Environmental Engineering Reference
In-Depth Information
Sidebar 9.1: Velocity Profiles in Steady Compacted Aquatic Sediments
Sedimentary deposits of all kinds near the surface often show a characteristic
decrease of the pore space in vertical direction. The process that causes the
decrease is compaction. Due to rearrangement of sediment particles and to
compression of particles, i.e. the porosity, the volumetric share of pore space,
decreases with distance from the interface.
Here we take the Lagrangian approach, where the origin of the coordinate
system is fixed at the sediment interface and is thus moving in space. In an
Eulerian system, which is fixed in space, no steady state can be expected for
compacting sediments. A constant burial velocity
v
bur
and a constant porosity
'
0
at the interface are assumed, a necessary prerequisite for a steady-state in
the Lagrangian system.
The mass conservation equation for the fluid filling the pore space is given
by the continuity equation
@
@x
yrðÞ¼
0
(compare Chaps 3 and 4), which in case of constant fluid density
r
reduces to
@
@x
yðÞ¼
0
The solution obviously is
yv ¼ C
with integration constant
C
. The constant
C
can be evaluated in the deep
sediments:
C ¼ y
1
v
1
with
v
1
denoting the fluid velocity in the deep sediments, where porosity does
not change any more.
v
1
can be expressed differently by taking into account
that the burial velocity at all locations is given by
v
bur
¼
ð
1
yðxÞ
Þv
sed
ðxÞþyðxÞvðxÞ
where
v
bur
denotes the burial velocity and
v
sed
the velocity of the sediment
(solid) phase. The latter changes with depth. In the deep sediments, out of
reach for compaction processes, holds
vð1Þ¼ v
sed
ð1Þ¼ v
1
(continued)
