Effect of early overloading of concrete on strength at later ages

Effect of early overloading of concrete on strength at later ages

CEMENT and CONCRETE RESEARCH. %'ol.22, pp. 92%936° 1992. Printed in the USA. 0008-8846D2. $5.00+00. Copyright © 1992 Pergamon Press Ltd. EFFECT OF EA...

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CEMENT and CONCRETE RESEARCH. %'ol.22, pp. 92%936° 1992. Printed in the USA. 0008-8846D2. $5.00+00. Copyright © 1992 Pergamon Press Ltd.

EFFECT OF EARLY OVERLOADING OF CONCRETE ON STRENGTH AT LATER AGES

Yahia Abdel-Jawad , Rami Haddad Civil E n g i n e e r i n g Department Jordan University of Science and Technology Irbid - Jordan (Refereed) (Received Nov. 20, 1991; in final form April 28, 1992)

ABSTRACT An experimental investigation to study the effect of early over-loading of concrete on its strength development is reported. Concrete and mortar samples were subjected to different loading levels at ages of 8, 16, 24 and 72 hours. The samples were then retested, along with control specimens, at ages of 7, 28, and 90 days. More than 900 specimens were used in this investigation. Ultrasonic pulse velocity measurements were taken to evaluate the healing capacity of damaged specimens. The results indicate that loading concrete, beyond 8 hours after casting, up to 90Z of its compressive strength has no effect on later strength development. However, loading concrete up to failure resulted in strength loss between lOt to 50Z ,depending on age at time of loading, age at time of retesting and curing conditions. Introduction

Modern construction methods have been developed with the objective to reduce construction time as much as possible. This results in situations, during construction or within the first few days after construction, in which concrete is subjected to exceptionally high loads. Typical examples of such situations are slip form construction and precast concrete. In slip-forming ,a continuous construction is usually carried out with rate of climb between 150-600 mm per hour. This may produce high stresses, as compared to its strength at such an e a r l y age, on the fresh concrete at the bottom layers. In precast concrete, it is very often to lift or move the concrete members at very early ages which may result in severe cracking or damaging. In conventional concrete construction, the concrete may subject to e a r l y cracking or damaging as a result of pre-mature removal of forms. The question that usually asked in such situations is : Does the concrete receive permanent damage?, and to what extent?. The healing of concrete was first recognized by Abrams in 1913 (I), when he noticed the disappearance of cracks in a highway bridge after three years of their appearance. In 1925, Abrams used the term " Autogenous Healing" (2). Since that time, quite limited work has been done in the subject. In 927

928

Y. Abdel-Jawad and R. Haddad

Vol. 22, No. 5

1926 and 1929, H.J. Gilkey (3,4) studied the autogenous healing of concrete and mortar. The general conclusion of his work was that specimens salvaged without much visible damage will often develop later strength almost equal to what they would have had without previous tests. In badly shattered specimens the strength may never attain that at the former test. Thirty years later, the interest in the subject was sparked again by E.F. Whitlam (5), A. ~ f j o r d (6), and K.R. Laver and others (7). In Whitlam study a series of concrete cylinders were damaged at ages of 3, 7, and 28 days and retested at different times later, ranged from 7 days to 2 years. He concluded that healing took place in all specimens what ever the age, under a condition that water curing is available a11 the time. ~ f j o r d subjected the concrete to a specific deformation (1.5 and 2.5 Z) at a very early age (2- 8 hours). When testing for compressive strength at 7 days, he noticed that concrete is particularly sensitive to deformations at an age of 4-6 hours. Laver et.al used petrographic and chemical tests to evaluate qualitatively the extent of the healing action. They showed that the bonding materials formed during autogenous healing of cement pastes and concrete are 100 percent calcium hydroxide crystals. No amorphous hydrated products of cement were found to be present. In 1973, R.K. Dhir et.al (8) studied the strength and the deformation properties of autogenously healed mortars. The main conclusion of their work was that, a full recovery in strength was possibleatallages. Later in 1980, Byfors (9) showed that complete healing was not achievable especially for very low strength and high strength concretes. From the literature survey, it is noticed that little work has been done on autogenous healing of concrete subject to loading at very early ages (from the time of final set up to three days after casting), which is the most critical period during construction. The main objective of this work is to investigate the healing capacity of concrete subject to overloading within the first three days after casting. This has been achieved by determining the following information: The percent of permanent damage which concrete may receive as a result of early overloading. The age of concrete at which early overloading will have minimal effect. The period required for concrete to have complete healing (if possible). The effect of curing conditions on the healing process. The effect of concrete strength on the rate of healing. The internal cracking system during the healing period, using ultrasonic pulse velocity measurements. Materials and Experimental Methods The testing variables: I2345-

