Engineering methods to deal with pier-scour problems include placing coarse riprap stones around the bridge pier. This study aims to investigate the stability of a riprap layer around a cylindrical bridge pier. Experiments conducted in a laboratory flume identified three different modes of riprap failure. They can act singly or combine to render a complete failure of the riprap layer. These modes of failure are riprap shear failure, winnowing failure, and edge failure. The study proposes a semiempirical method to size stones for riprap protection. The procedure for this method was illustrated with field data from three different bridge sites. The experimental data show that a thick riprap layer can prevent winnowing in the absence of a filter layer. The thick riprap layer can also sustain a partial breakup of the layer with the capability of rearmoring the scour hole, preventing a total disintegration of the riprap layer. Finally, the study proposes two empirical relationships, which describe the effect of riprap thickness and cover on the stability of the riprap layer.