Improved estimation of long-term relaxation function from compliance function of aging concrete

Zdeněk P. Bažant*, Mija H. Hubler, Milan Jirásek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


Based on asymptotic considerations, this paper develops an improved approximate formula for estimating the relaxation function from the given compliance function of concrete, which is considered as aging, linearly viscoelastic material. Compared with the formula developed in 1979 by Bažant and Kim, the new formula prevents any violation of the thermodynamic requirement of nonnegativeness of the relaxation function. It is significantly more accurate for long-time relaxation of concrete loaded at a young age, and, for this reason, it is particularly useful for compliance functions that correctly describe multidecade creep, which is the case for model B3 compliance function (a 1995 international RILEM recommendation) and not, for example, for the compliance functions of the American, European, Japanese, and Canadian standard recommendations, for which the benefit is smaller. The main application of the new formula is to evaluate the aging coefficient of the age-adjusted effective modulus method (AAEM) from the compliance function specified by the standard recommendation. The AAEM, developed in 1972 at Northwestern University and embodied in most standard design recommendations including those of the American Concrete Institute (ACI) and the Fédération internationale du béton ( fib), provides an approximate estimate of the creep effects in structures according to the principle of superposition, which itself is a simplification neglecting nonlinear and diffusion effects.

Original languageEnglish (US)
Pages (from-to)146-152
Number of pages7
JournalJournal of Engineering Mechanics
Issue number2
StatePublished - 2013


  • Aging
  • Concrete
  • Creep
  • Creep analysis of structures
  • Stress relaxation

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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