The use of adaptive finite-element limit analysis to reveal slip-line fields

Abstract

The numerical method known as finite-element limit analysis (FELA) is generally employed as a tool for obtaining lower and upper bounds on the exact collapse load of a perfectly plastic structure or continuum. Most applications of FELA in geotechnical engineering have focused on plane strain problems involving the classical Tresca and Mohr–Coulomb yield criteria, and considerable computational effort has been expended on the calculation of lower- and upper-bound solutions for particular problems. This paper discusses and demonstrates an alternative use of FELA – as a tool for ascertaining slip-line fields for plane strain problems. A simple but effective strategy for adaptive mesh refinement is a key feature of the process; it allows the layout of plastic regions, rigid regions and velocity discontinuities to be determined by inspection of the FELA mesh. The corresponding slip-line field can then be constructed numerically in the usual way. The examples presented are restricted to purely cohesive soil, but the same approach is applicable in principle to frictional or cohesive-frictional materials.