ACI 224R-1990

ACI 224R-90

Control of Cracking

in Concrete Structures

Reported by ACI Committee 224

The principal causes of cracking in concrete and recom-mended crack control procedures are presented. The cur-rent state of knowledge in microcracking and fracture me-chanics is discussed. The control of cracking due to drying shrinkage and crack control for flexural members, layered systems and mass concrete are covered in detail. Long-term effects on cracking are considered, and crack control procedures used in construction are presented. Informa-tion is provided to assist the engineer and the constructor in developing practical and effective crack control pro-grams for concrete structures.

Keywords: adiabatic conditions; aggregates: air entrainment;

an-chorage (structural); beams (supports); bridge decks; cement-ag-gregate reactions; cement content; cement types; compressive strength: computers; concrete construction; concrete pavements; concrete slabs; concretes; conductivity: consolidation; cooling; crack propagation; cracking (fracturing); crack width and spacing: creep properties; diffusivity; drying shrinkage; end blocks; expan-sive cement concretes; extensibility; failure; fibers; heat of hydra-tion; insulahydra-tion; joints (junctions); machine bases; mass concrete; microcracking; mix proportioning; modulus of elasticity; moisture content; Poisson ratio; polymer-portland cement concrete; pozzo-lans; prestressed concrete; reinforced concrete; reinforcing steels; restraints; shrinkage: specifications; specific heat; strain gages; strains; stresses; structural design; temperature; temperature rise (in concrete); tensile stress; tension; thermal expansion; volume change.

ACI Committee Reports, Guides, Standard Practices , and Com-mentaries are Intended for guidance in designing, planning, executing, or inspecting construction, and in preparing speci-fications Reference to these documents shall not be made in the Project Documents. If items foun d in these documents are desired to be part of the Project Documents, they should be phrased in mandatory language and incorporated into the Proj-ect Documents.

Copyright 0 1990, American Concrete Institute. All rights reserved including rights of reproduction and use in any form or by any means, including the making of copies by any photo process, or by any electronic or mechanical device, printed or

Contents

Chapter 1 - Introduction, page 224R-2

Chapter 2 - Crack mechanisms in concrete, page 224R-2

2.1 - Introduction 2.2 - Microcracking 2.3 - Fracture

Chapter 3 - Control of cracking due to drying shrinkage, page 224R-9

3.1 - Introduction 3.2 - Crack formation 3.3 - Drying shrinkage

3.4 - Factors influencing drying shrinkage 3.5 - Control of shrinkage cracking 3.6 - Shrinkage-compensating concretes

Chapter 4 - Control of cracking in flexural members, page 224R-16

4.1 - Introduction

4.2 - Crack control equations for reinforced concrete beams 4.3 - Crack control in two-way slabs and plates

4.4 - Tolerable crack widths versus exposure conditions in re-inforced concrete

4.5 - Flexural cracking in prestressed concrete 4.6 - Anchorage zone cracking in prestressed concrete 4.7 - Tension cracking

Cbapter 5 - Long-term effects on cracking, page 224R-21 5.1 5.2 5.3 5.4 5.5 -Introduction

Effects of long-term loading Environmental effects Aggregate and other effects

Use of polymers in improving cracking characteristics

written or oral, or recording for sound or visual reproduction or for use in any knowledge or retrieval system or device, unless permission in writing is obtained from the copyright proprietors.

ACI COMMITTEE REPORT

Chapter 6 - Control of cracking in concrete layered systems, page 224R-23

6.1 - Introduction

6.2 - Fiber reinforced concrete (FRC) overlays 6.3 - Latex modified concrete (LMC) overlays 6.4 - Polymer impregnated concrete (PIC) systems

Chapter 7 - Control of cracking in mass con-crete, page 224R-26

7.1 - Introduction 7.2 - Crack resistance

7.3 - Determination of temperatures and tensile strains 7.4 - Control of cracking

7.5 - Testing methods and typical data

7.6 - Artificial cooling by embedded pipe systems

7.7 - Summary - Basic considerations for construction controls and specifications

Chapter 8 - Control of cracking by correct construction practices, page 224R-36

8.1 - Introduction 8.2 - Restraint 8.3 - Shrinkage 8.4 - Settlement 8.5 - Construction

8.6 - Specifications to minimize drying shrinkage 8.7 - Conclusion

Chapter 9 - References, page 224R-42

9.1- Specified and/or recommended references 9.2 - Cited references

Chapter 1 - Introduction

Cracks in concrete structures can indicate major structural problems and can mar the appearance of monolithic construction. They can expose reinforcing steel to oxygen and moisture and make the steel more susceptible to corrosion. While the specific causes of cracking are manifold, cracks are normally caused by stresses that develop in concrete due to the restraint of volumetric change or to loads which are applied to the structure. Within each of these categories there are a number of factors at work. A successful crack control program must recognize these factors and deal with each of them, in turn.

This report presents the principal causes of crack-ing and a detailed discussion of crack control pro-cedures. The body of the report consists of seven chapters designed to help the engineer and the con-tractor in the development of effective crack control measures.

This report is an update of a previous committee report, issued in 1972.1. 1 _{The original report was}

supplemented by an ACI Bibliography on cracking,1 . 2

also issued by this committee. In the updating pro-cess, many portions of the report have undergone sizeable revision, and the entire document has been subjected to a detailed editorial review. Chapter 2, on crack mechanisms, has been completely rewritten to take into account the experimental and analytical work that has been done since the completion of the first committee report. Chapter 6, on crack control in concrete layered systems, is new to the report and deals with a form of concrete construction that was in its infancy at the time the first report was drafted. Individual chapters on crack control in

re-inforced and prestressed concrete members have been condensed into a single chapter, Chapter 4, on crack control in flexural members. The resulting pre-sentation is more concise and, hopefully, more useful to the structural designer. Chapter 5, on long-term effects, details some interesting findings on the change of crack width with time. Chapters 3, 7, and 8, which consider drying shrinkage, mass concrete, and construction practices, respectively, have been expanded and updated to take into account the most recently developed procedures in these areas. In ad-dition, new sections have been added to Chapters 7 and 8 which provide specific guidance for the devel-opment of crack control programs and specifications.

The committee hopes that this report will serve as a useful reference to the causes of cracking and as a key tool in the development of practical crack con-trol procedures in both the design and the construc-tion of concrete structures.

References

1.1. ACI Committee 224, “Control of Cracking in Con-crete Structures,” _ACI JOURNAL, Proceedings V. 69, NO. 12, Dec. 1972, pp. 717-753.

1.2. ACI Committee 224, “Causes, Mechanism, and Con-trol of Cracking in Concrete,” ACI Bibliography No. 9, American Concrete Institute, Detroit, 1971, 92 pp.

Chapter 2 - Crack mechanisms in concrete* 2.1 - Introduction

Beginning with the work at Cornell University in the early 1960s,2 .1

a great deal has been learned about the crack mechanisms in concrete, both at the microscopic and the macroscopic level. Of special in-terest during the early work was the realization that the behavior of concrete, under compressive as well as tensile loads, was closely related to the formation of cracks. Under increasing compressive stress, mi-croscopic cracks (or microcracks) form at the mortar-coarse aggregate boundary and propagate through the surrounding mortar, as shown in Fig. 2.1.

During the first decade of research, a picture de-veloped that closely linked formation and propaga-tion of these microcracks to the load-deformapropaga-tion be-havior of concrete. Prior to load, volume changes in cement paste cause interfacial cracks to form at the mortar-coarse aggregate boundary.2.2,2.3

Under

short-term compressive load, no additional cracks form un-til the load reaches approximately 30 percent of the compressive strength of the concrete.2.1

Above this value, additional bond cracks initiate throughout the matrix. Bond cracking increases until the load reaches approximately 70 percent of the compressive strength, at which time microcracks begin to propa-gate through the mortar. Mortar cracking continues at an accelerated rate until the material ultimately fails. For concrete in uniaxial tension, experimental work indicates that major microcracking begins at about 60 percent of the ultimate tensile strength.2.4

CONTROL OF CRACKING 224R-3

Studies of the stress-strain behavior and volume change of concrete 2.5 _{indicate that the initiation of}

major mortar cracking corresponds with an observed increase in the Poisson’s ratio of concrete. The term “discontinuity stress” is used for the stress at which this change in material behavior occurs.

