1. An introduction to cohesive sediment transport modelling
Bas van Maren

2. Contents (1) Introduction (2) Sand transport and morphology
(3) Mud transport and morphology
(4) Sediment transport and morphology in Delft3D
E = Erosion rate [kg/m^2/s]
M = Erosion parameter [kg/m^2/s]
Τb = bed shear stress [Pa]
Τe = erosion treshold shear stress [Pa]
Destabilizers => Arenicola / Lugworm: lives in burrows in the sediment at depths of 20-40cm. It feeds on organic matter in the sediment by drawing water into the burrow and filtering organic particles.

3. Introduction Definition of mud Mud clay cohesive 2 m silt
pseudo-cohesive
63 m
Sand
non-cohesive
2000 m
Gravel

4. Introduction sand mud Definition of mud
Modelling of sand and mud require a fundamentally different approach
Bedload transport
Bed material
sand
Suspended sediment transport
Total transport
mud
washload
Suspended sediment transport

5. Introduction sand mud Definition of mud
Modelling of sand and mud require a fundamentally different approach
Several conceptually different approach to modelling of mud exist: supply-limited (washload) or erosion-rate limited (bed material)
Bedload transport
Bed material
sand
Suspended sediment transport
Total transport
mud
washload
Suspended sediment transport

6. Sand transport and morphology
Sand is deposited (almost) instantaneously when bed shear stress < critical bed shear stress, and eroded when bed shear stress > critical bed shear stress

7. Sand transport and morphology
Sand is deposited (almost) instantaneously when bed shear stress < critical bed shear stress, and eroded when bed shear stress > critical bed shear stress
Transport of sand can be well predicted using empirical sediment transport formula
Van Rijn (1993) Bed load + suspended
Engelund-Hansen (1967) Total transport
Meyer-Peter-Muller (1948) Total transport
General formula Total transport
Bijker (1971) Bed load + suspended
By default, the formula of Van Rijn (1993) is applied in Delft3D.
T = f(u3, 1/h, 1/D50, …)

8. Sand transport and morphology
Sand is deposited (almost) instantaneously when bed shear stress < critical bed shear stress, and eroded when bed shear stress > critical bed shear stress
Transport of sand can be well predicted using empirical sediment transport formula
Sand morphology can be predicted with reasonable accuracy
Advanced coupling with wave modules (wave-generated bed shear stress and flows)

9. Sand transport and morphology
Sand is deposited (almost) instantaneously when bed shear stress < critical bed shear stress, and eroded when bed shear stress > critical bed shear stress
Transport of sand can be well predicted using empirical sediment transport formula
Sand morphology can be predicted with reasonable accuracy
Advanced coupling with wave modules (wave-generated bed shear stress and flows)
Note the use of ‘well predicted’ and ‘reasonable accuracy’!

10. Mud transport and morphology
General formulations
Transport of mud
Transport of silt: in-between mud and sand
Transport of sand-mud mixtures

11. Mud transport: general formulations
3D advection-diffusion equation
with erosion and deposition terms as bed boundary conditions

12. Mud transport: general formulations
3D advection-diffusion equation
Erosion and deposition:
But:
critical shear stress for deposition does probably not exists (although sometimes useful)

13. Mud transport: general formulations
3D advection-diffusion equation
Erosion and deposition:
But:
critical shear stress for deposition does probably not exists (although sometimes useful)
ws depends on sediment concentration and turbulence
Mud modelling: define settling velocity (flocculation?), critical shear stress for erosion, and erosion parameter

14. Transport of mud Transport of mud depends on
Fluid dynamics (bed shear stress AND flow velocity profile)
Availability of sediment: sediment concentration depends on the erosion rate of sediments or the availability of sediments
Age of the sediment deposit (consolidation increases the critical shear stress of the sediment)

15. Transport of mud: fluid dynamics
Sediment density coupling
Suspended sediment influences the density of water
Water density influences mixing of turbulence
Turbulent mixing influences the sediment concentration profile (upward sediment transport by turbulent mixing and downward transport by settling)
 positive feedback loop resulting in deposition
Accurate 3D flow and sediment concentration
Net transport of mud is often a delicate balance between
phasing in flow velocity and sediment concentration
vertical and horizontal distribution (of velocity and sediment)
example: harbour dock sedimentation

16. Example: harbour sedimentation
Minimizing harbor siltation: Deurganckdok.

17. Example: harbour sedimentation
Minimizing harbor siltation: Deurganckdok.

18. Example: harbour sedimentation
Minimizing harbor siltation: Deurganckdok.

19. Transport of mud: erosion rate vs sediment availability
Mud transport limited by sediment availability
Sediment enters model domain through open boundaries, no initial amount of sediment!!!
Concentration in water column and sediment on the bed is limited by sediment influx and outflux imposed by hydrodynamics
Low critical shear stress for erosion ( Pa) and high erosion parameter M ( kg/m2/s)
Dynamic equilibrium  suitable for long-term simulation and process studies
Very long initialisation (spin-up)

20. Transport of mud: erosion rate vs sediment availability
Mud transport limited by sediment availability
Mud transport limited by erosion rate
Sediment in water column generated by erosion of bed sediment
C=f(u)
Short-term, ‘engineering-type’ studies or erosion of consolidated bed sediment
High critical shear stress for erosion (0.5-1 Pa) and low erosion parameter ( – kg/m2/s)
Requires map of initial sediment availability
Sediment concentration based on initial conditions, no dynamic equilibrium!

21. Transport of mud: erosion rate vs sediment availability
Initial sediment bed NO
YES
Boundaries
YES/NO
Critical shear stress
LOW
HIGH
Erosion parameter M
Dynamic equilibrium
Timescales
LONG
SHORT

22. Mud transport: consolidation
Compaction of sediment in time through pressure exerted by overlying grains and resulting expulsion of interstitual pore water
Decrease of erosion rate with time and with depth
Modelling consolidation requires high vertical resolution and small timesteps  not useful for long-term large-scale simulations (Delft3D research version)
‘Simple’ consolidation model needed

23. Mud transport: sand-mud
Mud in sand matrix: mud gradually released by bed reworking during storm season (Netherlands: gradual increase offshore sediment concentration during winter)
Sand-mud mixture: Sand transport strongly reduced when bed consists of 5-10 % clay ( ≈ 20-40% mud)
Few models simulate interaction, several research versions of Delft3D

24. Mud transport: silt
Increase of critical shear stress due to shear dilatance

25. Modelling: Delft3D
Hydrodynamics Sediment transport Advantages / disadvantages
+ Accurate morphological feedback
+ Sediment-density coupling
+ Easy to use, flexible
+ DLL ‘open source’ parts for sediment transport module, and erosion / deposition terms
- relatively slow: for each sediment the computationally expensive hydrodynamics need to be re-run
Delft3D flow with online sediment
+ Less computationlly expensive (especially with aggregation)
+ Mud-buffer model (and future sand-mud?)
+ Not easy to learn
Delft3D flow
Delft3D WAQ

26. Modelling: Delft3D
Exercise 6: ETM formation

27. Modelling: Delft3D
Exercise 7: Mudflat sedimentation