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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. 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?.

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Z.C. Grasley, D.A. Lange, A.J. Brinks, M.D. D’Ambrosia University of Illinois at Urbana-Champaign

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  1. 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

  2. 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

  3. 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.

  4. Evidence of Pickett Problem Creep

  5. > Sviscoelastic Sdilution > Selastic Aggregate Shrinkage considering dilution only Shrinkage of viscoelastic material Shrinkage predicted by elastic model Paste Visualizing the effect of aggregate restraint

  6. qagg = qconc qconc qagg Physical model representation

  7. 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

  8. 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.

  9. Materials modeled

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

  11. Measuring shrinkage and creep

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

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

  14. Kelvin Chain Determining creep function Mix-1

  15. Measuring elastic response

  16. Determination of Aging Function

  17. New model improves fit Model prediction of Mix-1 shrinkage

  18. Improvement again Model prediction of Mix-3 shrinkage

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

  20. 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

  21. 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

  22. 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

  23. 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

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

  25. 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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