MECHANISMS

J )11

(3 0KK

S

J

Constant Uniaxial Tension Autogenous Shrinkage

Elastic ElasticViscoelastic Viscoelastic

JJ 0K K

)11

(3 0KK

S

0K K

Time

Stress

Time

Stress

* *

* Not an exact analytical solution for partially saturated material

K0 = viscoelastic non-ageing

K = viscoelastic ageing

Saturated pore

Empty pore

70

75

80

85

90

95

100

0 10 20 30 40 50 60

Elapsed time (d)

Inte

rnal

RH

(%

)

0.25 w/c0.30 w/c0.35 w/c

-1600

-1400

-1200

-1000

-800

-600

-400

-200

0

200

0 10 20 30 40 50 60Elapsed time (d)

Shr

inka

ge (

mst

rain

)

0.25

0.30

0.35

-700

-600

-500

-400

-300

-200

-100

0

100

200

0 10 20 30 40 50Elapsed time (d)

Shr

inka

ge (

m str

ain)

SRA25 avg

SRA30 avg

SRA35 avg

0.50 0.50 w/cw/c

0.30 0.30 w/cw/c

Cement grains initially separated by

water

Initial set locks in paste structure

Chemical shrinkage ensures some porosity remains even at

“Extra” water remains in small pores even at =1

Pores to 50 nm emptied

Internal RH and pore fluid pressure reduced as

smaller pores are emptied

Autogenous Autogenous shrinkageshrinkage

Increasing degree of hydration

Autogenous Shrinkage as a Viscoelastic Response to Self-Desiccation

MEASUREMENTS

EXPERIMENTAL RESULTS

MOTIVATION

Modern concretes incorporate mineral admixtures and low w/cHydration and pozzolanic reaction of these materials leads to self- dessication (internal drying that causes a reduction in internal RH)Reduction in RH reduction in capillary pressure bulk shrinkageIf shrinkage is restrained, early-age cracking may be a significant problem

Why is autogenous shrinkage important?

Hardened cement paste acts as a viscoelastic material under shrinkage stresses (see Fig. 1)To accurately predict stress distributions in concrete caused by self-desiccation or drying, we need to determine the time-dependent stress- strain relationship

Why do we need a viscoelastic model?

Since autogenous shrinkage and drying shrinkage are driven by the same mechanism, viscoelastic models for predicting autogenous shrinkage may be useful for predicting drying shrinkage as well

Are there any other uses for this model?

80

82

84

86

88

90

92

94

96

0 50 100 150 200 250 300 350

Elapsed Time (hr)

Inte

rnal R

ela

tive H

um

idity

(%

)

-500

-400

-300

-200

-100

0

100

Shrinka

ge (

m)

Internal RH

Shrinkage

Fig. 1: RH (~stress) and shrinkage plots indicating probable viscoelastic response of hardened cement paste

Zachary C. Grasley & David A. Lange

'

)ln(

v

RTRH

As water is removed from small pores, curved menisci develop This causes a pressure reduction in the pore fluid which can be related to RH through the Kelvin-Laplace equationIn low w/c materials, enough water is removed from small pores to cause curved menisci simply by hydration

= pore fluid pressureRH = internal humidityR = univ. gas constantT = temp. in kelvinsv’ = molar vol. of water

C-S-HC-S-H

MODEL BASICS

The reduction in pore fluid pressure caused by self-desiccation and the development of curved menisci may be used by modeling the hardened cement paste as a solid with spherical pores

Strain indicator boxHydraulic pump and pressure regulator

Embedment strain gage

FUTURE WORK

)11

(3 0kk

Spastesh

The approximate linear elastic solution for the strain in the model system is given by:

S = saturation factor = pore fluid pressure determined by K-L equation and RHK = bulk modulus of porous solidK0 = bulk modulus of solid material alone

To obtain the viscoelastic solution, the transform analogy may be used Viscoelastic stiffness parameters are shown with a barShrinkage is simply a response to pore pressure and is analogous to any other loading such as uniaxial tension

Since hardened cement paste exhibits instantaneous deformation plus some recoverable creep, some variation of the standard linear model should be used for the viscoelastic stiffness parametersAging should be accounted for (e.g. solidification theory)

Time

Autogenous shrinkage

Viscoplastic

Viscoelastic Recoverable shrinkage

Instantaneous elastic

Standard linear model

Flexible corrugated tubing for sealed, restraint-free measurement of autogenous shrinkage

Embedded pins for length measurement

Internal RH measurement

Hydrostatic creep test for determination of viscoelastic bulk modulus

80

82

84

86

88

90

92

94

96

98

100

0 10 20 30 40 50

Elapsed time (d)

Inte

rnal

RH

(%

)

SRA25 avg

SRA30 avg

SRA35 avg

Fig. 2: Autogenous shrinkage of 0.25, 0.30, and 0.35 w/c pastes.

Fig. 2: Autogenous shrinkage of 0.25, 0.30, and 0.35 w/c pastes with SRA.

Fig. 2: Internal RH reduction in 0.25, 0.30, and 0.35 w/c pastes.

Fig. 2: Internal RH reduction in 0.25, 0.30, and 0.35 w/c pastes with SRA.

Finish hydrostatic creep testingPredict autogenous and drying shrinkage strains using modelExpand model to determine stress development due to aggregate, external restraint, and moisture gradientMeasure viscoelastic Young’s modulus to complete constitutive relations for hardened cement pasteUse FEM to apply model to more complex structures