Keywords: hydration, cement, rate, maturity

Transcription

1 Thermo-kinetics of Cement Hydration: Temperature effect and Activation Energy Yanfei Peng *, Will Hansen, Claus Borgnakke, Ivindra Pane, J.C.Roumain ** & Joseph J. Biernacki Abstract The purpose of this study is to quantify the temperature effect on cement hydration. In this study, long-term ( 2 days) isothermal heat of hydration rate data is obtained at three different temperatures (5 o C, 23 o C, 35 o C) for ordinary portland cement (OPC) and for blends of OPC containing supplementary cementitious materials (SCM). Between 000 and 2000 data points are obtained for rate of hydration between the ages of hour and 2 days. The results show that the absolute rate decreases by three orders of magnitude as the hydration process gradually becomes diffusion controlled. The cumulative heat of hydration is evaluated using the exponential hydration function of Freiesleben-Hansen. A new rate model for absolute hydration rate is proposed. This model predicts that the rate of hydration is a product of a temperature function (absolute rate constant) and a degree of hydration function (diffusion controlled) that is unique for a given system. The absolute rate, instead of the conventional relative rate, is used so that the effect of temperature on long-term hydration can be incorporated. This model is then used to predict the temperature effect on total rate in the temperature range of 5 to 40 o C. Within this range the temperature effect on rate of hydration at 40 o C is rapidly decreasing to less than % of total peak rate within 3 days, while at 5 o C temperature effect is still pronounced at the age of 7 days. During the deceleration stage of hydration the relative temperature sensitivity (i.e. activation energy) is constant at about 50 KJ/mole. Keywords: hydration, cement, rate, maturity Introduction Temperature has been shown to significantly influence cement hydration [, 2, 3, 4, 5], especially during early age. Previous studies have demonstrated that higher curing temperature will result in higher early degree of hydration (strength), but lower long-term hydration (strength) [, 6, 7, 8], and vice versa. It has also been shown that curing temperatures can change the cement paste microstructure [4]. The understanding of the temperature effect on cement hydration and concrete * Research Assistant, Department of Civil and Environmental Engineering Professor, Department of Civil and Environmental Engineering Associate Professor, Department of Mechanical Engineering Computational Materials Laboratory, Swiss Federal Institute of Technology ** Holcim Co., Colorado Professor, Tennesee Technological University

2 strength is crucial to the construction industry. In concrete construction, there is a great need to predict the in-place strength of concrete. This need stems from the benefit derived by using accelerated construction schedules, but such schedules require methods to monitor the in-place strength so that adequate structural strength can be guaranteed at all times. As is well known, the strength of a given concrete mixture will be a function of its temperature-time history. The maturity concept was developed to consider the combined effect of temperature and time on strength gain [9, 0]. Although it is known that the early curing temperature has a great impact on strength development, and it is suggested that this effect must be accurately accounted for [6, 7], most maturity concepts take the form of the summation of a temperature multiplier to the incremental time segment, without the consideration of temperature-time history [9, 0,, 2]. There have been some modified maturity functions [6], however the temperature effect is not clearly explained. Another feature of conventional maturity functions is that rates relative to a reference temperature are used to account for the acceleration or deceleration effect at specific temperatures [6, 9, 0, 2]. However, these functions can not take into account the effect of temperature-time history on long-term hydration [6] which has been demonstrated by many researches [, 6, 7, 8, 2]. Also, the relative rate is specific to a given system, and no useful correlations among different systems can be made. A possible solution may be to use absolute hydration rates. Generally, temperature is found to affect the rate of reaction and its influence is often embedded inside the rate constant [2, 3, 4]. Furthermore, it has been shown that the function that describes the temperature effect can be expressed by an Arrhenius equation [, 2, 4]. Numerous experimental and analytical studies have been conducted in the past to characterize the effects of temperature using the Arrhenius equation, and to determine the activation energy [, 2, 4,5]. Two contradicting conclusions are drawn on the relationship between activation energy and degree of hydration. Some reported that cement hydration could not be characterized by a single activation energy. Instead, it was found to be a function of degree of hydration [, 8, 4,6]. Some suggested that the activation energy is independent of temperature and degree of hydration [7, 8]. Kinetics models originally developed for chemical reactions have been adopted to investigate cement hydration. Among the various models, Avrami-Erofeev s nucleation model [9, 20] and Kondo s diffusion model [2] are the most widely used. In addition, a phenomenological model proposed by Freisleben-Hansen [22] has been shown to fit the experimental data well [, 8]. The general form of rate function for cement hydration can be written as: dα = f ( T, α) () dt where α = degree of hydration 2

