# Presentation: 806702

## Z.C. Grasley, D.A. Lange, A.J. Brinks, M.D. D’Ambrosia

University of Illinois at Urbana-Champaign

- University of Illinois at Urbana-Champaign

**MODELING AUTOGENOUS SHRINKAGE OF CONCRETE ACCOUNTING FOR CREEP CAUSED BY AGGREGATE RESTRAINT**

**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.

## Evidence of Pickett Problem

- Creep

## Visualizing the effect of aggregate restraint

## Physical model representation

## Conversion of Pickett’s model

- where

- where

- Viscoelastic

- Elastic

- 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

## 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.

## Materials modeled

## Required model parameters

- Elastic modulus
- Paste autogenous shrinkage
- Concrete autogenous shrinkage
- Concrete creep
- Aging function (elastic and creep)
- Aggregate elastic properties

## Measuring shrinkage and creep

## Measured paste shrinkage

- w/cm = 0.38

- w/cm = 0.33

- w/cm =0.32

## Measured concrete shrinkage 

- High paste content

- w/cm = 0.38

- w/cm = 0.33

- w/cm =0.32

## Determining creep function

**Mix-1**

## Measuring elastic response

## Determination of Aging Function

## New model improves fit

- Model prediction of Mix-1 shrinkage

## Improvement again

- Model prediction of Mix-3 shrinkage

## Even better

- Model prediction of Mix-2 shrinkage

- Does high paste content  better fit? Why? Less damage?

## Tangential stress is function of b/c

- Damage/nonlinearity

- Measured shrinkage

- Predicted shrinkage – viscoelastic model

- Time

- b

- c

- Paste

- Aggregate

## 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.