# Dynamics of mud transport

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## Introduction

Mud in coastal areas is mainly found in intertidal deposits [1].
Migniot [2] was probably the first to present a comprehensive overview of all the processes involved in mud dynamics.
In order to understand the dynamics of mud in coastal environments, it is necessary to properly define mud and its properties, in contrast to sand and other non-cohesive particles.

### Definition

Mud is defined as a mixture of mainly fine-grained sediments (clays, silt and sand), organic matter and water [3], where the cohesive properties of the clay fraction, enhanced by the properties of the organic matter, dominate the overall behaviour. Studies on erosion behaviour of sand-mud mixtures indicate that the bed exhibits cohesive behaviour for clay contents above 15-20% [4].
In daily language "mud" refers to the deposited state of mud particles. In this state mud can occur as a fluid-like of soil-like entity. The dynamics of mud then refers to the formation, deformation and erosion of such layers.

### Flocculation

A key feature of mud particles is their cohesive nature that distinguishes them from non-cohesive solid particles such as sand.
Clay particles in an aquatic environment tend to stick together (coagulate) as the result of the van der Waals forces into aggregates or flocs. This process is enhanced by slimes (EPS) and mucus produced by micro-benthos and bacteria (that feed on decaying organic matter).
The size, structure and density of flocs are determined by the forces the aggregate-particles undergo. These forces comprise: hydrodynamic forces (especially shear), collisions between particles and electrochemical forces (determined by the composition of solid particles and dissolved ions in the ambient water). The latter explains also why mud particles in fresh and saline water have a different structure.
The basic building blocs of flocs are the primary particles and/or flocculi (compact aggregates, O(10 µm), which rarely break down into primary particles), which form micro-flocs (silt size), macro-flocs (fine-sand size) and organic-rich mega-flocs (coarse-sand size, linked to seasonal biological events, such as algae-bloom). The simultaneous occurrence of micro- and macro-flocs is attributed to the tidal dynamics, and/or sometimes to the mixing of sea- and river-born aggregates. Further research is necessary to understand better the dynamics of the different floc populations.
Despite the trend to characterize the floc structure by a fractal number [5], the structure is not self-similar. In general, the fractal dimension decreases with increasing floc size, which implies that the floc structures becomes more and more open and its strength decreases.

 Schematic representation of mud floc dynamics. © Maggi (2005). [6].

### Settling velocity

Since size, structure and density of a mud particle vary dynamically, the same applies to its settling velocity. The value of the parameter “settling velocity” actually should correspond to the averaged value for the entire local floc population, i.e. the settling flux per unit concentration. It has been demonstrated that the sediment flux can much more accurately be calculated when considering the major floc populations individually [7].
For hindered settling of mud particles, it is important to express the hindrance correction factor in terms of the effective volumetric concentration occupied by the aggregates, including the immobilized water captured in the porous structure of the floc.

### Mud Bed Formation

 Fluid mud at the Suriname Coast. © Hydraulics Laboratory, KULeuven
Accumulation of mud particles on the bottom generates an open-spaced soil, which network structure is sometimes compared with a card-house (or sponge). When the layer grows in thickness, the overburden will cause a stress on the structure by which it will slowly collapse. During this process, known as self-weight consolidation, pore water is expelled to the surface and the pressure of the pore water increases relative to the hydrostatic pressure, generating excess pore pressures. The process continues until the strength of the soil skeleton (the effective stress) is in equilibrium with the submerged weight it has to carry and the excess pore pressures are dissipated.

The critical volumetric concentration at which soil formation starts is called the gel point. In principle it could be predicted if the effective volume of the flocs is known. For North-Sea mud, the gel point is found for soil bulk densities of about 1100 kg/m³, which implies a solids concentration of the order of only 8%. This explains the apparent fluid-like behaviour of freshly deposited mud, since its structure is easily disturbed. This is better understood in the light of the rheological characteristics of fluid mud.
Due to flocculation and hindered settling, instant bed formation is retarded and a near-bottom high-concentrated (HC) suspension layer (also known as high-concentrated benthic suspension, HCBS) is formed.

### Mud Bed Destruction

Considering the fact that the soil consists of aggregated particles, which are bound by electrochemical forces of varying origin and strength, these bonds may be broken by various mechanical forces, either shear forces (at the surface or internally) or excess pore pressures that exceed the effective stress (usually due to wave action, but also by e.g. earthquakes). Local micro-cracks may grow to larger cracks and eventually create failure planes in the bed. Erosion is the process where the structure is broken to such degree that the loose parts may be picked-up by the flow and transported. A distinction is furthermore made into the following three erosion modes:

• Surface erosion = particle-by-particle erosion at the surface;
• Mass or Bulk erosion = erosion of a patch of mud above a failure plane;
• Cliff erosion = break-up of solid clumps of over consolidated mud by (boat) waves, which after mechanical rolling erosion may become rounded mud pellets.

