SOME NOTES ON MORPHODYNAMIC MODELING OF VENICE LAGOON

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SOME NOTES ON MORPHODYNAMIC MODELING OF VENICE
LAGOON Gary Parker, Spring, 2004
Venice Lagoon was formed by the action of
deposition of mud and sand from rivers, sea level
rise and compaction of fine-grained sediment
under its own weight. Today the source of
sediment has been cut off, but the deposit
continues to compact, or consolidate under its
own weight. Consolidation is made worse by
groundwater withdrawal and possibly sea level
rise caused by global warming.
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A CLOSER VIEW OF VENICE AND THE LAGOON
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EXNER EQUATION OF SEDIMENT CONSERVATION WITH
COMPACTION
Let ?p porosity, and c 1 - ?p fraction of bed
volume that is solid (not pores). Exner from
some level ?b below which only tectonic effects
are felt to the water-sediment interface ?
Apply Leibnitz
where cD solids fraction in freshly deposited
material at z ? and cb solids fraction at
interface below which only tectonics is felt.
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EXNER EQUATION OF SEDIMENT CONSERVATION WITH
COMPACTION contd.
Define ?t - ??b/?t tectonic subsidence rate.
As a fine-grain layer compacts, ?c/?t gt 0, and so
a subsidence rate due to compaction can be
defined as
Thus Exner becomes
Now in general ?t can be specified independently
of the local process of deposition. In case of
the deposition of fine-grained material, however,
?c is a function of the deposition itself
deposition induces compaction, which creates
accomodation space for more deposition. Compactio
n progresses as water is slowly squeezed out of a
mud layer by the process of consolidation.
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QUICK REVIEW OF CONSOLIDATION
Consider a layer of fine-grained material (mud)
bounded by highly permeable sand below and above.
The water table is located in the upper sand
layer. The water supports the water above in
hydrostatic balance, and the mud supports its
weight (minus the buoyant weight) by means of the
contacts between the mud grains.
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QUICK REVIEW OF CONSOLIDATION contd.
At some time t 0 a load is placed on the
surface (above the water table). The sand layers
quickly respond to the load. Initially, however,
the particles in the mud layer do not have enough
contacts to support the added load, so an excess
pore pressure above and beyond hydrostatic
pressure is created.
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QUICK REVIEW OF CONSOLIDATION contd.
DArcys law assumes that groundwater flows from
zones of high excess pore pressure to low excess
pore pressure. Defining the excess piezometric
head he as he pe/(?g), the relation takes the
form
where w is the groundwater flow velocity in the z
direction and K is the hydraulic conductivity of
the mud. Excess pore pressure in the mud layer
is dissipated to the sand layers as illustrated
below
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INTEGRATING CONSOLIDATION INTO A MORPHODYNAMIC
MODEL
Consider the subaqueous deposition of mud with
consolidation
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INTEGRATING CONSOLIDATION INTO A MORPHODYNAMIC
MODEL contd.
Relation between equilibrium solids concentration
and depth in mud Here cD denotes the
concentration of solids in freshly-deposited
surface mud. Note that in this linearized
treatment cE increases linearly with vertical
distance below the surface. Lc is a length scale
associated with the linearization. Relation
between excess piezometric head he and the
difference between the actual solids
concentration and the equilibrium value
where again Lh is a length scale associated
with consolidation in a linearized
treatment. Mass conservation of fluid phase
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REDUCTION
Now then So or reducing, Thus using
Darcys law, Assuming water at hydrostatic
pressure at z ? and e.g. a porous sand layer at
z ?b , the boundary conditions become
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REDUCTION contd.
Reduce to
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CONCLUSION
The coupled groundwater-morphodynamic problem is
In order to finish the problem formulation, it is
necessary to specify relations for D and E of mud
as functions of flow conditions. For example,
subsidence under compaction increases flow depth,
which may in turn increase the overall rate of
deposition of fine-grained material. The same
model for hydrodynamics and erosion and
deposition of mud should easily incorporate the
effect of sea level rise, which will appear as a
boundary condition on the morphodynamic model.