# Rebar Shape Time-Evolution During a Reinforced Concrete Corrosion Test: An Electrochemical Model
## 1 Introduction  
Corrosion of steel is one of the main mechanisms limiting the service life of reinforced and pre-stressed concrete structures, both in buildings and civil infrastructure [1]. The expansive character of the steel corrosion products is at the origin of the damage suffered by concrete [2], whose early symptoms are micro and macro cracking [3, 4], which is followed by spalling or delamination of the concrete cover. Further consequences of the corrosion of embedded steel are the following: loss of bond between concrete and steel, loss of steel ductility, and loss of cross-sectional area of steel [5]. These phenomena contribute to reducing the serviceability and load bearing capacity of the structures.  
Usually the appearance of cracking is considered as the limit state regarding the durability of concrete structures affected by steel reinforcement corrosion [6, 7]. Thus, great effort on cracking the understanding has been done [8, 9, 10, 11, 12, 13, 14, 15, 16]. Corrosion products' volume is higher than metal volume, and most of the corrosion products remain as a solid layer around the rebar [2, 17]. Thus, corrosion implies a rebar volume increase that causes concrete cracking [2]. Moreover, as metal converts in its corrosion products, the structure's strength weakens due to a metal section loss [5].  
Cracking is experimentally studied usually by accelerated corrosion tests [9, 12, 17, 18, 19, 20]. Additionally, mechanical models have been developed to obtain numerical simulations [8, 10, 11, 13, 14, 15, 16, 21]. A key factor on mechanical modelling is the rebar shape time-evolution, which will determine the applied loads on concrete. Some authors accept a uniform expansion along the rebar perimeter [22, 23]. Nevertheless, the corrosion rate can vary along the rebar perimeter depending on the exposure conditions. When corrosion is due to a depassivating agent that ingress into concrete from the environment, the corrosion rate of the outer part of the rebar will be higher. The corrosion rate along the rebar perimeter in a forced corrosion test will depend on the cathode location. This non-uniform corrosion has been observed experimentally [19, 20] and has also been modelled [10, 11, 13, 14, 15, 16, 21]. Usually, geometrical models are used to describe the rebar section and the rebar shape is considered as an ellipsoid [11, 14, 15, 21], a combination of ellipsoids [18], or other geometries [12, 13] depending onexposure conditions. This is a convenient simplification for a modelling purpose, but a more realistic model would be desirable. Some detailed models [10; 11] have been developed for chloride exposure conditions by taking into account chloride transport in order to estimate the non-uniform corrosion along the rebar perimeter. The present paper focuses on a forced corrosion test method, where an electrical current is applied to induce corrosion. An electrochemical model for the estimation of rebar shape time-evolution is presented in order to get a more realistic approach of the rebar shape during the test. This shape could be taken as input for mechanical models trying to simulate concrete cracking due to embedded steel corrosion under these conditions.