Fractal expression of sand grain equivalent roughness

Accurate determination of sand grain equivalent roughness is the key to calculate sand grain resistance. In this paper, fractal dimensions were used to describe self-similar complexity and irregularity of sand bed profile. The fractal expression of sand grain equivalent roughness was obtained based on a large number of sand grain resistance experiments, which include sediment-glued flat bed, initially flat stationary bed and armoring bed. The median size d₅₀, fractal dimension D and Froude number Fr are introduced in the proposed expression along with corresponding validation, comparison and discussion of results. The results showed that the expression can comprehensively reflect how equivalent roughness of sand grain is influenced by external factors such as grain size, gradation composition, random arrangement and flow condition.