2009 06 cia achieving durability in design crack control (5)

8/6/2019 2009 06 CIA Achieving Durability in Design Crack Control (5)

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Achieving Durability In Design : Cracks and Crack Control(Early Age Cracking Sections First Presented CIA Conference 2007.

Updated 2009 to include assessment of AS 4997 steel stress requirements)

F.Papworth P. BamforthBCRC Consultant, Perth, Australia BCRC Consultant, London, UK

1. IntroductionThere are three stages in the design life where cracking can occur, the plastic stage due to changesin concrete while it is hardening, early age due to changes while concrete cures in the hardened stateand long term load induced cracks. Designers generally follow Australian Code requirements formaximum allowable strain in the reinforcement and assumes that will take care of early age strains,and in most concrete it does. However, where fine crack widths are required, or where concrete with ahigh heat output is used, code requirements alone may be insufficient to control crack widthsadequately. Designers also often leave the plastic crack control entirely to the contractor.Unfortunately that may not be the best approach as specifications for mix design have a high impacton the requirements for plastic crack control. This paper considers requirements for all three stagesfrom a design perspective to highlight where additional guidance might be given in Australian codes.

Plastic CrackingThere are three types of plastic cracking that the designer can influence plastic shrinkage, plasticsettlement and autogenous shrinkage cracking.

Plastic shrinkage cracks occur when the rate of evaporation (e, lt/m 2/hr) exceeds the rate of bleedwater arriving at the concrete surface (b, lt/m2/hr). There are many documents that suggest that if e 35

*BCRC recommendations for cracks intermittently wet so that oxygen available

The water retaining requirements are based on research that shows autogenous crack healingcapacity at different pressure gradients. However, it is known that concrete that includes SCMs has aslower capacity for autogenous healing. When dealing with marine structures research has shownthat leakage at cracks is not a significant concern for the first 3 months at least. Taking the crack

width limits in Table 2c) as applying to GP cements (the cement used in the research) it may benecessary to define finer crack widths when SCMs are used.

The New Zealand Standard DZ 3106 provides definitions (Table 3 columns 1 and 2) for differentlevels of water tightness. This may provide a system for more economical or conservative designs fordifferent situations. Provisions for achieving leakage requirements are given in DZ 3106 butalternative provision for achieving the requirements that may appropriately allow for Australian Codesand use of SCMs are given in Table 3 column 3.

Table 3 : DZ3106 Tightness Class

TightnessClass

Leakage Requirements Possible Interpretation of Provisions forAchieving Leakage Requirements

0 Leakage acceptable or

leakage of liquids irrelevant

Crack control provisions of AS 3600 may be

adopted1 Leakage to be limited to

small amount. Some surfacestaining or damp patchesacceptable

Crack widths to be controlled so that they are highlylikely to be healed by autogenous healingultimately. Limits given in Table 2 c) to apply.

2 Leakage to be minimal,Appearance not to beimpaired by staining

Crack widths to be controlled so that they are highlylikely to be healed by autogenous healing within 1week. Limits given in Table 2 c) to be reduced by30% for GP cements and 50% for SCMs

3 No leakage permitted Special measures required, e.g. liners or prestress

Early Age StrainsEarly age thermal cracking (EATC) is the result of restraint to contraction as concrete cools from itspeak hydration temperature. In many normal situations EATC may be difficult to avoid and eventhough reinforced concrete is designed to crack EATC may still be a source of dispute. It is important,therefore, that clients understand that EATC is not necessarily inconsistent with good practice and inmany cases it may be either unnecessary or uneconomical to avoid cracking entirely. Measures tominimise or avoid EATC are available through the selection of concreting materials; reducing the mixtemperature; cooling of the concrete in situ; planning the construction sequence to minimise restraint;or prestressing. These may have significant cost implications and the client must be made aware ofthese if demanding crack free concrete or onerous limits on crack width.

In the UK, design for EATC has been dealt with using BS8007 (1) and together with modifications tosuit Australian conditions (2) this provided a basis for the recommendations of Australian Standards.

BS8007 was supported by CIRIA 91 (4) which provided background to the design method and datafor use in the design process. CIRIA 91 has been updated and replaced by CIRIA C660 (5) to takeaccount of new knowledge of the performance of a range of concreting materials; the increasing useof higher strength concrete; and changes in the design process arising from the introduction of Euro-codes, in particular EN1992-1-1 (6) which will replace BS8110 (7) as the general design code in theUK in 2009; and EN1992-3 (8) which will replace BS8007 for water retaining structures in 2011. Inaddition to bringing the design into line with Euro-codes, CIRIA C660 differs from CIRIA 91 in thefollowing respects.

