2009 06 CIA Achieving Durability in Design Crack Control

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 changes in concrete while it is hardening, early age due to changes while concrete cures in the hardened state and long term load induced cracks. Designers generally follow Australian Code requirements for maximum 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 a high heat output is used, code requirements alone may be insufficient to control crack widths adequately. 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 impact on the requirements for plastic crack control. This paper considers requirements for all three stages from a design perspective to highlight where additional guidance might be given in Australian codes.

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

Plastic shrinkage cracks occur when the rate of evaporation (e, lt/m2/hr) exceeds the rate of bleed water arriving at the concrete surface (b, lt/m2/hr). There are many documents that suggest that if e < 1 lt/m2/hr plastic cracking will be a low risk and evaporation retardation is not requiredThis may have been a reasonable approximation for typical concretes when it was first developed but concrete bleed in modern concretes can be very low and the evaporation rate at which plastic cracking could occur may now be lower than 0.2 lt/m2/hr for some concretes.

Plastic settlement cracks occur when the solids settle so much that the surface level of the concrete drops (s, mm) and where it gets hung up by the reinforcement or bridges between formwork in walls cracks form. Settlement cracks may also occur when there is a change in section thickness and differential settlement occurs. As solids settle water rises and hence plastic settlement occurs when the bleed is higher than acceptable. There is no absolute upper bleed limit for all concrete as the pour thickness and concrete rise rate are also strongly influential.

Bleed can be measured in accordance with AS1012 Pt 6 but this is seldom undertaken as it is hard work for the premix supplier and most specifies do not know how to interpret the result. Bleed test results are the single biggest tool in determining the risk of plastic settlement and plastic shrinkage cracking. The principle factors affecting bleed rate (b, lt/m2/hr) and settlement (s, mm) are:

B (%) = Bleed (% free water) measured in AS 1012 Part 6 bleed testW (lts/m3) = the free water in the concreteH (m) = the thickness of pourT (hrs) = the length of the bleed period as obtained from the bleed test. P (m/hr) = rise rate of concrete

For any concrete pour there are three possibilities:

i) For pours where the concrete is placed to full thickness on one placements = BWH and b = BWH/T

ii) For pours where H/P<T (concrete all placed before bleed of first concrete placed ceases)s=BWH – {0.5[(H/P)/T] and b=(BWH – {0.5[(H/P)/T]BWH})/T

iii) For pours where H/P>T (concrete being placed after bleed of first concrete placed ceases)

s= 0.5BWPT b = BWP

The bleed rate needs to exceed the evaporation rate (i.e. b<e) or evaporation retarders are needed. Evaporation rates can be calculated from the ambient temperature, wind speed, relative humidity and concrete temperature. The ultimate settlement should be less than 2mm (i.e. s<2mm) or the concrete rise rate needs to be reduced. A more precise calculation of allowable settlement can be estimated

based on cover, concrete properties and bar size and spacing. The importance of controlling bleed and placing rate can be seen by considering the two cases shown in Figure 1. In case b) the concrete is highly susceptible to plastic cracking while in case a) the concrete is likely to have plastic settlement issues. By adjusting the concrete mix and placing rate suitable settlements can be obtained for most elements.

Figure 1 : Bleed Rate (b) Compared to Evaporation Rate (e) for Two Applications

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Excessive plastic settlement does not always exhibit itself as cracking over bars. The concrete may hang up over bars without cracking while settlement channels form under the bars. Several cases have been reported where corrosion has commenced at the underside of bars as seawater flushed through these ‘irrigation channels’. This also affects the bond and hence the efficiency of the steel in controlling crack spacing and width.

It would be possible to include this assessment method in a code and require that the construction procedures and mix be designed such that b<e and s<2mm. Whether in a code or not designers could include a specification requirement for contractors to demonstrate that b<e and s<2mm based on measured concrete bleed, the mix design and proposed placing method. The limits on rise rate would then become part of the Inspection & Test Plans (ITP’s)

Autogenous shrinkage occurs throughout the hydration period but can be very high as early as 8 hrs. Cracking can occur at a very early age (4hrs) and be very similar in appearance to plastic shrinkage cracking. Like plastic cracking it tends to occur in high performance concrete (low w/c concrete with slag or silica fume) and may only be detected because extreme measures to protect against plastic cracking does not prevent them. As autogenous shrinkage cracking occurs with no net loss of water it can only be prevented by having an appropriate mix. Designers and concrete suppliers need to be sure they do not specify or supply concrete where autogenous cracking is inevitable.

