HYDRATION IN CEMENT-BASED SYSTEMS

1	Introduction

On contact with water Portland cement particles start to dissolve and react with water under formation of hydration products. The rate of reaction depends on a number of factors, such as:

clinker composition of the cement

fineness of the cement

water/cement ratio (or water/binder ratio)

temperature at which the reaction takes place

presence of admixtures

These parameters determine the rate of reaction and, intimately associated with it, the rate at which the microstructure of the hydrating system is formed. Actually, the rate of hydration and of microstructural development are mutually interdependent. In essence, it is the microstructure, including the state of the pore water, that has our interest. The microstructure determines the the pore structure and hence the permeability. Moreover, it also determines the thermal and physical/mechanical properties. When dealing with concrete, also the microstructure at the matrix-aggregate interfacial zone has to be considered as an important factor which determines the materials behaviour.

Concepts

The predominant role of the microstructure of a hardening paste or concrete, including the state of water in the pore system, justifies attempts to relate engineering properties of hardening concrete to this microstructure. This, however, is not so easy. Even though much progress has been made in recent years with research on the relationship between microstructure and materials properties and performance of the hardened product, we are still in a stage that we have to adopt "indirect methods" for relating the evolution of materials properties to the development of the microstructure. Several indirect methods have been proposed in the past, each of them with their pros and cons and with different "distance" from a pure microstructural approach. Two methods, or concepts, for quantification of the evolution of the materials properties at early ages are:

1.	Maturity concept

2.	Degree-of-Hydration concept

The philosophy behind the maturity concept is that there is unique relationship between a materials property, for example the strength, and the maturity of the concrete. The maturity is defined as a quantity in "degree celcius hour [°C.h]". Other defintions are found as well. The relationship between maturity and a particular materials property of a certain mix has to be determined in advance by experimental testing.

With the degree of hydration concept the evolution of the materials properties is described as a function of the degree of hydration. The degree of hydration is considered to be the unique parameter (for a particular mix and a certain temperature history) with the help of which the microstructure, and hence the evolution of the materials properties, can be described. Once the relationship between the degree of hydration and the evolution of the materials properties is known (by testing), the problem is brought back to the determination of the degree of hydration in the real structure and the influence of the temperature on the relationship between degree of hydration and the individual materials properties.

Aim of this report

A major aim of this report is to discuss the main features, advantages and drawbacks of these concepts, as well as the relationship between them. Emphasis will be on the degree-of-hydration concept. Not because it is the most widely used concept today, but just because it is the concept that really tries to address some tedious problems which are circumvented elegantly in the maturity concept. For the engineering practice this has his advantages. However, circumventing problems does not mean that we solved them.

2.	Degree of hydration)

2.1	Definition of degree of hydration

To what extent the hydration process has proceeded is indicated with the term "degree of hydration". The ultimate stage of complete hydration has trivially been defined as the stage in which all the cement has reacted. In formula form:

The charm of this definition is its relative convenience when stereological aspects of microstructural development are to be dealt with.

For the determination of this "true" degree of hydration several direct methods are used, for example quantitative X-ray diffraction analysis (QXDA), 29Si NMR and SEM image analysis (see Kjellsen 1997). Furthermore, the true degree of hydration can be approximated by a number of more easy accessible parameters, for example the heat of hydration.

2.2	Parameters to indicate the degree of hydration

Parameters that can be used to indicate, or approximate, the "true" degree of hydration as defined with eq. (1) are:

1.	Liberated heat of hydration:	(t) =	Q(t)/Qmax	(2a)

2.	Amount of chemically bound water:	(t) =	Wn(t)/Ŵn	(2b)

3.	Chemical shrinkage [121,185,185,305]	(t) =	(t)/ max	(2c)

4.	Amount of Ca(OH)2:	(t) =	VCH(t)/{VCH} max	(2d)

5.	Specific surface of the cement gel:	(t) =	SS(t)/ŜS	(2e)

6.	Strength:	(t) =	f(t)/fmax	(2f)

7.	Dielectric properties of the cement	(2g)

For application in the engineering practice the liberated heat of hydration is considered the most convenient indicator of the degree of hydration. The liberated heat of hydration and the amount of chemically bound water will be briefly dealt with here.