Values of temperature drop (T1) for Portland cement (GP cement) have been revised andadditional information is provided on concretes containing fly ash and ground granulated blast-furnace slag (ggbs). Silica fume can be treated as GP cement and provision made for reducedcement content.

Information is provided on autogenous shrinkage

Additional information is given on different forms of restraint, how they may be calculated andhow they affect crack width

Tensile strain capacity is dealt with more comprehensively


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A method for reinforcement design has been developed to deal with cracking caused bytemperature differentials in thick sections

Guidance is given on methods for minimising the risk of cracking

Advice is provided on specification, testing and in situmonitoring.

EATC cracking is influenced by decisions made by both the designer and the constructor as follows;

Designer: element geometry; concrete strength class (and possibly cement type and minimumcement content); design of reinforcement; location of movement and (some) construction joints.

Constructor: procuring concrete to meet specification and buildability requirements; planning theconstruction sequence, selecting formwork and striking and curing times; additional measures.

As there is a joint responsibility it is important that the design assumptions are very clearly stated.The benefits are twofold. Firstly, if cracking is out of specification, comparing assumed and achievedconcrete properties and thermal histories may help with dispute resolution. And secondly, as designassumptions are generally conservative, advantage may be obtained when project specific data areavailable. These and other issues may be overcome if Designer and Constructor work together.

BS8007 uses a strain based approach (9) and this has been maintained in EN1992-3. It is generally

assumed that compressive stresses induced during heating are relieved by creep. Hence therestrained contraction, r that may lead to cracking, is related to the drop from the peak temperaturein the section to the mean ambient temperature T1, the coefficient of thermal expansion of concrete

cthe restraint R, and a creep coefficient Kaccording to the equation r= c. T1. K. R

C660 provides data in chart form for various combinations of GP cement with fly ash or ggbs asshown in Figure 2. Semi-adiabatic test results (10) provided the input to a thermal model used topredict T1. A comparison of predicted and measured results (11, 12, 13) validated the model for arange of concrete mix types and temperatures. Although C660s methods for calculating thermalstrains can be used for Australian conditions the heat generating capacity of the concrete may not beapplicable. The adiabatic temperature rise of a concrete mix can be obtained by direct measurement,or via semi adiabatic temperature rise (e.g. 1 m3 hot box tests), and input into C660s calculator toassess insitu temperature rise until Australian research can provide similar graphs to those in CIRIA

C660.

220

260

300

340

380

420

460

500

0

10

20

30

40

50

60

200 300 400 500 600 700 800 900 1000

Thickness (mm)

Tem

peratureDropT1

(oC)

20% fly ash - Plywood formwork

Figure 2 Design Values forT1 For 20% Fly

Ash Concrete Cast in 18mm Plywood Formwork

During the early age period (after 1 day) autogenous shrinkage is treated in a similar manner to

thermal strains. Although not specifically measured in the past autogenous shrinkage strains will haveformed part of drying shrinkage. However long term autogenous shrinkage has now measuredseparately to drying shrinkage to give some indication of what allowance should be made for it.EN1992-1-1 estimates autogenous shrinkage based on the strength alone and assumes that it occurs


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to some degree in all structural concretes and this is supported by research data (Appendix 4 ofC660). EN1992-1 takes no account of the cement type but there is evidence that mineral additionsaffect autogenous shrinkage with an increase using silica fume or ggbs and a reduction with fly ash.CIRIA C660 includes a calculator for autogenous shrinkage based on EN1992-1 but this should notbe used for Australian materials as values that may better reflect Australian Materials and exposuresare included in the proposed AS 3600 revision. A comparison of E1992-1-1 and AS 3600 values aregiven in Figure 3.

Figure 3 : AS 3600 and EN 1992-1-1 Autogenous shrinkage for 25MPa and 60Mpa Concrete

AS3600

EN1992-1-1

C25/30

0

5

10

15

20

25

30

35

40

1 10 100 1000 10000

Time (days) - log scale

AS3600

EN1992-1-1

C60/750

20

40

60

80

100

120

140

1 10 100 1000 10000

Time (days) - log scale

C660 provides drying shrinkage estimates for elements but these are also different to Australiandrying shrinkage calculations and values from the new draft of AS 3600 should be used. Theshrinkage of concern is the shrinkage of an element relative to the element that is restraining it. Figure4 shows calculations for a wall cast on a slab 20 days after the slab was cast. The slab dries from oneface so drying is slower but eventually the differential shrinkage tends to zero.

