A three-dimensional slope stability analysis method using the upper bound theorem Part I: Theory and methods

Zuyu Chen, Xiaogang Wang, C. Haberfield, Jianhua Yin, Yujie Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

178 Citations (Scopus)


A three-dimensional (3D) slope stability analysis method, based on its two-dimensional approaches proposed by Donald and Chen (Can. Geotech. J. 34 (1997) 853.) is presented in this paper. It starts from establishing a compatible velocity field and obtains the factor of safety by the energy and work balance equation. Optimisation is followed to approach the critical failure mode that offers the minimum factor of safety. The method is demonstrated to be identical to Sarma's limit equilibrium method (1979) that employs inclined slices, if it is extended to the 3D area. However, it has been established on a sound theoretical background supported by the upper bound theorem of plasticity. Test problems have demonstrated its feasibility. A feature of the method is its very simple way to obtain the factor of safety without complicated 3D force equilibrium evaluations. Limited assumptions are involved in this method and their applicability has been justified.
Original languageEnglish
Pages (from-to)369-378
Number of pages10
JournalInternational Journal of Rock Mechanics and Mining Sciences
Issue number3
Publication statusPublished - 1 Apr 2001


  • Limit analysis
  • Slope stability analysis
  • Three-dimensional analysis
  • Upper bound theorem

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology

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