 Cliff erosion of an intertidal mudflat in the Western Scheldt Estuary. © Michiel Taal / Deltares

### Mud Rheology

The deformation and flow of fluid mud requires a rheological description, i.e. mathematical expressions (closure laws) relating stress to deformation and/or deformation rate.
Deformation under wave action has traditionally been described by visco-elastic or plastic models, which allow analytical solutions under (over)simplified (1D) conditions.
However, considering the link between strength and bed structure, a description by a thixotropic characterization seems more promising. This approach shows (logical) analogies to the structural kinetics approach to flocculation [8].

## Transport modes

### Suspended Load Transport of Mud

Traditionally, it has been assumed that cohesive sediments have such low settling velocities that the dominant transport mode is by suspended load. Usually, only dilute suspension transport is considered.

The importance of high-concentrated (HC) suspension transport in the inner layer above the bed (often named “fluid mud”, but this term is more consistently restricted to another state > see Fluid Mud) is often underestimated or ignored. However, the amount of sediment transported in this layer can be very significant. Research on this topic is still ongoing.

The thickness of the HC suspension layer above the bottom can be significantly larger than in the case of sand. A relatively sharp interface, a lutocline, can be found between this layer and the dilute layer above. Instabilities can be observed along this lutocline in the form of internal waves.

Contrary to HC sand suspension layers, HC mud suspension layers usually exhibit strong turbulence damping (or even laminarization) and drag reduction. A well known example is that of the Yellow River (China), where roughness values have to be taken corresponding to smoother than a smooth glass plate, in order to predict the hydrodynamic resistance correctly.

### Turbidity maximum

Due to interaction of heavier saline sea water and lighter fresh river water, a zone with high suspended loads of cohesive sediments, an estuarine turbidity maximum (ETM), is formed in estuaries. The turbulence due to the interaction keeps particles in suspension, while large fresh water flocs may alter into more compact flocs with a lower settling rate due to the increased salinity. The ETM location moves up- and downstream with the tide, depending on the strength of the tide and the river discharge. In some estuaries, more than one ETM can occur.

Despite the traditional approach of only considering suspended transport for mud, two observations suggest that bedload transport of mud should not too easily be discarded.

1. High-concentrated near-bottom transport of mud should not be treated as suspended load, since the theory for the latter requires fully-developed turbulent flow, while the former typically shows the properties of low-Reynolds-number flow, requiring another mathematical treatment (which is still under development). Because of the high amounts of sediment transported in this layer, and the physical similarities with bedload transport of non-cohesive sediments, it seems justified to consider this mode as bedload transport of mud.
2. Large clumps of overconsolidated may break off from mud layers that are exposed to the air for longer time such that they dry and show cracks. Once the water line reaches these areas in combination with significant wave action (either wind waves or boat traffic induced waves), large clumps may break off, resulting in cliff erosion. Pulled up and down by the tidal currents, they role over the bottom, they may break up into smaller clumps, erode more or less, and eventually become rounded mud pebbles which can role even better and be transported over longer distances or accumulate in deeper areas. For example, mud pebbles are formed along the low water line of the intertidal flats of the Yzer Mouth (Nieuwpoort, Belgium) and found back in the mud dredged from the navigation channel. – Laboratory observations suggest that bulk erosion may also generate submarine mud pebbles. As far as known, no evidence from the field on the latter is available.

 Mud pebble formation after cliff erosion along the Yzer mouth intertidal mudflat. © Erik Toorman / KULeuven

### Fluid Mud Flow & Density Currents

Mud bottoms in underconsolidated state are prone to fluidization and/or liquefaction. The resulting fluid mud can deform under wave action and, when there is no barrier, even flow driven by gravity.
As long as the density remains below the gel point, the effective viscosity is so high that the flow behaviour will remain laminar. When accelerating, the shear and resulting instabilities at the interface will cause entrainment in the two directions (i.e. water into the fluid mud and mud particles into the water column), resulting in dilution of the fluid mud below the gel point, and the water-sediment mixture should now be considered a (highly-concentrated) suspension, which can flow turbulently.
When depositing on a sloping bottom (e.g. river banks on dredged channel slopes), self-weight induced shear may avoid consolidation and keep the deposit liquefied, such that the deposit may flow as a gravity current to the lowest point.
This knowledge is used in low-cost agitation dredging, where a mud deposit is mechanically disturbed and liquefied in low-energy locations, such as lock entrances, with the purpose to accumulate the fluid mud in deeper areas where the mud, if necessary, can be removed during maintenance dredging.
Mud gravity currents (or avalanches) may also be induced due to liquefaction by earth-quakes.
Mud gravity currents may carry large amounts of mud to the deeper ocean where rivers end in a canyon. Example: It has been estimated that about 50% of the mud from the Amazon flows down the continental slope in front of its mouth. About 20% is transported to the west by wave action as migrating mud banks along the Guyanas coast and eventually flows down the Orinoco river canyon into the deeper ocean.