In general, it has been agreed that the micro-cracking that occurs prior to loading has very little effect on the strength of concrete. However, work by Brooks and Neville 2.6 indicates that the effect of

early volume change on microcracking of concrete may result in a reduction of both tensile and com-pressive strength as concrete dries out. Their study shows that upon drying, the strength of test speci-mens first increases and then decreases. They postu-late that the initial increase is due to the increased strength of the drier cement paste and that the ulti-mate decrease in strength is due to the formation of shrinkage induced microcracks.

Work by Meyers, Slate, and W i n t e r2 . 7 _{and Shah}

and Chandra2.8 _{demonstrates that microcracks}

in-crease under the effect of sustained and cyclic load-ing. Their work indicates that the total amount of microcracking is a function of the total compressive strain in the concrete and is independent of the method in which the strain is applied. Sturman, Shah, and Winter2.9 _{found that the total degree of}

microcracking is decreased and the total strain ca-pacity in compression is increased when concrete is subjected to a strain gradient.

At about the same time that the microcracking studies began, investigators began applying fracture mechanics to the studies of concrete under load. The field of fracture mechanics, originated by Griffith2.10

in 1920, serves as the primary tool for the study of brittle fracture and fatigue in metal structures. Since concrete has for many years been considered a brittle material in tension, fracture mechanics is con-sidered to be a potentially useful analysis tool for concrete by many investigators. 2. .12

The field of fracture mechanics was first applied to concrete by Kaplan2.11_{in 1961. The classical}

the-ory serves to predict, the rapid propagation of a macrocrack through a homogeneous, isotropic, elas-tic material. The theory makes use of the stress in-tensity factor, K_I, which is a function of crack geom-etry and stress. Failure occurs when K_I reaches a critical value, K_Ic , known as the critical stress-in-tensity factor under conditions of plane strain. K_Icis thus a measure of the fracture toughness of the ma-terial. To properly measure K_Ic for a material, the test specimen must be of sufficient size to insure maximum constraint (plane strain) at the tip of the crack. For linear elastic fracture mechanics (LEFM) to be applicable, the value of K_Icmust be a material constant, independent of the specimen geometry (as are other material constants such as yield strength). The earliest experimental work utilized notched tension and beam specimens of mortar and

con-$EGlrgyj

m _0.0012 m _{0. CKI}

STRAIN STRAIN

Fig. 2.1 - Cracking maps and stress-strain curves

for concrete loaded in uniaxial compression. *

*From S. P. Shah, and F. O. Slate, “Internal Microcracking, Mortar-Aggregate Bond and the Stress-Strain Curve of Con-crete,” Proceedings, International Conference on the Structure of Concrete (London, Sept. 1965), Cement and Concrete Association, London, 1968, pp. 82-92.

crete.2.11-2.14 _{The crack resistance was expressed in}

terms of the strain energy release rate at the onset of rapid crack growth, G, which is directly related to the fracture toughness of the material. Later in-vestigations evaluated the crack resistance of paste, mortar and concrete in terms of the fracture tough-ness, itself.2.15 _{Work by Naus and Lott}2.16 _indicated

that the fracture toughness of paste and mortar in-creased with decreasing water-cement ratio, but that the water-cement ratio had little effect on the frac-ture toughness of concrete. They found that K_Ic in-creased with age, and dein-creased with increasing air content for paste, mortar, and concrete. The effec-tive fracture toughness of mortar increased with in-creasing sand content, and the fracture toughness of concrete increased with an increase in the maximum size of coarse aggregate.

Additional work by Naus,2.17 _{presented just prior}

to the previous committee report,1.1 _{indicated that}

fracture toughness was not independent of speci-men geometry for tensile specispeci-mens of paste, mortar and concrete and that fracture toughness was a func-tion of the crack length. These observafunc-tions lead to the possibly erroneous conclusion that fracture me-chanics may not be applicable to concrete. Because certain size requirements must be met, before frac-ture mechanics is applicable, these results may only indicate that the test specimen did not satisfy all of the minimum size requirements of linear elastic frac-ture mechanics.

The balance of this chapter describes some of the more recent studies of crack mechanisms in concrete and gives a somewhat different picture from that presented in the previous committee report.

224R-5 l/3 0 w oz

z

-

Fig. 2.4 - Stress-strain curves as influenced by coating aggregates (Reference 2.36).

seemed to indicate a very large effect, thus empha- Work by Carino,2.38 _{using polymer impregnated}

sizing the importance of interfacial strength on the concrete, seems to corroborate these two studies. behavior of concrete. These studies utilized rela- Carino found that polymer impregnation did not in-tively thick, soft coatings on the coarse aggregate to crease the interfacial bond strength, but did increase reduce the bond strength. Since these soft coatings the compressive strength of concrete. He attributed isolated the aggregate from the surrounding mortar, the increase in strength to the effect of the polymer the effect was more like inducing a large number of on the strength of mortar, thus downgrading the im-voids in the concrete matrix. portance of the interfacial bond.

Two other s t u d i e s2 . 3 6 , 2 . 3 7 _{which did not isolate the}

coarse aggregate from the mortar indicate that the interfacial strength plays only a minor role in con-t r o l l i n g con-t h e s con-t r e s s - s con-t r a i n b e h a v i o r a n d u l con-t i m a con-t e strength of concrete. Darwin and Slate2 . 3 6 _{used a}

thin coating of polystyrene on natural coarse aggre-gate. They found that a large reduction in interfacial bond strength causes no change in the initial stiff-ness of concrete under short-term compressive loads and results in approximately a 10 percent reduction in the compressive strength as compared to similar concrete made with aggregate with normal inter-facial strength (see Fig. 2.4). They also found that the lower interfacial strength had no appreciable ef-fect on the total amount of microcracking. However, in every case, the average amount of mortar crack-ing was slightly greater for the specimens made with coated aggregate. This small yet consistent dif-ference may explain the difdif-ferences in the stress-strain curves.

The importance of mortar, and ultimately cement paste, in controlling the stress-strain behavior of concrete is illustrated by the finite element work of Buyukozturk2.37 _{and Maher and D a r w i n .}2 . 3 1 , 2 . 3 2 _Using

a linear finite element representation of a physical model of concrete, Buyukozturk was able to simulate the overall crack patterns under uniaxial loading.

Perry and Gillott 2 . 3 7_{used glass spheres with}

dif-ferent degrees of surface roughness as coarse aggre-gate. Their results indicate that reducing the inter-facial strength of the aggregate decreases the initiation stress by about 20 percent, but has very little effect on the discontinuity stress. They also ob-served a 10 percent reduction in the compressive strength for specimens with low mortar-aggregate bond strength.

Mortar

Fig. 2.5 - Stress-strain curves for concrete model. * *From A. Maher. and D. Darwin, “Microscopic Finite Element Model of Concrete,” presented at the First International Confer-ence on Mathematical Modeling (St. Louis. Aug.-Sept. 1 9 7 7 ) .

224R-6 ACI COMMl=lTEE REPORT w-\ . _ -- Normal fnterfaclal Str. - ._ _{I nfuxte I nterfaciaf Str} ._ _{Zwo Tenstle and Cohewe}

I nterfaclal Str. -- - Z e r o InterfacIal Str. S t r e s s . PSI 4 lMPar L_._ 1 *l. 0 *2. 0 0. 0 1.0 Strdln. 0.001 In/in ,’ A g g r e g a t e Mortar .?. 0

Fig. 2.6 - Stress-strain curve for finite element model of concrete with varying values of mortar-ag-gregate bond strength (Reference 2.32).

However, his finite element model could not dupli-cate the nonlinear experimental behavior of the physical model using the formation of interfacial bond cracks and mortar cracks as the only nonlinear effect. Maher and Darwin 2 .31,2.32

have shown that by using a nonlinear representation for the mortar con-stituent of the physical model, a very close represen-tation of the actual behavior can be obtained. The results for Buyukozturk’s model are shown in Fig. 2 5. .

