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 a1
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