INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2010; 83:452–481 Published online 9 March 2010 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.2838 Modelling of reinforced-concrete structures providing crack-spacing based on X-FEM, ED-FEM and novel operator split solution procedure Adnan Ibrahimbegovic 1, ∗, † , Amor Boulkertous 1 , Luc Davenne 1 and Delphine Brancherie 2 1 Ecole Normale Sup´ erieure de Cachan, LMT-Cachan, 61 Avenue du President Wilson, 94235 Cachan, France 2 Universit´ e de Technologie de Compi` egne, LMR Centre de Recherches, BP 20529, 60205 Compi` egne, France SUMMARY In this work, we present a novel approach to the finite element modelling of reinforced-concrete (RC) structures that provides the details of the constitutive behavior of each constituent (concrete, steel and bond-slip), while keeping formally the same appearance as the classical finite element model. Each component constitutive behavior can be brought to fully non-linear range, where we can consider cracking (or localized failure) of concrete, the plastic yielding and failure of steel bars and bond-slip at concrete steel interface accounting for confining pressure effects. The standard finite element code architecture is preserved by using embedded discontinuity (ED-FEM) and extended (X-FEM) finite element strain representation for concrete and slip, respectively, along with the operator split solution method that separates the problem into computing the deformations of RC (with frozen slip) and the current value of the bond-slip. Several numerical examples are presented in order to illustrate very satisfying performance of the proposed methodology. Copyright 2010 John Wiley & Sons, Ltd. Received 23 November 2009; Accepted 30 November 2009 KEY WORDS: RC structure; crack-spacing; X-FEM; ED-FEM; localized failure; bond-slip 1. INTRODUCTION Modelling of reinforced-concrete (RC) structures in order to ensure the optional design with respect to structure integrity has long tradition, which has been summarized in several reference works ∗ Correspondence to: Adnan Ibrahimbegovic, Ecole Normale Sup´ erieure de Cachan, LMT-Cachan, 61 Avenue du President Wilson, 94235 Cachan, France. † E-mail: ai@lmt.ens-cachan.fr Contract/grant sponsor: French Ministry of Research Contract/grant sponsor: IRSN: Institute for Radioprotection and Nuclear Safety Copyright 2010 John Wiley & Sons, Ltd.