# Fractional-Order Ultrasonic Sensing for Monitoring Microstructural Evolution in Cementitious Materials

## TL;DR

A new ultrasonic sensing method using fractional-order models tracks cement hardening, offering better accuracy than traditional methods.

## Contribution

A novel fractional-order ultrasonic framework is introduced to monitor cement hydration with physics-based accuracy.

## Key findings

- The fractional-order model outperforms classical and empirical models in tracking hydration.
- The parameter β reflects the viscoelastic transition during cement hardening.
- The framework enables real-time, physics-informed monitoring of cementitious materials.

## Abstract

Monitoring the early-age evolution of cementitious materials is essential for ensuring the quality and reliability of concrete structures. However, most ultrasonic approaches rely on empirical correlations and lack a physics-based mechanism to describe the continuous viscoelastic transition during hydration. This study proposes a fractional-order ultrasonic sensing framework that couples a fractional Zener viscoelastic model with ultrasonic attenuation theory to quantitatively link microstructural evolution and measured acoustic responses. A custom ultrasonic measurement system was developed to capture real-time attenuation during hydration under different water-cement ratios. Results show that the fractional-order model achieves higher accuracy and robustness than classical integer-order and empirical models. The fractional parameter β serves as a physically interpretable indicator that reflects the transition from viscous-dominated to elastic-dominated behavior and aligns with known hydration development. The proposed framework provides a compact, physics-informed sensing strategy for early-age characterization of cementitious materials and offers potential for intelligent construction and high-end structural monitoring.