Cracks And Crack Control In Concrete Structures
Special ReportCracks and Crack Controlin Concrete StructuresFritz LeonhardtProfessor EmeritusDr.-Ing. Dr.-Ing. h.c. mull.Consulting EngineerStuttgart, FRGing in concrete structures. In this paper,causes of concrete cracking are discussed, including tensile strength ofconcrete, temperature, shrinkage andcreep effects. Recommended crackwidths are presented along with designmethods for sizing reinforcement tocontrol crack widths.he material presented in this paper isbased on more than 30 years of research, observations and experienceconcerning causes, control, and consequences of cracking in concrete structures. This extensive background washelpful in the preparation of this paperwhich deals with questions of concretecracking.The presence of cracking does notnecessarily indicate deficiency instrength or serviceability of concretestructures. While currently available design code provisions lead to reasonablecontrol of cracking, additional controlcan be achieved by understanding thebasic causes and mechanisms of crack-Tensile Strength of ConcreteNote: This paper is a revised and updated version ofan article originally published in the Proceedings ofthe International Association for Bridge and Structural Engineering (1ABSE), Zurich, Switzerland,1987, p. 109.The tensile strength of concrete is awidely scattering quantity. Cracking occurs when tensile stresses exceed thetensile strength of concrete. Therefore,to control concrete cracking, the tensilestrength of concrete is of primary im-T124CAUSES OF CRACKINGConcrete can crack due to a number ofcauses. Some of the most significantcauses are discussed in detail.
portance. Laboratory test data conducted by H. Busch were analyzedstatistically. As presented in Ref. 1, thisanalysis furnished the following relationships for the mean direct tensilestrength, f tm , related to the 28-daycompressive cylinder strength f,' of concrete:fcm fi'm 2.1(fc)z (psi)/30.34 (ff)2"'(N/mm2)The statistical analysis indicated thatthe coefficient in this equation can bemodified to 1.4 (0.22) and 2.7 (0.45) toobtain the 5 and the 95 percentiles, respectively, of the tensile strength, fI.The tensile strength of concrete isslightly higher in flexure. However, it isrecommended that values for direct tension be used in practice. Concretecracks when the tensile strain, t, exceeds 0.010 to 0.012 percent. Thislimiting tensile strain is essentially independent of concrete strength.The 5 percentile of the tensilestrength, f, should be used in design tolocate areas in the structure that arelikely to crack by comparing calculatedstresses with the expected concretestrength. The 95 percentile, f 5 , shouldbe used to obtain conservative values forrestraint forces that might occur beforethe concrete cracks. These restraintforces are used to calculate the amountof reinforcement needed for crack widthcontrol.Causes of Cracking DuringConcrete HardeningConcrete cracking can develop duringthe first days after placing and beforeany loads are applied to the structure.Stresses develop due to differentialtemperatures within the concrete.Cracking occurs when these stresses exceed the developing tensile strength, f;,of the concrete as indicated in Figs. 1and 2. Differential temperatures aremainly due to the heat of hydration ofPCI JOURNAUJuly-August 1988SynopsisSimple design rules are presentedto control cracking in concrete structures. Causes of cracking and its effect on serviceability and durability arediscussed. The paper is primarily applicable to large structures such asbridges. However, general conceptspresented are applicable to any concrete structure. Prestressing forcesare considered. A numerical exampleshowing application of the methodand use of simple design charts is included.cement during concrete hardening. Thiseffect is usually neglected except inmassive structures as indicated in Ref. 2.However, depending on cement contentand type of cement, the temperaturewithin concrete members with dimensions of 12 to 36 in. (30 to 91 cm) canincrease approximately 36 F to 108 F(20 C to 60 C) during the first 2 daysafter casting.If concrete members are allowed tocool quickly, tensile stresses may reachvalues higher than the developing tensile strength of the concrete. Even if thisprocess results only in microcracking,the effective tensile strength of thehardened concrete is reduced. However, very often wide cracks appeareven when reinforcement is provided.In addition, the reinforcement may notbe fully effective since bond strength isalso developing and is yet too low. It isnecessary to minimize such early cracksby keeping temperature differentialswithin the concrete as low as possible.This can be done by one or more of thefollowing measures:1. Choice of cement — A cement withlow initial heat of hydration should beselected. Table 1 shows that there is asignificant variation in heat develop125
