Damage detection in concrete using diffuse ultrasound measurements and an effective medium theory for wave propagation in multi-phase materials
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Heterogeneities in concrete caused by the random distribution of aggregate in the cement-paste matrix lead to strong scattering of ultrasound waves at wavelengths on the order of the aggregate. Use of these high frequencies is necessary to detect damage at an early stage, something that is not possible with conventional ultrasonic methods. The ultrasound energy density in this regime can be described by the diffusion equation. The objective of this research is to develop a quantitative understanding of the effects of additional scattering sources, such as small cracks in the cement-paste matrix, on the parameters of the diffusion equation; these parameters are the diffusion and the dissipation coefficients. Experimentally measured ultrasonic waves are processed using the diffusion theory to determine the diffusivity and the dissipation coefficients as a function of frequency. The samples employed are made of a Portland cement-paste matrix and regular aggregate such as gravel and sand. The results provide a basic understanding of the repeatability and consistency of diffusion measurements, with an emphasis on the nondestructive evaluation of damage in concrete. In addition, a method to describe concrete in the coherent regime is examined. Existing wave propagation models for inhomogeneous materials deal with two-phase mixtures, mostly the matrix-inclusion system such as fiber-reinforced composites. There are, however, numerous examples of multi-phase materials in which more than one phase is suspended in a matrix-phase. This research considers concrete, in which cement paste and aggregates with different sizes and mechanical properties are mixed together. Most of the models for two-phase composites cannot be extended to a multi-phase composite. Among others, the effective medium theory is considered here for two reasons: first, the formalism in this theory can easily be extended to multi-phase cases; second, the theory does not strictly define a specific microstructure between phases, which allows for a simulation of the microstructure in which different inclusions are in contact. The mathematical formulation is presented that yields the formulae for the effective density and the effective bulk and shear moduli. Finally, the calculated wave speeds and attenuations for different materials are compared with experimental results.