sensitivity analysis of the early-age properties of high-performance

Sensitivity analysis of the early-age properties ofhigh-performance concrete - a case study on bridgebarrier walls

Cusson, D.

A version of this paper is published in / Une version de ce document se trouve dans :Creep, Shrinkage and Durability Mechanics of Concrete and Other Quasi-Brittle

Materials Conference, Cambridge, Mass., August 20-22, 2001, pp. 325-330

www.nrc.ca/irc/ircpubs

NRCC-44773

6th Int. Conf. on Creep, Shrinkage & Durability Mechanics of Concrete D. Cusson, Page 1 of 6and Other Quasi-Brittle Materials, Cambridge MA, 20-22 August 2001

Sensitivity analysis of the early-age properties of high-performance concrete –a case study on bridge barrier walls

D. Cusson

National Research Council Canada, Institute for Research in ConstructionBuilding M-20, Montreal Road, Ottawa, Canada, K1A 0R6

1. INTRODUCTION

Early-age cracking of high-performance concrete (HPC) is a major concern for bridgeowners, since it results in premature reinforcement corrosion, concrete spalling, highmaintenance cost and reduced service life. Current design codes do not completely addressearly-age behavior of concrete and therefore leave a degree of uncertainty about fieldperformance and cracking of concrete bridges at early age. The paper presents a sensitivityanalysis in which a finite element model of a bridge barrier wall constructed over an existingslab is used with actual field data to assess the sensitivity of relevant concrete properties to thedevelopment of total stress in the concrete barrier wall at early age. The parametersconsidered in the analysis include tensile strength, modulus of elasticity, maturity, thermaleffects, shrinkage and creep. Limitations of existing models and research needs are suggested.

2. REVIEW OF EXISTING CODE PROVISIONS

High-performance concrete has proven to be quite sensitive to cracking, especially at earlyage [1]. The problem often occurs in concrete bridge decks and other bridge componentsthroughout North America [2]. One of the major concerns of designers, contractors andowners is whether or not cracking will actually occur at early age. The resulting highmaintenance costs and reduced service life could defeat the purpose of using high-performance concrete. Existing models for the prediction of time-dependent concreteproperties are briefly reviewed, and their limitations with respect to early-age behavior arediscussed.

2.1. MaturityTemperature of concrete has a direct influence on the rate of cement hydration. The effect

of elevated or reduced temperature on the maturity of concrete may be taken into account byadjusting the concrete age, tT, according to [3]:

+

−∆= Σ= i

i

n

iT T

tt273

400065.13exp

1(1)


where ∆ti is the period of time for which a temperature Ti prevails.Equation 1 is only valid for Portland-cement concrete. The constant values 13.65 and 4000

are factors related to the activation energy of concrete, which depends on cement type andadditives used in the concrete mix. With the frequent use of high-performance concrete,which is normally composed of fine cements and special additives, more experimentalevidence is therefore needed to extend the range of applicability of Eq. 1 and to provide newactivation energy factors for various concrete types.

2.2. Thermal expansionThermal strains due to steep temperature gradients or to rapid temperature fluctuations can

be rather large in outdoor applications. Excessive heat due to cement hydration in high-performance concrete can aggravate the problem if uncontrolled. The thermal strain, εcT, iscalculated as follows:

TTcT ∆= αε (2)

where αT is the coefficient of thermal expansion of concrete and ∆T is the increment oftemperature.

It is commonly assumed that αT depends only on the aggregate type with no dependenceon time. This is true for mature concrete, but limited studies, however, infer that αT may alsovary with time at very early age [4].

2.3. ShrinkageDrying shrinkage in high-performance concrete at early age is often not significant because

of the low permeability of HPC and the short drying period considered. Autogenousshrinkage, however, is known to be quite significant in concrete with a low water-cementratio [5]. The development of the shrinkage strain, εcs, with time can be calculated accordingto [3]:

scsocs βεε = (3)

where εcso is the ultimate value of the total shrinkage strain, βs is a coefficient that describesthe development of shrinkage as a function of drying time.

However, it is uncertain whether current design codes account for autogenous shrinkage inthe prediction of the total shrinkage strain. Most shrinkage models were developed from testson normal-strength concrete, which exhibit very little autogenous shrinkage. It was shown in acase study [6] that the total shrinkage strain predicted by the CEB Design Code was largelyexceeded by the corresponding autogenous shrinkage strain predicted by an empirical model[5].

2.4. CreepCreep, or relaxation of concrete, can relieve part of the tensile stress. The creep strain, εcc,

can be calculated with [3]:

φσ

ε28c

ccc E

= (4)


where σc is the actual total stress, Ec28 is the 28-day modulus of elasticity, and φ is the creepcoefficient, which depends on the time elapsed and the time at loading.

