Path-Integrated Ultrasonic Attenuation Modeling for Concrete with Random Aggregates Based on Modified Waterman–Truell Theory

Ultrasonic sensing is an effective tool for characterizing heterogeneous concrete structures, yet quantitative interpretation of ultrasonic attenuation remains challenging due to aggregate-induced multiple scattering and spatial non-uniformity. This study proposes a path-integrated ultrasonic attenuation modeling framework for concrete with random aggregates. A quasi-one-dimensional discretized wave equation is coupled with a modified version of the Waterman–Truell effective medium theory, in which multiple scattering effects are corrected by incorporating a Percus–Yevick structure factor and a geometric equivalence scheme for non-spherical aggregates. By discretizing the propagation path into locally homogeneous layers, cumulative attenuation is evaluated through explicit path integration, allowing spatial variations in aggregate volume fraction to be captured. Low-frequency ultrasonic transmission experiments (25 kHz) are conducted using serially assembled concrete specimens with controlled aggregate contents. The results reveal pronounced path-dependent attenuation behavior governed by local aggregate distribution. Compared with classical and effective Waterman–Truell models, the proposed approach significantly improves prediction accuracy, achieving a mean absolute percentage error of 7.29%. The framework provides a physically interpretable and experimentally validated method for ultrasonic sensing of heterogeneous concrete, with potential applications in non-destructive evaluation and structural health monitoring of high-end concrete-based engineering structures.