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# SED2D

The TABS finite element model for sediment transport prior to 1995 was called STUDH. The STUDH model underwent considerable improvement and modernization in June 1995 and was renamed to SED2D.

# Background

The TABS finite element model for sediment transport prior to 1995 was called STUDH. The STUDH model underwent considerable improvement and modernization in June 1995 and was renamed to SED2D.

SED2D can be applied to clay or sand bed sediments where flow velocities can be considered two-dimensional in the horizontal plane (i.e., the speed and direction can be satisfactorily represented as a depth-averaged velocity). It is useful for both deposition and erosion studies and, to a limited extent, for stream width studies. The program models two categories of sediment:

- Noncohesive, which is referred to hereafter as sand.
- Cohesive, which is referred to hereafter as clay.

Both clay and sand may be analyzed, but the model considers a single, effective grain size during each run. Therefore, a separate model run is required for each effective grain size. Fall velocity must be prescribed along with the water surface elevations, x-velocity, y-velocity, diffusion coefficients bed density, critical shear stresses for erosion, erosion rate constants, and critical shear stress for deposition.

The program does not compute water surface elevations or velocities; these data must be provided from an external calculation of the flow field. For most problems, a numerical model for hydrodynamic computations, RMA2, is used to generate the water surface elevations and velocities. An implicit assumption of the SED2D model is that the changes in the bed elevation due to erosion and/or deposition do not significantly affect the flow field. When the bed change calculated by the model does become significant and the externally calculated flow field supplied by the user is no longer valid, then the SED2D run should be stopped, a new flow field calculation should be made using the new channel bathymetry generated by SED2D, and the SED2D run should be restarted with the new flow field as input.

Either steady-state or transient flow problems can be analyzed. The exchange of material with the bed can be calculated or suppressed. Default values may be used for many sediment characteristics or these values may be prescribed by input data. Either the smooth wall velocity profile or the Mannings equation may be used to calculate bed shear stress due to currents. Shear stresses for combined currents and wind waves may be calculated.

# Computational Model

The program is based on the following conceptual model:

- Basic processes in sedimentation can be grouped into erosion, entrainment, transportation, and deposition.
- Flowing water has the potential to erode, entrain, and transport sediment whether or not sediment particles are present.
- Sediment on the streambed will remain immobile only as long as the energy forces in the flow field remain less than the critical shear stress threshold for erosion.
- Even when sand particles become mobile, there may be no net change in the surface elevation of the bed. A net change would result only if the rate of erosion was different from the rate of deposition-two processes which go on continuously and independently.
- Cohesive sediments in transport will remain in suspension as long as the bed shear stress exceeds the critical value for deposition. In general, simultaneous deposition and erosion of cohesive sediments do not occur.
- The structure of cohesive sediment beds changes with time and overburden.
- The major portion of sediment in transport can be characterized as being transported in suspension, even that part of the total load that is transported close to the bed

# Bed Types

Sand beds are considered to consist of a sediment reservoir of finite thickness, below which is a non-erodible surface. Sediment is added to or removed from the bed at rate determined by the value of the sink/source term at the previous and present time-steps. The mass rate of exchange with the bed is converted to a volumetric rate of change by the bed porosity parameter.

Clay beds are treated as a sequence of layers. Each layer has its own characteristics as follows:

- Thickness
- Density
- Age
- Bulk shear strength
- Type

In addition, the layer type specifies a second list of characteristics.

- Critical shear stress for erosion.
- Erosion rate constant.
- Initial and 1 - year densities.
- Initial and 1 - year bulk shear strengths.
- Consolidation coefficient.
- Clay or sand material.

# Boundary Condition Buffering

In the case of tidally fluctuating flow across a model boundary the specification of an accurate concentration is not simple. In earlier versions of the model, boundary condition was either always specified or always not specified. If a node along the boundary had flow entering the model the normal convention would be to specify a concentration. However, in older versions when the tide turned and flow left the model that specification was still applied. This creates artificial conditions that lead to severe oscillations near the boundary.

