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Z.C. Grasley, D.A. Lange, A.J. Brinks, M.D. D’Ambrosia University of Illinois at Urbana-Champaign MODELING AUTOGENOUS SHRINKAGE OF CONCRETE ACCOUNTING FOR CREEP CAUSED BY AGGREGATE RESTRAINT Sponsors: PCA, NHI/FHWA, IDOT, CEAT

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Why a composite model? Models that allow the prediction of concrete shrinkage as f(S p, mech. properties) are valuable modeling tools Predict the effect of segregation on shrinkage of SCC layers Input for FEM model that considers differential drying shrinkage with depth Bridge deck or pavement Curling or cracking While our model will be validated using autogenous shrinkage, should apply to drying also

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Many models have already been developed, but… Existing models based on theory of elasticity An example: Pickett’s model uses elasticity theory to predict concrete shrinkage S=S(E,E g, , g,S p,g) Problem: cement paste is viscoelastic, so Pickett’s model tends to over-predict shrinkage as time increases because creep relaxes restraining stress Solution: rework Pickett’s model using a viscoelastic constitutive theory rather than elastic Pickett, G., Effect of aggregate on shrinkage of concrete and hypothesis concerning shrinkage. American Concrete Institute -- Journal, 1956. 27(5): p. 581-590.

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Evidence of Pickett Problem Creep

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Visualizing the effect of aggregate restraint Shrinkage predicted by elastic model Shrinkage of viscoelastic material Shrinkage considering dilution only Aggregate Paste > S viscoelastic S dilution > S elastic

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Physical model representation q agg q conc q agg = q conc

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Conversion of Pickett’s model where Viscoelastic Elastic f(t) = loading function = Poisson ratio of concrete g = Poisson ratio of aggregate E = Young’s modulus of concrete E g = Young’s modulus of aggregate J(t,t’) = viscoelastic compliance of concrete S p = paste shrinkage g = aggregate volume fraction

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Accounting for aging Solidified gel da( ) a(t) Pore water Gel solidifying at time g (a, ) Constitutive equation for aging viscoelastic material Solidification theory Bazant, Z.P., Viscoelasticity of Solidifying Porous Material - Concrete. J. of the Eng. Mech. Div., ASCE, 1977. 103(EM6): p. 1049-1067.

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Materials modeled

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Required model parameters Elastic modulus Paste autogenous shrinkage Concrete autogenous shrinkage Concrete creep Aging function (elastic and creep) Aggregate elastic properties

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Measuring shrinkage and creep

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Measured paste shrinkage w/cm = 0.38 w/cm = 0.33 w/cm =0.32

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Measured concrete shrinkage High paste content w/cm = 0.38 w/cm = 0.33 w/cm =0.32

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Determining creep function Mix-1 Kelvin Chain

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Measuring elastic response

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Determination of Aging Function

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New model improves fit Model prediction of Mix-1 shrinkage

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Improvement again Model prediction of Mix-3 shrinkage

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Even better Model prediction of Mix-2 shrinkage Does high paste content better fit? Why? Less damage?

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Tangential stress is function of b/c Higher g Higher likelihood of damage, nonlinearity of creep Reduction in shrinkage Damage/nonlinearity Measured shrinkage Predicted shrinkage – viscoelastic model Time b c Paste Aggregate

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Why not perfect fit? Linear viscoelasticity is assumed No damage such as microcracking is considered around aggregates Dependence of J(t,t’) on g is ignored Aging function determined from elastic tests A time-independent, stress history independent Poisson’s ratio was assumed

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Current work Importance of aggregate dependence Solve model equations with J(t,t’) as f(g) Use paste creep and elastic properties Assumption of constant Poisson ratio Solve model in terms of E(t,t’) and K(t,t’) (substitute for Poisson ratio) Use new experimental methods to measure K Compare to existing model predictions Combine model with paste shrinkage prediction model Account for nonlinearity and/or damage effects

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Summary New model has been developed for predicting concrete shrinkage Model is extension of Pickett’s model Includes creep Improves on Pickett’s elastic model Creep is present as result of aggregate restraint Model still over-predicts concrete autogenous shrinkage Nonlinearity and damage Increasing g in mixture design may reduce shrinkage not only by reducing paste content, but also by inducing stress-relaxing damage ~ additional creep

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Effect of creep on alpha Larger alpha = lower predicted shrinkage better fit

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Evidence of tangential cracks around aggregates Bisschop, J., Drying shrinkage microcracking in cement-based materials. 2002, Delft University: Delft, The Netherlands.

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