3. Long Term Crack ControlAS 3600, AS 3735 and AS 4997 all provide the allowable maximum steel stress to control tensile and flexural cracking. The requirements are summarised in Table 1 to show applicable values for each exposure. AS 3600 gives no specific crack widths that the steel strains match but notes that specific design to control crack widths to specific limits can follow the procedures in BS 8110 Pt 2. AS 3735 provides for cracking at 3 days for full restraint and to control tensile crack widths (i.e. due to early age strains) to an average of 0.1mm but also notes “For thick sections or extremely hot climates, with a high cement content, higher values may be required..”. AS 4997 notes that the stresses will limit crack width to values suitable for marine exposures.

There is one school of thought that it is better to limit steel stresses and not specify maximum crack widths as the latter opens the potential for disputes. There is some logic to this, designing for 0.15mm crack widths to the 95% confidence limit in accordance with CIRIA C660 (equivalent to 0.1mm mean width in AS 3735) some cracks will be 0.2mm wide. Not only is responsibility for the crack width not clear cut but reliable crack width measurement is also difficult as crack widths vary with ambient temperature. AS 3735 commentary reports the crack width that the code calculations are based on and it may be appropriate to at least include the crack width guide in all code commentary’s.

The two key reasons for providing a method of checking the design for crack widths are that:i) It is the crack width that is critical for durability there should be a method of checking that

early age strains are adequately catered forii) Design for one steel stress will sometimes be highly conservative and at other times may be

inadequateiii) In the event of excessive cracking occurring the design method will provide a basis of

resolving the cause of crackingiv) End restraint can lead to very high steel requirements

Hence, it would seem appropriate to design flexural cracks for the steel stress in the codes and to then check that the reinforcement will adequately control crack widths for early age strains.

Table 1 : Australian Standard Allowable Steel Stress fs (MPa) for Different Applications

Bar diameter db(mm) 10 12 16 20 24 28 32 36 40

C1 and C2 exposuresAS 4997 Table 6.6

185 175 160 150

Non- Water Retaining A1, A2, B1 or B2 Exposures AS 3600 Table 8.6.1 A and B

360 330 280 240 210 185 160 140 120

Water Retaining A1, A2, B1 or B2 ExposuresAS 3735 Table 3.2Note Y1, Y2 and Y3 = 1.

150 140 130 120 110 -

The latest guide for early age crack control is CIRIA C660 and this is discussed at length in this paper. However, CIRIA C660 is not the end of the story for development of methods for early age crack width control. The Institute of Engineers in the UK is currently funding research that questions some of the fundamental assumptions underlying design to BS8007 (and also its replacement, EN1992-3). In particular the study is investigating the role of edge restraint in the distribution of cracking. It is currently assumed that higher restraint leads to wider cracks. This assumption may not be correct. While higher restraint certainly increases the risk of cracking and the integrated crack width, the restraint may also act in the same way as reinforcement, with higher restraint distributing the cracks to achieve a larger number of finer cracks. The study also considers alternative design procedures that cater for the possibility of cracks originating at the centre of a pour rather that at the surface where the reinforcement is located. It is also considering how to design for situations where early age strains may be additive to load induced strains. In general the current design practice is to assume early age thermal strains will have been largely relieved by creep at the time of loading and are in any event in a different direction to the main load induced strains.

4. Allowable Crack WidthsWhere designers feel that they should at least check for early age crack widths in high restraint, high ambient temperatures and/or high cement content concretes then some form of crack width limit is required. These might be the same crack widths that the code steel strains were based on.

CIRIA C660 provides guidance on allowable crack widths and these are shown in Table 2 together with some additional requirements recommended by BCRC.

