J.G.Wilson N.K. Gupta

Indexing terms: Concrete, Electrokeat, Heat distribution

I I Abstract: The problem of the distribution of heat in long curing beds used for the accelerated curing of concrete by electroheat is considered. A travelling wave solution is obtained for two configurations using experimental values of the electrical properties of concrete. From these solutions, recommendations are made regarding the optimal electrical layout to allow accelerated curing to be carried out while achieving the highest possible quality of the material.

1 Introduction

The acceleration of gain in strength of concrete by ele- vating the temperature is a standard technique used mainly in the production of prestressed precast compo- nents such as lintels, roof and floor beams, and railway sleepers. The primary object of the accelerated curing is to allow a throughput of components within the shift patterns of a normal working day. There are two com- mon methods used to raise the temperature of concrete by electrical heating, in one method an electric current is passed through the reinforcing bars, which heat up, and transfer heat into the concrete by thermal conduc- tion, and in the other, an electric current is passed directly through the concrete which, in this early stage, is a good ionic conductor. This generates heat directly within the material thus causing a rise in temperature. In this case the reinforcing bars form one electrode in this system, and the steel mould, the other. Alternating current at normal supply frequencies is generally used in both methods. The use of these techniques has been reported by a number of authors including McIntosh [I], Khoroshavin et al. [2], Kafrey [3], and Bredenkamp et al. [4].

In each of the methods, the concrete and reinforce- ment are normally placed in a long rectangular metal channel, which acts as a mould. Individual components can be separated by partitions within the mould. The reinforcement is normally continuous through the mould system, which simplifies prestressing, and must be cut before the individual components can be removed from the mould. 0 IEE, 1996 ZEE Proceedings online no. 19960156 Paper first received 18th January 1995 and in revised form 1st November 1995 The authors are with the Department of Electrical, Electronic, and Com- puter Engineering, Napier University, 219 Cohton Road, Edinburgh EH14 IDJ. UK

Neville [5] suggests that accelerated curing by eleva- tion of the temperature may reduce the long-term strength and durability of concrete. This degradation can be minimised by limiting the maximum tempera- ture achieved and the initial rate of rise of temperature.

fl neutral

\ base plate

concrete reinforcement

base plate Fig. 1 Short-circuited transmission line

2

There are additional heating effects in both of the sys- tems described. In the case where heating is intended to be due to current passing through the reinforcement, one end will be connected to the line voltage and the other end to neutral. Assuming that the neutral and the mould are at earth potential, there will be leakage cur- rents along the length of the reinforcement into the concrete which will generate heat by direct electrical conduction. This configuration is shown in Fig. 1, and while the position of the earth point on the mould may be randomly located, a possible arrangement is that of a short-circuited transmission line. In the case where direct electrical conduction is intended, current must be passed through the reinforcing bars, which will heat up and provide heat by thermal conduction. This configu- ration is shown in Fig. 2, which can be identified as an open-circuited transmission line.

In both cases therefore, heating of the concrete takes place because of thermal conduction of heat generated in the reinforcement, and also because of direct electri- cal conduction in the concrete. Analysis of the heating effects must take into account the distributed nature of the resistance of the reinforcement and the conductance of the concrete. Travelling wave theory must therefore

Problem of assessing the heating effect

IEE Proc -Electr Power Appl , Vol 143, No 2, March 1996 172

be used to assess the power distribution in such a system.

In the case of heat generation in the reinforcement bars, it is to be expected that the temperature gradients will be large because of the isolated geometry of the heat source.

concrete interconnections

line \ \

base plate

concrete reinforcement

k, base plate

neutraland earth

Fig. 2 Open-circuited transmission line

A X ___c

b

C p A x

Rp /A X

Fig. 3 Trunsmission ‘i- 3 line element

I --c

T

vt

Fig. 4 Transmission line vulues

3 Travelling wave analysis of the system

Because of its ionic conduction mechanism and hetero- geneous nature, the electrical properties of concrete are very complex. There is evidence to suggest that for fre- quencies below lOkHz, a concrete sample between two electrodes may be approximated by a series RC circuit (Wilson and Whittington [SI). Taking this to be the case, a transmission line formed by the reinforcing bars and metal mould as conductors, and concrete as the dielectric, could be regarded as a cascade of the infini- tesimal elements shown in Fig. 3, where L,, R,, Cp and l/Rp, are values per metre. Ax is an infinitesimal incre- ment in length. For this transmission line:

where 2, = L,/R,

The complex travelling wave parameters of propaga- tion constant y and characteristic impedance 2, are then given by:

r = m

Currents, voltages and impedances for the transmission line are shown in Fig. 4. The sending-end impedance is given by:

2, + Zo tanh yl Zo + Z, tanhyl

z- -

where 2, = load impedance 1 = length of transmission line

In the open-circuit case 2, = 00 and 2, = Zo/tanhyl. In the short-circuited case 2, = 0 and 2, = 2, tanhyl. The distribution of voltage and current along the line is then given by:

= 5 zt (cosh yz -

At point x a small change in position Ax will cause a change in series resistance of R,Ax. The series power dissipated in this resistance will be APT = I2R,Ax. The series power dissipated per metre will then be

