Fractional Stochastic Wave Modeling of Ultrasonic Attenuation in Particulate Cementitious Heterogeneous Media

Ultrasonic attenuation in particle–cementitious heterogeneous media results from the coupled effects of matrix memory dissipation and particle-induced random heterogeneity, which cannot be readily distinguished using conventional homogeneous-medium models. This study develops a unified stochastic fractional wave framework that couples Caputo fractional dissipation with a random-potential representation of spatial heterogeneity. The main contribution is an analytically tractable amplitude–phase formulation that separates the leading-order roles of the two mechanisms: fractional dissipation primarily governs exponential amplitude attenuation, with k(w)∝w α−1, whereas the random potential mainly modulates local phase propagation and introduces finite scattering-type amplitude corrections. By transforming the governing equation into a frequency-domain Helmholtz form and applying Wentzel–Kramers–Brillouin (WKB) asymptotic analysis, explicit scaling relations are obtained for both attenuation and phase fluctuations. Two-dimensional Helmholtz simulations support the predicted attenuation law and show that the relative L2 error of the WKB phase prediction decreases from 25.23% to 5.36%, while the covariance-based fixed-receiver ensemble phase-variance prediction lies within the 95% confidence interval of 30 independent realizations. Single-frequency ultrasonic transmission experiments provide complementary trend-level evidence, showing reduced tail retention and increased descriptive tail attenuation with increasing particle volume fraction. The proposed framework provides a mechanistically interpretable basis for distinguishing dissipation-dominated and heterogeneity-induced ultrasonic responses.