Analytical model of corrosion-induced cracks in concrete considering time-varying deformations of layers, mechanical properties of rust

Abstract

This paper presents an analytical model to simulate the evolution of corrosion-induced cracks in concrete considering the combined effects of time-dependent deformations of layers and mechanical properties of corrosion products applying the principle of equilibrium of force and compatibility of deformations. Stress, strain and deformation in respective layers of corroding steel, rust and uncracked concrete are determined based on elasticity theory, while coupling tensile softening model and elastic modulus reduction is applied to simulate the cracked concrete. Time-varying deformations of four layers and the influence elastic modulus and Poisson's ratio of rust are considered in force equilibrium and compatibility conditions to determine crack length, stress and strain distributions. It is shown that not only the time-to-surface cracking is shortened, the trend of crack development is also altered if the deformations of layers are considered. A higher elastic modulus results in a faster time for cracks to reach the concrete surface, while a larger Poisson's ratio would lead to slower propagation of cracks. By analysing the results obtained from the proposed model and test data, a semi-empirical relationship between applied current density and elastic modulus of rust is recommended. This correlation could be used to predict the elastic modulus of rust which is an important parameter in modelling corrosion-induced cracks in concrete.