APS P3(x) = - A X

= I ~ R ,

1 v,” - I zt r sinh yx RS

Similarly, a change Ax will cause a change in shunt conductance of AxIRp. The shunt power dissipated in

173 IEE Proc -Elear Power Appl , Vol 143, No 2, March 1996

this conductance will be AP, = V2AxlRp. The shunt power dissipated per metre will then be

= V,’ 2 0 1

zt coshyx - - sinhyz

The total power density along the line will then be

For a given line voltage V,, the power density distribu- tion will depend on the parameters pertaining at a par- ticular instant. It is convenient to consider the power density in comparison with the average power density along the line, which depends on the input power and the length of the line. This will give a relative power density. Taking:

PT(Z) = PS(.) + P p ( 4

1 - = Gt + jBt zt

= P A 2 where pf = GJl = power density factor, gives, for the relationship between the relative power densities,

M-4 - PS(4 PP(4 +- ~ _ _ -

PAV PAV PAV

4 Estimation of transmission line parameters

The geometry of the reinforcement in a precast compo- nent can be very complex. To allow computation the simple geometry given in Figs. 1 and 2 is used. This consists of a single layer of reinforcement near the top surface of the sample and a conducting plate on the bottom surface. The resistance of 1 m of 1Omm mild- steel reinforcing bar is estimated to be 1.7571 x 10-3R, assuming a resistivity of 13.8 x 10-8Qm. Taking a l m wide section containing nine such bars, and assuming a similar resistance in the return path, gives

x 2 1.7571 x 10W3

9 R, =

= 3.905 x lop4 Om-’ Consider the behaviour of the concrete. Measurements were carried out on a sample 0.6 x 0.6 x 0.15m with reinforcement 30mm below the top surface and a stain- less steel plate on the bottom. Converting a parallel resistance value to that for l m width and l m length, gives the shunt resistance for a metre:

R, = R,(0.6)’ = 0.36R, where R, is the value measured on the sample. The concrete also has a time constant associated with the series representation which is independent of dimen- sions. The following values were measured on a sample of concrete with mix proportions by mass, water1 cement ratio 0.5, cementisandlcoarse aggregate ratio 1: 133 .0

Table 1: Concrete electrical parameters

State of concrete R, (0) C, (mF) -cP ( s ) R, (Rm) Immediately after 2.145 18.75 4.039 x IO” 0.772 mixing

After one day 11.254 7.09 7.937 x 4.048

174

Because the series resistance per metre R, is small, the series inductance per metre L, might be important. Considering a parallel-plate line configuration, the inductance per metre is

d L, = 4.ir x W

Taking width w = l m and thickness d = 0.12m gives

L, = 47r x l op7 x = 1.508 x Hm-I 0 12 1

Thus

= 3.862 x lop4 s L, - 1.508 x R, 3.905 x

rs=--

and at 50Hz, az, = 2n x 50 x 3.862 x the minimum value of

(UT,)’ = (271. x 50 x 4.039 x

= 0.121 also

= 161.0

Thus, as ms is substantially less than 1, the series inductance is unlikcly to haw a significant effect on the result. Nevertheless it has been left in the compu- tation. (mJ2 is very much greater than 1. Therefore the approximation regarding the shunt admittance is justified.

5 Theoretical results

The lengths of curing beds vary and beds as long as 100111 are used. Calculations were carried out using a length of 50m, and results are presented with electrical characteristics appropriate to both freshly mixed con- crete and to concrete which has cured naturally for one day. Results are given for both open-circuited and short-circuited cases.

0 10 20 30 40 50 position,m

Fig.5 50m sample, open circuit Senes res. 3.905 x 104Wm Parallel res. 0.775D.m Parallel time const. 4.039 x lo-% Power density factor 9.323 x lO-’S/m

Fig. 5 gives the results for the relative power density against distance along the curing bed for the open- circuited case with freshly mixed concrete, while Fig. 6 gives similar information but for concrete which has cured for one day. For the low resistance concrete in Fig. 5 , there is considerable variation in the relative power density for both the series power and the shunt power, giving a large variation in the total power den- sity, of nearly 1:5. For the higher resistance concrete of Fig. 6, the variation in total power density is reduced to about 1:1.6.

Figs. 7 and 8 give the corresponding results for a short-circuited system. Fig. 7 is for the low resistance concrete, and Fig. 8 for the high resistance material.

IEE Proc-Electr. Power Appl., Vol. 143, No. 2, March 1996

The results for the short-circuited case are very similar to those for the open-circuited case, except that the series power contribution is greater in the short-circuit case, and the shunt power is greater in the open- circuited case. The variations in power density along the bed are very similar for both the open and short- circuited cases.

I----I---I 3.0 -----

Thus, for a power density factor of 9.323 x lO-'S/m and a line voltage of lOOV, the average power per metre would be 9.323kWlm. The calculations were repeated for a bed of length 10m. Figs. 9 and 10 give the results for the open-circuited case, and Figs. 11 and 12 for the short-circuited case. The results for the total relative power density are again very similar for the two configurations, but for the low resistance concrete the variation in total relative power density with dis- tance along the bed has now been reduced to less than 1:l.l.

