Temperature Calculations during Hardening

HEADNOTE

A case study of a concrete bridge deck

In the early stages of hydration, concrete can be especially vulnerable to both thermal and mechanical effects. Therefore, it's useful to determine early-age heat development

and heat loss to evaluate the risk of thermal cracking (by comparing the calculated temperature gradients with maximum levels normally given in the codes of practice) or to determine when the formwork can be removed. Other authors have indicated the need to determine these values.1,2 This article discusses a finite element program that can predict the early-age heat development in and the maturity of a concrete member. We also present a case study of a concrete bridge deck constructed under cold weather conditions using two different concrete mixtures.

HARDENING CALCULATIONS

In the context of this article, the hardening process begins when water and cement are mixed and ends when the concrete is fully hydrated and hardened. We performed hardening calculations using 4C-Temp&Stress, a commercially available program developed for concrete structures. We used this program to define a cross section for a member and to solve the heat equation in the plane of the defined section. Heat flow perpendicular to the cross section was not considered. Although we did not use the feature in this example, each concrete placement within a system can be modeled, allowing the modeling of a casting sequence-for example, the casting of a foundation, a wall, and a supported slab.

The temperature calculations performed by 4C-Temp&Stress can include consideration of:

* The initial temperature of the fresh concrete;

* The casting rate;

* The heat of hydration of the concrete;

* Ambient wind and temperature effects;

* The type of formwork;

* The type of insulation;

* The time of stripping; and

* The use of cooling pipes, heating wires, and heating mats.

Calculations convert the time and temperature history to an equivalent time, applying the maturity concept based on the Arrhenius equation.3 Figure 1 gives an overview of the program facilities (see Reference 4 for additional background information).

In the following case study, we shall consider a highway bridge cross section cast under winter conditions in Denmark. While only the temperature calculations are presented in this article, an outline is provided showing how the analysis may be extended to include early-age stress calculations.

MATERIAL DATA

Two different concrete mixtures were considered in the calculations, both from an aggressive environment exposure class. Each mixture had an equivalent water-cementitious materials ratio (w/cm) of 0.42 and a 28-day compressive strength of about 50 MPa (7500 psi). We calculated the equivalent cement content using activity factors of 2.0 for silica fume and 0.5 for fly ash. Concrete Type A0 is conventional Danish concrete, incorporating both silica fume and fly ash (Table 1). In Concrete Type A1, we replaced about 100 kg (220 lb) of cement with fly ash (Table 1). To calculationobtain equivalent w/cm in the two concretes, we reduced the amount of water in A1, introducing the need for a water-reducing admixture to maintain workability.

Figure 2 depicts the heat development for the mixtures, based on semi-adiabatic measurements of about a one-week duration. The results of such tests were curve-fit into an analytical expression as shown in Fig. 2. It is seen that A0 generates more heat at a faster rate than A1, mainly due to its higher content of portland cement. It is also possible that the addition of a water-reducing admixture has some influence on the retardation of concrete A1 compared to A0. The setting time of the two concrete types, however, was of the same order of magnitude (5 to 6 maturity hours), indicated by the dotted lines in Fig. 2. The compressive strength gain of the two concretes showed no significant differences.

The two curves in Fig. 2 were adopted for the numerical calculations presented in the following section. The analytical representation is given by means of the parameters listed in Table 1.

GEOMETRIC MODEL

Figure 3 shows the cross section of the bridge deck together with information on the protection and formwork; boundary conditions are ambient weather conditions by:

* Constant wind velocity of 5 m/s; and

* Sinusoidal temperature variation between 0 and 5 C (32 and 41 F) over each 24 h period.

Thermal and moisture protection covers for the exposed concrete surfaces were assumed to be provided about 20 h after casting.

TEMPERATURE RESULTS

In Fig. 4, the result of a calculation is shown for concrete types A0 and A1. The maximum temperature was located within the central part of the cross section, while the minimum temperature was located on the surface, near the edge beam (Fig. 5). Figure 4 directly reflects the implication of A0 developing more heat than A1, where A0 generally shows significantly higher temperatures than A1.

