Free shrinkage

1
INTERNAL RELATIVE HUMIDITY AND DRYING STRESS
GRADIENTS IN CONCRETE
Z.C. Grasley, D.A. Lange, M.D. DAmbrosia
Discussion
Experimental
Introduction Theory

• 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

• 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

• 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 Hookes Law
• ?T ?sh ?cr ?el
• Fully restrained shrinkage specimens have both
  internal and external restraint

p vapor pressure (constant) p pore fluid
pressure RH internal RH R universal gas
constant T temperature in kelvins v molar
volume of water
Results
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
Conclusions

• 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

?T measured free shrinkage strain ?sh
potential free shrinkage strain ?cr creep
strain from B3 Econcrete modulus of elasticity
of concrete
Failed at 3.5 days
Failed at 7.7 days
References

• 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.

scr stress relaxed due to drying stress
gradient and applied restraint