ACME 2011 Proceedings of the 19 UK National Conference of the ...

2 DLO FORMULATION
A basic explanation of the plane strain DLO formulation will initially be given with reference to the
simple example problem shown in Figure 1; the alterations necessary to permit three dimensional analysis
will then be briefly outlined. In Figure 1, a surcharge is applied to a block of soil close to a vertical
cut. The area occupied by the block of soil is first populated with nodes as shown in Figure 1(b), with
each pair of nodes then interconnected with potential linear discontinuities as shown in Figure 1(c). The
critical failure mechanism for the given nodal discretization can then be identified, Figure 1(d).
Figure 1: Stages in DLO procedure: (a) starting problem (surcharge applied to block of soil close to a
vertical cut); (b) discretization of soil using nodes; (c) interconnection of nodes with potential discontinuities;
(d) identification of critical subset of potential discontinuities using optimization (giving the
layout of slip-lines in the critical failure mechanism) (after Gilbert et al. [?])
Bearing Capacity Factor
Reference Other Lower bound Upper bound
Skempton [?] 6.17 a
Gourvenec et al. [?] 6.41
5.91 b
Michalowski [?] 6.56
Salgado et al. [?] 5.52 6.22
Present study (DLO) 6.42
a. Empirical
b. Elasto-plastic finite element
Table 1: Selected published results for a rough square based punch on weightless cohesive (Tresca)
material
From Smith & Gilbert [?], the primal kinematic DLO formulation can be written as:
subject to
min λf T L d = −f T Dd + g T p
Bd = 0 (1)
Np − d = 0
f T L d = 1
p ≥ 0
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