b concretecompression G OT a T Ec GTtensionInternal stressesin equilibriumFig. 1. Temperature distribution due to heat of hydration andinternal stresses caused by outside cooling in a free standingconcrete block.ment among different types of cements.The cement content of concrete shouldbe kept as low as possible by goodgrading of the aggregates. Heat development can also be reduced by adding fly ash or using slag furnace cement.2. Curing — Evaporation of watermust be prevented by using curingcompounds or by covering the concretewith a membrane. Rapid evaporationcan lead to plastic shrinkage cracking.3. Curing by thermal insulation Rapid cooling of the surface must beprevented. The degree of thermal insulation depends not only on the climate,but also on the thickness of the concretemember and on the type of cement used.Spraying cold water on warm young126concrete, as it was done years ago, is notrecommended.4. Precooling — This is a necessity forlarge massive concrete structures suchas dams. For more usual structures, inwhich shortening after cooling can takeplace without creating significant restraint forces, precooling is expensiveand unnecessary. In this case, thermalinsulation is preferable and it also hasthe benefit of accelerating concretestrength development. An exceptionmay be made in very hot climates sinceprecooling can keep concrete workablefor a longer period of time.Often shrinkage is considered as acause of early cracking. However, this isnot true under normal climatic conditions. Shrinkage needs time to produce a
Table 1: Heat of hydration of various types ofcements.*Heat of hydration (Btu/1b)Type ofcementt1 day3 days7 days28 94117V5888101124*Data obtained from Concrete Manual, U.S. Bureau ofReclamation, 1975, pp. 45-46.t Federal Specifications SS-C-192G, including InterimAmendment 2, classified the live types according to usage asfollows: Type I for use in general concrete construction whenTypes 11, 111, 1V, and V are not required; Type 11 for use inconstruction exposed to moderate sulfate attack; Type III for usewhen high early strength is required; Type IV for use when lowheat of hydration is required; and Type V for use when high sulfateresistance is required.Note: 1.0 Btu/Ib 2.32 J/g.shortening as high as the tensile rupturestrain. Only in very hot and dry airshrinkage can cause early cracks inyoung concrete, if measures againstevaporation are not applied.Causes of Cracking AfterConcrete HardeningTensile stresses due to dead and liveloads cause cracking. Normal rein-cracking due to restrainttensile strength fitInternal Stress5101520hConcrete hardening time, hoursFig. 2. Development of the tensile strength and stresses due to nonlineartemperature distribution within the concrete.PCI JOURNAL/July-August 1988127
Deformed Shape considering Upper Faceof Beam Warmer Than Bottom Face andassuming beam freed from interior Supports IIIIMDTMoment DiagramVATShear DiagramFig. 3. Forces in a concrete beam due to a temperature rise OT atthe upper face of the beam and external restraint provided byinterior supports.forcement or prestressing should be designed to provide required strength andkeep crack widths within permissiblelimits. Tensile stresses due to serviceloads can be controlled by prestressing.The degree of prestressing can be chosen based on structural or economicconsiderations. Normally, partial prestressing leads to better serviceabilitythan full prestressing.Cracks can also be initiated by tensile stresses due to restrained deformations from temperature variations orfrom shrinkage and creep of concrete.Imposed deformations such as differential settlement between foundationscan also cause cracks.There are two types of restraint whichcause stress in concrete members,namely, internal restraint as shown inFig. 