Pseudo-static Slope Stability Analysis for Cohesive-Frictional Soil by Using Variational Method

  • Sourav Sarkar
  • Manash ChakrabortyEmail author
Conference paper
Part of the Lecture Notes in Civil Engineering book series (LNCE, volume 55)


In this research work, the factor of safety of a rectilinear slope consisting of cohesive-frictional soil subjected to seismic load is determined on the basis of the calculus of variation theory and pseudo-static analysis. Unlike the conventional limit equilibrium method, variational calculus method neither requires kinematical assumption (i.e. the shape of the critical slip surface) nor any static assumption (i.e. distribution of normal stress along the slip surface). The factor of safety (F) is defined as a functional of normal stress and slip surface. The functional is minimized using Euler-Lagrangian equation. The critical slip surface and consequently critical factor of safety, Fs is being obtained by employing the (i) transversality conditions and the boundary conditions at the intersection of slip surface and the slope surface and (ii) continuity conditions and natural boundary conditions at the intermediate point of the slip surface. The value of Fs is obtained for different combinations of soil friction angle, and slope angle, β corresponding to varying horizontal (kh) and vertical (kv) seismic coefficients. The results suggest that the seismic coefficients, especially the value of kh have significant impact on the stability of the slope. The design charts are prepared for different combinations of , β, kh and kv. For a certain , the factor of safety decreases with the increase of kh, kv and β. The available solutions compare quite well with the available solution for the pseudo-static slope stability analysis.


Variational calculus Slope stability Seismic coefficient Limit equilibrium method 



The corresponding author acknowledges the support of ‘Department of Science and Technology (DST), Government of India’ under grant number DST/INSPIRE/04/2016/001692.


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Indian Institute of Technology (Banaras Hindu University)VaranasiIndia

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