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This study presents a composite model for predicting concrete shrinkage, specifically autogenous shrinkage, while considering the effect of aggregate restraint caused by creep. The model incorporates a viscoelastic constitutive theory and accounts for differential drying shrinkage with depth. The research aims to validate the model for autogenous shrinkage and its potential application to drying shrinkage as well. The study also explores the influence of aggregate volume fraction on shrinkage and the possibility of reducing shrinkage through stress-relaxing damage. The new model is compared to existing models and suggests improvements in predicting concrete shrinkage.
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MODELING AUTOGENOUS SHRINKAGE OF CONCRETE ACCOUNTING FOR CREEP CAUSED BY AGGREGATE RESTRAINT Z.C. Grasley, D.A. Lange, A.J. Brinks, M.D. D’Ambrosia University of Illinois at Urbana-Champaign Sponsors: PCA, NHI/FHWA, IDOT, CEAT
Why a composite model? • Models that allow the prediction of concrete shrinkage as f(Sp, 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
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,Eg,, g,Sp,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.
> Sviscoelastic Sdilution > Selastic Aggregate Shrinkage considering dilution only Shrinkage of viscoelastic material Shrinkage predicted by elastic model Paste Visualizing the effect of aggregate restraint
qagg = qconc qconc qagg Physical model representation
Conversion of Pickett’s model Elastic where Viscoelastic where • f(t) = loading function • = Poisson ratio of concrete • g = Poisson ratio of aggregate E = Young’s modulus of concrete Eg = Young’s modulus of aggregate J(t,t’) = viscoelastic compliance of concrete Sp = paste shrinkage g = aggregate volume fraction
g(a,) Gel solidifying at time Solidified gel Pore water a(t) da() Accounting for aging 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.
Required model parameters • Elastic modulus • Paste autogenous shrinkage • Concrete autogenous shrinkage • Concrete creep • Aging function (elastic and creep) • Aggregate elastic properties
Measured paste shrinkage w/cm = 0.38 w/cm = 0.33 w/cm =0.32
Measured concrete shrinkage w/cm = 0.38 High paste content w/cm =0.32 w/cm = 0.33
Kelvin Chain Determining creep function Mix-1
New model improves fit Model prediction of Mix-1 shrinkage
Improvement again Model prediction of Mix-3 shrinkage
Even better Does high paste content better fit? Why? Less damage? Model prediction of Mix-2 shrinkage
Higher g Higher likelihood of damage, nonlinearity of creep Reduction in shrinkage Tangential stress is function of b/c Paste Aggregate c b Measured shrinkage Damage/nonlinearity Predicted shrinkage – viscoelastic model Time
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
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
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
Effect of creep on alpha Larger alpha = lower predicted shrinkage better fit
Evidence of tangential cracks around aggregates Bisschop, J., Drying shrinkage microcracking in cement-based materials. 2002, Delft University: Delft, The Netherlands.
