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

Abstract

Discontinuity layout optimisation (DLO) is a generally applicable numerical limit analysis procedure that can be used to identify critical plastic collapse mechanisms in geotechnical problems. Previous research has focused on using plane-strain DLO to identify mechanisms that are purely translational, or which involve rotations only along predefined boundaries. In this paper a more general formulation, capable of identifying mechanisms that can involve arbitrary rotations and/or translations in cohesive media, is presented. The formulation is then verified through investigation of the yield surface and evolution of the collapse mechanism associated with a footing under combined vertical and moment (V, M) loading, and through study of the well-known anchor uplift problem. It is shown that results of very high accuracy can be obtained, in terms of the collapse load and of the predicted failure mechanism. In the light of the new results, the Bransby design formula for combined vertical and moment loading has been modified to improve its accuracy. Additionally, the more general DLO formulation presented is shown to have several inherent advantages compared with existing numerical limit analysis approaches.

Modelling rotational failure in confined geometries using DLO

“…Following Smith and Gilbert (2013), the full rotational compatibility relationship in (1b) for any node pair AB for geometrically unrestricted problems can be stated as follows 2:…”

“…The general dead load work component may be written as follows (note this is in a slightly different form to that presented in Smith and Gilbert, 2013) 3:…”

“…Lysmer, 1970;Makrodimopoulos and Martin, 2006;Sloan, 1988) and the method of characteristics (Sokolovskii, 1965), through its ability to identify directly critical failure mechanisms in the form of velocity discontinuities for a prescribed numerical discretisation, and to handle singularities in a natural and fully general way. The application of DLO to three-dimensional problem and plane-strain problems involving purely translational failure mechanisms has been described by Hawksbee et al (2013) and Smith and Gilbert (2007), respectively, and to plane-strain rotational mechanisms in non-dilational materials by Smith and Gilbert (2013). Recently, a formulation suitable for the analysis of slabs has been also presented (Gilbert et al, 2014).…”

“…The critical layout of discontinuities is then identified using rigorous mathematical optimisation techniques (hence the name 'discontinuity layout optimisation'), with the objective being to find the solution which minimises overall energy dissipation. Smith and Gilbert (2013) showed that curved discontinuities could alternatively be employed, as shown in Figures 1(e)-1(f), which replaces stages in Figures 1(c)-1(d). This allows fully rotational mechanisms to be modelled with high accuracy.…”

“…(a) initial problem (eccentric rigid load applied to a block of soil close to a vertical cut); (b) discretisation of soil using nodes; (c) interconnection of nodes with potential straight-line discontinuities interlinking all nodes; (d) identification of critical subset of potential discontinuities using optimisation (giving layout of slip lines in the critical translational failure mechanism); (e) interconnection of nodes with potential linear and curved discontinuities (for clarity only a small subset of possible curved discontinuities are shown); and (f) identification of critical subset of potential discontinuities using optimisation (giving the layout of slip-lines in the critical rotational failure mechanism) (after Smith and Gilbert, 2013) 2. Modelling rotational failure in DLO 2.1 General procedure…”