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

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Abstract

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.

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Abbreviations

[K]:

Stiffness matrix

[M]:

Mass matrix

U :

Relative displacement

{U}:

Displacement vector

{Ü}:

Acceleration vector

G :

Shear modulus

L :

Physical dimension

E :

Elasticity modulus

a :

Acceleration

c :

Cohesive force

f :

Frequency

g :

Gravitational acceleration

s :

Displacement

t :

Time

v :

Velocity

C a :

Similarity ratio of the acceleration

C c :

Similarity ratio of the cohesive force

C E :

Similarity ratio of the elasticity modulus

C f :

Similarity ratio of the frequency

C L :

Similarity ratio of the physical dimension

C s :

Similarity ratio of the displacement

C t :

Similarity ratio of the time

C v :

Similarity ratio of the velocity

σ :

Stress

ε :

Strain

ρ :

Density

μ :

Poisson’s ratio

φ :

Internal fraction angle

λ :

Damping ration

π :

Dimensionless item

ω i :

i-th Natural circular frequency

C μ :

Similarity ratio of Poisson’s ratio

C σ :

Similarity ratio of the stress

C ρ :

Similarity ratio of the density

C φ :

Similarity ratio of the internal fraction angle

C ε :

Similarity ratio of the strain

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Acknowledgements

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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Authors and Affiliations

  1. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200040, China

    Danqing Song, Ailan Che, Renjie Zhu & Xiurun Ge

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  1. Danqing Song
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  2. Ailan Che
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  3. Renjie Zhu
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  4. Xiurun Ge
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Correspondence to Ailan Che.

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Song, D., Che, A., Zhu, R. et al. Natural Frequency Characteristics of Rock Masses Containing a Complex Geological Structure and Their Effects on the Dynamic Stability of Slopes. Rock Mech Rock Eng 52, 4457–4473 (2019). https://doi.org/10.1007/s00603-019-01885-7

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  • DOI: https://doi.org/10.1007/s00603-019-01885-7

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