3 t = hydration time T = temperature It has also been proposed that the rate expressed as a multiplicative function of temperature and degree of hydration [7, 23, 24], as in Equation (2): dα = k( T ) g( α) (2) dt where k(t ) = rate constant, /time This form of rate function is very desirable since it is easier to evaluate the effect of temperature and other factors on hydration. It is well-supported by chemical kinetics, which tells that the general form of the rate functions of single-step processes may be described as two separable functions. In the stimulating work by Brunauer et. al [23], the hydration rate was assumed to be directly proportional to the product of the rate constant, the function of water cement ratio and the amount of unhydrated cement, and inversely proportional to the weight of hydration products raised to a positive power. One objective of this paper is to develop a kinetic model in the form of Equation (2) for cement hydration. The rate constant k (T ) generally varies with the absolute temperature of the system according to Arrhenius law: Ea k( T ) = Aexp( ) (3) RT where E a = apparent activation energy of the reaction, J/mol R = gas constant, 8.34J/mol o K T = absolute temperature, o K A = preexponential constant When studying the kinetics of cement hydration, degree of hydration determined by the loss of ignition method is often used [, 23]. This method, although providing valuable information on cement hydration, is inadequate for the investigation of hydration mechanisms due to the limited number of data points. When it comes to model evaluation or development, it is hard to tell the differences among different models. Furthermore, it is difficult to determine the degree of hydration for blended cements. An alternative method is to use isothermal calorimeter, which continuously measures the absolute rate of heat release during cement hydration. The measured rate, after integration, gives the cumulative heat of hydration. Since cement hydration is usually accompanied by heat generation, isothermal heat can be used to study hydration assuming the 3

4 proportionality between the released heat and the quantity of materials hydrated. This assumption can be justified by a unique relationship between chemically bound water and heat of hydration [8]. Isothermal calorimetry has the advantage of providing continuous data, which makes it possible to closely evaluate the hydration mechanisms. Also, it has been shown that strength development is closely related to heat generation [8], and suggests that heat data may be used as a nondestructive technique to predict strength development. An additional benefit includes the applicability to blended cements, since the released heat is a measure of both cement and pozzolanic reaction. Unfortunately, in the past, the measurements could only be conducted during the first few days of hydration [7, 25]. With the advent of modern sensitive isothermal calorimeters, it is now possible to measure long-term hydration up to three weeks (2 days). This time frame, although still short compared to the time it takes for the cement to approach full hydration, is the most important period in cement hydration and covers the time span for which 70 to 90% of the hydration has occurred. The objective of this paper is to evaluate the effect of temperature on cement hydration for both OPC (ordinary portland cement) and blended cements, and to obtain the activation energy for cement hydration. Isothermal calorimetry will be used to investigate the temperature effect over time. A novel normalization methodology is used to collapse hydration curves at different temperatures into one curve. Based on this, a new rate model is proposed, which is written as a product of temperature factor (absolute rate constant) and degree of hydration. Finally, the effect of temperature on the absolute rate over time is evaluated at different temperatures. Research Significance A new rate function expressed as a product of temperature and degree of hydration is proposed, and is shown to fit the experimental data well. From the new rate function, the temperature effect on the total rate of hydration is identified and shown to be a decay function of time. Such models can be used to develop new maturity functions which can predict strength development under non-isothermal conditions. Experimental Regime This study uses isothermal heat of hydration data to evaluate the effect of temperature on cement hydration. Compressive strength is also obtained to illustrate the relation between heat and strength development. Three cement systems were analyzed, including an OPC, a binary blended system containing ground granulated blast furnace slag (GGBFS), and a ternary blended system containing GGBFS and alkali activator. The water to cementitious material ratio was The mix identification, material proportions are shown in Table. The chemical compositions are summarized in Table 2. 4