Liberated heat of hydration

As early as the beginning of the thirties the liberated heat of hydration has been used as an indicator of the degree of hydration (Lerch et al. 1948, Woods et al. 1932). According to Lehmann et al. (1965) there exists an excellent linear relationship between these two quantities. Discrepancies between the degree of hydration and the degree of heat liberation, however, have been reported by Bombed (1974), Daimon et al. (1980) and Brown et al. (1985). The relationship between degree of hydration and degree of heat liberation has been found to be affected by the curing temperature (Gebauer et l. 1966, Odler et al. 1966).

Chemically bound water

According to Le Sueur, a linear relationship exists between the amount of combined water and the degree of hydration determined using QXRD. This conclusion is in line with earlier work by Powers et al. 1946/1947). They found a constant ratio between the amount of water required to cover the hydration products with one single monolayer of water and the amount of non-evaporable, chemically bound water. This constant ratio suggests that the chemically bound water is a reliable indicator of the amount of cement that has reacted, even for a poly-mineral material like cement. The linear relationship is applicable from 1 day up to complete hydration. From the latter observation the conclusion has been drawn that from 1 day hydration onward the nature of the hydration products would remain the same (also Odler 1970).

Several authors have found a very good linear correlation between the heat of hydration and the amount of non-evaporable water. This suggests the two parameters to be equivalent as far as their applicability as hydration parameters is concerned. According to Bombed (1974), however, the non-evaporable water concept would yield more reliable values than the heat of hydration concept. Deviations from a linear relationship between the degree of hydration and Wn-values have to be expected for low hydration values (Le Chatelier 1905, Locher 1976). Also for very high degrees of hydration, 0.95< <1.0, the Wn(t)/ (t) - relationship would be less distinct (Le Chatelier, 1905). According to Granju et al. (1988) deviations of more than 10% have to be considered. Figure 1 shows the correlation beteen materials conversion, the heat of hydration and the chemically bound water as found by Röhling et al. (1990).

Fig. 1. Correlation between materials conversion (+), heat of hydration ( ) and the relative amount of chemically bound water (◦) (Röhling et al. 1990).

3	Clinker composition of Portland cement

3.1	Why attention for the clinker composition

If we want to approximate the "true" degree of hydration by the degree of heat evolution

of by the relative amount of chemically bound water

both the intermediate values Q(t) and Wnmax and the maximum values Qmax and Wnmax must must be known. The intermediate values are supposed to be measured according to standard test procedures during the relevant period of the hydration process. For the determinaion of the maximum values Qmax and Wnmax, can be calculated, in principle, directly from the clinker composition of the cement. For that purpose the clinker composition of the cement must be known.

3.2	Methods for determination of the clinker composition (Portland cement)

For the determination of the chemical composition of the cement clinker two basically different approaches exist, viz., the indirect and the direct methods. The indirect or ma-thematical methods are most attractive for desk research purposes. Direct or experimental methods are considered to be more accurate but tend to be tedious and laborious and are, therefore, expensive (Aldridge 1982). Direct methods have the advantage that they inherently account for the effect of the cooling history on the final clinker composition.

Indirect Methods

The most often applied mathematical procedure for the determination of the compound composition was proposed by Bogue in 1929 (1955). With the original version of his calculation procedure the amounts of C3S, C2S, C3A and C4AF were calculated form the mineral composition of the raw mateirals. Modifications of the Bogue method, and even fundamentally differently based calculation procedures, have been proposed by Lea (1970), Newkirk (1952), Locher (1961), Glauser (1962,1968,1971) and Taylor (1991). Major points of difference referred to the extent to which the effect of minor constituents and the burning and cooling processes were taken into account.

Results of compound calculations according to different procedures are shown in Fig. 2. The calculations refer to two Dutch Portland cements, viz. a coarse A and a fine C cement with mineral compositions as shown in the inserts of the figure. As a general trend it can be observed, that the C3S content according to Bogue and Lea is substantially lower than according to Locher and Glauser. With respect to the C2S content the reverse appears to be the case. Similar results have been reported by Roth (1970) for completely different cements. It is noted that the calculated cement composition is very sensitive to small variations in the mineral composition of the cement (compare the calculated composition of Type A and Type C cement).

