DELFT UNIVERSITY OF TECHNOLOGY
DEPARTMENT OF CIVIL ENGINEERING
Report 5-79-1
On the heat of hydration of cements
by Dr. Ing. H.W. Reinhardt
STEVIN LABORATORY
CONCRETE STRUCTURES
s t e v i n - r e p o r t : 5 - 7 9 - 1
J^
^^-^ M^'oOn the heat of hydration of cements
by
Dr.-Ing. H.W, Reinhardt
Cf
- •] - Bibliotheek
afd. Civiele Techniek T.h\. Stevinweg 1 - Delft.
On the heat of hydration of cements
D r . - I n g . H.W, R e i n h a r d t , S t e v i n - L a b o r a t o r y , D e l f t
1. Introduction
There are many structures where the temperature rise due to the heat of hydration is of great importance in respect to cracking. Most of these structures occur in hydraulics construction and tunneling. Suitable means which decrease the heat liberation, are the use of low heat cement, low begin temperature, less cement content or in-ternal cooling. Demands of the practice like rapid continuation of the work are sometimes antagonistic. In order to optimize the pro-duction, analysis of temperature distribution and thermal stresses during concrete hardening is required.
For such an analysis, some material quantities are needed as a function of temperature and time, for instance the rate of heat liberation of the cements, the development of strength, elasticity, thermal conduc-tivity, and thermal expansion. In this paper, the main interest will lie in the heat liberation and a little in the mechanical properties.
2. Experimental approach 2.1. Test methodes
Generally, there are two methods for determining the heat of hydration of cements. The first is the adlabatic method which uses a sample of cement paste with a certain begin temperature which is allowed to hydrate in such a way that no heat may escape from the specimen. That means that during hydration the temperature in the specimen will rise to a maximum value. .. ::
-Differentiation of the time-temperature curve [multiplied by the spe-cific heat of the specimen] leads to the rate of heat liberation
The other method is the isothermal one which uses cement paste samples with a certain begin temperature which is forced to be constant. The heat of hydration which would lead to a temperature rise is being withdrawn and measured. By integration over a time period one gets the total heat up to this time. Physically, this method is clearer because the temperature is constant.
In practice, for instance in a several meter thick wall, both regimes can occur: the center of the wall will be sinnilar to the adiabatic case, while the surfaces resemble more the isothermal case. For analysis, isothermal measurements seem to be more versa-tile and are therefore prefered.
Way of presentation of the results
«
For the following treatment, experimental results of Lerch and Ford (1] are used. In that publication the heat of hydration of a
great lot of different cements under isothermal conditions are reported, An example of these is given in fig. 1.
time, hours
3
-The influence of temperature on the rate of heat liberation during time of hydration is evident. Using these curves in a thermal analysis would mean switching from one to another line according to the ruling temperature distribution. Important would be the correct consideration of the state of hydration, i.e. the real time t must be ajusted to the time - temperature history. In order to avoid problems, the real time t is proposed to be
1] replaced by the -cate of reaction r which is defined as
get)
On CI]
with Qj-j the total heat of hydration of cement and QCt] the amount of heat liberated until the time t.
Using r on abscissa, fig, 1 becomes fig, 2 with the
10" r3_J_
gs
Fig, 2. Rate of heat liberation as a function of state of reaction r
remarkable feature that all curves show a similar shape. The physical meaning behind this result is that the heat production during hydration is similar for all temperatures, only the maximum value of heat liberation is influenced by temperature. The question rises if this phenomenon is true only for this chosen cement or if it could be valid for other cements and temperatures as w e l l .
As an answer, four cements from (1] (Portland, low heat] were
taken. Moreover, the ordinate of fig, 2 is standardized by deviding by q which is the maximum value of the rate of heat liberation
max
at a certain temperature. The results are plotted in fig, 3. It seems
Ftj.S. Standardized rate of heat liberation versus state of reaction. (Results used from (1] ]
that a single line can be drawn for all results. That would mean that the reaction of various cements follow the same rule, independant of temperature and composition. Only the axes of the diagramme must be chosen in this appropriate way.