program

was

designed

to cover

Water-cement (W/C) ratio : 0.50 and 0.70 Age at time of first loading : 8,16,24 and Age at time of retesting : 7,28 and 90 Loading levels : 60Z, 75Z, 90Z and 100Z of of first loading. Curing conditions : moist or dry curing at

the following

experimental

72 hours. days. compressive strength at room temperature ( 2 3 ° C )

time

Vol. 22, No. 5

OVERLOADING, EARLY AGE, CONCRETE STRENGTH

929

Materials The coarse aggregate is crushed limestone, graded wlthln the AETM grading limits (ASTM C 33) with a maximum size of I in. and saturated specific gravity of 2.58. The fine portion was a mixture of crushed limestone and natural siliceous sand with a ratio of 4:1 respectlvely. This mixture was prepared in order to meet the ASTM grading limits of fine aggregate (max size = 4.76 mm). The saturated specific gravity of this mixture was 2.53. Commercially available pozzolanlc portland cement produced by Jordan Cement Factories C o m p a n y , according to Jordan Standard Specifications 219-1981, was used throughout this study. Samples Preparation Concrete mlxes of 0.50 and 0.70 W/C ratlos were proportloned according to the ACI- 211 mix design procedure. The amount of mixing water was controlled to produce workable concrete with a slump of 75 to 100mm. Concrete batches were mixed using a 115 liter-capaclty mechanical mixer and complete series of specimens were prepared using 150mm cubical steel molds. Placing and compacting were conducted according to relevant standards. Mortar mixes of 0.50 and 0.70 W/C ratios were proportioned accordlng to ASTM C-270. The amount o£ water necessary to produce normal consistency (flow of 110Z Z 5Z) was used. 50.8 mm cubic specimens were prepared and molded according to AETM C-109 procedure. Concrete and mortar molds were kept in moist condition untll demoldlng. Demolding was done between 8 and 24 hours, depending on age at time of first loading. After demolding the specimens were cured in water at temperature of o + o 25 C _ 3 C. To investigate the effect of curing conditions on the healing process of damaged specimens, some of the concrete and mortar specimens were cured in dry condition (kept on dry shelves in the laboratory). Test Procedures Concrete and mortar specimens were loaded up to fallure using automatic compression machines (stop when the load falls to 90Z of the max. recorded load). The rate of loading was maintained as specified by ASTM standards for testing concrete and mortar in compression. In the cases of loading concrete or mortar to less than its compressive strength, first the compressive strength was obtained and then the required load was determined according to the required load level. In each time of loading or retestlng, the compressive strength was determined as the average of three specimens. The coefficient of variation was less than 6Z . Ultrasonic pulse velocity measurements were taken on damaged mortar specimens to evaluate the cracking condition at time of damage and at time of retesting. The instrument used is a portable ultrasonic digital indicating tester known as "PUNDIT". This instrument displays digitally the time of travel o£ a pulse from the time it leaves the transmittlng transducer to the time reaches the receiving transducer. Results

and

and Discussions

Table 1 presents the compressive strength of concrete at tlme o£ loading at time of retesting for both the loaded and the control (virgin)

930

Y. Abdel-Jawad and R. Haddad

Vol. 99, No. 5

specimens. Each strength value shown is the average of three specimens. The results demonstrate that loading concrete at age beyond 8 hours and up to 90~ of its failure load has no effect on strength development; same strength was almost obtained for both loaded and control specimens. While, loading concrete at age of 8 hours resulted in strength loss of 5 to 12 percent. Concrete specimens loaded to failure show a strength loss of about 25 percent.

Compressive Strength

14

°.°

CURING

COND I T I ON

C

(H~i~)

,6

0,;

STRENGTH (MP,)

1,,3 10, ~7

gET

:m

RT TIME OF RETESTING

RT T I B E ' O F LORDIN-'-~GLORI

,

0,~

TABLE 1 Results of Concrete Specimens

Z4

11, 58

72

25, 3a

X

S1

90

30 4, ,,t;:, o9

~g

30,66

60 75 90 I Ol 60

75

60

75

]

s2

] s z , sl

.. ......... .. .. ...... .

