Stochastic modelling of crackwidth in reinforced concrete beams subjected to fatigue loading

Cracking is one of the serviceability limit states to be considered in the design of reinforced concrete members subjected to fatigue loading. Due to variations in material properties and cross-sectional dimensions, the evolution of crackwidth with applied load cycles should be treated as a stochastic process. In this paper a nonhomogeneous Markov chain (NHMC) model is proposed to model the evolution of maximum crackwidth with applied load cycles. Formulations for calculating the elements of transition probability matrix and unconditional probability vector at any applied load cycle have been presented. Assuming that the maximum crackwidth at any stage of loading cycle and at any two successive loading cycles can be described by truncated uni-variate and bi-variate normal distributions, respectively, the unconditional probability vectors have been computed, at different applied load cycles, for four beams subjected constant amplitude fatigue loading, and whose test results are available in the literature. By comparing the estimated state with the experimentally observed state at different applied load cycles, it is inferred that (1) it is important to consider the correlation between the maximum crackwidths between two successive applied load cycles (especially at lower applied load cycles); and (2) NHMC model shows promise for modelling fatigue cracking in reinforced concrete beams.