free shrinkage tensile stresses in surface layer exceed tensile strength of material surface...
TRANSCRIPT
•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
•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
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 creepel - remaining strain required for strain compatibility, this strain has an associated stress through Hooke’s LawT= sh + cr + el
•Fully restrained shrinkage specimens have both internal and external restraint
•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:
•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:
•In a fully restrained specimen, the total measured strain is zero, so the stress across the specimen cross section is:
INTERNAL RELATIVE HUMIDITY AND DRYING STRESS GRADIENTS IN CONCRETE
Z.C. Grasley, D.A. Lange, M.D. D’Ambrosia
Introduction & Theory Experimental•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
Discussion
•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
Results
Conclusions
v
RTRHpp
)ln('"
p”= vapor pressure (constant)p’= pore fluid pressureRH= internal RHR= universal gas constantT= temperature in kelvinsv= molar volume of water
t
psh v
v
kkpS ]
3
1
3
1[
0
p= reduction in pore fluid pressureS= saturation factorK= bulk modulus of hardened cement pastek0= bulk modulus of solid hydration products skeletonvp= volume of pastevt = volume of concrete
concretecrconcreteshTel EE )(T = measured free shrinkage strainsh = potential free shrinkage straincr = creep strain from B3Econcrete = modulus of elasticity of concrete
crconcreteshel E scr = stress relaxed due to drying stress gradient and applied restraint
-1
0
1
2
3
4
5
6
7
0 10 20 30 40 50 60 70Specimen width (mm)
Stre
ss (M
pa)
3 day5 day7 day
Free shrinkage stress gradient evolution (mixture A-44)
-1
0
1
2
3
4
5
6
7
0 10 20 30 40 50 60 70Specimen width (mm)
Stre
ss (M
pa)
3 day5 day7 day
Restrained shrinkage stress gradient evolution (mixture A-44)
0
5
10
15
20
25
30
35
40
45
50
0 10 20 30 40 50 60 70
Specimen Width (mm)
Inte
rnal
RH
cha
nge
(%)
A-44 3 days
A-44 5 days
A-44 7 days
32 3 days
32 5 days
32 7 days
Internal RH gradient evolution for 2 mixtures
ft
Free shrinkage drying stresses
Applied tensile load or restraint
Overall stress gradient in restrained
concrete
Separation of free shrinkage drying stress gradient and applied restraintft represents the tensile strength of the concrete
Small, digital internal RH sensor
Sensor encased in a plastic tube with GoreTex cap, ready to be cast in concrete
Schematic of the twin uniaxial specimens (fully restrained and free)
Special mold for casting RH sensors at incremental depths in concrete prism
Schematic of moisture gradient, deformation and surface cracking, and capillary pressure in different stages of progressively drying hardened cement paste (from [3])
0
1
2
3
4
5
6
0 10 20 30 40 50 60 70
Specimen Width (mm)
Stre
ss (M
Pa)
A-44A-44 AverageB-44B-44 AverageC-44C-44 AverageD-44D-44 Average4141 Average3838 Average3232 Average
Restrained shrinkage stress distribution at time of failure (load removed from B-44 prior to failure)
Failed at 3.5 days Failed at 7.7 days
References
0
1
2
3
4
5
6
2 3 4 5 6 7 8 9
Failure Age (Days)
Diff
eren
tial S
tress
(MP
a)
A-44B-44C-44D-44413832
Correlation between failure age and drying stress gradient severity in restrained, drying concrete
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.
Affect of increasing stress gradient slope on the width of surface cracking in fully restrained, drying concrete
ft
wcrack
el
cr Average Stress
ft
wcrack
el
cr Average Stress
Increasing slope of gradient at surface
ft
wcrack
el
cr Average Stress
ft
wcrack
el
cr Average Stress
Increasing slope of gradient at surface
Schematic of strain components in free shrinkage and restrained concrete
sh
cr
el
Drying Stress (surface)
T
cr-app
el-app
Applied Load-Restraint
T Tcr-app
el-app
Cumulative Stress
sh
el
cr
Surface Strain Schematic
T
cr
el
Drying Stress (core)
T
cr-app
el-app
Applied Load-Restraint
sh shcr-app
el-app
Cumulative Stress
T
el
cr
Inner Core Strain Schematic
sh
cr
el
Drying Stress (surface)
T
cr-app
el-app
Applied Load-Restraint
T Tcr-app
el-app
Cumulative Stress
sh
el
cr
Surface Strain Schematic
T
cr
el
Drying Stress (core)
T
cr-app
el-app
Applied Load-Restraint
sh shcr-app
el-app
Cumulative Stress
T
el
cr
Inner Core Strain Schematic