Unified modeling of setting and strength development R.C.A. Pinto a, ⁎, A.K. Schindler b a Department of Civil Engineering, Federal University of Santa Catarina, Florianópolis, SC 88040-910, Brazil b Department of Civil Engineering, Auburn University, Harbert Engineering Center, Auburn, AL 36849, USA abstract article info Article history: Received 19 December 2008 Accepted 13 August 2009 Keywords: Maturity method Aging (C) Compressive strength (C) Temperature (A) The effect of temperature on the development of concrete compressive strength can be modeled by the maturity approach once the temperature sensitivity of the mixture, quantified by the activation energy (E a ) of its chemical reactions, is known. It is common in maturity applications to use a unique value of E a obtained for the hardening period, even though the effect of temperature is different on the rate of setting and hardening. E a -values presented in the literature suggest that the temperature sensitivity is lower before hardening. This paper proposes a new approach to the traditional maturity method unifying the distinctly different temperature sensitivities before final setting and during hardening. Results of setting and compressive strength of mixtures with different cementitious materials were analyzed with activation energy values calculated for the periods before final setting and during hardening. For the investigated mixtures, the new approach led to improved strength predictions, suggesting that it is useful to take into account setting behavior in the development of the strength–maturity relationship. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction The maturity approach has been used to model temperature effects on the development of concrete compressive strength since around 1950 when steam curing treatments were initially applied to accelerate compressive strength gain [1]. Maturity accounts for the combined effects of temperature and time on the development of compressive strength (and other properties such as setting, degree of hydration, etc.), being evaluated from the temperature history of the concrete investigated. In maturity applications, a strength–maturity relationship is established for a given mixture cured at known temperature conditions. Several mathematical relationships for the strength– maturity relationship have been proposed since Saul [2] defined the term maturity, in 1951. An appropriate strength–maturity relationship should take into account the dormant period of a concrete mixture, in which the material is still in a plastic state. This is essential, as strength development starts at final set, and inaccuracies in the estimated final set time may affect the early-age predicted strength. The extent of this period is related to the setting behavior of the concrete mixture which depends on the curing history of the concrete [3]. The precise definition of the time when setting starts and ends is somewhat subjective, since setting is caused by a gradual stiffening process. Nevertheless, this transition period starts when concrete loses its plasticity, and ends when measurable mechanical properties start to develop [4]. The hardening period follows in which concrete continu- ously gains strength with time. The setting and hardening processes are physical consequences of the chemical activity in a mixture, and thus, are greatly affected by temperature. Arrhenius-based maturity functions have been pro- posed to the setting and to the hardening periods [3,5]. The temperature sensitivity of a given mixture can be quantified by the apparent activation energy (E a ) of its chemical reactions [6]. Traditionally, when the maturity approach is used to estimate strength, a single value of E a is used [7] for the periods preceding final set and during hardening, even though the temperature sensitivity of the cement hydration reactions decreases as they turn from chemically controlled to diffusion controlled [8]. Researchers have attempted to include variable E a -values during the hardening period [9,10]; however, it is common practice to use a single E a -value to estimate setting and strength development. Some values of activation energy reported in the literature [11–21] for mixtures with Type I cement and replacements of various supplementary cementitious materials, obtained for the setting and hardening periods are summarized in Table 1. While there is a wide range of values due to the composition of the mixtures, the reported activation energies up to final set are generally less than those reported for the hardening period, suggesting that there may be differences in temperature sensitivity during the setting and hardening periods. Thus, the utilization of a fixed E a -value obtained for the hardening period may lead to poor estimates of strengths at very early ages since the temperature sensitivity of the mixture up to final set has not properly been taken into account. Cement and Concrete Research 40 (2010) 58–65 ⁎ Corresponding author. Tel.: +55 48 3721 7768; fax: +55 48 3721 5191. E-mail address: rpinto@ecv.ufsc.br (R.C.A. Pinto). 0008-8846/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.cemconres.2009.08.010 Contents lists available at ScienceDirect Cement and Concrete Research journal homepage: http://ees.elsevier.com/CEMCON/default.asp