Use of internal and external variables and extremum principle in limit equilibrium formulations with application to bearing capacity and slope stability problems

Yung Ming Cheng, T. Lansivaara, R. Baker, N. Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

12 Citations (Scopus)


Limit equilibrium methods, satisfying both force and moment equilibrium can be formulated using assumptions on the internal variables or the external variables. Even though most stability methods are based on force and moment equilibrium, as well as the Mohr-Coulomb yield criterion, there are great differences between the results of the different formulations due to variations in the assumptions. The authors believe that the use of the interslice force function f(x), the thrust line or the base normal forces should provide an equivalent concept at the ultimate/failure state. In the present study, the authors have used the well-known bearing capacity solutions to determine f(x), the thrust line and the base normal forces for a "horizontal slope". The equivalence between the different formulations under the ultimate condition is demonstrated. It is shown that it is not important which forces are used in the stability formulation, external boundary forces or internal forces, if only that the ultimate state is considered. It is also demonstrated in the present paper that the maximum extremum from the limit equilibrium analysis is equivalent to the slip line solution using a classical bearing capacity problem.
Original languageEnglish
Pages (from-to)130-143
Number of pages14
JournalSoils and Foundations
Issue number1
Publication statusPublished - 1 Jan 2013


  • Interslice force
  • Janbu rigorous method
  • Morgenstern-Price method
  • Slip line
  • Thrust line
  • Ultimate limit state

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Geotechnical Engineering and Engineering Geology

Cite this