Affinity and similarity of local scour holes at bed sills

Excessive erosion of gravel bed rivers represents a hazard, which is often controlled by the construction of bed sills. Shape and volume of equilibrium local scour holes at bed sills in high-gradient streams were investigated by analyzing steady-flow experimental data. Scour profiles were normalized by scaling the depths and the longitudinal distance from the upstream sill with the maximum dimensions of the scour hole. Results exhibited a universal geometrical affinity of the scour. Geometrical similarity was also found to occur, but only in a limited range of physical conditions. Evidence on the scaling nature of the scour hole shapes have important implications on the prediction of the eroded volume. In turn, a correct evaluation of the eroded volume is necessary for the optimization of the design of the inter-sill distance. Prediction formulae are proposed which link the eroded volume to the geometrical, hydraulic and sediment properties.