Abstract
A general formulation framework for an age-dependent constitutive equation of concrete is presented to account for the development of the elastic modulus at an early age. This is achieved by expanding the total stress vs. strain relation with respect to the time-varying elastic modulus. Two types of constitutive formulation frameworks are derived depending on whether (or not) the time-varying effect of the elastic modulus was taken into account in the linearized series expansion. The causes for the age-dependent deformations under sustained loads are defined in the formulation based on the two internal mechanisms of delayed elasticity and the ageing phenomenon. The ageing phenomenon is incorporated in a conventional delayed strain concept in terms of the variable elastic modulus with time. Four cases of age-dependent constitutive equations are formulated within the presented formulation framework by employing different types of creep models. The mechanical characteristics of the terms that comprise the various constitutive equations are examined and compared. Numerical application of the time-dependent test results of cylindrical specimens indicate that the creep formulation that considered the elastic modulus development showed a good agreement with the experimental result while the formulation that did not consider the elastic modulus development underestimated the result by 15%.
Highlights
At present, with the advances in concrete and construction technologies, concrete formworks are removed at an early concrete age during the construction of concrete structures in order to reduce the work term
Once the creep and shrinkage strains in a concrete structure are restrained, the time-varying value of elastic modulus as well as the mechanical strain due to a restraining effect is a significant factor in determining the internal stress state that persistently changes with time [7,8,9]
It is observed from Equations (1) and (3) that the delayed concept of this creep model does not account for the ageing phenomenon in concrete because the value of the elastic modulus maintains a constant value for E(t0 ) at the time of loading t0, throughout the entire age-dependent process of concern
Summary
With the advances in concrete and construction technologies, concrete formworks are removed at an early concrete age during the construction of concrete structures in order to reduce the work term. This paper presents a general formulation framework for an age-dependent constitutive equation of concrete to account for the ageing phenomenon of the elastic. Phenomenon that gradually progresses with time immediately after the development of the load-induced strain Another recent aspect in the creep and shrinkage phenomena is a dissipative mechanism and the related plasticity due to the age-dependent deformation process, which is a typical problem in heterogeneous materials such as concrete [11,12]. A constitutive formulation that features both the material and mechanical aspects was recently presented by Park and Lee [9], and it expanded the age-dependent total stress-strain relation using a first-order Taylor series expansion with respect to the three age-dependent material characteristics of creep, shrinkage, and elastic modulus. Based on this research work, this study presents a general formulation framework for the age-dependent constitutive equation to accommodate creep models derived in terms of the creep compliance function. Creep tests of cylindrical concrete specimen subjected to stepwise loads, and the age-dependent behavior of an axially reinforced compressive member, are analyzed using the four constitutive equations examined and the time-dependent behaviors at an early concrete age are addressed
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