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Rock Mechanics and Rock Engineering

, Volume 52, Issue 10, pp 3809–3823 | Cite as

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

  • Gang Fan
  • Limin ZhangEmail author
  • Jianjing Zhang
  • Changwei Yang
Original Paper
  • 326 Downloads

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.

Keywords

Obsequent slope Rock slopes Safety factor Slope stability Time–frequency method Earthquake 

List of Symbols

\(\alpha_{1}\)

Incident angle

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

Reflection angle of reflection P waves

ξmin

Minimum critical damping ratio

ηH

Horizontal earthquake influence coefficients

ηV

Vertical earthquake influence coefficients

θ

Dip angle

λ

Lame constant

μ

Poisson’s ratio

ρ

Density

σ0

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

ωmin

Minimum central frequency

a

Acceleration

AH

Horizontal peak acceleration

Ai

Area of analytical unit i

AV

Vertical peak acceleration

c

Cohesion

Ca

Scaling factor for acceleration

CL

Scaling factor for geometric dimension

Cρ

Scaling factor for mass density

EMD

Empirical mode decomposition

Fs

Sliding force

Fa

Resistance force

G0

Slope gravity

HHT

Hilbert–Huang transform

IMF

Intrinsic mode function

Kp

Pseudo-static safety factor

Ks

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

Notes

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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Copyright information

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

Authors and Affiliations

  1. 1.College of Water Resource and HydropowerSichuan UniversityChengduPeople’s Republic of China
  2. 2.Department of Civil and Environmental EngineeringThe Hong Kong University of Science and TechnologyHong KongPeople’s Republic of China
  3. 3.School of Civil EngineeringSouthwest Jiaotong UniversityChengduPeople’s Republic of China

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