Abstract
To more reasonably evaluate the dynamic stability of rockfall masses under seismic action, a mass viscoelastic model was employed to simulate the two primary controlling surfaces of toppling-type rockfall. Based on the principles of structural dynamics, a dynamic response analysis model and equations of motion for toppling rockfall were established, and a computational method for the dynamic stability coefficient of toppling rockfall was developed using the Newmark-β method. This method was applied to the WY2 rockfall mass developed in a cliff zone at Luoyi Village, Leshan City, Sichuan Province, yielding a dynamic stability coefficient of 1.198, which represents a 10.6% increase compared to the result obtained from the traditional pseudo-static method. Subsequently, acceleration response signals of the rockfall mass in different directions were analyzed using wavelet packet transform. The results indicated that the wavelet packet energy proportion in the low-frequency portion (0.1–18.76 Hz) exceeded 50% in all cases, and the sum of energy proportions E1, E2, and E3 for frequency bands 1 through 3 in the n1 and s2 directions was greater than 95%. This demonstrates that the WY2 rockfall mass first experiences seismic damage in the n1 and s2 directions under bidirectional seismic action, causing the rockfall mass to primarily fail along these two directions. Finally, seismic waves with different PGA values were applied to the rockfall mass, and the marginal spectrum variation patterns of acceleration response signals in different directions were analyzed based on HHT. The results showed that the marginal spectrum amplitude in the n1 direction > that in the s2 direction > that in the s1 direction ≈ that in the n2 direction, with the seismic energy in the n1 and s2 directions being most pronounced for the rockfall mass under seismic loading. Rockfall failure always initiates with seismic damage along these two directions, revealing that the failure mode of this rockfall mass is outward toppling failure, which is consistent with the wavelet packet analysis results. When the PGA exceeds 0.2g, the marginal spectrum peak values of acceleration signals in the n1 and s2 directions increase rapidly, at which point the rockfall mass becomes completely unstable and fails.
Full Text
Preamble
Title: Study on Dynamic Stability and Spectral Characteristics of Toppling Perilous Rock Under Earthquake
Authors: Zhang Jixu¹,²,³, Fu Xiaodong¹,², Wang Linfeng³*
Affiliations:
¹State Key Laboratory of Geomechanics and Geotechnical Engineering Safety, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China
²University of Chinese Academy of Sciences, Beijing 100049, China
³Key Laboratory of Geological Hazards Mitigation for Mountainous Highway and Waterway, Chongqing Jiaotong University, Chongqing 400074, China
Abstract: To more reasonably evaluate the dynamic stability of perilous rock masses under seismic action, this study employs a mass-viscoelastic model to simulate the two primary controlling surfaces of toppling perilous rock. Based on structural dynamics principles, a dynamic response analysis model and equations of motion are established, and a calculation method for the dynamic stability coefficient is developed using the Newmark-β method. This method is applied to the WY2 perilous rock mass developed in a steep cliff zone at Luoyi Village, Leshan City, Sichuan Province, yielding a dynamic stability coefficient of 1.198—representing a 10.6% increase compared with results from the traditional pseudo-static method. Acceleration response signals in different directions are subsequently analyzed using wavelet packet transform, revealing that the wavelet packet energy proportion in the low-frequency range (0.1–18.76 Hz) exceeds 50% in all cases, while the sum of energy proportions E1, E2, and E3 for frequency bands 1–3 in the n1 and s2 directions surpasses 95%. This indicates that under bidirectional earthquake action, seismic damage in the WY2 perilous rock mass initiates first in the n1 and s2 directions, causing failure to develop primarily along these orientations. Finally, seismic waves with different peak ground accelerations (PGA) are applied to analyze marginal spectrum variations of acceleration response signals in different directions using Hilbert-Huang Transform (HHT). The results demonstrate that marginal spectrum amplitudes follow the relationship n1 direction > s2 direction > s1 direction ≈ n2 direction, with seismic energy being most pronounced in the n1 and s2 directions under seismic loading. Damage consistently initiates along these two directions, revealing an outward toppling failure mode for this perilous rock mass that is consistent with wavelet packet analysis results. When PGA exceeds 0.2g, marginal spectrum peaks of acceleration signals in the n1 and s2 directions increase rapidly, indicating complete instability and failure of the perilous rock mass.
Keywords: toppling perilous rock; dynamic stability; Newmark-β method; wavelet packet transform; Hilbert-Huang transform; failure mode