The inability of linear elastic models2.25,2.26,2.39 _to

duplicate the nonlinear behavior of concrete utilizing microcracking alone has been explained as being due to the fact that concrete is really a “statistical mate-rial.” When the proper statistical variation is se-lected, the nonlinear behavior of concrete can be

v MORTAR@21 v 0 CONCRETE 0 ti * OS I I I I I * lJ4 l/2

314 1

(6.4) (12.7)(19. 1)(2X

Fig. 2.7 - Effect of notch depth on flexure strength (Reference 2.42).

duplicated2.25 _{While the statistical variations}

un-doubtedly play a part, the major nonlinear behavior can also be matched by considering the non-linearities of the mortar constituent.2.31,2.32 _{Fig. 2.6}

il-lustrates the results obtained for a highly simplified model of concrete under uniaxial compression using a nonlinear representation for mortar. The stress-strain curve for the model without cracking differs very little from that of models that have a normal, or above normal, amount of microcracking. Micro-cracks have a relatively minor effect on the primary stress-strain behavior of the models. The dominant effect of microcracking is to increase the lateral strain. In every case the failure of the model is gov-erned by “crushing” of the mortar which occurs at an average strength below that of the mortar alone.

Newman2.5_{s and Tasuji, Slate, and Nilson}2.40

lhave

observed that the principal tensile strain in concrete at the “discontinuity stress” appears to be a function of the mean normal stress, 0, = (0,+0,+0,)/3. In their study of the biaxial strength of concrete, Ta-suji, et al., observe that the final failure of their specimens consists of the formation of macroscopic tensile cracks. They also observe that the stress at discontinuity occurs at approximately 75 percent of the ultimate strength in compression and at about 60 percent of the ultimate strength for those cases in-volving tension, matching the levels at which mortar cracking begins.2.3,2.4

l Their work seems to point very

strongly toward a “limiting tensile strain” as the governing factor in the strength of concrete.

Overall, the damage to cement paste seems to play an important role in controlling the primary stress-strain behavior of concrete under short-term axial load. In normal weight concrete, aggregate particles act as stress-raisers, increasing the initial stiffness and decreasing the strength of the paste. For cyclic and sustained loading, a great deal of the bond cracking results from load induced volume changes within the paste, but has no significant ef-fect on strength. A number of investigators feel that the onset of mortar cracking marks the “true” ulti-mate strength of concrete.2.6-2.8,2.33,2.34,2.41

l Whether

mortar cracking itself controls the strength of con-crete or whether it only signals intimate damage of the cement paste remains to be seen. Additional studies in this area are clearly warranted.

2.3 - Fracture

Since the publication of the previous report, a number of investigations have shed additional light on the applicability of fracture mechanics to con-crete and its constituent materials.

Shah and McGarry utilized flexure specimens sub-jected to three-point loading.2.42 _{Their work indicates}

that while paste is notch sensitive, neither mortar nor concrete are affected by a notch (Fig. 2.7). Shah and McGarry also ran a series of tests using notched tensile specimens and determined that paste

speci-CONTROL OF CRACKING 224R-7

mens, and mortar specimens made with fine aggre-gate that passed the #30 sieve, are notch sensitive, but that mortar specimens containing larger sizes of aggregate are not notch sensitive.

Brown utilized notched flexure specimens and double cantilever beam specimens of paste and mor-tar2.18 _{8 His tests show that the fracture toughness of}

cement paste is independent of crack length and is therefore a material constant. The fracture tough-ness of mortar, however, increases as the crack propagates, indicating that the addition of fine ag-gregate improves the toughness of paste. This be-havior is similar to the bebe-havior found in structural steels that exhibit a plane strain-plane stress transi-tion. Because the plane strain-plane stress transition occurs beyond the limits of LEFM, the analysis is more complex. To re-establish the applicability of LEFM, larger test specimens must be used with tougher materials such as mortar.

Mindess and Nadeau investigated the effect of notch width on KI for both mortar and concrete.

2.20

Utilizing notched beam specimens of constant length and depth, with varying widths, they found that within the range studied, there was no dependence of fracture toughness upon the length of crack front. Since their work utilized small specimens with a depth of only about 50 mm (2 in.), there is some in-dication that rather than measuring the fracture toughness of the material, they were simply measur-ing the modulus of rupture.

The applicability of these results, and much of the other fracture mechanics work, has been brought into perspective based on the experimental work by Walsh. In separate investigations of notched beam specimens2.21 _{’ and beams with right angle re-entrant}

notches2.22 _{Walsh has demonstrated that specimen}

size has a marked influence on the applicability of linear elastic fracture mechanics to the failure of plain concrete specimens. As illustrated in Fig. 2.8, for specimens of similar geometry but below a cer-tain critical size, the specimen capacity is governed by the modulus of rupture of concrete, calculated from the linear stress distribution. For specimens above this size, the strength is governed by the frac-ture toughness, which he approximated as a function of the square root of the compressive strength of the concrete. Walsh concluded that, for valid toughness testing of concrete, the depth of notched beams must be at least 230 mm (9 in.). This type of behav-ior is also observed in metals, i.e., for valid fracture mechanics test results, the test specimens must meet minimum size requirements (ASTM E 399). These size requirements are dependent upon the square of the toughness levels being measured. Thus a material whose toughness level is twice that of another material (all other properties being equal), must have specimen dimensions four times that of the first material for the test results to be equally valid.

Gjorv, Sorensen and, Arnesen2.23 _{investigated the}

0.10

L

1

4

a/a0

(log

scale)

Fig. 2.8 - Relationship bet ween test results and theory for notched concrete beams (Reference 2.22).

L-__ -- ~_. - -~ 1

Fig. 2.9 - Effect of notch depth on flexural strength (Reference 2.23).

notch sensitivity of paste, mortar and concrete using three-point bend specimens similar to those used by Shah and McGarry2.42 _{As shown in Fig. 2.9, they}

de-termined that both mortar and concrete are notch sensitive, but less sensitive than cement paste. They conclude that the disagreement with the earlier re-sults is due in part to their improvement in the load-ing procedure. They feel that linear elastic fracture mechanics is applicable to the small specimens of

ACI COMMITTEE REPORT

paste, but not to the small size specimens of mortar and concrete. Even the small specimens of mortar and concrete, however, have some degree of notch sensitivity since the failure is not consistent with the modulus of rupture based on the net cross section. C i t i n g W a l s h ’ s e a r l i e r work,2.21 _{they agree that}

LEFM is applicable to large concrete specimens, but that it is not applicable to small specimens.

Hillemeier and Hilsdorf2.43 utilized wedge loaded, compact tension specimens to measure the fracture toughness of paste, aggregate and the paste-aggre-gate interface. They feel that, while the failure of concrete in tension and compression is controlled by many interacting cracks rather than by the propaga-tion of a single crack, fracture mechanics does offer an important tool for evaluating the constituent ma-terials of concrete. They found that paste is a notch sensitive material and that the addition of entrained air or soft particles has only a small affect on K_{I c}. Their work indicates that the K_Ic values for inter-facial strength between paste and aggregate is only about one-third of the K_Ic value for paste alone, and that the characteristic value of K_IC for aggregate is approximately ten times that of paste.

Swartz, Hu, and Jones2.24 _{used compliance}

mea-surement to monitor crack growth in notched con-crete beams subjected to sinusodial loading. They conclude that this procedure is useful for monitoring crack growth in concrete due to fatigue. Based on the appearance of the fracture surface, which shows a combination of both aggregate fracture and bond failure, they feel that fracture toughness is not a pertinent material property. However, they state that an “effective” fracture toughness might be a significant material property if related to specific material and specimen variables such as aggregate size and gradation, and proportions of the mix, and if the calculation considers the nonlinear material re-sponse of concrete.

A number of investigators do not feel that the Griffith theory of linear fracture mechanics is di-rectly applicable to all concrete2.23,2.24* 2.42 (ASTM E 399). Some like Swartz, et a1.2.24 feel that the theory has application when the limitations and specific nonhomogenous effects are taken into account. Clearly, specimen size requirements must be given more attention. Of key interest in future work are the observations by Walsh2.21’ 2.22 that show that if the specimens are large enough, the effects of heterogeneity are greatly reduced and that concrete may approximate a homogenous material to which the principles of fracture mechanics can be applied.

