Constitutive equation for concrete creep and shrinkage based on thermodynamics of multiphase systems

Abstract

RESUME L'action des variations d'humidite et de temperature sur Ie beton, compte tenu des facteurs de dimension et de forme, ainsi que de la repartition des contraintes est traduite par I'equation fondamentale du f1uage, du retrait et de la dilatation thermique. La pate de ciment et Ie beton sont etudies en tant que materiaux composites multiphases dans lesquels les conditions d'equilibre, tant statique que thermodynamique, doivent etre considerees. (28), (25), (40), (38) = 10-7 , mm, it = (u)· = ou lot, sign, ~ " approximately equal ", -7 +-" assign " SUMMARY

Concrete creep at variable humidity: constitutive law and mechanism

“…Thus we may conclude that the present formulation is mathematically a special case of the previous thermodynamic theory from references [5], [6], [8] and [19]. Significant simplification has been achieved by virtue z. P. BazJant -J. C. Chern of hypothesis II, which was not introduced in those previous works in which a finite delay of response between the macropores and micro pores was considered.…”

“…At low h, the Z. P. 8azJant -J. C. Chern hydration rate is virtually zero, and then there is no aging. This is usually described by means of a change of time scale, considering that the age-dependent material parameters, i. e., Ell and 111-" rather than being functions of the actual age of concrete t, are functions of the socalled equivalent hydration period te ([7], [8], [12]). (2) in which I3h is an empirical function of pore humidity h, and may be considered as I3h=[1+(a-ah)4r 1 . According to test data [50], [59], [44], a ~ 5.…”

“…The present theory is a special case of a previously advanced thermodynamic theory ( [5], [6], [8], [19]), except for the fact that a sudden stress drop due to cracking is generalized to gradual strain-softening with irreversibility. The present special case avoids all the hypothetical features of that earlier theory and does not invoke any of the various specific assumptions about creep mechanism and cement paste microstructure made in that theory.…”

“…This conclusion is a consequence of the fact that the chemical potential of water is a function of not only its pressure but also temperature, and that the sorption relation between the water content and the pressure also involves temperature. (The existence of stress-induced thermal expansion was implied in Bazant's 1969 thermodynamic model [6,7,8]: see discussion of equation 21 below. )…”

“…It is interesting to relate our formulation to a previous thermodynamically based theory from references [5], [6], [8], [19], [39]. In that theory, distinction was made between stress (Jw transmitted by load-bearing water in the gel pores (hindered absorbed layers and interlayer water) and stress (Js transmitted only by solid-to-solid contacts.…”