Figure 4 : Differential Shrinkage Between anElement and its Restraining Element (C660

Shrinkage Values)

Figure 5 : Comparison of AS 3600 and C660Shrinkage values for Wall and Floor Elements

Using Same Mix & Curing

0

50

100

150

200

250

300

10 100 1000 10000

Time (days)

Wall C40/50N Cem400mmthick, cure3days

Slab C40/50N Cem400mmthick, cure 3days

Difference if 20days between pours

0

100

200

300

400

500

10 100 1000 10000

Time (days)

Wall C40/50 N Cem 400mm thick, cure 3 days

Slab C40/50 N Cem 400mm thick, cure 3 days

AS 3600 Wall

AS3600 Floor

2. Internal RestraintSpecifications often state The temperature differential between the centre of a pour and the surfaceshall not exceed 20C. This was popular in the UK 30 years ago. It was intended to ensure no internalrestraint cracking and was applicable to gravel aggregates. At the point of cracking the strain capacityis equal to the restrained strain i.e.:

ctu = ac . T . K1 . R - wherectu = Strain Capacityac = Coefficient of thermal expansion

T = Temperature differentialK1 = Creep = 0.65R = Restraint = 0.42

Hence T = 3.7 . ctu / ac -

Table 4 : Calculated Temperatures to Cause Cracking for Internal & Edge Restraint

Aggregate Coefficient Tensile Temperature (C) to Avoid EATC


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Type ThermalExpansion

( /C)

StrainCapacity

( )

Max Temp.Differential

Internal RestrainR=0.42

Maximum Temperature DropExternal Restraint Factor

Edge Restraint

1.0 0.7 0.5 0.3

Gravel 13 65 20 6 9 14 24

Granite 10 75 28 9 14 21 36

Limestone 9 85 35 12 18 27 46

Using equation 2 the temperature to cause cracking due to internal restraint has been calculated andis shown in Table 4. Clearly a restriction on temperature differential to 20C would often beconservative. It is even more conservative/expensive if there is no real reason to prevent crackingaltogether rather than allow limited crack widths.

The tensile strain capacity ctu is the maximum strain that the concrete can withstand without acontinuous crack forming. A comprehensive review of data (19) demonstrated a linear relationshipbetween ctu under rapid loading and the ratio of the tensile strength fctm to the elastic modulus Ecm incompression. Using property data and age functions provided in EN1992-1-1, values for ctu havebeen estimated and adjusted to take account of sustained loading during the early-age thermal cycle.Values for strength class C30/37 (EN1992 presents strength class as both cylinder/cube, hence forC30/37, fc = 30 MPa) estimated on this basis are given in Table 5. To estimate the strain capacity forother strength classes, the value obtained for C30/37 is multiplied by 0.63 + (1.25 fc/100) forfcin the

range from 20 to 50 MPa. For higher strength concrete the value obtained for 50 MPa is used.

Table 5 : Estimated Values ofctu (In Microstrain) for Strength Class C30/37 under SustainedLoading Using Different Aggregate Types [Early-age = 3 Days, Long-term 28 Days]

Aggregate

type

Basalt Flintgravel

Quartzite Granite,Gabbro

Limestone,Dolerite

Sandstone Lightweight

Early-age 63 65 76 75 85 108 115

Long term 90 93 108 108 122 155 165

Edge RestraintEdge restraint occurs when one element is cast against another element such that the restrainingelement will help distribute the cracks along its length.

In line with BS8007, EN1992-3 provides a single coefficient of 0.5 to take account of restraint andcreep. This simple approach must be assumed to deal with the worst case, but prevents benefitbeing taken in situations where the worst case does not occur. Based on published data (15, 16, 17)C660 recommends a creep coefficient K= 0.65. This implies a worst case R= 0.5/0.65 0.8. Thefact that the worst case is not R = 1 is is not surprising as a new element does have some inherentstiffness when cooling commences and, in general, will not be totally dominated by the elementagainst which it is cast.

C660 describes a basis for calculating edge restraint (18) for walls on slabs which has been validated

by comparison with measured restraints in walls. The restraint at the joint is calculated from :

whereAn = cross-sectional area (c.s.a.) of the new (restrained) pourA0 = c.s.a. of the old (restraining) pourEn = modulus of elasticity of the new pourE0 = modulus of elasticity of the old pour

Values at the joint are commonly in the range for 0.4 to 0.7 indicating values of R x K in the rangefrom 0.26 to 0.46 and hence that the coefficient of 0.5 given in EN1992-3 is safe in the majority of

cases. The restraint, and hence reinforcement required to control cracking, can reduce quickly withdistance from the base. This reduction is calculated based on the length : height ratio of the wall asshown in Figure 6.


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Figure 6 : Reduction in Restraint With Distance from Joint

The design approach adopted by EN1992 is broadly similar to that of BS8007 but there are some

significant and important differences as follows; Different values of surface zone are used to estimate the minimum area of reinforcement

Different surface zones are used to estimated the steel ratio for calculating of crack width

EN1992-1-1 includes cover in the expressions for crack spacing and width

The term fct/fb(tensile strength/bond strength) has been replaced by the coefficient k1

Cracking develops depends on whether the element is subject to edge restraint or endrestraint (20) and this is reflected in different expressions for calculating crack width

Autogenous shrinkage is assumed to occur in all grades of structural concrete.

