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> Figure 19. Slope vs. discharge, showing inrease in slope after jam failure
Figure 18. Measured velocity profile with fitted log-law equations for the ice and bed-affected areas
Discussion - CR97_070035
CR97_07
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27
28
29
30
31
32
24
18x10
5
After
Failure
16
14
8
10
Before
Failure
6
0.02
0.03
0.04
0.05
0
0.02
0.04
0.06
Discharge
(m
3
/s)
Discharge
(m
3
/s)
Figure
19.
Slope
vs.
discharge,
showing
in-
Figure
20.
Calculated
equilibrium
jam
crease
in
slope
after
jam
failure.
thickness
vs.
discharge.
in
which
u
is average
flow
velocity
and
R
is
the
composite
or
total
hydraulic
radius.
An average
value
of
f
o
was
calculated
and
used
for
the
conditions
before
and
after
failure.
The
detailed
velocity
profiles
from
each
test
provided
data
on
the
ratio
of
the
bed-affected
to
ice-affected
hydraulic
radii
.
Then,
using
the
Sabaneev
equa-
tions
f
i
+
f
b
f
o
=
(32)
2
and
f
R
i
=
i
(33)
R
b
f
b
it is
possible
to
determine
ratios
of
f
i
to
f
b
and
f
i
to
f
o
.
Average
values
of
these
ratios
for
the
conditions
before
and
after
failure
were
calculated
and
used
to
calculate
the
equilibrium
cover
thickness
expected
for
each
experiment.
Figure
20 is a
plot
of
the
equilibrium
thickness
vs.
discharge
for
this
series
of
experiments,
using
average
values
of
f
o
and
f
i
/
f
o
.
Figure
21
follows
the
changes in
thickness
experienced
with
step
changes in
discharge
for
one of
the
experiments.
The
initial
thickness
of a bead
jam
is
slightly
greater
than
that
predicted
using
the
equilibrium
theory
(eq
30)
and
was
between
one
and
two
beads
thick.
Two
step
increases
in
discharge
were
necessary
before
a
shoving
and
thickening
event
occurred,
with
the
resulting
thickness
again
slightly
greater
than
that
expected
by
theory.
This
first
failure
was
a
progressive
jam
failure
with
very
small
ice
velocities.
Two
more
step
increases
in
discharge
were
necessary
to
again
cause
jam
failure.
The second
failure
was
a
complete
jam
failure,
with
the
whole
cover
mobilizing
en masse
and
thickening
taking
place
initially
at
the
down-
stream
screen.
The
final
thickness
was
significantly
greater
than
the
equilibrium
value
for
that
flow
level.
The
jam
failures
in
each
experiment
were
identified
as
either
progressive
or
com-
plete
jam
failures.
The
final
thickness
following
failure
was
plotted
in
Figure
22
against
the
equilibrium
thickness
predicted
using
eq
30.
The
progressive
jam
fail-
ures
resulted
in
accumulation
thicknesses
that
plotted
on or
very
slightly
above
the
equality
line
in
the
figure.
The
complete
jam
failures,
however,
exceeded
the
equi-
librium
thickness
in
every
case,
often
by a
significant
amount.
27
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