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


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.


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

List of Symbols


Incident angle


Reflection angle of reflection P waves


Minimum critical damping ratio


Horizontal earthquake influence coefficients


Vertical earthquake influence coefficients


Dip angle


Lame constant


Poisson’s ratio




Normal component of slope gravity


Normal stress


Tangential component of slope gravity


Shear stress


Internal friction angle


Instantaneous frequency


Minimum central frequency




Horizontal peak acceleration


Area of analytical unit i


Vertical peak acceleration




Scaling factor for acceleration


Scaling factor for geometric dimension


Scaling factor for mass density


Empirical mode decomposition


Sliding force


Resistance force


Slope gravity


Hilbert–Huang transform


Intrinsic mode function


Pseudo-static safety factor


Seismic safety factor


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


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


Geometric dimension






Number of analytical units


Peak ground acceleration


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





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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