The minimum area of reinforcement As required to control the crack width is determined by ensuringthat the stress transferred to the steel after a crack has occurred is below the yield strength of thesteel. Expressions used by BS8007 and EN1992-1-1 are shown in Table 6.

Table 6 : Expression for Estimating the Minimum Area of Reinforcement

BS8007 BS1992-1-1

critc

y

ctcs Af

fAA = )Ak(k

f

fAkkA critctc

ky

effct,ctcmins, =

Ac is the surface zone of 250mm or h/2,whichever is less

Act is the area of concrete in tension

fct is the tensile strength of the concrete fct,eff is the tensile strength of the concrete

fy is the yield strength of the steel fyk is the yield strength of the steel

kallows for non-uniform and self-equilibrating stresswhich leads to a reduction in restraint forces.

kctakes account of the stress distribution in the section

A review of the development of the approach of both BS8007 and EN1992-1-1 was undertaken tounderstand the bases for the assumed surface zones. In doing so it was identified that theassumption that cracking is initiated from the surface may not be correct (21, 22). Under conditions ofexternal restraint it is most likely that cracking will be initiated at the point where the temperature dropis the greatest, i.e. at the centre of the section (Figure 7) transferring stress from the full section to thereinforcement when a crack occurs.


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Restraint

RestraintR

estraint

Restraint

Cracking propagated

from the centre wheretemperature change is

greatest

t0

t1

t2

t3Temperature profile

Figure 7 : Cross-Section Through a Thick Wall Subject External Restraint

C660 has therefore developed appropriate surface zones taking account of both the temperatureprofile and the fact that in practice some compressive stresses must be relieved by a drop intemperature before tensile stress are generated. A comparison of the values recommended by C660with those of the existing recommendations of EN1992-1-1 and BS8007 is shown in Figure 8.

0

100

200

300

400

500

600

700

800

0 500 1000 1500 2000

Section thickness (mm)

Surfacezone(mm)

BS8007

CIRIA C660

EN1992-1-1

Figure 8 : Surface Zones used in Estimating the Minimum Area of Reinforcement in Sectionsthat are Dominated by External Restraint and Subject to Tension Through the Full Thickness

Table 7 Expressions for the Calculation of Crack Width

BS8007 EN1992-1-1

cr

f

f0.5w

b

ct=cr

+

effp,

1k

.k0.4253.4cw

No cover term cis the cover (mm)

fct/fb is the ratio of the tensile strength ofthe concrete to the bond strength = 0.67

k1 is a coefficient which takes account of the bondproperties of the reinforcement = 0.8 increased in C660 to1.14

is the bar diameter (mm)

is the steel ratio based on a surfacezone of 250mm ofh/2, whichever is less

e,effis the effective steel ratio based on a surface zone toa depth of2.5 (c + /2) orh/2, whichever is less

cr is the crack inducing strain

Hence, cr

0.335w = and, cr + effp,k 0.343.4cw

The expressions for calculating crack width for elements subject to continuous edge restraint aregiven in Table 7. It should be noted that in EN1992-1-1 the characteristic crack width, wk is


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estimated, this being a value with only a 5% chance of being exceeded. This value is expected to beabout 30% higher than the mean value (22, 23).

The second term in the EN1992-1-1 expression appears to be very similar to that of BS8007.However, the way in which e,eff is calculated leads to very different results being based on a surfacezone he,ef = 2.5(c + /2) or h/2 whichever is smaller, compared with a BS8007 value ofh/2 or 250mm.For a 500mm thick wall, ifc= 40mm and = 20mm he,ef = 2.5(40 +20/2) = 125mm, only half the value

of 250mm used by BS8007. As the value ofp,eff is inversely proportional to he,ef this will result inp,effbeing double the value used by BS8007, thus halving the value of the second term in the crack widthexpression. This difference is partially offset by a cover term but the net effect is for crack widths,estimated using EN1992-1-1, to be significantly lower than crack widths estimated using BS8007.With no other changes this would lead to a significant reduction in crack control reinforcementcompared with that currently used as shown in Figure 9 (a).