Deviations between different methods and inaccuracies of the Bogue method have been reviewed by Aldridge (1982), Locher (1961) and by Bogue himself. According to Aldridge none of the methods proposed so far can be considered a significant improvement of the classic Bogue method. Locher (1961) concluded in a similar way that,

Fig. 2 Clinker compound composition of two Dutch cements as calculated according to different authors.

although the Bogue composition was not very accurate, it could nevertheless be used for a rough indication of the predominant chemical characteristics of the cement.

An indicator of the accuracy with which the major constituents of the clinker can be predicted is the multi-method standard deviation. The quantity can be deduced from the calculated C3S contents in the Portland cement A and C, presented in Fig. 2. For the C3S contents mean values of 56% and 67% are found with multi-method standard deviations of 6% and 10%, respectively.

Direct Methods

Direct methods for the determination of the compound composition are the electron mi-croscopy (Harrisso 1985), X-ray diffraction spectroscopy and X-ray fluerence analysis. It has been found that the C3S content obtained with microscopic methods are higher than the Bogue values (Aldridge 1982, Kristmann 1987, Locher 1961). According to Knofel et al. (1969) the microscopic C3S content are even up to 30%(!) higher than according to Bogue.

Kjellsen et al. (1997) compared the phase composition of sulphate resistant cement as obtained with the Bogue and modified Bogue methed (Taylor's method) with the quantitative X-ray diffraction analysis (QXDA) and SEM image analysis. The Bogue method and the modified Bogue method gave ferrite percentage of the clinker of 14.6% and 12.3%, respectively, wherease the QXDA and the SEM method gave 11.0% and 11.2%.

Direct versus Indirect Methods

According to Odler et al. (1981) it is hard to say which method yields the most realistic results. All currently used methods would suffer from method-bound systematic and non-systematic errors. Harrisson et al. (1985) found the results obtained by electron-optical analysis to be systematically better than those obtained with the Bogue method. Aldridge (1982), on the other hand, is quite clear in stating that of all methods only the microscopic method gives accurate results. He also found a pretty good correlation between the microscopic C3S content and the corresponding Bogue value. Apart from the good correlation between Bogue values and microscopically obtained data, it was because microscopic determinations were tedious and lengthy and most of the cement literature describes cement in terms of the Bogue composition, that Aldridge recommended the use of the Bogue method.

Uncertainties, or just scatter, in the clinker composition of the cement has consequences for the calculated values of the maximum heat of hydration and maximum chemically bound water. The limited accuracy that can be reached has be considered when the degree of hydration is used for describing the evolution of materials properties.

4	Heat of hydration

4.1	Adiabatic Calorimetry

In an adiabatic test the liberated heat Q(t) is calculated from the measured temperature T(t) from (see also subtask 2.2 and 2.3):

where ( c.cc) is the specific heat of the concrete, C [kg/m3] the cement content and T(t) the temperature rise in the concrete. The specific is generally considered constant, which is actually not the case (to be considered in more detail in subtask 2.3).

Adiabatic heat measurements are most convenient for producing continuous heat of hydra-tion curves under curing conditions close to or almost identical with mass curing. Many authors have judged this to be a major advantage of this method, since it enhances the possibility of direct application of the results for practical purposes (Basalla 1962, Catharin 1966, Huber 1988). Adiabatic hydration curves would be the most suitable starting point for temperature calculations in hardening structures. The fact that hydration of cement in concrete and mortar develops differently from that in neat pastes has been mentioned as another reason why adiabatic calorimetry is judged to be of great practical importance (Catharin 1966).

Accuracy

The high accuracy that can be reached with adiabatic calorimetry has been mentioned by Meissner (1933) in 1933 already. Particularly in the most interesting stage of the hydration process, i.e. up to about 7 days, accurate information is obtained. From 7 days onwards the accuracy decreases. For the majority of practical purposes, however, this does not constitute a serious problem.

Alègre (1961) mentioned a systematic error at 8 days in the order of 2°C. This can be estimated to be equivalent with an error of about 4%. Adiabatic hydration curves are re-ported to be reproducible within a scatter zone of ±0.15°C, equivalent with a coefficient of variation of 0.25...0.6% (Catharin 1966). In a Round Robin test, conducted in the framework of RILEM-committee TC 119, a multi-laboratory standard deviation was computed at 3.8°C (Koenders et al. 1944).