5 Table. Material Proportions Mix Type I cement (%) GGBFS (%) Alkali activator 00/0/ /25/ /25/ Note: 00/0/0 contains 00% type I cement. 75/25/0 contains 75% type I cement, and 25% GGBFS by weight. 70/25/5 contains 70% type I cement, and 25% GGBFS, and 5% alkali activator by weight. Table 2. Chemical Compositions % by weight Type I cement GGBFS Alkali activator SiO Al 2 O Fe 2 O CaO MgO Na 2 O K 2 O Cl SO C 3 S C 2 S C 3 A C 4 AF (Na 2 O) eq * Blaine (cm 2 /g) * (Na 2 O) eq = Na 2 O K 2 O The heat was measured by isothermal conduction calorimeter on paste samples at 5, 23, and 35 o C. In order to produce mixes with temperatures close to the desired ones, cementitious material and water were conditioned to the target temperatures. The constituents were then mixed, put into vials, sealed, and placed in the calorimeter. The compressive strength testing was only conducted for samples cured at 23 o C. The concrete mix design used is a typical Michigan concrete pavement design. The water/cementitious ratio was 0.45, same as that used for calorimetry. The total cementitious content was 350 kg/m 3 (590 lb/yd 3 ). Sand meeting Michigan 2NS gradation 5

6 was used at 720 kg/m 3 (24 lb/yd 3 ). Natural gravel of 080 kg/m 3 (820 lb/yd 3 ) was used as coarse aggregate. The concrete was air-entrained with an air content of 3 to 5% mm (4 8 in.) cylinders were tested at 0.5,, 3, 7, and 28 days according to ASTM C39. Experimental Results Isothermal Heat of Hydration The results from the isothermal calorimeter are shown in Figure through 3. Note that the data shown in the figures are already reduced for clarity. In Figure, the data are shown on a linear scale (Figures a and b), and on a log-log or semi-log scale (Figure c and d). Temperature dependent differences are difficult to discern over the entire 600 hours experiment when linear plots are used. Log-log and semi-log plots illustrated the temperature effect better. For the cumulative heat of hydration, the semi-log plot gives a better illustration of the first 00 hours, which are of great interest in cement hydration. Log plots are used in all subsequent discussions when necessary. Two distinct stages are observed from the rate plots: the acceleration and deceleration stages. During the acceleration stage, the hydration rates are greater at higher temperatures than those at lower temperatures. As the hydration proceeds and goes into the deceleration stages, this trend is gradually reversed. The cumulative heat has the same trend, with more heat generation at higher temperatures early on, and lower long-term heat. This phenomenon is very clearly seen for the 00/0/0 (00%OPC) system. For the blended cements, although the cumulative heat at low temperature is still low at about 500 hours, the slope of the heat curve is higher than that at high temperature, which predicts a higher long-term heat. This lower long-term heat at higher temperature agrees with the findings from hydration and strength by other researchers [, 6, 8]. The Freisleben-Hansen equation was used to model the cumulative heat of hydration data and obtain the long-term heat. τ a Q = Q exp[ ( ) ] (4) t where Q = the heat of hydration at time t Q = the ultimate heat of hydration τ = the time characteristic, in hours a = a curvature parameter In our experiments, the Q predicted by Equation (4) will not be the real ultimate heat of hydration, since the heat measurements are done for three weeks. However, it is reasonable to state that the predicted long-term heat is an accurate estimate 6

