Mechanism of Packing Rigidity Gain in Sand Aging: From the Perspective of Structural Order Evolution

Rigidity gain can be observed in sand aging but is usually accompanied by minute densification. This phenomenon is inconsistent with the conventional diagram of rigidity/jamming transition for granules and therefore too enigmatic to be utilized in the field by engineers. Therefore, this study aims to reveal the mechanism of rigidity gain and reconcile the inconsistency in sand aging. The aging processes of two sand packings with the same mono-sized spheres but different initial densities were reproduced via discrete element method simulations. In the simulations, sudden increases in the solid fraction destroyed the similarity between the evolution processes of rigidity gain and densification, confirming the inadequacy of explaining this gain considering densification alone. The bond-orientational order remained almost unchanged, while the contact-force order generally increased over time with distinct drops, similar to the change in rigidity gain. This evolution pattern is attributed to the laws of thermodynamics, which require the Gibbs energy of the sand packing to decrease over time, and contact-force order reduction assists with this decrease. Simultaneously, this reduces the nonaffinity under shear and rigidity demolition, consequently dominating the rigidity gain mechanism in sand aging. Based on these findings, the conventional diagram of rigidity transition was modified to jointly consider the effects of the solid fraction and structural orders. The proposed diagram can depict how the sand packing rigidity is enhanced over time and can better guide the consideration of the sand aging effect in the field.