4.2	Isothermal calorimetry

4.2.1	Conduction calorimetry

Particularly for research on reaction kinetics isothermal methods for measuring the liberation of heat is used (Prosen 1985). The conduction method is one of the currently utilized isothermal methods. Just like the adiabatic calorimeter the conduction calorimeter produces continuous heat liberation curves. The maximum values for the liberated heat of hydration obtained with the conduction calorimeter are higher than those measured adiabatically (Catharin 1966). The formation of different hydration products, including changes (decrease) in the specific heat of the hydration products, are responsible for the observed phenomenon (to be addressed in subtask 2.3).

Accuracy

For the standard deviation of the conduction calorimeter values have been reported of 1.9 J/g at 3 days up to 4.0 J/g at 7 days, corresponding to a coefficient of variation of 1% (Q3d=220 J/g) and 1.5% (Q7d=280 J/g), respectively (Killoh 1988). Cembureau (Ibid. Killoh 1988) reports standard deviations of 3.1 J/g and 2.9 J/g at 3 and 7 days respectively, whereas the multi-laboratory standard deviations would vary between 8.5 J/g and 12.2 J/g.

4.2.2	Heat of solution method

The heat of solution method gives the heat of hydration at discrete points of time. The method is very convenient for routine work and is relatively inexpensive, but suffers from several chemistry-related complications (Catharin 1966, Killoh 1988). Its main advantage is its applicability for long-term measurements.

Accuracy

According to Catharin (1966) the accuracy is ±13 J/g, equivalent to a coefficient of variation ±3%. Earlier Woods (1932) had mentioned an accuracy of ±6 J/g. These values are in good agreement with those of Alègre, who found an error of ±13 J/g. A literature review carried out by Alègre (1961) shows coefficients of variation at 28 days from 0.8 to 8%. Estimating the amount of liberated heat at 28 days Q28d at 350 J/g, a standard deviation of 3 to 28 J/g has to be considered. Recently Killoh (1988) concluded that the minimum standard deviation that is likely to be achieved would be about 6 J/g, a value in good agreement with the early results of Woods in 1932. The "multi-laboratory standard deviation" was reported to range between 6.7....39.7 J/g (Cembureau/Killoh 1988). The ASTM standard (1982) mentions a value of 16.9 J/g.

According to Killoh, the standard deviation for the conduction calorimeter is about 5 times lower at 3 days and 3 times lower at 7 days than for the heat of solution data. He further found an excellent agreement between the heat of solution data and those obtained with the conduction calorimeter. From experimental work carried out by Lerch et al. (1949) it can be deduced, however, that the conduction calorimeter yields values about 5% higher than obtained with the heat of solution method (Q3d of 25 cements, cured at 21°C).

4.3	Maximum Heat of Hydration

4.3.1	General calculation format

The total amount of heat measured at macro level is the sum of mainly the heat of chemical reaction and heat of adsorption, the latter being about 25% of the total heat (Power 1946/47). The potential heat of hydration, i.e. the amount of heat liberated when all the cement has reacted, can be calculated from the clinker composition of the cement provided that the heats of hydration of the individual constituents are known and superposition of the individual heats of hydration is justified. For the maximum heat of hydration of Portland cement the following calculation format has been proposed (Verbeck 1960):

Qmax	= q1.(C3S) + q2.(C2S) + q3.(C3A) + q4.(C4AF) + q5.(C) + q6.(MgO)	(5)

with:	Qmax	= maximum amount of heat liberated at complete hydration	[J/g]

q1...q2	= heat of hydration of the constituents considered (see Table 1)	[J/g]

(...)	= content of constituents of the cement considered	[g]

The accuracy of the calculated heat of hydration depends on the accuracy with which the clinker composition has been determined and on the accuracy of the heats of hydration of the constituents.

