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Probabilistic evaluation of concrete freeze-thaw design guidance

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Abstract

A novel limit-state function using Powers’ models is developed to assess current freeze-thaw exposure categories and design criteria for concrete placements established by American, Canadian, and European standards organizations. Based upon performance assessments by standardized accelerated testing, the current specifications are shown to provide sufficient levels of reliability pending an appropriate mean air-void spacing factor. Sensitivity assessments of the model demonstrate that the spacing factor, saturation state, permeability, and freezing rate significantly influence the response of the air-entrained concrete. The model is validated with a large dataset derived from standard freeze-thaw tests, and an equation is developed to probabilistically design concrete for freeze-thaw resistance.

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Abbreviations

FT:

Freeze-thaw

ACI:

American Concrete Institute

CSA:

Canadian Standard Association

BS EN:

British Standard European Norm

LS:

Limit-state

DF:

Durability factor

OPC:

Ordinary Portland cement

w/c :

Water-to-cement ratio

FORM:

First order reliability method

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Acknowledgements

This material is based upon work support under a Department of Energy, Office of Nuclear Energy, Integrated University Program Graduate Fellowship. The authors would also like to acknowledge the ACI Concrete Research Council for their interest and support for modernizing of freeze-thaw design provisions.

Funding

The only funding source received was a graduate fellowship provide to author Scott Smith from the Department of Energy, Office of Nuclear Energy, Integrated University Program. Any opinions, findings, conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the Department of Energy Office of Nuclear Energy.

Author information

Authors and Affiliations

  1. Georgia Institute of Technology, 790 Atlantic Drive NW, Room 5132, Atlanta, GA, 30318, USA

    Scott H. Smith

  2. Georgia Institute of Technology, 790 Atlantic Drive NW, Room 4154, Atlanta, GA, 30318, USA

    Kimberly E. Kurtis

  3. Georgia Institute of Technology, 790 Atlantic Drive NW, Room 4140A, Atlanta, GA, 30318, USA

    Iris Tien

Authors
  1. Scott H. Smith
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  2. Kimberly E. Kurtis
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  3. Iris Tien
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Corresponding author

Correspondence to Kimberly E. Kurtis.

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Appendix: Notation list

Appendix: Notation list

  • A: Total entrained air content (%)

  • \(\alpha_{\text{H}}\): Degree of cement hydration (%).

  • \(\beta\): Reliability index.

  • DF: Measurement ASTM C666 Durability Factor (%).

  • \(\epsilon\): Paste capillary porosity (Volume fraction).

  • fc: Concrete compressive strength (MPa).

  • Fp: Paste fraction of concrete mixture (Volume fraction).

  • K: Permeability of saturated, hardened cement paste (cm2).

  • L: Approximate thickness of hardened cement paste shell (m).

  • \(\bar{L}\): ASTM C457 Powers’ spacing factor.

  • \(\overline{{L_{1} }}\): Powers’ spacing factor for pf/A less than 4.32.

  • \(\overline{{L_{\text{h}} }}\): Powers’ spacing factor for pf/A greater than 4.32.

  • \(\mu\): Distribution mean.

  • \(\eta\): Viscosity of water near 0 °C, Pa * s.

  • Pf: Probability of failure, (%).

  • \(P_{\text{f}} \left( {\overline{{L_{\text{H}} }} } \right)\): Probability of failure function (%), \(\overline{{L_{\text{h}} }}\) has units of millimeters.

  • U: Weight of water present per volume of cement paste, (kg * °C−1).

  • R: Freezing rate, (°C * h−1).

  • rb: Radius of entrained air void, (m).

  • \(\rho_{\text{c}}\): Density of cement, (kg * m−3).

  • \(\rho_{\text{w}}\): Density of water, (kg * m−3).

  • Scp: Saturation of paste capillary porosity.

  • Sfc: Slope of the tensile strength model.

  • \(\sigma\): Distribution standard deviation.

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Smith, S.H., Kurtis, K.E. & Tien, I. Probabilistic evaluation of concrete freeze-thaw design guidance. Mater Struct 51, 124 (2018). https://doi.org/10.1617/s11527-018-1259-z

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