Dirichlet Series Creep Function for Aging Concrete

A simple method is presented by which the linear creep function of concrete can be approximated, with any desired accuracy, by Dirichlet series with variable coefficients. Smooth fits of the best known data on creep at constant temperature and water content are demonstrated. It is shown that the approximation is equivalent to the Kelvin chain model with age-dependent properties. Other approximations leading to the Kelvin chain are also presented. It is found, however, that no Kelvin chain approximation can avoid negativeness of some spring moduli for some periods of time, which precludes physical interpretation of hidden strains. But representations with Maxwell chain are free from this deficiency. The Dirichlet series approximation allows formulation of an efficient algorithm of step-by-step time integration of creep problems, for which arbitrary increase of the time step is possible and storage of the stress history can be dispensed with.