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China
2. University of Chinese Academy of Sciences, Beijing 100049, China
3. Key Laboratory of Geological Hazards Mitigation for Mountainous Highway and Waterway, Chongqing Jiaotong University, Chongqing 400074, China
Abstract: Perilous rock masses are highly susceptible to collapse under seismic action. To calculate the stability of toppling perilous rocks under bidirectional earthquake excitation and investigate the influence of ground motion randomness on their dynamic fuzzy reliability, this study analyzes the dynamic response of toppling perilous rocks using structural dynamics and random process theory. First, a mechanical model for seismic dynamic response and equations of motion on two main control surfaces are established based on structural dynamics theory. The Wilson-θ method and pseudo-excitation method are employed to solve these equations, establishing computational methods for dynamic response under deterministic seismic waves and random seismic excitation. Next, based on limit equilibrium theory, the calculation formula for dynamic stability coefficient under deterministic seismic action is derived. Treating random earthquakes as stationary random processes, the mean and variance of peak seismic force response are obtained using the first-passage failure criterion, thereby establishing a computational method for random dynamic stability of perilous rocks. Finally, by treating the instability event as a fuzzy event, a fuzzy failure criterion is introduced and an improved Monte-Carlo method is used to calculate the fuzzy reliability of the rock mass, establishing a rapid computational method for dynamic fuzzy reliability and analyzing the influence of ground motion randomness on fuzzy reliability.
The proposed method is applied to an engineering case study. Results demonstrate that considering ground motion randomness increases the dynamic stability coefficient and fuzzy reliability of toppling perilous rocks by 6.34% and 22.83%, respectively, thereby reducing the failure probability of the rock mass. Furthermore, the fuzzy reliability calculated using the fuzzy failure criterion is more conservative regarding engineering safety. Considering both the bidirectionality and randomness of ground motion provides a better assessment of the dynamic stability of toppling perilous rocks, offering a valuable reference for evaluating the random seismic dynamic stability of perilous rocks.
Keywords: toppling perilous rock; bidirectional random earthquake; Wilson-θ method; pseudo-excitation method; fuzzy reliability