References

2.1. Hsu, Thomas T. C.; Slate, Floyd O.; Sturman, Ger-ald M.; and Winter, George, “Microcracking of Plain Con-crete and the Shape of the Stress-Strain Curve,” ACI JOURNAL Proceedings V. 60, No. 2, Feb. 1963, pp. 209-224.

2.2. Hsu, Thomas, T. C., “Mathematical Analysis of Shrinkage Stresses in a Model of Hardened Concrete,” ACI JOURNAL, Proceedings V. 60, No. 3, Mar. 1963, pp. 371-390.

2.3. Slate, Floyd O., and Matheus, Ramon E., “Volume Changes on Setting and Curing of Cement Paste and Con-crete from Zero to Seven Days,” ACI JO U R N A L,

Pro-ceedings V. 64, No. 1, Jan. 1967, pp. 34-39.

2.4. Evans, R. H., and Marathe, M. S., “Microcracking and Stress-Strain Curves for Concrete in Tension,”

Mate-rials and Structures, Research and Testing (Paris), V. 1,

No. 1, Jan. 1968, pp. 61-64.

2.5. Newman, Kenneth, “Criteria for the Behavior of Plain Concrete Under Complex States of Stress,”

Pro-ceedings, International Conference on the Structure of

Concrete (London, Sept. 1965), Cement and Concrete Asso-ciation, London, 1968, pp. 255-274.

2.6. Brooks, J. J., and Neville, A. M., “A Comparison of Creep, Elasticity and Strength of Concrete in Tension and in Compression,” Magazine of Concrete Research (London), V. 29, No. 100, Sept. 1977, pp. 131-141.

2.7. Meyers, Bernard L.; Slate, Floyd O.; and Winter, George, “Relationship Between Time-Dependent Deforma-tion and Microcracking of Plain Concrete,” ACI JOURNAL,

Proceedings V. 66, No. 1, Jan. 1969, pp. 60-68.

2.8. Shah, Surendra P., and Chandra, Sushil, “Fracture of Concrete Subjected to Cyclic and Sustained Loading,” ACI JOURNAL, Proceedings V. 67, No. 10, Oct. 1970, pp. 816-824.

2.9. Sturman, Gerald M.; Shah, Surendra P.; and Winter, George, “Effects of Flexural Strain Gradients on Micro-cracking and Stress-Strain Behavior of Concrete,” ACI JOURNAL, Proceedings V. 62, No. 7, July 1965, pp. 805-822. 2.10. Griffith, A. A., “The Phenomena of Rupture and Flow in Solids,” Transactions, Royal Society of London, No. 221A, 1920, pp. 163-198.

2.11. Kaplan, M. F., “Crack Propagation and the Frac-ture of Concrete,” ACI JOURNAL, Proceedings V. 58, No. 5, Nov. 1961, pp. 591-610.

2.12. Glucklich, Joseph, “Static and Fatigue Fractures of Portland Cement Mortars in Flexure,” Proceedings, First International Conference on Fracture, Sendai, Japan, V. 2, 1965, pp. 1343-1382.

2.13. Romualdi, James P., and Batson, Gordon B., “Me-chanics of Crack Arrest in Concrete,” Proceedings, ASCE, V. 89, EM3, June 1963, pp. 147-168.

2.14. Huang, T. S., “Crack Propagation Studies in Micro-concrete,” MSc Thesis, Department of Civil Engineering, University of Colorado, Boulder, 1966.

2.15. Lott, James L., and Kesler, Clyde E., “Crack Prop-agation in Plain Concrete,” Symposium on Structure of Portland Cement Paste and Concrete, Special Report No. 90, Highway Research Board, Washington, D.C., 1966, pp. 204-218.

2.16. Naus, Dan J., and Lott, James L., “Fracture Toughness of Portland Cement Concretes,” ACI JOURNAL, Proceedings V. 66, No. 6, June 1969, pp. 481-489.

2.17. Naus, Dan J., “Applicability of Linear-Elastic Frac-ture Mechanics to Portland Cement Concretes,” PhD Thesis, University of Illinois, Urbana, Aug. 1971.

2.18. Brown, J. H., “Measuring the Fracture Toughness of Cement Paste and Mortar,” Magazine of Concrete

CONTROL OF CRACKING 224R-9

2.19. Evans, A. G.; Clifton, J. R.; and Anderson, E., “The Fracture Mechanics of Mortars,” Cement and Con-crete Research, V. 6, No. 4. July 1976, pp. 535-547.

2.20. Mindess, Sidney, and Nadeau, John S., “Effect of Notch Width of K_IC for Mortar and Concrete,” Cement and Concrete Research, V. 6, No. 4, July 1976, pp. 529-534.

2.21. Walsh, P. F., “Fracture of Plain Concrete,” Indian Concrete Journal (Bombay), V. 46, No. 11, Nov. 1972, pp. 469-470, 476.

2.22. Walsh, P. F., “Crack Initiation in Plain Concrete,” Magazine of Concrete Research (London), V. 28, No. 94, Mar. 1976, pp. 37-41.

2.23. Gjorv, O. E.; Sorensen, S. I.; and Arnesen, A., “Notch Sensitivity and Fracture Toughness of Concrete,” Cement and Concrete Research, V. 7, No. 3, May 1977, pp. 333-344.

2.24. Swartz, Stuart E.; Hu, Kuo-Kuang; and Jones, Gary L., “Compliance Monitoring of Crack Growth in Con-crete,” Proceedings, ASCE, V. 104, EM4, Aug. 1978, pp. 789-800.

2.25. Shah, Surendra P., and Winter, George, “Inelastic Behavior and Fracture of Concrete,” ACI JO U R N A L ,P r o -ceedings V. 63, No. 9, Sept. 1966, pp. 925-930.

2.26. Testa, Rene B., and Stubbs, Norris, “Bond Failure and Inelastic Response of Concrete,” Proceedings, ASCE, V. 103, EM2, Apr. 1977, pp. 296-310.

2.27. Darwin, David, Discussion of “Bond Failure and In-elastic Response of Concrete,” by Rene B

.

2.28. Spooner, D. C., “The Stress-Strain Relationship for Hardened Cement Pastes in Compression,” Magazine of Concrete Research (London), V. 24, No. 79, June 1972, pp. 85-92.

2.29. Spooner, D. C., and Dougill, J. W., “A Quantitative Assessment of Damage Sustained in Concrete During Compressive Loading,” Magazine of Concrete Research (London), V. 27, No. 92, Sept. 1975, pp. 151-160.

2.30. Spooner, D. C.; Pomeroy, C. D.; and Dougill, J. W., “Damage and Energy Dissipation in Cement Pastes in Compression,” Magazine of Concrete Research (London), V. 28, No. 94, Mar. 1976, pp. 21-29.

2.31. Maher, Ataullah, and Darwin, David, “A Finite Element Model to Study the Microscopic Behavior of Plain Concrete,” CRINC Report-SL-76-02, The University of Kansas Center for Research, Lawrence, Nov. 1976, 83 pp.

2.32. Maher, Ataullah, and Darwin, David, “Microscopic Finite Element Model of Concrete,” Proceedings, First In-ternational Conference on Mathematical Modeling (St. Louis, Aug.-Sept. 1977), University of Missouri-Rolla, 1977, v. III, pp. 1705-1714.

2.33. Karsan, I. Demir, and Jirsa, James 0.. “Behavior of Concrete under Compressive Loadings,” Proceedings, ASCE, V. 95, ST12, Dec. 1969, pp. 2543-2563.

2.34. Neville, A. M., and Hirst, G. A., “Mechanism of Cyclic Creep of Concrete,” Douglas McHenry Symposium on Concrete and Concrete Structures, SP-55, American Concrete Institute, Detroit, 1978, pp. 83-101.

2.35. Nepper-Christensen, Palle, and Nielsen, Tommy P. H., “Modal Determination of the Effect of Bond Between Coarse Aggregate a n d M o r t a r o n t h e C o m p r e s s i v e Strength of Concrete,” ACI JO U R N A L,Proceedings V. 66, No. 1, Jan. 1969, pp. 69-72.

2.36. Darwin, David, and’ Slate, F. O., “Effect of Paste-Aggregate Bond Strength on Behavior Concrete,” Jour-nal of Materials, V. 5, No. 1, Mar. 1970, pp. 86-98.

