Correlation of Elastic Modulus and Permeability in Concrete Subjected to Elevated Temperatures

The laboratory testing of concrete has shown that elevated temperatures cause air permeability index (API) increase and elastic modulus $E$ decrease. Indeed, the API response typically spans several orders of magnitude making it a sensitive indicator of elastic modulus reduction. However, the API versus $E$ data has been historically assumed to be both event and concrete composition specific, thus limiting its applicability for predictive or modeling purposes. In response, a theoretical model is developed here by (1) establishing that the API is equivalent to the Darcy permeability; (2) developing a microcrack flow model accounting for tortuosity, crack density, and microcrack geometry; and (3) interpreting the Giordano and Colombo elastic modulus damage formulas in terms of the corresponding increase in permeability. The resulting general model depends on stress conditions (plane stress versus plane strain) and a single microcrack flow parameter. For materials with small Poisson’s ratios, however, the model becomes independent of stress condition and both equations converge on the same simple solution. The model is verified with both field and laboratory data of concrete response to typical fire elevated temperatures and shown to be comparable in accuracy to previous empirical approaches requiring many more degrees of freedom. Moreover, the data on fire damaged concrete were found to collapse to a single curve suggesting that the microcrack flow parameter is sensitive to elevated temperature but insensitive to concrete composition. The success of the model implies certain limits to microcrack geometry and airflow turbulence in damaged concrete, both of which are discussed.