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

## TL;DR

This paper introduces a new model to predict ultrasonic attenuation in concrete with random aggregates, improving accuracy for non-destructive evaluation.

## Contribution

A path-integrated ultrasonic attenuation model is proposed using a modified Waterman–Truell theory with multiple scattering corrections.

## Key findings

- The proposed model achieves 7.29% mean absolute percentage error in predicting ultrasonic attenuation.
- Path-dependent attenuation behavior is governed by local aggregate distribution in concrete.
- The model captures spatial variations in aggregate volume fraction through path integration.

## Abstract

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.