Weirs are constructed inside rivers to manage the water level. On the one hand they need to be designed sufficiently strong to prevent failure or destruction, while on the other hand they need to be economically feasible. If a structure is designed too strong, unnecessary costs are made and the structure becomes too expensive.

One of the potential failure mechanisms for weirs is erosion of the soil downstream of the weir. Bed protections consisting of rock and concrete are placed to prevent this erosion. Numerical modelling can give additional insight in the design of such a bed protection. This thesis aims to improve the design of bed protections downstream of underflow weirs through numerical modelling. This is done through two research objectives, being 1) proposing a numerical modelling strategy to create a design method for riprap bed protections downstream of underflow weirs, and 2) preserving a small computation time compared to full scale 3D models, as this is ideal for a future application in engineering.

A new approach is formulated by using the stability parameter of Steenstra (2014), ψRS, as basis. This parameter is based on multiple flow situations, except the underflow gate. For this reason the underflow gate is investigated in the current research. The output of the created OpenFOAM models can be applied to this parameter, leading to ψ-curves that can be compared with measured damage.

The first research objective is obtained by the application of three different turbulence mixing length approaches, of which two approaches created interesting results. The first approach is the Bakhmetev approach, leading to a conservative design outcome with a gradual decreasing stability pattern. The second is the Shear Stress Relation (SSR), leading to a promising result with better defined instability regions that compare with measured bed damage. From the desire to work conservatively, the results reveal that in the design phase of a bed protection downstream of a weir, the application of the Bakhmetev approach for the mixing length is recommended over the SSR approach.

Extended physical testing containing three aspects is needed to strengthen the promising findings of the SSR. These aspects are 1) a damage stone count including a sieve distribution, 2) a setup with varying gate heights and stone dimensions, and 3) varying water levels and discharges per different gate height and stone size. In addition a preliminary 2D numerical model study is advised, which allows to investigate the areas of interest for PIV flow measurements.

The second research objective is achieved by the application of a 2D RANS model and the simplification of the water level through a rigid lid. This simplification still leads to workable results, with computation time that are in the range of two to eight hours, operating on ten cores in one computer. This makes the approach attractive for engineering applications and for future applications in renovation tasks for weirs in the Meuse.