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Analysis of Seismic Stability of an Obsequent Rock Slope Using Time–Frequency Method

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Abstract

Obsequent rock slopes are often thought to be more stable than consequent slopes and passive sliding is unlikely to occur under earthquake loading. However, failures in obsequent rock slopes were indeed observed in recent large earthquakes. This paper presents a time–frequency solution to the seismic stability of obsequent rock slopes fully considering the time–frequency characteristics of earthquake waves. Large-scale shaking table tests were conducted to illustrate the application of the time–frequency method to an obsequent rock slope containing multiple weak layers with a small dip angle. The seismic stability of the obsequent rock slope is analyzed combining the time–frequency method, outcomes from the shaking table test, and conventional pseudo-static and dynamic numerical analyses. The results show that passive sliding can develop in the obsequent rock slope when taking the time–frequency components of the earthquake waves and the vertical seismic force into account. The middle–upper part of the obsequent rock slope is more vulnerable to seismic damage. The slope bulges under the earthquake loading; the maximum permanent surface displacement occurs at the middle–upper part of the slope, rather than the slope crest. Additionally, the response of seismic safety factor lags behind the responses of acceleration and surface displacement.

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Fig. 1

(after Huang et al. 2013)

Fig. 2

(modified from Hoek and Bray 1981)

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Abbreviations

\(\alpha_{1}\) :

Incident angle

\(\alpha^{\prime}_{1}\) :

Reflection angle of reflection P waves

ξ min :

Minimum critical damping ratio

η H :

Horizontal earthquake influence coefficients

η V :

Vertical earthquake influence coefficients

θ :

Dip angle

λ :

Lame constant

μ :

Poisson’s ratio

ρ :

Density

σ 0 :

Normal component of slope gravity

\(\sigma_{\text{n}}\) :

Normal stress

\(\tau_{0}\) :

Tangential component of slope gravity

\(\tau_{\text{s}}\) :

Shear stress

φ :

Internal friction angle

ω :

Instantaneous frequency

ω min :

Minimum central frequency

a :

Acceleration

A H :

Horizontal peak acceleration

A i :

Area of analytical unit i

A V :

Vertical peak acceleration

c :

Cohesion

C a :

Scaling factor for acceleration

C L :

Scaling factor for geometric dimension

C ρ :

Scaling factor for mass density

EMD:

Empirical mode decomposition

F s :

Sliding force

F a :

Resistance force

G 0 :

Slope gravity

HHT:

Hilbert–Huang transform

IMF:

Intrinsic mode function

K p :

Pseudo-static safety factor

K s :

Seismic safety factor

\(k_{x}^{(j)}\) :

Wave vectors of \(S_{0}^{j}\) in X direction

\(k_{z}^{(j)}\) :

Wave vectors of \(S_{0}^{j}\) in Z direction

L :

Geometric dimension

l :

Length

m :

Mass

n :

Number of analytical units

PGA:

Peak ground acceleration

\(S_{0}^{j}\) :

Elastic displacement of seismic wave \(S^{j}\)

t :

Time

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Acknowledgements

This research was financially supported by the Research Grants Council of the Hong Kong Special Administrative Region (16202716), the National Key Research and Development Plan of China (2017YFC0504901) and the Fundamental Research Funds for the Central Universities (20822041B4038).

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Authors and Affiliations

  1. College of Water Resource and Hydropower, Sichuan University, Chengdu, Sichuan, People’s Republic of China

    Gang Fan

  2. Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, People’s Republic of China

    Gang Fan & Limin Zhang

  3. School of Civil Engineering, Southwest Jiaotong University, Chengdu, Sichuan, People’s Republic of China

    Jianjing Zhang & Changwei Yang

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  1. Gang Fan
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  2. Limin Zhang
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Correspondence to Limin Zhang.

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Fan, G., Zhang, L., Zhang, J. et al. Analysis of Seismic Stability of an Obsequent Rock Slope Using Time–Frequency Method. Rock Mech Rock Eng 52, 3809–3823 (2019). https://doi.org/10.1007/s00603-019-01821-9

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