Table 2 : Maximum Crack Widths To CIRIA C660

Limit State Max Crack Width (mm)

Comments

a) Appearance0.50.30.1

Distant in buildings, All civil.Moderately close in buildings.Important architectural

b) Rebar Durability

0.50.30.20.1

Exposure class A.All other exposure classes.Cracks flushed*. Non aggressive.Cracks flushed*. Aggressive.

c) Water Retaining0.20

0.05-0.200.05

Water pressure/wall thickness <5Linear increase from pressure gradient 5-35Water pressure/wall thickness >35

*BCRC recommendations for cracks intermittently wet so that oxygen available

The water retaining requirements are based on research that shows autogenous crack healing capacity at different pressure gradients. However, it is known that concrete that includes SCM’s has a slower capacity for autogenous healing. When dealing with marine structures research has shown that 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 be necessary to define finer crack widths when SCM’s are used.

The New Zealand Standard DZ 3106 provides definitions (Table 3 columns 1 and 2) for different levels of water tightness. This may provide a system for more economical or conservative designs for different situations. Provisions for achieving leakage requirements are given in DZ 3106 but alternative provision for achieving the requirements that may appropriately allow for Australian Codes and use of SCM’s are given in Table 3 column 3.

Table 3 : DZ3106 Tightness ClassTightness

ClassLeakage Requirements Possible Interpretation of Provisions for

Achieving Leakage Requirements

0 Leakage acceptable or leakage of liquids irrelevant

Crack control provisions of AS 3600 may be adopted

1 Leakage to be limited to small amount. Some surface staining or damp patches acceptable

Crack widths to be controlled so that they are highly likely to be healed by autogenous healing ultimately. Limits given in Table 2 c) to apply.

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

Crack widths to be controlled so that they are highly likely to be healed by autogenous healing within 1 week. Limits given in Table 2 c) to be reduced by 30% for GP cements and 50% for SCM’s

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

5. Early Age StrainsEarly age thermal cracking (EATC) is the result of restraint to contraction as concrete cools from its peak hydration temperature. In many normal situations EATC may be difficult to avoid and even though 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 in many cases it may be either unnecessary or uneconomical to avoid cracking entirely. Measures to minimise or avoid EATC are available through the selection of concreting materials; reducing the mix temperature; 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 of these 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 to suit 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 data for use in the design process. CIRIA 91 has been updated and replaced by CIRIA C660 (5) to take account of new knowledge of the performance of a range of concreting materials; the increasing use of 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 the UK in 2009; and EN1992-3 (8) which will replace BS8007 for water retaining structures in 2011. In addition to bringing the design into line with Euro-codes, CIRIA C660 differs from CIRIA 91 in the following respects.

Values of temperature drop (T1) for Portland cement (GP cement) have been revised and additional 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 reduced cement content.

Information is provided on autogenous shrinkage Additional information is given on different forms of restraint, how they may be calculated and

how they affect crack width Tensile strain capacity is dealt with more comprehensively

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

Guidance is given on methods for minimising the risk of cracking Advice is provided on specification, testing and in situ monitoring.

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 minimum cement content); design of reinforcement; location of movement and (some) construction joints.

Constructor: procuring concrete to meet specification and buildability requirements; planning the construction 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 achieved concrete properties and thermal histories may help with dispute resolution. And secondly, as design assumptions are generally conservative, advantage may be obtained when project specific data are available. 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 the restrained contraction, εr that may lead to cracking, is related to the drop from the peak temperature in the section to the mean ambient temperature T1, the coefficient of thermal expansion of concrete c

the restraint R, and a creep coefficient K according to the equation εr = c. T1. K. R

C660 provides data in chart form for various combinations of GP cement with fly ash or ggbs as shown in Figure 2. Semi-adiabatic test results (10) provided the input to a thermal model used to predict T1. A comparison of predicted and measured results (11, 12, 13) validated the model for a range of concrete mix types and temperatures. Although C660’s methods for calculating thermal strains can be used for Australian conditions the heat generating capacity of the concrete may not be applicable. 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 C660’s calculator to assess insitu temperature rise until Australian research can provide similar graphs to those in CIRIA C660.

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Figure 2 Design Values for T1 For 20% FlyAsh 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 have formed part of drying shrinkage. However long term autogenous shrinkage has now measured separately 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

to some degree in all structural concretes and this is supported by research data (Appendix 4 of C660). EN1992-1 takes no account of the cement type but there is evidence that mineral additions affect 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 not be used for Australian materials as values that may better reflect Australian Materials and exposures are included in the proposed AS 3600 revision. A comparison of E1992-1-1 and AS 3600 values are given in Figure 3.

