Granular matter is ubiquitous in both natural and industrial settings, and its unique physical properties have long been a focus of research. As a central theme in this field, granular packing is of particular significance due to its direct relevance to industrial applications. Among various particle shapes, spheres, owing to their high symmetry and geometric simplicity, serve as the most ideal model for investigating packing problems.
In this study, the granular packing was subjected to continuous external vibration by tapping. The volume fraction at different times was obtained by combining X-ray tomography with Watershed image processing algorithms and Voronoi tessellation.
The results show that under different vibration intensities, the relationship between volume fraction and the number of vibrations is described by the Kohlrausch–Williams–Watts (KWW) function. However, a non-monotonic relationship was observed between the steady-state volume fraction and vibration intensity, indicating that external excitation does not simply "accelerate densification" but may also alter the accessible configuration space and rearrangement pathways of the system. To uncover the structural mechanisms behind this non-monotonic behavior, we introduced structural descriptors such as contact number and Minkowski tensors. The analysis revealed that even when systems reach the same volume fraction under different vibration intensities, their internal structures exhibit significant differences in their scale and morphological features. By further calculating relevant thermodynamic quantities and combining with the Adam–Gibbs (AG) relation, we find that a crossover in the AG relation occurs at the turning point of the volume fraction. This phenomenon is hypothesized to be related to a transition in relaxation mechanisms: at higher vibration intensities, granular packing relaxation is dominated by inertial vibration; as vibration intensity decreases, relaxation shifts to a combination of vibration-driven inertial motion and contact sliding; and at very low vibration intensities, relaxation becomes entirely governed by interparticle contact sliding. These findings not only provide important experimental evidence for understanding the aging behavior of granular materials but also suggest that multiple relaxation mechanisms may exist in granular systems under different vibrational conditions, offering insights for further research in related fields.