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Channel Curvature Effects on the Critical Froude Number for Shear Failure of Riprap Stones Used to Protect Abutments Against Erosion

Author(s): Hao Wu; Jie Zeng; George Constantinescu

Linked Author(s): Hao Wu, George Constantinescu

Keywords: Riprap protection; Wing wall abutments; Spill-through abutments; Numerical simulations

Abstract: Using riprap stone aprons around the base of a bridge abutment is one of the most common ways to ensure abutments will not fail due to severe erosion. The riprap size of the stones forming the apron should be large enough to avoid dislocation, in particular, via shear failure. Most design formulas for minimum riprap stone size at aprons used to protect abutments against erosion give the value of the critical Froude number, Fr, as a function of the ratio between the mean diameter of the riprap stone, D₅₀, and the local flow depth, ym. These formulas are obtained using data sets collected in laboratory studies conducted with abutments placed in straight channels. Severe erosion problems were observed at some riprap aprons designed based on these formulas. One possible reason is that such formulas do not account for cases where bank curvature effects are significant and, as a result, the maximum bed shear stress increases at the outer-bank abutment compared to the case the same abutment is placed in a straight channel. To account for such effects, the critical Froude number should also be a function of the ratio between the radius of curvature of the channel and the width of the channel, R/W. The present research describes a methodology based on fully, three-dimensional numerical simulations to improve the performance and range of applicability of riprap size design formulas used for erosion protection at wing-wall and spill-through abutments. In this method, the bed shear stress distributions are obtained from RANS simulations conducted in straight and curved open channels containing identical abutments at their two banks. The formula of Melville and Coleman (2000) is used to determine the shear-failure entrainment threshold for riprap stone of a certain size. For each channel configuration and abutment type, a series of simulations is performed to determine the critical Froude number corresponding to the shear-failure entrainment threshold when the maximum bed shear stress over the riprap apron will be equal to the threshold value for shear failure. Using the data sets generated using these series of numerical simulations, two parameter design formulas for riprap size selection at wing-wall and spill-through abutments are proposed. The new design formulas retain the same functional relationship as that of commonly used design formulas (e.g., Pagan-Ortiz, 1991; Lagasse et al., 2001), in which the nondimensional riprap diameter is a function of the critical Froude number (D₅₀/ym=C^α/2*Fr^α). In the new formulas, the model parameters, C and α, rather than being constants are a function of the main nondimensional geometrical parameters, including the nondimensional radius of curvature, R/W. Results show that α is not a function of R/W while C increases monotonically with decreasing R/W.


Year: 2022

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