COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Commun. Numer. Meth. Engng 2008; 24:1107–1119 Published online 5 June 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/cnm.1018 Three-dimensional Mohr–Coulomb limit analysis using semidefinite programming K. Krabbenhøft ∗,† , A. V. Lyamin and S. W. Sloan Centre for Geotechnical and Materials Modelling, School of Engineering, University of Newcastle, Callaghan, NSW 2308, Australia SUMMARY Recently, Krabbenhøft et al. (Int. J. Solids Struct. 2007; 44:1533–1549) have presented a formulation of the three-dimensional Mohr–Coulomb criterion in terms of positive-definite cones. The capabilities of this formulation when applied to large-scale three-dimensional problems of limit analysis are investigated. Following a brief discussion on a number of theoretical and algorithmic issues, three common, but traditionally difficult, geomechanics problems are solved and the performance of a common primal– dual interior-point algorithm (SeDuMi (Appl. Numer. Math. 1999; 29:301–315)) is documented in detail. Although generally encouraging, the results also reveal several difficulties which support the idea of constructing a conic programming algorithm specifically dedicated to plasticity problems. Copyright 2007 John Wiley & Sons, Ltd. Received 12 December 2006; Revised 5 April 2007; Accepted 17 April 2007 KEY WORDS: limit analysis; Mohr–Coulomb; optimization; semidefinite programming; plasticity 1. INTRODUCTION The Mohr–Coulomb criterion is the most commonly used criterion for the description of the plastic failure of geomaterials such as sands and clays. Although a number of other, slightly different, criteria have been proposed over the years [1, 2], the Mohr–Coulomb criterion remains the most widely used criterion in practice and forms the basis of almost all available analytical and semi- analytical solutions for problems such as slope stability, bearing capacity of foundations, earth pressure calculations, etc. In principal stress space, the Mohr–Coulomb criterion consists of six linear planes which intersect to form the yield envelope. These intersections give rise to discontinuities in the yield surface ∗ Correspondence to: K. Krabbenhøft, Centre for Geotechnical and Materials Modelling, School of Engineering, University of Newcastle, Callaghan, NSW 2308, Australia. † E-mail: kristian.krabbenhoft@newcastle.edu.au Copyright 2007 John Wiley & Sons, Ltd.