Service life of concrete structures is limited by the susceptibility of the reinforcement to corrosion. Oxidation of iron leads to the formulation of various products (such as ferrous and ferric oxides), some of which occupy much greater volume than the original iron that gets consumed by the corrosion process. As corrosion progresses, these products accumulate, thereby generating expansive pressures on the surrounding concrete. The pressure builds up to levels that cause internal cracking around the bar and eventually leads to through cracking of the cover and spalling. Loss of cover marks the end of service life for corrosion-affected concrete structures, because at that stage the reinforcement loses its ability to develop its forces through bond and is no longer protected against further degradation from corrosion. In this paper, a simple analytical model is formulated to demonstrate the mechanical consequences of corrosion-product buildup around the bar. Service life is estimated as the time required for through cracking of the cover, which is identified in the model by a sudden drop of the internal pressure exerted by the corroding bar eventually relaxing to zero. Cracking time is found to be a function of cover, material properties of the surrounding concrete, and rust product, and is controlled by the rate of rust accumulation. In formulating the associated boundary-value problem, the governing equation expressed in terms of radial displacements is discretized using finite differences, whereas cracked concrete is treated as an orthotropic material. Calculated cracking times are correlated against published experimental data. The parametric sensitivity of the model is established with reference to published experimental evidence, and the role of the important design variables in the evolution of this mechanical problem is identified and discussed.