7 of the heat at three months, say Q 00 d, and will be very close to the real ultimate. Thus Q 00 d is used instead of Q and will not induce significant discrepancy in the analysis. The Freisleben-Hansen modeling parameters are listed in Table 3, and the curvefits are shown in Figure through 3 as solid lines. The model is seen to fit the experimental data very well by both visual observation and high R 2 value. The modeling parameters further verify that the long-term heat decreases with temperature, see Figure 4. Table 3. Optimized Model Parameters for Isothermal Heat Data Temp( o C) /0/0 Q 00 (kj/kg) d /25/0 τ (hours) a Q 00 (kj/kg) d /25/5 τ (hours) a Q 00 (kj/kg) d τ (hours) a The reason for the lower long-term hydration at higher temperatures, or blocking effect, is only speculative. Apparently, the micro- and possibly the nano-structure of the hydration products are affected by hydration temperature. At high temperature, the micro-/nano-structure is effectively more restricted thereby inhibiting later stage hydration. The exact mechanism for this observation is yet unknown. As a result, however, the same level of ultimate hydration cannot be expected for all temperatures. Usually for each isothermal temperature, there is an ultimate degree of hydration that can be reached. Once that ultimate degree of hydration is reached, the hydration process will stop even though there are still unhydrated cement grains. The ultimate degree of hydration is found to be a decreasing function of temperature [, 25]. The lower the temperature, the closer the ultimate hydration will approach the real ultimate value. The above blocking effect cannot be accounted for by conventional maturity functions, as the hydration at any arbitrary temperature is simply converted to equivalent hydration by a relative rate to a reference temperature, say 20 o C. This approach is based on the assumption that the long-term strength at 20 o C is valid for any temperature-time 7

8 history, which have been shown to be faulty by many researchers [6, 7, 2]. This difficulty may be overcome by using absolute rate, which will be discussed in details later. Compressive Strength The results from the compressive strength testing are listed in Table 4. Table 4. Compressive Strength(MPa) Age (days) /0/ /25/ /25/ When relating heat and strength, it is observed that blended cements can develop similar or higher strength than OPC with lower cumulative heat. Thus the relationship between heat and strength development is specific to a given system. To investigate the possibility of predicting strength for one system from the information on another system, the heat is normalized by its long-term value Q 00 d, then plotted against the compressive strength in MPa, as seen in Figure 5. Figure 5 indicates that the strength of different systems all fall on one curve, which shows the potential of using heat data to predict strength development, even for different systems. Here the importance of using absolute rate is demonstrated again: it is possible to relate different systems through absolute rate. Quantifying Temperature Effect on Hydration In this section, the temperature effect will be identified and separated out from other factors that influence hydration. A normalization procedure is used to collapse the heat and rate curves at different temperatures into one curve. From this, a new rate function is proposed and shown to fit the experimental data well. Then the activation energy is obtained for different cement systems. Normalization of Cumulative Heat of Hydration Curves An observation of the cumulative heat curves at three temperatures reveals that the shape of the curves is similar, although the magnitude and extent are different. Since temperature is the only difference among the curves, if the heat curves at different temperatures can be collapsed into one curve through a normalization procedure, then the temperature effect is incorporated in the procedure and can be identified. For the y-axis, which represents the heat of hydration, the easiest way is to normalize the heat by its long-term heat Q 00 d. In addition, normalizing Q by Q 00 d cancels out the effect of 8

9 degree of hydration so the temperature effect can be compared of the same basis. The x-axis, which is the hydration time, also needs to be normalized. Look at Equation (2) again, and substituteα by ~ = α Q Q 00d rewritten as: d ~ α = k( T ) f ( ~ α ) (2a) dt If this relation is true, it can be reformatted as: d ~ α = f ( ~ α ) (5) k( T ) dt, then (2) can be The dimension of the rate constant k(t ) is /time, and k ( T ) dt is a dimensionless variable. Equation (5) can be written as: d ~ α = f ( ~ α ) (5a) dβ or d ~ α f ( ~ α ) = dβ (5b) where β = k( T ) t Upon integration: d ~ α = dβ f ( ~ α ) F ( ~ α ) = β (6) where F ( ~ α ) = d ~ α f ( ~ α ) This shows that for a given system, if Equation (2a) is valid, a dimensionless variable β can be identified, and can be expressed as a unique function of hydration degree. In this case, the temperature effect is account for in the parameter β. In constructing the dimensionless parameter β, the concept of fraction time in chemical kinetics is used. Fraction time t α (0<α <) is defined as the time when α fraction of the raw material has reacted, or when the degree of reaction is α. When 9

