Application of the Upper and Lower-bound Theorems to Three-dimensional Stability of Slopes

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5 Citations (Scopus)


A finite element software implementing both the upper and the lower-bound theorems of limit analysis has been recently developed in the Civil Engineering Department of FCT/UNL. This tool has the ability to automatically determine compatible velocity fields for the upper-bound case and equilibrated and plastically admissible stress fields for the lower-bound case. The upper and lower bounds are obtained by a common iterative solution scheme. The latter is suitable for parallelization, allowing large three-dimensional problems to be solved more rapidly. These tools can therefore be applied to three-dimensional geotechnical problems such as 3D slope stability analyses. The paper will present a brief description of the algorithm and its application to three-dimensional slopes with different geometries and soil properties.

Original languageEnglish
Pages (from-to)674-681
Number of pages8
JournalProcedia Engineering
Publication statusPublished - 2016
Event3rd International Conference on Transportation Geotechnics (ICTG 2016) - Guimarães, Portugal
Duration: 4 Sep 20167 Sep 2016
Conference number: 3rd


  • Limit Analysis
  • Three-Dimensional Slope Stability
  • Parallelization
  • Finite Elements


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