Transcript Slide 1

INTERNAL RELATIVE HUMIDITY AND DRYING STRESS
GRADIENTS IN CONCRETE
Z.C. Grasley, D.A. Lange, M.D. D’Ambrosia
Discussion
Experimental
Introduction & Theory
Objective:
•Create a 1-D model that quantifies the stress gradient in free shrinkage and fully
restrained drying concrete
Theory:
•Drying stress gradient is caused by restraint of shrinkage
•Restraint can either be internal or externally applied
•Internal restraint is provided by the requirement for translational symmetry (section
remains planar)
•Free shrinkage specimens have only internal restraint
•Measured free shrinkage strain, T, consists of 3 components
•sh - potential free shrinkage strain (in absence of any restraint)
•cr - strain relaxed by creep
•el - remaining strain required for strain compatibility, this strain has an
associated stress through Hooke’s Law
•T= sh + cr + el
•Fully restrained shrinkage specimens have both internal and external restraint
•Experimental methods
•An internal RH measurement system designed at the University of Illinois at
Urbana-Champaign was used to measure the internal RH gradient
•A special mold was used to cast RH sensors at incremental depths from the
drying surface
•RH sensors are packaged in small plastic tube with Gore-Tex cap
•Uniaxial test used to measure
•Free shrinkage
•Fully restrained average stress accumulation
•Average creep of fully restrained concrete
•Modulus of elasticity
•Materials
•Seven different concrete mixtures were tested for up to 7 days of age (6 days of
drying)
•The mixtures included w/cm ranging from 0.32 to 0.44 and mineral admixtures
such as fly ash and silica fume
•Free shrinkage
•Tensile stresses in surface layer exceed tensile strength of material
•Surface microcracking is likely result
•Stresses in surface layer are highest at beginning of drying, decreasing as drying
progresses
•Microcracks likely close up over time
Schematic of moisture gradient, deformation and surface cracking, and capillary
pressure in different stages of progressively drying hardened cement paste (from [3])
Drying Stress (surface)
Surface Strain Schematic
Applied Load-Restraint
T
sh
el
T
el
cr
sh
Inner Core Strain Schematic
Applied Load-Restraint
cr-app
Free shrinkage
drying stresses
Applied tensile
load or restraint
cr
Overall stress
gradient in restrained
concrete
•Fully restrained shrinkage
•Tensile stresses progressively increase as drying continues
•The time to tensile failure appears to be dependent on the severity of the drying
stress gradient
•In general, the lower w/cm materials exhibited more severe gradients and failed
at the earliest ages
•Low w/cm  lower permeability/diffusivity, which causes a steeper gradient in
the surface layer of the material
•Steeper gradient in surface layer may lead to wider surface cracks and thus
earlier failure
Sensor encased in a plastic tube with
GoreTex cap, ready to be cast in concrete
Special mold for casting RH sensors at incremental
depths in concrete prism
ft
Cumulative Stress
sh
el-app
T
el-app
el
cr-app
sh
T
T
el-app
cr
Drying Stress (core)
Cumulative Stress
T
cr-app
el-app
cr-app
Separation of free shrinkage drying stress gradient and applied restraint
ft represents the tensile strength of the concrete
el
cr
Schematic of strain components in free shrinkage and
restrained concrete
6
A-44
B-44
C-44
D-44
41
38
32
•Internal relative humidity (RH) has a fundamental relationship to the reduction in pore
fluid pressure that leads to early-age drying shrinkage in concrete
•Kelvin-Laplace equation:
p”= vapor pressure (constant)
Results
•Potential shrinkage strain, sh, can be determined by [1,2]:
•Creep strain, cr, can be determined using the B3 model
•So, the stress at any point across a free shrinkage specimen cross section is:
 el  ( T   sh )Econcrete   cr Econcrete
3 day
5 day
7 day
6
Stress (Mpa)
3
2
0
10
20
30
40
50
Specimen width (mm)
60
Econcrete = modulus of elasticity of concrete
5
Stress (MPa)
el
cr
ft
Average Stress
wcrack
el
cr
ft
Average Stress
3
4
5
6
7
8
9
Affect of increasing stress gradient slope on the width of
surface cracking in fully restrained, drying concrete
4
3
2
Conclusions
0
70
Free shrinkage stress gradient evolution (mixture A-44)
10
20
30
40
50
Specimen width (mm)
60
70
Restrained shrinkage stress gradient evolution (mixture A-44)
50
Failed at 3.5 days
4
A-44
A-44 Average
B-44
B-44 Average
C-44
C-44 Average
D-44
D-44 Average
41
41 Average
38
38 Average
32
32 Average
A-44 3 days
A-44 5 days
A-44 7 days
32 3 days
32 5 days
32 7 days
45
40
Failed at 7.7 days
3
2
 el   sh Econcrete   cr
1
Correlation between failure age and drying stress
gradient severity in restrained, drying concrete
-1
-1
6
scr = stress relaxed due to drying stress gradient
and applied restraint
wcrack
Increasing slope of
gradient at surface
0
0
T = measured free shrinkage strain
sh = potential free shrinkage strain
cr = creep strain from B3
•In a fully restrained specimen, the total measured strain is zero, so the stress across
the specimen cross section is:
2
Failure Age (Days)
1
1
3
2
3 day
5 day
7 day
5
4
4
0
6
5
Stress (Mpa)
1
1 vp
 sh  pS[  ]
3k 3k 0 vt
p= reduction in pore fluid pressure
S= saturation factor
K= bulk modulus of hardened cement paste
k0= bulk modulus of solid hydration products
skeleton
vp= volume of paste
vt = volume of concrete
7
7
Internal RH change (%)
ln( RH ) RT
p" p' 
v
Small, digital internal RH sensor
Schematic of the twin uniaxial specimens
(fully restrained and free)
p’= pore fluid pressure
RH= internal RH
R= universal gas constant
T= temperature in kelvins
v= molar volume of water
Differential Stress (MPa)
5
35
30
References
25
20
15
10
1
5
0
0
0
10
20
30
40
50
60
70
Specimen Width (mm)
Restrained shrinkage stress distribution at time of failure
(load removed from B-44 prior to failure)
•1-D Drying stress gradient can be modeled from the internal RH gradient
•In fully restrained concrete, the drying stress gradient appears to affect the time
to tensile failure (cracking)
•Materials that exhibit a more severe drying gradient may fail sooner
•Materials that are less permeable/diffusible may have a more severe drying
gradient, with a steeper gradient slope in the surface layer
0
10
20
30
40
50
60
70
Specimen Width (mm)
Internal RH gradient evolution for 2 mixtures
1. Mackenzie, J.K., The Elastic Constants of a Solid Containing Spherical Holes, Proc Phys Soc B
683 (1950), 2-11
2. Bentz, D.P., Garboczi, E.J., Quenard, D.A., Modelling Drying Shrinkage in Reconstructed Porous
Materials: Application to Porous Vycor Glass, Modelling Simul Mater Sci Eng 6 (1998), 211-236.
3. Hwang, C.-L., Young, J.F., Drying Shrinkage of Portland Cement Pastes I. Microcracking During
Drying, Cem and Conc Res 14 (1984), 585-594.