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

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C660 provides drying shrinkage estimates for elements but these are also different to Australian drying shrinkage calculations and values from the new draft of AS 3600 should be used. The shrinkage of concern is the shrinkage of an element relative to the element that is restraining it. Figure 4 shows calculations for a wall cast on a slab 20 days after the slab was cast. The slab dries from one face so drying is slower but eventually the differential shrinkage tends to zero.

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

Shrinkage Values)

Figure 5 : Comparison of AS 3600 and C660 Shrinkage values for Wall and Floor Elements

Using Same Mix & Curing

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6. Internal RestraintSpecifications often state “The temperature differential between the centre of a pour and the surface shall not exceed 20C”. This was popular in the UK 30 years ago. It was intended to ensure no internal restraint cracking and was applicable to gravel aggregates. At the point of cracking the strain capacity is equal to the restrained strain i.e.:

ɛctu = ac . T . K1 . R - whereɛctu = Strain Capacityac = Coefficient of thermal expansionT = Temperature differential K1 = Creep = 0.65R = Restraint = 0.42Hence

T = 3.7 . ɛctu / ac - Table 4 : Calculated Temperatures to Cause Cracking for Internal & Edge Restraint

Aggregate Coefficient Tensile Temperature (°C) to Avoid EATC

Type Thermal Expansion

(µɛ/°C)

Strain Capacity

(µɛ)

Max Temp. Differential

Internal Restrain R=0.42

Maximum Temperature Drop External Restraint Factor

Edge Restraint 1.0 0.7 0.5 0.3

Gravel 13 65 20 6 9 14 24Granite 10 75 28 9 14 21 36Limestone 9 85 35 12 18 27 46Using equation 2 the temperature to cause cracking due to internal restraint has been calculated and is shown in Table 4. Clearly a restriction on temperature differential to 20°C would often be conservative. It is even more conservative/expensive if there is no real reason to prevent cracking altogether rather than allow limited crack widths.

The tensile strain capacity εctu is the maximum strain that the concrete can withstand without a continuous crack forming. A comprehensive review of data (19) demonstrated a linear relationship between εctu under rapid loading and the ratio of the tensile strength fctm to the elastic modulus Ecm in compression. Using property data and age functions provided in EN1992-1-1, values for εctu have been 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 for C30/37, f’c = 30 MPa) estimated on this basis are given in Table 5. To estimate the strain capacity for other strength classes, the value obtained for C30/37 is multiplied by 0.63 + (1.25f’c/100) for f’c in the range from 20 to 50 MPa. For higher strength concrete the value obtained for 50 MPa is used.

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

Aggregatetype

Basalt Flint gravel

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

7. Edge RestraintEdge restraint occurs when one element is cast against another element such that the restraining element 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 and creep. This simple approach must be assumed to deal with the worst case, but prevents benefit being 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. The fact that the worst case is not R = 1 is is not surprising as a new element does have some inherent stiffness when cooling commences and, in general, will not be totally dominated by the element against 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 range from 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 with distance from the base. This reduction is calculated based on the length : height ratio of the wall as shown in Figure 6.

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 end

restraint (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 ensuring that the stress transferred to the steel after a crack has occurred is below the yield strength of the steel. 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

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 concretefy is the yield strength of the steel fyk is the yield strength of the steel

k allows for non-uniform and self-equilibrating stress which leads to a reduction in restraint forces.kc takes 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 to understand the bases for the assumed surface zones. In doing so it was identified that the assumption that cracking is initiated from the surface may not be correct (21, 22). Under conditions of external restraint it is most likely that cracking will be initiated at the point where the temperature drop is the greatest, i.e. at the centre of the section (Figure 7) transferring stress from the full section to the reinforcement when a crack occurs.