The relations given in design codes to calculate the creep coefficient are empirical andwere calibrated on the basis of laboratory tests on concrete samples under compressive loadsonly. Furthermore, the minimum age at which the concrete samples were tested for creep was3 days. Since severe cracking can occur in concrete only a few hours after setting [6], moreexperimental evidence on creep at very early age is needed.

2.5. Modulus of elasticity and tensile strengthThe high modulus of elasticity of high-performance concrete combined with its relatively

low tensile strength makes it susceptible to cracking, especially at early age when concretehas yet to develop its design strength.

The development of the modulus of elasticity, Ec, and tensile strength, fct, with time can becalculated with the following equations [3]:

28cccc EE β= (5)

28ctccct ff β= (6)

where βcc is a coefficient describing the development of strength with time, and Εc28 and fct28

are the modulus of elasticity and tensile strength at the age of 28 days, respectively.The coefficient βcc in Equations 5 and 6 was calibrated on the basis of laboratory tests on

concrete samples under compressive loads only. The CEB Design Code indicates thatEquation 6 may overestimate the calculated tensile strength for an age lower than 28 days.This is because tensile strength is more influenced than compressive strength by curing,drying and member size.

3. MODELLING THE EARLY-AGE BEHAVIOUR OF HPC

A summary of a field study is first given in which severe early-age cracking in HPC bridgebarriers was observed. It serves as a case study for the finite element modeling of the early-age behavior of high-performance concrete that is presented thereafter. The results of asensitivity analysis of predicted concrete properties at early age are then presented.

3.1. Case study: highway bridge barrier wall in Montreal, Canada

In 1996, the Quebec Ministry of Transportation undertook a major rehabilitation of theVachon Bridge, located near Montreal. Part of the work involved rebuilding the barrier walls.The concrete in the new barriers contained 450 kg/m3 of Type 10 cement, had a water-cementratio of 0.36 and a 28-day compressive strength of 45 MPa. Forms were strippedapproximately 24 hours after concreting. Concrete strain, temperature and relative humiditywere monitored during and after construction with sensors embedded in the concrete of thebarrier walls.


An inspection of the barrier walls, carriedout approx. 36 hours after casting, revealedclosely spaced transverse cracks runningcompletely through the 34-m long segments ofthe walls. Analytical and numerical analyseswere conducted to understand the causes of thissevere early-age cracking. Details of the fieldinvestigation and the analytical study are givenin [6]. The main causes of early-age crackingwere identified to be thermal stress due to steeptemperature gradients, and autogenousshrinkage that is typical of high-performanceconcrete. The study confirmed that the use ofhigh-performance concrete does not in itselfassure the durability of bridge barrier walls.The use of appropriate construction techniquesis essential in improving concrete durability.

3.2. Finite element analysis of the barrier wall at early ageA finite element (FE) analysis was conducted in two steps using the ABAQUS finite

element software package. The FE model is illustrated in Fig. 1 and represents a 0.9-m highbarrier wall cast on top of an existing cantilever slab. Using the geometry and the field datafrom the case study described above, a transient thermal analysis was first performed todetermine the variation in time of the temperature distribution in the barrier wall cross-section. The effects of solar radiation, cooling due to wind, ambient temperature and heatgenerated by hydration of cement were accounted for in the analysis.

In order to calculate the resulting distribution of stresses in the cross-section at varioustimes, a transient stress analysis using 2D solid plane-strain elements was conducted assumingthat the barrier wall was fully restrained at the base by the old concrete slab. Concretematurity was accounted for in the calculation of the strains from thermal effects, shrinkageand creep, and in thecalculation of the elasticmodulus and tensilestrength as a function oftime. The period of timeconsidered in the analyseswas three days.

Figure 2 presents theresulting longitudinalshrinkage and thermalstresses computed on thefront face near the top ofthe wall. Stresses startedto develop at 12 hoursafter casting (setting timeobserved in the field). Theeffect of creep on the

-8

-6

-4

-2

0

2

4

0 8 16 24 32 40 48 56 64 72Time after casting (hour)

Stre

ss (M

Pa)

Figure 2. Effect of creep on shrinkage and thermal stresses

thermal

shrinkagestress

with creepno creep

Old cantileverslab

New barrier wall

0.9 m

0.3 m

Figure 1. Finite element model


stresses is also evident. Asexpected, creep cansignificantly reduce theshrinkage stress, and thusthe risk of cracking.However, in this casestudy, creep reduces onlythe compressive thermalstress, and actuallyincreases the tensilethermal stress. This is dueto the creep recovery thatis slower than the rapidchange in the thermalstress. This raises aconcern for some specialconcretes that areformulated to exhibit ahigh creep to shrinkageratio in order to compensate for shrinkage. They may not be as effective as expected inoutdoor applications with high thermal stresses.

