Numerical estimation of upward pressure differences over a placed block revetment under wave loading on a dike

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Abstract

Placed block revetments on dikes are used for the protection of the structure against wave loading. The dimensions of the revetment are determined with empirical relations and design tools. The stability of the design solution needs to be checked by physical flume tests to ensure the safety of the structure. However, these tests can be costly and time-consuming. Research has to show whether computational fluid dynamics (CFD) can be used to improve the design process of the revetment and reduce the number of required physical flume tests. The most important load on a placed block revetment is an uplifting force that results from a (porous media) flow through the top and filter layer of the structure during wave-structure interaction. This study aimed to determine whether CFD modelling can accurately predict the uplift of the top layer of a placed block revetment and identify the optimal approach for modelling this type of revetment.

In order to reach this goal, an existing CFD model is used and validated with a physical test performed in the Delta Flume. First, the data from the physical test is extensively analysed to check how the results relate to the physical processes described in the literature. Next, a two-dimensional CFD model has been set up with the open-source software package OpenFOAM. To mimic the physical test, the model is created in 1:1 scale with all the structure dimensions similar to the Delta Flume set-up. The top layer in the physical test consisted of C-star blocks that have been schematized in order to model the structure as a two-dimensional model. Two different schematizations are proposed and tested on their performance. In the first schematization, the top layer is modelled as a continuum in which the resistance is determined by the Darcy-Forchheimer equations, just as in the filter layer. In the second schematization, the top layer is modelled by rectangular blocks alternated by small gaps. The CFD model results and the physical test are compared based on trends and statistics.

The model performance has been evaluated for three consecutive processes. First, the wave generation and propagation are analysed by comparing the wave spectra of the incoming waves and monitoring the wave conditions along the numerical flume. The model could reproduce a wave spectrum accurately, and the wave properties remained constant during propagation. The second process that has been evaluated is the wave-breaking that results in wave loads on the slope. It has been shown that the quasi-static wave loads are predicted with reasonable accuracy (i.e. measured values deviate less than 10%) while the dynamic wave loads deviate up to 35% from the physical test results. It is concluded that there is room for improvement in modelling the wave-breaking. The last evaluated process is the porous media flow that leads to pressure differences over the top layer. The optimal schematization of the top layer was the rectangular blocks alternated with gaps. Just as in the physical test, only the dynamic wave loads lead to upward forces. These predicted forces deviate less than 20%.

To model the flow through the top layer, the local inertia, advective inertia and resistance terms are important in the conservation of momentum equation. For the top layer schematized with a continuum layer, the advective inertia term is underestimated by orders of magnitude leading to inaccurate results. The top layer schematized with rectangular blocks led to load predictions with reasonable accuracy. The resistance term was underestimated because no shear stress in the gaps between the blocks was included. However, the resistance term is small compared to the local inertia and advective inertia.

In future research, additional attention should be given to determining the optimal grid resolution. Results have shown that decreasing the grid sizes leads to increased predicted pressures. It could also be beneficial to further investigate the modelling strategy of the top layer. Schematization 2 has led to the most accurate model results. However, this model requires a fine grid resolution to resolve the flow through the gaps, leading to high computational times. A CFD model in which the top layer is schematized as a continuum would be beneficial in terms of computational times. Increasing the fictional porosity and grain size increase the contribution of the inertia term in the momentum balance, leading to better results. Investigating a method for obtaining these values may be of added value.