2.37. Perry, C., and Gillott, J. E., “The Influence of Mor-tar-Aggregate Bond Strength on the Behavior of Concrete in Uniaxial Compression,” Cement and Concrete Research, V. 7, No. 5, Sept. 1977, pp. 553-564.

2.38. Carino, Nicholas J., “Effects of Polymer Impregna-tion on Mortar-Aggregate Bond Strength,” Cement and Concrete Research, V. 7, No. 4, July 1977, pp. 439-447.

2.39. Buyukozturk, Oral, “Stress-Strain Response and Fracture of a Model of Concrete in Biaxial Loading,” PhD Thesis, Cornell University, Ithaca, June 1970.

2.40. Tasuju, M. Ebrahim; Slate, Floyd 0.; and Nilson, Arthur H., “Stress-Strain Response and Fracture of Con-crete in Biaxial Loading,” ACI JO U R N A L,Proceedings V .

75, No. 7, July 1978, pp. 306-312.

2.41. Shah, Surendra P., and Chandra, Sushil, “Critical Stress, Volume Change, and Microcracking of Concrete,” ACI JO U R N A L,Proceedings V. 65, No. 9, Sept. 1968, pp. 770-781.

2.42. Shah, Surendra P., and McGarry, Fred J., “Griffith Fracture Criterion and Concrete,” Proceedings, ASCE, V. 97, EM6, Dec. 1971, pp. 1663-1676.

2.43. Hillemeier, B., and Hilsdorf, H. K., “Fracture Me-chanics Studies of Concrete Compounds,” Cement and Con-crete Research, V. 7, No. 5, Sept. 1977, pp. 523-535.

Chapter 3 - Control of cracking due to drying shrinkage*

3.1 - Introduction

Cracking of concrete due to drying shrinkage is a subject which has received more attention by archi-tects, engineers, and contractors than any other characteristic or property of concrete. It is one of the most serious problems encountered in concrete construction. Good design and construction practice can minimize the amount of cracking and eliminate the visible large cracks by the use of adequate re-inforcement and contraction joints.

Although drying shrinkage is one of the principal causes of cracking, temperature stresses, chemical reactions, frost action, as well as excessive tensile stresses due to loads on the structure, are fre-quently responsible for cracking of hardened con-crete. Cracking may also develop in the concrete prior to hardening due to plastic shrinkage.

Information presented in this chapter concerns only the subjects of cracking of hardened concrete due to drying shrinkage; factors influencing shrink-age; control of cracking; and the use of expansive ce-ments to minimize cracking.

The subject of construction practices and specifica-tions to minimize drying shrinkage is covered in Chapter 8 (Sections 8.3 and 8.6) of this report.

224R-10 ACI COMMITTEE REPORT

3.2 - Crack formation

Why does concrete crack due to shrinkage? If the shrinkage of concrete caused by drying could take place without any restraint, the concrete would not crack. However, in a structure the concrete is al-ways subject to some degree of restraint by either the foundation or another part of the structure or by the reinforcing steel embedded in the concrete. This combination of shrinkage and restraint develops ten-sile stresses. When this tenten-sile stress reaches the tensile strength, the concrete will crack. This is illus-trated in Fig. 3.1.

Another type of restraint is developed by the dif-ference in shrinkage at the surface and in the inte-rior of a concrete member, especially at early ages. Since the drying shrinkage is always larger at the exposed surface, the interior portion of the member restrains the shrinkage of the surface concrete, thus developing tensile stresses. This may cause surface cracking, which are cracks that do not penetrate deep into the concrete. These surface cracks may with time penetrate deeper into the concrete mem-ber as the interior portion of the concrete is subject to additional drying.

ORIGINAL LENGTH

UNRESTRAINED

SHRINKAGE

t-RESTRAINED SHRINKAGE

DEVELOPS TENSILE STRESS

IF TENSILE STRESS IS

GREATER THAN TENSILE

STRENGTH, CONCRETE CRACKS

Fig. 3.1 - Cracking of concrete due to drying shrinkage.

The magnitude of tensile stress developed during drying of the concrete is influenced by a combination of factors, such as (a) the amount of shrinkage, (b) the degree of restraint, (c) the modulus of elasticity of the concrete, and (d) the creep or relaxation of the concrete. Thus, the amount of shrinkage is only o n e factor governing the cracking. As far as cracking is concerned, a low modulus of elasticity and high creep characteristics of the concrete are desirable since they reduce the magnitude of tensile stresses. Thus, to minimize cracking, the concrete should have low drying shrinkage characteristics and a high de-gree of extensibility (low modulus and high creep) as well as a high tensile strength. However, a large ex-tensibility of a concrete member subjected to bend-ing will cause larger deflections.

3.3 - Drying shrinkage

When concrete dries, it contracts or shrinks, and when it is wetted again, it expands. These volume changes, with changes in moisture content, are an inherent characteristic of hydraulic cement con-cretes. It is the change in moisture content of the ce-ment paste that causes the shrinkage or swelling of concrete, while the aggregate provides an internal restraint which significantly reduces the magnitude of these volume changes.

When cement is mixed with water, several chem-ical reactions take place. These reactions, commonly called “hydration,” produce a hydration product con-sisting essentially of some crystalline materials (prin-cipally calcium hydroxide) and a large amount of hardened calcium silicate gel called “tobermorite gel.” This rigid gel consists of colloidal size particles and has an extremely high surface area. In a hard-ened cement paste, some of the water is in the capil-lary pores of the paste, but a significant amount is in the tobermorite gel. Shrinkage is due to the loss of adsorbed water from the gel. On drying the first wa-ter lost is that which occupies the relatively large size capillaries in the cement paste. This loss of wa-ter causes very little, if any, shrinkage. It is the loss of the adsorbed and inter-layer water from the hy-drated gel that causes the shrinkage of the paste. When a concrete is exposed to drying conditions, moisture slowly diffuses from the interior mass of the concrete to the surface where it is lost by evapo-ration. On wetting this process is reversed, causing an expansion of the concrete.

In addition to drying shrinkage, the cement paste is also subject to carbonation shrinkage. The action of carbon dioxide, CO₂, present in the atmosphere on the hydration products of the cement, principally cal-cium hydroxide, Ca(OH)₂, results in the formation of calcium carbonate, CaCO,, which is accompanied by a decrease in volume. Since carbon dioxide does not penetrate deep into the mass of concrete, shrinkage due to carbonation is of minor importance in the overall shrinkage of a concrete structure. However,

CONTROL OF CRACKING 224R-11

carbonation does play an important role in the shrinkage of small laboratory test specimens, partic-ularly when subjected to long-term exposure to drying. Thus, the amount of shrinkage observed on a small laboratory specimen will be greater than the shrinkage of the concrete in the structure. The sub-ject of shrinkage due to carbonation is discussed in detail by Verbeck.3.1

3.4 - Factors influencing drying shrinkage

The major factors influencing shrinkage include the composition of cement, type of aggregate, water content, and mix proportions. The rate of moisture loss or the shrinkage of a given concrete is greatly influenced by the size and shape of the concrete member, the environment, and the time of drying exposure. These and other factors influencing magni-tude and rate of shrinkage are herein discussed.

3.4.1 Effect of cement - Results of an extensive

study made by Blaine, Arni, and Evans,3.2 _{of the}

Na-tional Bureau of Standards on a large number of portland cements indicate that it is not possible to say that a cement, because it conforms to the re-quirements of one of the standard types of cements, will have greater or less shrinkage than a cement meeting requirements for some other type of ce-ment. Their results on neat cement pastes showed a wide distribution of shrinkage values especially for the Type I cements. The 6 month drying shrinkage strain of the neat pastes ranged from about 0.0015 to more than 0.0060 with an average for the 182 ce-ments tested of about 0.0030. They found that lower shrinkage of pastes was associated with: 1. lower C

3A/SO3 ratios, 2. lower Na2O and K2O contents,

and 3. higher C

4AF contents of the cement. Tests by

Brunauer. Skalny, and Yudenfreund3.3 _{show that for}

short curing periods Type II cement pastes exhib-ited considerably less shrinkage than Type I pastes. However, the shrinkage of pastes cured for 28 days was about the same for the two types of cements.