4.3.2	Heat of hydration of constituents

With respect to the maximum heat of hydration of the constituents of cement, the pub-lished data shows a fairly consistent picture. An extract of the published data is given in Table 1. Particular attention must be given to the heat of hydration of C3A. C3A reacts with gypsum under formation of ettringite and liberation of 624 J/g C3A (Lerch et al

Table 1 Relative contribution to heat of hydration of clinker compounds [J/g]

q1	q2	q3	q4	q5	q6

Author	C3S	C2S	C3A	C4AF	free C	MgO	KC23S12	NC8A3

Woods (1932)	570	260	840	125	---	---	---	---

Bogue (1929)	500	260	866	125	---	---	---	---

Lerch et al. (1935)	500	260	866	1) 420	1166	850	2) ---	---

Thorwaldson (1930)	---	---	---	1166	---	---	---	---

Chatharin (1978	500	251	1340	420	1172	---	---	---

Adam (1976)	---	---	500	/ 170	/ 840	---	---	500/

---	---	630	290	1256	---	---	630

Newkirk (1952)	560	1360	300	---	---	---	310	1205

1)	Accounting for reaction of tricalcium aluminate hydrate and gypsum. Some extra 624 J/g SO3 must be considered (Lerch et al. 1935)

2)	Taken from literature (see Lerch et al. 1935)

1935). This amount of heat should be added to the 866 J/g C3A liberated during the conversion of ettringite into stable monosulphate, totalling 1,490 J/g. In order to account for the fact that not all the C3A will react with gypsum an apparent heat of hydration of 1,350 J/g is generally adopted. This value is in good agreement with the results of a least square analysis carried out by Verbeck et al. (1960).

4.4	Accuracy of predicted maximum heat of hydration

According to formula (5) the maximum heat of hydration of two Portland cements, indicated as cement A and C, has been determined. The mineral composition of the cements is given in the inserts of Fig. 2. The compound composition of these cements was calculated according to the methods proposed by Bogue, Lea, Newkirk, Locher and Glauser (see section 3.2). For the heats of hydration q1 ... q6 of the constituents the values were used as given in Table 1. Results are shown diagrammatically in Fig. 3.

From a straightforward statistical evaluation of the calculated heat of hydration data of these two cements mean values of 476 J/g and 502 J/g with standard deviations of 34 J/g and 33 J/g, i.e. coefficients of variation of 7.1% and 6.6%, were obtained. In these cal-culations two degrees of freedom are allowed for, viz. the calculation procedures for, firstly, the clinker composition and, secondly, the heat of hydration. Yong (1961) calculated a coefficient of variation by simply choosing the clinker composition as a degree of freedom. From his analysis, in which 20 cements were involved, coefficients of variation were deduced in the range from 1.5 to 4%. The major cause of scatter originated from the influence of alkalies. For practical applications a coefficient of variation of 4% was recommended.

In conclusion it can be stated that:

1.	Compound compositions determined according to different calculation formats can result in differences in the calculated maximum heat of hydration of up to 70...90 J/g (Fig. 3).

Fig. 3 Predicted heat of hydration of two Portland cements A and C. Clinker composition calculated according to procedures as proposed by different authors (section 3).

2.	Once having chosen a calculation format for the determination of the maximum heat of hydration, a coefficient of variation of about 4% for the obtained values should be considered.

4.5	Accuracy of the determination of the degree of heat liberation

For many practical and research purposes it is convenient to approximate the degree of hydration (t) with the degree of heat liberation (Q(t)), viz.:

where Q(t) is the heat liberated at time t. The absolute error (t) of the degree of heat liberation calculated according to eq. (6) can be approximated with:

Let us assume the absolute error Q(t) and Qmax to be equivalent with the five percent fractile of Q(t) and Qmax, respectively. For the absolute deviations from the best possible values for Q(t) and Qmax it follows:

Q(t) =	1.64 * 0.6% = 1%	(section 4.1: 0.6%)

and:	Qmax =	1.64 * 4.0% = 6.5%	(section 4.4: 4.0%)

For the absolute error (t) it follows:

(t) = 0.075 (t)

If both the intermediate and maximum amounts of heat of hydration were determined with the conduction calorimeter and were found to be 210 J/g at 7 days and 420 J/g at com-plete hydration with standard deviations of 3 J/g at 7 days and 4 J/g at complete hydration, the absolute error (t7) calculated according to the foregoing format would be 3.6%, or 0.036*210=7.6 J/g. The latter value can be estimated as the minimum possible error, i.e. the best possible result.