30 mm

40 mm

50 mm

60 mm

70 mm

0

20

40

60

80

100

120

140

160

180

200

300 400 500 600 700 800 900 1000

Thickness (mm)

Percentsteelrela

tivetoBS8007

30 mm

40 mm

50 mm

60 mm

70 mm

0

20

40

60

80

100

120

140

160

180

200

300 400 500 600 700 800 900 1000

Thickness (mm)

PercentsteelrelativetoBS8007

(a) k1 = 0.8 (EN1992-1-1) (b) k1 = 1.14 (CIRA C660)

Figure 9 The Ratio of Reinforcement Requirements for Design to EN1992 and BS8007 (C30/37Concrete; Plywood Formwork; Limiting Early-age Crack Width to 0.15 Mm; Cover as Shown)

Bamforth suggest that the requirements of BS8007, while having been generally applicable, haveoccasionally led to crack widths in excess of those predicted and on this basis it would be unsafe toadopt a design that significantly reduces the current reinforcement requirements. The factors used inthe design were therefore investigated and the bond coefficient k1 has been increased from 0.8 to1.14 by applying the EN1992-1-1 factor of 0.7 applied when good bond cannot be guaranteed(0.8/0.7 = 1.14). The calculations shown in Figure 9 (a) have been repeated with the revisedcoefficient and the results are shown in Figure 9 (b). With the revised coefficient the steelrequirements are closer to those of BS8007 with the normal range of cover. Higher steel ratios thanthose suggested by BS8007 are generally associated with high cover.

The net effect of cover alone on the crack width is shown in Figure 10. This has been recognised formany years. For example, Campbell-Allen & Hughes (2) recommended that the placing of suchreinforcement shall be as near to the surface of the concrete as is consistent with the requirements ofadequate cover. However, in relation to control of EATC, the effect of cover has previously not beenquantified. Acknowledging that the crack will taper from the surface to the reinforcement it may beappropriate, when using high cover for durability, to design for a crack width at a cover of, say, 50mm,and to accept that the crack width at the surface will be wider. This approach is recommended byBamforth, although not included in C660, as it is justified by considerable evidence which indicatesthat protection of steel is related more to the quality and depth of the cover than to the crack width(24). As an example this approach might lead to acceptance of 0.2mm cracks at 65mm cover asopposed to 0.15mm cracks at 50mm cover.


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0.00

0.05

0.10

0.15

0.20

0.25

30 40 50 60 70

Cover (mm)

Cra

ckwidth(mm)

0

500

1000

1500

2000

30 40 50 60 70

Cover (mm)

Areaofr

einforcement(mm

2)

(a) Effect of cover on crack width (b) Area of reinforcement (mm2/m/face) requiredto achieve a crack width of 0.15mm

Figure 10 The Effect of Cover in a 300mm Wall Subject to a 30oc Temperature Drop and 70%Restraint

3. End Restraint

The method of BS8007 (and AS 3600 and AS3735) EATC assumes continuous edge restraint.EN1992-3 also recognises end restraint and C660 provides a design approach for both conditions.End restraint occurs when an element is fixed between two points such that the restraining elementsdo not assist in distributing cracking. End restraint leads to substantially more reinforcement to controlcracking because the restraint itself plays no part in preventing the cracks from widening (as it doesunder conditions of edge restraint). The crack width wk is determined by the tensile strength of theconcrete fct; the stress transferred to the steel determined by the steel ratio, the modular ratio e; theelastic modulus of the steel Es; and the length over which debonding occurs Sr,max (forkand kc seeTable 7). Hence,

r.max

es

effctcek S

11

E

..k.f.k0.5 w

+ (1)Even when the minimum steel ratio is exceeded, crack widths may be significantly wider thanachieved under conditions of edge restraint, although fewer cracks may occur (Table 8).

Table 8 Estimated Crack Widths (300mm Section, End Restraint, 16mm Bars at 150mm)

Cylinder Strength fc (MPa) 20 25 37 45 50 55 60

Crack width (mm) 0.42 0.48 0.54 0.60 0.66 0.71 0.76

It is important, therefore, to recognise the nature of the restraint when designing reinforcement tocontrol cracking.End restraint typically occurs in the following situations;

Suspended slabs cast between rigid core walls or columns

Ground slabs cast on piles

The top of infill walls with a low length/height ratio such that the edge restraint from thebase is not effective at the top

Large area ground slabs cast onto membranes which are either restrained locally, e.g.by columns, or by a build up of friction when the area is very large.

C660 give a basic mechanism to calculate restraint in end restraint situations but does not givedetailed analysis of typical situations. As end restraint can give rise to very high reinforcingrequirements the method of assessing the restraint requires some attention. Three typical situationsare shown in Figure 11, 12 and 13.