The best fit of the results can be expressed by the following function
q(t] max
48r^e'^^^ + 0.12 sin^ (irr) (2]
wliich is valid for 0 < r < 1
This somewhat surprising result will be analysed and discussed in the following chapter.
5
-For analysis purposes, the maximum heat liberation q must be
max known as a f u n c t i o n o f t e m p e r a t u r e . I n f i g . 4 , t h e v a l u e s o f q o f e i g h t c e m e n t s f r o m ( 1 ) a r e p l o t t e d a g a i n s t t h e t e m p e r a t u r e max _ - I- & K w h e r e t h e known f a c t can be s e e n 10 3 J 20 g s 1 5 - 10-s y m b o l 10-s cement nr. from [1] 11 25 31 43 16 18 24 41 o A ^ a • A • •
u
A A • a a 20 30 40 t e m p e r a t u r e , ' C 50Fig. 4. Maximum rate of heat liberation against temperature
that with increasing temperature, q also increases. The temperature
* •> max ^ d e p e n d e n c e f o l l o w s a l i n e [A rrhi^ius retd-noty]
max
b
ae~ T ( 3 ]
with T the absolute temperature in K and a and b two constants which are characteristic values of the cement used. These values must be determined by isothermal tests at at least two temperature levels. (For greater accuracy similar diagrammes would be necessary for different water-cement-ratios, too].
Theoretical treatment
This chapter will deal with the question if a function like eq (2] or a single line like in fig. 3 is justifiable for different cements and
temperatures.
For this purpose, a publication of Double et al. (2] is taken as a reference where an Avrami-type expression [3] is used for the reaction of cement. This expression is
-kt"
r^ = 1 - a ^"^ C4)
with r the volume fraction of cement transformed at any time t and
V
k and n two factors depending on cement type and temperature. r = 0 is taken at the end of the so-called dormant stage.
V
If r = 1 , the reaction should be finished and the whole cement should
V
be transformed. But that is not true. The reaction rate is only decreased to a very low level comparable with the one after the dormant stage. Tenou-tasse and Donder (4] use the Avrami-expression, too, and they conclude that this expression is valid for the period of time untill the reaction has decreased to the level mentioned above. At this time, only a fraction of about 40% of the total heat has been developed.
In terms of the state of reaction r speaking, r is zero at r = 0,05 and r
'^ ^ V V
is one at r = 0,40. The following demonstration is therefore restricted to the region 0,05 < r < 0,40 which is indentical with Q < r < 1 . The
trans-" ' V V
formation of the r-axis can be expressed by
r = 0,35.r + 0,05 (5)
V .
With the definition r by eq. (1) r gets the form
Q(t] - 0,05 Qo
V
0,35 Q„
7
-Using eq. (4] for r , the rate of heat liberation is got by differentiation with respect to the time t
,, , dq(t] n oc n ., "I^t" ^n-1 ,,, q(t} = = 0,35 g kne . t (7)
dt
In order to arrive at a function according to fig. 2, the real time t has to be substituted by r . Using the relation (4] one gets
ln(1-r ] = -kt" (3}
and
n-1
^-^"1 r ^ 1 r^, ^ \ ^
t
= { - ]^ In (1-rJ } (gj
These two expressions lead to the new expression
1
nzl
q(t] = 0,35 Q^K ' n(1-r ] { -In (1 - r ]} " (10]
which consists of two parts, namely a first part O^k .35and a second part with r as a variable. According to Double et al. (2], the coefficient k takes account of the temperature whereas n is a rather constant coefficient for all temperatures. If we regard n as a constant equal to an average value, the second term of eq[.10] is a function of r only, independent of the temperature. The first term is a factor which determines the ordinates of the lines, but does not affect their shape.
The place where the maximum value of q occurs, is given by n - 1
rj" = 1 - e' " • (11)
as can be seen from the appendix. Typical values of n for cements are lying between 2 and 2,5_^and for pureC S n is found to be 3 (4] That means for cements that r^ bsccmss 0.39 till 0.45
which is identical with r = 0,19 and 0,21 respectively.
Thus, n does not affect the result so much and the assumption of an average and constant n is justified for practical use.