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t0t1

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

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

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Figure 8 : Surface Zones used in Estimating the Minimum Area of Reinforcement in Sections that 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

No cover term c is the cover (mm)

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

k1 is a coefficient which takes account of the bond properties of the reinforcement = 0.8 increased in C660 to 1.14

φ is the bar diameter (mm)

ρ is the steel ratio based on a surface zone of 250mm of h/2, whichever is less

ρe,eff is the effective steel ratio based on a surface zone to a depth of 2.5 (c + φ/2) or h/2, whichever is less

εcr is the crack inducing strain

Hence, and,

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

estimated, this being a value with only a 5% chance of being exceeded. This value is expected to be about 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 ρe,eff is calculated leads to very different results being based on a surface zone he,ef = 2.5(c + φ/2) or h/2 whichever is smaller, compared with a BS8007 value of h/2 or 250mm. For a 500mm thick wall, if c = 40mm and φ = 20mm he,ef = 2.5(40 +20/2) = 125mm, only half the value of 250mm used by BS8007. As the value of ρp,eff is inversely proportional to he,ef this will result in ρp,eff

being double the value used by BS8007, thus halving the value of the second term in the crack width expression. 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 reinforcement compared with that currently used as shown in Figure 9 (a).

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Figure 9 The Ratio of Reinforcement Requirements for Design to EN1992 and BS8007 (C30/37 Concrete; 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, have occasionally led to crack widths in excess of those predicted and on this basis it would be unsafe to adopt a design that significantly reduces the current reinforcement requirements. The factors used in the design were therefore investigated and the bond coefficient k1 has been increased from 0.8 to 1.14 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 revised coefficient and the results are shown in Figure 9 (b). With the revised coefficient the steel requirements are closer to those of BS8007 with the normal range of cover. Higher steel ratios than those 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 for many years. For example, Campbell-Allen & Hughes (2) recommended that “the placing of such reinforcement shall be as near to the surface of the concrete as is consistent with the requirements of adequate cover”. However, in relation to control of EATC, the effect of cover has previously not been quantified. Acknowledging that the crack will taper from the surface to the reinforcement it may be appropriate, 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 by Bamforth, although not included in C660, as it is justified by considerable evidence which indicates that 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 as opposed to 0.15mm cracks at 50mm cover.

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(a) Effect of cover on crack width (b) Area of reinforcement (mm2/m/face) required to 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

8. 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 elements do not assist in distributing cracking. End restraint leads to substantially more reinforcement to control cracking because the restraint itself plays no part in preventing the cracks from widening (as it does under conditions of edge restraint). The crack width wk is determined by the tensile strength of the concrete fct; the stress transferred to the steel determined by the steel ratio ρ, the modular ratio αe; the elastic modulus of the steel Es; and the length over which debonding occurs Sr,max (for k and kc see Table 7). Hence,

(1)

Even when the minimum steel ratio is exceeded, crack widths may be significantly wider than achieved 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 f’c (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 to control 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 the

base 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 give detailed analysis of typical situations. As end restraint can give rise to very high reinforcing requirements the method of assessing the restraint requires some attention. Three typical situations are shown in Figure 11, 12 and 13.

Figure 11 : Restraint of Slab Restrained by Walls

Figure 12 : Restraint of Slab With Openings Restrained by Walls

Figure 13 : Restraint of Infill Walls

9. Implications for AS 3735AS 3735-2001 (3) provides values for minimum steel ratio pmin for the control of crack widths (Table 1). For ‘restrained concrete’ Clause 3.2.2 (b) gives values that are related to the bar diameter (Table 9) and according to the Supplement to AS 3735 Supp 1 – 2001 (25) the values have been derived for a 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 maximum allowable temperature drop, T1 may be calculated. To do this it has been assumed that the coefficient of thermal expansion = 12 microstrain/oC; restraint (including the creep coefficient) = 0.5; and tensile strain capacity = 75 microstrain. This leads to an estimated value of T1 = 36oC above which the mean crack width is likely to exceed 0.15mm. This value may be compared with estimated T1 values. The

results are shown in Table 10 for walls from 300mm to 500mm thick with cement contents ranging from 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 30oC or more. AS 3735 acknowledges the difficulty in evaluating precisely the amount of reinforcement required due to the numerous and highly variable factors which influence cracking and notes that in extremely hot climates 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 are given in Table 11 for three wall thicknesses, each using a different bar diameter. It can be seen that to maintain a surface crack width of ≤ 0.15mm, lower T1 values are acceptable when there is high cover; or conversely, as shown in Figure 6, the area of reinforcement must be increased.