Tests made by the California Division of High-ways3.4 on mortar or paste as a measure of behavior in concrete indicate that Type II cements generally produce lower shrinkage than Type I cements, and much lower than Type III cements. Tests by Lerch1.5 show that the proportion of gypsum in the cement has a major effect on shrinkage. Cement producers moderate the differences in shrinkage due to cement composition by optimizing its gypsum content.

The fineness of a cement can have some influence on drying shrinkage. Tests by Carlson3.6 _{showed that}

finer cements generally result in greater concrete shrinkage, but the increase in shrinkage with in-creasing fineness is not large. His results show that the composition of the cement is a factor and thus for some cements an increase in fineness may show little change and in some cases even a lower con-crete shrinkage.

TABLE 3.1 - Effect of type of aggregate on shrinkage of concrete3.6

S p e c i f i c

l-year Absorption, shrinkage, Aggregate gravity percent percent

t Sandstone 2.47 5.0 0.116 Slate 2.75 1.3 0.068 Granite 2.67 0 . 8 0.047 Limestone 2.74 0.2 0.041 Quartz 2.66 0.3 0.032

3.4.2 Influence of type of aggregate - Coarse and

fine aggregates, which occupy between 65 and 75 percent of the total concrete volume, have a major influence on shrinkage. Concrete may be considered to consist of a framework of cement paste whose large potential shrinkage is being restrained by the aggregate. The drying shrinkage of a concrete will be only a fraction (about l/4 to l/6) of that of the ce-ment paste. The factors which influence the ability of the aggregate particles to restrain shrinkage in-clude (a) the compressibility of aggregate and the ex-tensibility of paste, (b) the bond between paste and a g g r e g a t e , (c) the degree of cracking of cement paste, and (d) the contraction of the aggregate par-ticles due to drying. Of these several factors, com-pressibility of the aggregate has the greatest in-fluence on the magnitude of drying shrinkage of concrete.

The higher the stiffness or modulus of elasticity of an aggregate, the more effective it is in reducing the shrinkage of concrete. The absorption of an aggre-gate, which is a measure of porosity, influences its modulus or compressibility. A low modulus is usually associated with high absorption.

The large influence of type of aggregate on drying shrinkage of concrete was shown by Carlson.3.6 As an example some of his shrinkage data for concretes with identical cements and identical water-cement ratios are given in Table 3.1.

Quartz, limestone, dolomite, granite, feldspar, and some basalts can be generally classified as low-shrinkage producing types of aggregates. High-shrinkage concretes often contain sandstone, slate, hornblende and some types of basalts. Since the ri-gidity of certain aggregates, such as granite, lime-stone or dolomite, can vary over a wide range, their effectiveness in restraining drying shrinkage will vary accordingly.

Although the compressibility is the most impor-tant single property of aggregate governing concrete shrinkage, the aggregate itself may contract an ap-preciable amount upon drying. This is true for sand-stone and other aggregates of high absorption capac-ity. Thus, in general, aggregate of high modulus of elasticity and low absorption will produce a low-shrinkage concrete. However, some structural grade lightweight aggregates, such as expanded shales,

224R-12 ACI COMMITTEE REPORT + 119 142 166 190 5 0.060 u % 0.050 I ," 0.020 z

z

is

WATER CONTENT OF CONCRETE

kg/m3

Ib/yd3

Fig. 3.2 - Typical effect of water content of con-crete on drying shrinkage (Reference 3.8).

clays, and slates which have high absorptions, pro-duced concretes exhibiting low shrinkage character-istics.3.7

Maximum size of aggregate has a significant effect on drying shrinkage. Not only does a large aggre-gate size permit a lower water content of the con-crete, but it is more effective in resisting the shrink-age of the cement paste. Aggregate gradation also has some effect on shrinkage. The use of a poorly graded fine or coarse aggregate may result in an oversanded mix, in order to obtain desired work-ability, and thus prevent the use of the maximum amount of coarse aggregate resulting in increased shrinkage.

3.4.3 Effect of water content and mix proportions

-The water content of a concrete mix is another very important factor influencing drying shrinkage. The large increase in shrinkage with increase in water content was demonstrated in tests made by the U.S. Bureau of Reclamation.3.8

A typical relationship be-tween water content and’drying shrinkage is shown in Fig. 3.2. An increase in water content also re-duces the volume of restraining aggregate and thus results in higher shrinkage. The shrinkage of a

con-400’

MAXIMUM SIZE OF AGGREGATE

Fig. 3.3 - Effect of aggregate size on water require-ment of non-air-entrained concrete (ACI 211.1).

crete can be minimized by keeping the water con-tent of the paste as low as possible and the total ag-gregate content of the concrete as high as possible. This will result in a lower water content per unit volume of concrete and thus lower shrinkage.

The total volume of coarse aggregate is a signifi-cant factor in drying shrinkage. Concrete propor-tioned for pump placement with excessively high sand contents will exhibit significantly greater shrinkage than will similar mixes with normal sand contents.

Tests reported by Tremper and Spellman3.4 _show

that the cement factor has little effect on shrinkage of concrete. Their data show that as the cement fac-tor was increased from 470 to 752 lb/yd3 _{(279 to 446}

kg/m3) the water content remained nearly constant, while percentage of fine aggregate was reduced.

The amount of mixing water required for concrete of a given slump is greatly dependent on the max-imum size of aggregate. The surface area of aggre-gate, which must be coated by cement paste, de-creases with increase in size of aggregate. The large effect that the maximum size of aggregate has on the water requirement of concrete is shown in Fig. 3.3. The data plotted in this figure, taken from ACI 211.1 shows, for example, that for a 3 to 4 in. (75 to 100 mm) slump concrete, increasing the aggregate size from 3/4 in. (19 mm) to 11_/2 in. (38 mm) decreases

the water requirement from 340 to 300 lb/yd3 ₍₂₀₂ to

178 kg/m3). This 40 lb (24 kg) reduction in water content would reduce the 1 year drying shrinkage by about 15 percent.

Also shown in Fig. 3.3 is the effect of slump on water requirement. For example, the water require-ment of a concrete made with 3/4 in. (19 mm) size ag-gregate is 340 lb/yd3 (202 kg/m3) for a 3 to 4 in. slump, but only 310 lb/yd3 (184 kg/m31 for a 1 to 2 in. slump (25 to 50 mm). This substantial reduction in water content would result in a lower drying shrinkage.

Another important factor which influences the wa-ter requirement of a concrete, and thus its shrink-age, is the temperature of the fresh concrete. This effect of temperature on water requirement as given by the U.S. Bureau of Reclamation3. _{is shown in}

Fig. 3.4. For example, if the temperature of fresh concrete were reduced from 100 to 50 F (38 to 10 C), it would permit a reduction of the water content by 33 Ib/yd3 _{(20 kg/m}3_{) and still maintain the same}

slump. This substantial reduction in water content would significantly reduce the drying shrinkage.

From the above discussion it must be concluded that, to minimize the drying shrinkage of concrete, the water content of a mix should be kept to a min-imum. Any practice that increases the water re-quirement, such as the use of high slumps, high tem-peratures of the fresh concrete or the use of smaller size coarse aggregate, will substantially increase shrinkage and thus cracking of the concrete.

CONTROL OF CRACilNG 224R-13 0 0 4.4 10.0 15.6 21.1 26.7 32.2 378 OC 310 084) 300 (I 78) 290 (I 72) 280 (166) 270 (160) 260 (154140 50 60 70 80 90 100 OF TEMPERATURE OF FRESH CONCRETE

Fig. 3.4 - Effect of temperature of fresh concrete _{Fig. 3.5 - Rates of drying of concrete exposed to 50}

on its water requirement (Reference 3.8). _{percent relative humidity (Reference 3.9).} 3.4.4 Effect of chemical admixtures - Chemical

ad-mixtures are used to impart certain desirable prop-erties to the concrete. Those most commonly used include air-entraining admixtures, water-reducing admixtures, set-retarding admixtures, and accelera-tors.

It would be expected that when using an air-en-training admixture, the increase in the amount of air voids would increase drying shrinkage. However, be-cause entrainment of air permits a reduction in wa-ter content with no reduction in slump, the shrink-age is not appreciably affected by air contents up to about 5 percent.3.8 Some air-entraining agents are strong retarders and contain accelerators which may increase drying shrinkage by 5 to 10 percent.