Figure 4 also depicts the extreme temperature difference over the cross section. During the first day (before the insulation was established), the minimum temperature in the edge beam decreased along with the ambient temperature. As a result, a significant temperature difference started to build up over the cross section. For A0, this difference peaked around 21 C (38 F) and for A1 it peaked around 18 C (32 F). Comparing the calculated temperature differences with the upper limit of 19 to 20 C (35 F), a rule-of-thumb normally applied to avoid early-age cracking,1 it is seen that the bridge deck should have been better protected against the weather-especially within the first 24 h after casting.

Due to the higher temperatures generated by A0, it is not surprising that the concrete maturity of this concrete is higher than that of A1 (Fig. 6). It is generally accepted that the degree of hydration follows the heat development since the heat is generated by the hydration process. In Fig. 6, the average maturity is converted into degree of hydration based on the exponential expression in Fig. 2 and the parameters in Table 1. In the Danish code on execution of concrete structures (DS 482),5 the duration of drying protection is governed by the degree of hydration. For a bridge deck in aggressive environment exposure class with deicing agents, DS 482 states that the hydration should be at least 85% before the protection is removed to achieve sufficient durability. Figure 6 shows that for concrete A0, the degree of hydration reaches 85% only 3 days after casting (corresponding to 87 maturity hours). For concrete A1, it takes 187 maturity h to reach the same level of hydration, which is more than 15 days after casting. Thus, the significant effect of the heat of hydration on the hardening behavior is once again demonstrated.

EARLY-AGE STRESSES

Figure 1 indicates how the data obtained from a temperature calculation can be combined with information regarding the early-age development of strength and stiffness to carry out a stress calculation. In 4C-Temp&Stress, the risk of early-age cracking is evaluated by relating the tensile stress at a given point with the tensile strength at that point.

It should be mentioned, however, that modeling of early-age behaviors such as thermal and autogeneous deformations, as well as stress relaxation from early-age creep, is a rather complicated matter requiring comprehensive material tests. A more detailed presentation of the stress calculations is therefore outside the scope of this article.

FURTHER INFORMATION

4C-Temp&Stress has been applied to all major civil engineering works in Denmark over the past 10 years, including the Great Belt Link and the resund Link. Recently, the Federal Highway Administration (FHWA) acquired the program for their mobile concrete laboratory. More information regarding the program is found at www.danishtechnology.dk/4CTempStress or by contacting Germann Instruments, Inc.

Acknowledgments

The presented work was carried out within a 4-year R&D project "Green Concrete" on sustainable concrete solutions, partly financed by the Danish Ministry of Science, Technology, and Innovation. Refer also to www.greenconcrete.dk.

REFERENCE

References

1. Gajda, J., and Vangeem, M., "Controlling Temperatures in Mass Concrete," Concrete International, V. 24, No. 1, Jan. 2002, pp. 59-62.

2. Selna, D., and Monteiro, P. J. M., "Cathedral of Our Lady of the Angels," Concrete International, V. 23, No. 11, Nov. 2001, pp. 27-33.

3. Carino, N. J., "The Maturity Method: Theory and Application," ASTM Journal of Cement Concrete and Aggregates, V. 6, No. 2, Winter 1984, pp. 61-73.

4. Pedersen, E. S., "Prediction of Temperature and Stress Development in Concrete Structures," Thermal Cracking in Concrete at Early Ages, R. Springenschmid, ed., RILEM Proceedings No. 25, E&FN Spon, London, 1995, pp. 297-304.

5. Danish Standards Association, "Udfrelse af Beton Konstruktioner (Execution of Concrete Structures)," DS 482, Charlottenlund, 1999, Denmark.

Selected for reader interest by the editors.

-Germann Instruments

CIRCLE 58

AUTHOR_AFFILIATION

Claus V. Nielsen, PhD, is a consultant at the Danish Techno-logical Institute in Copenhagen. He has worked in the field of civil engineering for concrete structures since 1990. Nielsen specializes in the hardening technology and fire behavior of concrete.

Annette Berrig, BSc, has been a consultant at the Danish Technological Institute since 1990. She is a well-respected specialist within the fields of concrete material technology and all aspects of concrete standardization.