Simplified formula of riprap initiation for bridge pier local scour protection based on Hertz contact theory

In order to study the riprap initiation for bridge pier local scour protection in theory, the horseshoe vortex was simplified to analyze the bottom velocities around the bridge, including velocities at the front and both sides of bridge pier. The Hertz contact theory was used to analyze the motion of riprap and a simplified formula of the riprap initiation for bridge pier local scour protection was proposed, which was compared with the empirical equation and practical projects. The results show that bottom velocities at the sides of bridge pier are larger than that at the front of bridge pier. When the approach velocity is smaller than 4 m·s^-1, the riprap protection can be used, with the rock diameter less than 0.9 meter and rock quality less than 1 t. When the approach velocity is larger than 4 m·s^-1, other measures are recommended for local scour protection. The simplified formula is proved to be in accord with the empirical equation and practical projects.