9=7s,

30.44

29.54 29.51 29,60 23,97

40. 9~' 40. 47 40. 02 29. 33

0.9884 0_1,7244

30,63

30, 34 I . 0000 41. 76 1 , 0 0 0 0 1 ........... 30,1::' 0 , 9 8 3 3 41 . 37 40. 83 o.9069 4 ~ , 1 1 1 . . . . . . . . . . . 3 0 , 0 5 O, 9 8 0 9 41, 57 I oooo ____,,~4., 2 E o , 9_EI~

18,78

18, 1 I 16.0t

O, 9643 0,9590

18,51 t9,13

0.9936 1,0000

~!

18,63

24

7,18

60 75 90

18,79

75 90

|~:~| oo'

a~E= 9 ~ a , ~ S!

t 00001 ........... 1'. 0000146, ~71 . . . . . . . . . . . I 0000l 47,07 1.0000 O, 7 q q a .....+36 ,__._~.~5 _ 0 , 7 8 2 8

4,37

60

I

62,sll

~'1. 16 40.74 41. 49 30. "1"9

16

11,57

IHi

,~.Is

sz

3 1 . 0 3 I , 0000 3 1 , 2 5 '=.uuuu 4 0 , 6 9 3 0 , 7 1 1, UOgg 22, 14

1,16

72

sl

~ t 6 9 I'ts. 6 z l 0_,'9 1 3 9 i ~3,3L0.9494

B

90

52IS1

$7,$I

90

MET

52

'~g 90 101

aGE= 2, ~ s

AGE: 7 DaYS

LE¥1

~__

18,82

0,9704 0.9699

0,9724 O, 7874

17.1~ o, 7119

40.49

?oZ

27, 26, __125, 26,

19.o6 , , o o o o

1.0000 1 8 , 8 8 0,984Lt 2 6 , 8 7 q 2'q 1 , 0 0 0 0 _ _ _ _ 16.03 1,0000 18,69 1.0000 25,91 19.66 1, 0000

I~R. 5'#

1,00001

1 , o o o o l 4 4 . ssI

........... . . . . . . . . . . .

4 4 . 3 6 O, 9935 .__,.38, 09_.0, 8530

05 ~, 9661 I ........... 27 04 32 ~ [ ~ : _ / L _ _ _~~ : 49 0_°,3.,, 71 1 , 0 0 0 0 I ........... 0, 9 9 8 1 1 3 1 , 2 5 i . . . . . . . . . . . 0,97151 ...._~.31,4 5 1 , 0 0 0 C

33 I.ooooi i --:-7 -- ..... 1,oooo 3 3 , 8 9 1 . . . . . . . . . . . zg. 7_s L o o0o __---L3~ ? ! ±. ooo_o 26.

28, 96

26, 67 1 , 0 0 0 0 1 ........... 27, 09 1. 0 0 0 0 32, 20 [ . . . . . . . . . . . 27, 14 1_ o ooo _ _ 32.___Z._± ooo_o

$I = Compressive strength of control specimens $2 = Compressive strength of loaded specimens Table 2 shows the compressive strength results of mortar specimens. The specimens were loaded only to 90Z and 100Z of compressive strength, because it had been shown that loading concrete up to 90~ of compressive strength did not affect later strength development. The loading ages were, also, 8,16,24 and 72 hours. It is demonstrated, again, that loading mortar up to 90Z of compressive strength has neglected effect on strength development , as long as loading takes place beyond 8 hours after casting and specimens kept in moist curing condition. The data show that more strength loss has occurred in damaged specimens when they were kept in dry conditions as compared to those cured in water. It becomes very clear that loading concrete and m o r t a r , beyond 8 hours casting, up to 90~ of their compressive strength (at time of loading), will not harm later strength development. It should be mentioned that, in cyclic loading, full strength can be obtained in a second cycle of loading as long as the load does not exceed 90Z of the compressive strength (10,11). In this study It is demonstrated that strength will continue to develop in normal fashion as well. However, loading the specimens to 100~ of their capacity ,resulted in significant effect on subsequent strength development. A strength loss of about 50 percent was obtained in some cases, depending on different factors. These factors are the following :age of concrete at a f t e r

