Transcript Slide 1

Autogenous Shrinkage as a Viscoelastic Response to Self-Desiccation
Zachary C. Grasley & David A. Lange
MODEL BASICS
MOTIVATION
Why is autogenous shrinkage important?
Modern concretes incorporate mineral admixtures and low w/c
Hydration and pozzolanic reaction of these materials leads to selfdessication (internal drying that causes a reduction in internal RH)
Reduction in RH  reduction in capillary pressure  bulk shrinkage
If shrinkage is restrained, early-age cracking may be a significant problem
96
94
Embedded pins for length measurement

Saturated pore
0
Internal RH
Shrinkage
-100
90
88
-200
86
-300

Strain indicator box
84
-400
82
80
50
100
150
200
250
300
Empty pore
K = viscoelastic
ageing
-500
350
EXPERIMENTAL RESULTS
Fig. 1: RH (~stress) and shrinkage plots indicating
probable viscoelastic response of hardened cement paste
To obtain the viscoelastic solution, the transform analogy may be used
Viscoelastic stiffness parameters are shown with a bar
Shrinkage is simply a response to pore pressure and is analogous to any
other loading such as uniaxial tension
MECHANISMS
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 equation
In low w/c materials, enough water is removed from small pores to cause
curved menisci simply by hydration
C-S-H
 = pore fluid pressure
RH = internal humidity
R = univ. gas constant
T = temp. in kelvins
v’ = molar vol. of water


  J



Viscoelastic
Chemical shrinkage
ensures some porosity
remains even at a1
Time
Viscoelastic
S 1
S 1
1

(  )*
3 K K0
1

(  )*
3 K K0
  J
J
J
K0
K0
K
-800
-1000
90
85
80
75
-1400
70
-1600
0
10
20
30
Elapsed time (d)
40
50
0
60
K
10
20
30
Elapsed time (d)
100
100
98
-100
SRA35 avg
60
SRA30 avg
96
SRA30 avg
50
SRA25 avg
SRA25 avg
0
40
Fig. 2: Internal RH reduction in
0.25, 0.30, and 0.35 w/c pastes.
200
SRA35 avg
94
-200
-300
-400
92
90
88
86
-500
84
-600
82
-700
80
10
20
30
Elapsed time (d)
40
Fig. 2: Autogenous shrinkage of 0.25,
0.30, and 0.35 w/c pastes with SRA.
Standard linear model
Autogenous
shrinkage
Viscoplastic
Internal RH and pore fluid
pressure reduced as
smaller pores are emptied
-600
0
Autogenous
shrinkage
Pores to 50 nm
emptied
0.35
-400
50
0
10
20
30
40
50
Elapsed time (d)
Fig. 2: Internal RH reduction in 0.25,
0.30, and 0.35 w/c pastes with SRA.
* Not an exact analytical solution for partially saturated material
0.50
w/c
0.30
w/c
0.30
-1200

Elastic
0.25 w/c
0.30 w/c
0.35 w/c
95
Fig. 2: Autogenous shrinkage of
0.25, 0.30, and 0.35 w/c pastes.
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 parameters
Aging should be accounted for (e.g. solidification theory)
Initial set locks in
paste structure
0.25
-200
Stress
Time
“Extra” water remains in
small pores even at a=1
Cement grains
initially separated by
water

Stress

Elastic
0
Autogenous Shrinkage
Constant Uniaxial Tension

100
200
Internal RH (%)
 sh  paste
S 1 1

(  )
3 k k0
S = saturation factor
 = pore fluid pressure determined by K-L equation and RH
K = bulk modulus of porous solid
K0 = bulk modulus of solid material alone
Shrinkage (mstrain)
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
The approximate linear elastic solution for the strain in the model system
is given by:
Shrinkage (mstrain)
Are there any other uses for this model?
C-S-H
Internal RH measurement
Elapsed Time (hr)
ln( RH ) RT
 
v'
Hydraulic pump and
pressure regulator
Hydrostatic creep test for determination
of viscoelastic bulk modulus
Internal RH (%)
92
Shrinkage (m)
Internal Relative Humidity (%)
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
K0 = viscoelastic
non-ageing
100
0
Flexible corrugated tubing for sealed, restraint-free
measurement of autogenous shrinkage
Embedment
strain gage
Why do we need a viscoelastic model?
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 stressstrain relationship
MEASUREMENTS
Viscoelastic
Instantaneous elastic
Recoverable shrinkage
Increasing degree of hydration
Time
FUTURE WORK
Finish hydrostatic creep testing
Predict autogenous and drying shrinkage strains using model
Expand model to determine stress development due to aggregate,
external restraint, and moisture gradient
Measure viscoelastic Young’s modulus to complete constitutive relations
for hardened cement paste
Use FEM to apply model to more complex structures