Although the use of water-reducing and set-re-tarding admixtures will permit a reduction in the water content of a concrete mix, it will usually not result in a decrease in drying shrinkage. Actually some of these admixtures may even increase the shrinkage at early ages of drying, although the later age shrinkage of these concretes will be about the same as that of corresponding mixes with no admix-tures.

The use of calcium chloride, a common accelerator, will result in a substantial increase in drying shrink-age, especially at the early ages of drying. Tests made by the California Department of Transporta-tion3.4_{4showed that the 7 day shrinkage of a concrete}

containing 1.0 percent of calcium chloride was about double that obtained for the control mix without ad-mixture. However, after 28 days of drying, the shrinkage of the concrete containing calcium chloride was only about 40 percent greater than that of the control mix.

3.4.5 Effect of pozzolans - Fly ash and a number of

natural materials such as opaline cherts and shales, diatomaceous earth, tuffs and pumicites are pozzo-lans used in portland cement concrete. The use of some natural pozzolans can increase the water

de-mand as well as the drying shrinkage of the con-crete. Also, it was observed that the use of some of these pozzolans increased drying shrinkage although they had little effect on the water content of the concrete. Some fly ashes have little effect on drying shrinkage, while others may increase the shrinkage of the concrete. All of these observations are based on results of tests made on laboratory size speci-mens. However, as noted in Section 3.4.7 and Fig. 3.6, the larger the concrete member, the lower the shrinkage. This may explain the negligible difference in shrinkage cracking of field structures, with and without pozzolan, despite clearly greater shrinkage of the concretes with pozzolans in laboratory tests on small size specimens.

3.4.6 Effect of duration of moist curing - Car1son3.6

reported that the duration of moist curing of con-crete does not have much effect on drying shrink-age. This is substantiated by the test results of the California Department of Transportation3.’ which show substantially the same shrinkage in concrete that was moist cured for 7, 14, and 28 days before drying was started. As far as the cracking tendency of the concrete is concerned, prolonged moist curing may not necessarily be beneficial. Although the strength increases with age, the modulus of elastic-ity also increases by almost as large a percentage, and the net result is only a slight increase in the tensile strain which the concrete can withstand.

Steam curing at atmospheric pressure, which is commonly used in the manufacture of precast struc-tural elements, will reduce drying shrinkage (AC1 517). Also, because stream curing will produce a high early-age strength of the concrete, it will re-duce its tendency to crack, since the pre’cast mem-bers are unrestrained.

3.4.7 Influence of size of member - The size of a concrete member will influence the rate at which moisture moves from the concrete and thus in-fluence the rate of shrinkage. Carlson3*’ has shown

w iii a a

-0 4 8 I2 16 20 24 28 in. w _{DEPTH BELOW CONCRETE SURFACE}

224R-14 ACI COMMITTEE REPORT

that for a concrete exposed to a relative humidity of 50 percent, drying will penetrate only about 3 in. (75 mm) in 1 month and about 2 ft (0.6 m) in 10 years. Fig. 3.5 shows his theoretical curves for the drying of slabs. Hansen and Mattock3.10 made an extensive investigation of the influence of size and shape of member on the shrinkage and creep of con-crete. They found that both the rate and the final values of shrinkage and creep decrease as the mem-ber becomes larger.

This significant effect of size of member on drying shrinkage of concrete must be considered when eval-uating the potential shrinkage of concrete in struc-tures based on the shrinkage of concrete specimens in the laboratory. The rate and magnitude of shrink-age of a small laboratory specimen will be much greater than that of the concrete in the structures. Test results of several studies carried out to com-pare the shrinkage of concrete in walls and slabs in the field with the shrinkage of small laboratory specimens have shown, as expected, that the shrink-age of the concrete in a field structure is only a frac-tion of that obtained on the laboratory specimens. Even in laboratory tests the size of the specimen used has a significant influence on shrinkage. As an example of the effect of specimen size on shrinkage is the data presented in Fig. 3.6, giving the results of shrinkage tests obtained on four different size concrete prisms. It will be noted that the shrinkage of the prisms having a cross section of 3 x 3 in. (7.5 x 7.5 cm) was more than 50 percent greater than that of the concrete prism having a cross section of 5 x 6 in. (12.5 x 15 cm).

3.5 - Control of shrinkage cracking

Concrete tends to shrink due to drying whenever its surfaces are exposed to air of low relative humid-ity. Since various kinds of restraint prevent the

con-7 . 5 x con-7 . 5 10 x 10 10x12 5 12.5x 15 cm

I

I

I

3 x 3 4 x 4 4 x 5 5x6 in AVERAGE END AREA DIMENSION OF CONCRETE PRISM

( LOG SCALE )

Fig. 3.6 - Effect of specimen size on drying shrink-age of concrete (Principal author’s data).

crete from contracting freely, the possibility of cracking must be expected unless the ambient rela-tive humidity is kept at 100 percent or the concrete surfaces are sealed to prevent loss of moisture. The control of cracking consists of reducing the cracking tendency to a minimum, using adequate and prop-erly positioned reinforcement, and using control joints. The CEB-FIP Code give quantitative recom-mendations on the control of cracking due to shrink-age, listing various coefficients to determine the shrinkage levels that can be expected. Control of cracking by correct construction practices is covered in Chapter 8 of this report, which includes specifica-tions to minimize drying shrinkage (Section 8.6).

Cracking can also be minimized by the use of ex-pansive cements to produce shrinkage-compensating concretes. Shrinkage-compensating concretes are dis-cussed in Section 3.6.

3.5.1 Reduction of cracking tendency - As

men-tioned previously, the cracking tendency is due not only to the amount of shrinkage, but also to the de-gree of restraint, the modulus of elasticity, and the creep or relaxation of the concrete. Some factors which reduce the shrinkage at the same time de-crease the creep or relaxation and inde-crease the mod-ulus of elasticity, thus offering little or no help to the cracking tendency. Emphasis should be placed, therefore, on modifying those factors which produce a net reduction in the cracking tendency.

Any measure that can be taken to reduce the shrinkage of the concrete will also reduce the crack-ing tendency. Drycrack-ing shrinkage can be reduced by using less water in the mix and larger aggregate size. A lower water content can be achieved by us-ing a well-graded aggregate, stiffer consistency, and lower initial temperature of the concrete. As dis-cussed in Section 3.4.4, however, the reduction of water content by the use of water-reducing admix-tures will not usually reduce shrinkage.

Another way to reduce the cracking tendency is to use a larger aggregate size. A larger aggregate size allows an increase in aggregate volume and a reduction in the total water required to obtain a given slump. The larger aggregate also tends to strain the concrete more, and although this may re-sult in internal microcracking, such internal cracking is not necessarily harmful.

A third way to reduce the cracking tendency is to apply a surface coating to the concrete, which will prevent the rapid loss of moisture from within. This means of controlling cracking has not been used to its full potential and should be given better consider-ation. However, many surface coatings such as all-purpose paints are ineffective, because they permit the moisture to escape almost as fast as it reaches the surface. Chlorinated rubber and waxy or resin-ous materials are effective coatings, but there are probably many other materials which will slow the evaporation enough to be beneficial. Any slowing of

CONTROL OF CRACKING 224R-15 the rate of shrinkage will be beneficial, because

con-crete has a remarkable quality of relaxing under sus-tained stress. Thus, concrete may be able to with-stand two or three times as much slowly applied shrinkage as it can rapid shrinkage.

3.5.2 R e i n f o r c e m e n t - Properly placed re-inforcement, used in adequate amounts, will not only reduce the amount of cracking but prevent unsightly cracking. By distributing the shrinkage strains along the reinforcement through bond stresses, the cracks are distributed in such a way that a larger number of very fine cracks will occur instead of a few wide cracks. Although the use of such reinforcement to control cracking in a relatively thin concrete section is practical, it is not needed in massive structures such as dams due to the low drying shrinkage of these mass concrete structures. The minimum amount and spacing of reinforcement to be used in floors, roof slabs, and walls is given in AC1 318. 3.6.3 Joints - The use of joints is the most effective method of preventing formation of unsightly crack-ing. If a sizable length or expanse of concrete, such as walls, slabs or pavements, is not provided with adequate joints to accommodate shrinkage, it will make its own “joints” by cracking.

