Analytical framework for modelling body-wave scattering and diffusion in concrete

This work presents a concrete-specific analytical framework for modelling body-wave scattering by explicitly tailoring multiple-scattering theory to the microstructural characteristics of concrete. Instead of treating scattering parameters as abstract statistical quantities, the framework parameterizes the key inputs of scattering theory in terms of physically measurable concrete attributes, including coarse aggregate size, volume fraction, and the material property contrast between the matrix and the dominant scattering phase, whether coarse aggregates or the interfacial transition zone. By embedding these microstructure-informed parameters into a two-phase spatial statistical formulation, closed-form expressions for total and transport scattering cross-sections are derived and directly linked to ultrasonic diffusivity through diffuse wave theory. Experimental validation using geopolymer concrete members and published data for ordinary concrete demonstrates consistent agreement between theoretical predictions and experimental measurements across a broad frequency range. The proposed framework therefore renders body-wave scattering in concrete quantitatively computable from material composition, providing a physically grounded basis for quantitative interpretation of diffuse wave transport, energy equilibration, and coda-wave velocity changes without reliance on ad hoc fitting parameters.