 Mud density currents generated in laboratory flume. © Erik Toorman / KULeuven

### Mud-Wave Interaction

An important property of fluid mud layers is their capacity to absorb energy from surface waves in the overflowing water layer. Famous examples are the Guyanas coast [9] and the Lousiana coast [10] , where this has been studied.
It has been demonstrated that wave damping can well be simulated using a thixotropic closure [11].
The well known nearshore spectral wave model SWAN has also been extended with a semi-empirical sink term to account for wave damping by fluid mud [12].

## Mud transport modelling

Cohesive sediment transport models for short to medium term predictions of morphological (trend) studies combine the hydrodynamic equations for the sediment-water mixture with a sediment mass balance (or transport) equation. The latter is an advection-diffusion equation with sink (deposition) and source (erosion) terms to allow exchange of sediment fluxes with the bottom.

### Erosion laws

The most famous surface erosion law for cohesive sediments has been named after Partheniades’ experimental work [13]. The erosion flux is the product of an erosion rate multiplied with a probability factor as a function of the shear stress in excess of a critical erosion shear stress. Subsequent research has found that modifications had to allowed in the case of soft, freshly deposited mud [14]. Partheniades’ law has recently been extended to account for the statistical turbulent fluctuations on the hydrodynamic shear stress [15].

### Deposition laws (2D vs. 3D)

There still is much confusion on applying the correct deposition law for (cohesive) sediments. The exact bottom boundary condition at the bottom is simply imposing the sedimentation flux (the product of sediment concentration and settling velocity) at the bottom. This has to be used in 3D and 1- and 2DV models where the vertical water column is resolved.

The famous empirical deposition law from Krone [16] may only be used in the case of depth-averaged (2DH) modelling. Here the bottom flux is approximated by the product of depth-averaged sediment concentration with the settling velocity of a single particle, multiplied with a probability p of the fraction of the total suspended load which may deposit. i.e., the complementary probability $1-\rho$ actually represents the amount of sediment which can be held in suspension by the turbulent energy in the flow. Introducing this probability compensates for the fact the no vertical energy balance is computed in 2DH models.

### Flocculation modelling

Since the settling velocity of the dynamically varying mud aggregate particles changes as the floc structure changes, many attempts have been made to account for flocculation. The first simple models were empirical relationship correcting the settling velocity with a factor as a function of instantaneous concentration and turbulent dissipation rate. The next generation introduced a kinetic equation describing the aggregation and break-up of flocs [17]. Following, more elaborate population balance equation modelling has been introduced, applied to multiple floc size fractions. In order to reduce the computational effort for large scale applications, new strategies have been proposed to work with a continuous particle size distribution [18] and to distinguish at least two floc populations [19] .

### Sand-mud mixture modelling

In most coastal environments mud and sand coexist and influence each others’ behaviour. Because cohesive sediment was thought to be transported predominantly as suspended load and sand as bed load, the two were often treated independently. Current understanding of sediment transport strongly suggests that the two should be solved in a coupled way. The major reason is the interaction in the inner layer above the bottom, where there are high concentrations and four-way coupling fluid-particle interactions. Furthermore, the sand-mud ratio in the bed determine the availability of each fraction and the erosion behaviour of the surface.
To date, the most advanced modelling approaches have been proposed by van Ledden [20] and Waeles [21].

### Bed models

In order to account for dynamical erosion properties of the bed surface, several models have been proposed to predict the erosion resistance. The most detailed models rely on the geotechnical self-weight consolidation theory of Gibson [22].
Because of the computational effort and the high uncertainty on the model parameters, Sanford [23] proposed a much simpler relaxation model.
The latter has been investigated to be extended with a fluidisation model, to account for the counter action of wave induced pore pressure build up.
In all these models the bed is subdived into layers. Exchange with the water column is allow with the surface layer only (the “active” layer). A practical problem remains the book-keeping of the thickness of each layer and of the sand-mud ratio, when the model takes into account sediment mixtures.

## Biomediation

The importance of organic matter in mud has been acknowledged for a long time. They change time scales of certain processes (such as consolidation) and strength parameter by one order of magnitude.
Unfortunately, the characterization and quantification of the effects of organic matter is very complex because the many biological agents and seasonal effects.