3.3. Sensitivity analysis A sensitivity analysis was performed in order to assess the effect of introducing an error in

the calculation of various concrete properties (Equations 1 to 6) on total stress, the algebraicsum of the thermal and shrinkage stresses considering creep. The analysis was conductedthree times for each property by multiplying the nominal values of the property underconsideration, as given by the applicable equation, by a factor of 0.8, 1.0 or 1.2, while using amultiplication factor of 1.0 for the remaining properties. Figure 3 presents the results of a setof analyses for which the elastic modulus was the property under consideration (cracking notaccounted for). Theobjective of this analysiswas to identify theproperties that are mostsensitive to modelingerrors, which may resultin poor design andunexpected prematurefailure.

Figure 4 presents theresults of the sensitivityanalysis on the sixvariables of interest. Thevertical axis representsthe normalized stress,which is the maximumtotal stress in tension

Figure 3. Sensitivity analysis done on E-modulus showingtotal stress (†cracking disregarded) in wall (top of front face)

-6

-4

-2

0

2

4

6

0 8 16 24 32 40 48 56 64 72Time after casting (hour)

Tot

al s

tres

s (M

Pa)

cracking

tensilestrength

total stress†

at 1st peak

Ec x 1.2Ec x 1.0Ec x 0.8

0

1

2

3

4

Conc

rete

matu

rity

Therm

alstr

ainSh

rinka

ge st

rain Cr

eep

strain Elas

ticm

odulu

s

Tens

ilestr

engt

h

Nor

mal

ized

str

ess

0.8 1.2 0.8 1.2 0.8 1.2 0.8 1.2 0.8 1.2 0.8 1.2

Figure 4. Results of the sensitivity analysis


(shortly after tensile strength was exceeded) divided by the corresponding tensile strength.Note that the absolute values of the normalized stress are somewhat fictitious since the effectof cracking on total stress was disregarded in the analysis. The non-proportionality of theeffects observed in Fig. 4 is explained by the interdependence of some properties.

The results indicate that an error in modeling maturity, thermal effects, shrinkage or creepresulted in a relatively small error in the total stress. However, an error in modeling themodulus of elasticity or the tensile strength resulted in a nearly proportional error in theresulting total stress, as can be expected. This indicates the need for further research for moreaccurate formulas for the tensile modulus of elasticity and tensile strength of high-performance concrete at early age.

4. CONCLUSIONS

Early-age cracking is a serious problem with high-performance concrete. It is a frequentproblem in concrete bridge decks throughout North America. Most existing models are basedon either compressive test data or data on mature concrete, leaving a degree of uncertaintyabout field performance and cracking of concrete bridges at early age.

Based on the case study, the sensitivity analysis indicated that the normalized stress (totalstress divided by corresponding tensile strength) is more sensitive to errors in predicting themodulus of elasticity and the tensile strength than to errors in predicting other properties,namely thermal, shrinkage and creep strains, and maturity. Therefore, future experimentalwork on high-performance concrete at early-age (t < 7 days) should focus on the modeling ofits modulus of elasticity under tensile loading, and tensile strength.

5. ACKNOWLEDGMENT

The author wishes to acknowledge Ministère des transports du Québec for its contributionin the field investigation.

6. REFERENCES

1. Springenschmid (1998): “Prevention of Thermal Cracking in Concrete at Early-Ages,”State-of-the-Art Report No. 15, RILEM TC 119, E&FN Spon, London, 348 p.2. TRB (1996): “Transverse cracking in newly constructed bridge decks,” National Co-operative Highway Research Program Report 380, Transportation Research Board, NationalAcademy Press, Washington, 126 p.3. CEB (1993a): “CEB-FIP Model Code 1990,” Information Bulletin No. 213/214, Euro-International Concrete Committee, Lausanne, 437 p.4. RILEM 42-CEA (1981): “Properties of set concrete at early-ages – State of the ArtReport,” Matériaux et Constructions, V. 14, No. 84, pp. 399-450.5. Tazawa, E. and Miyazawa, S. (1997): “Influence of curing conditions on autogenousshrinkage of concrete,” Int. Conference on Engineering Materials, Ottawa, V. 1, pp. 373-384.6. Cusson, D. and Repette, W. (2000): “Early-Age Cracking in Reconstructed ConcreteBridge Barrier Walls,” ACI Materials Journal, 97(4), July/August, 438-446.

sensitivity analysis of the early-age properties of high-performance

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