1, and external restraint in indeterminate structures, as shown in Fig. 3.Restrained deformations caused cracking in concrete bridges and it wasprimarily due to temperature differences produced by heating under thesun and cooling during the night. Ex128treme temperatures that occur at 20 to50-year intervals must be considered. Asindicated in Refs. 3, 4, 5 and 6, temperatures in bridge structures were measured in several countries. Recently, theU.S. Transportation Research Boardpublished in Ref. 7 temperature data forbridge design.Temperature differentials should beconsidered along with recommendedmean temperatures, Tm , used for calculating maximum and minimumchanges in the lengths of structuralmembers. In Central Europe values forT. are specified for concrete bridges asvarying from 68 F to –22 ( 20 C to–30 C).The temperature distribution over abeam cross section can be subdividedinto three parts as shown in Fig. 4. Theconstant part, 0 T,, causes axial forces ifoverall length changes are restrained.The linear part, AT,, causes restraintforces, M AT and V AT, in indeterminatestructures as shown in Fig. 3 for a threespan continuous beam. The nonlinearpart, AT3i causes stresses, which are in
Table 2. Recommended cross section temperaturedifferentials for bridge design in Europe.Box girderType ofcross sectionand exposureMaritimeTop ofcross sectionwarmer thanbottom ( F)18Bottom ofcross sectionwarmer ntal14.421.67.210.8Note: 1.0 A N' (9/5) A C.equilibrium over the cross section andproduce no action forces. Thesestresses, which also exist in staticallydeterminate structures, can be calculated by imposing equilibrium conditions and considering that:JcT AT3aTEcwhere a T is equal to 6 x 10 -6 / 0 F(10-5 / C), the coefficient of thermal ex-rig.4.pansion for concrete. Cooling causestensile stresses in areas near extremitiesof the section.For bridges in Europe, the AT valuesgiven in Table 2 are recommended. Inaddition to temperature, restrained concrete creep and shrinkage can causestresses. Shrinkage often leads to cracksbetween connected members of significantly different sizes. Stress due to restrained creep and shrinkage can be cal-uivision of temperature aiagram into its constant, unear ana noniinear parts.PCI JOURNAL/July-August 1988129
iihiiHplan A-A'— –'--Gcompressive Gdue to DL w LL Pcracks due toAT, AS and ACrFig. 5. Transverse cracks in thin bottom slab of box girder due todifferential temperature, creep and shrinkage despite prestressing.culated in the same way as stresses dueto temperature.Transverse cracks due to temperature,creep and shrinkage effects are frequently found in the relatively thinbottom slabs of box girders despite thefact that calculations show considerablelongitudinal compressive stresses due toprestressing. Compressive stresses tendto shift towards the thick webs whichundergo less creep and shrinkage strainsas illustrated in Fig. 5.Box sections are indeterminate structures. Therefore, restraint moments aredeveloped when the section is heatedon one side by the sun. This leads tovertical cracking in bridge piers andtower shafts as shown in Fig. 6. Ref. 8shows examples of temperature cracksin prestressed concrete structures.Determination of AreasLikely to CrackCracking occurs whenever the principal stresses due to service loads or dueto restraint forces or due to a combination of service loads and restraints exceed the tensile strength of concrete.These stresses can be calculated using130the linear theory of elasticity, considering the structure initially uncracked. Inthese calculations, f,s should be taken asthe tensile strength of the concrete. Inthe tension side of a beam, cracking willoccur in areas where bending momentsdue to service loads and restraint causestresses in the extreme tensile fiberabove f15 . As bending increases, thedepth of cracking can be calculated byconsidering a maximum concrete tensilestrain of 0.015 percent as shown in Fig.7.Calculation of possible maximumbending moments due to restraintshould be based on f 5 . As shown in Fig.8, consideration of such moments increases the areas in which cracking maybe expected to occur.Bending moments due to restraintdefine only the location and quantity ofreinforcement or prestressing necessaryto limit the crack width for serviceabilitypurposes. As proven long ago byPriestley, and illustrated in Fig. 9,these moments do not decrease the ultimate strength of the structure becausethey are reduced and finally disappeardue to cracking and plastic deformationas service loads are increased until the