10 applied to cement hydration, tα needs to be changed to t ~, where ~ α α = Q Q 00d, based on the discussions in previous sections. t t α ~ is a dimensionless parameter and is also a measure of relative reaction. In this study, t 0. 5 is used because it provides a sort of midpoint picture for the hydration process. Theoretically, other values of α ~ can also be chosen. But it is suggested to use values close to 0.5 since low or high values of α ~ may not be as representative of the whole hydration period. A similar normalization procedure has been done in [26] to study various solid state reactions. t 0.5 is determined from the Freisleben-Hansen model. First divide both sides of Equation (4) by Q 00 d (the effective Q ) Q Q τ = exp[ ( ) t a ] Let Q =0.5 and solve for t to obtain t 0. 5 : Q τ = (7) (ln 2) t 0.5 / a t 0.5 for the three cement systems are listed in Table 5. The normalized curves are shown in Figure 6. For all systems, the normalized curves at different temperatures merge into one curve. This indicates that the temperature factor is incorporated in the normalization method, and hence the temperature effect can be separated from other factors. Table 5. t 0. 5 from Isothermal Heat Data Temp( o C) /0/0 t 0. 5 (hours) /25/0 t 0. 5 (hours) /25/5 t 0. 5 (hours) t 0.5 is temperature dependent and can be written as an exponential function of 0

11 temperature, and is shown in Figure 7: t = D exp( E ) (8) 0.5 T where D, E = modeling constants To try to formulate a rate function in the form of Equation (2), the Freisleben-Hansen model was used again for each unified system in Figure 6. Since ~ α approaches in each system, ~ Q τ a α = = exp[ ( ) ] (9) Q t / t 00d 0.5 where τ and a are parameters for the normalized curves that are unique for a given system. In the above normalized Equation (9), the temperature effect still cannot be explicitly written as formatted in Equation (2), since the temperature factor t 0. 5 is combined with t, the time factor. However, this normalization procedure verifies that the temperature effect can be factored out, and serves as the basis for the following discussion. Normalization of Rate of Heat Generation Curves Consider the rate of heat generation. For simplicity, only the deceleration stage is investigated. Disregarding the acceleration stage may not be a bad idea when mechanical properties are concerned. It was pointed out in [27] that a certain degree of hydration must occur before the concrete starts to develop mechanical properties (compressive strength, Young s modulus, etc.). This certain amount of hydration usually corresponds to 5 to 20% relative heat development. The deceleration stage of our systems all begin at around 20% relative heat development and likely coincides with the starting point of mechanical properties development. A similar normalization procedure used for the cumulative heat is applied to the rate. That is, normalized both dq dq t and t by t 0., and obtain vs., see dt 5 d t / ) Figure 8. The benefit of this will soon become clear. ( t 0. 5 The rates, after normalization, also merge into one curve, which can be modeled by a power function, see Equation (0). The modeling parameters are listed in Table 6, and the curvefits by the power function are also shown in Figure 8. d dq X ( t ) Y = (0) ( t / t0.5 ) t0. 5 t 0.5

12 where X and Y are modeling constant Both t and t 0. 5 have the dimension of time, to get the equation dimensionally correct, X must have the unit of energy per mass, i.e., kj/kg. Table 6. Modeling Parameters for Normalized Rate by Equation (0) 00/0/ /25/ /25/ X Y It is significant that Equation (0) can fit the normalized rate over three orders of magnitude, which is not possible by any existing hydration model. Furthermore, the rate in the above equation is absolute instead of relative, incorporates the effect of temperature on long-term hydration, and can relate properties of different systems. In Equation (0), t 0. 5 is a constant for each isothermal temperature and can be moved to the right hand side: dq dt X t Xt ( () Y Y = ) = + Y t0.5 t0.5 t0.5 Because t 0. 5 is temperature dependent, Equation () is written as a product of a temperature function and time function: where dq = f ( T ) g( t) (2) dt f ( T ) = t and (+ Y ) 0.5 g ( t) = Y Xt Equation (2) can be converted to a function of T and ~ α. From Equation (9), t can be expressed as a function of ~ α. t τ = (3) 0.5 t ~ a [ ln( α )] Upon substitution of Equation (3) into (): dq dt Y Y Xt.5τ = Y [ ln( ~ a α )] t Y Xτ = [ ln( ~ α )] t = Z F( T ) G( ~ ) 0 Y α + Y 0.5 a 0.5 (4) 2

