Sand-mud interaction
Large scale sand-mud segregation is found in estuaries and tidal basins all over the world. Sand and mud mixtures have been studied separately in the past because of important differences in their behaviour. Van Ledden (2003) has developed a morphological model which accounts for both sand and mud. This model is incorporated in the FINEL2D model. This model extends currently used morphodynamic models in a number of ways:
- Firstly the erosion characteristics of sand and mud depend on the mud content at the bed surface.
- Secondly the temporal and spatial variations in mud content are taken into account. The bed composition varies due to erosion and deposition of sand and mud at the bed surface and mixing in the bed itself.
Erosion of sand-mud mixtures
A key element in this model is the erosion formulation for sand-mud mixtures. A distinction is made between cohesive and non-cohesive behaviour of these mixtures. A critical mud content (pm,cr) is defined for this transition between cohesive and non-cohesive behaviour. In estuaries in the Netherlands a typical critical mud content of 30% is found.
Non-cohesive behaviour
When the mud content at the bed surface is less than the critical mud content the bed layer is treated as non-cohesive. This implies for the sand fraction the ‘normal’ sediment transport formula is used. However the erosion flux of sand is limited by the availability of sand in the bed. The erosion of the silt fraction becomes:
Cohesive behaviour
Experiments with cohesive sand-mud mixtures have shown that the erosion characteristics strongly differ from non-cohesive sand-mud mixtures. Therefore erosion of a cohesive bed layer is treated differently in the model. The following formulas are used for the erosion flux of sand and mud:
Bed module
The bed level change follows directly from the bed load transport gradient of sand and the erosion and the erosion and deposition fluxes of sand and mud (see Figure 1)
Figure 1: Bed level and bed composition
Bed composition variations in time and space are induced by three processes: upward and downward fluxes of sand and mud at the bed surface, physical mixing near the bed surface and biological mixing processes in the sediment itself. Several layers in the active bed layer can be defined with a fixed layer thickness (dz). Since the bedlevel z is not fixed the layers shift accordingly in the vertical direction. The mud content pm below the bed surface (-infinite < z < z b) then reads:
In the sub-layer a fixed silt percentage (pm,sub) must be applied. This silt percentage becomes important in an eroding case. In that case this sub layer silt percentage is introduced in the lowest layers. A Cranck-Nicholson scheme is applied for solving the bed composition equation. See for a further explanation of the numerical implications of the bed module Van Ledden (2003).
Example: Nature development in the Western Scheldt Estuary, The Netherlands
The Province of Zeeland is looking for ways to restore estuarine nature in the Western Scheldt. Svašek Hydraulics has investigated several locations in the estuary using the FINEL2D morphological model. Since these locations are shallow and located near the dike both sand and silt contribute to morphological developments. Both fractions are accounted for in the model using a sand-silt interaction module.
The model was calibrated against historical morphological developments at a location which served as role model for the other locations. A large nature development has taken place since the construction of dams in this area, because the velocities decreased and as a result sedimentation occurred. The same idea of reducing velocity and stimulating sedimentation is also used in other locations, which currently have a low nature value.
The figure above shows an example of the morphological developments calculated using FINEL2D near a location called “Osenisse”. The velocities in a small channel near the dike are reduced by constructing dams in the channel (upper figure).
After 10 year the area between the dams is filled up (lower figure) with silt and the sandy channel is relocated more northwards. The areas between the dams can become valuable nature areas.
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