Furthermore, because of the richness in nutrients, intertidal mud flats are an important food resource to many animals. Benthos living in the mud, moreover, alter the properties of the mud to their benefit and may remix the sediments, a process called bioturbation. It remains very difficult to include these processes in morphodynamic models.

Benthic organisms tend to modify cohesive sediment characteristics [24]. Individual particles are ingested and form large, low density faecal pellets with settling velocities much higher than the individual particles contained in them. Estuarine sediment transport conditions are altered e.g. by change of bed roughness due to deposition of fecal pellets or by biological activity in the surface layers causing either binding or destabilizing of the bed surface [25].

Density, size and settling velocity of fecal pellets are important in describing sediment transport processes [26]. Faecal pellets are low density faeces from suspension-feeding and mud-ingesting marine and estuarine benthic animals including oysters, worms, and barnacles. They consist of large amounts of fine sediments mainly single particles in the 1-5 μm range [27] and flocs ingested by the feeding animal, compacted in the gut and excreted as large aggregates glued together by mucus. Up to 25 % of the deposited sediment may in some areas originate from biodeposition.

Decay of organic matter generates methane gas in the pores of the soil skeleton. This results in changes in the mechanical properties of the mud layer [28].

## Major application fields

### Morphodynamics & Sediment transport

Erosion and/or deposition change the boundaries between land and water. Human interventions into the natural environment disturb the natural trend of streams to reach their regime. The impact of anthropogenic changes on the environment needs to be assessed and, if possible, quantified through model studies. The interest goes to the prediction of sediment fluxes, sediment balances and morphological trends, necessary to assess their impact on economy (navigability), safety (against flooding) and ecology.

Because of the large complexity and the multi-scale processes involved, the required modelling technique will depend very much on the purpose of the study and the spatial and temporal scales involved.

### Dredging & Nautical Depth

Navigation channels, lock entrances and harbour docks are prone to accumulation of mud on the bottom. In order to maintain navigation, these areas must frequently be dredged.
The design of dredging equipment, the estimation of dredging operation costs and the environmental impact assessment of dredging activities requires the understanding of hydraulic transport of mud and sand-mud mixtures.
The least studied problem related to the occurrence of mud in navigation channels, is the determination of a practical and meaningful criterion to determine when a fluid mud bottom becomes harmful to navigation. This is of importance to optimize the economical cost of the maintenance of navigation ways and harbours.
At present, the criterion is still based on a critical bulk density of fluid mud, since it can relatively easily be determined and there is a clear relationship between bulk density and rheological parameters. The traditional density criterion, however, overlooks the time-dependence of the rheological parameters (i.e. thixotropy). For this reason, further research is required to establish a better criterion which accounts the latter. For this purpose a research programme has started at Flanders Hydraulics (Antwerp, Belgium) [29].

## Literature

General books on cohesive sediments (mud):

• Partheniades, E. (2009). “Cohesive sediment in open channels”. Butterworth-Heinemann, Burlington (MA), xv + 358 pp.
• Whitehouse, R., R. Soulsby, W. Roberts & H. Mitchener (2000). “Dynamics of estuarine muds”. HR Wallingford & Thomas Telford, London (UK), xxii + 210 pp.
• Winterwerp, J.C. & W. van Kesteren (2004). “Introduction to the physics of cohesive sediment in the marine environment”, Elsevier, Amsterdam (NL), xiii + 466 pp. + annexes.

## References

1. Eisma, D. et al. (1997). Intertidal Deposits: River Mouths, Tidal Flats and Coastal Lagoons. CRC Press, Boca Raton (FL), 525 pp.
2. Migniot, C. (1968). Etude des propriétés physiques de différents sediments très fins et leur comportement sous des actions hydrodynamiques. La Houille Blanche, 1968(No.7):591-620 (in French).
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19. Lee, B.J., E.A. Toorman, F. Moltz & J. Wang (2011). A two-class population balance equation yielding bimodal flocculation of marine or estuarine sediments. Water Research, 45:2131-2145.
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Gibson, R. E., Schiffman, R. L., & Cargill, K. W. (1981). The theory of one-dimensional consolidation of saturated clays: II. Finite non-linear consolidation of thick homogeneous layers. Can. Geotech. J., 18:280–293.
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 The main authors of this article are Toorman, Erik and Berlamont, JeanPlease note that others may also have edited the contents of this article. Citation: Toorman, Erik; Berlamont, Jean; (2019): Dynamics of mud transport. Available from http://www.coastalwiki.org/wiki/Dynamics_of_mud_transport [accessed on 21-02-2020] For other articles by this author see Category:Articles by Toorman, Erik For other articles by this author see Category:Articles by Berlamont, Jean For an overview of contributions by this author see Special:Contributions/Erik Toorman For an overview of contributions by this author see Special:Contributions/Jean Berlamont