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

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Abstract

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.

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Abbreviations

K h :

Horizontal seismic pseudo-static coefficient

U :

Global displacement vector

K :

Global stiffness vector

F :

Global force vector

K e :

Elemental stiffness matrix

F e :

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

γ e :

Unit weight of the slope material (kN/m3)

ϕ T :

Transpose of interpolation function matrix

K EQ :

Pseudo-static earthquake coefficient

C ijkl :

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

ρ :

Mass density

W i :

Weight function of soil-root material

ρ i :

Density function of soil-root material

W r :

Weight function of roots

W s :

Weight function of soil

ρ r :

Density of roots

ρ s :

Density of soils

a r :

Root area ratio (RAR)

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

Factored friction component (°)

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

Factored cohesive component (kN/m2)

C r :

Additional root cohesion

h r :

Root zone

β :

Slope angle

SRF :

Strength reduction factor

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Acknowledgments

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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  1. Graduate School of Science and Engineering, Ehime University, Matsuyama, Japan

    R. C. Tiwari, N. P. Bhandary & R. Yatabe

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Tiwari, R.C., Bhandary, N.P. & Yatabe, R. 3-D Elasto-Plastic SEM Approach for Pseudo-Static Seismic Slope Stability Charts for Natural Slopes. Indian Geotech J 44, 305–321 (2014). https://doi.org/10.1007/s40098-013-0086-y

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