The result of this theoretical treatment with n = 2,5 is illustrated by the dotted line in fig. 3 which shows a very good agreement between the experimental results and eq. (11] with respect to the position of the peak value. The agreement is less with respect to the behaviour after the peak value but still acceptable. The reaction is not stopped with r = 0,40 but does continue with a low heat liberation which will steadily attenuate untill r = 1.
Three points can be concluded from this theoretical excursion:
first, the rate of heat liberation of various cements follows one line when the abscissa is scaled in the state of reaction r, because the coefficient n can be taken constant. Second, the temperature does not affect the shape of the lines, i.e. by deviding by the maximum value one single line comes out. Third, this theoretical demonstration is - strictly speaking - only valid up to a state of reaction equal to 0.5, but beyond this point the rate of heat liberation is rather low and there is no evidence for different behaviour.
Some reflections on mechanical properties
Because there is a strong relation between rate of heat liberation on one side and gain in strength and rigidity on the other side, one could think upon that there may exist similar diagrammes for strengths and .rigidity development as it exists for heat liberation in fig. 3. The most simple case would be that the same diagramme holds true for various properties. For instance, the development of the elastic modulus
Bibliotheek
afd. Civiele Techniek T.H. Stevinweg 1 - D e l f t
9
-O .25 .50 .75 1.00
Fig. 5. Development of the elastic modulus as function of r
could be according to fig. 5.
2
If - as an example - E = 30 000 N/mm (E is the elastic modulus at r -3
0 = 400 J/H and q =6.10 J/g.s - then the maximum development 0 ^ max
of E could be calculated from
,dE, 0 dt max On
max 0
(11]
which would be 0,45 N/mm .s. The same example for the compressive strength with a strength of / = 60 N/mm at r=1, using
df'c { —- } ^ dt max f' c,0 max Or (13] - 3 2 would g i v e a maximal s t r e n g t h growth o f 0 , 9 . 1 0 N/rrm .s o r 3,24 N/mm^.h,
The existence of these type of diagrammes would be very helpful for the calculation of thermal stresses during hydration. Up till now, this consideration is only an assumption but more effort will be taken to establish this sort of diagrammes,
Conclusion
The aim of this paper is to give a simple formulation of the rate of heat liberation of cements during hydration. This is done in an empirical way using isothermal measurements from (1]. It came out that there exists a single curve which is valid for various cements at different temperatures if the rate of heat liberation is plotted against the state of reaction r.
Using an Avrami-type expression for the reaction, the existence of a single curve has been demonstrated. The chemo-physical background has not been treated because this can be read much better in the literature, i.e. (2,3,4].
The empirical formulation can be used in the analysis of the temperature distribution of thick walled structures where the temperature varies from point to point.
Further effort will be focussed on the development of strength and rigidity as a function of the state of reaction r in order to provide the necessary relations for the appropriate analysis of thermal stresses during hydration.
••^ • • .
Acknowledgement
This study has been carried out in close contact with a working group of CUR (Research Committee of tthe Dutch Concrete Association]. The author would like to thank all members of the group for valuable suggestions and discussions.
11
-7. References
(1] Lerch, W. and C.L. Ford. Long-Time Study of Cement Performance in Concrete, Chapter 3. Chemical and Physical Tests on the Cements. J.ACI 19(1948], no. 8, p, 745/795,
(2] Double, D.D., A. Hellawell and S.J. Perry. The hydration of Portland cement. Proc.Roy. See. London A 359 (1978), p. 435/451.
(3] Avrami, M. Kinetics of Phase Change. J. chem. Physics 7 (1939], p. 1103/1113, and 8 (1940], p. 212/224.
(4] Tenoutasse, N. and A. de Donder. La cinetique et le mecanisme de 1'hydratation du silicate tricalcique.
8. Appendix
In order to determine the ctatc of reaction r where the maximum rata of
heat liberation does occur eq. (9] must be differentiated in respect
to r:
V
1
^_
rr1_
^ O S O g n k ^ {(1-r,]i^ {-ln(1-r,]}"'^ C- : j 4 ^ ] (-1] - {-ln(1-r;} ^ } (Al)
This expression can be simplified to
1 - - "•''