Against the background of these accuracy considerations it is worthwhile to realize that predictive models, which can generate heat liberation curves, and hence curves for the degree of hydration, with an accuracy of 3.6...7.5% as related to the mean value of a series of experimental results, can be considered as equally reliable. Individual predictive models can only be further improved if it was possible, for example, to quantify explicitly the influences of minor constituents on the heat liberation and the hydration process. As long as these effects cannot be modelled reliably, one has to consider a scatter in the ex-perimentally obtained results as indicated.

Further it is emphasized that in order to obtain reliable values for the degree of hydra-tion, the intermediate and maximum amounts of heat of hydration should preferably be determined according to one and the same experimental method. This would eliminate one of the major sources of inaccuracy.

Note:

Assuming a linear relationship between the degree of hydration and compressive strength (see Task 3), the standard deviation of the theoretical strength will be equal to that of the degree of hydration, i.e. 3.6...7.5%. In this respect it is interesting to bear in mind that the standard deviation of the cube compressive strength for one and the same cement, i.e. one and the same concrete mix, obtained under laboratory conditions generally varies between 3...5%.

5	Chemically bound water

5.1	General Aspects

At complete hydration of cement, an amount of water of about 22%...25% of the weight of the anhydrous cement is chemically bound to the cement (Keil 1971, Powers et al. 1946/47). In this form, which actually includes water molecules which are most tightly adhered to the surfaces of reaction products, it is considered to be an inherent part of the solid matter. The resulting volume of the reaction products is less than that of the summarized volumes of the constituents cement and water. This volume reduction is equivalent with 18% to 26% of the volume of the chemically bound water (Copeland 1956, Czernin 1954).

5.2	Determination of chemically bound water Wn

The non-evaporable water is defined as the part of the total water content that is lost, i.e. has chemically reacted with the cement, when a specimen, which has been brought to the "bare surface condition", is ignited at 1,000°C (Mills 1966). This bare surface condition can be obtained with one of the following methods (Mills 1966, Powers et al. 1946/47):

Oven drying at 105°C (O-drying)

Drying at room temperature over magnesium perchlorate (P-drying);

Drying under vacuum by the dry-ice method (D-drying);

According to Mills (1966) the non-evaporable water content determined according to the O-drying method is about 11% less than the P-drying values and 3% less than the D-dry-

Table 2 Chemically bound water Wnmax [g/g] according to different authors.

Author	C3S	Portland cement Comments / Drying methods Powers et al. (1946/47)

Locher (1966)

Brunauer et al. (1964)

Locher (1976)

Mills (1966)

Odler et al. (1972)

Odler et al. (1979)

Le Sueur et al.	0.23

0.21

0.204

0.21

---

---

---

0.26-0.30	0.21 - 0.25

---

---

---

0.24 - 0.26

0.20 - 0.22

0.20 - 0.22

--- P- and D-drying

Vacuum drying

Oven drying

American cements Type I and III

Review of different authors

O-drying in dry N-atmosphere

ing values. Lea (1970) has emphasized the influence of the height of the ignition tempera-ture on the non-evaporable water content, whereas Rechenberg (1976) discussed the pros and cons of several measurement methods, such as the Penfield method.

Table 2 summarizes values of non-evaporable or combined water as reported by different author. Differences in measuring methods and curing conditions sometimes allow for great differences in these values. An increase of the w/c ratio has been reported to in-crease the non-evaporable water content (Huang Cheng-Yi et al. 1985, Koster et al. 1986, Rossler 1985). Some authors, however, could not find a significant effect of this parameter (Locher 1966). Curing at elevated temperatures would result in a decrease of the non-evaporable water content (Koster et al. 1986, Odler et al 1986).

From foregoing considerations it must be evident that, in order to avoid misinterpretations of literature and experimental data, the drying method and the ignition temperature should always be indicated!

Table 3 Chemically bound water of constituents [g/g].