13 where Z τ Y = X, F ( T ) =, t 0.5 G( ~ α ) = [ ln( ~ α )] Y a Because X, Y, τ, a, and F(T ) are all constants, Equation (4) can be simplified to give the new proposed rate function: dq dt [ ~ ] ln( α ) n = k (5) where k = rate constant, kj/hr/kg n= modeling constant, and ~ = α Q Q 00d This form is very similar to the rate function for 2-dimensionl diffusion [3], see Equation (6), and can be seen as a modified diffusion rate function. dα = k[ ] (6) dt ln( α) Equation (5), the new rate function, was used to model the rate of heat generation, and the optimized modeling constants were obtained, see Table 7 and Figure 9 for the curvefits. Considering the complexity of cement hydration, the proposed model predicts the measured rates well, except for α ~ >0.9 at high temperature (35 o C). Similarly, it should not be used at α ~ close to since a log form is used in the model. Table 7. Modeling Parameters for Rate by Equation (5) Temp( o C) /0/0(n=-.7) k /25/0 (n=-2.0) k /25/5 (n=-.9) k In Equation (5), the rate function is represented as a product of absolute rate constant and effect of degree of hydration. The rate constant k obeys the Arrhenius law, and activation energy can be determined by plotting ln(k) vs. T, see Figure 0 and Table 8. The activation energy compares well with those reported in the literature [28]. Note that the activation energy is obtained from the rate constant k, which is effective for the whole deceleration stage. Therefore the activation energy is a constant in that stage. It is seen that the activation energies of the three systems are very close to each other. However, one should be very careful about the meaning of activation energy: it represents 3

14 the relative temperature sensitivity of a given system, and does not say anything about the absolute rate. Table 8. Activation Energy E a E a (kj/mol) 00/0/ /25/ /25/5 50 The functions of degree of hydration g (α~ ) are shown in Figure for the three systems, which are very similar to each other. g (α~ ) decays fast as hydration proceeds, from 2.5 to almost 0. The evolution of g(α~ ) explains the seemingly contradiction between a constant activation energy and the importance of early curing temperature. The temperature effect is a constant over time when the rates at the same degree of hydration are compared; however, its effect on the total rate is attenuating because g(α~ ) becomes dominant. The new proposed model is used to predict the rate and cumulative heat at other temperatures. Utilizing the activation energy listed in Table 8, the rate constant can be determined at any arbitrary temperature. Assuming the same g (α~ ), the absolute rate can be calculated together with the cumulative heat, see Figure 2. To move a step further, the percentage of reduction in peak rate (absolute) is determined and plotted in Figure 3. At high temperature 40 o C, the temperature effect on the absolute hydration rate decreases very fast, to less than % within the first 72 hours. At low temperature 5 o C, the absolute hydration rate can still be affected for 7 days or more. This tells that the temperature effect on rate of hydration is insignificant after about 72 hours at 40 o C, whereas the effect is still significant after 7 days at low temperature 5 o C. Conclusions The purpose of this paper was to quantify the temperature effect on cement hydration from isothermal heat of hydration data. A normalization procedure was used and shown to be able to collapse the heat and rate curves at different temperatures into one curve. Based on this, a new rate function, which is written as the product of temperature effect (rate constant) and degree of hydration effect is proposed. The findings can be 4

