Abstract
The dependence of creep on load duration (t−t′) as well as age at loading t′ is described by the law [1+ϕ 1 t′-m(t-t′)n]/E 0 in which m, n,ϕ 1 E0=material parameters which are determined from test data by optimization techniques. The law is limited to basic creep, but with different values of material parameters it can also describe drying creep up to a certain time. The previous formulations are extended by introducing the age dependence. This also enhances the reliability in long-term extrapolation of creep data. Substituting t−t′=0.001 day, the law also yields the correct age dependance of the conventional elastic modulus, E. If E0, which is much larger than E, were replaced by E (as implied by previous power laws without age dependence), the age dependence of creep curves obtained by data analysis would be more scattered, the age dependence of E would have to be described by a separate formula, and more material parameters would be necessary to fit test data. The simplicity of the double power law is a major advantage for statistical evaluation of test data.
Résumé
La dépendance du fluage à la durée de chargement comme à l'âge du béton au temps t′ de mise en charge est traduite par la loi [1+ϕ 1 t′-m(t-t′)n]/E 0 où m, n,ϕ 1, E0 sont des paramètres du matériau déterminés décrits par des techniques d'optimisation d'après les résultats d'essai. Cette loi ne s'applique qu'au béton en état de confinement (sans échanges avec l'ambiance), mais avec différentes valeurs des paramètres du matériau, elle peut rendre compte également du fluage de séchage à un moment donné. L'introduction dans les formules de la fonction d'âge recule leurs limites d'application et accroît aussi la fiabilité des extrapolations à long terme des données de fluage. Si l'on pose t−t′=0,001 jour, la loi fournit aussi la relation correcte à l'âge du module conventionnel d'élasticité E. Si l'on remplaçait E par E0 (qui est beaucoup plus grand)— comme l'impliquent les lois de puissance antérieures sans fonction d'âge—, la fonction d'âge des courbes de fluage obtenues par l'analyse des résultats donnerait lieu à une plus grande dispersion, il faudrait alors traduire la fonction d'âge de E par une formule indépendante, et il faudrait plus de paramètres du matériau pour avoir une bonne correspondance avec les résultats d'essai. La simplicité de la loi de puissance double présente un avantage majeur pour l'évaluation statistique des résultats d'essai.
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Bažant, Z.P., Osman, E. Double power law for basic creep of concrete. Mat. Constr. 9, 3–11 (1976). https://doi.org/10.1007/BF02478522
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DOI: https://doi.org/10.1007/BF02478522