Vol. 22, No. 5

OVERLOADING, EARLY AGE, CONCRETE STRENGTH

time of loading, concrete retesting. The effect of specimens will be discussed

931

strength, curing conditions and age at these factors on the healing process of in some details in the followlng sections.

time of damaged

TABLE 2 Compressive Strength Results of Mortar Specimens I

CURING ;ONDITION

MET

DRY

gET

IRT TIME OF LORDING ROE (HRS)

STRENGTH (MPo)

LORD LEYE L X

RT TIME OF RETESTING ROE: 7 ORT5 Sl

S2

RGE: 28 DRYS

S2/S1

8

0,66

90 I00

2 7 . 2 9 2 7 . 2 8 0.99'J4 2.5.~78. ,32 0 , 6 7 2 0 ~5,46

51

52

$2151

"11,~28 3 6 , 3 5 0 . 8 8 0 6 35, 19,~5 0 . ~ 3 1

16

;54

780

24

11,3t

90 100

72

18,59

90 100

8

0,60

90

16

6,62

90

3 0 , 7 0 2,~.06 0.9465 43,84 43.3,+ 25,62 2 0 3 , o7929 3 0 , 5 2 8 . 3 3 2 5 : ~ 26.22 ,oooo 31,56 29o~1 2 7 , 7 6 26,24 0,8452 3 0 , 6 9 3 0 . 9 4

RGE: SO DRTS SI

S2

5~.10 ~7,S~ ~7.32 29,20

40 I. 0000

., ,~1 ~ : . o.15 |1:|~ ~,3:|8 2761 27.54 01886, 42,36 4 2 . 26,6 22. 66 0,8414 4 0 , 5 0 31,41

1,DUO0 51, 36"50, 88

0, 7756 50. 46 42, 36 0 , 8 8 6 3 : 5 3 , 80 49,98 0.742514D, 62 3 3 , 4 0 0.92t7

31, 71 2 8 . 2 3

I,OOOO 3 3 , 6 0 3 1 , 9 3

24

ll,4O

90

2 6 . 8 8 27,27

1,000032,56

72

22,76

90

25,73 26,87

1.0000 3 1 . 0 0 3 0 . 1 2

8

0.32

100

1 3 . 6 2 8 , 8 0 0 0,7268

16

2,01

80 100

13,31

24

4.76

90 100

72

9, 9D

90 ~00

8

0,32

100

~3.9, 12,84 0.9231 21,17 20,97 o 9 9 o 5 3 , o2=297, ,3.35 ~0.68 0.80__~2 20 10 ,5.32 o 7622 20 52 LLo:lo / ,3.62 ~ . ~ -g. 6~,~ 17.34 g ; - ~ 0 . 6 2 6 ,7 58 9,95

t6

1,85

90 100

t 3 , 2 2 13.32 12,26 9,55

72

1o .2

,o

T~;~

DRY

,,

100

1,000032,46

19,80 1 3 , 2 5 0.6691

30,4D

31,02 16.80

12,86 0,8662 18,74 2 0 , 4 8

1.0000130,0830,30 12.52 1o.45 o. 8349 2o.oi 14.39 0,7463_ 3 0 , 9 8 1 2 1 . 2 & 1346 4,78 1:ODD0 21.34 2,.81 1 0000 30,41 3 1 , 8 0 12.42 1.41 8181 20,25 17,73 o:8576 31,3o 2 4 7 2

1, oooo O, 7786

14,66 ~ 8 2 9 6 1 3 , 8 6 % 6 9 i0,6958

.

3 2 . 5 0 0 , 9 9 8 2 130, 12 3 2 , 9 0

17.~7 1 5 , 3 e 15,72 18, t 7

0.52,7

18,91 15.78

16.½2 10.06

1 7 4 o 16 .4 0 . 9 4 4 5 t 6 , 7 8 15,20 18,00 3 . 4 0 0,75~5 17,67 13,16

13.27 ~:oooo 16.4o=16 7e

1 4 , 0 7 9, z7

o,eeo4

6586 tD,eOL11:eo ~:

16.0o

11,41

$I = Compressive strength of control specimens $2 = Compressive strength of loaded specimens

