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

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.

(1 )pS S g

Evidence of Pickett Problem

-200

-150

-100

-50

0

0 20 40 60 80 100

ViscoelasticElasticAlpha = 1.7Mix-1

Stra

in x

10-6

Age (d)

Creep

Visualizing the effect of aggregate restraint

Shrinkage predicted by elastic modelShrinkage of viscoelastic materialShrinkage considering dilution only

Aggregate

Paste

2(1 )pS S g

> Sviscoelastic

(1 )pS S g

Sdilution

1(1 )pS S g

> Selastic

Physical model representation

qagg

qconc

qagg = qconc

Conversion of Pickett’s model

0

3(1 )( )(1 2 )

1 2( , ') ( ') '

gt

g

f t

E J t t f t dt

(1 )pS S g gg EE /)21(21

)1(3

where

where

(1 )pS S g Viscoelastic

Elastic

f(t) = loading function= Poisson ratio of concreteg = Poisson ratio of aggregateE = Young’s modulus of concreteEg = Young’s modulus of aggregateJ(t,t’) = viscoelastic compliance of concreteSp = paste shrinkageg = aggregate volume fraction

Accounting for aging

')'()',()(0

dttttJtt

0 '

( ')1 1( , ')( ') ( )

th

t

J tJ t t d

E a t a

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.

Materials modeledSG Unit Mix-1 Mix-2 Mix-3

Cement (Type I) 3.15 kg/m3 392 357 403

Fly Ash (Class C) 2.65 kg/m3 93 193 90

Coarse Aggregate, 3/4" (20 mm) 2.70 kg/m3 218 810 343

Coarse Aggregate, 3/8" (10 mm) 2.70 kg/m3 638 0 604

Fine Aggregate (FM = 2.57) 2.64 kg/m3 832 792 824

Water 1.00 kg/m3 185 179 158

Superplasticizer (CAE) 1.06 l/m3 2.44 1.12 1.38w/cm 0.38 0.33 0.32

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

-1300

-1100

-900

-700

-500

-300

-100

0 20 40 60 80 100 120 140 160

Age (d)

Stra

in x

10-6

Mix-1Mix-2Mix-2 repeatMix-3

w/cm = 0.38

w/cm = 0.33w/cm =0.32

Measured concrete shrinkage

-200

-150

-100

-50

0

0 20 40 60 80 100

Mix-1Mix-2

Mix-3

Stra

in x

10-6

Age (d)

High paste content

w/cm = 0.38

w/cm = 0.33

w/cm =0.32

Determining creep function

100

150

200

250

300

350

400

0 50 100 150 200 250

Cre

ep S

train

x 1

06

Age (d)

Mix-1

Kelvin Chain

Measuring elastic response

Determination of Aging Function

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30

Agi

ng fu

nctio

n (n

orm

aliz

ed a

t 28

d)

Age (d)

New model improves fit

-200

-150

-100

-50

0

0 20 40 60 80 100

ViscoelasticElasticAlpha = 1.7Mix-1

Stra

in x

10-6

Age (d)

Model prediction of Mix-1 shrinkage

(1 )pS S g

Improvement again

-400

-350

-300

-250

-200

-150

-100

-50

0

0 20 40 60 80 100

ViscoelasticElasticAlpha = 1.7Measured

Stra

in x

10-6

Age (d)

Model prediction of Mix-3 shrinkage

Even better

-400

-350

-300

-250

-200

-150

-100

-50

0

0 20 40 60 80 100

ViscoelasticElasticAlpha = 1.7Measured

Stra

in x

10-6

Age (d)

Model prediction of Mix-2 shrinkage

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

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

PasteAggregate

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

(1 )pS S g

Larger alpha = lower predicted shrinkage better fit

1

1.2

1.4

1.6

1.8

2

0 20 40 60 80 100

Mix-1 Viscoelastic AlphaMix-1 Elastic Alpha Mix-2 Viscoelastic AlphaMix-2 Elastic Alpha Mix-3 Viscoelastic AlphaMix-3 Elastic Alpha

Alp

ha V

alue

s

Age (d)

Evidence of tangential cracks around aggregates

Bisschop, J., Drying shrinkage microcracking in cement-based materials. 2002, Delft University: Delft, The Netherlands.