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 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 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 p”= vapor pressure (constant) p’= pore fluid pressure RH= internal RH R= universal gas constant T= temperature in kelvins v= molar volume of water p= reduction in pore fluid pressure S= saturation factor K= bulk modulus of hardened cement paste k 0 = bulk modulus of solid hydration products skeleton v p = volume of paste v t = volume of concrete  T = measured free shrinkage strain  sh = potential free shrinkage strain  cr = creep strain from B3 E concrete = modulus of elasticity of concrete s cr = stress relaxed due to drying stress gradient and applied restraint Free shrinkage stress gradient evolution (mixture A-44) Restrained shrinkage stress gradient evolution (mixture A-44) Internal RH gradient evolution for 2 mixtures ftft Free shrinkage drying stresses Applied tensile load or restraint Overall stress gradient in restrained concrete Separation of free shrinkage drying stress gradient and applied restraint ft 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]) 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 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), 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), Hwang, C.-L., Young, J.F., Drying Shrinkage of Portland Cement Pastes I. Microcracking During Drying, Cem and Conc Res 14 (1984), Affect of increasing stress gradient slope on the width of surface cracking in fully restrained, drying concrete Schematic of strain components in free shrinkage and restrained concrete