15 summarized as follows:. The proposed rate model is the product of absolute rate constant and function of degree of hydration, and can predict the rate and cumulative heat well for the deceleration stage. 2. The temperature effect on the absolute hydration rate is a decay function of time, since the other part of the rate function, degree of hydration factor, decreases rapidly with time. The effect of temperature on relative rate, however, is a constant during the deceleration stage. 3. During the deceleration stage, an activation energy that is independent of degree of hydration is obtained from the rate constant. The predicted values are comparable to those obtained by other investigators. 4. From the proposed model, the temperature effects on the absolute hydration rates can be predicted at different temperatures. The temperature effects are shown to decrease very fast at high temperatures, and remain significant for a longer period of time at low temperatures. These predictions agree with field experience. 5. Absolute hydration rate was used to incorporate the effect of temperature on long-term hydration. This should improve the existing maturity functions for the use of non-isothermal conditions. Also, it makes it possible to relate the properties from different systems. Acknowledgements This project was supported in part by a grant from Holcim Inc. to the University of Michigan. 5

16 Reference: Abdel-Jawad, Y. A., The Relationships of Cement Hydration and Concrete Compressive Strength to Maturity, Ph.D Thesis, Univ. of Michigan, Van Breugel, K., Simulation of Hydration and Formation of Structure in Hardening Cement-Based Materials, revised Ph.D Thesis, Delft Univ. Press, Geiker, M., Measurement of Chemical Shrinkage and a systematic Evaluation of Hydration Curves by Means of the Dispersion Model, Ph.D Thesis, Tech. Univ. of Denmark, Kjellsen, K. O., and Detwiler, R. J., and Gjorv, O. E., Development of Microstructure in Plain Cement Pastes Hydrated at Different Temperatures, Cement and Concrete Research (2), pp. 79, 99 5 Taplin, J. H., The Temperature Dependence of the Hydration Rate of Portland Cement Paste, Australian Journal of Applied Science(3), pp. 64, Kim, J. K., Moon, Y. H., Eo, S. H., Compressive Strength Development of Concrete with Different Curing Time and Temperature, Cement and Concrete Research, Vol. 28, No. 2, 998, pp 76~773 7 Volz, C. K., Tucker, R. L., Burns, N. H., and Lew, H. S., Maturity Effects on Concrete Strength, Cement and Concrete Research (98), 4~50 8 Pane, I., Hydration Kinetics and Thermomechanics of Blended Cement Systems, PhD thesis, Univ. of Michigan, Carino, N. J., Temperature Effects on the Strength-Maturity Relation of Mortar, National Bureau Standard, NBSIR , Washington DC, pp 98, 98 0 Carino, N. J, Knab, L. I., and Clifton, J. R., Applicability of the Maturity Method to High-Performance Concrete, NISTIR 489, Building and Fire Research Laboratory, NIST, May 992 Kjellsen, K. O., and Detwiler, R. J., Later-age Strength Prediction by a Modified Maturity Model, ACI Materials Journal (90), pp 220, Guo, C., Maturity of Concrete: Method for Predicting Early-Stage Strength, ACI 6

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18 25 Wu, X., Roy, D.M., and Langton, C.A., Early Stage Hydration of Slag-Cement, Cement and Concrete Research 3, 983, 277~ Sharp, J. H., Brindley, G. W., and Achar, B. N. N., Numerical Data from Some Commonly Used Solid State Reactions, Journal of American Ceramic Society(49), pp. 379, Kanstad, T, Hammer, T.A., BjØntegaard, Ø, and Sellevold, E.J., Mechanical Properties of Young Concrete: Part II: Determination of Model Parameters Test Program Proposals, Materials and Structures, V. 36, May 2003, 226~ Tank, R. C., Carino, N. J., Rate Constant Functions for Strength Development of Concrete, ACI Materials Journal, V. 88, No., 99, pp74~83 8

19 30 00/0/0 dq/dt (kj/hr/kg) C 23C 35C w/c= Time (hours) (a) /0/0 300 Q(kJ/kg) C 23C 35C w/c= Time(hours) (b) 9

20 00 00/0/0 dq/dt (kj/hr/kg) C 23C 35C w/c= Time (hours) (c) /0/0 5C C 35C Q(kJ/kg) 200 Model R 2 = Time(hours) (d) Figure. Heat of hydration for 00/0/0 (a) dq/dt vs. t, linear scale (b) Q vs. t, linear scale (c) dq/dt vs. t, log-log scale (d) Q vs. t, semi-log scale 20