I I i I I 1

0 10 20 30 40 50 position,rn

Fig.6 50m sample, open circuit Series res. 3.905 x 104R/m Parallel res. 4.048Qm Parallel time const. 7.973 x 10Ps Power density factor 2.291 x 10-'S/m

3.0

0 10 20 30 40 50 position,m

Fig.7 50m sample, short circuit Series res. 3.905 x I04R/m Parallel res. 0.775Qm Parallel time const. 4.039 x 10-2s Power density factor 1.408Sim

position,m Fig.8 50m sample, short circuit Series res. 3.905 x lO4Q/rn Parallel res. 4.04XQm Parallel time const. 7.973 x 10-2s Power density factor I .90 I Slm

The power density factor given on the graphs allows the average power per metre to be calculated if the input line voltage is known: average power per metre = power density factor x v2 IEE Proc.-Elects. Power Appl., Vol. 143, No. 2, March 1996

1 0 2 4 6 a 10

position,rn

I I I

Fig.9 lorn sample, open circuit Series res. 3.905 x I04Q/m Parallel res. 0.775Qm Parallel time const. 4.039 x 10-2s Power density factor 1.270Sim

3.0

2.5

0 2 4 6 a 10 position,m

IOm sample, open circuit Fig. 10 Series res. 3.905 x 10411/m Parallel res. 4.04XRm Parallel time const. 7.973 x 10-2s Power density factor 2.463 x 10-'S/m

3 0

0 0 , I I I I 0 2 4 6 a 10

position, rn IOm sample, short circuit Fig. 11

Series res. 3.905 x 10 4Q/m Parallel res. 0.775Rm Parallel time const. 4.039 x lo-% Power density factor 2.567 x lOS/m

175

bulk of the material reaches the highest acceptable tem- perature, the temperature gradients within the concrete must be minimised, and therefore variations in power density with position should be minimised.

Heating by passing current through the reinforce- ment will produce a significant temperature gradient because of the isolated nature of the heat source but generation of heat by direct conduction through the concrete itself will give a much more dispersed system which can be expected to have much lower temperature gradients. This would suggest that the series power should be minimised, and hence the open-circuited con- figuration is to be preferred.

However, even in the open-circuited case, it would be expected that for freshly mixed concrete in long beds, the wide variation in total power density in end-fed sys- tems would result in considerable variation in tempera- ture along the length of the bed. This can be reduced by minimising the active length of the bed. This could be achieved by having multiple supply feed points along the length of the bed. For concrete similar to the type considered, and using similar dimensions for the bed, the distance between feed points should be limited to between 10 and 20m.

Ps

2 1 0 I 1 I , I

0 2 4 6 8 10 positi0n.m

Fig. 12 Series res. 3.905 x 104n/m Parallel res. 4.0480m ~ a r a l ~ e l time const. 7.973 x lO-*s Power density factor 2.523 x 10S/m

1Om .sample, short circuit

6 Conclusions

The results presented are purely theoretical and are limited to an estimation of the power distribution. To allow comparison with a practical case it would be nec- essary to carry out a thermodynamic calculation to obtain the temperature distribution. In turn, the curing process, which causes a change in the electrical proper- ties of the concrete with time, is very much dependent on temperature, resulting in a complex relationship between power density, temperature, and electrical properties. However, provided that the thermal con- ductivity is not high, which will be the case within the concrete, inference can be drawn regarding the temper- ature distribution, from the variation in power density.

To ensure control of the quality of the concrete it is necessary that both the maximum temperature and the rate of temperature rise be controlled. To ensure that the maximum temperature is not exceeded, while the

7 References

1 MCINTOSH, J.D.: ‘Electrical curing of concrete’, Mug. Concr. Res., 1949, (January), pp. 21-28

SKAYA, S.A., and SUROVTSEV, L.A.: ‘Hardening of cast mag- nesia-spinel concrete by electric heating’, Ogneupory, (USSR), 1978, 19, (5), pp. 3942; Refractories, 1978, 19, (5-6), pp. 305-308

3 KAFREY, I.D.: ‘Direct electrical curing applied to battery cast- ing machines’, Concr. Plant Prod., 1985, (November), pp. 435437

4 BREDENKAMP. S.. KRUGER. D.. and BREDENKAMP,

2 KHOROSHAVIN, L.B., POPOVA, V.I., PREOBRAZHEN-

G.L.: ‘Direct electric’curing of concrete’, Mag. Concr. Res., 1993;

5 NEVILLE, A.M.: ‘Properties of concrete’ (Longman, 1981), 3rd 45, (162), pp. 71-74

edn. 6 WILSON, J.G., and WHITTINGTON, R.W.: ‘Letter on “The

electrical response characteristics of setting cement paste” by McCarter and Curren’, Mag Concr. Res., 1985, 37, (130), pp. 52- 53

176 IEE Puoc.-Electr. Power Appl., Vol. 1432 No. 2, Mavch 1996