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Figure 11 : Restraint of Slab Restrained by Walls

Figure 12 : Restraint of Slab With Openings Restrained by Walls

Figure 13 : Restraint of Infill Walls

Implications for AS 3735

AS 3735-2001 (3) provides values for minimum steel ratiopmin for the control of crack widths (Table1). For restrained concrete Clause 3.2.2 (b) gives values that are related to the bar diameter (Table9) and according to the Supplement to AS 3735 Supp 1 2001 (25) the values have been derived fora mean crack width of 0.15mm

Table 9 Minimum Percentage Reinforcement for Fully Restrained Concrete (Table 3.1 AS 3735)

Bar diameter (mm) 8-12 16 20 24 28 32

pmin(%) 0.48 0.64 0.80 0.96 1.12 1.28

Working backwards using the approach of BS8007 upon which AS 3735 was based, a maximumallowable temperature drop, T1 may be calculated. To do this it has been assumed that the coefficientof thermal expansion = 12 microstrain/oC; restraint (including the creep coefficient) = 0.5; and tensilestrain capacity = 75 microstrain. This leads to an estimated value of T1 = 36

oC above which the meancrack width is likely to exceed 0.15mm. This value may be compared with estimated T1 values. The


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results are shown in Table 10 for walls from 300mm to 500mm thick with cement contents rangingfrom 300 to 450 kg/m3 and for placing temperatures of 20oC and 30oC.

It is apparent that there are some conditions for which AS3735 may provide insufficient reinforcement,particularly when concreting in the summer months when placing temperatures may be 30 oC or more.AS 3735 acknowledges the difficulty in evaluating precisely the amount of reinforcement required dueto the numerous and highly variable factors which influence cracking and notes that in extremely hotclimates or for concretes with high cement contents, the recommended minimum steel requirements

may be higher than shown in Table 9.

A similar analysis to EN1992 is more difficult as the crack width is also dependent on the cover.Estimates of the maximum T1 values required to ensure a mean surface crack width of 0.15mm aregiven in Table 11 for three wall thicknesses, each using a different bar diameter. It can be seen thatto maintain a surface crack width of 0.15mm, lowerT1 values are acceptable when there is highcover; or conversely, as shown in Figure 6, the area of reinforcement must be increased.

Table 10 Estimated Values ofT1 (OC) using the CIRIA C660 Model for UK Portland Cement

Cement(kg/m3)

Placing temp = 20oC Placing temp = 30oC

h = 300mm h = 400mm h = 500mm H = 300mm h = 400mm h = 500mm

300 25 28 31 30 34 37350 28 32 36 35 39 42

400 32 37 40 39 44 48 450 36 41 45 44 50 54

Table 11 : Estimated Maximum Temperature Drop T1 to Achieve a Crack Width 0.15mm

Cover(mm)

h = 300 mm h = 400mm h = 500mm

= 16 mm = 20mm = 24mm

30 43 51 5840 35 42 4850 30 36 4160 29 31 3670 28 28 32

Also to be taken into account is the fact that concrete strengths are now commonly higher thanassumed in BS8007 which was developed specifically for concrete with a characteristic cylinderstrength of about 30MPa and with an assumed early-age tensile strength of 1.6 MPa. When appliedto much higher strength concretes the tensile stress transferred to the steel is proportionally higherand hence more steel is required to maintain the steel stress at an acceptable level.

Implications For AS 4997Table 6.6 of AS4997-2005 provides provisions for maximum steel stress in order to control crackwidths as shown in Table 1. The relationship between the steel stress and the crack width may bederived by considering the strain distribution in the steel after cracking as shown in Figure 14.

At the crack it is assumed that the bond between steel and concrete is lost and the strain (and hence

stress) in the steel is at its maximum smaxa. At the crack the strain in the concrete reduces to zero. Asbond is re-established along the bar, the strain in the steel reduces to a level no greater than thestrain capacity of the concrete ctu at some distance from the crack. [If the strain exceeds ctu thenanother crack will form].

Hence the mean strain in the steel sm, i.e. the value that will determine the crack width, may beestimated from the expression;

sm= 0.5 (smaxa + ctu) (2)

The maximum allowable strain in the steel smaxmay be estimated from ft/ Es, where Es is the modulusof elasticity of the reinforcement = 200,000 MPa. Estimated values are given in Table 10. Hence, inunits of microstrain (1 x 10-6 strain)

sm= 0.5 (106ft/ Es + ctu) (3)


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Figure 14 : Strain distribution in the steel and the concrete after cracking

The tensile strain capacity of the concrete is a function of the mix design and will increase with thestrength. For simplicity it will be assumed that ctu= 100 microstrain.

Hence sm= 0.5 (106ft/ Es + 100) (4)

Again, estimated values are given in Table 12. The crack width is estimated using the expression,

Wk = Sr,max(sm - cm) (5)

where Sr,maxis the characteristic crack spacing. As shown in Figure 14, the mean strain in the concretein the crack affected zone, cm = 0.5 ctu

Substituting in equ.4 forsm (equ.1) and cm

Wk = Sr,max [0.5 (smaxa + ctu) 0.5 ctu] = 0.5 Sr,maxsmaxa (6)

AS4997 does not give assumed values for crack spacing but values may be derived from AS3735 forwater retaining structures. Table C3.1 of the supplement to AS3735 provides values of maximumsteel stress to achieve a mean crack width of 0.1mm. This would be consistent with a characteristiccrack width of about 0.17mm (a factor of 1.7 is used in EN1992-3 for water retraining structures) andthis value has been used in the derivation of the characteristic crack spacing in Table 13.

