Multiscale wave dispersion in Sand–Gravel mixtures: Insights from micromorphic modeling

Abstract

This study presents a novel micromorphic continuum model for sand–gravel mixtures with low gravel contents, which explicitly accounts for the influences of the particle size distribution, gravel content, and fabric anisotropy. This model is rigorously formulated based on the principle of macro–microscopic energy conservation and Hamilton’s variational principle, incorporating a systematic analysis of the kinematics of coarse and fine particles as well as macro–microscopic deformation differentials. Dispersion equations for plane waves are derived to elucidate wave propagation mechanisms. The results demonstrate that the model effectively captures normal dispersion characteristics and size-dependent effects on wave propagation in these mixtures. In long-wavelength regimes, wave velocities are governed by macroscopic properties, whereas decreasing wavelengths induce interparticle scattering and multiple reflections, attenuating velocities or inhibiting waves, especially when wavelengths approach interparticle spacing. The particle size, porosity, and stiffness ratio primarily influence the macroscopic average stiffness, exhibiting consistent effects on dispersion characteristics across all wavelength domains. In contrast, the particle size ratio and gravel content simultaneously influence both macroscopic mechanical properties and microstructural organization, leading to opposing trends across different wavelength ranges. Model validation against experiments confirms its exceptional predictive ability regarding wave propagation characteristics, including relationships between low-pass threshold frequency, porosity, wave velocity, and coarse particle content. This study provides a theoretical foundation for understanding wave propagation in sand–gravel mixtures and their engineering applications.