Table 10 Estimated Values of T1 (OC) using the CIRIA C660 Model for UK Portland Cement

Cement (kg/m3)

Placing temp = 20oC Placing temp = 30oCh = 300mm h = 400mm h = 500mm H = 300mm h = 400mm h = 500mm

300 25 28 31 30 34 37350 28 32 36 35 39 42400 32 37 40 39 44 48450 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 = 500mmΦ = 16 mm Φ = 20mm Φ = 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 than assumed in BS8007 which was developed specifically for concrete with a characteristic cylinder strength of about 30MPa and with an assumed early-age tensile strength of 1.6 MPa. When applied to much higher strength concretes the tensile stress transferred to the steel is proportionally higher and hence more steel is required to maintain the steel stress at an acceptable level.

10. Implications For AS 4997Table 6.6 of AS4997-2005 provides provisions for maximum steel stress in order to control crack widths as shown in Table 1. The relationship between the steel stress and the crack width may be derived 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 εsmaxa. At the crack the strain in the concrete reduces to zero. As bond is re-established along the bar, the strain in the steel reduces to a level no greater than the strain capacity of the concrete εctu at some distance from the crack. [If the strain exceeds εctu then another crack will form].

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

εsm = 0.5 (εsmaxa + εctu) (2)

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

εsm = 0.5 (106ft / Es + εctu) (3)

εsm

εc

εs

εcm≈ 0.5 εctu

ε = 0

εctu

εsmaxa

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 the strength. For simplicity it will be assumed that εctu = 100 microstrain.

Hence εsm = 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 (εsm - εcm) (5)

where Sr,max is the characteristic crack spacing. As shown in Figure 14, the mean strain in the concrete in the crack affected zone, εcm = 0.5 εctu

Substituting in equ.4 for εsm (equ.1) and εcm

Wk = Sr,max [0.5 (εsmaxa + εctu) – 0.5 εctu] = 0.5 Sr,max εsmaxa (6)

AS4997 does not give assumed values for crack spacing but values may be derived from AS3735 for water retaining structures. Table C3.1 of the supplement to AS3735 provides values of maximum steel stress to achieve a mean crack width of 0.1mm. This would be consistent with a characteristic crack width of about 0.17mm (a factor of 1.7 is used in EN1992-3 for water retraining structures) and this 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 stressBar diameter, db (mm) ≤ 12 16 20 ≥ 24

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

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

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

Characteristic crack spacing derived from AS3735-2001 (see Table 2)

452 487 523 566

Estimated characteristic crack width (mm) based on 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 for a mean crack width of 0.12 mm

0.89 1.10 1.28 1.42

Estimated characteristic crack width (mm) based on minimum steel ratio AS3735-2001 and maximum steel 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 maximum steel stress of AS4997-2005

0.388 0.367 0.335 0.314

It is of interest to note that the estimated crack spacing for each of the combinations of maximum steel stress and minimum reinforcement in AS3735 lead to the same value for crack spacing. This suggests that an underlying assumption behind the values in AS3735 is that the crack spacing is constant. However, this assumption is inconsistent with the theory. If the steel stress is higher then for a given crack spacing the crack width must also be higher, as increased strain occurs over the same 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 that the required steel ratios are in the order of 0.4 - 0.5% greater than those specified by AS3735 and it is these values that have been used to assess the crack width associated with the maximum steel stresses 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, εsmaxa (microstrain) 725 700 650 600 550

Mean strain in steel, εsm (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 steel requirement

838 838 838 838 838

Estimated crack width (mm) based on crack maximum steel stress and estimated crack spacing of 838mm

0.31 0.29 0.27 0.25 0.23

Estimated crack spacing (mm) required for mean crack 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 for a 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 the reinforcement provided by AS4997-2005 may limit the mean crack width to about 0.22mm with a characteristic value of about 0.38mm provided that the steel ratio is sufficiently high to control the crack 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 crack spacing. The steel stress alone is therefore insufficient to limit crack widths – the minimum steel ratio must 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 be reduced with the smaller bars, thus reducing the length over which the strain in the steel occurs and reducing the crack width accordingly.

If the minimum reinforcement required by AS3735 is used with the maximum steel stress of AS4997 then the mean crack widths will be in the order of 0.2mm with a characteristic value of around 0.35mm.

11. SummaryPlastic cracking is influenced by the design and as there are methods of assessing the risk of plastic cracks 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 retaining structures 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 by BS8007. 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”.

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

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