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Sensitivity analysis of the early-age properties of highperformance concrete - a case study on bridge barrier walls Cusson, D.

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

Cusson, D.

NRCC-44773

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

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

D. Cusson, Page 1 of 6

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 Construction Building M-20, Montreal Road, Ottawa, Canada, K1A 0R6

1. INTRODUCTION Early-age cracking of high-performance concrete (HPC) is a major concern for bridge owners, since it results in premature reinforcement corrosion, concrete spalling, high maintenance cost and reduced service life. Current design codes do not completely address early-age behavior of concrete and therefore leave a degree of uncertainty about field performance and cracking of concrete bridges at early age. The paper presents a sensitivity analysis in which a finite element model of a bridge barrier wall constructed over an existing slab is used with actual field data to assess the sensitivity of relevant concrete properties to the development of total stress in the concrete barrier wall at early age. The parameters considered in the analysis include tensile strength, modulus of elasticity, maturity, thermal effects, 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 early age [1]. The problem often occurs in concrete bridge decks and other bridge components throughout North America [2]. One of the major concerns of designers, contractors and owners is whether or not cracking will actually occur at early age. The resulting high maintenance costs and reduced service life could defeat the purpose of using highperformance concrete. Existing models for the prediction of time-dependent concrete properties are briefly reviewed, and their limitations with respect to early-age behavior are discussed. 2.1. Maturity Temperature 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 by adjusting the concrete age, t T, according to [3]: n  4000  tT = Σ ∆ti exp 13.65 − 273 + Ti  i =1 

(1)



where ∆t i 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 and additives used in the concrete mix. With the frequent use of high-performance concrete, which is normally composed of fine cements and special additives, more experimental evidence is therefore needed to extend the range of applicability of Eq. 1 and to provide new activation energy factors for various concrete types. 2.2. Thermal expansion Thermal 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 highperformance concrete can aggravate the problem if uncontrolled. The thermal strain, ε cT, is calculated as follows: ε cT = α T ∆T

(2)

where α T is the coefficient of thermal expansion of concrete and ∆T is the increment of temperature. It is commonly assumed that α T depends only on the aggregate type with no dependence on time. This is true for mature concrete, but limited studies, however, infer that α T may also vary with time at very early age [4]. 2.3. Shrinkage Drying 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. Autogenous shrinkage, however, is known to be quite significant in concrete with a low water-cement ratio [5]. The development of the shrinkage strain, ε cs, with time can be calculated according to [3]: ε cs = ε cso β s

(3)

where ε cso is the ultimate value of the total shrinkage strain, β s is a coefficient that describes the development of shrinkage as a function of drying time. However, it is uncertain whether current design codes account for autogenous shrinkage in the prediction of the total shrinkage strain. Most shrinkage models were developed from tests on normal-strength concrete, which exhibit very little autogenous shrinkage. It was shown in a case study [6] that the total shrinkage strain predicted by the CEB Design Code was largely exceeded by the corresponding autogenous shrinkage strain predicted by an empirical model [5]. 2.4. Creep Creep, or relaxation of concrete, can relieve part of the tensile stress. The creep strain, ε cc, can be calculated with [3]:

ε cc =

σc φ Ec 28

(4)



where σc is the actual total stress, Ec28 is the 28-day modulus of elasticity, and φ is the creep coefficient, which depends on the time elapsed and the time at loading. The relations given in design codes to calculate the creep coefficient are empirical and were calibrated on the basis of laboratory tests on concrete samples under compressive loads only. Furthermore, the minimum age at which the concrete samples were tested for creep was 3 days. Since severe cracking can occur in concrete only a few hours after setting [6], more experimental evidence on creep at very early age is needed. 2.5. Modulus of elasticity and tensile strength The 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 concrete has yet to develop its design strength. The development of the modulus of elasticity, Ec, and tensile strength, f ct, with time can be calculated with the following equations [3]: Ec = βcc Ec 28

(5)

f ct = β cc f ct 28

(6)

where β cc is a coefficient describing the development of strength with time, and Εc28 and f ct28 are the modulus of elasticity and tensile strength at the age of 28 days, respectively. The coefficient β cc 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 that Equation 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 bridge barriers was observed. It serves as a case study for the finite element modeling of the earlyage behavior of high-performance concrete that is presented thereafter. The results of a sensitivity 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 the Vachon 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-cement ratio of 0.36 and a 28-day compressive strength of 45 MPa. Forms were stripped approximately 24 hours after concreting. Concrete strain, temperature and relative humidity were monitored during and after construction with sensors embedded in the concrete of the barrier walls.


An inspection of the barrier walls, carried out approx. 36 hours after casting, revealed closely spaced transverse cracks running completely through the 34-m long segments of the walls. Analytical and numerical analyses were conducted to understand the causes of this severe early-age cracking. Details of the field investigation and the analytical study are given in [6]. The main causes of early-age cracking were identified to be thermal stress due to steep temperature gradients, and autogenous shrinkage that is typical of high-performance concrete. The study confirmed that the use of high-performance concrete does not in itself assure the durability of bridge barrier walls. The use of appropriate construction techniques is essential in improving concrete durability.


