Estimating diffusive body-wave properties in bounded concrete members using an energy-contribution-based image-source method

Reliable characterization of diffusive body-wave properties in concrete is essential for damage assessment and diffuse-wave-based imaging. However, existing approaches either neglect boundary reflections, thereby biasing the fitted properties, or rely on full analytical solutions for bounded domains, which greatly increase the complexity of curve fitting. In this study, an energy-contribution-based image-source method is proposed for concrete members with external planar concrete-air boundaries. The method retains only the image sources whose energy contributions are sufficiently large, thereby reducing model complexity while maintaining agreement with the bounded-domain solution. The method is evaluated using four concrete members with multiple pairs of ultrasonic sensors embedded. The experimental comparisons show that neglecting reflected energy underestimates both diffusivity and dissipation, with the strongest influence occurring at low frequencies. The comparisons across the four members show that retaining the dominant reflection terms achieves close agreement with the cuboid-domain benchmark, with only marginal improvement from additional reflections. These comparisons, together with the estimated reflection contributions, suggest approximately 30% as an empirical reference level for reflection screening in similar configurations. For the retained reflection configurations, the mean relative differences of diffusivity and dissipation remain below 2% for all four members when compared with the cuboid-medium reference solution, while the computational cost is much lower than that of the full analytical formulation. Across all members, diffusivity decreases with increasing frequency, and dissipation increases with increasing frequency. These results indicate that the proposed method provides a benchmark-consistent and computationally efficient approach to estimate frequency-dependent diffusive properties in bounded concrete members with approximately planar free concrete-air boundaries in the monitored region.