21 00 75/25/0 dq/dt(kj/hr/kg) 0 0. w/c=0.45 5C 23C 35C w/c= Time(hours) (a) /25/0 5C Q(kJ/kg) C 35C Model R 2 = Time(hours) (b) Figure 2. Heat of hydration for 75/25/0 (a) dq/dt vs. t (b)q vs. t 2

22 00 70/25/5 dq/dt (kj/hr/kg) 0 0. w/c=0.45 5C 23C 35C Time(hours) Q(kJ/kg) C 23C 35C Model (a) 70/25/5 R 2 = Time(hours) (b) Figure 3. Heat of hydration for 70/25/5 (a) dq/dt vs. t (b)q vs. t 22

23 450 w/c=0.45 Q00d(kJ/kg) /0/0 75/25/0 70/25/ Temperature ( o C) Figure 4. Q 00 d vs. T 60 Compressive strength(mpa) /0/0 75/25/0 70/25/5 w/c=0.45, 23C Figure 5. Compressive strength vs. Q / Q 00 d 23

24 00/0/0 0.8 Q/Q00d C 23C 35C t/t 0.5 (a) 75/25/0 0.8 Q/Q00d C 23C 35C t/t 0.5 (b) 24

25 70/25/5 0.8 Q/Q00d C 23C 35C t/t 0.5 (c) Figure 6. Normalized heat curves Q Q 00d t vs. t 0.5 (a) 00/0/0 (b) 75/25/0 (c) 70/25/ t0.5 (hours) y = 8.8e x R 2 = /0/0, w/c= Temperature ( o C) Figure 7. t 0. 5 vs. T ( o C) 25

26 000 00/0/0 y = * x^(-.4064) R 2 = dq/d(t/t0.5) (kj/kg) C 23C 34C curvefit for all temperatures t/t 0.5 (a) /25/0 y = * x^(-.3609) R 2 = dq/d(t/t0.5) (kj/kg) C 23C 35C 0. curvefit for all temperatures t/t 0.5 (b) 26

27 000 70/25/5 y = 8.06 * x^(-.3327) R 2 = dq/d(t/t0.5) (J/hr/gr) C 23C 34C curvefit for all temperatures t/t 0.5 (c) Figure 8. Normalized rate curves dq ( t / t 0. 5 ) t vs. t 0.5 (a) 00/0/0 (b) 75/25/0 (c) 70/25/ /0/0 n=-.7 dq/dt(kj/hr/kg) 0 R 2 =0.98 Measured rate-5c Modeled rate-5c Measured rate-23c 0. Modeled rate-23c R 2 =0.96 measured rate-35c modeled rate-35c Q/Q 00d (a) 27

28 00 75/25/0 dq/dt(kj/hr/kg) n=-2.0 R 2 =0.97 measured rate-5c modeled rate-5c measured rate-23c Modeled rate-23c measured rate-35c R 2 =0.96 Modeled rate-35c Q/Q 00d 00 (b) 70/25/5 n=-.9 dq/dt(kj/hr/kg) 0 R measured rate-5c 2 =0.98 modeled rate-5c 0. measured rate-23c modeled rate-25c R 2 =0.96 measured rate-35c modeled rate-35c R 2 = Q/Q 00d Figure 9. Modeled rate vs. Q Q 00d (c) (a) 00/0/0 (b) 75/25/0 (c) 70/25/5 28

29 /0/0 Linear (00/0/0) 2 ln(k).5 y = x /T( o K^-) Figure 0. ln(k) vs. T, 00/0/ g(α) /0/0 75/25/0 70/25/ Q/Q 00d Figure. g (α~ ) vs. Q / Q 00 d 29

30 Predicted Heat of hydration (kj/kg) C 20C 40C 0/0/0 w/c= Time(hours) Figure 2. Predicted cumulative heat for 00/0/0 20 % Reduction in absolute rate of hydration C 20C 40C 00/0/0, w/c= Time(hours) Figure 3. % reduction in absolute peak rate, 00/0/0 30