Rock Mechanics and Rock Engineering

, Volume 52, Issue 11, pp 4457–4473 | Cite as

Natural Frequency Characteristics of Rock Masses Containing a Complex Geological Structure and Their Effects on the Dynamic Stability of Slopes

  • Danqing Song
  • Ailan CheEmail author
  • Renjie Zhu
  • Xiurun Ge
Original Paper


The seismic failure of rock slopes is commonly a cumulative damage process; in particular, local slope damage usually occurs before the occurrence of landslides. The local damage in rock slopes is often caused by the high-frequency components of the waves. Special attention should be paid to the relationship between the local damage and the dynamic failure of landslides, which is of great significance to the study of the cumulative failure evolution of landslides. Based on a numerical modal analysis and dynamic characteristics determined using shaking-table tests, the relationship between the local damage and the dynamic failure of a rock slope with discontinuous joints and its failure mechanism is investigated in the frequency domain. The modal analysis clarifies the natural frequencies and vibration modes of the slope. The tests investigate the effects of the natural frequencies on the slope dynamic characteristics. The numerical and test results show that the high- and low-frequency components mainly induce local and overall deformation of the surface slope, respectively. The analyses of the peak Fourier spectrum amplitude (PFSA) suggest that the dynamic failure process of the slope includes a local damage stage (< 0.297 g) and an overall failure stage (> 0.297 g). The high-frequency components play a major role in the slope cumulative deformation process, and the low-frequency components determine the failure mode of the landslide. The local damage induced by high-frequency components first occurs and progressively develops; then, when the damage is accumulated to a certain extent, the surface slope fails because of the low-frequency components.


Dynamic stability Rock slope Complex geological structure Natural frequency Modal analysis Shaking-table tests 

List of Symbols

Roman Alphabet


Stiffness matrix


Mass matrix


Relative displacement


Displacement vector


Acceleration vector


Shear modulus


Physical dimension


Elasticity modulus




Cohesive force




Gravitational acceleration








Similarity ratio of the acceleration


Similarity ratio of the cohesive force


Similarity ratio of the elasticity modulus


Similarity ratio of the frequency


Similarity ratio of the physical dimension


Similarity ratio of the displacement


Similarity ratio of the time


Similarity ratio of the velocity

Greek Symbols








Poisson’s ratio


Internal fraction angle


Damping ration


Dimensionless item


i-th Natural circular frequency


Similarity ratio of Poisson’s ratio


Similarity ratio of the stress


Similarity ratio of the density


Similarity ratio of the internal fraction angle


Similarity ratio of the strain



This work is supported by the National Key R&D Program of China (2018YFC1504504). The authors would like to express their gratitude to the Key Laboratory of Loess Earthquake Engineering, CEA Gansu Province, for their helpful advice.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Danqing Song
    • 1
  • Ailan Che
    • 1
    Email author
  • Renjie Zhu
    • 1
  • Xiurun Ge
    • 1
  1. 1.School of Naval ArchitectureOcean and Civil Engineering, Shanghai Jiao Tong UniversityShanghaiChina

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