Indian Geotechnical Journal

, Volume 44, Issue 3, pp 305–321 | Cite as

3-D Elasto-Plastic SEM Approach for Pseudo-Static Seismic Slope Stability Charts for Natural Slopes

  • R. C. TiwariEmail author
  • N. P. Bhandary
  • R. Yatabe
Original Paper


This paper briefly discusses on spectral element method, one of the recent method applied to evaluate the stability of natural slope. The parametric study is made to prepare stability charts in 3-D for the different seismic coefficient in case of dry and fully saturated soil slope conditions. This paper utilizes common soil engineering properties under the unified soil classification system (USCS). Stability charts of some representative soil slopes along with USCS material models can be useful to analyze the stability of slopes for general purposes. This paper analyzes the stability of dry and fully saturated soil slopes with horizontal seismic pseudo-static coefficient, K h , of 0.1, and 0.2 to prepare the stability charts. It is believed that dry and fully saturated soil slope conditions are the best and worst scenario of the stability and seismic coefficient, K h , of 0.1, and 0.2 are sufficiently addressed the seismic slope instability of severe damages. The results show that the stability condition of fully saturated soil slope is equivalent to dry seismic slope instability of pseudo-static coefficient, K h , 0.2 in most of the cases. This paper employs two roots related factors: (1) root cohesion, C r , of 0–20 kN/m2; (2) root zone h r , of 2.0 m to represent the vegetated soil slope stability. A significant change in safety factor is observed as per the soil slope models as well as soil material models including root related parameters. A linear relationship of factor of safety is found with root-cohesion up to, C r , of 20 kN/m2. It may not be true for lower and higher values of root-cohesions. This paper also presents a typical numerical problem and solution to illustrate the application of design charts.


Slope stability Natural slopes Stability chart Spectral element method 

List of Symbols


Horizontal seismic pseudo-static coefficient


Global displacement vector


Global stiffness vector


Global force vector


Elemental stiffness matrix


Elemental force matrix

\( f_{e}^{G} \)

Elemental matrices of gravity force

\( f_{e}^{T} \)

Elemental matrices of traction force

\( f_{e}^{EQ} \)

Elemental matrices of pseudo-static earthquake load


Unit weight of the slope material (kN/m3)


Transpose of interpolation function matrix


Pseudo-static earthquake coefficient


Elasticity tensor for linearly elastic isotropic material representing soil-root matrix continuum


Mass density


Weight function of soil-root material


Density function of soil-root material


Weight function of roots


Weight function of soil


Density of roots


Density of soils


Root area ratio (RAR)

\( \varphi^{\prime}_{f} \)

Factored friction component (°)

\( c^{\prime}_{f} \)

Factored cohesive component (kN/m2)


Additional root cohesion


Root zone


Slope angle


Strength reduction factor



The authors would like to acknowledge to the suggestions provided by Prof. Padma Bahadur Khadka from Institute of Engineering, Tribhuvan University, Nepal.


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© Indian Geotechnical Society 2013

Authors and Affiliations

  1. 1.Graduate School of Science and EngineeringEhime UniversityMatsuyamaJapan

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