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MECHANISMS Constant Uniaxial Tension Autogenous Shrinkage Elastic Viscoelastic Time Stress Time Stress * * * Not an exact analytical solution for partially saturated material K 0 = viscoelastic non-ageing K = viscoelastic ageing Saturated pore Empty pore Autogenous Shrinkage as a Viscoelastic Response to Self-Desiccation MEASUREMENTSEXPERIMENTAL RESULTSMOTIVATION 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 is autogenous shrinkage important? 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 Why do we need a viscoelastic model? 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 Are there any other uses for this model? Fig. 1: RH (~stress) and shrinkage plots indicating probable viscoelastic response of hardened cement paste Zachary C. Grasley & David A. Lange 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 C-S-H MODEL BASICS 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 Strain indicator box Hydraulic pump and pressure regulator Embedment strain gage FUTURE WORK The approximate linear elastic solution for the strain in the model system is given by: S = saturation factor = pore fluid pressure determined by K-L equation and RH K = bulk modulus of porous solid K 0 = 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 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) Time Autogenous shrinkage Viscoplastic Viscoelastic Recoverable shrinkage Instantaneous elastic Standard linear model Flexible corrugated tubing for sealed, restraint-free measurement of autogenous shrinkage Embedded pins for length measurement Internal RH measurement Hydrostatic creep test for determination of viscoelastic bulk modulus Fig. 2: Autogenous shrinkage of 0.25, 0.30, and 0.35 w/c pastes. 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. Fig. 2: Internal RH reduction in 0.25, 0.30, and 0.35 w/c pastes with SRA. 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

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