New formula for scour depth at piles based on energy equilibrium

Abstract

An accurate prediction of local scour depth at piles is essential for bridge safety. Lots of formulae were proposed but most of them are empirical ones without rigorous analysis. In this study a new formula for predicting maximum scour depth is established on the basis of the balance between the energy required for scour caused by downflow, longitudinal flow as well horseshoe vortex and the energy of sediment moving out of the scour hole. The present formula including its coefficient is entirely derived from theoretical analysis, making it more convincing and precise, hence is more reliable than other existing formulas for predicting maximum scour depth at piles. It is of both theoretical and computational significance that the exponents of our formula items are all rational numbers, namely the dimensionless scour depth at piles is proportional to 2/3 power of the Froude number, 1/3 power of the relative pier width and 1/3 power of the characteristic sediment parameter. The maximum scour depth calculated from our formula agrees well with the measured data from laboratory and field site.