It is well known that water is essential for cement hydration. Therefore, it is expected that curing in dry conditions will reduce the healing capacity of damaged mortar specimens. The data in Table 2 confirmed this. Figures I and 2 illustrate the effect of loading age and age at time of retesting on the amount of strength loss occurred in the damaged specimens of the 0.5 and 0.7 W/C ratio mortar, respectively. The strength loss (~) is given as: S1 - $ 2 x 100 $1 It can be seen that the maximum strength loss (35~ to 50Z) occurred when the specimens subjected to damage at age of 8 hours, while the minimum strength loss (102 to 20~) took place when the damage occurred at an age of 24 hours. Intermediate values (20Z to 30~) were obtained for loading at 16 and 72 hours. This may be attributed to the fact that using load control to define the failure status, might result in different types of deformations and cracks at the different loading ages. Loading the specimens to failure at age of 8 hours, which is about the time of final set of cement, resulted in large deformations and wide cracks to an extent that later hydration is

932

Y. Abdel-Jawad and R. Haddad

Vol. 22, No. 5

7 days 5O

O

g

1G

24

Age at Time of Loading, hrs. FIG. 1 Compressive strength loss of 0.5 W/C ratio mortar not capable of filling these cracks and developing the necessary bonds. However, at age of 24 hours, good portion of mortar final strength is usually obtained. Therefore, loading to maximum capacity did not result in severe cracking as in the case of loading at 8 hours. Therefore, subsequent hydration might be able to heal the cracks and to develop more strength as well. Loading at the age of 16 hours, resulted in an intermediate value (as expected) , as compared to the strength losses occurred at 8 and 24 hours.

7 days 28 days e,t) "

.>

90 days 33

23

E o

U

10

0

B

16

24

Age at Time of Loading, hrs. Compressive

FIG. 2 strength loss of 0.7 W/C ratio mortar

Vol. 22, No. 5

OVERLDADING, EARLY AGE, CONCRETE STRENGTH

933

Loading at 72 hours resulted, also, in an intermediate value . Although the loading at this age might result in less cracking than the case of the 24 hours, but the cement available for further hydration is less. Therefore, more strength loss has been resulted, as compared to the strength loss of loading at 24 hours. It is also shown that retesting a t 90 d a y s r e s u l t e d higher than that occurred when retesting was done at regardless of the loading age. Ultrasonic Pulse V e l o c i t y

in the

a strength age of 7

loss days,

Measurements

It is well known that the velocity of ultrasonic pulses through any solid material is affected by the existence of cracks and flaws in the material. Therefore, this technique has been employed by scientists and engineers to locate and to detect cracks and defects in materials. In this investigation, the technique has been used to monitor the healing of the cracks created in the damaged specimens. Ultrasonic pulse velocity (UPV) measurements were taken at the following stages: I.

At the time of damaging, i.e. at the ages of 8, 16, 24 and ?2 hours. The transit time was determined for each specimen b~fore and after loading.

2.

At the time of retesting the previously damaged specimens. The pulse transit time was determined for both the damaged and the control specimens.

UPV measurements were taken in the three perpendicular directions of each specimen. Almost, the same value was obtained in each direction. Three specimens were tested for each case of study (i.e. age of loading, or age of retesting). Therefore, the travel time is the average of nine measurements. In the case of damaged specimens, only the readings through the directions perpendicular to the loading direction were considered, because the cracks are parallel to the loading direction and thus the travel time in the loading direction was found to be the same as that of the undamaged specimens. Therefore, the travel time of the damaged specimens is the average of six readings (two directions for each of the three tested specimens). The ratio of the pulse travel time obtained through the damaged specimens to that obtained through the undamaged ones (for each series, damaged and undamaged specimens were prepared from the same batch), at same age, was calculated for each of the above mentioned stages and presented in shape of histograms in Figures 3, 4 and 5. Figure 3 shows the results of the 0.5 W/C ratio mortar. Clearly, it is shown that the severity of cracking due to loading up to failure decreases as the age at time of loading increases. For example, the ratio of the pulse travel time through the damaged specimens to the travel time through the undamaged ones ,at age of 8 hours, is 60Z higher than the ratio obtained when the damage was done at an age of 72 hours. Complete filling of the cracks may be achieved within the first week, as the ratio of the pulse travel times approaches one, except for the case of loading at the age of 8 hours, where the ratio is 1.2 ( even after 90 days of curing). It is worth to mention that although complete filling of cracks is achievable as predicted by the ultrasonic pulse veloclty measurements, strength loss still exists (as shown in Figure I).

