Flow rule effects in the Tresca model

The Tresca failure criterion is used regularly in geotechnical engineering to compute the failure loads of clay soils deforming under undrained conditions. When this criterion is used together with the finite element method a plastic flow rule must also be incorporated in the elasto-plastic soil model.

The effects of the flow rule on the performance of a non-linear analysis using an elastic perfectly plastic soil model obeying the Tresca failure criteria are discussed in this note. Application of this model in a three-dimensional analysis causes computational difficulties, due to the gradient discontinuities that exist at the corner of the Tresca yield surface. Such discontinuities can be removed from the yield (or failure) surface using different methods. Two of the most widely used methods in removing singularities from the yield surface and their overall performances in a three-dimensional finite element analysis are discussed.

The motivation for this study comes from a concern raised by Randolph and Puzrin Randolph MF and Puzrin AM Upper bound limit analysis of circular foundations on clay under general loading. Geotechnique, (2003);53(9):785–796, 5]] about reported instances of under predictions of the collapse loads by finite element analysis Taiebat HA and Carter JP Numerical studies of the bearing capacity of shallow foundations on cohesive soil subjected to combined loading. Geotechnique, (2000);50(4):409–418, 7]] and Taiebat HA and Carter JP Bearing capacity of strip and circular foundations on undrained clay subjected to eccentric loads. Geotechnique, (2002);52(1):61–64, 8]], Gourvenec S and Randolph M Effect of strength non-homogeneity on the shape of failure envelopes for combined loading of strip and circular foundations on clay, Geotechnique, (2003);53(6):575–586, 4]], when it is usually expected that finite element results should overestimate the true collapse loads. The intent of this study is to demonstrate and reiterate that although the finite element method is an extremely powerful analytical tool for solution of engineering problems, it is nevertheless subjected to approximation errors due to simplifications that are necessarily made to prevent other numerical difficulties.