Table 12 Estimated characteristic crack width based on the maximum allowable steel stress

Bar diameter, db (mm) 12 16 20 24

Maximum stress in steel, ft(MPa) 185 175 160 150

Maximum strain in steel, smaxa (microstrain) 925 875 800 725

Mean strain in steel, sm (microstrain) 512.5 487.5 450 425

Characteristic crack spacing derived fromAS3735-2001 (see Table 2)

452 487 523 566

Estimated characteristic crack width (mm) basedon crack spacing derived from AS3735-2001

0.210 0.213 0.209 0.213

Estimated mean crack width (mm)(=charactristic/1.7)

0.123 0.125 0.123 0.125

Steel ratio required to achieve crack spacing fora mean crack width of 0.12 mm

0.89 1.10 1.28 1.42

Estimated characteristic crack width (mm) basedon minimum steel ratio AS3735-2001 and maximumsteel stress of AS4997-2005

0.228 0.216 0.197 0.185

Estimated mean crack width (mm) based on

minimum steel ratio AS3735-2001 and maximumsteel stress of AS4997-2005

0.388 0.367 0.335 0.314


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It is of interest to note that the estimated crack spacing for each of the combinations of maximumsteel stress and minimum reinforcement in AS3735 lead to the same value for crack spacing. Thissuggests that an underlying assumption behind the values in AS3735 is that the crack spacing isconstant. However, this assumption is inconsistent with the theory. If the steel stress is higher thenfor a given crack spacing the crack width must also be higher, as increased strain occurs over thesame length of reinforcement.

Values of minimum reinforcement ratio and the associated crack spacing required to achieve a mean

crack width of 0.1mm have been estimated and these are also given in Table 13. It can be seen thatthe required steel ratios are in the order of 0.4 - 0.5% greater than those specified by AS3735 and it isthese values that have been used to assess the crack width associated with the maximum steelstresses in AS4997.

Table 13 : The requirements of AS3735 to achieve a characteristic crack width of 0.17mm(equivalent to a mean crack width of 0.1mm)

Bar diameter, db(mm) 8 - 12 16 20 24 28-32

Maximum stress in steel, ft (MPa) 150 140 130 120 110

Maximum strain in steel, smaxa (microstrain) 725 700 650 600 550

Mean strain in steel, sm (microstrain) 425 400 375 350 325

MInimum steel ratio (%) 0.48 0.64 0.80 0.96 1.12

Crack spacing (mm) based on minimum steelrequirement

838 838 838 838 838

Estimated crack width (mm) based on crackmaximum steel stress and estimated crack spacingof 838mm

0.31 0.29 0.27 0.25 0.23

Estimated crack spacing (mm) required for meancrack width of 0.1mm according to AS3735-2001(characteristic crack width = 0.17mm) at maximum

steel stress

452 487 523 566 617

Steel ratio required to achieve crack spacing fora mean crack width of 0.1mm

0.89 1.10 1.28 1.42 1.52

Based on the above analysis it may be inferred that the maximum allowable stresses in thereinforcement provided by AS4997-2005 may limit the mean crack width to about 0.22mm with acharacteristic value of about 0.38mm provided that the steel ratio is sufficiently high to control thecrack spacing (as indicated in Table 10).

The crack width is a function of both the strain in the steel (and hence the stress) and the crackspacing. The steel stress alone is therefore insufficient to limit crack widths the minimum steel ratiomust also be specified. This is why a larger number of smaller bars is more efficient than fewer larger

bars. For a given steel ratio, while the stress in the steel will be the same, the crack spacing will bereduced with the smaller bars, thus reducing the length over which the strain in the steel occurs andreducing the crack width accordingly.

If the minimum reinforcement required by AS3735 is used with the maximum steel stress of AS4997then the mean crack widths will be in the order of 0.2mm with a characteristic value of around0.35mm.

SummaryPlastic cracking is influenced by the design and as there are methods of assessing the risk of plasticcracks it may be appropriate to include design methods and criteria in Australian Codes.

The introduction of Euro-codes EN1992-1-1 for general design and EN1992-3 for water retainingstructures has resulted in some changes in the design process for reinforced concrete in Europe.These changes have implications for the control of early age thermal cracking, previously provided byBS8007. To reflect these, and other changes which have occurred since the publication of CIRIA 91(revised edition, 1992) CIRIA has published report C660 Early-age thermal crack control in concrete.


