A novel model for predicting the permeability of square and cylindrical particle assemblies under creeping flow

Particles are a type of discrete structure commonly found in nature and engineering. They are characterized by large particle sizes, low tortuosity, and high porosity. The flow behavior within these particle swarms differs from seepage in traditional porous media and fractures, exhibiting significant cross-scale characteristics that influence the water cycle. Existing permeability models designed for porous media fail to accurately predict the permeability of discrete particle swarms, making the prediction of such a permeability a key focus and research hotspot in engineering practice. This paper focuses on the structures of massive and circular granular assemblages, develops a novel model to describe the permeability of granular swarms based on the creeping flow theory, and validates the model via computational fluid dynamics methods. Studies have shown that within the relatively high porosity range of 0.3–0.4, the permeability of discrete blocky assemblages can be characterized by the novel normalized model k/r2 = α31/1−φ−12, with an applicable Reynolds number (Re) range of Re < Rec (where the critical Reynolds number Rec = 1.5). For discrete pillar assemblages, their permeability can be characterized by another improved normalized model k/r2 = β30.9523/1−φ−12, with an applicable range of Re < Rec (where Rec = 6.2). It is found that the permeability of discrete bodies is higher than that of traditional porous media, which well explains the effect of low tortuosity on permeability. The proposed improved permeability model can provide valuable references for the engineering evaluation of permeability in discrete blocks and pillars.