deflection linevertical cracks-MATII MOT MATFig. 6. Bridge pier cross section and moments dueto temperature rise on one side of the pier.-EGXII-O,015 /.crackedZone of webrLE7,5dbflange Zone illSFig. 7. Cracked zones in webs of beams under combined moment dueto dead load, live load and restraint.limit state is reached. However, thestructure must be checked for possiblebrittle failure of the compression zone ifa relatively high degree of prestressingis used, especially for continuous Tbeains. Therefore, to satisfy strength requirements, bending moments due torestraint should not be added to moPCI JOURNAL/July-August 1988ments due to service loads in sizing ofmain reinforcement. It must, however,be observed that restraint due to prestressing does not decrease on the wayup to limit state.Restraint forces decrease beginningwith the first crack since the stiffness ofthe structure is progressively reduced131
Fig. 8. Increased cracked area due to restraint moment.with each crack that occurs. Steelstresses due to restraint are highestwhen the first crack occurs and decreasewith each further crack. This tends to reduce crack widths. Fig. 9 shows the effecton moment due to reduction of restraint.Evaluation of CracksAs indicated in Fig. 10, crack widthsare greater at the surface and decreasetowards the reinforcement. Long yearsof research reported in Refs. 9 and 10,and experience indicate that crackservice loadsultimate lim. stateM due to load andrestraint forcesbrittle failureby too high prestress1,75M DL LLductile failure1,75 MDLM ATeffect of ATM DL LLeffect of 1,5TMDL0Curvature 4OTDCurvatureOTFig. 9. Illustration of reduction of restraint forces as the limit state is approached.132
Ag. 10. Crack width at the surface is used as a measure ofthe effect of cracking on concrete members.Table 3. Allowable crack widths.Ambientcondition ofexposuretw90t(in.)Maximum wpermitted erate0.0080.016Severe0.0040.0012Difficult to seewith the nakedeye* w90 denotes the 90 percentile of the crack width, w.t Defined as indicated in the CEB-FIP Model Code:Mild exposure— The interiors of buildings for normal habitation or offices.— Conditions where a high level of relative humidity is reachedfor a short period only in any one year (for example 60 percentrelative humidity for less than 3 months per year).Moderate exposure— The interior of buildings where the humidity is high andwhere there is a risk for the temporary presence of corrosivevapors.— Running water.— Inclement weather in rural or urban atmospheric conditions,without heavy condensation of aggressive gases.— Ordinary soils.Severe exposure— Liquids containing slight amounts of acids, saline or stronglyoxygenated waters.— Corrosive gases or particularly corrosive soils.— Corrosive industrial or maritime atmospheric conditions.Note: 1 in. 2.54 cm.PCI JOURNALJJuly-August 1988133
widths up to 0.016 in. (0.4 mm) do notsignificantly harm the corrosion protection of the reinforcement furnished bythe concrete, provided the cover is sufficiently thick and dense. However, toavoid undue concern by casual observers, crack widths should be limited to0.008 in. (0.2 mm) at surfaces which areoften seen from a short distance.Polluted air containing CO 2 (whichcauses carbonation), and SO 2 (whichforms acids), or chlorides from deicingsalts, can cause damage to concretestructures. Having cracks or not, concrete structures must be protectedagainst such attacks.Despite the evidence that crackwidths up to 0.016 in. (0.4 mm) do notsignificantly affect the corrosion protection of reinforcement, different levels ofenvironmental exposure and differentsensitivity to corrosion of various typesof reinforcement led to different requirements for concrete cover. It isprudent to vary crack width limitations depending on environmental conditions.For the environmental criteria of CEBand Eurocode No. 2, crack widths can bedefined as presented in Table 3. Thesevalues are valid for a concrete cover, c,of 1.18 in. (30 mm) and for bar diameters, db , smaller than c/1.2 but not greaterthan 1 in. (25 mm). For larger cover, theallowable crack width should be increased to c130 (c in mm). For covergreater than 2 3/s in. (60 mm) and bar diameters of main reinforcement greateror equal to No. 10 (32 mm), small diameter and closely spaced reinforcementshould be provided within the cover tocontrol crack widths.Fig. 11. Stress-strain diagram of a reintorced concrete member under direct tension.134