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Australian Standards used the approach of BS8007 with modifications to suit Australian conditions butin some circumstances crack widths have been larger than permitted. It may therefore be appropriateto reconsider the recommendation of Australian Standards.

References

1. British Standards Institution, BS 8007:1987, Design of Concrete Structures for RetainingAqueous Liquids.

2. Campbell-Allen, D and Hughes, G W, Reinforcement to Control Thermal and ShrinkageCracking. Transaction of the Institution of Engineers, Australia, Civil Engineering, August1981, Vol. CE23. No. 3.

3. Australian Standards, AS3735-2001, Concrete Structures Retaining Liquids

4. Harrison, T A, Early-age Thermal Crack Control in Concrete CIRIA Report 91, 1992

5. Bamforth, P B, Early-age Thermal Crack Control in Concrete CIRIA C660, 2007

6. EN1992-1-1:2004, Eurocode 2. Design of Concrete Structures. General Rules and Rules forBuildings.

7. British Standards Institution, BS8110-2: 1985 Structural Use of Concrete.

8. EN1992-3:2006 Eurocode 2: Design of Concrete Structures Part 3: Liquid Retaining andContainment Structures

9. Hughes, B (1971) Control of Early Age Thermal and Shrinkage Cracking in RestrainedReinforced Concrete Walls CIRIA Technical Note 21, 1971

10. Dhir, R, Paine, K A and Zheng, L Design Data for Use where Low Heat Cements are UsedDTI Research Contract No. 39//680, CC2257, University of Dundee, Report No CTU2704,November 2006

11. Anson, M and Rowlinson, P M Early-age Strain and Temperature Measurements in ConcreteTank Walls Magazine of Concrete Research, Vol. 40, No. 145, December 1988

12. Concrete Society In Situ Strength of Concrete An Investigation into the Relationship

between Core Strength and the Standard Cube Strength Report of a Working Party of theConcrete Society, Project Report No. 3, 2004

13. Fan, S C Aw, K M and Tan, Y M Peak Temperature-rise for Early-age Concrete underTropical Climatic Conditions Journal of the Institution of Engineers, Singapore, Vol.44, Issue1, 2004

14. Pigeon, M Bissonnette, B Marchand, J Boliy, D and Barcelo, L Stress Relaxation of Concreteunder Autogenous Early-Age Restrained Shrinkage American Concrete Institute, SpecialPublication, SP-227-16, 2005, ACI Detroit Michigan

15. Altoubat, S A and Lange D A Creep, Shrinkage and Cracking of Restrained Concrete atEarly Age ACI Materials Journal, July/August 2001 Vol. 98, No.4. 323-331

16. Bamforth, P B Early Age Thermal Cracking in Concrete Institute of Concrete Technology,Technical Note TN/2, 1982, Camberley, Surrey

17. Vitharana, V and Sakai, K Early Age Behaviour of Concrete Sections under Strain InducedLoadings Proceedings of 2nd International Conference on Concrete under severeconditions CONSEC 95, Sapporro, Japan, 2-4 August 1995, Ed K Satai, N Banthai and O E,Gjorv, E&F Spon, 1571-1581

18.ACI Committee 207 Effect of Restraint, Volume Change and Reinforcement on Cracking of

Mass Concrete ACI Manual of Concrete Practice, Part 1, 207.2R-73 (reapproved 1986),

Detroit, Michigan.

19. Tasdemir, M A Lydon, F D and Barr B I G The Tensile Strain Capacity of ConcreteMagazine of Concrete Research, 1996, 48, No. 176, Sept., 211-218

20. Beeby, W and Forth, J P Control of Cracking in Walls Restrained Along Their Base AgainstEarly Thermal Movements University of Dundee, International Congress on Global


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Construction, Ultimate Concrete Opportunities, 5-7 July, 2005, Thomas Telford pp123-132,ISBN: 0727733877

21. Anchor, R D, Hill, A W and Hughes, B P, Handbook on BS 5337:1976 (The structural use ofconcrete for retaining aqueous liquids) Viewpoint. Publications, Cement & ConcreteAssociation, Slough. 1979

22. Narayanan, R S and Beeby A W, Designers Guide to EN 1992-1-1 and EN 1992-1-2

Eurocode 2: Design of Concrete Structures. General rules and rules for buildings andstructural fire design Thomas Telford.

23. Beeby, A W Fixings in cracked concrete The Probability of Coincident Occurrence andLikely Crack Width CIRIA Technical Note 136, 1990

24. Bamforth, P B, Price, W F and Emerson, M An International Review of Chloride Ingress intoStructural Concrete Contractor Report 359, TRL Scotland, 1997

25. Australian Standards, AS3735 Supp 1 -2001, Concrete Structures Retaining Liquids commentary (Supplement to AS3735-2001)

2009 06 cia achieving durability in design crack control (5)

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