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.

Modelling rotational failure in confined geometries using DLO

“…This compares well (numerically within 0·2%) with the solution by Martin (2011), who derived what may be regarded as a highly accurate solution of 3·77649 using the method of characteristics. For a shallower slope, β = 20°, n = 1·2, Taylor predicts a stability Figure 12.…”

Identification of rotational failure mechanisms in cohesive media using discontinuity layout optimisation

“…Selected results are listed in Table 2. Assuming that the present extrapolated results represent the exact solution, it can be seen that highly accurate DLO results, very close to the SLF results of Martin (2011), can again be obtained when using high nodal resolutions. These results also improve on the best available FELA results currently reported in the literature for this problem.…”

“…It can also be seen from these results that the DLO procedure is capable of representing closely the SLF results of Martin (2011). (The reader is also referred to Martin (2011) with these mechanisms, in the form of deformed meshes.)…”

“…5 that although the form of the mechanism identified is similar to that proposed by Martin (2011), the funnel-shaped SLF that meets the ground surface is not reproduced well. To obtain an improved solution, more nodal divisions could be employed.…”

“…(The reader is also referred to Martin (2011) with these mechanisms, in the form of deformed meshes.) However, it is important to note that the new solutions described here can be obtained directly, without the need for a two-stage approach of the sort proposed by Martin (the second stage of Martin's approach appears to rely on a solution-specific manual interpretation of the form of the finite-element solution obtained in the first stage).…”