New barrier wall

0.9 m

Old cantilever slab

0.3 m

Figure 1. Finite element model

Stress (MPa)

3.2. Finite element analysis of the barrier wall at early age A 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 high barrier wall cast on top of an existing cantilever slab. Using the geometry and the field data from the case study described above, a transient thermal analysis was first performed to determine the variation in time of the temperature distribution in the barrier wall crosssection. The effects of solar radiation, cooling due to wind, ambient temperature and heat generated by hydration of cement were accounted for in the analysis. In order to calculate the resulting distribution of stresses in the cross-section at various times, a transient stress analysis using 2D solid plane-strain elements was conducted assuming that the barrier wall was fully restrained at the base by the old concrete slab. Concrete maturity was accounted for in the calculation of the strains from thermal effects, shrinkage and creep, and in the 4 calculation of the elastic shrinkage modulus and tensile stress 2 strength as a function of time. The period of time 0 considered in the analyses was three days. -2 Figure 2 presents the resulting longitudinal -4 shrinkage and thermal stresses computed on the -6 with creep front face near the top of thermal no creep the wall. Stresses started -8 to develop at 12 hours 0 8 16 24 32 40 48 56 64 72 after casting (setting time Time after casting (hour) observed in the field). The Figure 2. Effect of creep on shrinkage and thermal stresses effect of creep on the



Total stress (MPa)

stresses is also evident. As 6 expected, creep can total stress† cracking significantly reduce the at 1st peak 4 shrinkage stress, and thus the risk of cracking. 2 However, in this case study, creep reduces only 0 the compressive thermal stress, and actually -2 increases the tensile Ec x 1.2 -4 Ec x 1.0 thermal stress. This is due tensile Ec x 0.8 to the creep recovery that strength -6 is slower than the rapid change in the thermal 0 8 16 24 32 40 48 56 64 72 stress. This raises a Time after casting (hour) concern for some special analysis done on E-modulus showing concretes that are Figure 3. Sensitivity † formulated to exhibit a total stress ( cracking disregarded) in wall (top of front face) high creep to shrinkage ratio in order to compensate for shrinkage. They may not be as effective as expected in outdoor applications with high thermal stresses.

Te stre nsile ngt h

Cre stra ep in Ela mo stic dul us

Shr i stra nkage in

Th stra ermal in

Co ma ncrete turi ty

Normalized stress

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 algebraic sum of the thermal and shrinkage stresses considering creep. The analysis was conducted three times for each property by multiplying the nominal values of the property under consideration, as given by the applicable equation, by a factor of 0.8, 1.0 or 1.2, while using a multiplication factor of 1.0 for the remaining properties. Figure 3 presents the results of a set of analyses for which the elastic modulus was the property under consideration (cracking not accounted for). The 4 objective of this analysis was to identify the 3 properties that are most sensitive to modeling errors, which may result 2 in poor design and unexpected premature 1 failure. Figure 4 presents the results of the sensitivity 0 0.8 1.2 0.8 1.2 0.8 1.2 0.8 1.2 0.8 1.2 0.8 1.2 analysis on the six variables of interest. The vertical axis represents the normalized stress, which is the maximum total stress in tension 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 effect of cracking on total stress was disregarded in the analysis. The non-proportionality of the effects 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 creep resulted in a relatively small error in the total stress. However, an error in modeling the modulus of elasticity or the tensile strength resulted in a nearly proportional error in the resulting total stress, as can be expected. This indicates the need for further research for more accurate formulas for the tensile modulus of elasticity and tensile strength of highperformance concrete at early age. 4. CONCLUSIONS Early-age cracking is a serious problem with high-performance concrete. It is a frequent problem in concrete bridge decks throughout North America. Most existing models are based on either compressive test data or data on mature concrete, leaving a degree of uncertainty about field performance and cracking of concrete bridges at early age. Based on the case study, the sensitivity analysis indicated that the normalized stress (total stress divided by corresponding tensile strength) is more sensitive to errors in predicting the modulus of elasticity and the tensile strength than to errors in predicting other properties, namely thermal, shrinkage and creep strains, and maturity. Therefore, future experimental work on high-performance concrete at early-age (t < 7 days) should focus on the modeling of its modulus of elasticity under tensile loading, and tensile strength. 5. ACKNOWLEDGMENT The author wishes to acknowledge Ministère des transports du Québec for its contribution in 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 Cooperative Highway Research Program Report 380, Transportation Research Board, National Academy Press, Washington, 126 p. 3. CEB (1993a): “CEB-FIP Model Code 1990,” Information Bulletin No. 213/214, EuroInternational Concrete Committee, Lausanne, 437 p. 4. RILEM 42-CEA (1981): “Properties of set concrete at early-ages – State of the Art Report,” Matériaux et Constructions, V. 14, No. 84, pp. 399-450. 5. Tazawa, E. and Miyazawa, S. (1997): “Influence of curing conditions on autogenous shrinkage 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 Concrete Bridge Barrier Walls,” ACI Materials Journal, 97(4), July/August, 438-446.