934

Y. Abdel-Jawadand R. Haddad

Vol. 22, No. 5

2

Ik'x~q

1.4 .O e-"

_

ays~

~

"e-. ~ oE O2 "N r'¢)

13I

8

16

24

72

Age at Time of Loading, hrs.

Ultrasonic pulse time s p e c i m e n s o f 0 . 5 W/C and retested at later

FIG. 3 ratio of damaged to undamaged r a t i o mortar, c u r e d i n w a t e r . ages.

I at damage ] I

O m

•N r.~

°°

~

o

B

16

llmm 1 24

Age at Time of Loading, hrs. FIG. Ultrasonic pulse time ratio of damaged to undamaged specimens of 0.7 W/C ratio mortar, cured in water. and retested a t later ages.

Vol. 22, No. 5

OVERLOADING, EARLY AGE, CONCRETE STRENGTH

Same behavior for the 0.70 W/C ratio system is However, more cracking is predlcted in this case (higher time o£ the ultrasonlc pulses). Loading at the ages of seems to produce same cracking system; the travel tlme these ages.

shown ratio 16, 24 ratios

in Figure 4. of the travel and 72 hours are equal at

[ 90 days

1

.il 0

935

g

16

24

72

A g e at Time of Loading, hrs. FIG. 5 Ultrasonic pulse time ratio of damaged to unda,*aEed specimens of 0.7 W/C ratlo mortar, cured in dry condition, and retested at later ages.

Figure 5 shows the results of the 0.70 W/C ratlo mortar specimens cured in dry condition (the specimens were kept on dry shelves in the laboratory). It is shown that a higher degree of cracking was obtained, especially when the damage was done at an age of 72 hours. Complete filling of the cracks was not achievable because the vital cause of healing (water) was not available. From these observatlons and the results shown in Tables 1 and 2 and in Figures I and 2, one can say that although fllling of cracks may be achieved, as predicted by the ultrasonic pulse measurements, the damaged specimens will never approach the same strength obtained by their undamaged companions. A strength loss of about 50Z has been obtained in many cases. This may suggemt that the filllng materials do not develop good bond between the opposite sides of the crack. This suggestion is supported by visual observation. It has been noticed that ,at tlme of retesting, the failure of damaged specimens is always initiated from the cracks resulted from the first loading.

Conclusions Based conclusions

1.

on the results are drawn:



the

investigation

L o a d l n g c o n c r e t e up t o 90~ o f I t s strength not affect its later strength development.

carried

,at

out,

the

following

age b e y o n d 8 h o u r s ,

does

936

Y. Abdel-Jawad and R. Haddad

Vol. 22, No. 5

2.

In completely damaged specimens, minimum strength loss has been obtained when loading took place at an age of 24 hours.

3.

Moist curing strength.

4.

Complete healing o f cracks strength regain.

5.

C r a c k s d o not disappear in healed specimens, a r e present in these cracks.

6.

It has been observed that ,at time of retestlng, failure specimens is always initiated from the existing cracks.

is

an

essential

requirement

(filling

to

the cracks)

obtain

maximum

healing

does not mean complete

but deposits of white salts

of

healed

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

D.A. Abrams, Proc. ASTM, V. 13, 884 (1913). D.A. Abrams, concrete, V. 10, 50 (1925). H.J. Gilkey, Proc. ASTM, V. 26, Part 2, 470 (1926). H.J. Gilkey, Proc. ASTM, V. 29, Part 2, 593 (1929). E.P. Whitlam, The struct. Engr. V. 32, 235 (1954). A. ~fjord, Betongen Idag, V. 19, No.3, 57 (1954). K.R. Lauer, and F.O. Slate, J. ACI, V. 52, No.60, 1083 (1956). R.K. Dhir, and C.M. Sangha, J. ACI, V. 70, No. 24, 231 (1973). J. Byfors, Swedish Cem. Conc. Res. Inst., No. 80, p. 345 (1980). S.P. Shah, and S. Chandra, J. ACI, V. 67, No. t0, 816 (1970). ACI Committee 215R, ACI Manual of Concrete Practice, Part I, (1987).