In the current version of the model, this situation has been addressed in two steps. First, the logic has been added to the code to allow the model to determine whether to apply the concentration specification (Dirichlet BC) or whether to apply a zero concentration gradient BC (von Neuman). The gradient BC allows the concentration to be solved from the interior concentration field of the model. This provides some relief; but strong concentration gradients reaching the boundary can result in abrupt jumps in the concentration as the tide turns to enter the model and the concentration returns to the Dirichlet specification. This is the result of not accounting for the concentration history of waters that have crossed the boundary.

In order to provide a form of memory of the concentration history under dynamic tidal conditions a method termed "boundary condition buffering" was developed. This technique assigns a finite number of buffer chambers to each boundary node. The program maintains the specified nominal boundary concentration Cb in the last chamber. At the beginning of the simulation all buffer chambers are initialized to Cb. As flow leaves the model the concentration of the exiting water is stored in the first chamber and all remaining buffer chamber concentrations are shifted to the next higher chamber, keeping the last chamber at Cb. Then a mixing factor is applied to the chambers to simulate the diffusive processes external to the model. When the currents turn and begin to enter the model the chamber values are shifted back one chamber per time step and the mixing process repeated. This procedure results in memory of the history of concentrations crossing the boundary, delays full specification of the nominal boundary concentration Cb and generally provides more realistic boundary conditions. Furthermore, the buffering also provides a buffer for the changes that any plan alternatives to be tested may have on the boundary conditions.

# One Dimensional Elements

The ability to simulate 1D elements has been added to SED2D. The formulation assumes a trapezoidal cross section, consistent with the 1D formulation in RMA2. The implementation is provided as a convenience to allow the user to efficiently utilize the benefits of 1D elements in RMA2 for ease of domain discretization and boundary condition placement.

The 1D capability in SED2D is not meant to give the ability to seriously model sediment transport as an alternative to HEC-6, for example, which is a fully developed 1D sediment model This simply allows for use of the benefits of simplified schematization.

The current formulation incorporates 1D junctions, and transitions to 2D elements. The formulation for control structures is not fully operational for the current version of this model.

# Required Field Data

All sediment simulations must have first obtained a hydrodynamic solution from RMA2. Field data needs are therefore at least two fold; hydrodynamic and sediment. The answer is also site dependent. The type of data required to support the sediment model would include items such as:

- Pre- and post-dredging bathymetric surveys
- Bottom grab samples
- Suspended sediment samples
- Sieve analysis of sands
- Landsat information
- Settling velocity tests
- Flocculation tests
- Core samples
- etc.

# Delta Time Stamp Selection

Typically the time step is 2 times smaller for the SED2D sediment model than for the RMA2 hydrodynamic model. For instance, a 30 minute time step might be used in SED2D, while a 1 hour time step was sufficient for RMA2.

Timing and run length control (TZ) card specifies the computational interval and number of timesteps to be run. Choice of a computational interval is dependent on the size of mesh cells used, speed of the flow, effective settling velocity of the sediment, and how well the modeler wishes to resolve small scale bed features. It is recommended that the time interval for SED2D be identical to the RMA2 time interval.

The DT parameter is the length of a time step for SED2D simulation (input as decimal hours and converted to seconds inside SED2D). The capability exists to specify a time step that is different from the RMA2 time step when using a dynamic RMA2 solution file. However, this is not recommended. If the SED2D time step is less than the RMA2 time step, then a linear interpolation will be performed to evaluate the velocities at the intermediate time steps. The SED2D time step cannot be larger than the RMA2 time step.

However, it is highly recommended that the SED2D time step be set exactly equal to the RMA2 time step. Severe accuracy errors can result from using an interpolated flow field.

The above comments are because of the concern for the conservation of water mass when the time steps are not identical. Other concerns are raised if the hydrodynamic solution was not converged tight enough, or the time step was too large to capture the changing tide. That would produce a solution that, if it were linearly interpolated for the sediment simulation, could produce interpolated hydrodynamics that are not accurate. Therefore, the possibilities of severe accuracy errors could result in the SED2D solution.

Given all the above, work has been and is still in progress to more accurately address the time step issue and to document the modifications.

# Sedimentation at Bridge Piers

A question that is sometimes asked is whether SED2D is appropriate for modeling flow and sedimentation around a bridge pier. Unfortunately, SED2D is not an appropriate model, This is primarily because the TABS 2D models operate using hydrostatic assumption limitation, meaning that vertical pressure is balanced by gravitational forces.