Contraction joints in walls are made, for example, by fastening to the forms wood or rubber strips which leave narrow vertical grooves in the concrete on the inside and outside of the wall. Cracking of the wall due to shrinkage should occur at the grooves, relieving the stress in the wall and thus preventing formation of unsightly cracks. These grooves should be sealed on the outside of the wall to prevent pene-tration of moisture. Sawed joints are commonly used in pavements, slabs and floors.

Joint location depends on the particulars of place-ment. Each job must be studied individually to de-termine where joints should be placed.*

3.6 - Shrinkage-compensating concretes

Shrinkage-compensating concretes made with ex-pansive cements can be used to minimize or elimi-nate shrinkage cracking. The properties and use of expansive cement concretes is published in numer-ous papers and reports.3-11* 3*12 Of the several types

of expansive cements produced, the Type K shrinkage-compensating expansive cement is most commonly used in the United States.

In a reinforced concrete, the expansion of the ce-ment paste during the first few days of curing will develop a low level of prestress inducing com-pressive stresses in the concrete and tensile stresses in the steel. The level of compressive stresses devel-oped in the shrinkage-compensating concretes ranges from 25 to 100 psi (0.2 to 0.7 MPal. When subjected to drying shrinkage, the contraction of the concrete will result in a reduction or elimination of its precompression. The initial precompression of the

STEEL\

_B---

_----ORIGINAL LENGTH

T

A b T

___++IC~*___

EXPANSION PUTS STEEL IN

TENSION AND CONCRETE IN

COMPRESSION

M

STRESS LOSS DUE TO

SHRINKAGE AND CREEP

RESIDUAL EXPANSION OR, -+j

SMALL CONTRACTION

.

Qr

Basic concept of shrinkage-compensating

CURING

r/ .

AGE OF CONCRETE, DAYS

Fig. 3.8 - Length change characteristics of shrink-age-compensating and portland cement concretes (Relative humidity = 50 percent).

concrete minimizes the magnitude of any tensile stress that may ultimately develop due to shrinkage, and thus reduce or eliminate the tendency to crack-ing. This basic concept of the use of expansive ce-ment to produce a shrinkage-compensating concrete is illustrated in Fig. 3.7.

A typical length change history of a shrinkage-compensating concrete is compared to that of a port-land cement concrete in Fig. 3.8. The amount of re-inforcing steel normally used in reinforced concrete

*Guidance on joint sealants and control joint location in slabs is avail-able in ACI 504 and in ACI 302, respectively.

224R-16 ACI COMMITTEE REPORT

made with portland cements is usually more than ad-equate to provide the elastic restraint needed for shrinkage-compensating concrete. To take full advan-tage of the expansive potential of shrinkage-com-pensating concrete in minimizing or preventing shrinkage cracking of unformed concrete surfaces, it is important that positive and uninterrupted water curing (wet covering or ponding) be started immedi-ately after final finishing. For slabs on well satu-rated subgrades, curing by sprayed-on membranes or moisture-proof covers have been successfully uti-lized. Inadequate curing of shrinkage-compensating concrete may result in an insufficient expansion to elongate the steel and thus subsequent cracking dur-ing drydur-ing shrinkage. Specific recommendations and information on the use of shrinkage-compensating concrete are contained in ACI 223.

References

3.1. Verbeck, George J., “Carbonation of Hydrated Port-land Cement,” Cement and Concrete, STP-205, American Society for Testing and Materials, Philadelphia, 1958, pp. 17-36.

3.2. Blaine, R. L.; Arni, H. T.; and Evans, D. N., “Inter-relations Between Cement and Concrete Properties: Part 4 - Shrinkage of Hardened Portland Cement Pastes and Concrete,” Building Science Series No. 15, National Bu-reau of Standards, Washington, D.C., Mar. 1969, 77 pp.

3.3. Brunauer, S.; Skalny, J.: and Yudenfreund, H., “Hardened Cement Pastes of Low Porosity: Dimensional Changes,” Research Report No. 69-8, Engineering Re-search and Development Bureau, New York State Depart-ment of Transportation, Albany, Nov. 1969, 12 pp.

3.4. Tremper, Bailey, and Spellman, Donald L., “Shrink-age of Concrete - Comparison of Laboratory and Field Performance,” Highway Research Record. Highway Re-search Board, No. 3, 1963, pp. 30-61.

3.5. Lerch, William, “The Influence of Gypsum on the Hydration and Properties of Portland Cement Pastes,”

Proceedings, ASTM, V. 46, 1946, pp. 1252-1297.

3.6. Carlson, Roy W., “Drying Shrinkage of Concrete as Affected by Many Factors,” Proceedings, ASTM, V. 38, Part II, 1938, pp. 419-437.

3.7. Reichard, T. W., “Creep and Drying Shrinkage of Lightweight and Normal Weight Concrete, ” M o n o g r a p h

74, National Bureau of Standards, Washington, D.C., 1964, 30 pp.

3.8. Concrete Manual, 8th Edition, U.S. Bureau of Re-clamation, Denver, 1975, 627 pp.

3.9. Carlson, Roy W., “Drying Shrinkage of Large Con-crete Members,” ACI JOURNAL , Proceedings V. 33, No. 3, Jan.-Feb. 1937, pp. 327-336.

3.10. Hansen, Torben C., and Mattock, Alan H., “In-fluence of Size and Shape of Member on the Shrinkage and Creep of Concrete,” ACI JOURNAL, Proceedings V. 63, No. 2, Feb. 1966, pp. 267-290.

3 . 1 1 . ACI C o m m i t t e e 2 2 3 , “ E x p a n s i v e C e m e n t Concretes-Present State of Knowledge,” ACI JO U R N A L, Proceedings V. 67, No. 8, Aug. 1970, pp. 583-610.

3.12. Klein Symposium on Expansive Cement Concretes,

S P - 3 8 , American Concrete Institute, Detroit, 1973, 491 pp.

Chapter 4 - Control of cracking in flexural

members*

4.1 - Introduction

With the regular use of high strength reinforcing s t e e l a n d t h e s t r e n g t h d e s i g n a p p r o a c h f o r r e -inforced concrete, and higher allowable stresses in prestressed concrete design, the control of cracking may be as important as the control of deflection in flexural members. Internal cracking in concrete can start at stress levels as low as 3000 psi (20.7 MPa) in the reinforcement. Crack control is important to pro-mote the aesthetic appearance of structures, and for many structures, crack control plays an important role in the control of corrosion by limiting the possi-bilities for entry of moisture and salts which, to-gether with oxygen, can set the stage for corrosion.

This chapter is concerned primarily with cracks caused by flexural and tensile stresses, but temper-ature, shrinkage, shear and torsion may also lead to cracking.”4.1 _{Cracking in certain specialized}

struc-tures, such as reinforced concrete tanks, bins and silos, is not covered in this report. For information on cracking concrete in these structures, see Refer-ence 4.2 and ACI 313.

Extensive research studies on the cracking be-havior of beams have been conducted over the last 5 0 y e a r s . M o s t o f t h e m a r e r e p o r t e d i n ACI Bibliography No. 9 on crack control.4.3 _{Others are} referenced in this chapter. Reference 4.1 contains an extensive review of cracking in reinforced concrete structures. Several of the most important crack pre-diction equations are reviewed in the previous com-mittee report. 1.1’_{Additional work presented in the} CEB-FIP Model Code for Concrete Structure gives the European approach to crack width evaluation and permissible crack widths.

Recently, fiber glass rods have been used as a reinforcing material.4.4_{To date, experience is}

lim-ited, and crack control in structures reinforced with fiber glass rods is not addressed in this report. It is expected, however, that future committee docu-ments will address crack control in structures using this and other new systems as they come into use.

4.2 - Crack control equations for reinforced con-crete beams

A number of equations have been proposed for the prediction of crack widths in flexural members; most of them are reviewed in the previous committee re-port1.1Pand in key publications listed in the refer-

ences. Most equations predict the probable max-imum crack width, which usually means that about 90 percent of the crack widths in the member are below the calculated value. However, research has shown that isolated cracks in beams in excess of twice the width of the computed maximum can