1. Autogenous Shrinkage as a Viscoelastic Response to Self-Desiccation s s  MOTIVATION MEASUREMENTS MODEL BASICS FUTURE WORK EXPERIMENTAL RESULTS Embedded pins for length measurement Embedment strain gage Strain indicator box Hydraulic pump and pressure regulator Autogenous Shrinkage Constant Uniaxial Tension MECHANISMS  Stress Stress  s s s s Time Time Elastic Viscoelastic Elastic Viscoelastic * *  Saturated pore C-S-H C-S-H K0 = viscoelastic non-ageing * Not an exact analytical solution for partially saturated material  “Extra” water remains in small pores even at a=1 Fig. 1: RH (~stress) and shrinkage plots indicating probable viscoelastic response of hardened cement paste 0.50 w/c Empty pore K = viscoelastic ageing Chemical shrinkage ensures some porosity remains even at a=1 Cement grains initially separated by water Initial set locks in paste structure Autogenous shrinkage Standard linear model 0.30 w/c Autogenous shrinkage Viscoplastic Instantaneous elastic Pores to 50 nm emptied Internal RH and pore fluid pressure reduced as smaller pores are emptied Viscoelastic Recoverable shrinkage Increasing degree of hydration Time Zachary C. Grasley & David A. Lange Why is autogenous shrinkage important? Flexible corrugated tubing for sealed, restraint-free measurement of autogenous shrinkage • 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 • Modern concretes incorporate mineral admixtures and low w/c • Hydration and pozzolanic reaction of these materials leads to self- dessication (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 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 stress- strain relationship Hydrostatic creep test for determination of viscoelastic bulk modulus Internal RH measurement Are there any other uses for this model? • The approximate linear elastic solution for the strain in the model system is given by: • 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 • 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 • 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 Fig. 2: Autogenous shrinkage of 0.25, 0.30, and 0.35 w/c pastes. Fig. 2: Internal RH reduction in 0.25, 0.30, and 0.35 w/c pastes. • 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  = pore fluid pressure RH = internal humidity R = univ. gas constant T = temp. in kelvins v’ = molar vol. of water Fig. 2: Autogenous shrinkage of 0.25, 0.30, and 0.35 w/c pastes with SRA. Fig. 2: Internal RH reduction in 0.25, 0.30, and 0.35 w/c pastes with SRA. • 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) • 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