Design Formula for Sizing Rock Riprap at Spill-Through Abutments in Compound Channels

Abstract

A numerically based investigation is carried out to determine the minimum median diameter of the riprap stone needed to avoid shear failure inside the riprap apron used to protect spill-trough abutments against erosion. The study considers identical spill-through abutments placed on the floodplains of a compound channel. Several series of Reynolds-averaged Navier-Stokes (RANS) simulations are conducted with varying floodplain width, $B_f$ , ratio between the abutment length and the floodplain width, $L_a/B_f$ , mean diameter of the riprap stone, $D_{50}$ , and channel curvature, $R$ , to estimate the maximum Froude number, Fr, at which riprap stones in aprons placed at the base of spill-through abutments will resist shear failure by the flow. A design formula for riprap size selection in aprons protecting spill-through abutments is proposed. The formula is expressed as $D_{50}/y=C^{0.5\alpha }*{\mathrm{Fr}}^{\alpha }$ , where $y$ is the flow depth next to the toe of the abutment. The two model parameters are $C$ and $\alpha$ . Results show that $\alpha$ is only a function of $B_f$ for abutments that do not extend until close to the main channel and $\alpha =1.85$ for abutments extending over the whole width of the floodplain.