## 1 Introduction
In [25] a FE model is developed and validated using the results obtained from three different sets of experimental tests available in literature and used to investigate the effect of localised and uneven distribution of corrosion on the cyclic response of RC columns, showing the pitting influence on the plastic hinge length. However, according to recent guidelines [26], the prediction of the bearing capacity of RC elements affected by reinforcement corrosion can be made with simplified approaches, based on the reduction of the steel area. It is worth to highlight that these methodologies could be suitable for predicting the load bearing capacity of the RC element but could be misleading in the evaluation of the local and global ductility, significantly affected by corrosion. Aim of the paper is the development of a numerical model for the evaluation of the influence of localized corrosion on the cyclic behaviour and failure modes of RC columns. The paper follows and completes previous research developed by some of the authors in experimental [15] and numerical [21] way, on the influence of the corrosion of the longitudinal rebars on the cyclic response of column specimens. Indeed, a numerical model is developed, able to catch and highlight all the phenomena occurring in elements characterized by localised corrosion, under cyclic loads, paying much care in the definition of the 3D model and in the simulation of the rebar corrosion. To this aim, different modelling strategies (MS) are adopted, respectively based on: reduction of constitutive law by uniform or pitting corrosion; bar discretization and section reduction; bar discretization and morphology based constitutive law reduction. The described models are validated through a comparison with the results of experimental tests developed at the Laboratory of the University of Rome \"Tor Vergata\" on four full-scale square RC columns subjected to cyclic loads and characterised by localised rebar corrosion [27]. The reference experimental survey on the four full-scale RC columns, cast and tested under cyclic load is presented in Section 2. The column geometry, the details of the artificial corrosion process of the steel reinforcement, and the cyclic loading system are here presented. The main outcomes of the performed tests are outlined, in terms of effective corrosion amount and morphology evaluated after the tests and in terms of load-horizontal displacements graphs. Section 3 is devoted to the description of the developed numerical models, with particular reference to the definition of the geometry of the specimen, boundary conditions, material properties (concrete and steel reinforcement) and load patterns. As previously described, different strategies are proposed and compared for the modelling of the corroded reinforcement. The section ends with a description of the modelling of the bond between reinforcement and concrete and of the expectations about results, on the basis of the visual inspection and morphological study of the reinforcement. In Section 4 the results of the performed numerical analysis are shown, with reference to un-corroded and corroded elements, to outline the pros and cons of the different modelling strategies to study the effect of non-uniform steel rebars corrosion on the cyclic behaviour of RC columns. Finally, in Section 5 the main findings are summarized, underlining the sharp effect of localised corrosion on the structural behaviour and failure mode of RC columns and the importance to perform cyclic analysis for existing structures subjected to decay phenomena.