tension between cracks, referred to as tension stiffeningeffect (see Fig. 11)DESIGN OFREINFORCEMENTReinforcement can be designed tocontrol crack widths using informationpresented in the following sections.Basic Analysis(1)wherew m mean crack widthEm mean crack spacing mean strain Al/lAs the load increases, reinforcementstress at a potential crack location varieslinearly. When the crack occurs, reinforcement stress at the crack, o- , increases suddenly without a significantchange in the mean strain. As the loadcontinues to increase and more cracksappear, the relationship between themean strain, E m , and reinforcementstress at the crack, a-8 , approaches that ofthe reinforcement alone, as indicated inFig. 11. Conditions before cracking willbe referred to as State I and conditionsassuming the reinforcement working ina cracked section will be referred to asState II:E,n ES' — AEg(2)whereE'',' steel strain in State IIAE s strain reduction by concrete inPCI JOURNAL/July-August 1988AE 8 (1/E 3 ) ( o2scr / aAE S)can be ex-(3)whereThe following presentation followsthe 1978 CEB-FIP Model Code and the1983 CEB Manual. The material isbased on theoretical considerations andexperimental results.Fig. 11 shows a plot of steel stress versus longitudinal strain over a givenlength, 1, of a reinforced concrete element in direct tension. As the load increases, cracks are assumed to occurwithin this length. The crack spacingand the longitudinal mean strain definethe mean crack width:Wm S can E mAs indicated in Ref. 9,pressed as: reinforcement stress immediately after crackingmss' steel stress in cracked stateE s Young's modulus for the reinforcement(T ,.The strains E and A E S are significantlyaffected by concrete strength and reinforcement ratio.The mean crack spacing can be expressed as:s c ,.m 2(c s/10) k,kzd b /p e(4)wherec concrete cover in mms bar spacing in mmk l 0.4 for deformed reinforcement,considering bond strengthk2 0.125 for bending members,considering shape of E diagram 0.25 for members under directtension, 0.125 for combined bending a
basic causes and mechanisms of crack-Note: This paper is a revised and updated version of an article originally published in the Proceedings of the International Association for Bridge and Struc-tural Engineering (1ABSE), Zurich, Switzerland, 1987, p. 109. ing in concrete structures. In this paper, causes of concrete cracking are dis-
Crack repair consists of crack sealing and crack filling. Usually, crack sealing re-fers to routing cracks and placing material on the routed channel. Crack filling, on the other hand, refers to the placement of mate-rial in/on an uncut crack. For the purposes of this manual, crack sealing will refer to both crack filling and sealing.
crack growth as a mutual competition between intrinsic mechanisms of crack advance ahead of the crack tip (e.g., alternating crack-tip blunting and resharpening), which promote crack growth, and extrinsic mechanisms of crack-tip shielding behind the tip (e.g., crack closure and bridging), which impede it. The widely differing
Crack filling is the placement of materials into nonworking or low movement cracks to reduce infiltration of water and incompressible materials into the crack. Filling typically involves less crack preparation than sealing and performance requirements may be lower for the filler materials. Filling is
As seen in Figure 2, crack maps are color coded by crack width. The block crack density determines severity of block and fatigue cracking. Block Crack density is a measurement of how tight or concentrated the cracks are over the area covered. Crack severity is summarized in Table 2.
crack spacing (Eq. (1)) and their widths. In BS8007,23 the method of calculating the crack width was, to a certain extent, very similar to the current provisions of EN 1991-1-3. 1 The width of the crack was calculated from the formula shown as follows w max s max · ε (2) where the spacing of the cracks was defined as in the model
Crack tunneling is a crack growth feature often seen in stable tearing crack growth tests on specimens made of ductile materials and containing through-thickness cracks with initially
measured crack sizes at failure [6,7] . sizes of detected msd in aircraft [6,7] size distribution when largest crack . is 0.1 inch number of cracks and size of largest crack - example of statically arbitrary size distribution . when largest crack i
A. ANSI A118.12 provides two levels of crack isolation, one for cracks less than 1/16", and one for higher performance with crack movement up to 1/8". Membranes are available to isolate tiles from crack movement in the concrete slab up to 3/8". There are many reasons for using a membrane in a ceramic or stone tile project. Membranes