Author	w1

C3S	w2

C2S	w3

C3A	w4

C4AF

Comment Power et al. (1946/47)

Copeland et al. (1960)	0.187

0.228

0.234

0.230	0.158

0.168

0.178

0.196	0.665

0.429

0.514

0.522	0.213

0.132

0.158

0.109 paste 0.5 years old

paste 1.0 years old

paste 6.5 years old

paste 13 years old 5.3	General calculation format for maximum chemically bound water Wnmax

A general format for calculating the maximum amount of chemically bound water has been put forward by, among others, Copeland et al. (1960):

Wnmax = w1*(C3S) + w2*(C2S) + w3*(C3A) + w4*(C4AF)	(8)

with:	Wnmax	= maximum chemically bound water at complete hydration	[ g/g]

w1...4	= chemically bound water of individual constituents	[g/g]

(...)	= content of major constituents of the cement considered	[g]

Values for the amounts of chemically bound water wi (i=1,2,3,4) of the individual constituents as proposed by different authors are given in Table 3.

5.4	Example of prediction of maximum chemically bound water Wnmax

For the two Portland cements A and C, with chemical composition as shown in Fig. 2, the maximum amounts of chemically bound water have been calculated according to eq. (8). The results are shown diagrammatically in Fig. 4. From a statistical evaluation, similar to that carried out for the maximum heat of hydration data, the mean values and standard deviations of the maximum amount of chemically bound water can be calculated. Mean values for Wnmax were found to be 0.219 g/g and 0.229 g/g with standard deviations 0.0047 g/g and 0.0038 g/g for cements A and C, respectively. The corresponding coefficients of variation are 2.2% and 1.7%. A comparison of these coefficients with those obtained for the maximum heats of hydration, i.e. 7.1% and 6.6%, reveals that the calculated maximum chemically bound water seems to be less susceptible to the method according to which the clinker composition is determined.

From the standard deviations of the chemically bound water of the constituents, Copeland computed the coefficient of variation for the maximum amount of chemically bound water of Portland cement clinker at 7.3% to 5.5% (Copeland 1960), which is close to the coefficients of variation found for the heat of hydration values. These values can be compared with the coefficient of variation of 4% recommended by Yong (1961) for the accuracy with which the heat of hydration could be determined for any arbitrarily chosen clinker composition.

Fig. 4. Calculated maximum values of chemically bound water of two Dutch Portland cements A and C. Clinker composition according to different authors (Fig. 2).

5.5	Relative amount of chemically bound water. Accuracy and reliability

Particularly for theoretical and research purposes the relative amount of chemically bound water, i.e.

is often used as a measure of the degree of hydration (t). With respect to the reliability and accuracy of this concept it should first of all be emphasized that substantial errors can be introduced when data obtained according to the O-, P- and D-drying methods are confused. This might already give rise to an error in the relative amount of chemically bound water, and hence in the degree of hydration, of up to 10%. Further it can easily be seen that the accuracy with which the relative amount of chemically bound water (Wn(t)) is calculated can never exceed the accuracy of the quantities involved in eq. (7). Assuming a coefficient of variation for Wn-measurements of about 1.5%, and for the calculated maximum amount of chemically bound water of 5.5% (Copeland, section 5.4), the coefficient of variation of (Wn(t)) would amount to 7%, which is similar to the estimated accuracy with which the degree of heat liberation can be determined.

6.	Non-Portland and blended cements

6.1	Identification of state of hydration in non-Portland cements

For Portland cements the calculation procedures for the heat of hydration and chemically bound water at complete hydration are well defined. For non-Portland cements and blended cements the situation is less well developed.

To be extended

6.2	Slag cement

To be done

6.3	Effect of silica fume

The effect of silica fume on the hydration process has been studied by Atlassi and Kjellsen. According to Kjellsen the presence of silica fume hardly affect the hydration of the Portland cement to which it was added. No data was given about any release of heat of the silica fume itself.

To be worked out further

6.4	Effect of fly-ashes

To be done

7	Rate of reaction

7.1	General

Different processes

7.2	Temperature effects

Rate of processes dependent on temperature. Temperature effects described with actication energy.

7.3	Activation energies

7.3.1	Literature data

7.3.2	Procedure for determination EA experimentally

Activation energy determined from adibatic or isothermal hydration curves.

Description of procedures

Examples

8.	Degree of hydration in the practice

8.1	Determination of the degree of hydration in hardening concrete structures

8.2	Examples

9	"Degree of hydration concept" and "Maturity concept"

9.1	History of maturity concept

9.2	Relation between maturity and degree of hydration

10.	Evaluation