Morphological predictor for mixed beds


Changes in level and composition of the bed of surface water systems may affect both their economic and ecological functions. It is therefore often desirable to predict trends in bed level and composition due to human interventions or autonomous natural developments. This facilitates, for instance, a habitat assessment of future Building with Nature projects. A sand-mud bed composition module has been developed to predict of bed level and composition changes as computed from deposition and erosion of multiple sediment fractions. Depending on the mud fraction, the bed may behave cohesive or non-cohesive, resulting in different erosion behaviour. The bed module consists of multiple layers and may include mixing by bioturbation or bedform migration. The bed module is open-source and has been developed by Deltares. It is available both within Delft3D and as a stand-alone tool. For a quick assessment of potential bed level and bed composition changes due to human or natural changes of the environment, it can be run in 1D-mode. It is also applicable for a comprehensive 3D model study in the detailed design phase of a project. The intended users of the bed module are scientists or professionals with some affinity to sediment transport.

Building with Nature interest

The tool is applicable in the Planning and Design Phase of a BwN project, to analyse the effects of different strategies on morphology and bed composition. Projects that can benefit from the tool are those in which morphology and/or bed composition are expected to have a large impact on ecological or economic system functions. The tool is also beneficial for turbidity modelling, if sediment resuspension from the bed is an important source of turbidity.

The bed module is intended to be used in projects in which significant changes in bed level and bed composition are expected which cannot be quantified straightforwardly. It is a tool to compute bed composition and bed level changes due to erosion and deposition of multiple sediment fractions, which may range from gravel to clay. Depending on the mud fraction, the bed may behave cohesive or non-cohesive, each of which yields a different erosion behaviour. The bed module takes multiple bed layers into account and may include mixing by bioturbation or bedform migration . The output consists of the bed level and the vertical profile of the bed composition as a function of time in the nodal points of a horizontal numerical grid (or at a single position in 1D-mode). The output can be visualised or used as input for habitat assessment, for instance. As compared with existing bed modules (e.g. Sanford, 2008), the present one combines open-access with sophistication in numerical techniques and advanced process description of sand-mud interaction.

The tool consists of the following elements:

Bed module: the bookkeeping system for the bed, taking into account an arbitrary number of sediment fractions and bed layers. Layer thickness may be constant or varying with time. The uppermost layer and layers of constant thickness below it behave Lagrangian, i.e. they move in vertical direction along with the eroding or accreting water-bed interface. Lower layers of variable thickness behave Eulerian, i.e. they have a fixed vertical position and may disappear upon erosion or be split upon deposition. This hybrid approach combines the advantages of an active (mixing) layer concept at the interface with those of no numerical mixing deeper down. Physical mixing (e.g. by bioturbation) is described as a diffusion process, with a user-defined mixing coefficient and active depth below the water-bed interface. Consolidation remains to be included.

Erosion formulations: given the composition of the upper bed layer and the shear stress exerted on it by the water flow, an erosion flux is computed:

  • Below the critical mud content, the bed is non-cohesive and mud is assumed to be eroded in proportion with sand; the presence of mud only influences the erosion velocity of sand via a change in the critical bottom shear stress. This means that the erosion flux of each sand fraction can be computed using a standard erosion formula (e.g. Van Rijn, 1993 and 2004) with a modified critical shear stress.
  • Above the critical mud content the bed is cohesive and considered to be homogeneous, i.e. the properties of the sediment mixture determine the erosion behaviour instead of the properties of the individual sediment fractions. The erosion fluxes of mud and sand fractions are proportional to their percentage in the cohesive mixture. For pure mud, the standard Partheniades-Krone formulations apply, with a critical shear stress for erosion tau_e and an erosion parameter M. For a mud content p above the the critical value but below 100% there is a gradual transition between the non-cohesive regime and the all-mud regime. Both the critical shear stress and the erosion parameter are interpolated according to the Van Ledden et al. (2004) expressions extended for multiple sand and mud fractions. These formulations are described in detail in the Zhou et al. (2016) and Baart et al. (2017).

Fluff layer: a fluff layer concept is implemented to improve the description of fine sediment transport. The fluff layer only contains mud fractions and no sand. It is an intermediate state for mud between water column and bed. Mud in the fluff layer is stationary (unlike suspended sediment), but is very easily resuspended due to its low critical shear stress for erosion. Mud that becomes part of the bed is more resistant to erosion.

Consolidation module: In addition, a consolidation module has been developed, using  existing  consolidation  theory,  which is suitable  for  long-term  morphodynamic simulations – we refer to the DECON model (Dynamic Equilibrium CONsolidation). This model is applicable for muddy systems, with small fractions of sand, where sedimentation rates are smaller than consolidation rates. Thus, the model  assumes  quasi-equilibrium of the consolidating bed. It is derived from the full consolidation (Gibson) equation  and  is  implemented  in  a  mixed  Lagrangian-Eulerean  bed  model  guaranteeing  stable  and  non-negative solutions, while numeric diffusion remains small. Erosion and deposition of sand and mud is accounted for, whereas internal mixing (e.g. bioturbation) is modeled through diffusion. Parameter settings for the new consolidation model (hydraulic conductivity, consolidation coefficient and strength) can  be  obtained  from  consolidation  experiments  in  the  laboratory.  The  model  reproduces  one-dimensional consolidation experiments and the qualitative behavior of erosion and deposition in a tidal flume. Next, the DECON model has been applied to more natural conditions,  simulating the fine sediment dynamics on a schematised mud flat  and  in  a  schematised  tidal  basin  under  tide  and  wave  forcing.  The  computational  results  of  the  mudflat simulations compare well with simulations with the full Gibson equation. For the tidal basin simulations, DECON predicts the expected landward tidal transport of fine sediment during tide-dominated conditions while withstanding erosion during more energetic wave-dominated periods. Computational times in the morphodynamic simulations of the tidal basin example increased by a factor five for simulations without waves, and a factor two when waves are included. Applying a complete consolidation model would be prohibitive. The DECON model therefore serves as a useful  tool  to  simulate  fine sediment  dynamics in  complex  wave-  and  tide-dominated  conditions,  as  well  as  the effects of seasonal variations (for more detailed information refer to Winterwerp et al., 2018).