Universal power-law scaling in the packing structure of frictional granular materials

Friction-induced energy dissipation is one of the key factors contributing to the unique properties of granular materials, such as the preparation history dependence of the packing structure. However, it remains unclear whether or not more realistic systems that involve two or more types of friction possess unique properties distinct from those that are frictionless or with a single type of friction. Here, we use numerical simulations to investigate the packing structure of binary mixtures of particles with particle type-dependent friction coefficient. Taking single-component systems as reference, we use an effective friction coefficient μ_{e} to represent the overall frictional strength in granular systems prepared via different protocols. Our results demonstrate that μ_{e} exhibits a power-law dependence on the individual friction coefficients. Furthermore, we propose models that accurately predict the packing structure of frictional particle systems across a range of compositions, size ratios, and preparation protocols.